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ht120815_readings.zipHT120815 Readings/%28asce%291090-0268%282006%2910%3A5%28419%29.pdf
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Analysis and Design Procedure for FRP-Strengthened Prestressed Concrete T-Girders Considering
Strength and Fatigue Hayder A. Rasheed1; Kyle H. Larson2; and Robert J. Peterman3
Abstract: Controlling the prestressing strand-stress range in precracked prestressed concrete girders is critical in the FRP strengthening process to avoid long-term fatigue failures. This paper will address the details of a design procedure that was developed to satisfy target-strengthening requirements while imposing stress range serviceability limits. Two main CFRP flexural strengthening designs were established for use in the experimental program herein. In the first, the amount of CFRP was designed to limit the average strand-stress range to 125 MPa �18 ksi�, as per AASHTO requirements, under service live load while maintaining the service-ultimate moment relationship constant. The second design was intended to double the strand-stress range under service live load while keeping the same service-ultimate moment relationship. This was accomplished with iterative cycles of nonlinear sectional analysis to determine the amount of external CFRP reinforcement needed to yield both the targeted stress range and ultimate capacity. The girders were overly reinforced for shear with internal steel stirrups. However, external CFRP stirrups were used to prevent the longitudinal CFRP from premature separation and to develop full flexural capacity. The ACI 318-05 model for shear friction was used for this purpose. The paper also presents analysis results to qualify the experimental behavior of the tested girders. Load-deflection, load-strain, and moment-strand stress variations are seen to have excellent correlation with corresponding experimental curves. CFRP is shown to develop higher strains across cracks relieving strand stresses at these critical locations.
DOI: 10.1061/�ASCE�1090-0268�2006�10:5�419�
CE Database subject headings: Concrete, prestressed; Bridge girders; Fatigue; Design; Fiber reinforced polymers.
Introduction
The volume of literature on the use of FRP �fiber-reinforced poly- mer� to strengthen reinforced concrete members is rapidly grow- ing �Bakis et al. 2002�. Interest in developing strengthening analysis and design procedures is evident �Picard et al. 1995; Chaallal et al. 1998; Saadatmanesh and Malek 1998, Triantafillou and Antonopoulos 2000; Rasheed and Pervaiz 2003�. Knowledge in this area has matured enough to introduce design guidelines �ISIS Canada 2001; ACI 440.2R-02�. On the other hand, attention has been primarily given to investigating reinforced concrete be- havior, rather than prestressed concrete behavior, because rein- forced concrete is easy to use in construction and its static flexural response is similar to prestressed concrete. Thus, an important behavioral difference between the two systems has been over- looked. Unlike reinforced concrete, prestressed concrete members are susceptible to strand fatigue problems under an elevated
1Associate Professor, Dept. of Civil Engineering, Kansas State Univ., Manhattan, KS 66506.
2Graduate Research Assistant, Dept. of Civil Engineering, Kansas State Univ., Manhattan, KS 66506.
3Associate Professor, Dept. of Civil Engineering, Kansas State Univ., Manhattan, KS 66506.
Note. Discussion open until March 1, 2007. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on February 5, 2004; approved on March 8, 2006. This paper is part of the Journal of Composites for Construction, Vol. 10, No. 5,
October 1, 2006. ©ASCE, ISSN 1090-0268/2006/5-419–432/$25.00.
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strand-stress range. This difference is especially critical because strengthening concrete allows higher service live-load levels and a majority of longer-span bridge girders utilize prestressed con- crete. AASHTO �2004� limits the strand service stress range to 69 MPa �10 ksi� for harped strands and 125 MPa �18 ksi� for straight strands, which are used in this study.
El-Tawil and Okeil �2002� addressed design aspects for pre- stressed concrete beams strengthened with FRP, without consid- ering the fatigue limit state. They examined the LRFD strength provisions of prestressed bridge girders strengthened in flexure with FRP. They used numerical analysis to conduct thousands of Monte Carlo simulations of a number of bridges designed accord- ing to 1998 AASHTO LRFD. El-Tawil and Okeil studied the effects of span length, the dead load to live load ratio, and the amount of CFRP used on the reliability of the strength reduction factor ���. They used first-order reliability method to propose a � equation for prestressed concrete girders strengthened with CFRP. However, the study only focused on flexural failure modes and assumed that they can be fully developed by proper detailing.
Reed �2002� repaired and strengthened 30-years-old pre- stressed concrete T-girders with CFRP. The girders were removed from an existing bridge that had been overloaded during its lifespan. Although the levels of strengthening were very limited �20%�, a relatively high stress range and possible corrosion ef- fects caused the girders to fail prematurely in strand fatigue. Other recent studies presented innovative techniques to apply pre- stressed FRP sheets to prestressed or reinforced concrete mem- bers �Wu et al. 2003; Wight and Erki 2003; El-Hacha et al. 2003�. However, this subject is beyond the scope of the present study.
This paper presents the details of the strength-fatigue design
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procedure that was developed to satisfy the target strengthening requirements. Two main CFRP flexural strengthening designs were established for an experimental program. The first design furnished the amount of CFRP to satisfy AASHTO requirements for limiting the average strand-stress range to 125 MPa �18 ksi� under service live load and related this amount to the ultimate level of strengthening �AASHTO 2004�. The second design was based on doubling the average prestressing strand-stress range under service live load while maintaining the same service- ultimate load relationship. The experimental results of the girders tested with these designs, under both ultimate and fatigue load- ings, correlated well with the analysis results yielding important findings.
Sectional Analysis Procedure
A nonlinear analysis program was used for all strengthening de- signs in this study �Reed 2002�. This program determines both the moment-curvature and load-deflection responses of prestressed concrete girders with a tapered T-section. The program uses an incremental deformation approach to generate the sectional re-
Fig. 1. Flexural test setu
Fig. 2. Strand-stress variation with applied
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sponse. The algorithm divides the section into thin concrete, mild steel, prestressing strand steel, and FRP layers. Using the linear strain distribution at any load level, the strain of any layer is determined by the section curvature � and the neutral axis depth c. By gradually increasing the top concrete strain while solving for the correct neutral axis depth to satisfy force equilibrium, the full moment-curvature response is generated. The following as- sumptions and material models are used to accomplish this analysis: 1. Plane sections before bending remain plane after bending
and perpendicular to mid-surface �i.e., a linear strain profile with no shear deformations�.
2. Perfect bond exists between the concrete and bonded rein- forcement �prestressing strands, mild steel, and external FRP sheets�. This is particularly applicable because of the study’s use of external transverse FRP U-wraps.
3. The effect of the initial strain in the concrete extreme fiber during FRP strengthening, on FRP levels of strain, is taken into account.
4. The concrete response in compression is modeled using Hog- nesteds’ classical parabola up to the maximum useful con- crete strain, �cu = 0.003.
wing the spreader beam
t: design iteration 1 �unstrengthened beam�
p sho
momen
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5. Concrete is assumed to carry tension in between flexural cracks based on the smeared crack approach. Accordingly, a linear descending branch of the tensile stress-strain curve is used when considering global load-deflection response. However, tension stiffening is ignored when local cracked sections are analyzed for critical strand stresses.
6. The prestressing strands follow the PCI 1860 MPa �270 ksi� low-relaxation stress-strain curve �PCI 2004�.
7. A bilinear stress-strain model is used for mild steel bars in- cluded as compression and web reinforcement.
8. The unidirectional CFRP sheets have a linear-response up to brittle failure.
Flexural Design Procedure
An iterative design approach was devised by the authors to deter- mine the amount of CFRP reinforcement needed to maintain the desired stress range under service live load while producing the ultimate moment specified by the AASHTO LRFD bridge design specification �2004�. The prestressing strand stress � f se� prior to loading was found to be 1,138 MPa �165 ksi� from prestress cal- culations of losses confirmed by precracking of girders as pre- sented by Larson et al. �2005�. The first design target was to determine the amount of flexural CFRP area to satisfy AASHTO �2004� requirements for limiting the average strand-stress range to 125 MPa �18 ksi� under service live load conditions. For this stress range design, the average stress estimate in the prestressing strands corresponding to the upper service live-load level is, ac- cordingly, 1,263 MPa �183 ksi�. The final design was completed once the analytical nominal moment capacity �Mn�, calculated by the analysis program with the beam geometry, material properties, and added amount of CFRP, converged at the same factored ulti- mate moment capacity �Mu� that AASHTO specifies �� = 1.0 used per section 5.5.4.2.1�. The ultimate moment relates to the service live-load moment as follows:
Mu = �Mn = �pMD + �LMLL�1 + IM/100� �1�
where MD = the dead-load moment of the beam self-weight �5.8 kN · m , 4.3 k-ft�; MLL = the live-load moment corresponding to the upper limit of the target stress range, including the weight
Table 1. Design Iterations for the 125 MPa �18 ksi� Stress Range Case
Design iteration
Af mm 2
�in.2� Mn kN · m
�k-ft� Ms
1 0 66.3 �48.9� 36
2 29.3 �0.0455�
95.0 �70.1� 37
3 33.5 �0.052�
97.5 �71.9� 37
4 35.6 �0.05525�
100.1 �73.8�
37
Table 2. Design Iterations for the 250 MPa �36 ksi� Stress Range Case
Design iteration
Af mm 2
�in.2� Mn kN · m
�k-ft� Mse
�
1 50.3 �0.078�
109.5 �80.7�
46.0
Final 62.9 �0.0975�
126.1 �93.0�
47.7
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of the spreader beam given below �Fig. 1�; �p = 1.25; �L = 1.75; and IM = 33% based on Strength I limit state in Tables 3.4.1-1, 3.4.1-2 and 3.6.2.1-1 of AASHTO �2004�. It is important to note that the load factors used in this study were �p = 1.3, �L = 2.17, IM = 30% per the AASHTO specifications that were current at the time the design and testing was performed.
The design process starts with a section analysis for the un- strengthened beam. The analysis program plots the average prestressing stress at the centroid of all the strands against the applied moment �Fig. 2�. The desired stress range is mapped in place on the y-axis of the graph. Then, the service moment �Mservice� corresponding to the upper level of the stress range is determined �Fig. 2�. The corresponding live moment for the fa- tigue strand-stress range is computed as
ML = Mservice − MD − MSB
�L,fatigue �2�
where MSB = the maximum moment caused by the weight of the spreader beam used to impose the four-point bending �1.9 kN · m , 1.4 k-ft�; ML = the live moment excluding the weight of the spreader beam; MD = the moment caused by the dead weight of the girder; and �L,fatigue = 0.75 per AASHTO �2004�. However, �L,fatigue was set to 1.0 in this study because it took place prior to AASHTO �2004�. MD+SB+lower, in Fig. 2, is the moment applied to the beam at the lower level of cyclic loading. This moment corresponds to a load of 2.22 kN �0.5 kip� so that the loading actuator does not separate from the beam at the end of each fatigue cycle because of full unloading.
The ML moment is substituted into Eq. �1� to determine Mu, which is not expected to equal Mn from the sectional analysis during the first few iterations. Accordingly, CFRP sheets are added to the section and a new section analysis is performed to generate the updated average prestressing stress versus applied moment graph. The steps in iteration 1 are then repeated up to convergence. Step-by-step procedures for calculating Mu are de- tailed below: 1. Run the analysis program with the desired amount of CFRP
and obtain Mn for that section and a curve like the one in Fig. 2.
2. After specifying a lower limit for the applied moment
m ML kN · m �k-ft�
Mu kN · m �k-ft�
CFRP needed
7� 28.5 �21� 93.3 �68.8� more
6� 29.7 �21.9� 96.9 �71.4� more
7� 29.8 �22.0� 97.0 �71.5� more
7� 29.8 �22.0� 97.0 �71.5� stop
ML kN · m �k-ft�
Mu kN · m �k-ft�
CFRP needed
� 38.3 �28.2� 121 �89.1� more
� 40.0 �29.5� 125.9 �92.8�
stop
er kN · �k-ft�
.2 �26.
.4 �27.
.5 �27.
.5 �27.
r kN · m k-ft�
�33.9
�35.2
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�2.0 kN · m or 1.5 k-ft in this case� to avoid the separation of the hydraulic actuator from the beam during cycling, find the average prestressing stress for that moment �1140.1 MPa or 165.25 ksi in Fig. 2�.
3. Add the desired stress range to the value found in step 2 �125 MPa or 18 ksi�. This will be the upper limit of the pre- stressing stress �1264.2 MPa or 183.25 ksi in Fig. 2�.
4. Mservice is the moment found by taking the value that corresponds to the upper limit of the stress range �Mservice = 36 kN · m or 26.7 k-ft in Fig. 2�.
5. ML is then found using Eq. �2�. 6. Finally, Mu is calculated by using Eq. �1� and compared to
Mn from the sectional analysis of the current CFRP design. 7. If Mn is less than Mu, then more CFRP needs to be added for
convergence to happen. If Mn is greater than Mu, then some CFRP needs to be removed for convergence to occur in sub- sequent iterations. Convergence is assumed when the mo- ment difference is less than a tolerance
� Mn − Mu Mn
� � 0.01 �3� Detailed calculations that are pertinent to the two design cases
considered are presented in Tables 1 and 2. Table 1 shows four iterations required to converge to the final design selected for the 125 MPa �18 ksi� stress range. Although the values of iteration 3 were converged, a small amount of CFRP was added so that the longitudinal CFRP would have a final height slightly above the level of the lower prestressing strand. This allows strain gauges to be mounted on the CFRP at that level �See Fig. 4�. Accordingly, the numbers for iteration 4 were within a 3% tolerance. Never- theless, this design was accepted to satisfy the instrumentation requirement mentioned. The resulting CFRP values are expected to be rounded for practical reasons. This trial then became the final design and was used for the 125 MPa �18 ksi� strand-stress range strengthening �Fig. 3�. Fig. 4 shows the final dimensions of the longitudinal CFRP used to furnish this design case. One layer
Fig. 3. Final converged design c
of wrapped CFRP sheet covering the entire bottom of the web and
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extending 57 mm �2.25 in.� up the two sides was applied along the entire clear span of beams 2 and 3. The beams’ experimental and analysis results are compared below.
This first design provides an ultimate nominal moment capac- ity of 100.1 kN · m �73.8 k-ft� and a live moment level of 29.8 kN · m �22.0 k-ft�. This corresponds to a strengthening index of 51% and a service live load upgrade index of 63% where
strengthening index % = M̄n − Mn
Mn � 100 �4�
LL upgrade index % = M̄L − ML
ML � 100 �5�
where M̄n = the ultimate moment of the strengthened beam;
Mn = the ultimate moment of the unstrengthened beam; M̄L = the live load moment of strengthened beam; and ML = the unstrength-
r 125 MPa �18 ksi� stress range
Fig. 4. Strengthening dimensions for 18 ksi stress range
urve fo
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ened live-load moment. To find both of the live-load moments, take their respective Mn and use Eq. �1� to back calculate them �Mn should be substituted for Mu in Eq. �1��.
Table 2 shows the first and the last iteration in the process of converging to the final design selected for the 250 MPa �36 ksi� stress range. The last iteration shows that Mu is close enough to Mn. This trial was the final design, which was used in the strengthening case. Fig. 5 shows the graph of this last design iteration. Fig. 6 illustrates the final CFRP dimensions, which were used to accomplish the 250 MPa �36 ksi� stress range design. Two layers of wrapped longitudinal CFRP sheets covered the bot- tom of the web extending 13 mm �0.5 in.� up the sides for layer 1 and 76 mm �3 in.� on each side for the second layer. The longi- tudinal CFRP was applied along the entire clear span of beams 4 and 5.
The 250 MPa �36 ksi� stress range design yielded an ultimate nominal moment capacity of 126.1 kN · m �93.0 k-ft� and a live moment value of 40.0 kN · m �29.5 k-ft�. This corresponds to a strengthening index of 90% and a service LL upgrade index of 112%. Fig. 7 shows the analytical prestressing strand-stress curves for all three beams, the unstrengthened beam, the first strengthening design �125 MPa, 18 ksi stress range�, and the sec- ond strengthening design �250 MPa, 36 ksi stress range�. It is evident that the more CFRP added, the higher the live load ad- mitted for the same strand-stress range level.
Shear Design Procedure
The beams were overly reinforced for shear with internal steel stirrups �see Appendix. Shear Calculations�. However, external CFRP stirrups were also used to prevent the premature separation failure of flexural CFRP caused by horizontal shear cracking. The ACI 318-05 �2005� model on shear friction was used in the design of external stirrups. This model allows computation of the tension force in transverse reinforcement during horizontal shear crack- ing. Transverse reinforcement is then proportioned to minimize
Fig. 5. Final converged design c
the separation of the normal crack. Thus by limiting the level of
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tensile CFRP strains, a stirrup distribution or spacing is obtained. To maintain a consistent external stirrup layout for both flexural designs 1 and 2, the required stirrup dimensions and spacing in the more extreme case of 250 MPa �36 ksi� stress range were implemented. The maximum axial tension in the CFRP is found first by taking the CFRP fiber area times the elastic modulus of the CFRP fibers times the CFRP strain at ultimate flexural failure
T = EfAf�f u in case of FRP rupture
= EfAf��f = df − c c
.003� in case of concrete crushing �6� Then the horizontal shear force per unit length of shear span is
calculated directly
r 250 MPa �36 ksi� stress range
Fig. 6. Strengthening dimensions for 36 ksi stress range
urve fo
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Vhu = T
La �7�
where Vhu = the horizontal shear force per unit length; and La = the shear span. Third, the tension force per unit length in the transverse CFRP from the shear friction model is
Tsf = Vhu �
�8�
with � = 1.4. Finally, the area of transverse CFRP external stirrups per unit length is determined by specifying the allowable tensile strain of the bonded FRP stirrups. ACI 440.2R-02 �2002� section 10.4.1.2 limits this strain ��f e� to 0.00375 for this girder design. To be more conservative, this limit is reduced to 0.003 in the present study. This corresponds to CFRP tensile stress f f e = 690 MPa �100 ksi�
Tsf = �Av f�f eEf = .85Av f f f e �9�
where Av f = the area of transverse CFRP used to prevent prema- ture separation failure
Fig. 7. Analytical prestressing strand-stress range com
Fig. 8. External
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Av f = 2ntfwf �10�
where tf = the thickness of one stirrup layer; wf = the width of each stirrup; and n = the number of stirrup layer plies. Based on the above equations, it was found that T = 190 kN �42.8 kips�, Vhu = 103.6 kN / mm �7.1 k / ft�, and Av f = 127 mm
2 / m �0.06 in2 / ft�. Thus stirrups that are 140 mm �5.5 in.� wide and spaced 305 mm �12 in.� center to center were used. The two end stirrups were cut to be 203 mm �8 in.� wide to control any pos- sible end shear cracks causing plate end shear stress concentration and premature separation. Also, the stirrups were extended 203 mm �8 in.� up the web sides �Fig. 8�. They were stopped at this height so that they did not get bonded to the rounded web- to-flange juncture to avoid potential peeling problems.
Experimental Results
All five specimens were precracked and instrumented prior to strengthening and destructive testing. Beam 1 was tested as a
n for three beams with different strengthening levels
U-wrap layout
pariso
CFRP
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control beam, while the remaining beams �2–5� were strengthened with CFRP sheets. Beams 2 and 3 had the first CFRP strengthen- ing design and beams 4 and 5 were strengthened with the second CFRP design. Static tests were performed on beams 2 and 4 to determine their monotonic response. Fatigue tests were run on beams 3 and 5 to investigate their cyclic performance. Table 3 summarizes the material mechanical properties, the experimental loading scenarios, and results obtained. Complete details of the experimental program were reported earlier by Larson et al. �2005�.
Analytical Comparisons with Experimental Results
The results of the nonlinear analysis program were compared against the actual experimental results, which were presented by Larson et al. �2005�. For the load-deflection graphs, two different types of analysis were performed. In the first analytical curves, the entire beam was fully precracked so the concrete tensile strength � f r� was set to zero. This was not truly the case during the experimental testing because each beam had only a single
Table 3. Summary of Mechanical Properties and Experimental Results
Specimena Loading type Failure load kN �Kips�
Control �Beam 1�
MFb 67 �15.1�
Beam 2 MFb 114 �25.7�
Beam 3 1MC-MFb 113 �25.3�
Beam 4 MFb 143 �32.2�
Beam 5 3MC-MFb 117 �26.2� af c� = 48.6 MPa �7,043 psi�, Eps = 195 GPa �28,300 ksi�, f pu = 1,860 MPa �f u = 0.014. bM-F: Monotonic to failure, 1MC-MF: 1 million cycles fatigue then mon cPSR: Prestressing strand rupture, FR: FRP rupture.
Fig. 9. Analytical versus experimen
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precracked section at mid-span. The other analytical case as- sumed the beam to be initially uncracked. This model had f r of
the concrete set to 0.27 �f c� in MPa �3.3 �f c� in psi� based on the agreement with the experimental results, which were further sup- ported by the values reported by Scanlon and Murray �1982�. The tensile model also took into the account the tension stiffening effects between flexural cracks by using a linear descending branch in the stress-strain curve. This descending line extends from f r and �cr = f r / Ec at first cracking to a zero tensile stress at k�cr, when tension stiffening has negligible contribution. The fac- tor k is determined as the value beyond which the fully cracked analytical curve closely matches the experimental response. It can be seen that the load-deflection curves of the experimental results compare fairly well to those of the analysis �Figs. 9–11�.
It can be seen that the results of the load-deflection analysis for the control beam, assuming an initially uncracked beam, yield noticeably good correlation with experiment and thus provide a more representative means for predicting the behavior of the beam �Fig. 9�. The analysis is seen to yield a much larger deflec- tion at failure because the experiments were run in force control
Deflection at failure mm �in.�
FRP strain at failure ����
Failure mode
59 �2.32� N/A PSRc
88 �3.45� 14,730 FRc
84 �3.3� 18,333 FRc
102 �4.0� 14,000 FRc
66 �2.6� 10,000 FRc
si�, Ef = 227.5 GPa �33,000 ksi� per fiber area, tf = 0.17 mm �0.0065��,
to failure, 3MC-MF: 3 million cycles fatigue then monotonic to failure.
d-deflection results of control beam
�270 k
otonic
tal loa
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and data points were recorded every second so that the deflection at the ultimate failure point may not have been instantly recorded, whereas the analysis is based on deformation control. Tension stiffening was found to be effective in this beam up to a tensile concrete strain of 50�cr or �k = 50�.
Comparing the experimental response of beams 2 and 3 with the analytical results, the load-deflection curve is also seen to produce good correlation �Fig. 10�. The analysis for the initially uncracked beam compares very well with beam 2, which had only one precrack at mid-span, up to the yielding point. The compari- son between both beams is still good after the yielding point, and
Fig. 10. Analytical versus experimen
Fig. 11. Analytical versus experimen
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the small difference could be attributed to the slightly stiffer ac- tual strand response compared to that of the standard 270 ksi strand assumed in the analysis. The additional stiffening effect of CFRP by tightly bridging flexural cracks made tension stiffening effective up to 70�cr. It is interesting to note that the response of beam 3 matches that of the fully cracked analysis curve at the level of the crack opening, confirming the accuracy of internal prestressed force computation. It is important to mention that the specimen was precracked but the crack was held shut by the prestressing force. After the beam was reloaded, the crack re- opened, then widened.
d-deflection results of beams 2 and 3
d-deflection results of beams 4 and 5
tal loa
tal loa
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The load-deflection curves also produced good correspon- dence with the responses of beams 4 and 5 �Fig. 11�. The analysis for the initially uncracked beam showed excellent correspondence against the beam 4 curve up to the yielding point and compared very well after that all the way to failure. Beam 5 compared well with the analytical results of the fully precracked beam after the crack opening point. The fact that the initial stiffness of all the experimentally strengthened beams matched the analytical initial stiffness once again shows that the bond between the CFRP and the concrete is excellent.
Fig. 12. Analytical versus experimental com
Fig. 13. Analytical versus experimental com
JOURNAL OF COMPOSITES F
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When comparing the experimental and analytical strains, a precracked section analysis is implemented to show the response of a beam at the critical precracked section. Comparing the ana- lytical top concrete compression strains against the corresponding actual strains for beams 2 and 3 as well as beams 4 and 5 resulted in very good correspondence �Figs. 12 and 13, respectively�. The analysis and experimental tensile strains in the CFRP compared very well in the post yielding range �Figs. 14 and 15�. The CFRP had much higher experimental strains within the service live-load range than the strains from the analysis primarily because the
on strains for beams 2 and 3 �top concrete�
on strains for beams 4 and 5 �top concrete�
pressi
pressi
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CFRP in the tested beams has picked up much greater strains across cracks than expected from strain compatibility. This is be- cause the bond between the CFRP and the concrete across cracks is much better than that between concrete and the prestressing strands �Larson et al. 2005�. The minor difference in the load- strain curves between the different gauges and the analysis is attributed to the localized nature of this response that change strain values according to their proximity to cracks.
The bottom experimental CFRP strains showed noticeably higher strains than the analytical results after cracking for the beams strengthened with the 125 MPa �18 ksi� stress range de-
Fig. 14. Bottom CFRP strains for
Fig. 15. Bottom CFRP strains for
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sign �Fig. 14�. These strains recover their strain compatibility val- ues at and beyond the strand yielding range of the curve. The beams strengthened with the 250 MPa �36 ksi� stress range show a much closer comparison �Fig. 15�. The center-east gauge of beam 5 had very high post-cracking strain attributed to possible direct bridging of the mid-span crack. However, it returned to the typical response as it slipped. The center-east gauge of beam 4 initially read compression but eventually picked up a stiffness reading identical to that on the other gauges. This discrepancy was likely caused by an air bubble trapped in a concrete depres- sion under the CFRP at the location of the gauge.
i stress range strengthened beams
i stress range strengthened beams
18 ks
36 ks
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The side CFRP experimental strains at the lower strand level �at 51 mm or 2 in. up from the bottom of the web� of the second design �250 MPa, 36 ksi stress range� reconfirms the superior CFRP bond effects across the crack �beam 4� compared to those of beam 5 after fatigue cycling. The latter corresponded closely to strain compatibility analysis in the service live-load range �Fig. 16�.
To verify the actual stress range that the strands have under- gone under the service load limits for the 125 MPa �18 ksi� de- sign case, the top strand in the constant moment region of beam 3
Fig. 16. Side CFRP strains for 3
Fig. 17. Experimental and analytic
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was exposed and instrumented �Larson et al. 2005�. Gauges were installed on the upper prestressing strand to fully investigate the stress range that it was experiencing. Fig. 17 shows that the ex- perimental values at service load are slightly less than those from the analytical strain compatibility results. A slightly lower stress range in the top prestressing strand was expected because the CFRP was shown to be picking up more strain at this load and because the installation of the gauge required the strand to be debonded from the concrete at that location.
Comparing the CFRP strains of the bottom of the web in beam
stress range strengthened beams
ss ranges of top strand for beam 3
6 ksi
al stre
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5 with the analytical results �from strain compatibility� for service load conditions shows that the experimental measurement yields a noticeably greater strain in the CFRP �Fig. 18�. This is where it was first noticed that the CFRP was experiencing a much greater stress range than the prestressing strand because of the better CFRP bond across cracks.
Conclusions
In this study, an analytical investigation was conducted to develop an iterative design procedure relating the serviceability require- ment of targeted prestressing strand-stress range level to the ulti- mate strengthening moment capacity through the AASHTO load factor equation. This procedure was based on a detailed nonlinear sectional analysis program of tapered concrete prestressed T-girders. Two flexural CFRP designs were developed to limit the average strand-stress range to 125 MPa �18 ksi� and 250 MPa �36 ksi�. These designs corresponded to a nominal strengthening index of 51% and 90%, respectively. They have also corre- sponded to a higher nominal level of service live-load upgrade, 63% and 112%, respectively. Although additional transverse rein- forcement was not needed for shear, external CFRP stirrups were used to provide enough anchorage against premature separation failure. Accordingly, the ACI 318-05 �2005� model on shear fric- tion was used here to furnish the transverse reinforcement needed. Because CFRP rupture was attained, this design against separa- tion failure was shown to be sufficient experimentally, in the present cases, to develop the full flexural capacity. The analysis program was further used to qualify the experimental behavior of the girders tested under the same program and reported elsewhere �Larson et al. 2005�. The envelope curve of the experimental load-deflection response was found to compare well with the analysis results of initially uncracked girders when tension stiff- ening effects are included. The analysis response of fully pre- cracked girders was seen to capture the crack opening and initial widening load levels pretty closely. The analytical load-strain re- sponse and moment-strand stress variation further confirmed the accuracy of the experimental measurements reported for all the
Fig. 18. Bottom CFRP strains at m
beams. An interesting new phenomenon is further proved appli-
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cable through comparisons among experimental results and analy- sis findings. Its superior bonding to concrete across cracks, allows CFRP to develop higher strains at critical sections than those determined from strain compatibility. This is found to result in a reduction of the strand-stress range at such critical sections prov- ing to be an extra beneficial outcome of strengthening.
Acknowledgments
This study was funded by the Kansas Department of Transporta- tion and by the University Transportation Center at the University of Missouri, Rolla. CFRP strengthening materials were provided by Master Builders, Inc. Thanks are extended to Mr. Calvin E. Reed of Wilson and Company for several useful discussions.
Appendix. Shear Capacity of Internal Steel Stirrups
Using ACI 318-05 �2005� equations �chapter 11� for shear �diag- onal tension� capacity for prestressed concrete beams.
s = �Av f yd
Vu − �Vc
4 = .85*0.12*11*80
Vu − �Vc
Vu − �Vc = 22.44
f pc = Pe Ac
= 28050
125 = 224.4 psi
wself = 0.125 k-ft
bw = 4� d = 11�
f� = 7,043 psi L = 16�
n in beam 5 after 2 million cycles
id-spa
c
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e = 6.18� c = 9.22�
r2 = 14.8 I = 1849 in.4
Mo = 0.875 kip-ft Vp = 0
Vd = .875 kips
Vu = L
2 �1.2wself + 1.6wlive� = 1.2 + 12.8wlive kips
f pe = − Pe Ac �1 + ec
r2 � = − 1089 psi
f d = Moc
Ic = 52.4 psi
Mcr = � I yt ��6�f c� + f pe − f d� = 25.7 kip-ft
Vi = wlive� L 2
− 1� = 7wlive Mmax =
wlive 2
�L − 1� = 3.5wlive
Vci = 0.6�f c�bwd + Vd + ViMcr Mmax
= 54.5 kips
Vcw = �3.5�f c� + 0.3f pc�bwd + Vp = 15.9 kips
Vc = min�Vci, Vcw� = 15.9 kips
22.4 = 1.2 + 12.8wlife − 0.85 � 15.9
wlife = 2.71 k/ft Max applied live load
Þ Vlife = 2.71 � 16
2 = 21.68 kips
The maximum applied shear was encountered in beam 4 with a magnitude of �32.2 k / 2 = 16.1 k� �Table 3�. This is smaller than the Vlife calculated above. Accordingly, there were enough internal shear stirrups to prevent a shear failure. However, the external CFRP stirrups were added to prevent horizontal shear or CFRP separation failure.
Notation
The following symbols are used in this paper: Avf � area of transverse CFRP stirrups per unit length
of shear span; Af � area of flexural CFRP; Av � area of shear reinforcement within distance s; d � depth of centroid of longitudinal tension
reinforcement from extreme compression fiber; df � depth of centroid of FRP reinforcement from top
extreme fiber; Ef � FRP Young’s modulus along fiber direction
based on fiber area;
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J. Compos. Constr., 2006
e � eccentricity of prestressing force to centroid of section;
f c� � compressive strength of concrete based on standard cylinders;
f d � stress caused by unfactored dead load at extreme fiber where tension is caused by external loads;
f r � effective modulus of rupture of concrete; f pc � compressive stress in concrete at centroid of
cross-section resisting external loads; f pe � compressive stress in concrete caused by
effective prestress force only at extreme fiber where tension is caused by external loads;
f y � yielding strength of shear reinforcement; La � shear span;
Mcr � moment causing flexural cracking at section caused by externally applied loads;
MD � dead load moment of beam caused by self weight;
M̄L � live load moment of strengthened beam; ML � live load moment of unstrengthened beam;
MLL � live load moment, including weight of spreader beam;
Mmax � maximum factored moment at section caused by externally applied loads;
M̄n � ultimate moment of strengthened beam; Mn � ultimate moment of unstrengthened beam;
MSB � maximum moment caused by weight of spreader beam used to impose four-point bending;
Mu � factored ultimate moment capacity based on AASHTO 3.22.1;
n � number of layers in each stirrup; tf � thickness of one CFRP stirrup layer; s � spacing of shear reinforcement in direction
parallel to longitudinal reinforcement; T � maximum axial tension in FRP sheets in flexure;
Tsf � transverse tension force per unit length of CFRP stirrups;
Vhu � horizontal shear force per unit length; Vc � nominal shear strength provided by concrete; Vci � nominal shear strength of concrete when
diagonal cracking is because of shear and moment; Vcw � nominal shear strength of concrete when
diagonal cracking is excessive principal tensile stress in web;
Vi � factored shear force at section caused by externally applied loads occurring with Mmax;
Vu � factored shear force at cross-section; wf � width of each CFRP stirrup; �cr � cracking strain of concrete; �fe � allowable limit of FRP transverse strain; �fu � design ultimate value of FRP strain caused by
rupture flexural failure mode; and � � friction coefficient of shear friction model = 1.4.
References
AASHTO. �2004�. LRFD bridge design specifications, 3rd Ed., American Association of State Highway Transportation Officials, Washington, D.C.
ACI 318-05. �2005�. “Building code requirements for structural concrete and commentary.” ACI Committee 318, American Concrete Institute,
Farmington Hills, Mich.
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ACI 440.2R-02. �2002�. “Guide for the design and construction of exter- nally bonded FRP systems for strengthening concrete structures.” ACI Committee 440, American Concrete Institute, Farmington Hills, Mich.
Bakis, C. E., Bank, L. C., Brown, V. L., Cosenza, E., Davalos, J. F., Lesko, J. J., Machida, A., Rizkalla, S. H., and Triantafillou, T. C. �2002�. “Fiber-reinforced polymer composites for construction— State-of-the-art review.” J. Compos. Constr., 6�2�, 73–87.
Chaallal, O., Nollet, M.-J., and Perraton, D. �1998�. “Strengthening of reinforced concrete beams with externally bonded fiber-reinforced- plastic-plates: Design guidelines for shear and flexure.” Can. J. Civ. Eng., 25, 692–704.
El-Hacha, R., Wight, R. G., and Green, M. F. �2003�. “Innovative system for prestressing fiber-reinforced polymer sheets.” ACI Struct. J., 100�3�, 305–313.
El-Tawil, S., and Okeil, A. M. �2002�. “LRFD flexural provisions for prestressed concrete bridge strengthened with carbon fiber-reinforced polymer laminates.” ACI Struct. J., 99�2�, 181–190.
ISIS Canada. �2001�. “Design manual 4: Strengthening reinforced con- crete structures with externally-bonded fiber reinforced polymers.” Canadian Network of Centers of Excellence on Intelligent Sensing for Innovative Structures, University of Manitoba, Winnipeg, Manitoba.
Larson, K. H., Peterman, R. J., and Rasheed, H. A. �2005�. “Strength- fatigue behavior of fiber-reinforced polymer strengthened prestressed concrete T-beams.” J. Compos. Constr., 9�4�, 313–326.
Picard, A., Massicotte, B., and Boucher, E. �1995�. “Strengthening of
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reinforced concrete beams with composite materials: Theoretical study.” Compos. Struct., 33, 63–75.
Precast/Prestressed Concrete Institute �PCI�. �2004�. PCI design hand- book, 6th Ed., Chicago, Ill.
Rasheed, H. A., and Pervaiz, S. �2003�. “Closed form design equations for flexural strengthening of RC beams.” Composites, Part B, 34�6�, 539–550.
Reed, C. �2002�. “Strengthening of 30 year old prestressed concrete bridge girders with carbon fiber reinforced polymers.” MS thesis, Kansas State University, Manhattan, Kan.
Saadatmanesh, H., and Malek, A. M. �1998�. “Design guidelines for flex- ural strengthening of RC beams with FRP plates.” J. Compos. Constr., 2�4�, 158–164.
Scanlon, A., and Murray, D. W. �1982�. “Practical calculations of two- way slab deflections.” Concrete Int., Nov., 43–50.
Triantafillou, T. C., and Antonopoulos, C. P. �2000�. “Design of concrete flexural members strengthened in shear with FRP.” J. Compos. Con- str., 4�4�, 198–205.
Wight, R. G., and Erki, M. A. �2003�. “Prestressed CFRP sheets for strengthening concrete slabs in fatigue.” Adv. Struct. Eng., 6�3�, 175– 182.
Wu, Z. S., Iwashita, K., Hayashi, K., Higuchi, T., Murakami, S., and Koseki, Y. �2003�. “Strengthening prestressed-concrete girders with externally prestressed PBO fiber reinforced polymer sheets.” J. Reinf.
Plast. Compos., 22�14�, 1269–1286.
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Engineering Structures 27 (2005) 1476–1487
www.elsevier.com/locate/engstruct
ed
the use of polymer
, and was ducted on ormance of ormance al data to ccelerate
erimenta
Numerical study on retrofit and strengthening performance of spray fiber reinforced polymer
H.K. Leea,∗, G. Avilab, C. Montanezc
aDepartment of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Guseong-dong, Yuseong-gu, Daejon 305-701, South Korea
bDeSimone Consulting Engineers, 2600 Douglas Road, Coral Gables, FL 33134, United States cLichtenstein Consulting Engineers, 2700 W. Cypress Creek Road, Fort Lauderdale, FL 33309, United States
Received 29 March 2004; received in revised form 6 April 2005; accepted 19 April 2005 Available online 13 June 2005
Abstract
Recent experimental results have demonstrated the great advantages in using composites in a more innovative manner, composites in a spray gun, for strengthening and rehabilitating structures. The results showed that the sprayed fiber reinforced (SFRP) was capable of substantially increasing the load capacity, ductility and energy absorbing capacity of concrete structures effective in strengthening and repair of damaged concrete structures. This paper presents the results of numerical studies con damaged reinforced concrete beams and bridge superstructures coated with SFRP to evaluate the retrofit and strengthening perf SFRP. A computational model is developed by implementing a damage constitutive model in a finite element code to predict the perf of SFRP retrofitted concrete structures during service. Numerical simulations based on the model are compared with experiment assess the predictive capability of the proposed model. This study, in conjunction with the previous experimental observations, will a the introduction of SFRP to infrastructure rehabilitation. © 2005 Elsevier Ltd. All rights reserved.
Keywords: Strengthening and rehabilitating structures; Sprayed fiber reinforced polymer; Bridge superstructures; Damage constitutive model; Expl and numerical comparison
he ted te is te se
se
te te ha
the
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nd ng P)
1. Introduction
Bridges like many other concrete structures suffer t impact of environment, daily use, and other unexpec effects day after day. This daily exposure deteriora concrete, creating loss in strength and durability. It reported that about 50% of all bridges in the United Sta were built before 1940, and approximately 42% of the bridges are structurally deficient [21]. This alarming statistic is the result of the deteriorated conventional materials u for design and construction of bridges.
Different methods of strengthening back concre structures have been in use over the years. Using s plates to accommodate losses in strength and ductility
∗ Corresponding author. Tel.: +82 42 869 3623. E-mail address: [email protected] (H.K. Lee).
0141-0296/$ - see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2005.04.013
od the ly
s
s
d
el s
been a reliable and quantifiable method [1]. Various types of concretes such as high-strength concretes have been major repair materials for damaged concrete [19]. These two materials are highly compatible and innumerable stud and examples are available to investigate the implementa of these materials into the rehabilitation and retrofitting concrete structures. On the other hand, the use of compo materials has been widely used in other structures (e aerospace and automotive structures). Due to the ama qualities found in these materials, the construction indus finally saw an application in design and building.
There are different types of composite materials a methods suitable for strengthening and rehabilitati concrete structures. Fiber reinforced polymer (FR laminates have been widely used due to their go engineering properties. However, the characteristics of FRP laminates to easily peel off and exhibit a relative
H.K. Lee et al. / Engineering Structures 27 (2005) 1476–1487 1477
re R
s
a s en
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n ul
in n
fo xy n ti
ir ca ca o e ng c
e ia s
a ng is
ng e y b
th en
io iv
ge
e e It he r in
d ix, gs ce es tly tic ks rs
e e
t, wn
r or
be
ts
e
and
nd
low strain at rupture can lead to a catastrophic failu of the reinforced concrete structures strengthened by F laminates [13,7]. The use of an external anchor system can prevent the peel-off; however, it will increase the co of the project and its complexity [7]. In addition to the peel-off failure, partial or complete debonding and she delamination can also lead to catastrophic failure. The drawbacks of FRP laminates have led to the developm of more promising rehabilitation techniques.
A new retrofit/strengthening technology using spraye fiber reinforced polymer (SFRP) pioneered by Banth et al. [4] has been studied by many researchers [3,22,2,7, 20,16]. This technology promises an easy application o concrete, a more affordable price and equal or better res than other composites technologies [2,7,16]. SFRP consists of random fibers in a polymeric matrix. It has been used the automotive and boat building industries. A spray gu with a chopper unit and epoxy containers are needed the application of the SFRP. After spraying fibers and epo resin on the concrete surface, a roller is used to roll out a entrapped air. More detailed description of the characteris of SFRP and the application of SFRP can be found in [22,2] and [16].
Evaluations of the performance of the new repa system require extensive experimentation and/or analyti and numerical techniques. The analytical and numeri approach is more economical and expedient than laborat and in-situ testing. Finite element codes have shown th great capabilities in predicting the behavior and evaluati the performance of conventional engineering materials su as metal [5]. However, predictions of the performance of th system composed of concrete and new composite mater are rather complex since the new materials exhibit a le straightforward damage constitutive behavior.
The primary objective of this study is to develop reliable and accurate computational model for simulati the retrofit and strengthening performance of SFRP. It also intended to study the capability of SFRP in increasi the bending and shear capacities of reinforced concr (RC) beams. A computational model is developed b implementing the damage constitutive model proposed Lee [14] and Karihaloo and Fu [11,12] into the finite element code ABAQUS [25] to simulate the performance of SFRP retrofitted concrete structures. The accuracy of computational model is evaluated by comparing the pres numerical predictions with experimental data.
2. Computational model
2.1. Recapitulation of damage constitutive model
The damage constitutive model described in this sect is based on a combination of a micromechanical constitut model [14] and damage models [17,11,12], and is also explained elsewhere [15].
P
t
r e t
ts
r
y c
l l
ry ir
h
ls s
te
y
e t
n e
An evolutionary debonding model [23,24,17] to describe the interfacial fiber debonding and a continuum dama model [11,12] to model the nucleation of microcracks are incorporated into the micromechanical constitutiv model [14] to predict the damage evolution and constitutiv behavior of concrete structures retrofitted with SFRP. is assumed that damage in concrete is controlled by t nucleation of microcracks, and both the interfacial fibe debonding and nucleation of microcracks control damage SFRP.
Let us start by considering an initially perfectly bonde three-phase composite consisting of an elastic matr aligned fibers and penny-shaped microcracks. As loadin or deformations are applied, aligned fibers may experien partial debonding on the top and bottom of the interfac between the matrix and fibers. The composite subsequen becomes a four-phase material, consisting of an elas matrix, perfectly bonded fibers, penny-shaped microcrac and partially debonded fibers. The partially debonded fibe will lose their load-carrying capacity, but they are still abl to transmit internal stresses into the matrix through th bonded portion [23,24,9]. Following Zhao and Wong [23, 24], a partially debonded fiber is replaced by an equivalen perfectly bonded fiber that possesses as yet unkno transversely isotropic moduli.
By combining the governing field equations for linea elastic composites containing arbitrarily non-aligned and/ dissimilar ellipsoidal inclusions [8] and the orientation averaging process proposed by Lee and Simunovic [17], the effective elasticity tensorC∗ for randomly oriented, chopped fiber composites containing microcracks can derived as [14]
C∗ = C1δi j δkl + C2(δik δ j l + δil δ j k) (1) with
C1 = 1
15 [τ1 + 5(τ3 + τ4 + 3τ5)] (2)
C2 = 1
15 [τ1 + 10τ2 + 15τ6] (3)
whereδi j signifies the Kronecker delta and the componen τ1, . . . , τ6 are given in the Appendix of [14]. The details of micromechanical formulations for the elastic moduli of th four-phase composite can be found in [14].
According to Karihaloo and Fu [11,12], the density of nucleated microcracks in concrete can be defined as
ω =
ωv0 a ≤ t h;
ωv0 + c1 (
1 − t h
a
)c2
a >
t h .
(4)
whereωv0 is the initial volume fraction of microcracks.c1 and c2 are material constants that depend on the shape
distribution of microcracks; t h = √
t hi j t h i j is the effective
strain threshold below which no nucleation takes place; a a = √ i j i j = [ 211 + 222 + 233 + 2( 212 + 223 + 231)]1/2 is the current accumulated effective strain [11].
1478 H.K. Lee et al. / Engineering Structures 27 (2005) 1476–1487
in n ia
e e e k o o a g rm
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n
re ke e g a ri e ’
f e th o s
e
r
s
n d te
e
r
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TS
ded RC mid the nd
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2.2. Finite element implementation
The damage constitutive model is implemented the nonlinear finite element code ABAQUS installed o the IBM supercomputer using a user-supplied mater subroutine to solve large-scale, boundary value problem By incorporating damage models into the constitutive mod and then implementing them into the nonlinear finit element program, the progressive damage evolutions du the interfacial fiber debonding and nucleation of microcrac are taken into account into the constitutive relation concrete and SFRP. This finite element implementati allows us to simulate the performance of SFRP rep system, to simplify investigation of the effects of modelin variables such as coating thickness, and to perfo customized post-processing of numerical data.
The numerical algorithms employed in the computation model are based on the strain driven algorithm in which t stress history is to be determined by a given strain histo Therefore, the current computational model can addre the softening behavior of concrete structures. The deta of finite element implementation and algorithms employe in the development of computational model can be fou in [18].
3. Simulation of performance of RC beams with SFRP
3.1. Numerical simulations and experimental comparison
A series of numerical three-point bending tests a conducted on the undamaged and damaged (pre-crac RC beams with and without SFRP to predict load–displac ment curves from which the increase in load-carryin and energy absorption capacities is evaluated. For beam models, the energy absorbed by the beams p to failure is calculated by taking the area under th loading curve. This area is calculated using Simpson integration method in conjunction with MATLAB. This failure energy is used to quantify the ductility o the beams. To assess the potential of the pres computational model, we compare our predictions wi an experiment conducted by authors at the University Miami in 2003. The typical load–displacement curve obtained from the experiment can be found in [16]. The material properties of concrete, steel and SFRP used in th simulations are summarized inTable 1. The aspect ratios and volume fractions of the fibers and microcracks in SFRP a estimated to bea f = 1000, ac = 0.0001; φ f = 0.15, φc = 0.0001. The damage parameters involving in the simulations are summarized inTable 2.
The damage constitutive model explained inSection 3is used for modeling the behavior of both concrete beams a SFRP coating, and a rebar element in ABAQUS is utilize for modeling the behavior of the steel rebar in concre beams. Only one volume fraction of fibers(φ f ) and fiber length(l f ) are considered for these numerical tests to ke
l s. l
to s f n ir
l e y. s
ls
d
d) -
ll or
s
nt
f
se
e
e
d
p
Table 1 Material properties used in the simulation
Concrete T-310 Resin E-glass fiber Reba
Tensile modulus (GPa) 29.0 1.3 69.0 200.0 Poisson’s ratio 0.17 0.35 0.17 0.30
Table 2 Damage parameters used in the simulation
Parameters So M t h c1 c2
2.25E+07 4.0 0.20E−05 0.95 10.80
the number of test parameters manageable. While the eight-node linear brick solid element C3D8 in ABAQUS utilized for modeling the concrete beam and SFRP coati the two-node linear truss element T3D2 in ABAQUS used for modeling the rebar. The RC beams are loa proportionally with the rate of 0.015 mm/s at the center of the beam corresponding to the head-loading rate of the M testing machine used in experiment [16]. Fig. 1 shows a finite element (FE) model where the steel rebar is embed in an RC beam. To model the damage (pre-crack) in beams, a small and very thin notch was modeled at the span so that it acts as a crack trigger for the failure of beams. The length and width of the notch are 10 mm a 0.1 mm, respectively. The main advantage of this model approach in comparison with most computational dama modeling techniques is that the damage evolution is fu coupled with the constitutive equation by incorporatin damage laws into the constitutive model.
Comparisons of peak load and energy absorbed du the three-point bend tests between the present predic and the experiment are summarized inTables 3 and 4, respectively. The details of numerical simulations a experimental comparison are described below.
3.1.1. Undamaged RC beams without SFRP coating In order to examine whether the computational mod
is able to predict the behavior of undamaged R beams without SFRP coating, the load–displacem curve of undamaged RC beams is presented inFig. 2. The load–displacement curves of undamaged RC be obtained from the experiment are also depicted in the fig for comparison. InFigs. 2–7, solid lines represent the experimental data and dotted lines are used for the nume results. In Fig. 2, a peak load of 18.64 kN is observed fro the numerical simulation, while an average peak load 11.90 kN is obtained from the experiment. The total ene absorbed in failure of the specimen is computed to be 9.9 from the numerical simulation, while the average of to energy absorbed in failure of the specimen is computed be 11.89 J from the experiment.
H.K. Lee et al. / Engineering Structures 27 (2005) 1476–1487 1479
Fig. 1. A finite element model of an RC beam.
Table 3 Summary of simulation results compared with the experiment for peak load of RC beams
Specimen Peak load (kN) Percent of prediction/ Prediction Test data test data
Undamaged RC beams without SFRP coating 18.64 11.90 156.64 Undamaged RC beams with thin SFRP coating 20.84 15.47 134.71 Undamaged RC beams with thick SFRP coating 24.90 24.20 102.89 Pre-cracked RC beams without SFRP coating 11.68 10.64 109.77 Pre-cracked RC beams with thin SFRP coating 14.12 11.28 125.18 Pre-cracked RC beams with thick SFRP coating 16.52 14.91 110.80
Table 4 Summary of simulation results compared with the experiment for energy absorption of RC beams
Specimen Energy absorbed (J) Percent of prediction/ Prediction Test data test data
Undamaged RC beams without SFRP coating 9.91 11.89 83.35 Undamaged RC beams with thin SFRP coating 15.28 13.65 111.94 Undamaged RC beams with thick SFRP coating 27.94 25.73 108.59 Pre-cracked RC beams without SFRP coating 8.71 14.56 59.82 Pre-cracked RC beams with thin SFRP coating 14.03 12.18 115.19 Pre-cracked RC beams with thick SFRP coating 20.41 23.11 88.32
m
e ur
g he te e e
ms
es ure
ge he ted e en
3.1.2. Undamaged RC beams with thin SFRP coating The load–displacement curve of undamaged RC bea
with a thin SFRP coating (t = 3.2 mm) is presented in Fig. 3. The corresponding load–displacement curv obtained from the experiment are also depicted in the fig for comparison. InFig. 3, a peak load of 20.84 kN is observed from the numerical simulation, while an avera peak load of 15.47 kN is obtained from the experiment. T total energy absorbed in failure of the specimen is compu to be 15.28 J from the numerical simulation, while th average of total energy absorbed in failure of the specim is computed to be 13.65 J from the experiment.
s
s e
e
d
n
3.1.3. Undamaged RC beams with thick SFRP coating The load–displacement curve of undamaged RC bea
with a thick SFRP coating (t = 6.4 mm) is presented in Fig. 4. The corresponding load–displacement curv obtained from the experiment are also depicted in the fig for comparison. InFig. 4, a peak load of 24.90 kN is observed from the numerical simulation, while an avera peak load of 24.20 kN is obtained from the experiment. T total energy absorbed in failure of the specimen is compu to be 27.94 J from the numerical simulation, while th average of total energy absorbed in failure of the specim is computed to be 25.73 J from the experiment.
1480 H.K. Lee et al. / Engineering Structures 27 (2005) 1476–1487
ou
RP d
m
th n
o gy 1 al to
P
s
s
s re
e e d
Fig. 2. Comparison of load–displacement curves of RC beams with SFRP between the present prediction and the experiment.
Fig. 3. Comparison of load–displacement curves of RC beams with SF (t = 3.2 mm,l f = 13 mm,φ f = 15%) between the present prediction an the experiment.
3.1.4. Pre-cracked RC beams without SFRP coating The load–displacement curve of pre-cracked RC bea
without SFRP coating is presented inFig. 5. The corresponding load–displacement curves obtained from experiment are also depicted in the figure for compariso In Fig. 5, a peak load of 11.68 kN is observed from the numerical simulation, while an average peak load 10.64 kN is obtained from the experiment. The total ener absorbed in failure of the specimen is computed to be 8.7 from the numerical simulation, while the average of tot energy absorbed in failure of the specimen is computed be 14.56 J from the experiment.
t
s
e .
f
J
Fig. 4. Comparison of load–displacement curves of RC beams with SFR (t = 6.4 mm,l f = 13 mm,φ f = 15%) between the present prediction and the experiment.
Fig. 5. Comparison of load–displacement curves of pre-cracked RC beam without SFRP between the present prediction and the experiment.
3.1.5. Pre-cracked RC beams with thin SFRP coating The load–displacement curve of pre-cracked RC beam
with a thin SFRP coating (t = 3.2 mm) is presented in Fig. 6. The corresponding load–displacement curve obtained from the experiment are also depicted in the figu for comparison. InFig. 6, a peak load of 14.12 kN is observed from the numerical simulation, while an averag peak load of 11.28 kN is obtained from the experiment. Th total energy absorbed in failure of the specimen is compute to be 14.03 J from the numerical simulation, while the
H.K. Lee et al. / Engineering Structures 27 (2005) 1476–1487 1481
m
m
en
m
s
ure
ge he ted e en
the ior is se
in . A ing
ves
wer f ving
ly avior is
ill eters
de, nal To of
ze. the nd
f ent ams re.
st ss. ge
gly ore,
Fig. 6. Comparison of load–displacement curves of pre-cracked RC bea with SFRP (t = 3.2 mm, l f = 13 mm,φ f = 15%) between the present prediction and the experiment.
Fig. 7. Comparison of load–displacement curves of pre-cracked RC bea with SFRP (t = 6.4 mm, l f = 13 mm,φ f = 15%) between the present prediction and the experiment.
average of total energy absorbed in failure of the specim is computed to be 12.18 J from the experiment.
3.1.6. Pre-cracked RC beams with thick SFRP coating The load–displacement curve of pre-cracked RC bea
with a thick SFRP coating (t = 6.4 mm) is presented in Fig. 7. The corresponding load–displacement curve
s
s
s
obtained from the experiment are also depicted in the fig for comparison. InFig. 7, a peak load of 16.52 kN is observed from the numerical simulation, while an avera peak load of 14.91 kN is obtained from the experiment. T total energy absorbed in failure of the specimen is compu to be 20.41 J from the numerical simulation, while th average of total energy absorbed in failure of the specim is computed to be 23.11 J from the experiment.
3.2. Parametric study of nucleation parameters
To illustrate the influence of nucleation parameters of model on the damage evolution and constitutive behav of RC beams, a parametric analysis is carried out. It also intended to evaluate the model sensitivity to the parameters. We choose two nucleation parametersc2 and th given in Eq. (4), which are the most dominant ones the nucleation of microcracks, for the parametric analysis parametric analysis relating to the interfacial fiber debond can be found in [14].
Fig. 8shows the comparison of load–displacement cur of undamaged RC beams having various values ofc2. Five different values ofc2 are used:c2 = 0.108, 1.080, 10.80, 108.0, 1080. As shown inFig. 8, if c2 is low, microcracks nucleate at an early stage and the beam shows a lo stress–strain behavior.Fig. 9 shows the comparison o load–displacement curves of undamaged RC beams ha various values of th. Five different values of th are used in the study: th = 0.2 × 10−3, 0.2 × 10−4, 0.2 × 10−5, 0.2 × 10−6, 0.2 × 10−7. In Fig. 9, microcracks nucleate at an ear stage and the beam shows a lower stress–strain beh when th is low. It is observed from the parametric analys that the influence of nucleation parametersc2 and
th is quite remarkable; therefore, experimental verifications w be needed to accurately determine the nucleation param for more realistic numerical predictions.
3.3. Mesh sensitivity study
Once a constitutive model is implemented in an FE co numerical simulations using the implemented computatio model would be sensitive to the spatial discretization. illustrate the influence of FE mesh size on the behavior RC beams, a mesh sensitive study is conducted.Fig. 10 shows FE models for RC beams with different mesh si The coarse mesh model consists of 40 FEs, while intermediate and fine mesh models consist of 192 a 575 FEs, respectively.Fig. 11 shows the comparison o load–displacement curves of the RC beams with differ mesh sizes. The load–displacement curve of the RC be obtained from the experiment is also depicted in the figu As shown in Fig. 11, the fine mesh provides the mo accurate result throughout the whole deformation proce It is noted from the mesh sensitivity study that the dama evolution and constitutive behavior of RC beams stron depends on the fineness of the FE discretization; theref
1482 H.K. Lee et al. / Engineering Structures 27 (2005) 1476–1487
en
en
he
ly v
ed ds to
g., he
e e ded fit ed eld an ed re ted ent am een
n on ion
tic P
el of ear
lar
ear e
P
on st. ted
ls
of m
ore am r
the ded
Fig. 8. Comparison of load–displacement curves of RC beams with differ values ofc2.
Fig. 9. Comparison of load–displacement curves of RC beams with differ values of t h .
a fine mesh is required for more realistic predictions of t behavior of RC beams.
4. Simulation of performance of bridge superstructures strengthened with SFRP
When adding flexural reinforcement to a beam, it on needs to be added on the tension face of the beam. Howe
t
t
er,
shear strengthening has to deal with the complicat cross section of the beam. The web of the beam nee to be encased with the external shear reinforcement best provide shear reinforcement to the beam [6]. To accomplish a total encasement, a flexible material (e. flexible composites) can be easily applied to the web of t beam.
In order to encourage and convince the bridg engineering community to strengthen and retrofit bridg concrete structures with SFRP, more experiments are nee to show the effectiveness of this strengthening/retro method and reliable methods of analyzing the expect results also need to be developed before moving to the fi and repairing structures with SFRP. Numerical analysis c serve as a guide of the desired results in the retrofitt structures. The objectives of the simulation in this section a to study the benefits that SFRP can provide to a deteriora bridge superstructure, and to show how a shear defici RC beam can be strengthened with SFRP. The T-be bridge superstructure whose shear strengthening has b well studied [10] is analyzed in this study. Kaliakin and researchers [10] tested 12 T-beams bonded with wove composite fabrics and conducted numerical simulations the beams. The results obtained from the present predict are compared with those in [10] to show the superior characteristics of SFRP.
The dimension of the T-beam analyzed and the schema of the four-point bending test on the T-beam with SFR coating are shown inFig. 12 (see also [10]). The internal flexural reinforcement consists of one #5 Grade 60 ste bar. The low shear span-to-depth ratio and the lack shear reinforcement assure the beam fails in a brittle sh mode rather than in a flexure mode.Fig. 13 shows the 3D T-beam model and FE mesh used in the simulation. Simi to the FE model inSection 3, the 3D, eight-node linear brick solid element C3D8 in ABAQUS is utilized for modeling the concrete beam and SFRP coating, and the two-node lin truss element T3D2 in ABAQUS is used for modeling th rebar. The same damage parameters as used inSection 3 are adopted in this simulation. The thickness of the SFR coating is 3.2 mm.
Fig. 14 shows the sequence of deformed shape and v Mises effective stress during the four-point bending te The predicted load–displacement curve on the SFRP coa T-beam is shown inFig. 15. Experimental data on T-beams bonded with woven composite fabrics made of materia with two different moduli per unit width [10] are also presented in the figure for comparison. The comparison the resisting load at a displacement of 2 mm obtained fro the present prediction and [10] is summarized inTable 5. It is noted fromFig. 15andTable 5that while the beam coated with SFRP is able to sustain a larger load and absorb m energy at equal displacements in comparison with the be bonded with woven composite fabrics with low modulus pe unit width, it sustains almost the same load and absorbs same amount of energy as obtained from the beam bon
H.K. Lee et al. / Engineering Structures 27 (2005) 1476–1487 1483
FEs).
Fig. 10. (a) Coarse mesh (40 FEs); (b) intermediate mesh (192 FEs); (c) fine mesh (575
it
fit te on
s a
ed s
nd re, re ive al
he e
the
with woven composite fabrics with high modulus per un width.
5. Concluding remarks
A computational approach to the evaluation of retro and strengthening performance of SFRP was presen A damage constitutive model based on a combinati of a micromechanical constitutive model [14] and a continuum model [11,12] was developed and the model wa implemented in the finite element code ABAQUS by using
d.
user-supplied material subroutine. Based on the develop computational model, a series of numerical simulation were carried out to probe the behavior of RC beams a bridge superstructures retrofitted with SFRP. Furthermo the predictions based on the computational model we compared with experimental data to assess the predict capability of the model. The outcome from the numeric study can be summarized as follows.
1. The coating thickness has a significant influence on t load-carrying and energy absorption capacities of th beams. The peak load and energy absorbed prior to
1484 H.K. Lee et al. / Engineering Structures 27 (2005) 1476–1487
ating.
Fig. 11. Comparison of load–displacement curves of RC beams with different mesh size.
Fig. 12. The dimension of the T-beam and the schematic of the four-point bending test on the T-beam with SFRP co
ck a
ers ior f a
E e
a
failure are shown to be greater for the beams with a thi coating in comparison with those for the beams with thin coating.
2. From the parametric study, crack nucleation paramet are shown to influence the damage constitutive behav of concrete and SFRP. A more ductile fashion o constitutive behavior is observed with the use of smaller value of th and c2. It is shown from the mesh
sensitivity study that the effect of mesh size of the FE models is not negligible. Finer meshes result in more accurate predictions; thus, a fine mesh is required in F simulations for an accurate prediction of the performanc of the retrofitted concrete beams.
3. This numerical study has demonstrated an equal or little superior resistance quality of SFRP in comparison with woven composite fabrics in bridge superstructure
H.K. Lee et al. / Engineering Structures 27 (2005) 1476–1487 1485
Fig. 13. 3D T-beam model (a) and FE mesh (b) used in the simulation.
om
ed ca e
es rs tly
lly
l
r, re t to s
e te - the
al d
ld
Table 5 Comparison of the resisting load at a displacement of 2 mm obtained fr the present prediction and Kaliakin et al.’s [10] experiment
Specimen Load (kN)
T-beam coated with SFRP 52 T-beam bonded with woven composite fabrics with high 53 modulus per unit width T-beam bonded with woven composite fabrics with low 41 modulus per unit width
applications. It has also proved that the propos computation model is a reliable and accurate numeri tool for determining the expected behavior of futur design of concrete repairs.
4. A high load-carrying capacity is always in need in bridg to accommodate higher loads than designed for in the fi place. This constant need and difficulty can be grea
l
t
resolved if SFRP strengthening methods are successfu applied.
This study, in conjunction with the previous experimenta observations ([3,16] etc.), will accelerate the introduction of SFRP composites to infrastructure rehabilitation. Howeve an additional test with the T-beam bridge superstructu strengthened by SFRP coating needs to be carried ou compare the behavior of this beam with that of beam tested by Kaliakin et al. [10]. The comparison between the experimental and analytical results related to th performance of this additional T-beam will demonstra the validity the computational model. Furthermore, long term performance tests should be conducted to evaluate lasting performance of SFRP under harsh environments.
Acknowledgments
This research was partially supported by the Nation Computational Science Alliance under MSS020010N an utilized the IBM P690 supercomputer. The authors wou
1486 H.K. Lee et al. / Engineering Structures 27 (2005) 1476–1487
g test.
Fig. 14. A sequence of deformed shape and von Mises effective stress during the four-point bendin
se
ts o r rt
B:
h
al
s l
res.
s. .
Fig. 15. Comparison of load–displacement curves between the pre prediction on an SFRP coated T-beam and Kaliakin et al.’s [10] experiment on a T-beam bonded with woven composite fabrics.
nt
like to thank the reviewers for their elaborated commen on the original manuscript. The authors would also like t thank the Ministry of Science and Technology, Korea, fo the financial support by a grant (NL33676) from the Sma Infra-Structure Technology Center (SISTeC), Korea.
References
[1] Ascione L, Feo L. Modeling of composite/concrete interface of RC beams strengthened with composite laminates. Composites Part Engineering 2000;31:535–40.
[2] Banthia N. Monitoring world’s first bridge with sprayed fibre reinforced polymer repair. In: Proc. 1st int. conf. on structural healt monitoring. Winnipeg: ISIS Canada Corporation; 2002. p. 135–44.
[3] Banthia N, Nandakumar N, Boyd A. Sprayed fiber-reinforced polymers: From laboratory to a real bridge. Concrete Internation 2000;47–52.
[4] Banthia N, Yan C, Nandakumar N. Sprayed fibre reinforced plastic (FRPs) for repair of concrete structures. In: 2nd internationa conference on advanced composite materials in bridges and structu Montreal (QC, Canada): CSCE; 1996. p. 537–45.
[5] Biggs RM, Barton FW, Gomez JP, Massarelli PJ, McKeel WT. Finite element modeling and analysis of reinforced-concrete bridge deck Report: Virginia Transportation Research Council. September 2000
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[6] Chajes MJ, Januszka TF, Mertz DR, Thomson TA, Finch WW. She strengthening of reinforced concrete beams using externally appl composite fabrics. ACI Structural Journal 1995;92:295–303.
[7] Harries KA, Young SC. Sprayed-fiber-reinforced composite mat rials for infrastructure rehabilitation. Concrete International 200 47–51.
[8] Ju JW, Chen TM. Micromechanics and effective moduli of elas tic composites containing randomly dispersed ellipsoidal inhom geneities. Acta Mechanica 1994;103:103–21.
[9] Ju JW, Lee HK. A micromechancial damage model for effectiv elastoplastic behavior of ductile matrix composites considerin evolutionary complete particle debonding. Computer Methods Applied Mechanics and Engineering 2000;183:201–22.
[10] Kaliakin VN, Chajes MJ, Januszka TF. Analysis of concret beams reinforced with externally bonded woven composite fabric Composites Part B: Engineering 1996;27:235–44.
[11] Karihaloo BL, Fu D. A damage-based constitutive law for plai concrete in tension. European Journal of Mechanics, A-Solids 198 8:373–84.
[12] Karihaloo BL, Fu D. Orthotropic damage model for plain concrete i tension. ACI Materials Journal 1990;87:62–7.
[13] Kestner JT, Harries KA, Pessiki SP, Sause R, Ricles JM Rehabilitation of reinforced concrete columns using fiber reinforce polymer composite jackets. ATLSS Report 97-07. Lehigh Universit 1997.
[14] Lee HK. Computational approach to the investigation of impa damage evolution in discontinuously reinforced fiber composite Computational Mechanics 2001;27:504–12.
[15] Lee HK, Avila G, Schadler D. A computational approach fo prediction of the performance of concrete beams retrofitted wi sprayed fiber reinforced polymers. KSCE Journal of Civil Engineerin 2003;7:637–44.
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[16] Lee HK, Hausmann LR. Structural repair and strengthening o damaged RC beams with sprayed FRP. Composite Structures 20 63:201–9.
[17] Lee HK, Simunovic S. Modeling of progressive damage in aligned an randomly oriented discontinuous fiber polymer matrix composites Composites Part B: Engineering 2000;31:77–86.
[18] Lee HK, Simunovic S, Shin DK. A computational approach for prediction of the damage evolution and crushing behavior of choppe random fiber composites. Computational Materials Science 2004;2 459–74.
[19] Martos CL. Repair methods for corrosion-damaged reinforce concrete and the strengthening of concrete flexural members wi fiber-reinforced polymer wraps. Master’s thesis. Coral Gables (FL University of Miami; 2004.
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[23] Zhao YH, Weng GJ. Plasticity of a two-phase composite with partially debonded inclusion. International Journal of Plasticity 1996 12:781–804.
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- Numerical study on retrofit and strengthening performance of sprayed fiber reinforced polymer
- Introduction
- Computational model
- Recapitulation of damage constitutive model
- Finite element implementation
- Simulation of performance of RC beams with SFRP
- Numerical simulations and experimental comparison
- Undamaged RC beams without SFRP coating
- Undamaged RC beams with thin SFRP coating
- Undamaged RC beams with thick SFRP coating
- Pre-cracked RC beams without SFRP coating
- Pre-cracked RC beams with thin SFRP coating
- Pre-cracked RC beams with thick SFRP coating
- Parametric study of nucleation parameters
- Mesh sensitivity study
- Simulation of performance of bridge superstructures strengthened with SFRP
- Concluding remarks
- Acknowledgments
- References
HT120815 Readings/1-s2.0-S095006180600119X-main.pdf
Construction
www.elsevier.com/locate/conbuildmat
Construction and Building Materials 21 (2007) 764–776
and Building
MATERIALS
Flexural behavior of aged prestressed concrete girders strengthened with various FRP systems
Owen Rosenboom, Tare K. Hassan, Sami Rizkalla *
Department of Civil Engineering, North Carolina State University, Centennial Campus, Raleigh, NC 27965-7533, United States
Received 20 January 2005; received in revised form 24 May 2006; accepted 19 June 2006 Available online 7 September 2006
Abstract
Many prestressed concrete bridges are in need of upgrading in order to increase their posted capacities. Departments of transportation across the country have been faced with large financial burdens on the maintenance budget, negative psychological effects on highway users, long traffic delays during maintenance, potential safety hazards, and reduced service life as a result of the deficiencies. In response to considerable consultation with the North Carolina Department of Transportation (NCDOT), a research project with practical goals was initiated to evaluate the cost-effectiveness and value engineering of Carbon Fiber Reinforced Polymer (CFRP) repair and strength- ening systems for prestressed concrete bridge girders.
This paper presents the first phase of the research program, involving the testing under static loading conditions of eight prestressed concrete bridge girders, six strengthened with various CFRP systems. Results show that the ultimate capacity of prestressed concrete bridge girders can be increased by as much as 73% using CFRP without sacrificing the ductility of the original member. Transverse CFRP U-wrap reinforcements are recommended along the length of the girder to control debonding type failures. The second phase of the research will examine the fatigue behavior of the strengthened girders, and provide analysis under service loading conditions. � 2006 Elsevier Ltd. All rights reserved.
Keywords: Prestressed; Strengthening; Fiber reinforced polymers; Bridge girder; Near surface mounted; Externally bonded; Flexural behavior
1. Introduction
1.1. Research objectives
Many prestressed concrete bridges are in need of upgrading in order to increase their posted capacities. Departments of transportation across the country have been faced with large financial burdens on the maintenance budget, negative psychological effects on highway users, long traffic delays during maintenance, potential safety hazards, and reduced service life as a result of the deficien- cies. In response to considerable consultation with the North Carolina Department of Transportation (NCDOT),
0950-0618/$ - see front matter � 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2006.06.007
* Corresponding author. Tel.: +1 919 513 1733; fax: +1 919 513 1765. E-mail addresses: [email protected] (O. Rosenboom), tarek.hassan
@dargroup.com (T.K. Hassan), [email protected] (S. Rizkalla).
a research project with practical goals was initiated to eval- uate the cost-effectiveness and value engineering of Carbon Fiber Reinforced Polymer (CFRP) repair and strengthen- ing systems for prestressed concrete bridge girders.
The use of CFRP began after World War II in military high-performance applications. Use within the civil infra- structure, either as a retrofit material or in construction of new structures, gained popularity in the 1980s. Today, CFRP pre-cured bars, strips, and tendons, as well as wet lay-up sheets are commonly used in the repair and retrofit of concrete structures. Some of the major benefits of CFRP include its high strength to weight ratio, high fatigue endur- ance and the ease of fabrication, manufacturing, handling and installation. Codification of the use of CFRP in civil infrastructure is quickly catching up with the rapid growth in installations, with many code writing agencies around the world concerned with this task [1–3].
O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776 765
Included in this paper are results and analysis from the first phase of the research, concerned with the flexural behavior under static loading conditions of prestressed concrete girders strengthened with various CFRP systems. After a brief review of the literature on the topic, test results are presented on the static testing to failure of eight girders. Six were strengthened with various CFRP systems including externally bonded sheets and strips and near sur- face mounted bars and strips while two were control gird- ers. Two different analysis procedures are included which can determine accurately the ultimate capacity of a CFRP strengthened prestressed concrete girder. Details of an additional phase of the research program concerning the fatigue behavior and design under service loading condi- tions of such girders is provided elsewhere [4].
1.2. Background
One of the most common uses of CFRP materials is to externally bond the material directly to the concrete sur- face. Externally bonding CFRP systems to concrete can be achieved by bonding pre-cured laminates, or applying wet lay-up sheets. The systems are typically bonded to the tension side of the members to increase the flexural strength and/or on the sides of the member to improve the shear capacity. Installation of this technique is rela- tively simple and can be achieved in a very short time. The system must be designed to avoid premature failure due to possible delamination or debonding of the CFRP material from the concrete surface, a failure mode first noted in reinforced concrete beams strengthened with mild steel plates [5]. Many researchers today are concerned with the task of controlling and predicting debonding type fail- ures: terminology and methodology of the FRP to rein- forced concrete debonding failure proposed by Teng et al. [6] and Oehlers et al. [7] has been generally accepted and slowly makes it way into codification. ACI Commit- tee 440F [1] deals with the debonding mechanism by applying a bond reduction coefficient, but its use is overly conservative for CFRP strengthened prestressed concrete due to initial strains present in the concrete due to prestressing.
In response to premature debonding failures, the use of near surface mounted (NSM) CFRP systems was intro- duced by several researchers [8–10]. By inserting a CFRP bar or strip into a pre-cut groove and filling with epoxy, NSM systems can reduce the propensity for debonding fail- ures. In addition, the embedded nature of the technique provides superior environmental performance in compari- son to externally bonded techniques, as well as protection against possible accidental and intentional damage.
There has been little research on the strengthening of prestressed concrete with CFRP materials. There have been some field applications using CFRP to repair prestressed concrete [11], yet few full scale specimens have been tested to failure. Takacs and Kanstad [12] showed that pre- stressed concrete girders could be strengthened with exter-
nally bonded CFRP to increase their ultimate flexural capacity. Two 11.3 m (37 ft) specimens plated with pre- cured CFRP laminates achieved an increase in flexural moment capacity of 28% and 37%, respectively. They accu- rately predicted the behavior using a finite element model based on the smeared crack methodology. Hassan and Riz- kalla [13] examined the flexural behavior of prestressed concrete bridge slabs strengthened with various CFRP sys- tems. The flexural capacity of the slabs could be increased by as much as 50% using the CFRP strengthening, with the most cost effective solution being the CFRP sheets.
2. Experimental program
2.1. Test girders
As part of an extensive research program sponsored by the North Carolina Department of Transportation eight prestressed concrete C-Channel bridge girders were stati- cally tested to failure. The C-Channel prestressed concrete girder is a superstructure member commonly used for short span bridges in rural areas, typically used to span small streams or estuaries. Bridges using this type of girder were built between the late 1950s to the mid 1970s. Of the eight girders tested under static loading conditions, five had a Type I prestressing configuration with ten 1723 MPa (250 ksi) prestressing strands and came from a decommis- sioned bridge erected in 1961. The other three girders were Type II girders, prestressed with eight 1862 MPa (270 ksi) strands and also came from a decommissioned bridge. The two types of prestressing steel configurations along with the cross-sectional dimensions and other reinforce- ment details of the girders are shown in Fig. 1. The mea- sured camber for all the girders in both prestressing configurations was 32 mm (1.25 in.).
The Ramberg–Osgood function [14] was used to match the stress versus strain behavior of the prestressing strands.
fp ¼ Epeps A þ 1 � A
½1 þðBepsÞ C�1=C
" # ð1Þ
where fp is the prestressing strand stress, Ep is the modulus of elasticity of the prestressing strand, eps is the strain in the prestressing strand, and A, B, C are material constants. The constants A, B and C were determined from the stress– strain relationships generated from tension tests. For the Type I girders with 1724 MPa (250 ksi) strands, the average values for A, B and C were 0.025, 138.7 and 6, respectively. For the Type II girders with 1862 MPa (270 ksi) strands the average values for A, B and C were calculated to be 0.017, 106.0 and 7.
The nominal concrete strength specified for the C-Chan- nel prestressed concrete girders was 34.5 MPa (5000 psi) at 28 days and 27.6 MPa (4000 psi) at transfer of prestressing force. During the design stage for strengthening of these girders, the concrete compressive strength was estimated
EB2S
EB3S
Two-part epoxy
EB CFRP sheets
Prestressing strand
3 Plies/web (100 mm wide)
Sheet thickness = 1.0 mm
40
60 60
40
Sheet thickness = 1.0 mm
5 Plies/web (125 mm wide)
Prestressing strand
EB CFRP sheets
Two-part epoxy
Sec A-A
4572 mm
60
40
20 20
1 Ø10 /web CFRP bar
Two-part epoxy 20
40
Two-part epoxy
2 CFRP strips/web 2 x (2x16mm)
A
A
20
Prestressing strand Prestressing strand
4050 mm
750 750
150
750 750 300
U-Wrap for externally bonded FRP systems only
150 150 150150
40
Prestressing strand
Thickness=1.5 mm
(1.2x50 mm)
Two-part epoxy
1 CFRP strip/web
50
60
60 60
40
Sheet thickness = 2.4 mm
4 Plies/web (100 mm wide)
Prestressing strand
EB CFRP sheets
NSM1S NSM2S
EB1S
EB4S
Two-part epoxy
TYPE II
Ø12/330
775 775
TYPE I
114
3@44
38 114
Ø10/180 Ø/180 Ø/330
35 2@11
38 End strand
spacing CL strand spacing
CL strand spacing
End strand spacing
140 38
76 38
114 38
2@11
Fig. 1. C-Channel elevation, prestressing configurations, and strengthening details.
766 O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776
using the following equation which accounts for the strength increases due to aging [15].
f 0cðtÞ¼ f 0 cð28Þ
t 4 þ 0:85ðtÞ
� � ð2Þ
where f 0cðtÞ is the concrete compressive strength as a func- tion of time and t is the time in days.
Three concrete core samples were obtained from each of the tested girders. The average concrete strength was 69.5 MPa (10,100 psi) and 56.3 MPa (8200 psi) for the Type I and Type II girders, respectively.
2.2. Design of the strengthened girders
The design of the strengthened girders proceeded after testing the control girder. Three different levels of strength- ening were examined, the design criteria being to achieve a 20%, 40% or 60% increase in the ultimate load carrying capacity with respect to the control girder. The design of each strengthened girder was based on a cracked section analysis program, Response 2000 [16]. The base curve of the concrete compression model used in the cracked section analysis program was the Popovics curve, compression
Fig. 2. Typical test setup.
O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776 767
softening was determined using the Vecchio–Collins model and the tension stiffening was determined from the Bentz model [16]. In the preliminary design, the compression strength of the concrete was based on the compression strength specified in the original NCDOT drawings modi- fied according to Eq. (2) to account for the age of concrete at the time of testing. The compression strength used in the design was 41.4 MPa (6000 psi). The prestressing strands were all assumed to be 1724 MPa (250 ksi) for Type I pres- tressing configuration modeled using the Ramberg–Osgood equation with 0.030, 121 and 6 for the coefficients A, B and C, respectively. The CFRP systems used in the design were modeled as linear elastic up to failure using material prop- erties provided by the manufacturer.
Flexural failure, defined as rupture of the FRP or crush- ing of the concrete in compression, was the desired mode of failure. It was recognized that externally bonded systems are more prone to debonding failures than near surface mounted systems. According to Malek et al. [17], shear stresses developed at the FRP cut-off point for the exter- nally bonded systems were significantly lower than the shear strength of the concrete. Therefore, plate-end deb- onding was not expected to occur. However, in order to delay FRP delamination-type failures along the length of the girder, 150 mm (6 in.) wide U-wraps were installed at 900 mm (3 ft) spacing for all externally bonded strength- ened girders. This arrangement was selected to simulate typical anchorage details commonly used by the construc- tion industry for reinforced concrete members strengthened with FRP.
Three types of CFRP systems were used in this research: externally bonded wet lay-up type systems, externally bonded pre-cured laminates, and near surface mounted (NSM) systems. The shape, type and amount of CFRP applied to the soffits of the C-Channel girder are shown in Fig. 1. The strengthening systems used for girders NSM1S and NSM2S consisted of one CFRP bar or two CFRP strips placed in near surface mounted grooves in each soffit. The strengthening system used for girder EB1S consisted of one CFRP laminate per soffit. Girders
Table 1 CFRP tension test results
Girder strengthened Specimen Thickness (mm
NSM1S Manufacturer –
NSM2S Experimental average 2.5 Manufacturer 2.0
EB1S Experimental average 1.3 Manufacturer 1.3
EB2S Experimental average 2.3 Manufacturer 1.0
EB3S Experimental average 2.3 Manufacturer 1.0
EB4S Experimental average 2.0 Manufacturer 1.0
EB2S, EB3S and EB4S were strengthened with various configurations of either normal or high modulus CFRP wet lay-up sheets. The material properties of each CFRP system was determined through constitutive testing, the results of which are shown in Table 1.
2.3. Test setup and instrumentation
All girders were tested in three-point loading using a 490 kN (110 k) hydraulic actuator mounted to a steel frame at midspan as shown in Fig. 2. To simulate field loading conditions, a set of truck tires filled with silicon rubber were used as a contact surface while applying the load. The girder was supported at both ends on a 64 mm (2.5 in.) thick neoprene pad which in turn rested on a 25 mm (1 in.) steel plate. The behavior during testing was measured using a combination of string potentiometers placed along the girder span, and a combination of PI gauges (a strain gauge mounted to a spring plate) and
) Tensile strength (MPa) EF (MPa) efu (%)
2068 124,092 1.67
2130 115,357 1.85 2068 130,952 1.58
2758 160,444 1.73 2799 164,443 1.69
338 46,486 0.83 986 95,765 1
600 45,087 1.4 724 64,976 1
138 75,572 0.2 393 132,151 0.3
Fig. 3. Crushing of concrete failure in control girder, CS.
768 O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776
electric resistance strain gauges located around the mid- span section to determine the strain profile along the depth of the girder.
The loading sequence began by increasing the applied load up to a load level slightly higher than the cracking load. The girder was then unloaded, and reloaded again at a rate of 2.5 mm/min (0.1 in/min) up to the load level equivalent to yielding of the prestressing strands. This loading sequence was selected to determine the effective prestressing force in the girders by observing the re-open- ing of the flexural cracks. From the measured load at reopening of the flexural crack at midspan, Pro, the average effective prestressing strands, Peff, can be determined according to the following equation:
0 ¼ M D Sb þ
L � P ro 4 � Sb
� 10 � P eff
Ac � X d i � P eff
Sb ð3Þ
where MD is the moment due to the dead load, Sb is the bottom section modulus, L is the span, Ac is the area of the concrete section, and di are the locations of the different layers, i, of prestressing strand measured from the neutral axis of the section. When the girders were loaded beyond yielding of the prestressing strands, the rate of the applied load was increased to 5 mm/min (0.2 in/min) up to failure. The average prestress force for Type I and Type II girders was 70.5 kN (15.9 k) and 82.7 kN (18.6 k), respectively.
2.4. Type I girders
Five girders with a Type I prestressing configuration were tested statically to failure. One of these was a control girder, and four were strengthened with various CFRP sys- tems. Summarized test results are given in Table 2, includ-
Table 2 Summarized test results
Specimen designation CS NSM1S NSM2S
Strengthening – NSM bars NSM strips Prestressing configuration Type I Type I Type I Pcr (kN) 56.0 55.2 55.2 Pro (kN) – 39.1 37.8 Pe (kN) 71.2 70.7 69.4 Losses (%) 15.3 14.3 13.8 Pult (kN) 148 181 179 S (%) increase in capacity – 22.9 22.6 ec, ultimate compressive strain in
concrete (experimental) (%) 0.30 0.36 0.36
et, ultimate tensile strain in CFRP (experimental) (%)
– 1.34 1.45
Experimental/manufacturer tensile strain in CFRP (%)
– 80.2 85.3
Failure modea C C C Initial stiffness (kN/m)b 4970 4655 4673 Secondary stiffness (kN/m)c 175 525 525 Structural efficiency (%/kN)d – 1.42 1.33
a C = crushing of concrete, R = rupture of CFRP, D = debonding of CFRP b Defined from 9 to 44.5 kN (2–11 k). c Defined from 124.6 to 146.8 kN (28–33 k). d Defined as (% increase in capacity)/(EFRP AFRP).
ing the measured cracking load, crack reopening load and ultimate load for each tested girder. Brief test descriptions are provided below, while a discussion of the results is pre- sented in the next section.
No visible flexural cracks were observed in the control gir- der (girder CS) upon delivery to the laboratory. The girder was loaded statically up to failure. Yielding of the lower pres- tressing strands took place at a load level of 116 kN (26 k) according to readings of the PI gauges. Failure occurred due to crushing of concrete at a load level of 148 kN (33.2 k) at an ultimate deflection of 228 mm (9 in.) as shown in Fig. 3. Due to the confining effect induced by the loading tires, crushing of the concrete occurred first at the edge of the girder at midspan before it extended underneath the loading area.
EB1S EB2S CF2 EB3S EB4S
EB strips EB sheets – EB sheet EB HM sheets Type I Type I Type II Type II Type II 52.9 57.8 57.4 61.8 63.6 40.0 37.8 10.2 10.2 – 72.1 69.4 83.2 83.2 81.8 15.9 17.5 13.8 13.8 15.2 176 236 142 246 150 19.3 60 – 72.8 5.3 0.30 0.30 0.32 0.29 0.25
1.22 1.17 – 1.33 0.26
72.2 117 – 133 86.7
D R C C R 5075 5163 5355 5793 5985 595 1050 193 1160 2190 0.98 0.66 – 1.43 0.03
.
O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776 769
Behavior of the two girders, NSM1S and NSM2S, strengthened with a NSM system using either CFRP bars or strips, respectively, was similar during testing including the failure modes. No cracks were observed in either gir- der at the time of delivery. The initial stiffness of both girders was similar to that of the control girder, as was the post-cracking stiffness. After yielding of the prestress- ing strands, the presence of the CFRP reinforcement con- strained opening of the cracks and consequently reduced the midspan deflection compared to the control girder. Failure of both girders strengthened with NSM CFRP reinforcement was due to crushing of the concrete at the extreme compression zone followed by debonding of the NSM CFRP reinforcement at a load of 181 kN (40.8 k) for the NSM bars and 180 kN (40.7 k) for the NSM strips. Test results showed that strengthening of the pre- stressed girders using NSM CFRP bars and strips increased the ultimate load carrying capacity of the girder by 22.9% and 22.6%, respectively compared to the control girder.
The behavior of the prestressed concrete girder strength- ened with externally bonded CFRP strips (EB1S) matched that of the NSM strengthened girders before and after cracking. Failure occurred due to debonding of the CFRP strips at a load level of 176 kN (39.6 k) as shown in Fig. 4. The maximum recorded strain in the CFRP prior to deb- onding was 72% of the rupture strain measured during ten- sion coupon tests. Compared to the control girder, EB1S achieved an increase in the ultimate load carrying capacity of 19%.
The girder strengthened with externally bonded CFRP sheets (EB2S) was designed to achieve an increase of 60% in the ultimate load carrying capacity compared with the control girder. The initial stiffness of this girder was similar to that of the control. Failure was due to rupture of CFRP sheets at a load of 236 kN (53.1 k) providing an increase of 60% over the ultimate load of the control girder.
Fig. 4. Debonding failure in girder EB1S.
2.5. Type II girders
Three girders with a Type II prestressing configuration were tested under static loading conditions. Since it was not known prior to testing that the girders had different prestressing strand configurations, no control girder was tested for the Type II configuration. However, a Type II specimen was tested as a control girder under fatigue load- ing conditions [4] and showed very little degradation after 2 million cycles. It is the data from the monotonic load to failure which was applied after completion of the fatigue loading which is being used in this context as a control for the girders with a Type II prestressing strand configuration.
The control girder prestressed with a Type II configura- tion, CF2, behaved similar to the control girder with a Type I prestressing configuration, CS, before and after cracking. Failure occurred due to crushing of the concrete at a load of 142 kN (32.0 k) which was 3.6% less than the ultimate strength achieved in the static test of the control girder prestressed by a Type I C-Channel prestressing con- figuration (CS).
Flexural cracking of girder EB3S, strengthened with three layers of CFRP sheets, occurred at a load of 62 kN (13.9 k). At an applied load of 201 kN (45 k), interfacial debonding was initiated at the location of the flexural cracks at midspan spread to cause debonding between the U-wraps located on either side of midspan. The debonding did not cause failure, however, but occurred due to crush- ing of the concrete at a load of 246 kN (55.3 k). The energy released at failure due to crushing of concrete led to peeling of the U-wraps from the webs of the girder, but did not cause the CFRP to rupture. Girder EB3S achieved an increase of strength of 72.8% compared to the ultimate load of the Type II control girder (CF2). The measured performance of the girder exceeded the design values due to a high rupture strain measured in the CFRP during the test, which was 33.3% higher than the value reported by the manufacturer.
Flexural cracking of girder EB4S strengthened with high modulus CFRP sheets occurred at a load of 64 kN (14.3 k). At a load of 150 kN (33.7 k) failure occurred due to rup- ture of the CFRP sheets at midspan, which provides an increase of only 5.3% compared to girder CF2 during the final static test. The tensile strain in the CFRP achieved during this test was 13.3% lower than the value reported by the manufacturer. After rupture of the CFRP, the test was continued until ultimate failure occurred due to a com- bination of progressive CFRP rupture and concrete crush- ing close to the values of ultimate load and displacement of the control girder.
3. Analytical modeling
In order to present, the test results along with their ana- lytical predictions, the analytical procedures are presented
770 O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776
in this section. For the two types of analysis, the material properties used within were determined from constitutive material testing. The prestressing steel was modeled using Eq. (1) with coefficients determined from material testing. Characteristics of the CFRP material were also based on material testing and presented as linear elastic to failure. Concrete compressive strength was determined from core samples and the stress–strain characteristics described below.
3.1. Non-linear finite element simulation
ANACAP� is a non-linear finite element program for analysis of plain, reinforced and prestressed concrete mem- bers and structures and was developed by the ANATECH Corporation. The program was used to run finite element simulations on all the tested girders with the various strengthening configurations. ANACAP� uses the smeared cracking methodology for modeling of concrete where cracking is assumed to be distributed over an entire ele- ment. This mechanics-based philosophy uses plasticity the- ory that incorporates cracking and other concrete properties. The effect of concrete confinement at different stress levels was incorporated into the analysis as well as an elastic modulus allowing for changes between the three distinct zones of the stress–strain curve of concrete – the initial linear region, strain hardening region and strain soft- ening region. The concrete cross-section of the girder was modeled with 20 node elements using quadratic isopara- metric displacement interpolation with mesh shown in Fig. 5. Experimental verification of the accuracy of the pro- gram can be found elsewhere [9,10].
3.2. Cracked section analysis
In addition to the non-linear finite element simulation, a cracked section analysis was performed for the strength-
10x360=36
216
Supports
Z
XY
Fig. 5. Mesh used for fin
ened girders using Response 2000� software. Verification of this program can be found elsewhere [16]. The base curve of the concrete model used in the cracked section analysis program was the Popovics curve including com- pression softening which was based on the Vecchio–Collins model and the tension stiffening was based on the Bentz model [16]. The results from the cracked section analysis showed good agreement with the non-linear finite element analysis and the experimental results presented in the fol- lowing section. Based on good agreement achieved between the cracked section analysis and the experimental results, the need for a finite element simulation to predict the behavior of such girders is not warranted.
4. Test results and discussion
4.1. Crack development
Initiation of the flexural cracks was determined either by visual inspection or by analysis of the test data. Typ- ically, cracking occurred between the loads 52.9–63.6 kN (11.8–14.3 k) for both the Type I and Type II girders. Flexural cracks were located at the bottom of the C- Channel soffit near midspan, with a distance from mid- span equal to the depth of the girder from the edge of the loading area. Spacing of the cracks was approximately 330 mm (13 in.), which corresponds to the distance between the transverse stirrups used for the C-Channels. The CFRP strengthening reduced crack spacing, crack width and crack growth for all of the strengthened girders with respect to the control girder.
PI gauges were mounted at the level of the lower pres- tressing strand on both sides of the C-Channel soffit to measure the tensile strain in the concrete at various load levels. The average crack width at midspan can be calcu- lated using the measured strains at any applied load level from the following equation:
Axes of
Symmetry
00
6x127=762
Load
432
394
ite element modeling.
Fig. 6. Average crack width at midspan for Type I girders.
Fig. 7. Average crack width at midspan for Type II girders.
O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776 771
CWave ¼ ðeci � eccrÞ� lPI
n ð4Þ
where eci is the measured strain at a certain applied load level, eccr is the measured strain in the concrete at the flex- ural cracking load, lPI is the length of the PI gauge, and n is the number of cracks observed within the PI gauge length. The load versus the average crack width at midspan for the Type I and Type II girders are shown in Figs. 6 and 7, respectively. The figures indicate that the presence of the strengthening system restrained crack opening and growth with respect to the control girders. At ultimate, the crack widths of the strengthened girders were as much as 400% less than the control girder.
4.2. Stiffness
The initial stiffness and secondary stiffness of the Type I and Type II girders are given in Table 2. Comparing the initial stiffness of the strengthened girders which achieved a 20% increase in ultimate load capacity, with the initial stiffness of the control girder, it was obvious that the strengthening system has very little effect on the initial stiff- ness. However, using a strengthening system to achieve a 60% increase in ultimate capacity, modest increases in ini- tial stiffness can be obtained. The initial stiffness of the strengthened Type II girders was 9% and 11% higher than the control girder for girders EB3S and EB4S, respectively. The girder strengthened with the high modulus material
772 O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776
has a secondary stiffness nearly double the girder with nor- mal modulus material.
4.3. Structural efficiency
The structural efficiency, SE, of a CFRP strengthening system was evaluated using the following expression:
SE ¼ S
Ef � Af ; %=k ð%=MNÞ ð5Þ
where S is the percent increase in ultimate flexural capacity achieved using a CFRP system compared to the control gir- der and Ef and Af are the elastic modulus and area of CFRP material, respectively. Material properties of the CFRP, including thickness of the laminates, were measured for each case. The structural efficiency as defined represents how efficient the CFRP strengthening system is with respect
Fig. 8. Experimental load versus midsp
0
50
100
150
200
250
0 50 100 Midspan de
) N
k( d
a o
L
EB4S
Fig. 9. Experimental load versus midspa
to the amount of material and its stiffness. The results, given in Table 2, indicate that NSM systems had the highest struc- tural efficiency, around 1.4%/kN (6%/k). The NSM systems performed well under this definition as a result of the high rupture strains that were achieved during the test due to the superior bond characteristics that can be achieved for this type of system. The Type II girder strengthened with normal modulus CFRP sheets (EB4S) had a structural effi- ciency similar to the NSM strengthened girders as a result of the high level of strengthening achieved.
4.4. Ultimate load and displacement
Test results indicate that the addition of a brittle mate- rial such as CFRP, to a ductile structural member such as prestressed concrete does not reduce the overall ductility of the member. As shown in Figs. 8 and 9, the ultimate
an displacement for Type I girders.
150 200 250 300 flection (mm)
CF2: Control
EB3S: EB Sheets
EB4S: EB Sheets
EB3S
CF2
n displacement for Type II girders.
0
50
100
150
200
250
0 50 100 150 200 250 300 Midspan deflection (mm)
) N
k( d
a o
L d
eil p
p A Experimental
Cracked Section Analysis
Finite Element Simulation
Fig. 10. Analysis versus experimental for girder NSM1S.
O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776 773
loads of a prestressed concrete girder can be substantially increased using CFRP materials without sacrificing the ductility of the section.
Girder EB2S, strengthened with four layers of normal modulus CFRP sheets, failed due to rupture of the CFRP material. The measured concrete strain at ultimate was 0.3%. The measured tensile strain in CFRP at ultimate was 1.17% which is 117% of the manufacturer’s specified rupture strain. Two of the strengthened Type I girders (NSM1S and NSM2S) experienced failure at ultimate due to concrete crushing which was the same failure mode as the control girder (CS). The maximum measured compres- sive strain in concrete at failure for both girders was 0.36%.
The ductility of the prestressed concrete section was maintained in girder EB3S with the installation of normal modulus CFRP sheets. The ultimate load was 72.8% higher than the control girder, and the ultimate displacement was only 16% less than the control. The failure mode of girder EB3S was due to crushing of concrete, similar to the con- trol girder. The maximum measured compressive strain in concrete at failure was 0.29%, slightly lower than the observed value for the control girder of 0.32%. The maxi- mum tensile strain measured during testing of girder EB3S was 133% of the manufacturer recommended rupture strain. Girder EB4S failed due to rupture of CFRP mate- rial at a load of 150 kN (33.7 k), which represents an increase of 5.3% over the ultimate load measured in the testing of the control girder. The maximum measured ten- sile strain in the CFRP at the rupture event was 0.26%, which is 86.7% of the rupture strain used in design. The high modulus material was very sensitive to fiber orienta- tion and this could have played a role in the difference between the design and the measured rupture strain. The failure was due to concrete crushing, after numerous CFRP rupture events along the length of the girder, at a measured concrete compressive strain of 0.25%.
4.5. Predicted versus experimental
All girders strengthened with CFRP were analyzed using a cracked section analysis and finite element model. For the girder strengthened with NSM bars (NSM1S), the mea- sured ultimate load was 181 kN (40.8 k), whereas the ulti- mate load determined from cracked section analysis and the finite element model was 179.3 kN and 185.0 kN (40.3 and 41.6 k), respectively, a difference of �1.2% and 1.9% as shown in Fig. 10. The finite element analysis, cracked sec- tion analysis and experimental load versus deflection behav- ior for girder EB3S is shown in Fig. 11. For comparison, the analyses shown for this girder were conducted using design material properties provided by the manufacturer, not val- ues obtained during material testing. The strengthening scheme of girder EB3S was designed to increase the load carrying by 40% compared to the control girder. The mea- sured ultimate capacity was increased by 72.8% because the stiffness and ultimate strength values of the CFRP were lar- ger than the specified values used in design.
5. Cost-effectiveness analysis
To closely resemble field conditions during strengthen- ing, the girders were placed side by side, as they would be on a bridge, on top of a steel substructure approxi- mately 2.5 m (8 ft) off the ground. To determine the cost- effectiveness of each strengthening technique, the following items were considered: (1) labor costs of the professional FRP applicators, (2) time taken to complete all tasks, (3) material costs, and (4) equipment used for strengthening. The material costs include all primers, adhesives and CFRP required for field application for each technique. Equip- ment items include the rental of sandblasting pot, compres- sor, sand, and other items used in surface preparation. Also included in the equipment cost are items such as latex
0
50
100
150
200
250
0 50 100 150 200 250 300 Midspan deflection (mm)
) N
k( d
a o
L
Experimental
Cracked Section Analysis
Finite Element Simulation
Fig. 11. Analysis versus experimental for girder EB4S.
774 O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776
gloves, plastic mixing buckets and items used in the CFRP installation. Other equipment (such as grinders, mixers, safety equipment, etc.) is either assumed to be provided by the contractor or used equally in each of the strengthen- ing systems. A labor summary of the CFRP strengthening
Table 3 Labor summary for CFRP strengthening systems (h)
System designation NSM1 NSM2 EB1
Strengthening NSM bars NSM strips EB strips Gluing strips – 1 – Concrete repair 0.95 0.95 0.95 Groove cutting 5.5 5.5 – Grinding/chipping 5.5 5.5 4 Sandblasting 0.3 0.3 0.93 Cutting of fiber – – 0.5 CFRP lay-up 5.63 5.63 10 Total (h/girder) 17.88 18.38 13.88 Total (h/m)a 2.17 2.23 1.69
a Length of strengthening = 8.23 m (27 ft).
Table 4 Cost-effectiveness analysis for C-Channel CFRP strengthening systems (in US
System designation NSM1 NSM2 EB1
Strengthening NSM bars NSM strips EB strips Main CFRP (m) 27.7 21.1 214.7 CFRP U-wraps (m) – – 11.0 Main adhesive (m) 24.4 24.4 13.9 U-wrap adhesive (m) – – 4.8 Equipment (m) 11.6 11.6 11.1 Labor (m) 99.9 102.6 77.8 Total cost (m) 163.6 159.7 324.3 % increase in strengtha 22.9 22.6 19.3 Cost-effectivenessb 0.140 0.142 0.060
a For girders tested under static loading condition. b Based upon (percent increase in strength)/(total cost per meter).
and the results of the cost-effectiveness analysis are given in Tables 3 and 4, respectively. The labor costs were deter- mined using a wage of $45 per hour. Consultation with sev- eral FRP installers produced this value which is commonly used for cost estimation in FRP strengthening work.
EB2 EB4 EB5 EB6
EB sheets EB sheets EB sheets EB HM sheets – – – – 0.95 0.95 1.5 1.5 – – – – 2 3.75 2 2 0.93 0.75 0.5 0.5 1 1.59 1.75 2.25 8.75 11.59 9.95 14.3 13.63 18.63 15.70 20.55 1.66 2.26 1.91 2.50
dollars)
EB2 EB4 EB5 EB6
EB sheets EB sheets EB sheets EB HM sheets 11.2 20.1 26.8 53.0 11.0 12.3 11.0 10.4 4.9 Included 11.7 24.5 4.8 above 4.8 4.8 12.6 12.6 12.6 12.6 76.4 104.0 87.9 115.1 120.9 149.2 154.9 220.4 10.5 60 72.8 5.3 0.087 0.402 0.470 0.024
O. Rosenboom et al. / Construction and Building Materials 21 (2007) 764–776 775
The cost analysis indicates that the most cost-effective system, when comparing the variables described previously and combined with the percent increase in strength, were the girders which were strengthened using normal modulus CFRP sheets (girders EB2S and EB3S). The NSM systems also performed well using these criteria. When CFRP was used to increase the ultimate flexural capacity by 20% (NSM1S, NSM2S and EB1S), the labor required for instal- lation of a NSM system was substantially higher than for installation of an externally bonded system at the same strengthening level. The difference in labor costs between EB3S (EB Sheets) and EB4S (EB HM Sheets) should be noted. Although the girders strengthened with the high modulus sheets had more material, it was not only the amount of material that caused in increased labor costs. The contractors also said that the material itself was harder to work with and install than equivalent normal modulus CFRP sheets.
6. Conclusions
Eight 9.14 m (30 ft) prestressed concrete C-Channel girders were tested under static loading conditions, six strengthened with various CFRP systems and two tested as control girders. Based on the experimental program and analysis of the test results, the following conclusions can be made:
1. Proper design and installation of a CFRP strengthening system can lead to the failure mode of crushing of con- crete in the compression zone, preserving the ductile structural response of an unstrengthened girder.
2. Externally bonded CFRP sheets are the most cost-effec- tive strengthening technique and are the most applicable technique for these types of girders.
3. The most structurally efficient strengthening technique used is the near surface mounted (NSM) CFRP bars or strips system.
4. The ultimate flexural capacity of prestressed concrete can be increased substantially using CFRP materials. The flexural capacity of the C-Channel girders tested in this research program could be increased by as much as 73% with the use of externally bonded CFRP sheets.
5. The use of transverse CFRP U-wraps most likely delayed debonding failures in externally bonded CFRP systems.
6. For externally bonded CFRP wet lay-up systems, the experimental tensile strain in the CFRP outperformed the manufacturer’s provided value. Therefore, the use of a bond reduction coefficient, jm, in ACI 440F 2002, would be conservative.
7. The crack spacing and crack widths at ultimate can be substantially reduced using CFRP strengthening. Crack widths observed during the testing of the C-Channels were reduced by as much as 400% using CFRP materials in comparison to the unstrengthened girder.
8. The initial and secondary stiffness of C-Channel girders can be increased by the use of high modulus CFRP materials. Using strictly a serviceability criterion, high modulus CFRP materials outperformed the normal modulus CFRP materials.
Acknowledgements
The authors acknowledge the support of the North Car- olina Department of Transportation through Project 2004- 15. Valuable help was provided on this project by Ronald- son Carneiro, and Dr. Amir Mirmiran. Several industry members made much appreciated donations: David White of the Sika Corporation, Doug Gremel of Hughes Broth- ers, Akira Nakagoshi of Mitsubishi Chemical America, Pe- ter Emmons of Structural Preservation Systems and Ed Fyfe of Fyfe Corporation. Special thanks to Structural Preservation Systems and Fyfe Corporation for carrying out the strengthening and repair work. Thanks are also ex- tended to the personnel at the NCDOT Bridge Mainte- nance Department, especially Dallie Bagwell and Tracy Stephenson for providing Bridge Maintenance facilities and constructing steel substructures for the repair and strengthening work. The authors thank Jerry Atkinson and Bill Dunleavy, technicians at the Constructed Facilities Laboratory at North Carolina State University, for their invaluable help.
References
[1] ACI Committee 440F. Design and construction of externally bonded frp systems for strengthening concrete structures. American Concrete Institute: ACI Manual of Concrete Practice, 2002.
[2] Concrete Society. The design guidance for strengthening concrete structures using fibre composite materials. Technical Report 55. 2nd ed. United Kingdom: The Concrete Society; 2004.
[3] Japan Society of Civil Engineers. Recommendations for upgrading of concrete structures with use of continuous fiber sheets. Japan: Concrete Engineering Series 41; 2001.
[4] Rosenboom OA, Rizkalla S. Fatigue behavior of prestressed concrete bridge girders strengthened with various CFRP systems, ASCE J Compos Constr, accepted for publication.
[5] Oehlers DJ. Reinforced concrete beams with plates glued to their soffits. J Struct Eng 1990;118(1).
[6] Teng JG, Chen JF, Smith ST, Lam L. FRP strengthened RC structures. London: Wiley; 2002.
[7] Oehlers DJ, Seracino R. Design of FRP and steel plated RC structures. London: Elsevier Press; 2004.
[8] De Lorenzis L, Nanni A. Characterization of NSM FRP rods as near- surface mounted reinforcement. J Compos Constr 2001;5(2).
[9] Hassan T, Rizkalla S. Investigation of bond in concrete structures strengthened with near surface mounted CFRP strips. ASCE J Compos Constr 2003;7(3).
[10] Hassan T, Rizkalla S. Bond mechanism of NSM FRP bars for flexural strengthening of concrete structures. ACI Struct J 2004;101(6).
[11] Schiebel S, Parretti R, Nanni A. Repair and strengthening of impacted PC girders on bridge A4845. Missouri Department of Transportation Report RDT01-017/RI01-016.
[12] Takács PF, Kanstad T. Strengthening Prestressed Concrete beams with carbon fiber reinforced polymer plates. Norway: NTNU Report R-9-00, 2002.
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[13] Hassan T, Rizkalla S. Flexural strengthening of prestressed bridge slabs with FRP systems. PCI J 2002;47(1).
[14] Collins MP, Mitchell D. Prestressed concrete structures. New Jersey: Prentice Hall; 1991.
[15] MacGregor JG. Reinforced concrete: mechanics and design. New Jersey: Prentice Hall; 1996.
[16] Bentz EC. Section Analysis of Reinforced Concrete Members, Ph.D. Thesis, University of Toronto, 2000.
[17] Malek AM, Saadatmanesh H, Ehsani MR. Prediction of failure load of R/C beams strengthened with FRP plate due to stress concentra- tion at the plate end. ACI Struct J 1998;95(1).
- Flexural behavior of aged prestressed concrete girders strengthened with various FRP systems
- Introduction
- Research objectives
- Background
- Experimental program
- Test girders
- Design of the strengthened girders
- Test setup and instrumentation
- Type I girders
- Type II girders
- Analytical modeling
- Non-linear finite element simulation
- Cracked section analysis
- Test results and discussion
- Crack development
- Stiffness
- Structural efficiency
- Ultimate load and displacement
- Predicted versus experimental
- Cost-effectiveness analysis
- Conclusions
- Acknowledgements
- References
HT120815 Readings/1-s2.0-S0950061807002991-main.pdf
Available online at www.sciencedirect.com Construction
www.elsevier.com/locate/conbuildmat
Construction and Building Materials 23 (2009) 1495–1507
and Building
MATERIALS
Strengthening of prestressed concrete girders with composites: Installation, design and inspection
Owen Rosenboom a, Catrina Walter b, Sami Rizkalla b,*
a Department of Civil Engineering, Hong Kong Polytechnic University, Hong Kong, China
b Department of Civil Engineering, North Carolina State University, Raleigh, NC 27695, USA
Available online 10 January 2008
Abstract
The application of fibre reinforced polymer (FRP) or steel reinforced polymer (SRP) materials to the tension side of a reinforced/pre- stressed concrete member has been accepted as a strengthening technique to increase the load carrying capacity and in some cases can enhance member serviceability. Proper installation and regular inspection of a composite (FRP or SRP) strengthening system is impor- tant since quality of the bond is essential to internally transfer forces. This paper describes an experimental programme conducted to study the behaviour of six prestressed concrete bridge girders, which were tested under static and fatigue loading conditions. The test results were combined with the results of 16 other girders tested by the authors to develop structural design guidelines and guidelines on the installation and inspection of composite strengthening systems. The behaviour was also examined using value engineering to eval- uate the cost-effectiveness by investigating the overall system performance. Research findings indicate that SRP materials are more struc- turally efficient than carbon FRP (CFRP) materials. The results of an inspection demonstration programme, including the pull-off testing of over 150 CFRP samples, has shown that the most effective inspection techniques are visual inspection, pull-off testing, and acoustic sounding. � 2007 Elsevier Ltd. All rights reserved.
Keywords: Prestressed; Strengthening; Installation procedures; Fibre reinforced polymers; Steel reinforced polymers; Bridge girder; Inspection proced- ures; Value engineering
1. Introduction
1.1. Research objectives
The application of fibre reinforced polymer (FRP) or steel reinforced polymer (SRP) materials to the tension side of a reinforced/prestressed concrete flexural member has been accepted as a strengthening technique to increase the load carrying capacity and may also be used to enhance member serviceability. The strengthening is highly dependent on the quality of the bond between the strengthening material and
0950-0618/$ - see front matter � 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2007.11.010
* Corresponding author. Tel.: +1 919 513 1733; fax: +1 919 513 1765. E-mail addresses: [email protected] (O. Rosenboom),
[email protected] (S. Rizkalla).
the concrete surface which consequently depends on the installation and inspection techniques.
Guidelines for installation of composite strengthening systems have been published in addition to specific proce- dures often provided by the manufacturer [1]. These guide- lines are typically general in nature and do not cover the installation of the new SRP strengthening systems. Several structural design guidelines are provided by code bodies (e.g. [2]) and by numerous researchers (e.g. [3,4]). For flex- ural strengthening the two common bond failure modes have been identified by researchers: intermediate crack (IC) debonding and plate-end (PE) debonding. Recent ana- lytical models addressing IC debonding take into account the beneficial effect of multiple flexural cracks on the deb- onding mechanism [5] or the interfacial shear stress contri- butions from the applied loading and stress concentrations
1496 O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507
in the vicinity of flexural cracks [6,7]. Models for PE deb- onding are typically a function of the shear strength of the reinforced concrete beam [8]. To mitigate possible bond failures of externally bonded composites, near surface mounted (NSM) systems using bars and strips have been developed including analytical tools to predict their bond characteristics [9].
Very few studies have been reported on the behaviour of SRP strengthening systems for reinforced concrete struc- tures. Based on the testing of five beams strengthened with various configurations of SRP and monotonically tested to failure the observed failure modes were concrete crushing, PE debonding, or bond slip as reported in Kim et al. [10]. Bond slip was prevented in these beams by using SRP U- wraps. Prota et al. [11] found that the steel fibre strengthen- ing systems using epoxy resin outperformed the systems using a polymer-modified cementitious mortar. This was a result of the epoxy better engaging the concrete substrate prior to debonding failure. Research findings indicated that the specimens strengthened with CFRP outperformed the steel fibre strengthened specimens in terms of ultimate strength gains but that the SRP material exhibited more ductility at failure. The authors pointed out that corrosion resistance of the SRP system is of major concern and needs more research. To date no papers have been published regarding strengthening of prestressed concrete beams using SRP or the behaviour of SRP strengthening systems under fatigue loading conditions.
Extensive laboratory and field testing has resulted in the development of several guidelines for the inspection of composite strengthening systems [1,12,13]. NCHRP Report 514 [1] provides comprehensive but general guide- lines on inspection procedures, and supplies forms and checklists for post-application acceptance and quality assurance. The document published by The Concrete Soci- ety [12] recommends the use of acoustic sounding and the pull-off test as the two most effective of the inspection tech- niques for FRP strengthening systems.
This paper initially provides an overview of structural behaviour of six prestressed concrete bridge girders which
Fig. 1. Strengthening ex
were tested to failure. The test results were used to develop guidelines for the structural design, installation, and inspec- tion to ensure proper bond. In addition, the test results were examined using a value engineering methodology where the cost-effectiveness of the strengthening systems was exam- ined using the overall performance of the system. Although the work described here is focused on the flexural strength- ening of prestressed concrete bridge girders, the results are applicable for strengthening other types of concrete beam or slab systems.
2. Structural behaviour
In order to provide full characterization of the structural behaviour, an extensive experimental programme was undertaken at North Carolina State University [4,14]. The research included three main thrusts: (1) flexural behaviour: where various design details and strengthening configurations examined the structural efficiency and cost-effectiveness. (2) Fatigue behaviour: where various configurations were subjected to cyclic loading to simulate typical bridge operation and assess the fatigue behaviour of the system, and (3) bond behaviour: where the bond char- acteristics of the CFRP strengthening systems were assessed through fundamental research on large-scale gird- ers. The total experimental programme consisted of 22 large-scale prestressed concrete bridge girders as shown in Fig. 1. The research findings of 14 of the girders tested to examine the flexural and fatigue behaviour can be found in Rosenboom et al. [15] and Rosenboom and Rizkalla [16]. The experimental programme examining the bond behaviour can be found in Rosenboom and Rizkalla [17].
This paper focuses on the static and fatigue behaviour of six prestressed concrete bridge girders: two control girders, two strengthened with externally bonded CFRP wet lay-up sheets and two strengthened with externally bonded SRP. Details of the two composite strengthening systems and the 9.18 m prestressed concrete C-channel girders are shown in Fig. 2. All the girders were tested under 3-point loading using a 490 kN MTS actuator. Testing was per-
perimental program.
Fig. 2. Cross-section,elevation of girders.
Fig. 3. Applied load vs. midspan deflection.
O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507 1497
formed on all the materials used in the experimental pro- gramme and the results are shown in Table 1. Test results indicate that the tensile behaviour of both the SRP and CFRP materials was linear elastic to failure. Also shown in the table is a summary of the experimental results, including the results from the testing of two additional unstrengthened girders, whose complete results can be found elsewhere [15,16].
2.1. Behaviour under static loading conditions
The first girder tested (SRPS) was strengthened with one layer of SRP and was designed to achieve a 30% increase in ultimate capacity compared to the control girder. During the initial loading cycles the cracking load was found to
Table 1 Strengthening experimental summary
Specimen designation CS CF EB5S
Strengthening None None EB CFRP Type of test Static Static Static Concrete compressive
strength, f 0c (kN) 73.9 Not
available 43.9
Composite shape – – 2 plies per web 127 mm wide
Composite thickness (mm) – – 1.17 Composite area AF (mm
2) – – 594 Elastic modulus of composite
EF (GPa) – – 64.9
Composite stiffness – – – Cracking load (kN) 56.0 55.6 59.2 Ultimate load (kN)a 148 142 192 Effective prestress (kN) 71.2 83.2 73.2 % Increaseb – �3.8 30.2 Ultimate composite tensile
strain (le) – – 10500
Failure modec CC CC CC N, number of cycles achieved
(thousands) – 2000 –
a Residual strength for fatigue girders. b % Increase in ultimate load from girder CS for static tests,% change from c CC: concrete crushing.
be 58.7 kN and the effective prestress force (found using a procedure described in [15]) was found to be 69.4 kN per strand. Failure was due to concrete crushing at mid- span at a load of 217.1 kN, an increase of 46.5% over the ultimate load of the control girder. The second girder tested (EB5S) was strengthened with two layers of CFRP sheets and was also designed to achieve a 30% increase in ultimate capacity. The observed cracking load of the girder was 59.2 kN and the effective prestress force was deter- mined to be 73.2 kN. The failure was due to concrete crushing at a load of 192.3 kN, which represents a 30.2% increase in ultimate capacity over the control girder. From readings taken from the actuator load cell and several string potentiometers placed at midspan, the load vs. deflection behaviour of both SRPS and EB5S are shown in Fig. 3 along with the control girder. Fig. 3 shows that the girder strengthened with SRP shows similar ductility
EB5F SRPS SRPF
EB CFRP EB SRP EB SRP Fatigue Static Fatigue 50.6 46.9 56.6
2 plies per web 127 mm wide
1 ply per web 152 mm wide
1 ply per web 152 mm wide
1.17 1.93 1.93 594 587 587 64.9 46.8 46.8
– – – 57.4 59.6 62.3 197 216 226 70.0 69.3 74.3 2.24 46.5 4.28 9730 10200 9930
CC CC CC 2000 – 2000
statically-loaded girder for fatigue tests.
Fig. 5. Load vs. midspan deflection: girder SRPF.
1498 O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507
to the girder strengthened with CFRP. However, girder SRPS was more structurally efficient since it achieved an ultimate load 12.9% greater than girder EB5S with around 71% of the composite stiffness (EFAF) as shown in Table 1. Based on strain measurements along the midspan section using a series of PI gauges (a strain gauge mounted to a spring plate) the average crack width (CWave) was deter- mined as follows
CW ave ¼ ðeci � eccrÞ� lPI
n ð1Þ
where eci is the measured strain at a certain applied load le- vel, eccr is the measured strain in the concrete at the flexural cracking load, lPI is the length of the PI gauge, and n are the number of cracks observed within the PI gauge length. The measured load vs. CWave is shown in Fig. 4. As ex- pected, the girders strengthened with composites dramati- cally reduce the crack widths compared to the control girder. The structural efficiency of the SRP material is also evident in this figure since girder SRPS has crack widths substantially smaller than girder EB5S, although this could also have been a result of the wider shape of the SRP mate- rial used in the design.
2.2. Behaviour under fatigue loading conditions
Two girders similar to the ones tested under static con- ditions were tested under fatigue loading conditions. The fatigue load range used was designed to simulate typical service loading of an actual bridge, varying from a mini- mum load equivalent to the dead load and a maximum value equivalent to the dead load plus the live load. The dead load was calculated based on an assumed wearing thickness of 102 mm. The live load was calculated based on AASHTO HS13 type loading and assuming an impact factor of 1.33 and a distribution factor of 0.24. The strengthened girders were tested with a live load 30% greater than the control girder. Complete details can be found elsewhere [4]. The fatigue loading used in the testing of both girders varied from 8.9 kN to 54.0 kN and was applied at a frequency of 2 Hz. During the initial loading cycles, the effective prestress force for each girder was
Fig. 4. Applied load vs. crack width.
determined to be 74.3 kN and 70.0 kN for girders SRPF and EB5F, respectively. The girder strengthened with SRP (SRPF) achieved over 2 million cycles of loading with very little degradation. The load vs. displacement response is shown in Fig. 5. For the girder strengthened with CFRP (EB5F) an accidental overload condition of 133 kN was applied to the girder after 1.25 million cycles causing a residual displacement of 13.7 mm. The fatigue test was then resumed and the girder completed 2 million cycles of fati- gue loading with little additional degradation as shown in Fig. 6.
Since the purpose of the fatigue testing of these girders was to verify design principles which were set forth in an earlier stage of the research [16], the girders were not tested cyclically to failure, but monotonically tested to failure after 2 million cycles of fatigue loading. The final static test was performed to assess whether fatigue bond degradation of the FRP system occurred due to the cyclic loading. Actually, both of the girders showed slight increases in ulti- mate load capacity compared to their counterparts tested under static loading conditions (as shown in Table 1), but similar failure modes. This could be attributed to vari- ations in the cross-sectional dimensions, effective prestress force, or slight misalignment of the composite material between girders. The load vs. displacement behaviour of
Fig. 6. Load vs. midspan deflection for girder EB5F.
Fig. 7. Load vs. midspan deflection: residual strength.
O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507 1499
the final static test of girder SRPF is shown in Fig. 7 along with girder SRPS and the control girder.
3. Major design concepts
The following section discusses the major structural design concepts of a composite strengthening system for prestressed concrete: flexural design, design against bond failure, and design against fatigue failure. Other limit states and conditions required in the design (e.g. deflection limits) are not discussed in this paper. The accurate evaluation of the material properties of a composite strengthening system is an important part of the design. It is recommended that the laminate properties are used as determined from mate- rial testing.
3.1. Flexural design
An accurate prediction of the complete load vs. deflection curve of a prestressed concrete beam flexurally strengthened with composites can be determined using a layer-by-layer moment curvature analysis if the failure mode is concrete crushing. A detailed flexural model, including integration of the moment resultant of the internal stresses determined from the full stress–strain relationships of the high-strength prestressing steel, the composite material and concrete is presented in detail in a separate paper [4].
3.2. Design against bond failure
Shear stress at the FRP-concrete interface along the length of the beam comes from two distinct sources: the applied loading and stress concentrations at the toes of the flexural cracks [6]. This interface shear stress can lead to failure in two different forms: intermediate crack (IC) debonding and composite rupture due to stress concentra- tions. An iterative procedure has been developed [7] for reinforced and prestressed concrete beams strengthened with composites to determine the IC debonding strain (edb) and provide a check for composite rupture. The pro- cedure is summarized below:
1. Calculate the moment resistance corresponding to yield- ing of the internal tensile steel (My) and the correspond- ing strain level in the FRP material, ef@y.
2. Assume a value for edb. 3. Calculate the nominal moment resistance of the section
at debonding failure (Mdb) with the strain assumed in step 2.
4. Calculate the interface shear stress, scmax.
scmax ¼ nEf tf edb � ef@y
s � xy
� � þ 3 1 �
M y M db
� � ffiffiffiffi f 0c
p ð2Þ
for M y M db 6 1 ð3Þ
where n, Ef, and tf are the number of layers, elastic modulus and thickness of the composite material respectively, and f 0c and s are the compressive strength of the concrete and the shear span. xy depends on the loading configuration. For beams under 3-point or 4-point bending xy = sMdb/My. For beams with distributed loads.
xy ¼� L2
8M db �
4M db L þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4M db
L
� �2 –16
M db L2
� � M y
s0 @
1 A ð4Þ
5. Revise the value of edb until it reaches a maximum value, scmax = 1.8*(0.63)f
0 c .
6. Calculate the ‘‘real strain” in the composite material (esc- max), taking into account stress concentrations at the major flexural crack.
escmax ¼ edb þ 0:342ffiffiffiffiffiffiffiffiffiffi
nEf tf p 1 �
M y M db
� � ð5Þ
7. Rupture of the composite material will occur if escmax > eu, where eu is the composite tensile rupture strain after application of appropriate environmental reduction fac- tors [2].
The procedure above was derived with respect to the fundamental behaviour of the composite flexural strength- ening system. The addition of transverse FRP U-wraps at the composite termination point and throughout the length of the strengthened area is recommended as shown in Fig. 2.
Another bond failure mode which must be considered in a composite strengthening design is debonding propagating from the composite termination point, commonly called plate-end (PE) debonding. Many of the original models developed for the debonding of steel plates and the most recent models for composites [8] are dependent on the shear strength of the section.
3.3. Design against fatigue failure
The most fatigue critical component of a prestressed concrete beam strengthened with composites is the pres- tressing strands [16]. The maximum stress levels and stress ratios induced in the other system components are not likely to be large enough under service loading conditions
Fig. 8. Stress ratio vs. log of number of cycles.
1500 O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507
to lead to fatigue failure. The stress ratio in the prestressing strands (SRps) can be defined as follows
SRps ¼ fps2 � fps1
fpu � 100 ð6Þ
where fpu is the ultimate strength of the prestressing strand, and fps2 and fps1 are the stress levels in the prestressing strand induced from the upper and lower levels of loading, respectively. It is recommended to keep the stress ratio less than 6% for straight prestressing strands and 3% for in- clined prestressing strands [16]. The stress ratio in the lower prestressing strands vs. the log of the number of cycles is shown in Fig. 8 for the two girders tested in this phase of the research, along with the control girder tested earlier [16]. The figure shows a substantial rise in the stress ratio after the accidental overload was applied to girder EB5F, increasing the stress ratio beyond the recommended limits, yet the girder still achieved over 2 million cycles of loading.
It is possible that a girder tested in fatigue loading described in an earlier part of this research (EB1S) failed due to bond failure of the externally bonded precured CFRP system, although the presence of several ruptured prestressing wires observed in a post-test examination could have caused the premature failure [16]. Ongoing research efforts at other institutions are examining the bond behaviour of CFRP systems under fatigue loading [18].
4. Installation procedures
Proper installation of the FRP/SRP system is essential in ensuring the performance desired by the designer. Cor- rect techniques must be employed from the surface prepa- ration to the application of the final protective coating to ensure effective behaviour of the composite system. Several important guidelines are presented here based on state-of- the-art installation guidelines found in the literature [1,12,13] and the sizeable experience gained in conducting this research where 20 bridge girders were strengthened under simulated field conditions with qualified personnel.
This section presents an overview of the installation proce- dures and highlights several important aspects that are missing from the current published guidelines. Detailed information can be found in the dissertation of the first author [4].
Strengthening with composites has proven to consume less construction time and be more cost-effective compared to other traditional techniques and certainly to the cost and time required for total bridge or member replacement. The following section will focus on the installation of the new SRP materials, however, many of the items are applicable to the installation of FRP systems.
4.1. Shipping, storage and handling
Composite materials, in particular FRP pre-cured lami- nates, should be shipped in impact resistant containers. All components should be stored properly in clearly marked containers in ambient temperatures 10–24 �C. The shelf life of the composite system components should be specified by the manufacturer and marked on containers. Correct han- dling of the components of the FRP system is important to prevent damage or fibre misalignment. After cutting of FRP sheets they should be rolled at a radius no tighter than 300 mm [1]. The diameter may need to be increased for high modulus FRP material or SRP material. When mixing of the adhesive materials, it is important to scrape the sides of the container for each component with a plastic scraper to ensure that proper mixing ratios are achieved. In addi- tion, the adhesive materials should be kept out of direct sunlight during their working time.
4.2. Section restoration
Before beginning restoration, all defective concrete should be removed in accordance with ACI 546 [19] using an appropriate jack-hammer or electric saw to a depth of 13 mm beyond the repair area in order to expose sound aggregates. It should be noted that discovery of corroded reinforcing/prestressing steel may lead to the area of the steel being reduced in design calculations. Spray-on corro- sion inhibitors may be used to help isolate existing damage, or cementitious epoxy-modified products may provide anti- corrosion coating in addition to acting as a bonding agent for concrete repairs. The concrete repair material must have a compressive strength equal to or greater than the original concrete. Small areas of damage may be repaired with the same adhesive used in the composites installation and can be thickened by using silica sand material. Any concrete voids larger than 13 mm should be repaired with an appro- priate two-component polymer modified cementitious mor- tar. For large repair areas, aggregates of the same size and type as the original concrete should be used in the repair material to prevent an elastic modulus mismatch. One tech- nique to restore compressive stresses in the repaired con- crete is to preload the span during concrete repair and curing [20,21].
O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507 1501
4.3. Surface preparation
The performance of the externally bonded composite strengthening system is dependent on having a flat or con- vex surface to provide good bonding characteristics and to prevent irregularities in the composite from forming. Sur- face grinding should be performed to eliminate irregulari- ties, unevenness, paint, or sealant and the corners should be rounded to a minimum radius of 13 mm; in addition all surface cracks larger than 0.25 mm should be injected with epoxy [1]. The preparation of the concrete surface can involve either sandblasting with abrasive sand or grind- ing with a diamond bit blade. When grinding it is impor- tant to remove the concrete paste layer and expose the aggregates; when sandblasting the abrasive sand should expose the pores of the concrete. Prior to application of the composite system the surface should be wiped clean with a cloth, or blown with compressed air. It should be noted that compressed air should only be used when the air is filtered to remove oils.
4.4. Externally bonded FRP installation
Installation of externally bonded FRP precured lami- nates should begin by cutting the laminate to the specified dimensions and cleaning the FRP surface. After the adhe- sive is properly mixed, the FRP can be fed through an adhesive bed which deposits the adhesive on the FRP with a triangular cross-section as shown in Fig. 9. Once the strip is placed on the concrete surface it should be pressed firmly to release entrapped air and change the dimension of the triangular cross-section to a uniform thickness. Excess adhesive around the edges should then be wiped clean.
For the installation of an externally bonded wet lay-up system, all primers, putties and adhesives should be mixed in the appropriate ratios with an electric mixer for the cor- rect duration in ambient temperatures specified by the manufacturer. A primer coat is usually applied first to the concrete surface to penetrate open pores. Once this coat has become tack-free, a bonding agent can be applied with a trowel. The bonding agent is commonly made by mixing the primer with a thixotropic agent, like untreated fumed silicon dioxide, in the ratio of 1:1 by volume. Impregnation
Fig. 9. Adhe
of the FRP sheets with saturant is best performed using a resin-impregnating machine but can be performed by hand using a paint roller or trowel. Once the saturated sheet has become activated it will be slightly hot to the touch, and can be placed on the concrete surface once the bonding agent has become tack-free. The sheet should be rolled in the direction of the fibres using a plastic serrated roller to release entrapped air and prevent sagging in overhead applications. This must be done carefully as to not fracture the fibres. Sufficient adhesive should be used around the corners to prevent ponding effects. Successive layers may be added by applying an additional layer of bonding agent and installing another saturated sheet. Designs of more than five layers should be avoided for practical reasons and to avoid over-strengthening which can affect the ductil- ity of the strengthened system [2]. The manufacturer may provide their own guidelines which may differ slightly from the guidelines provided here.
4.5. Externally bonded SRP installation
The installation of an externally bonded SRP material differs from that of an FRP system. First and foremost it should be mentioned that the SRP material as cur- rently manufactured is susceptible to rapid corrosion when exposed untreated to environmental conditions. During shipping of the SRP material, the spools should be wrapped with plastic to keep out all moisture, and storage should occur in a dry, cool place. The cutting of uni-direc- tional SRP is straightforward in the longitudinal direction. A razor blade knife can be used to cut the rubber-like grid that holds the wires together. Cutting in the transverse direction requires the careful selection of a specialized tool. For wires up to gauge 10, a pair of electric shears may be used. The use of bent SRP material should be minimized during the design stage. Bending of the SRP material should be done by the manufacturer prior to site delivery. For anchorage of an SRP flexural strengthening system, two L-shaped clips should be used as opposed to U-wraps. If SRP L-clips are being used or other corner configura- tions, the corners of the concrete should not be rounded but prepared to the angle specified with no chamfer. It is recommended that the SRP be cut into multiple pieces as
sive bed.
Fig. 10. SRP installation recommendations.
1502 O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507
shown in Fig. 10. This relieves outward pressure caused by the transverse stiffness of the material and prevents voids from forming between the SRP and the concrete. Similar to a FRP wet lay-up installation, a primer coat should first be applied and allowed to become tack-free. A layer of sat- urant is then applied and the SRP is placed on the saturant at the correct orientation with the correct side up, and pressed firmly into place. The white rubbery grid which holds the wires together also acts as an indicator of adhe- sive thickness. When the SRP is pressed down suffi- ciently the adhesive will be at the level of the grid material. An additional layer of epoxy should then be applied to completely cover the SRP surface. Comprehen- sive quality control procedures should be employed to ensure that all wire surfaces as completely covered with the protective adhesive.
5. Inspection procedures
The effectiveness of composite strengthening systems for reinforced and prestressed concrete is highly dependent on the quality of the bond between the composite system and the concrete surface. One way to help guarantee effective bond is the implementation of an inspection programme of the strengthening system. The following section briefly summarizes the available inspection tests, describes a dem- onstration which was performed to assess the effectiveness of the pull-off test, and gives a recommended inspection procedure.
5.1. Inspection tests
There are three types of inspection procedures for com- posite strengthening systems: visual inspections, partially destructive testing (PDT), non-destructive testing (NDT). By keeping detailed records, routine visual inspection can notice the changes of the strengthened location over time. The inspector can check for cracking, crazing (fine random surface cracks) and delamination as well as possible
changes in adhesive thickness. The concrete structure itself can also be evaluated for signs of corrosion, additional cracking or deterioration. The composite system should be checked for dampness or moisture exposure: long-term exposure to moisture may significantly affect system perfor- mance. As visual inspection relies on the inspector’s ability to observe, auxiliary visual aids such as a magnifying glass may be used to improve the surface view.
A PDT provides a good estimate of the performance of the strengthening system, and may not be damaging to the structure if used sacrificially outside critical zones or used on witness panels placed on-site. The most common and effective PDT is the pull-off test as shown in Fig. 11. Prior to the installation of the strengthening system, the pull-off test can be used to determine the surface tensile strength of the concrete. After installation of the composite strength- ening system, the pull-off test can be used to determine the tensile bond strength between the composite system and the concrete. Three modes of failure are typically encountered: failure in the concrete substrate, failure at the laminate-concrete interface, or failure in the adhesive layer. Another PDT which can be performed after installa- tion of the composite strengthening system is the tensile testing of witness panels made from the FRP/SRP mate- rial. There are several other PDTs which are commonly used and are illustrated schematically in Fig. 11: (a) the shear test, which measures the mode II shear fracture behaviour of the strengthening system, (b) the torque test, which can estimate the bond strength using a simple torque wrench, and (c) core sampling, where the thickness of the FRP/SRP and adhesive can be measured.
NDT is a method where the testing does not disable or destroy the test specimen and impair its future usefulness. The most common type of NDT is acoustic sounding, which makes use of the varying sound frequency emissions of different materials. Inspectors must first be adequately trained to hear the difference between the sounds. Infrared thermography is another NDT technique which uses heat dissipation characteristics of the strengthening system to
Fig. 11. Partially destructive inspection tests.
Table 2 Inspection demonstration test matrix
Delamination level
Non-prepared surface None Level 1 Level 2
Precured 5 5 5 1 Layer wet lay-up 5 5 5 2 Layer wet lay-up 5 5 5
Defect type Sandblasted surface Precured 4 5 5 1 Layer wet lay-up 5 5 5 2 Layer wet lay-up 5 5 5
Grinded surface Precured 4 5 5 1 Layer wet lay-up 5 5 5 2 Layer wet lay-up 5 5 5
Grinded Non-prep Sandblast Baseline 10 5 5
Total number of tests R = 153
Note: Numbers indicate number of tests performed.
O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507 1503
detect voids and delaminations. Initial results show that the technology can detect voids in a laboratory environment when using relatively thin laminates [22]. Other NDTs which have been used to inspect composite strengthening systems include ultrasonic technology [12], impulse radar [23], or laser shearography [24]. Many of these methods are currently under evaluation for field implementation.
5.2. Inspection demonstration
A demonstration was performed to determine the pres- ence of delaminations between a CFRP strengthening sys- tem and the concrete surface using the most effective [12] inspection device: the pull-off tester. The concrete specimen used was a previously tested but uncracked 4600 mm long beam with a concrete compressive strength of 46.3 MPa. The specimen was divided into three distinct surface pro- files (unprepared, sandblasted, grinded) and tested for var- ious CFRP systems (precured, one layer wet lay-up, two layers of wet lay-up) and level of defects (none, 33% dela- minated, 66% delaminated) with the delaminated area being a rectangular strip purposefully placed in the middle of the testing dolly. Five pull-off tests were performed for each area along with twenty tests performed on the unstrengthened surface profile, resulting in a total of 153 pull-off tests. The full test matrix is shown in Table 2.
The three surface profiles were prepared as follows: (1) unprepared: the surface was lightly grinded to remove existing asphalt, dirt, sand, (2) sandblasted: the surface was sandblasted with an abrasive sand to open pores of the concrete until the surface was a relatively uniform height and roughness, (3) grinded: the surface was grinded with a diamond tooth blade until the top cement paste layer was completely removed exposing the aggregates. To induce defects into the composite system, masking tape
was used to intentionally create delaminations between the concrete and the CFRP system.
The pull-off testing apparatus used was a Hilti Test Meter 4 with an aluminum stand as shown in Fig. 12. A cir- cular plate was welded to the top of the 100 mm diameter aluminum stand in order to provide a stable support for the testing machine. Rectangular steel plates 38.1 � 38.1 � 9.50 mm with centred 12.7 mm diameter threaded holes were used as testing dollies. The dollies were affixed to the FRP system using the adhesive from the correspond- ing system. In the areas with defects, the dollies were placed in the centre of the induced delaminations. The system was allowed to cure for 7 days, after which a cutting wheel was
Fig. 13. Precured system inspection demonstration results.
1504 O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507
used to cut through the FRP system and into approxi- mately 15 mm (±5 mm) of the concrete surface on all four sides of the dolly. A threaded rod was then screwed into the dolly and the rod was then inserted into the pull-off tester as it stood flush with the stand. A direct tensile force was then applied by smoothly turning the hand wheel at a rate of approximately 1 MPa per second until failure. The pull- off strength was then determined by dividing the tensile force by the area of the dolly (which assumes an average distribution of stress), and the nature of the failure was recorded.
Test results show that there is a clear trend between the pull-off strength and the level of induced delamination, with higher levels of defects generating lower pull-off strengths. Out of the 153 tests, only 10 of the failures occurred in the adhesive layer, the rest occurred in the concrete layer. For the precured system, the unprepared surface was the least sensitive to the defect level, while the sandblasted sur- face most accurately predicted the effect of the defects. This trend is shown in Fig. 13 where the applied tensile pressure is shown for the three surface preparation conditions. For both of the wet lay-up systems, the unprepared and grinded surfaces were more effective than the sandblasted surface as shown in Fig. 14 for the wet lay-up system with two layers. Further analysis may show that the sandblasted surface affects the bond strength of the wet lay-up system. All of the tested areas, even those with a level of delamination cor- responding to 66% of the total area, passed the criterion of bond failure provided in ACI Committee 440 [2] of 1.34 MPa. Therefore, this specified bond stress criterion may be too low and might need reexamination.
5.3. Recommended inspection procedure
Based upon a review of the current literature including published codes and guidelines [1,12,13], the results of the
Fig. 12. Pull-off testing app
inspection demonstration and the experience of the research team the following recommendations are made for the inspection of prestressed concrete bridges strength- ened with a composite system:
1. Documentation – a file should be created to properly record the inspections performed on a composite strengthening system. The first entry should be a com- prehensive record of all materials used in the installation and their properties determined from testing.
2. Initial visual inspection – the initial visual inspection is crucial, since it will form a baseline for subsequent inspec- tions. It is also important to assess the effectiveness of the FRP system, in particular the presence of fibre misalign- ment, folds or kinks. Any misalignment greater than 10 mm should be repaired [1].
3. Initial coring – three core samples should be taken in each representative area of the strengthened structure. The representative area can be defined as within each span or within each 93 m2 of strengthening [1] but away
aratus, stand and dolly.
Fig. 14. Wet lay-up (2 layers) system inspection results.
O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507 1505
from critical regions. The thicknesses of the composite strengthening system obtained from the core sampling should be compared to the design values.
4. Regular visual inspection – careful visual inspection should be performed on the strengthened area. The fol- lowing items should be noted: the size, location and quantity of delaminations or flaws; the possible deterio- ration of the system over time; the presence of moisture or ponding; changes to the reinforced/prestressed con- crete structure (e.g. corrosion).
5. Pull-off testing – pull-off testing should be performed a minimum of five times for each representative area of the strengthened structure (as defined above).
6. Acoustic sounding – acoustic sounding with a steel rod should be performed on the entire strengthened region. A practice acoustic sounding box should be left on-site to educate the inspectors on the difference between bonded and unbonded laminates and for in situ inspec- tion comparison.
The initial visual inspection, initial coring and acoustic sounding inspection can occur after the composite strength- ening system has fully cured (not before 24 h). At this time, tensile testing of the witness panels of the composite mate- rial can also be performed. The initial pull-off tests can be performed 7 days after the installation [13]. The frequency of regular inspections should be determined by the owner and the engineer. A possible inspection regime could be:
Fig. 15. Bearing plate (left) and
1. Routine inspections – visual inspection, acoustic sound- ing. Every year.
2. Comprehensive inspections – visual inspection, acoustic sounding, pull-off testing. Every five years.
6. Value engineering
An important aspect of this research project was the cost-effectiveness and value engineering (VE) of composite strengthening systems. The most cost-effective structural system was determined to be externally bonded wet lay- up CFRP sheets [18]. Value engineering is a methodology for evaluating the cost-effectiveness by looking at the over- all performance of the system. The ability to provide fore- thought and guidance to the design problem from an engineering perspective was the goal of the VE analysis.
The VE analysis began with examining the existing state of the structure. In this particular case the structure was a forty-year-old two-span prestressed concrete bridge super- structure. The research team visited four bridge sites in the course of the research and gained some knowledge of the bridge condition: (1) Corrosion of bearing plate at support (Fig. 15), (2) corrosion of lower prestressing strands near midspan resulting in longitudinal cracking and spalling (Fig. 16), (3) shear cracks extending from area near support to deck, and (4) the cracking of deck near midspan as a result of improper lifting maneuvers during original girder installation. In addition to these issues with the superstruc- ture, poor conditions can also be found in the timber sub- structure (Fig. 15). In the VE analysis some of these items were found to be insignificant (e.g. the corrosion of the bearing plates and the light spalling near midspan could be easily repaired), but others could potentially seriously affect the behaviour and must be considered in the struc- tural design of the strengthening system (e.g. corrosion of prestressing strands). In addition, the state of the substruc- ture needs complete evaluation when subjected to the increased load demand occurring as a result of the strengthening operation.
The condition of the girders may lead to particular com- posite systems which may be more effective. If the soffits, or webs, of the girders have spalled concrete over a significant length of the strengthened length then the use of NSM sys- tems could be problematic and could lead to debonding
timber substructure (right).
Fig. 16. Concrete spalling repair (left) and corrosion (right).
1506 O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507
failures due to their lack of provided anchorage. If the con- crete is damaged in the cover concrete below the prestress- ing strand, the beam can be flexurally strengthened with an externally bonded CFRP system with sufficient transverse CFRP U-wrap reinforcements after the appropriate con- crete repair and corrosion inhibitation. The width of the soffits also may have a significant effect on the choice of composite strengthening system. The narrow width of the soffits in this research led to strengthening by externally bonded CFRP sheets being more effective simply because more material could be placed in successive layers, some- thing that was impossible with NSM systems. For one way slabs and negative moment regions, NSM strengthen- ing can be very cost-effective [9]. For overhead applica- tions, cutting of the groove for the NSM can be a challenging task. If large numbers of girders are being strengthened, a guidance system may be constructed to locate the groove in the correct position and to alleviate the weight burden on the installer. The easiest system to install overhead was the externally bonded precured strips.
The high modulus CFRP materials, installed either as sheets or strips, are not the most effective due to their lim- ited strain ultimate strain capacity. Due to their brittle characteristics, this material requires careful attention to transportation and handling which may increase the over- all cost of this material.
SRP strengthening systems encountered several difficul- ties in installation, mainly with the bent or wrapped config- uration. Because of the high in-plane and out-of-plane stiffness of the SRP material with the density of 0.90 wires per mm (23 wires per inch) did not conform to the soffit of the prestressed concrete bridge girder as envisioned and had to be cut into several different pieces to relieve pressure as shown in Fig. 10. In one instance the wrapped SRP was not cut, and significant sagging occurred prompting a repair operation to fill the voids with more adhesive mate- rial. The L-clips used as anchorage were also difficult to install due to their stiffness and the intrinsic convex shape of each leg, resulting in excess adhesive being added to fill voids. It is recommended that SRP material not be used in situations where the material must be bent to conform to a particular surface.
The environmental impact of the composite strengthen- ing system installation must also be considered in a VE
analysis. It is recommended that the mixing of all materials be performed in a flat location away from streams and other environmental sensitive areas due to the undesirable problem which would occur as a result of a spill. Encapsu- lation of the strengthening area during cutting of the NSM grooves or surface grinding the concrete should be required to prevent large quantities of dust being released into the surrounding areas. Safety precautions and environmental guidelines published in the recent NCHRP document [1] should be followed.
7. Conclusions
This paper has discussed the structural design and pro- vided installation and inspection guidelines of prestres- sed concrete strengthened with composite (FRP or SRP) strengthening systems. An experimental programme was described including the static and fatigue testing of six large-scale prestressed concrete bridge girders. In addition, a demonstration programme involving the pull-off testing of 153 specimens was described. The following conclusions can be drawn from the study:
1. The experimental programme on large-scale prestressed concrete beams has shown that SRP materials are more structurally efficient.
2. The installation of a composite strengthening system is crucial to produce quality bond which can internally transfer forces.
3. SRP installation differs from FRP installation, espe- cially relating to sheets bonded to non-flat surfaces.
4. Visual inspection, acoustic sounding and pull-off testing are the most effective inspection techniques.
5. It is recommended to conduct a routine inspection every year and a comprehensive inspection every five years.
Acknowledgements
The authors would like to acknowledge the support of the North Carolina Department of Transportation through research Projects Nos. 2004-15 and 2006-10 and the support of numerous industrial partners who provided time and materials to this research project, in
O. Rosenboom et al. / Construction and Building Materials 23 (2009) 1495–1507 1507
particular Structural Group, Inc. We would also like to thank Amir Mirmiran, Tarek Hassan, and Ronaldson Carneiro and the dedicated staff at the Constructed Facil- ities Laboratory (Jerry Atkinson, Bill Dunleavy and Amy Yonai).
References
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[2] ACI Committee 440. Design and construction of externally bonded FRP systems for strengthening concrete structures (ACI 440.2R-02). ACI manual of concrete practice, American Concrete Institute, 2002.
[3] Matthys S. Structural behaviour and design of concrete members strengthened with externally bonded FRP reinforcement. PhD thesis, University of Ghent, Belgium; 2000.
[4] Rosenboom OA. Behaviour of FRP repair/strengthening systems for prestressed concrete, PhD thesis, North Carolina State University; 2006.
[5] Chen JF, Teng JG, Yao J. Strength model for intermediate crack debonding in FRP-strengthened concrete members considering adja- cent crack interaction. In: Proceedings of the third international conference of composites in civil engineering; 2006. p. 67–70.
[6] Teng JG, Lu XZ, Ye LP, Jiang JJ. Recent research on intermediate crack-induced debonding in FRP strengthened RC beams. In: Proceedings of the advanced composite materials in bridges and structures (ACMBS), Calgary, Alberta, Canada; 2004. p. 1–12.
[7] Rosenboom OA, Rizkalla SH. Modeling of IC debonding of FRP strengthened concrete flexural members. ASCE J Compos Const, in press.
[8] Teng JG, Yao J. Plate end debonding in FRP-plated RC beams-II: strength model. Eng Struct 2007;29(10):2472–86.
[9] Hassan T, Rizkalla S. Bond mechanism of NSM FRP bars for flexural strengthening of concrete structures. ACI Struct J 2004;101(6).
[10] Kim YJ, Fam A, Kong A, El-Hacha R. Flexural strengthening of RC beams using steel reinforced polymer (SRP) composites. In: Proceed- ings of the eighth international conference on fibre reinforced polymer reinforcement for concrete structures; 2006. p. 1647–63.
[11] Prota A, Tan KY, Nanni A, Pecce M, Manfredi G. Performance of shallow reinforced concrete beams with externally bonded steel- reinforced polymer. ACI Struct J 2006;103(2).
[12] Concrete Society. Strengthening concrete structures using fibre composite materials: acceptance, inspection and monitoring, Techni- cal Report 57, The Concrete Society, Camberly; 2003.
[13] ISIS Canada. Strengthening reinforced concrete structures with externally-bonded fibre-reinforced polymers. Manual no. 4, report ISIS-MO5-00, ISIS Canada, University of Manitoba, Winnipeg, Canada; 2001.
[14] Miller AD. Repair of impact-damaged prestressed concrete bridge girders using carbon fibre reinforced polymer (CFRP) materials, MSCE thesis, North Carolina State University; 2006.
[15] Rosenboom OA, Hassan TK, Rizkalla S. Flexural behaviour of aged prestressed concrete girders strengthened with various FRP systems. Constr Build Mater 2007;21(4):764–76.
[16] Rosenboom OA, Rizkalla SH. Behaviour of prestressed concrete strengthened with various CFRP systems subjected to fatigue loading. ASCE J Compos Const 2006;10(6):492–502.
[17] Rosenboom OA, Rizkalla SH. Experimental study of IC debonding in FRP strengthened beams. ACI Struct J, in press.
[18] Harries KA, Zorn A, Aidoo J, Quattlebaum J. Deterioration of FRP- to-concrete bond due to failure loading. Adv Struct Eng 2006;9(6):779–89.
[19] ACI Committee 546. Concrete repair guide (ACI 546R-96). ACI manual of concrete practice, American Concrete Institute; 1996.
[20] Shanafelt GO, Horn WB. Damage evaluation and repair methods for prestressed concrete bridge members. National cooperative highway research program report 226, Transportation Research Board, 1980.
[21] Klaiber FW, Wipf TJ, Kempers BJ. Field laboratory testing of damaged prestressed concrete (P/C) girder bridges. Iowa department of transportation report HR-397, 1999.
[22] Hamilton HR, Brown JR, Ansley M. CFRP repair of impact- damaged bridge girders, volume II-inspection of FRP composite repairs using infrared thermography Florida department of trans- portation final report, BC354-55; January 2005.
[23] Helmerich R, Niederleithinger E, Wiggenhauser H. A toolbox with non-destructive testing methods for the condition assessment of railway bridges. TRB 2006 annual meeting.
[24] Newman J, Zweben C. Nondestructive inspection of composite- strengthened concrete structures. In: Proceedings of the 47th inter- national SAMPE symposium; May 12–16, 2002. p. 691–702.
- Strengthening of prestressed concrete girders with composites: Installation, design and inspection
- Introduction
- Research objectives
- Structural behaviour
- Behaviour under static loading conditions
- Behaviour under fatigue loading conditions
- Major design concepts
- Flexural design
- Design against bond failure
- Design against fatigue failure
- Installation procedures
- Shipping, storage and handling
- Section restoration
- Surface preparation
- Externally bonded FRP installation
- Externally bonded SRP installation
- Inspection procedures
- Inspection tests
- Inspection demonstration
- Recommended inspection procedure
- Value engineering
- Conclusions
- Acknowledgements
- References
HT120815 Readings/1-s2.0-S0950061811003680-main.pdf
Construction and Building Materials 27 (2012) 490–520
Contents lists available at ScienceDirect
Construction and Building Materials
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o n b u i l d m a t
Statistical analysis of existing models for flexural strengthening of concrete bridge beams using FRP sheets
Alfredo M. Ceci a, Joan R. Casas b,⇑, Michel Ghosn c a Dipartimento di Ingegneria delle Strutture, delle Acque e del Terreno, University of L’Aquila, Italy b Bridge Engineering, Technical University of Catalonia, Barcelona, Spain c Civil Engineering, The City College of New York/CUNY, New York, NY, USA
a r t i c l e i n f o
Article history: Received 2 November 2010 Received in revised form 27 June 2011 Accepted 18 July 2011 Available online 23 August 2011
Keywords: Fiber-reinforced plastic Flexural strengthening Model uncertainty
0950-0618/$ - see front matter � 2011 Elsevier Ltd. A doi:10.1016/j.conbuildmat.2011.07.014
⇑ Corresponding author. Tel.: +34 934016513; fax: E-mail address: [email protected] (J.R. Ca
a b s t r a c t
This paper performs a statistical analysis of previously proposed models for resisting the debonding of FRP sheets used in strengthening reinforced and prestressed concrete beams. End debonding and inter- mediate crack-induced debonding modes of failure are studied for beams in flexure. Two different dat- abases are assembled from published experimental debonding tests on concrete beams of different span lengths. The first database contains the results of four point bending tests performed to study the behavior of the FRP-concrete bond at the end of the FRP sheet. The second database which includes four point bending tests, three point bending tests and one point loading tests, has been created to examine intermediate crack-induced debonding. These two databases are significantly larger than those used in developing any of the existing debonding strength models and provide a solid basis for assessing the per- formance of such models. A regression analysis reviews the relationship between the experimentally measured loads that caused debonding to the model predicted values as well as the bias and the variabil- ity in the prediction models. This regression analysis allows for drawing conclusions on the most appro- priate and accurate models, from a statistical point of view, that may be used in a follow up reliability- based calibration of partial safety factors. The applicability of such information for the development of design specifications for strengthening of deteriorated concrete bridges is highlighted. This will be imple- mented in a forthcoming companion paper.
� 2011 Elsevier Ltd. All rights reserved.
1. Introduction
Bonding of Fiber-Reinforced Polymer (FRP) to the tension face of concrete beams has become a frequent strengthening method over the last decade. The application of FRP to the tension face of a con- crete beam or slab has multiple benefits, including: increased ulti- mate flexural strength capacity, increased post-cracking stiffness, as well as concrete crack control whereby the bonding of FRP sheets to concrete beams results in finer and more evenly distrib- uted cracks when compared to the cracks that develop in unstrengthened beams. Because of these benefits, it is clear that flexural strengthening of reinforced concrete beams with FRP has a great potential for becoming a primary strengthening scheme for deteriorated infrastructure systems. However, because of the relative novelty of this technology, a more complete understanding of the behavior of FRP-strengthened beams and their failure mech- anisms need to be gained before the wide spread adoption of this technology in engineering practice. As a minimum, the confidence levels in the safety margins of existing and proposed design criteria
ll rights reserved.
+34 934054135. sas).
should be ascertained. This would require an objective estimation of the biases implied in existing and recently proposed design cri- teria and an analysis of the variability of the expected loads that cause failure from the predicted loads.
The fibers used in common FRP strengthening schemes are usu- ally made of glass, carbon or aramid. To bond the fibers together and to the substrate surface on which they are being applied, a re- sin matrix is used. Two methods of application are frequently used. In situ installations require placing the fibers in an open mold, attaching the assembly to the surface and then saturating the assembly with resin. More commonly, the fibers may be first satu- rated with epoxy and then bonded to the prepared surface of con- crete. In situ assemblies of the fibers are usually referred to as wet lay-up. Preimpregnated plates or sheets of fibers (prepreg) can also be installed by applying resin to bond the sheets to the concrete surface.
Hollaway and Teng [1] recognized six main failure mechanisms for reinforced concrete beams flexurally strengthened with FRP. These are represented in Fig. 1 as: (a) FRP rupture, (b) crushing of concrete, (c) intermediate crack-induced interfacial debonding, (d) concrete cover separation, (e) plate end interfacial debonding, (f) concrete shear failure and (g) critical diagonal cracking. Modes
(a) (b)
(f)(d) (e)
(c)
(g)
Fig. 1. Failure modes of FRP-strengthened beams. a. FRP rupture; b. Crushing of compression concrete; c. Intermediate crack induced interfacial debonding; d. Concrete cover separation; e. Plate end interfacial debonding; f. Shear failure; g. Critical diagonal crack.
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 491
(a), (b) and (f) are classical concrete beam failure mechanisms and have been analyzed to a great extent in the past [2–4]. The remain- ing failure mechanisms are specific to FRP strengthened beams and are characterized as premature failure modes because they take place before realizing the full potential of the strengthening scheme. Modes (d), (e) and (g) are often indistinguishable and in fact, Smith and Teng [5,6] identified a mixed failure mode where the failure occurs at the same time by the concrete cover separa- tion and the plate end interfacial debonding mode. In this paper, modes (d), (e) and the combined mode will be grouped under the label end debonding failure mode. Yao et al. [7] explain that intermediate crack induced debonding, identified as mode (c), normally initiates in the high moment region due to a flexural or flexural-shear crack. On the other hand, end debonding is initiated by high interfacial stresses at the plate end as explained by Yao et al. [7].
Failures of FRP strengthened beams due to concrete crushing are easily predicted and this mode of failure would allow for the most efficient use of the materials while preserving an acceptable level of ductility. FRP rupture is also a mode failure that can be eas- ily determined. Although, the FRP rupture mode is permitted in most existing guidelines, it would be preferable to avoid it as it may lead to brittle failures.
When designing an FRP strengthening scheme, it is generally most difficult to predict and control the debonding modes of fail- ure. In fact, a large number of experimental studies reported pre- mature failures by debonding rather than concrete crushing or FRP rupture. For this reason, considerable research effort has been
expended on understanding the underlying factors that cause FRP debonding, to develop models for predicting debonding, and to propose design guidelines to minimize the risk of its occurrence under design loading conditions [2,8–10].
Most analytical and experimental studies have focused on studying the end debonding mode of failure, while intermediate crack induced debonding has received much less attention and few models have been developed for predicting its occurrence. Nevertheless, the debonding failure mechanisms are still found to be complicated processes that are not fully understood, making it difficult for engineers to estimate the actual capacity of FRP- strengthened concrete beams and thus making them reluctant to use this new technology on a wide scale.
Over the last decade, several guidelines for use of FRP in con- struction have been developed [11–15]. Many of these guidelines are under constant refinement as more information is gathered on the behavior of structural components strengthened using FRP. In particular, the American Concrete Institute (ACI) published the first version of its guidelines in 2002 and released a revised ver- sion in 2008. Most of these and other proposed design criteria have used equations that provide lower bounds for the beam’s capacity based on limited sets of experimental data or else developed ad- vanced fracture mechanics models without following modern methods for developing reliability-based design codes and specifi- cations that would take into consideration the uncertainties asso- ciated with the input parameters as well as the modeling assumptions. Triantafillou in 1992 [16] was the first to propose reliability-based sets of design equations for FRP-strengthened
492 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
beams but only looked at the concrete crushing and FRP rupture modes. A recent study by Atadero and Karbhari [17,18] developed reliability-based criteria for debonding using fracture mechanics models but the approach considered only randomness in the input parameters and did not account for the modeling uncertainties, also known as systemic uncertainties, which in many cases may be more significant than the parametric uncertainties. The imple- mentation of reliability-based design specifications is extremely important for FRP-strengthened concrete beams due to the large level of variability observed in experimental tests results and the uncertainties in determining the material properties.
The objective of a study currently underway at the Technical University of Catalonia (UPC), in Barcelona is to propose appropri- ate reliability-based design equations with properly calibrated safety factors that can be used during the design of a strengthening scheme to enhance the flexural capacity of existing concrete bridge beams. In a first step of this study, a statistical analysis of available models is performed and presented in this paper. The goal of this analysis is to study the systemic uncertainties associated with existing models. To this end, experimental results on strengthened concrete beams that failed due to either end debonding or interme- diate crack induced debonding are compared to several available proposed predictive and design models to determine the most appropriate ones for implementation in design codes. The experi- mental database was carefully constructed from an extensive sur- vey of the published literature, and presented in Appendices A and B. The statistical analysis of the selected existing debonding mod- els will provide the necessary information to calibrate appropriate safety factors that should be applied in conjunction with the se- lected models so that future design codes would provide the engi- neers with the tools necessary to use FRP-based concrete beam strengthening schemes that would lead to uniform and consistent reliability levels.
2. Experimental database
Several models have been developed over the last two decades to predict the debonding of FRP-strengthened concrete beams or to propose design equations to avoid its occurrence. Many of these models were calibrated using a limited database generated by each model’s own developers. To validate the accuracy of existing mod- els, it is important to compare the predicted results against a very broad set of experimental laboratory and in situ data that mimic as closely as possible the size and environmental conditions where FRP-strengthened beams will be applied. To perform a valid statis- tical analysis, each model should be compared to a wide data set that extends beyond the limited set which was used to calibrate the model. A rigorous statistical analysis that investigates the biases and variability of a model is the necessary first step toward performing a reliability analysis of strengthened concrete beams and calibrating a set of appropriate safety factors for implementa- tion in design specifications.
Over the last few years, several authors such as Smith and Teng [6], Colotti et al. [19] and Wu and Niu [3] have assembled from the existing literature exhaustive and useful experimental databases following clearly defined criteria. Due to the continuous ongoing effort in testing FRP strengthened beams, an updating of these pre- viously published databases has been undertaken as part of this study to assemble a more comprehensive list that specifically in- cludes recent test results and, to the extent possible, those con- ducted on large scale beams which may prove to be critical for the statistical analysis given the importance of scale effects. To that end, two large databases are assembled from the available litera- ture, as reported in Appendices A and B. The databases include re- sults for FRP strengthened concrete beams and small scale beam
specimens. The first database provided in Appendix A includes 161 four-point bending tests that resulted in end debonding fail- ures (see Tables A.1–A.6). The database was assembled from 34 testing programs carried out between 1991 and 2007. The test data is classified based on the material type and installation process as follows: 90 beams were reinforced by wet lay-up carbon sheets, 57 beams reinforced by prepeg carbon plates, 7 beams reinforced by wet lay-up glass sheets, and 7 beams reinforced by prepeg glass plates. This database includes beams that failed by end debonding including failures due to concrete cover separation, plate end inter- facial debonding, mixed concrete cover separation, end interfacial debonding mode, and critical diagonal crack debonding. Table 1 gives a summary of the experimental programs including the refer- ence from which the information was collected, the number of beams, the beam sizes, the FRP type and thickness as well as the shear load at failure. All the tests were performed for four-point bending labeled (f.p.b.t.) in Table 1. It is noted that all the tests were performed on laboratory scale models where the longest beam was about 4.5 m in length. The maximum observed failure load was 125 kN. These maximum length and load ranges are sig- nificantly smaller than would be expected in many structural applications particularly for bridges.
The second database provided in Appendix B includes strength- ened beams that failed as a result of intermediate crack induced debonding (Tables B.1–B.6). The data set consists of 187 beam tests from 38 experimental programs carried out between 1996 and 2007, as summarized in Table 2. When separated by material type, the list includes 125 beams reinforced by carbon sheets, 4 beams reinforced by glass sheets, and 32 beams reinforced by aramid sheets. The loading configurations for these test specimens con- sisted of: (a) four-point bending (f.p.b.t); (b) three-point bending (3.p.b.t); and (c) one-point bending of cantilevered beams (c.b.t). In this case, several researchers tested longer beams with spans up to 7.2 m and reported failure loads of up to 548.5 kN.
The experimental tests selected from the literature were those for which most material and geometric characteristics were clearly reported. To assemble a consistent database, the following criteria were used:
� all beams and slabs have rectangular cross-sections, are conven- tionally reinforced with steel rebars and strengthened with con- stant-thickness carbon, glass or aramid FRP sheets; � failure of the beam was by end debonding or intermediate
crack-induced debonding; � the FRP sheet was neither prestressed nor anchored in any form
at its ends; � the beam did not experience prior cyclic loading after being
repaired with FRP and before being tested statically to debond- ing failure; � sufficient details about various geometric and material param-
eters were provided to enable the use of the results with confidence.
The above stated criteria mostly follow those previously set by Smith and Teng [6]. However the 4th criterion has been restricted to eliminating repaired beams that were subjected to cyclic loading before the test. Therefore, the database assembled in this study will include beams that have been strengthened with FRP after being damaged from statically applied high loads. Because many of the reports did not provide all the data required as input for some models, a few assumptions are made to fill in the gaps. For that purpose, the recommendations of Smith and Teng [6] were followed. Specifically, when information is not provided, the con- crete cover is assumed to be 10% of the total depth. This value was suggested for being the average concrete cover ratio used in the beams that provided cover information. Also, a modulus of
Table 1 Experimental tests collected in end debonding database. f.p.b.t. = four point bending test. C = carbon, G = glass, W = wet lay-up, P = pultruded.
Reference No. of tests L (mm) h/b (–) Type of FRP tfrp (mm) Vexp (kN) Type of test
Ahmed et al. (1999–2000) 7 1500 2.00 C-W 0.33–0.67 41.5–70.1 f.p.b.t. Arduini et al. (1997) 4 – 1.00–1.30 C-W 0.20–1.30 114.0–45.0 f.p.b.t. Berber et al. (1999) 6 2350 2.08 C-P 0.22 50.3–68.5 f.p.b.t. Benjeddou et al. (2007) 6 1800 1.25 C-P 1.20 15.1–20.1 f.p.b.t. Breña and Macri (2004) 11 812 1.00 C-W/C-P 0.16–1.19 13.9–26.20 f.p.b.t. David et al. (1999) 4 2800 2.00 C-P 1.20–2.40 68.0–79.5 f.p.b.t. Esfahani et al. (2007) 2 1600 1.30 C-W 0.18 35.5–37.2 f.p.b.t. Fanning and Kelly (2000) 6 2800 1.56 C-P 1.20 31.0–51.5 f.p.b.t. Garden et al. (1997) 17 2200 1.00–1.77 C-W/C-P 0.50–1.30 15.4–30.0 f.p.b.t. Grace and Singh (2005) 4 2540 1.67 C-W/C-P 0.40–1.20 66.7–68.3 f.p.b.t. Hau et al. (1999) 5 1500 1.30–2.60 G-W 1.66 53.0–79.4 f.p.b.t. Juvandes et al. (1998) 2 1500 2.00 C-W/C-P 1.20 6.7–12.5 f.p.b.t. Matthys (2000) 6 – 2.25 C-W 1.20–0.20 95.8–186.0 f.p.b.t. Nguyen et al. (2001) 4 1330 1.25 C-P 1.20 28.1–65.1 f.p.b.t. Pham and Al-Mahaidi (2006) 11 2300 1.86 C-W 1.06–1.58 25.7–37.3 f.p.b.t. Quantrill et al. (1996) 4 900 1.00 G-P/C-P 1.20–1.60 20.4–12.3 f.p.b.t. Rahimi and Hutchinson (2001) 8 2742 1.33 C-W 0.80–1.20 35.3–29.7 f.p.b.t. Ritchie et al. (1991) 5 2438 2.00 G-P 1.27–4.76 50.6–72.1 f.p.b.t. Ross et al. (1999) 11 2742 1.00 C-P 0.50 35.6–84.5 f.p.b.t. Saadatmanesh and Ehsani (1991) 1 4575 2.22 G-P 6.00 125.0 f.p.b.t. Sharif et al. (1994) 2 1180 1.00 G-W 2.00–3.00 33.0–34.0 f.p.b.t. Spadea et al. (1998) 2 – 1.00 C-W 1.20–1.20 37.4–43.4 f.p.b.t. Tan et al. (1999) 7 – 1.50 C-W 0.20 19.8–27.5 f.p.b.t. Täljsten (1997) 6 3600 1.50 C-W/C-P 1.40–2.40 71.4–80.1 f.p.b.t. Teng and Yao (2007) 5 1500 1.66 C-W/C-P 1.20–2.63 76.0–99.4 f.p.b.t. Triantafillou and Plevris (1992–1998) 8 1220–2130 1.67–2.00 C-W 0.49–1.90 12.8–98.2 f.p.b.t.
Table 2 Experimental tests collected in I-C induced debonding database. f.p.b.t. = four point bending test; 3.p.b.t. = three point bending test; c.b.t = cantilever beam test.
Reference No. of tests L (mm) h/b (–) Type of FRP tfrp (mm) Vexp (kN) Type of test
Beber et al. (1999) 6 2349 2.08 C 0.44–1.10 50.3–68.5 f.p.b.t. Benjamin (2005) 8 4537 1.67 C 1.4 37.7–51.8 3.p.b.t. Bonacci and Maalej (2000) 1 3650 1.48 C 0.3 250.0 f.p.b.t. Chan et al. (2001) 4 4600 1.88 C 1.2 129.0–220. f.p.b.t. Delaney (2006) 4 1800 1.50 C 1.4 44.4–49.5 f.p.b.t. Esfahani et al. (2007) 1 1600 1.33 C 0.18 54.5 f.p.b.t. Gao et al. (2004) 3 1500 1.33 C 0.2 39.3–43.9 f.p.b.t. Kishi et al. (1998–2003) 11 2600 1.67–2.66 A/C 0.1–0.6 37.0–80.0 f.p.b.t. Kotynia (2005) 6 3000–4200 2.00 C 0.4–1.4 90.0–46.0 f.p.b.t., 3.p.b.t Kurihashi et al. (1999–2000) 8 1800–3400 1.66 A/C 0.2–0.6 34.9–77.5 f.p.b.t. Leung (2004) 16 7200–1800 2.66 C 0.2–1.8 32.1–548.5 f.p.b.t. Maleej and Leung (2005) 10 4800–1500 1.27 C 0.2–0.7 37.7–334.7 f.p.b.t. Maeda et al. (2001) 2 1800 1.00 C 0.2–0.3 39.2–54.5 f.p.b.t. M’Bazza et al. (1996) 1 3000 1.5 C 0.9 49.9 f.p.b.t. Mikami et al. (1999) 1 3000 1.66 C 0.3 40.2 3.p.b.t. Niu et al. (2006) 12 4200 0.21 C 1.2–2.6 54.2–133.8 f.p.b.t., 3.p.b.t. Seim et al. (2001) 6 2030 0.25 G/C 1.1–1.2 40.8–80.8 3.p.b.t. Spadea et al. (1998) 2 4800 2.14 G/C 1.2 37.4–43.4 f.p.b.t. Takahashi and Sato (2003) 5 1600 1.5 C 0.2–0.5 113.5–155.5 f.p.b.t. Takeo et al. (1999) 6 2000 1.62 C 0.2 33.8–85.6 f.p.b.t., 3.p.b.t. Teng and Yao (2007) 2 1500 1.67 G/C 1.67–2.01 71.3–82.0 f.p.b.t. Wu et al. (1999–2000) 5 1800 1.33 C 0.1–0.3 65.0–78.4 f.p.b.t. Yao et al. (2005) 10 1100 0.5 C 0.2–1.2 7.2–21.4 c.b.t., 3.p.b.t. Zarniç et al. (1999) 2 2900 0.15–1.5 C 1.2 31.5–58.4 f.p.b.t. Zhang et al. (2005) 20 1800–3500 1.66–2.66 A/C 0.2–0.6 34.0–78.1 f.p.b.t.
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 493
elasticity of 200 GPa was adopted for steel reinforcement when the modulus was not specified [6].
To calculate the concrete material characteristics, the ACI440 [11] models were used, as follows:
Ec ¼ 4730 ffiffiffiffi f 0c
q f ct ¼ 0:53
ffiffiffiffi f 0c
q f 0c ¼ 0:8f cu ð1Þ
where Ec (in MPa) is the elastic modulus of concrete, fct (in MPa) is the splitting tensile strength of concrete, f 0c (in MPa) the concrete cylinder compressive strength, and fcu (in MPa) the concrete cube compressive strength. These relationships are expected to produce on the average comparable results to experimental data [6].
In many instances, the adhesive layer thickness was not re- ported. In such cases, as proposed by Smith and Teng [6], the aver- age thickness obtained from available test data was adopted. Specifically, the adhesive layer thickness of pultruded plates was assumed, where it is not specified, to be ta = 2 mm. For wet lay- up installations, the adhesive layer thickness is worked out using the following formulas for a single layer of FRP:
ta ¼ tfrp;g � tsheet
2 ð2Þ
tfrp ¼ ta þ tsheet ð3Þ where tfrp,g is the gross thickness of all the FRP and adhesive layers assuming two equal layers of adhesive above and below the layer of
494 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
fibers. tfrp represents the total effective thickness of each single layer of FRP in the strengthened beam. If more than one sheet were used, tfrp must be multiplied by the number of sheet layers. If the available information was still insufficient for using Eqs. (2) and (3), ta was assumed to be 0.42 mm based on measurements of sam- ples formed from wet lay-up sheet by Smith and Teng [6]. Due to this additional uncertainty with wet lay-up plates, test data of beams with wet lay-up plates and those with pultruded plates are appropriately differentiated from each other during the data analy- sis process.
When the modulus of elasticity of the adhesive was not pro- vided, a value of 8500 MPa was used, as proposed by Smith and Teng [6].
The databases listed in Appendices A and B, provide the RC beam details as follows: width of beam b, overall depth of beam h, distance from beam compression face to centroid of steel tension reinforcement ds, distance from beam compression face to centroid of steel compression reinforcement d0s. The properties of concrete are listed if available from the experimental investigation or using Eq. (1).
The properties of the steel reinforcement are provided for the moduli of elasticity of the steel tension reinforcement Es, steel compression reinforcement E0s and steel shear reinforcement (stir- rups) Esv. The yield strengths of the tension, compression and shearing reinforcements are denoted respectively as fys, f 0ys and fys. The corresponding cross-sectional areas are respectively de- noted by As, A
0 s, and Asv.
The FRP material and installation procedure are provided under the column labeled ‘‘type’’ using the letters C, G or A in reference to Carbon, Glass or Aramid Fibers respectively. The letters W and P re- fer to wet lay-up procedure and pultruded fibers sheets respectively.
The FRP material properties are listed for the modulus of elas- ticity Efrp, and the tensile strength in the main fiber direction ffrp, sheet thickness tfrp, and sheet width bfrp as well as the distance from the support to the nearer end of the soffit plate a.
The adhesive properties provided are the modulus of elasticity Ea, and thickness of adhesive layer ta. The width of resin layer ba is assumed to be always equal to the FRP width bfrp.
The loading configuration and the failure load are described by the distance from the support to the nearest applied load, B, the span of the beam, L and the maximum shear force in the beam at debonding Vexp.
The statistical analysis of existing analytical and design models is verified by comparing the results predicted by the models to the experimental results assembled in the database. The analytical and design models that have been studied are briefly discussed next.
3. Review of models for debonding of FRP-strengthened RC beams
An exhaustive review of existing debonding models for end- debonding or intermediate crack (IC) debonding in FRP-strength- ened RC beams was performed. A distinction between models developed from beam tests (type-A models) and models based on prism tests (type-B models) was done. A preliminary analysis of both type-A and type-B models was performed to investigate their reliability. The models were applied to two different databases assembled from the scientific literature; one database is for prism tests and the other is for beam tests. A better agreement, between analytical and experimental results was shown by the models which were developed based on beam tests [20]. Therefore, this paper will only analyze the models which seem to provide the best representation of the bending behavior of strengthened RC beams.
Fifteen models, which had been proposed between 1990 and 2007and validated by experimental tests were selected for this
analysis. From a theoretical point of view, the existing models for debonding behavior may be classified into three categories based on their approach, namely: models based on: (a) materials strength, (b) on fracture mechanics and (c) on experimental data fitting. However, in practice, it is difficult to find models purely based on just only one of the mentioned approaches. In fact, many models are a combination of strength of materials and experimen- tal fitting [21–23]. Other models are based on fitting experimental data into empirical equations or used data fitting techniques to supplement or correct the strength of materials or fracture mechanics models, as done in the models by Zhang et al. [28], Wang and Ling (cited in [5]) and Raoof and Hassanen [25]. The Zir- aba model [26] combines the strength model with fracture mechanics approaches. The group of models based on fracture mechanics look at the delamination of FRP sheets from the con- crete substrate when a crack forms and propagates along the inter- face between the two materials. This group includes the Raoff and Zhang model [24], the Wang and Ling model (cited in [5]), Raoff and Hassanen model [25], Ziraba et al. model [26], Wu and Niu model [3], and Casas and Pascual model [27]. Several of these mod- els had been previously studied by Smith and Teng [5] and are ana- lyzed again in this paper using a consistent statistical method that is appropriate for implementation during the reliability-calibration of partial safety factors. The statistical analysis serves to provide a common basis for comparing the various models to the extended database assembled in this study.
Table 3 provides a summary of the principal methods used to predict the end-debonding and intermediate crack induced deb- onding along with the material parameters that these methods re- quire as input. A rough classification of the models into the three groups a–c listed above is provided based on the primary princi- ples used to develop them even though, as mentioned earlier, most theoretical models utilized empirical corrections to modify the equations. It is noted that the classification in Table 3 is different than that used by Smith and Teng [6]. Smith and Teng [6] used a classification where the models are grouped into: shear capacity based models, concrete tooth models and interfacial stress based model. The first group includes the models based on the shear strength of the concrete with no or only partial contribution of the steel shear reinforcement [5,6,21,22]. The concrete tooth mod- els take into account the concept of a cantilevered concrete ‘‘tooth’’ between two adjacent cracks. [5,24,25]. The last group assumes that end debonding occurs due to high interfacial stresses between the FRP and concrete cover [3,26,27]. Additional information on the models analyzed in this paper is provided in this section.
3.1. Oehlers’ model
One of the first models applied to study the debonding of FRP- strengthened RC beams was the model proposed by Oehlers [21] which was originally developed for RC beams strengthened with steel plates. The model is based on the shear force acting at the plate end while taking into account the effect of any coexistent moment. Using the classic ultimate strength analysis method, the flexural capacity of an externally plated reinforced concrete beam can be determined, considering the plate as part of the reinforce- ment. The moment applied to the end of the plate, which provoked the peeling, is given by the following equation:
Mdb;f ¼ ðEc I0;cÞfct
0:901Efrp tfrp ð4Þ
where Mdb,f is the moment capacity of the strengthened section; I0,c is the cracked strengthened section’s moment of inertia trans- formed into equivalent concrete. The value 0.901 is a constant which is applied to obtain a safe characteristic design value.
Table 3 Summary of principal methods used to predict the end-debonding and intermediate crack induced debonding. S.M. = strength materials, F.M. = fracture mechanics, E.F. = experimental data fitting, R.C. = reinforced concrete, Sl = longitudinal reinforcement steel, St = stirrups, FRP = fiber reinforced polymers, Rs = resin.
Model Mechanism criteria Parameter addressed Limitations
R.C. Sl St FRP Rs
Oehlers S.M.–E.F. p p p
1.4 � (d/200) P 1.1 Smith and Teng S.M.
p p p Mdb,end/Mu 6 0.61
Teng and Yao S.M.–E.F. p p p p
b/bfrp 6 3 Jansze et al. S.M.
p p Bmod > 0
Ahmed and van Germert S.M. p p p p
Colotti et al. S.M. p p p p
Raoof and Zhang F.M.–E.F. p p p
Wang and Ling F.M.–E.F. p p p
Raoof and Hassanen I F.M.–E.F. p p p
Raoof and Hassanen II F.M.–E.F. p p p
Ziraba I S.M.–F.M. p p p p
a/h < 3 Ziraba II S.M.–F.M.
p p p p a/h < 3
Wu and Niu F.M. p p p
Casas and Pascual F.M. p p p p
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 495
The Oehlers’ model also uses the shear capacity of the concrete in the RC beam alone Vc, based on the Australian code equation, gi- ven as:
V db;s ¼ V c ¼ ½1:4 �ðd=2000Þ�bd qs f 0 c
� �1=3 ð5Þ where qs = As/bd is the steel tension reinforcement ratio. The mo- ment–shear interaction equation that should be used for checking the adequacy of an FRP-strengthened design is:
Mdb;end Mdb;f
þ V db;end V db;s
6 1:17 ð6Þ
which considers the applied shear and moment at the end of the FRP plate, Mdb,end and Vdb,end.
3.2. Smith and Teng’s model
For the cases when the ratio of the applied moment to the ulti- mate moment capacity Mdb,end/Mu 6 0.67, Smith and Teng [6] pro- posed a safe design equation that considers only the shear force:
V db;end 6 1:5V c ð7Þ
where Vc is the concrete beam’s shear capacity as specified by the design codes.
3.3. Teng and Yao’s model
An empirical predictive model for flexural debonding of a plate end located in a pure bending region, was proposed by Teng and Yao [22,23]. Accordingly, the moment capacity is expressed as:
Mdb;f ¼ 0:488Mu;0
ðaflexaaxialawÞ 1=9 6 Mu;0 ð8Þ
where aflex, aaxial and aw are three dimensionless parameters de- fined respectively by:
aflex ¼ ðEIÞfrp;c �ðEIÞ0;c
ðEIÞ0;c ; aaxial ¼
Efrptfrp Ec d
; aw ¼ b
bfrp ;
b bfrp 6 3
ð9Þ
where (EI)c,frp and (EI)c,0 are the flexural rigidities of the cracked sec- tion with and without a strengthening plate, respectively and Mu,0 is the theoretical ultimate moment of the unplated section which is also the upper bound of the flexural debonding moment Mdb,f. The limitation imposed on the width ratio reflects the limitation of the test data used by Teng and Yao [22,23]. Eq. (8) is a best-fit expression of the results of eighteen tests.
The shear debonding strength is the sum of different values which represent the contributions of the concrete Vc, the strength- ening plate Vfrp, and the internal reinforcement Vs:
V db;s ¼ V c þ V frp þ ev;eV s ð10Þ
where V s ¼ Asv Esv de=sv . ev,e is the strain in the steel shear reinforce- ment, referred to here as the effective strain, and this effective strain may be well below the yield strain of the steel shear rein- forcement at debonding failure.
The best-fit expression for ev,e is given by
ev;e ¼ 10
ðaflexaEatawÞ 1=2
ð11Þ
where
aE ¼ Efrp Ec
; at ¼ tfrp d
� �1;3 ð12Þ
aE represents the elastic moduli ratio and at the ratio between the plate thickness and the effective depth of the section.
As done by Oehlers [21], an interaction between plate end shear and bending has been proposed as follows:
V db;end 0:85V db;s
� �2 þ
Mdb;end 0:85Mdb;f
� �2 ¼ 1:0 ð13Þ
Teng and Yao [22,23] explain that for design purposes, the shear capacity of concrete beams, Vc, to be used in Eq. (10) can be ob- tained from current code specified equations. The contributions of Vfrp are usually small enough to be ignored. These simplifications yield conservative predictions of the debonding load when com- pared to most test results. In their study, three different codes were used to calculate the shear capacity of the concrete, Vc: the British code (BS8110), the Australian code (AS600) and the American code (ACI318).
3.4. Jansze’s model
Another model originally developed for steel plated beams but has been proposed for application to RC beams was developed by Jansze (cited in [5]). The model considers that shear cracking starts in the RC beam, but does not account for the contribution of shear reinforcement. The critical shear force in the RC beam at the plate end that causes debonding Vdb,end is given as a function of the shearing stress, sPES, by:
V db;end ¼ sPESbd ¼ 0:18
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3
d Bmod
3
s 1 þ
ffiffiffiffiffiffiffiffiffi 200
d
r ! ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 100qsf 0c
3 q
bd ð14Þ
496 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
where Bmod is a modified shear span, equal to:
Bmod ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � ffiffiffiffiffiqsp� �2
qs da3
4
s ð15Þ
If Bmod is greater than the actual shear span, B, then the average va- lue of both should be used (Bmod+B)/2. Jansze model (cited in [5]) appears to be invalid for plates that extend all the way to the sup- port as Bmod becomes zero and Eq. (15) predicts that debonding will never take place.
3.5. Ahmed and van Germert’s model
Ahmed and van Germert (cited in [5]) modified Jansze’s model to make it more suitable for use with FRP-plated RC beams by introducing corrections to account for the differences in the FRP and steel material properties. The critical shear force is given as follows:
V db;end ¼ðsPES þ DsmodÞbd ð16Þ
with
Dsmod ¼ sPESbd Ss
Is;c bfrp �
Sfrp Ifrp;c ba
� � þ 6188:5
s � 4:121 bd
� � ð17Þ
s ¼ 0:15776 ffiffiffiffi f 0c
q þ
11:2366qs d B
� � þ 0:9
Asv fsv sb
ð18Þ
where sPES is the same shearing stress defined by Jansze, Sfrp and Ss are the first moments of the FRP plate area, and that of an equiva- lent steel plate about the neutral axis of a cracked plated section transformed to concrete. The equivalent steel plate is one that has the same total tensile capacity and width as that of the FRP plate, but with an equivalent thickness determined assuming that the yield stress of steel is 550 MPa, I,frp,c and Is,c are the moments of iner- tia of a cracked plated section transformed to concrete with a FRP plate and an equivalent steel plate respectively. The increase in shear strength offered by the shear reinforcement is also included as seen in Eq. (14).
3.6. Colotti et al.’s model
Colotti et al. [19] proposed a model based on truss analogy. The actual load-carrying capacity of a plated beam is then determined as the minimum value obtained from four different shear strength expressions corresponding to: (a) plate-debonding failure; (b) shear failure; (c) tension/concrete crushing failure; and (d) plate rupture.
The ultimate load for the bond failure mode:
V db;end ¼ py d / þ a � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð/ þ aÞ2 � 2/b
q� � ; py > 0 ð19Þ
where the terms a, b and / are defined by a = a/d, ratio of shear span to beam effective depth; b = la/d, ratio of plate length in shear to beam effective depth; and / = Uy/py, ratio of bond strength to stirrup strength. The limiting bond strength is given by, Uy ¼ bm 2:77 þ 0:06 f 0c � 20
� � for f 0c > 20 MPa. The effective width
of the plate-adhesive interface, bm, is assumed to be the average of the beam and plate widths such that: bm = (b+bfrp)/2.
Shear failure mode in the concrete web or yielding of the steel stirrups are assumed to occur when:
V ¼ bdfc
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2
p � a
h i þ py da for 0 6
py bfc 6
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2 p
� a 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2 p ð20aÞ
V ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pybd
2fc 1 � py bfc
� �s for
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2 p
� a 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2 p 6
py bfc 6 0:5 ð20bÞ
V ¼ bdfc
2 for
py bfc
> 0:5 ð20cÞ
The failure of the concrete web or the failure of the longitudinal reinforcement occurs when the shearing force is:
V ¼ py d ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2T y pyd þ a2
s � a
" # for
py bfc
>
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2 p
� a 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2 p ð21aÞ
V ¼ bdfc
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4T y bdfc
1 � T y
bdfc
� � þ a2
s � a
" # for
py bfc
6
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2 p
� a 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2 p ; T y 6 0:5bdfc ð21bÞ
V ¼ bdfc
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þa2
p �a
h i for
py bfc 6
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þa2 p
�a 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þa2 p ;T y 6 0:5bdfc ð21cÞ
FRP tensile rupture, failure of the longitudinal steel reinforce- ment or concrete crushing in compression occurs when:
V ¼ Mu a
ð22Þ
where the flexural capacity of the cross section is calculated as specified in ACI440 Guide [11], with ep = ecu (d/c) � ebi 6 kmepu.
The term km, defined to limit the strain in the FRP reinforcement to prevent debonding or delamination, is defined as follows:
km 1 � nEfrp tfrp1428000 for nEfrptfrp1 6 214; 000 N=mm 107000
nEfrp tfrp1 for nEfrptfrp1 > 214; 000 N=mm
( ð23Þ
where n is the number of plies of FRP reinforcement; tfrp1 is the nominal thickness of one ply.
In the numerical investigation, the authors made the following assumptions: d = 0.9 h, m = 0.7, sc = lc/5. Furthermore, the tensile strength of concrete f 0t and the crack spacing size lc, according to Eurocode2 [29] were assumed to be ftc ¼ 1:3x0:; 3f
2=3 c (MPa),
lc = 50 + 0.25k1k2u1/qr, with k1 = 0.8, k2 = 0.5, qr = As/(2.5bd) and u1 is the diameter of longitudinal bars.
3.7. Raoof and Zhang’s model
Zhang et al. [28] and Raoof and Zhang [24] developed a strength model for simply-supported RC beams reinforced by steel plates subject to three or four point bending that also could be used for FRP sheets. They base their model on the shear strength of a single concrete ‘‘tooth’’. To prevent the debonding failure mode, the pro- posed limiting value for the stress should be compared to the stress in the plate directly under a point load. Elastic behavior and no- interaction between adjacent cracks were assumed. The critical point in the concrete ‘‘tooth’’ is assumed to be at the point of con- tact between the concrete and the longitudinal steel reinforce- ment. The tensile stress at this point is represented by:
r ¼ M I
lmin 2
� � ð24Þ
where M = slminbfrpd0 and I = b (lmin) 3/12. Here lmin represents the
minimum crack spacing, s the shear stress at the interface between the concrete and the plate, I the moment of inertia of the tooth, and M the moment at the base of the tooth. Substituting M and I into Eq. (25) and assuming r = fct, the shear stress at the interface between the concrete and the strengthening plate based on a minimum sta- bilized crack spacing can be determined as follows:
smin ¼ fct lmin
6h0 b
bfrp ð25Þ
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 497
The authors assumed the simultaneous failure of all end anchorage teeth at debonding. The minimum width of a crack lmin, termed the minimum stabilized crack spacing, is given by:
lmin ¼ Ac fct
uðRObars þ bfrpÞ ð26Þ
where Ac is the area of concrete in tension, u the strengthening plate-to-concrete average bond strength, RObars the total perimeter of the tension reinforcing bars. It is assumed that u ¼ 0:28
ffiffiffiffiffi fcu
p (in
MPa) and fct ¼ 0:36 ffiffiffiffiffi fcu
p (in MPa). Considering a RC beam reinforced
by a single plate, Ae is twice the distance from the centroid of the tension reinforcement to the base of the RC beam multiplied by the width of the RC beam.
The minimum stress in the strengthening plate rs,min required to cause flexural cracking and failure of a tooth covering the min- imum stabilized crack spacing can then be determined as follows:
rsðminÞ ¼ 0:154 La h1 b
2 ffiffiffiffiffifcup h0bfrptfrpðRObars þ bfrpÞ
ð27Þ
where La is an effective length of the plate for end anchorage, and h1 is the distance from the centroid of the tension reinforcement to the base of the RC beam.
In Zhang et al. [28], the effective length for end anchorage was taken as the length of the plate in the shear span. Raoof and Zhang [24] assumed that the anchorage length is equal to the smaller va- lue between the length given in [28] and la, defined as follows:
la ¼ lminð21 � 0:25lminÞ; lmin 6 72 mm ð28Þ la ¼ 3lmin; lmin > 72 mm ð29Þ
This effective length model was calibrated to match test data of steel plated RC beams that failed by plate end debonding.
Once the stress in the plate is known, the moment that causes the separation of the plate, at the location where the stress is cal- culated, can be obtained using a conventional section analysis with the assumption that plane sections remain plane during bending and taking into account the tensile strength of the concrete. The higher bending moment is used assuming a minimum (lmin) and a maximum (lmax = 2lmin) stabilized crack spacing. If the end of the plate does not reach the shear span zone, the effective length should be obtained from Eq. (28).
3.8. Wang and Ling’s model
Wang and Ling (cited in [5]) modified the previous model [28] to adapt it to match the results for FRP strengthened beams. They modified the definition of the minimum width of a crack, proposed by Raoof and Zang in Eq. (26) by the following expression:
lmin ¼ Ac fct
usRObars þ ufrpbfrp ð30Þ
where us ¼ 0:313 ffiffiffiffi f 0c
p is the average bond strength between the
steel tension reinforcement and the concrete, while ufrp is the aver- age bond shear strength between the FRP and the concrete which was taken as 1.96 MPa.
3.9. Raoof and Hassanen’s models
Raoof and Hassanen [25] tried to improve Zhang et al. model [28] proposing two expressions for the effective anchorage length of the FRP plate. These models will be called model I and model II.
In the first model [25], Eq. (30) is used to calculate the mini- mum stabilized crack spacing. The effective length of the FRP plate for end anchorage is taken to be the smaller of the plate length in
the shear span and the following lengths which were calibrated based on the authors’ experimental test data:
la ¼ lminð24 � 0:5lminÞ; lmin 6 40 mm ð31Þ la ¼ 4lmin; lmin > 40 mm ð32Þ
In Raoof and Hassanen model II [25], ufrp is equal to 0.8 MPa, as defined by Wang and Ling (cited in [5]), while us is equal to 0:28
ffiffiffiffiffi fcu
p , as defined by Zhang model [28]. The effective length of
the FRP plate for end anchorage is calculated as done in the Raoof and Hassanen model I [25], using the new value of FRP to concrete bond strength:
Lp2 ¼ lminð11:6 � 0:17lminÞ; lmin 6 56:5 mm ð33Þ Lp2 ¼ 2lmin; lmin > 56:5 mm ð34Þ
Once the stabilized crack spacing and the effective length of FRP plate for end anchorage are determined, the remainder of the anal- ysis follows the same steps given by Zhang et al.
3.10. Ziraba et al. models
Two debonding strength models were proposed by Ziraba et al. [26] for steel plated RC beams. Model I is used to predict plate end interfacial debonding, while Model II is used for predicting con- crete cover separation.
Model I proposes an expression for the shear capacity of an RC beam, at the plate end, to cause plate end interfacial debonding:
V bd;end ¼ f 0c
CR1
C a1fctð1 þ a2 CR2 tan /Þ
� �4=5 ð35Þ
where
CR1 ¼ 1 þ K a
Efrpbfrptfrp
� �1=2 M0 V 0
" # bfrp tfrp Itrc;frpba
ðdfrp � xtrc;frpÞ; ð36aÞ
CR2 ¼ tfrp K n
4EfrpIfrp
� �1=4 ð36bÞ
while a1 and a2 are empirical multipliers calibrated from numerical studies for RC beams retrofitted with steel plates. C is the coefficient of cohesion and u the angle of internal friction. This is the first known model that takes into account the adhesive layer properties where the shear stiffness Ka and the normal stiffness Kn of the adhe- sive layer are defined as:
K a ¼ Gaba
ta ; K n ¼
Eaba ta
ð37Þ
with Ga being the shear modulus of the adhesive layer respectively. Itrc,frp is the moment of inertia of the cracked plated section trans- formed into FRP, xtrc,frp is the neutral axis depth of this transformed cracked section (distance from the compression face to the neutral axis), Ifrp the second moment of area of the FRP plate alone, dfrp the distance from the compression face of the RC beam to the centroid of the FRP plate, and M0 and V0 the bending moment and shear force respectively at the plate end.
This relationship is subject to the constraint of a/h < 3. The fol- lowing values for a1, a2 and / were specified in [26]: a1 = 35, a1 = 1.1 and / = 28. For the present study C has been taken as 7.15 MPa which is an average of the values given in [26].
In Model II, Ziraba et al. [26] defined the shear beam capacity by modifying the ACI code equation; the contribution of steel rein- forcement to the shear strength, Vs, is multiplied by a coefficient, k, which is empirically derived to account for the stirrup efficiency and is related to the peak interfacial normal stress at the plate end.
V db;end ¼ðV c þ kV sÞ¼ 1=6 ffiffiffiffi f 0c
q þ 100qs
� � bd þ kðAsv fyv dÞ=s ð38Þ
498 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
where Vc and Vs are respectively the contributions of concrete and steel shear reinforcement to the shear capacity of an RC beam. The k value is based on a regression analysis of the test results of fourteen steel plated RC beams which failed by concrete cover separation:
k ¼ 2:4en and n ¼�0:08CR1CR2 � 106 ð39Þ
3.11. Wu and Niu model
Wu and Niu [3] proposed a methodology for predicting the deb- onding failure caused by intermediate flexural cracks in flexural strengthening of RC beams with epoxy-bonded FRP sheets. The validity of the model was verified by comparing to an assembled database. The model based on fracture mechanics principles com- pares the maximum tensile force in the FRP to Pmax which repre-
Table 4 Statistical results of existing models compared to experimental database.
Model End debonding
Regression coefficient
Regression coefficient standard error
Regression standard error
R2
CW Smith and Teng 1.64 0.05 16.32 0.94 Teng and Yao ACI 1.34 0.06 22.74 0.87 Teng and Yao AS600 1.83 0.07 21.67 0.88 Teng and Yao BS 1.55 0.06 22.63 0.87 Jansze 0.55 0.03 24.41 0.85 Ahmed 0.53 0.02 23.60 0.86 Raoof and Zhang 0.90 0.09 41.87 0.55 Wang 0.90 0.08 40.89 0.57 Raoof and Hassanen I 1.05 0.08 36.72 0.66 Raoof and Hassanen II 1.43 0.11 37.67 0.64 Colotti 0.99 0.02 12.01 0.97 Ziraba I 1.44 0.08 7.45 0.95 Ziraba II 0.89 0.06 8.46 0.93 Casas and Pascual 2.18 0.10 5.91 0.97 Casas and Pascual
(with additional data)
1.65 0.06 20.92 0.89
CP Smith and Teng 1.47 0.06 13.57 0.93 Teng and Yao ACI 1.15 0.05 16.09 0.89 Teng and Yao AS600 1.60 0.07 15.30 0.90 Teng and Yao BS 1.31 0.06 15.57 0.90 Jansze 0.66 0.03 16.02 0.89 Ahmed 0.67 0.04 18.89 0.87 Raoof and Zhang 1.31 0.09 22.96 0.78 Wang and Ling 1.29 0.08 21.79 0.80 Raoof and Hassanen I 1.36 0.09 22.28 0.79 Raoof and Hassanen II 1.79 0.12 22.67 0.78 Colotti 1.02 0.06 13.65 0.90 Ziraba I 1.06 0.10 23.51 0.77 Ziraba II 0.77 0.05 17.94 0.86 Casas and Pascual 2.14 0.07 8.94 0.97 Casas and Pascual
(with additional data)
1.99 0.06 10.94 0.95
CW + CP Intermediate debonding
Casas IC 1.76 0.05 2.78 0.98 Casas IC + CasasD 1.08 0.05 8.34 0.96 Casas IC + CasasD (all
data) 1.48 0.03 31.95 0.92
Wu and Niu 0.57 0.03 3.82 0.96 Wu and Niu (all data) 0.37 0.02 39.59 0.86 ACI440.2R Case 1 0.70 0.03 3.63 0.97 ACI440.2R Case 2 0.91 0.03 36.73 0.94 ACI440.2R (all data,
Case 3) 0.77 0.02 34.08 0.90
sents the maximum transferable load, derived from a pull–push or pull–pull shear tests. Pmax can be expressed as follows:
Pmax ¼ bfrp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Gf Efrptfrp
q ð40Þ
where Gf is the interfacial fracture energy consumed during debonding.
Taking into account a cracked FRP-strengthened beam, Pmax represents the maximum stress value which the FRP can transfer at the beam without failing due to intermediate-crack (IC) debond- ing. This value is measured as difference between the FRP tension at maximum moment point and a L0e spacing section.
The equivalent transfer length, L0e is twice of the effective trans- fer length determined from the simple bond tests; it requires to de- velop the maximum transferable FRP tensile stress Pmax, and can be computed as:
Number of observations
Bias Standard deviation
COV Probability distribution
R2 Vmax Vmin
69 1.66 0.45 0.27 Lognormal 0.97 186.00 6.70 90 1.45 0.50 0.34 Normal 0.99 186.00 6.70 90 1.96 0.72 0.37 Lognormal 0.99 186.00 6.70 90 1.57 0.61 0.39 Lognormal 0.99 186.00 6.70 83 0.65 0.32 0.49 Lognormal 0.97 186.00 6.70 83 0.65 0.30 0.46 Lognormal 0.95 186.00 6.70 89 1.42 0.86 0.61 Lognormal 0.95 186.00 6.70 89 1.45 0.87 0.61 Lognormal 0.94 186.00 6.70 89 1.57 1.03 0.66 Lognormal 0.97 186.00 6.70 89 2.29 1.91 0.84 Lognormal 0.97 186.00 6.70 55 0.90 0.21 0.24 Normal 0.96 186.00 6.70 19 1.63 0.52 0.32 Normal 0.96 74.40 13.95 19 1.17 0.21 0.18 Normal 0.95 74.40 13.95 19 2.21 0.46 0.21 Normal 0.96 74.40 13.95 90 1.89 0.57 0.37 Normal 0.96 186.00 6.70
39 1.62 0.44 0.27 Lognormal 0.91 80.10 12.50 59 1.41 0.54 0.38 Normal 0.97 80.10 12.50 59 1.84 0.65 0.35 Lognormal 0.98 80.10 12.50 59 1.44 0.52 0.36 Lognormal 0.98 80.10 12.50 50 0.64 0.28 0.44 Lognormal 0.95 80.10 12.50 50 0.82 0.56 0.69 Lognormal 0.95 80.10 12.50 59 1.68 1.19 0.71 Lognormal 0.96 80.10 12.50 59 1.61 1.17 0.76 Lognormal 0.95 80.10 12.50 59 2.22 1.96 0.88 Lognormal 0.92 80.10 12.50 59 3.14 3.27 1.04 Lognormal 0.92 80.10 12.50 34 1.09 0.44 0.40 Normal 0.91 79.50 12.50 38 2.09 1.32 0.63 Normal 0.95 80.10 12.50 38 1.26 0.52 0.41 Normal 0.91 80.10 12.50 38 2.27 0.54 0.24 Normal 0.97 80.10 12.50 59 2.13 0.54 0.24 Lognormal 0.95 80.10 12.50
20 1.88 0.35 0.18 Lognormal 0.96 34.90 8.51 22 1.80 0.42 0.23 Normal 0.97 135.45 8.51
188 2.23 1.45 0.65 Lognormal 0.96 548.5 6.90
15 0.60 0.19 0.32 Normal 0.93 34.90 10.00 78 0.50 0.23 0.46 Lognormal 0.98 548.5 10.00 13 0.73 0.22 0.29 Lognormal 0.88 34.90 10 68 1.22 0.56 0.45 Normal 0.94 548.5 10
183 0.87 0.48 0.55 Lognormal 0.97 548.5 6.9
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 499
L0e ¼ 2Le ¼ 1:3
ffiffiffiffiffiffiffiffiffiffiffiffiffi Efrptfrp
p f 00;095c
ð41Þ
3.12. Casas and Pascual’s model
Casas and Pascual [27] proposed a new, easy to apply model for the end debonding and the intermediate crack induced debonding of FRP-strengthened concrete beams. Debonding occurs when the nominal average shear stress reaches the allowable stress value smax. Then, the tensile force per unit width in the FRP sheet, Tu, de- pends on the compressive strength of concrete, f 0c , and the effective bond length Le.
T u ¼ smaxLe ¼ 0:996 ffiffiffiffi f 0c
q Le ð42Þ
when the stiffness of the strengthened concrete element is much higher than the FRP stiffness, Le is defined as:
Le ¼
ffiffiffiffiffiffiffi kfrp gb
s ð43Þ
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.5 1
B
S ta
nd ar
d D
ev ia
te
Fig. 2. Plot of Vexp/Van of wet lay-up installations for the Casas and Pa
y = 3.91 R2
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.2 0.4 0 Bi
S ta
nd ar
d D
ev ia
te
Fig. 3. Plot of Vexp/Van of wet lay-up installations for the Casas and Pasc
where kfrp = Efrptfrp is the axial stiffness per unit length of the FRP. gb is the shear joint stiffness of concrete plus adhesive resin, expressed as
gb ¼ gagc
ga þ gc where ga ¼
Ga ta ; gc ¼
Gc tce
ð44Þ
Ga and Gc are the shear modulus of the resin and concrete. Poisson ratios for concrete and resin are taken as 0.50 and 0.38 respectively for the case where the concrete is in the plastic range as explained in [30]. ta is the resin thickness used in the application of the repair and tce is the concrete thickness that can be estimated as:
tce ¼ bfrp þ 50:8 6 h=2 ð45Þ
where bfrp and h are expressed in mm. The failure criteria in the case of beams with two or more
consecutive cracks spaced at a distance of s (s ffi d/2) can be found using an adjusted ultimate capacity expression by applying a coef- ficient b. Then, the ultimate force per unit width in the FRP is:
y = 1.9093x - 4.2167 R2 = 0.9625
1.5 2 2.5 3
ias
scual model on Normal probability scale (19 experimental tests).
38x - 3.0151 = 0.9407
.6 0.8 1 1.2 as
ual model on Lognormal probability scale (19 experimental tests).
500 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
T u ¼ bsmaxLe where b ¼ n1
1 � n2n3 ð46Þ
where the coefficients n1 and n2 are defined by the following functions:
n1 ¼ es=Le � e�s=Le es=Le þ e�s=Le
; n2 ¼ 2
es=Le þ e�s=Le ð47Þ
The simplified model is based on the moment–tension interac- tion M–T curve which relates the moments in the beam and the tension forces in the FRP characterized by the parameter n3 defined as:
n3 ¼ 1 � h k k0
1 � M2 M1
� � ð48Þ
Assuming a bilinear behavior, the M–T curve is characterized by the parameters k and k0 which represent the slope of the linear
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 1
Van
V ex
p (k
N )
Fig. 4. Regression analysis of Teng and Smith model for e
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 Van
V ex
p (k
N )
Fig. 5. Regression analysis of Colotti model for end d
elastic and post-yielding lines, respectively. The value of h was demonstrated to be approximately equal to 2/3. The ratio between the bending moment M2 at a distance d/2 from the section of inter- est and the bending moment at this section M1 is obtained from a linear-elastic analysis.
3.13. ACI 440.2R-08
For sections away from the section where externally bonded FRP terminates, ACI 440.2R-08 [11] indicates that intermediate crack induced debonding can be prevented if the effective strain in the FRP remains below efd, defined as:
efd ¼ 0:41 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f 0c nEfrp tfrp
s 6 0:9efu ð49Þ
where efu is the design rupture strain in the FRP.
00 120 140 160 180 200
(kN)
predicted upper 95% lower 95% prediction upper 95% prediction lower 95%
nd debonding for wet lay-up (69 experimental tests).
100 120 140 160 180 200 (kN)
predicted upper 95% lower 95% prediction upper 95% prediction lower 95%
ebonding for wet lay-up (55 experimental tests).
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120 140 160 180 200 Van (kN)
V ex
p (k
N )
predicted upper 95% lower 95% prediction upper 95% prediction lower 95%
Fig. 6. Regression analysis of Casas and Pascual model for end debonding for wet lay-up (19 experimental tests).
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120 140 160 180 200 Van (kN)
Ve xp
(k N
)
predicted upper 95% lower 95% prediction upper 95% prediction lower 95%
Fig. 7. Regression analysis of Teng and Smith model for end debonding for prepeg (39 experimental tests).
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 501
4. Analysis of end debonding models
In a first step of the analysis of the models, the shear force that led to the debonding of the FRP as obtained from the experimental data base Vexp, is compared to the shear value Van, predicted by each of the models. To be consistent with the way the results of experimental investigations on end debonding are reported, Van is calculated at the end of the beam. On the other hand, for crack induced debonding, Van is calculated in the maximum moment re- gion. The ratio of Vexp/Van is obtained for each applicable test result and the average ratio for each model is defined as the model’s bias. A model’s Coefficient of Variation (COV) is defined as the standard deviation of the ratios divided by the bias. The results for all the models studied in this paper are summarized in Table 4. In addi- tion to finding the mean bias and COV, the ratios for each model are plotted on Normal and Lognormal probability scales to identify which of these two probability distributions can best describe the scatter around the bias. The regression coefficient R2 for the regres- sion analysis performed on the probability scale plot is used as a measure of the goodness of the probability distribution. Thus,
when the R2 approaches 1.0 on the Normal probability plot, the bias is considered to be well represented by the Normal distribution.
In Table 4, the comparison of the results of the end debonding considering only carbon FRP sheets is divided into two groups based on the installation type: (i) carbon wet lay-up (C-W) and (ii) carbon prepeg plates (C-P). The very low number of beams reinforced by glass or aramid FRP sheets does not allow for a realistic analysis of the models. Also, in each case, the number of valid tests that could be used in the comparison was limited for various reasons. In many cases, the models require as input specific detailed information about material properties that were not reported by the experimen- talists. In other cases, the geometric and other conditions under which the models are applicable were not satisfied. These condi- tions and requirements have vastly limited the number of usable experimental test results. For instance, it was found that many tested specimens did not satisfy the flexural strength ratio range for which the Smith and Teng model [6] is applicable. In many cases, the Colotti et al. model [19] predicts a different failure mode than the one observed from test results. Casas and Pascual’s model [27]
502 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
as well as Ziraba’s model [26] base their predictions on the resin’s properties which have been reported by only a few experimental investigators. A large number of tested specimens have extended the FRP sheets all the way to the end supports which meant that these could not be used to verify Janze’s model nor that of Ahmed and van Gemert The number of valid test results for each model is provided in Table 4. For wet lay-up installations that failed by end debonding, the maximum number of usable tests is as high as 90 for the Teng and Yao model and as low as 19 for the Casas and Pasc- ual or the Ziraba models. For prepeg sheet installations that failed by end debonding, the number of usable tests ranged from 59 down to 38 for the Casas and Pascual and the Ziraba models.
The bias values and COV’s in Table 4 show large differences in the results between the models. Most models were developed to provide conservative envelopes to the experimental results for the specific objective of using the models for design purposes. These models show various levels of conservatism expressed in terms of bias ratios ranging from just above 1.0 (1.09) for the Col- otti et al. model [19] applied to CP sheets up to 3.1 for the Raoof and Hassanen Model II [25] applied to the CP sheets. On the other
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 1
Van
V ex
p (k
N )
Fig. 8. Regression analysis of Colotti model for end
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 1
Van
V ex
p (k
N )
Fig. 9. Regression analysis of Casas and Pascual model fo
hand, the models of Jansze and Ahmed and van Germert overpre- dict the experimental results for both the wet lay-up and prepeg installations by a considerable margin, yielding bias values varying between 0.64 and 0.82. This makes these two models less likely to be useful for application as predictive models or design models un- less augmented by high safety factors.
The model by Colotti et al. seems to provide on the average re- sults that are the closest to those from the tests with an average bias of 0.90 for wet layups and a bias of 1.09 for prepeg beams respectively. This gives an indication that Colotti is the closest to being used as a predictive model. It is noted however that in many instances, this model, which was developed to not only estimate the load at failure but also the failure mode, did not predict the cor- rect failure mode even when the predicted load at failure was close to the reported experimental value. Applying the model to the database, it is observed that only in 56.7% of the cases was the ana- lytically predicted failure mode consistent with the observed mode.
Several models, particularly, those of Ahmed, Raoof and Hassa- nen, Colotti and Ziraba I, show considerable differences exceeding
00 120 140 160 180 200
(kN)
predicted upper 95% lower 95% prediction upper 95% prediction lower 95%
debonding for prepeg (34 experimental tests).
00 120 140 160 180 200
(kN)
predicted upper 95% lower 95% prediction upper 95% prediction lower 95%
r end debonding for prepeg (38 experimental tests).
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 503
10% between the biases obtained for the wet lay-up specimens and the prepeg specimens. Although differences in the variability in the results may be expected due to the difficulty of controlling the re- sin’s thickness in the different installations procedures, none of the models distinguishes between installations methods. Therefore, good models should provide similar biases independent of the installation method, even though the standard deviations may be different to reflect the variability in the resin thickness associated with the different installation methods.
The standard deviation and the Coefficient of Variation (COV) provide a means to evaluate the consistency of the models. The models showing very high variability, with standard deviations on the ratios of Vexp/Van exceeding 1.0, include those of Raoof and Zhang [24], Raoof and Hassanen [25], and Ziraba I [26]. A normal- ized measure of the variability in the model accuracy is expressed in terms of the Coefficient of Variation. Table 4 shows that most models give very high COV’s emphasizing the difficulties associ- ated with predicting the debonding strength of FRP-strengthened
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 1 Va
V ex
p (k
N )
Fig. 10. Regression analysis of Wu and Niu mo
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 1 Van
V ex
p (k
N )
Fig. 11. Regression analysis of Casas and Pascual
concrete beams. In particular, the models by Raoof and Hasannen, Raoof and Zhang, Ziraba, Jansze and Ahmed and van Germert are associated with COV’s exceeding 40%.
The models showing the lowest COV values are those of Smith and Teng for both CP and wet lay-up installations and Casas and Pascual tested with the 19 data points that provided all the neces- sary input parameters as well as that of Colotti for wet lay-up.
The plots of Vexp/Van on Normal and Lognormal scale help asso- ciate the variability of each model with a probability distribution type. As an example, Fig. 2 shows the plot of the ratios obtained for the Casas and Pascual model for wet lay-up on Normal proba- bility scale. When the data points lie on a straight line, they give an indication that the data follow a Normal probability distribu- tion. The regression coefficient of determination R2 of the linear fit on this normal probability scale provides a measure of how well the probability distribution will predict future outcomes. Also, the regression equation provides an approach to obtain the mean and standard deviation of the Normal distribution that best describe
00 120 140 160 180 200
n (kN)
predicted upper 95% lower 95% prediction upper 95% prediction lower 95%
del for intermediate debonding (15 tests).
00 120 140 160 180 200 (kN)
predicted upper 95% lower 95% prediction upper 95% prediction lower 95%
model for intermediate debonding (20 tests).
504 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
the variation in the data. Specifically, the mean of the Normal dis- tribution is obtained by setting the ordinate ‘‘y’’ of the regression equation equal to zero and solving for x. In this example of the Casas and Pascual model, the mean ratio or the bias is obtained as 2.2 which is the same value obtained from the point estimation procedure of the bias. The standard deviation is obtained by setting the ordinate ‘‘y = 1’’ and solving for x which in this case is the sum of the mean plus the standard deviation. In this case, the standard deviation is found to be 0.52 which is higher than the 0.46 value obtained from the point estimates as shown in Table 4, but still reasonably close given the relatively large variability in the data. Thus, the Normal probability plot with a coefficient of determina- tion R2 = 0.96 indicates that 96% of the variation in the data can be explained by describing the ratio of Vexp/Van as a random variable that follows a Normal probability distribution with a mean = 2.21 and a standard deviation = 0.52 or a COV = 24%. The plot on the Lognormal scale (Fig. 3) shows a lower R2 = 0.94 value indicating that the Normal distribution gives a better description of the variability of the data.
-40
-20
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 1 Van
V ex
p (k
N )
Fig. 12. Regression analysis of Casas and Pascual model for interm
Regression Analys
-100
0
100
200
300
400
500
600
0 100 200 300
Van
V ex
p (k
N )
Fig. 13. Regression analysis of ACI model for intermediate debond
Because the number of valid tests for the Casas and Pascual model was relatively small with only 19 valid tests, more tests were fitted to this model by assuming that the properties of the resin are known and equal to the average properties from the 19 tests for which such data is available. This approach is similar to the one used by Smith and Teng [6]. In this case, the thickness of the resin is assumed to be ta = 2 mm for C-P and 0.42 mm for C-W. The modulus of elasticity for the resin is Ea = 8500 MPa. This increased the number of valid tests to 90 for C-W tests and to 59 for prepeg test beams. Applying the mod- el to all 90 C-W data points, the mean of the bias is slightly re- duced to 1.89 from the original 2.21, while the standard deviation increases from the original 0.46 to 0.57. The range of the tests however is widely increased to range from 186 kN to 6.70 kN. The same coefficient of determination R2 is reported. For the C-P beams, using 59 data points instead of the original 38 data for which all the information is provided the bias changes from 2.27 to 2.13 while the COV remains practically the same at 24%.
00 120 140 160 180 200 (kN)
predicted upper 95% lower 95% prediction upper 95% prediction lower 95%
ediate debonding including full scale beam tests (22 tests).
is of ACI440.2R IC (183 data)
400 500 600 700
(kN)
predicted upper 95% lower 95% prediction upper 95% prediction lower 95%
ing including the complete data set (183 experimental tests).
Table A.1 Database of beams failed by end debonding. Ahmed et al. (cited in [6]), Ahmed et al. (cited in [19]), Arduini et al. (cited in [19]), Beber et al. (cited in [6]), Benjeddou et al. [32].
Beam b (mm)
h (mm)
d (mm)
d0
(mm) a (mm)
B (mm)
L (mm)
f 0c (MPa)
Es (GPa)
fys (MPa)
As (mm 2) Reo
(tension) E0s (GPa)
f 0y (MPa)
A0s (mm2)
Ahmed et al. (1999) AF3 125 225 193 32 100 500 1500 46.0 185 568 101 2–8 195 553 57 CF2-1 125 225 193 32 100 500 1500 46.0 185 568 129 2–8, 1–6 195 553 57 CF3-1 125 225 193 32 100 500 1500 46.0 185 568 151 3–8 195 553 57 CF4-1 125 225 193 32 100 500 1500 46.0 183 586 207 2–10, 1–8 195 553 57 DF.2 125 225 193 32 50 500 1500 46.0 185 568 151 3–8 195 553 57 DF.3 125 225 193 32 50 500 1500 46.0 185 568 151 3–8 195 553 57 DF.4 125 225 193 32 50 500 1500 46.0 185 568 151 3–8 195 553 57
Ahmed et al. (2000) AF.2 125 225 196 25 200 500 – 41.0 200 568 101 �8 200 568 57 AF.2-1 125 225 196 25 150 500 – 41.0 200 568 101 �8 200 568 57 AF.4 125 225 196 25 50 500 – 41.0 200 568 101 �8 200 568 57 DF.l 125 225 196 25 50 500 – 42.0 200 568 151 �8 200 568 57 BF.2-1 125 225 196 25 50 500 – 41.0 200 568 101 �8 200 568 57 BF.3-1 125 225 196 25 50 500 – 41.0 200 568 101 �8 200 568 57 EF.1-1 125 225 196 25 50 500 – 46.0 200 568 151 �8 200 568 57 EF.3-1 125 225 196 25 50 500 – 38.0 200 568 151 �8 200 568 57 EF.4-1 125 225 196 25 50 500 – 33.0 200 568 151 �8 200 568 57 FF.2-3 125 225 196 25 70 700 – 39.5 200 568 151 �8 200 568 57
Arduini et al. (1997) A4 200 200 163 30 150 700 – 33.0 200 540 308 �14 200 540 308 A5 200 200 163 30 150 700 – 33.0 200 540 308 �14 200 540 308 B2 300 400 349.5 44 100 1100 – 30.0 200 340 398 �13 200 340 266 B3 300 400 349.5 44 100 1100 – 30.0 200 340 398 �13 200 340 266
Beber et al. (1999) VR5 120 250 214 34 75 783 2350 33.6 200 565 157 2–10 200 738 57 VR6 120 250 214 34 75 783 2350 33.6 200 565 157 2–10 200 738 57 VR7 120 250 214 34 75 783 2350 33.6 200 565 157 2–10 200 738 57 VR8 120 250 214 34 75 783 2350 33.6 200 565 157 2–10 200 738 57 VR9 120 250 214 34 75 783 2350 33.6 200 565 157 2–10 200 738 57 VR10 120 250 214 34 75 783 2350 33.6 200 565 157 2–10 200 738 57
Benjeddou et al. (2007) RBI 120 150 120 30 50 600 1800 21.0 200 400 157 2–10 200 400 157 RB2 120 150 120 30 50 600 1800 21.0 200 400 157 2–10 200 400 157 RB3 120 150 120 30 50 600 1800 21.0 200 400 157 2–10 200 400 157 RB4 120 150 120 30 50 600 1800 21.0 200 400 157 2–10 200 400 157 RB5 120 150 120 30 50 600 1800 21.0 200 400 157 2–10 200 400 157 RB6 120 150 120 30 50 600 1800 38.0 200 400 157 2–10 200 400 157
Beam Eyv (GPa)
fyv (MPa)
Asv (mm2)
s (mm) Ea (MPa)
ta (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfrp (mm)
bfip (mm)
vexp (kN)
Ahmed et al. (1999) AF3 195 553 57 71 7200 – C-W 240.00 3500 0.334 75 48.30 CF2-1 195 553 57 71 7200 – C-W 240.00 3500 0.334 75 52.40 CF3-1 195 553 57 71 7200 – C-W 240.00 3500 0.334 75 59.10 CF4-1 195 553 57 71 7200 – C-W 240.00 3500 0.334 75 70.10 DF.2 195 553 57 100 7200 – C-W 240.00 3500 0.334 75 60.30 DF.3 195 553 57 100 7200 – C-W 240.00 3500 0.501 75 60.00 DF.4 195 553 57 100 7200 – C-W 240.00 3500 0.668 75 62.80
Ahmed et al. (2000) AF.2 200 553 57 71 – – C-W 240.00 3500 0.3 75 41.50 AF.2- 1
200 553 57 71 – – C-W 240.00 3500 0.3 75 42.90
AF.4 200 553 57 71 – – C-W 240.00 3500 0.3 75 55.50 DF.l 200 553 57 100 – – C-W 240.00 3500 0.2 75 59.00 BF.2- 1
200 553 57 167 – – C-W 240.00 3500 0.3 75 45.00
BF.3- 1
200 553 57 100 – – C-W 240.00 3500 0.3 75 52.00
EF.1-1 200 553 57 100 – – C-W 240.00 3500 0.3 75 65.90 EF.3-1 200 553 57 100 – – C-W 240.00 3500 0.3 75 59.50 EF.4-1 200 553 57 100 – – C-W 240.00 3500 0.3 75 60.30 FF.2-3 200 553 57 100 – – C-W 240.00 3500 0.5 75 53.00
Arduini et al. (1997) A4 200 540 57 150 – – C-W 167.00 2906 1.3 150 55.00 A5 200 540 57 150 – – C-W 167.00 2906 2.6 150 45.00 B2 200 340 101 100 – – C-W 400.00 3000 0.2 300 85.00 B3 200 340 101 100 – – C-W 400.00 3000 0.5 300 114.00
Beber et al. (1999) VR5 200 738 57 110 8500 – C-P 230.00 3400 0.22 120 51.10 VR6 200 738 57 110 8500 – C-P 230.00 3400 0.22 120 50.30 VR7 200 738 57 110 8500 – C-P 230.00 3400 0.22 120 62.10 VR8 200 738 57 110 8500 – C-P 230.00 3400 0.22 120 62.00 VR9 200 738 57 110 8500 – C-P 230.00 3400 0.22 120 64.80 VR10 200 738 57 110 8500 – C-P 230.00 3400 0.22 120 68.50
(continued on next page)
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 505
Table A.1 (continued)
Beam Eyv (GPa)
fyv (MPa)
Asv (mm2)
s (mm) Ea (MPa)
ta (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfrp (mm)
bfip (mm)
vexp (kN)
Benjeddou et al. (2007)
RBI 200 235 28 10 12800 – C-P 165.00 2800 1.2 100 20.06 RB2 200 235 28 10 12800 – C-P 165.00 2800 1.2 100 18.83 RB3 200 235 28 10 12800 – C-P 165.00 2800 1.2 100 16.05 RB4 200 235 28 10 12800 – C-P 165.00 2800 1.2 100 15.38 RB5 200 235 28 10 12800 – C-P 165.00 2800 1.2 50 15.05 RB6 200 235 28 10 12800 – C-P 165.00 2800 1.2 100 18.69
506 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
Table 4 also lists which of the Normal or Lognormal probability distributions can best describe the variability in each of the models based on the R2 values which are also provided in the table. For example, the table shows that the variability in the results of the model of Teng and Yao [22] applied using the ACI equations for the shear capacity of concrete beams can very well be described using a Normal probability distribution whereas the application of the Colotti model [19] for prepeg installations shows the least good fit on either the Normal or Lognormal plots. It should be noted that during the plotting on the probability scale when occa- sionally a single data point would clearly shift the linear regres- sion, this point was designated as an outlier and removed from the linear regression analysis.
In summary, the results of this first set of statistical analyses can be used to relate the actual load that is expected to lead to the debonding of an FRP strengthened concrete beam to the analyt- ically predicted load using an equation of the form:
V actual ¼ kV analytical ð50Þ
where the analytically predicted load that causes failure Van is cal- culated using as input the basic geometric and material parameters relevant to the model being used, k is a random variable with a mean equal to the bias and a COV as given in Table 4 for each model and installation type and k would follow the appropriate probability distribution for the model being used. It should be noted that the variability in k as expressed in the COV values of Table 4 does not account for the variability in the input material and geometric parameters in actual installations where these parameters are not carefully controlled.
The use of Eq. (50) to represent the bias and the variability in the analytical model imply that the same bias is applicable for the whole range of loads and beam sizes and that the tests were performed on beams having geometries that adequately represent the geometries on which the models will apply. Unfortunately, as observed in the data presented in Appendices A and B, the range of beam sizes for the test specimens is relatively small and is not necessarily representative of the dimensions expected in engineer- ing applications such as for bridges. Furthermore, most of the tests were performed on very small scale beams and few of the tests are performed on medium or full scale beams. The value of k that is ob- tained from the average of the beams tested will be mostly influ- enced by the large number of small scale tests as compared to the fewer medium or full scale tests. A good representation of k, must be obtained when the tested beam sizes are adequately dis- tributed over the applicable dimension range. An approach is used next in an attempt to account for the fewer number of medium scale tests. The approach consists of applying a regression analysis rather than the point estimation method described above to study the relationship between experimental results and predicted ana- lytical results.
A second set of statistical analyses performed as part of this study consists of plotting the experimental results expressed as Vexp versus the model prediction Van and performing a linear regression fit of the data. The best linear expression that describes
the relationship between Van and Vexp is thus obtained. The regres- sion is executed such that the line goes through the origin (0, 0). The analysis of the regression residuals consists of a plot of the residuals (differences between Vexpand Van) to verify their distribu- tion around zero and the calculation of the residuals’ standard deviation. In addition, the standard error of the regression’s coeffi- cient is also calculated. Figs. 4–9 provide examples of the regres- sion analysis performed for a number of the models. Specifically, the figures illustrate the regression results for the wet lay-up and prepeg installations of beams that were compared to the Smith and Teng [6], Colotti [19] and Casas and Pascual model [27] for the end debonding of FRP. These results are selected for illustration because they showed relatively good relationship between the experimental and analytical as expressed in regression coefficients of determination R2 which are higher than 0.90 for both types of installation. The results of the analyses for the plotted data and all the other models are also summarized in Table 4.
The regression analysis shows how well the relation between the experimental results and the analytical results can be repre- sented by an equation of the form:
V exp ¼ aV an þ e ð51Þ
where the regression error e follows a Normal probability distribu- tion with an average value of zero and a standard deviation re. The coefficient a or the slope of the linear relationship can also be con- sidered to be a random variable with a standard deviation, ra. Table 4 gives a listing of the regression coefficient, a, the regression coef- ficient standard error, ra, the regression error, re and regression coefficient of determination R2. These data can be used to obtain the 95% confidence intervals on the regression equation as well as the 95% prediction intervals which are respectively shown in red and blue dashed lines in Figs. 4–9 for the cases with relatively high R2 values.
The results summarized in Table 4 indicate that all the slopes of the best fit line, ‘‘a’’, have very narrow bounds with standard errors of less than 0.10. On the other hand, large variations in the overall standard error expressed as re are observed where re varies be- tween a low of re = 5.91 for the Casas and Pascual model [27] for wet lay-up installations and re > 35 for the Wang and Ling (cited in [5]), Raoof and Hassanen [25] and Zhang models [28]. These same models have also very low regression coefficients R2.
In most cases, the value of the regression slope of Eq. (51) is quite similar to the bias obtained from Eq. (50) highlighting the robustness of the statistical analysis process for the given range of beam sizes and beam capacities. The cases where the difference between a and the bias k is significant are those for which the regression analysis produced low R2 values indicating that the var- iability in Vexp is not well described by the expression of Eq. (50) or for those in which the regression equation of Eq. (51) was driven by a few points at high values of Van and where the residuals are not evenly distributed around zero. This problem may be explained by the scaling effect since most of the available test results have been performed on small scale laboratory specimens. More tests
Table A.2 Database of beams failed by end debonding. Breña and Macri [33], David et al. (cited in [6]), Esfahani et al. [34], Fanning and Kelly [35], Garden et al. (cited in [6]).
Beam b (mm)
h (mm)
d (mm)
d0
(mm) a (mm)
B (mm)
L (mm)
f 0c (MPa)
Es (GPa)
fys (MPa)
As (mm2)
Reo (tension)
E0s (GPa)
f 0y (MPa)
A0s (mm2)
Breña and Macri (2004)
Al-I 102 102 89 13 25 330 812 42.2 200 435 71 1–9.5 200 435 71 Al-II 102 102 89 13 25 330 812 42.2 200 435 142 2–9.5 200 435 142 A2-I 102 102 89 13 25 330 812 42.2 200 435 71 1–9.5 200 435 71 A2-II 102 102 89 13 25 330 812 42.2 200 435 142 2–9.5 200 435 142 A3-I 102 102 89 13 25 330 812 53.3 200 435 71 1–9.5 200 435 71 A3-II 102 102 89 13 25 330 812 53.3 200 435 142 2–9.5 200 435 142 A4-I 102 102 89 13 25 330 812 53.3 200 435 71 1–9.5 200 435 71 A4-II 102 102 89 13 25 330 812 53.3 200 435 142 2–9.5 200 435 142 A5-I 102 102 89 13 25 330 812 53.3 200 435 71 1–9.5 200 435 71 A5-II 102 102 89 13 25 330 812 53.3 200 435 142 2–9.5 200 435 142 A6-I 102 102 89 13 25 330 812 47.7 200 435 71 1–9.5 200 435 71
David et al. (1999) P2 150 300 257 – 200 933 2800 40.0 200 500 308 2–14 – – – P3 150 300 257 – 200 933 2800 40.0 200 500 308 2–14 – – – P4 150 300 257 – 200 933 2800 40.0 200 500 308 2–14 – – – P5 150 300 257 – 200 933 2800 40.0 200 500 308 2–14 – – –
Esfahani et al. (2007)
B3-12D- 2L15
150 200 166 25 100 600 1600 25.2 200 400 226 2–12 200 365 157
B3-12D- 3L15
150 200 166 25 100 600 1600 25.2 200 400 226 2–12 200 365 157
Fanning and Kelly (2000)
F5 155 240 209 31 385 1100 2800 66.4 204 460 339 3–12 204 460 226 F6 155 240 209 31 385 1100 2800 66.4 204 460 339 3–12 204 460 226 F7 155 240 209 31 462 1100 2800 66.4 204 460 339 3–12 204 460 226 F8 155 240 209 31 462 1100 2800 66.4 204 460 339 3–12 204 460 226 F9 155 240 209 31 550 1100 2800 66.4 204 460 339 3–12 204 460 226 F10 155 240 209 31 550 1100 2800 66.4 204 460 339 3–12 204 460 226
Garden et al. (1997)
1Au 100 100 84 16 20 300 900 47.3 215 350 85 3–6 215 350 57 2Au 100 100 84 16 20 340 900 47.3 215 350 85 3–6 215 350 57 3Au 100 100 84 16 20 400 900 47.3 215 350 85 3–6 215 350 57 1Bu 100 100 84 16 20 300 900 47.3 215 350 85 3–6 215 350 57 2Bu 100 100 84 16 20 340 900 47.3 215 350 85 3–6 215 350 57 3Bu 100 100 84 16 20 400 900 47.3 215 350 85 3–6 215 350 57 1B2u 100 100 84 16 20 300 900 47.3 215 350 85 3–6 215 350 57
Beam Eyv (GPa)
fyv (MPa)
Asv (mm2)
s (mm)
Ea (MPa)
ta (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfrp (mm)
bfip (mm)
vexp (kN)
Breña and Macri (2004)
A1-I 200 420 28 51 3035 0.4 C-W 230.00 3790 0.165 51 13.95 A1-II 200 420 28 51 3035 0.4 C-W 230.00 3790 0.165 51 20.10 A2-I 200 420 28 51 3035 0.8 C-W 230.00 3790 0.33 51 15.70 A2-II 200 420 28 51 3035 0.8 C-W 230.00 3790 0.33 51 22.25 A3-I 200 420 28 51 3035 1.2 C-W 230.00 3790 0.495 51 19.50 A3-II 200 420 28 51 3035 1.2 C-W 230.00 3790 0.495 51 24.00 A4-I 200 420 28 51 3035 0.8 C-W 230.00 3790 0.33 76 18.40 A4-II 200 420 28 51 3035 0.8 C-W 230.00 3790 0.33 76 26.25 A5-I 200 420 28 51 3035 0.4 C-W 230.00 3790 0.165 102 17.60 A5-II 200 420 28 51 3035 0.4 C-W 230.00 3790 0.165 102 24.45 A6-I 200 420 28 51 4480 1.6 C-P 155.00 2400 1.19 51 17.40
David et al. (1999) P2 200 500 57 140 8500 1.0 C-P 150.00 2400 1.2 100 68.00 P3 200 500 57 140 8500 1.0 C-P 150.00 2400 1.2 100 71.10 P4 200 500 57 140 8500 1.0 C-P 150.00 2400 2.4 100 78.00 P5 200 500 57 140 8500 1.0 C-P 150.00 2400 2.4 100 79.50
Esfahani et al. (2007) B3-12D- 2L15
200 350 50 80 – – C-W 237.00 2845 0.176 150 35.47
B3-12D- 3L15
200 350 50 80 – – C-W 237.00 2845 0.176 150 37.22
Fanning and Kelly (2000)
F5 198 250 28 125 – – C-P 155.00 2400 1.2 120 50.00 F6 198 250 28 125 – – C-P 155.00 2400 1.2 120 51.50 F7 198 250 28 125 – – C-P 155.00 2400 1.2 120 48.75 F8 198 250 28 125 – – C-P 155.00 2400 1.2 120 32.00 F9 198 250 28 125 – – C-P 155.00 2400 1.2 120 31.00 F10 198 250 28 125 – – C-P 155.00 2400 1.2 120 41.00
Garden et al. (1997) 1Au 215 350 14 51 11560 2.0 C-P 111.00 1273 0.5 90 19.80 2Au 215 350 14 51 11560 2.0 C-P 111.00 1273 0.5 90 19.30 3Au 215 350 14 51 11560 2.0 C-P 111.00 1273 0.5 90 19.50 1Bu 215 350 14 51 11560 2.0 C-P 111.00 1273 0.7 65 18.30 2Bu 215 350 14 51 11560 2.0 C-P 111.00 1273 0.7 65 17.00 3Bu 215 350 14 51 11560 2.0 C-P 111.00 1273 0.7 65 17.30 1B2u 215 350 14 51 11560 2.0 C-P 111.00 1273 0.7 65 18.20
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 507
Table A.3 Database of beams failed by end debonding. Garden et al. (cited in [6]), Garden et al. [36], Grace and Singh [37], Hau et al. (cited in [6]), Juvandes et al. (cited in [22]), Matthys [38], Nguyen et al. [39], Pham and Al-Mahaidi [40].
Beam b (mm)
h (mm)
d (mm)
d0
(mm) a (mm)
B (mm)
L (mm)
f 0c (MPa)
Es (GPa)
fys (MPa)
As (mm2)
Reo (tension)
E0s (GPa)
f 0y (MPa)
A0s (mm2)
Garden et al. (1997) 1Cu 100 100 84 16 20 300 900 47.3 215 350 85 3–6 215 350 57 2Cu 100 100 84 16 20 340 900 47.3 215 350 85 3–6 215 350 57 3Cu 100 100 84 16 20 400 900 47.3 215 350 85 3–6 215 350 57
Garden et al. (1998) B1u, 1.0
100 100 84 16 20 300 900 43.2 215 350 85 3–6 215 350 57
B2u, 1.0
100 100 84 16 20 300 900 43.2 215 350 85 3–6 215 350 57
B1u, 2.3
130 230 206 25 20 844 2200 37.6 220 556 236 3–10 220 556 101
B3U1.0 100 100 87 10 20 340 – 44.8 215 350 85 �6 215 350 57 B4U1.0 100 100 87 10 20 400 – 44.8 215 350 85 �6 215 350 57 B5U1.0 100 100 87 10 20 400 – 44.8 215 350 85 �6 215 350 57 B1U4.5 145 230 214 15 40 1525 – 39.0 220 556 236 �12 220 556 111
Grace and Singh (2005)
Bb1 152 254 228.6 25.4 152.5 864 2540 31.0 200 414 397 3–15.9 200 414 142 Bb2 152 254 228.6 25.4 152.5 864 2540 31.0 200 414 397 3–15.9 200 414 142 Bb3 152 254 228.6 25.4 152.5 864 2540 31.0 200 414 397 3–15.9 200 414 142 Bb4 152 254 228.6 25.4 152.5 864 2540 31.0 200 414 397 3–15.9 200 414 142
Hau et al. (1999) 2 150 250 205 45 350 500 1500 35.4 231 537 157 2–10 231 537 157 4 150 250 205 45 200 500 1500 36.2 231 537 157 2–10 231 537 157 5 150 250 205 45 50 500 1500 40.6 231 537 157 2–10 231 537 157 6 150 250 205 45 200 500 1500 39.9 231 537 157 2–10 231 537 157 7 150 250 205 45 350 500 1500 37.6 231 537 157 2–10 231 537 157
Juvandes et al. (1998)
B7 75 150 131 22 10 650 1500 37.0 200 190 14 2–3 200 470 151 B.11 75 150 128.5 20 200 650 – 36.0 200 190 14 �3 200 190 151
Matthys (2000) BF2 200 450 409 – 70 1250 – 36.5 200 590 804 �16 200 590 – BF3 200 450 409 – 70 1250 – 34.9 200 590 804 �16 200 590 – BF4 200 450 409 – 70 1250 – 30.8 200 590 804 �16 200 590 – BF5 200 450 409 – 70 1250 – 37.4 200 590 804 �16 200 590 – BF8 200 450 409 – 71 1251 – 39.4 200 590 402 �16 200 590 – BF9 200 450 409 – 71 1251 – 33.7 200 590 402 �16 200 590 –
Nguyen et al. (2001) A950 120 150 120 34 190 440 1330 25.7 200 384 236 3–10 200 400 57 A1100 120 150 120 34 115 440 1330 25.7 200 384 236 3–10 200 400 57 A1150 120 150 120 34 90 440 1330 25.7 200 384 236 3–10 200 400 57 B2 120 150 120 34 115 440 1330 25.7 200 384 236 3–10 200 400 57
Pham and Al- Mahaidi (2006)
E1a 140 260 220 40 150 700 2300 53.7 205 551 339 3–12 205 551 226
Beam Eyv (GPa)
fyv (MPa)
Asv (mm2)
s (mm)
Ea (MPa)
ta (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfrp (mm)
bfip (mm)
vexp (kN)
Garden et al. (1997) 1Cu 215 350 14 51 11560 2.0 C-P 111.00 1273 1 45 16.00 2Cu 215 350 14 51 11560 2.0 C-P 111.00 1273 1 45 17.80 3Cu 215 350 14 51 11560 2.0 C-P 111.00 1273 1.0 45 15.40
Garden et al. (1998) Blu, 1.0 215 350 14 51 8600 2.0 C-P 111.00 1414 0.82 67 18.30 B2u, 1.0
215 350 14 51 8600 2.0 C-P 111.00 1414 0.82 67 16.00
Blu, 2.3 215 350 57 150 8600 2.0 C-P 115.00 1284 1.28 90 50.20 B3U1.0 215 350 14 50 – – C-W 111.00 1414 0.8 67 17.00 B4U1.0 215 350 14 50 – – C-W 111.00 1414 0.8 67 17.30 B5U1.0 215 350 14 50 – – C-W 111.00 1414 0.8 67 17.30 B1U4.5 220 350 57 150 – – C-W 115.00 1284 1.3 90 30.00
Grace and Singh (2005) Bb1 200 414 142 102 2140 – C-W 138.00 2070 1.2 152 68.30 Bb2 200 414 142 102 2140 – C-W 138.00 2070 1.2 152 68.30 Bb3 200 414 142 102 2140 – C-P 227.00 2758 0.4 152 66.75 Bb4 200 414 142 102 2140 – C-P 227.00 2758 0.4 152 66.75
Hau et al. (1999) 2 231 537 157 100 3260 0.4 G-W 19.72 259 1.32 150 53.00 4 231 537 157 100 3260 0.4 G-W 19.72 259 1.3 150 65.40 5 231 537 157 100 3260 0.4 G-W 19.72 259 2.6 150 79.40 6 231 537 157 100 3260 0.4 G-W 19.72 259 1.32 150 63.10 7 231 537 157 100 3260 0.4 G-W 19.72 259 1.32 150 53.90
Juvandes et al. (1998) B7 200 190 14 60 10250 2.5 C-P 150.00 2400 1.2 50 12.50 B.11 200 190 14 60 – – C-W 150.00 2400 1.2 50 6.70
Matthys (2000) BF2 200 560 101 100 – – C-W 159.00 3200 1.2 100 185.00 BF3 200 560 101 100 – – C-W 159.00 3200 1.2 100 186.00 BF4 200 560 101 100 – – C-W 159.00 3200 1.2 100 184.20 BF5 200 560 101 100 – – C-W 159.00 3200 1.2 100 177.00 BF8 200 560 101 100 – – C-W 159.00 3200 1.2 100 111.30 BF9 200 560 101 100 – – C-W 159.00 3200 0.2 100 95.80
508 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
Table A.3 (continued)
Beam Eyv (GPa)
fyv (MPa)
Asv (mm2)
s (mm)
Ea (MPa)
ta (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfrp (mm)
bfip (mm)
vexp (kN)
Nguyen et al. (2001) A950 200 400 57 50 12800 1.5 C-P 181.00 3140 1.2 80 28.10 A1100 200 400 57 50 12800 1.5 C-P 181.00 3140 1.2 80 28.70 A1150 200 400 57 50 12800 1.5 C-P 181.00 3140 1.2 80 29.50 B2 200 400 57 50 12800 1.5 C-P 181.00 3140 1.2 80 65.10
Pham and Al-Mahaidi (2006)
E1a 204 334 79 125 3500 – C-W 209.00 3900 1.056 100 35.35
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 509
need to be executed on full scale beams to verify the consistency of the current models for all pertinent scale levels.
The plots shown in Figs. 4–9 are for the models that showed the highest R2 values. These models also happen to have among the lowest regression standard errors. The figures show the plots of the Vexp versus Van as well as the regression line. Also, shown in the figure are the upper and lower 95% confidence intervals of the regression line as well as the upper and lower 95% prediction intervals. The plots are shown at the same scale varying between 0 kN and 200 kN to highlight the limitations in the applicable ranges for each of the models. For example while the Smith and Teng [6] and the Colotti [19] models show a wider range for the upper and lower 95% intervals than the Casas and Pascual model [27] for wet lay-up tests analyzed with the 19 data for which all the information is provided. The limited range for which the appli- cability of the Casas model can be tested is readily noticed. Increas- ing the number of valid tests for the Casas and Pascual model from 19 to 90 by using average values for the resin material increased the range of valid test results to 186 kN. This reduced the slope of the regression line from the original 2.18 to 1.65. The standard error however increases from the original 5.91 to 20.92. It should however be noted that some of the increase in the error may reflect the deviation of the true resin properties from those assumed by taking average values.
For the prepeg tests, the range of applicability of all models is approximately the same with a high shear force of 80.10 kN. The data plots in Fig. 9 show the regression results of the Casas and Pascual model. If the number of valid tests is increased from 38 to 59 by using the average properties of the resin, a smaller drop in the slope from the original 2.14 to 1.99 for the Casas and Pascual model is observed for the C-P samples as compared to the C-W samples. These results serve to further emphasize the importance of performing large scale tests for obtaining higher confidence lev- els in our ability to predict the strength of FRP strengthened beams and have more confidence in the design of such strengthening schemes.
5. Analysis of IC induced debonding strength models
The results shown in Table 4 for the intermediate crack-induced debonding case compare the analytical results from the Casas and Pascual Model [27], the Wu and Niu model [3] and the ACI model [11] for different subgroups of the experimental database. Differ- ent numbers of specimens are used in each comparison because the different models require different input that may not have been made available in the published test results. For example, the Casas and Pascual model requires the properties of the adhe- sive layer as input, whereas they are not required for the other models. Only 24 tests in Appendix B out of which 20 are reinforced concrete beams strengthened with CFRP, reported the values of the resin’s thickness. The second comparison made for the Casas and Pascual model adds two large scale experiments of two beams that had been previously damaged under static loading and then
strengthened using FRP sheets as reported by Casas et al. [27,31]. The third comparison of the Casas and Pascual model includes the whole set of experimental data including the tests for which no resin properties were available. In these cases, as done for the end debonding when necessary, a resin thickness ta is assumed to be equal to 2 mm for pultruded installations and according to Eqs. (2) and (3) for wet lay-up installations. The modulus of elastic- ity, Ea, is set equal to the average of the available values (7389 MPa). A parametric analysis has shown that the final results are not very sensitive to changes in this assumed value as demon- strated by Ceci [20]. For example, if Ea is changed to 3000 MPa the values of Van, increase by a maximum of +7.0%. When Ea is set at 12,000 MPa, the values of Van decrease by about 2.2%. Due to the low number of tests performed on beams with wet lay-up installa- tions, the analysis of intermediate crack induced debonding does not distinguish between the method of installation and the data in- cludes prepeg as well as wet lay-up installations.
Wu and Niu model is based on a fracture mechanics approach to study if the crack would progress along the interface between the FRP and the concrete. The model does not require input on the re- sin characteristics. This model considers the possibility that the beam fails due to either concrete crushing or FRP rupture. In 5 of the 20 tests considered, the model predicted the wrong failure mode (3 FRP rupture and 2 concrete crushing). For this reason, only 15 of the 20 beams for which all the properties are provided are compared for the Wu and Niu model in the IC group of Table 4. Subsequently, all the experimental data for which the Wu and Niu predicted the correct failure mode were included in the analysis.
Similarly, the ACI method does not require the resin’s properties and it only requires as input the FRP properties and the concrete strength. IC debonding occurs before concrete crushing which for design purposes, and according to ACI, is assumed to take place when the maximum concrete strain ecu reaches 0.003. However, it is well known that in actual situations concrete may exceed this nominal design strain value. Therefore, three cases are considered for the evaluation of the ACI model. Case 1 compares the ACI equa- tions to experimental results where the maximum strain in the concrete remains below 0.003 and for which all the resin proper- ties are known. Thirteen specimens satisfied these requirements. This Case 1 is checked to compare the ACI results to those of the Casas and Pascual model even though the ACI equations do not re- quire the resin properties as input. Case 2 performs the statistical analysis for all the 68 specimens where the concrete strain, accord- ing to ACI equations, remains below 0.003. Case 3 performs the statistical analysis for 183 specimens for which the concrete strain may have exceeded the 0.003 design limit, yet the actual test fail- ure was reported to be caused by IC debonding rather than concrete crushing.
The results of the statistical analysis summarized in Table 4 show that the Wu and Niu model [3] vastly over-predicts the fail- ure load. This is reflected by a point estimation of the bias k and a regression slope, a, significantly less than 1.0. The regression anal- ysis results for the Wu and Niu model [3] are shown in Fig. 10. The
Table A.4 Database of beams failed by end debonding. Pham and Al-Mahaidi [40], Quantrill et al. (cited in [6]), Rahimi and Hutchinson [10], Ritchie et al. [41], Ross et al. [9].
Beam b (mm)
h (mm)
d (mm)
d0
(mm) a (mm)
B (mm)
L (mm)
f 0c (MPa)
Es (GPa)
fys (MPa)
As (mm2)
Reo (tension)
E0s (GPa)
f 0y (MPa)
A0s (mm2)
Pham and Al-Mahaidi (2006)
E1b 140 260 220 40 150 700 2300 53.7 205 551 339 3–12 205 551 226 E2a 140 260 220 40 350 700 2300 53.7 205 551 339 3–12 205 551 226 E2b 140 260 220 40 350 700 2300 53.7 205 551 339 3–12 205 551 226 E3a 140 260 220 40 150 700 2300 53.7 205 551 339 3–12 205 551 226 E3b 140 260 220 40 150 700 2300 53.7 205 551 339 3–12 205 551 226 E4a 140 260 220 40 150 700 2300 53.7 205 551 339 3–12 205 551 226 E4b 140 260 220 40 150 700 2300 53.7 205 551 339 3–12 205 551 226 E5a 140 260 220 40 150 700 2300 53.7 205 551 339 3–12 205 551 226 E5b 140 260 220 40 150 700 2300 53.7 205 551 339 3–12 205 551 226 E3b2 140 260 220 40 150 700 2300 53.7 205 551 226 2–12 205 551 226
Quantrill el al. (1996) B2 100 100 84 16 20 300 900 42.4 215 350 85 3–6 215 350 57 B3 100 100 84 16 20 300 900 42.4 215 350 85 3–6 210 350 57 B4 100 100 84 16 20 300 900 42.4 215 350 85 3–6 215 350 57 B6 100 100 84 16 20 300 900 42.4 215 350 85 3–6 215 350 57
Rahimi and Hutchinson (2001)
A4 200 150 120 30 85 750 2100 41.5 210 575 157 2–10 210 575 101 A5 200 150 120 30 85 750 2100 41.5 210 575 157 2–10 210 575 101 A6 200 150 120 30 85 750 2100 41.5 210 575 157 2–10 210 575 101 A7 200 150 120 30 85 750 2100 41.5 210 575 157 2–10 210 575 101 A8 200 150 120 30 85 750 2100 41.5 210 575 157 2–10 210 575 101 A9 200 150 120 30 85 750 2100 41.5 210 575 157 2–10 210 575 101 A10 200 150 120 30 85 750 2100 41.5 210 575 157 2–10 210 575 101 A11 200 150 120 30 85 750 2100 41.5 210 575 157 2–10 210 575 101
Ritchie et al. (1991) C 152 305 251 – 203 914 2438 39.8 200 414 253 2–12.7 – – – D 152 305 251 – 203 914 2438 39.8 200 414 253 2–12.7 – – – G 152 305 251 – 0 914 2438 43.0 200 414 253 2–12.7 – – – I 152 305 251 – 203 914 2438 39.8 200 414 253 2–12.7 – – – M 152 305 251 – 0 914 2438 43.0 200 414 253 2–12.7 – – –
Ross et al. (1999) IB 200 200 152 48 1 914 2742 54.8 200 410 143 2–9.5 200 410 143 1C 200 200 152 48 1 914 2742 54.8 200 410 143 2–9.5 200 410 143 2B 200 200 152 48 1 914 2742 54.8 200 410 253 2–12.7 200 410 143 2C 200 200 152 48 1 914 2742 54.8 200 410 253 2–12.7 200 410 143 2D 200 200 152 48 1 914 2742 54.8 200 410 253 2–12.7 200 410 143
Beam Eyv (GPa)
fyv (MPa)
Asv (mm2)
s (mm)
Ea (MPa)
ta (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfrp (mm)
bfip (mm)
vexp (kN)
Pham and Al-Mahaidi (2006)
E1b 204 334 79 125 3500 – C-W 209.00 3900 1.056 100 37.30 E2a 204 334 79 125 3500 – C-W 209.00 3900 1.056 100 25.70 E2b 204 334 79 125 3500 – C-W 209.00 3900 1.056 100 26.70 E3a 204 334 79 125 3500 – C-W 209.00 3900 1.056 100 33.00 E3b 204 334 79 125 3500 – C-W 209.00 3900 1.056 100 32.60 E4a 204 334 79 125 3500 – C-W 209.00 3900 1.056 100 39.50 E4b 204 334 79 125 3500 – C-W 209.00 3900 1.056 100 30.60 E5a 204 334 79 125 3500 – C-W 209.00 3900 1.584 100 31.65 E5b 204 334 79 125 3500 – C-W 209.00 3900 1.584 100 31.60 E3b2 204 334 79 125 3500 – C-W 209.00 3900 1.056 100 30.00
Quantrill el al. (1996) B2 215 350 14 50 11560 2.0 G-P 49.00 1078 1.2 80 17.00 B3 215 350 14 50 11560 2.0 G-P 49.00 1078 1.2 30 12.30 B4 215 350 14 50 11560 2.0 G-P 49.00 1078 1.6 60 17.50 B6 215 350 14 50 11560 2.0 C-P 118.50 987 1.2 80 20.40
Rahimi and Hutchinson (2001)
A4 210 575 28 150 7000 2.0 C-W 127.00 1532 0.8 150 30.95 A5 210 575 28 150 7000 2.0 C-W 127.00 1532 0.8 150 31.60 A6 210 575 28 150 7000 2.0 C-W 127.00 1532 1.2 150 29.70 A7 210 575 28 150 7000 2.0 C-W 127.00 1532 1.2 150 35.30 A8 210 575 28 150 7000 2.0 C-W 127.00 1532 0.8 150 32.60 A9 210 575 28 150 7000 2.0 C-W 127.00 1532 0.8 150 31.95 A10 210 575 28 150 7000 2.0 C-W 127.00 1532 0.8 150 33.75 A11 210 575 28 150 7000 2.0 C-W 127.00 1532 0.8 150 34.70
Ritchie et al. (1991) C 200 414 99 102 8500 2.0 G-P 11.72 161 4.76 152 55.40 D 200 414 99 102 8500 2.0 G-P 11.72 161 4.76 151 59.60 G 200 414 99 102 8500 2.0 G-P 10.34 184 4.19 152 62.90 I 200 414 99 102 8500 2.0 C/G-
P 27.58 319 4.06 150 50.60
M 200 414 99 102 8500 2.0 C-P 117.91 1489 1.27 152 72.10
Ross et al. (1999) IB 200 410 143 102 8500 2.0 C-P 138.00 2206 0.5 200 40.10 1C 200 410 143 102 8500 2.0 C-P 138.00 2206 0.5 200 35.60 2B 200 410 143 102 8500 2.0 C-P 138.00 2206 0.5 200 49.00 2C 200 410 143 102 8500 2.0 C-P 138.00 2206 0.5 200 35.60 2D 200 410 143 102 8500 2.0 C-P 138.00 2206 0.5 200 40.10
510 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
Table A.5 Database of beams failed by end debonding. Ross et al. [9], Saadatmanesh and Ehsani [42], Sharif et al. [43], Spadea et al. [44], Tan et al. (cited in [22]), Täljsten et al. [45], Teng and Yao [23], Triantafillou and Plevris [16].
Beam b (mm)
h (mm)
d (mm)
d0
(mm) a (mm)
B (mm)
L (mm)
f 0c (MPa)
Es (GPa)
fys (MPa)
As (mm2)
Reo (tension)
E0s (GPa)
f 0y (MPa)
A0s (mm2)
Ross et al. (1999) 3B 200 200 152 48 1 914 2742 54.8 200 410 396 2–15.9 200 410 143 4B 200 200 150.5 40 0 914 – 54.8 200 410 567 �19 200 410 142 5B 200 200 149 40 0 914 – 54.8 200 410 774 �22 200 410 142 6B 200 200 147 40 0 914 – 54.8 200 410 1019 �26 200 410 142 3C 200 200 152 48 1 914 2742 54.8 200 410 396 2–15.9 200 410 143 3D 200 200 152 48 1 914 2742 54.8 200 410 396 2–15.9 200 410 143
Saadatmanesh and Ehsani (1991)
B 205 455 400 55 155 1983 4575 35.0 200 456 1013 2–25.4 200 456 253
Sharif et al. (1994) P2 150 150 114 36 75 393 1180 37.7 200 450 157 2–10 200 450 57 P3 150 150 114 36 75 393 1180 37.7 200 450 157 2–10 200 450 57
Spadea et al. (1998) A1.1 140 300 262 30 50 1800 – 24.9 200 435 402 �16 200 435 402 A3.1 140 300 262 30 50 1800 – 24.9 200 435 402 �16 200 435 402
Tan et al. (1999) A00 100 150 124 21 – 600 – 28.6 200 500 157 �10 200 500 57 A15 100 150 124 22 – 600 – 31.4 200 500 157 �11 200 500 57 A25 100 150 124 23 – 600 – 29.7 200 500 157 �12 200 500 57 A40 100 150 124 24 – 600 – 31.4 200 500 157 �13 200 500 57 A60 100 150 124 25 – 600 – 28.6 200 500 157 �14 200 500 57 A75 100 150 124 26 – 600 – 28.5 200 500 157 �15 200 500 57 A90 100 150 124 27 – 600 – 30.1 200 500 157 �16 200 500 57
Täljsten (1997) SB1 200 300 252 48 150 1300 3600 51.2 200 527 402 2–16 200 527 402 SB2 200 300 252 48 200 1300 3600 52.0 200 527 402 2–16 200 527 402 SB3 200 300 252 48 300 1300 3600 52.0 200 527 402 2–16 200 527 402 MB1 200 300 252 48 150 1300 3600 56.0 200 527 402 2–16 200 527 402 HB1 200 300 252 48 150 1300 3600 56.0 200 527 402 2–16 200 527 402 FBI 200 300 252 48 150 1300 3600 51.2 200 527 402 2–16 200 527 402
Teng and Yao (2007) CS 150.2 252.7 221.7 31 50 500 1500 25.5 199 536 157 2–10 199 536 157 CS-L3 151.1 253 222 31 50 500 1500 27.3 199 536 157 2–10 199 536 157 CS- W100
150.6 254 218.5 35.5 50 500 1500 31.4 199 536 157 2–10 199 536 157
CP 151.1 252.8 222.8 30 50 500 1500 30.7 199 536 157 2–10 199 536 157 CS- C10
151.1 252.7 240.7 12 50 500 1500 22.7 199 536 157 2–10 199 536 157
Triantafillou and Plevris (1992)
4 76 127 111 16 75 305 1220 44.7 200 517 33 2–4.6 – – – 5 76 127 111 16 75 305 1220 44.7 200 517 33 2–4.6 – – – 6 76 127 111 16 75 305 1220 44.7 200 517 33 2–4.6 – – –
Beam Eyv (GPa)
fyv (MPa)
Asv (mm2)
s (mm)
Ea (MPa)
ta (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfrp (mm)
bfip (mm)
vexp (kN)
Ross et al. (1999) 3B 200 410 143 102 8500 2.0 C-P 138.00 2206 0.5 200 54.50 4B 200 410 142 102 – – C-W 138.00 2206 0.5 200 53.80 5B 200 410 142 102 – – C-W 138.00 2206 0.5 200 73.40 6B 200 410 142 102 – – C-W 138.00 2206 0.5 200 84.50 3C 200 410 143 102 8500 2.0 C-P 138.00 2206 0.5 200 54.10 3D 200 410 143 102 8500 2.0 C-P 138.00 2206 0.5 200 54.30
Saadatmanesh and Ehsani (1991)
B 200 456 253 150 8500 1.5 G-P 37.23 400 6.0 152 125.00
Sharif et al. (1994) P2 200 450 28 60 – 1.0 G-W 14.90 170 2 100 34.00 P3 200 450 28 60 – 1.0 G-W 14.90 170 3 100 33.00
Spadea et al. (1998) A1.1 200 435 57 150 – – C-W 152.00 2400 1.2 80 43.40 A3.1 200 435 25 150 – – C-W 152.00 2400 1.2 80 37.40
Tan et al. (1999) A00 200 500 57 75 – – C-W 230.00 3400 0.2 100 27.50 A15 200 500 57 75 – – C-W 230.00 3400 0.2 100 24.70 A25 200 500 57 75 – – C-W 230.00 3400 0.2 100 24.30 A40 200 500 57 75 – – C-W 230.00 3400 0.2 100 24.70 A60 200 500 57 75 – – C-W 230.00 3400 0.2 100 26.00 A75 200 500 57 75 – – C-W 230.00 3400 0.2 100 21.90 A90 200 500 57 75 – – C-W 230.00 3400 0.2 100 19.80
Taljsten (1997) SB1 200 527 157 75 8500 2.1 C-P 155.00 2400 1.4 120 71.40 SB2 200 527 157 75 8500 2.4 C-P 155.00 2400 1.4 120 75.50 SB3 200 527 157 75 8500 3.0 C-P 155.00 2400 1.4 120 73.90 MB1 200 527 157 75 8500 2.4 C-P 210.00 2000 1.4 120 79.60 HB1 200 527 157 75 8500 2.1 C-P 300.00 1400 1.4 100 80.10 FBI 200 527 157 75 8500 0.4 C-W 95.00 1800 2.4 150 74.40
Teng and Yao (2007) CS 199 536 157 100 – 2.0 C-W 256.00 4114 1.74 148 81.50 CS-L3 199 536 157 100 – 2.0 C-W 256.00 4114 2.63 148 78.50
(continued on next page)
A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 511
Table A.5 (continued)
Beam Eyv (GPa)
fyv (MPa)
Asv (mm2)
s (mm)
Ea (MPa)
ta (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfrp (mm)
bfip (mm)
vexp (kN)
CS-W100 199 536 157 100 – 2.0 C-W 256.00 4114 1.95 100 80.80 CP 199 536 157 100 – 2.0 C-P 165.00 2800 1.2 148 76.00 CS-C10 199 536 157 100 – 2.0 C-W 256.00 4114 1.86 148 99.40
Triantafillou and Plevris (1992)
4 200 517 17 40 – – C-W 186.00 1450 0.7 63 14.78 5 200 517 17 40 – – C-W 186.00 1450 0.7 63 15.25 6 200 517 17 40 – – C-W 186.00 1450 0.9 63 13.95
512 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
results of the Casas and Pascual model [27] for the original 20 beam tests are shown in Fig. 11. The results of the Casas and Pascual model [27] show a point estimated bias value of 1.88 and a slope for the regression line of 1.76 which although slightly different are nevertheless within a close range. However, both Figs. 10 and 11 highlight the low range of values for which the Wu and Niu [3] as well as the Casas and Pascual models [27] were tested when only the beams with known resin properties were analyzed. In order to increase the range, two additional tests obtained from [27,31] have been added to the database. The inclusion of these two additional tests into the results of the Intermediate debonding database labeled Casas IC + Casas D in Table 4, show how the inclu- sion of a few large scale tests will alter the results of the regression analysis. As a matter of fact as noted in Table 4, the point estima- tion of the bias changes very little from 1.88 to 1.80 when the two large scale tests are added. These values are similar to the regres- sion coefficient of 1.76 obtained for the original data set. On the other hand, the lack of sufficient test data along the whole range of application has meant that the point estimation of the bias be- comes inconsistent with the regression fit of Eq. (50) when the additional tests are included. In this case, the regression line slope of 1.08 is significantly different from the point estimated bias. The reasons for this discrepancy are illustrated in Fig. 12 that shows how the large number of data points in the lower load ranges con- trols the point estimation statistics, while the regression analysis provides what seems to be a more balanced evaluation of the rela- tionship between Vexp and Van in the whole range of the tests. It should be noted that the addition of the two large scale tests have led to a higher regression standard error re of 8.34 as compared to the original standard error of 2.78. More large scale tests are needed in order to further verify the relationship between the pre- dicted values and experimental test results. Significant differences are observed in the bias and the regression coefficients as well as in the COV’s and regression errors when the data for which no resin properties are provided are included with the assumed resin prop- erties. These differences are due to both the increase in the data- base as well as the assumptions on the resin properties.
Table A.6 Database of beams failed by end debonding. Triantafillou and Plevris [16], Tumialan et al.
Beam b (mm)
h (mm)
d (mm)
d0
(mm) a (mm)
B (mm)
L (
Triantafillou and Plevris (1992)
7 76 127 111 16 75 305 1 8 76 127 111 16 75 305 1
Tumialan et al. (1999) A3 150 300 250 – – 1065 2 A8 150 300 250 – – 1065 2 C2 150 300 250 – – 1065 2
Beam Eyv (GPa)
fyv (MPa)
Asv (mm2)
s (mm)
Ea (M
Triantafillou and Plevris (1992)
7 200 517 17 40 – 8 200 517 17 40 –
Tumialan et al. (1999) A3 207 427 143 125 20 A8 207 427 143 125 20 C2 207 427 143 250 20
The inclusion of the additional experimental data for the analy- sis of the Wu and Niu model gives a lower bias value which changes from 0.60 to 0.50 increasing the gap between the model results and the experimental results. This difference is only due to the increase in the database and is not related to the resin prop- erties since the Wu and Niu model does not require the resin prop- erties as input.
The results of the ACI440.2R model demonstrate the importance of having a large database that extends to the whole range of prac- tical beam dimensions. The results show that when applied as in- tended for only the cases where concrete strain remains below 0.003 (Case 2), the ACI model shows a bias of 1.22 and a COV 0.45. While a bias above 1.0 indicates that on the average the ACI equation is conservative, the high COV of 45% would indicate that many beams will fail at lower loads than anticipated by the ACI equations. This is further confirmed when looking at the regression coefficient for Case 2 which falls to 0.91 with a regression error of 36.73. The high COV and regression error are practically similar to those of the Casas and Pascual model although in the latter case, the required resin properties have to be assumed while no such properties are needed for the ACI model. When all the data are con- sidered including those for which the concrete strain exceeds the nominal limit of 0.003 (Case 3) the value of the ACI bias drops back to 0.87 and the regression coefficient is 0.77 which are both signif- icantly lower than 1.0.
The large differences between the regression coefficient and the bias between Cases 2 and 3, reflect the fact that the regression analysis puts some additional weighting on the few large scale tests as compared to the bias which is an average value that may be more influenced by the many tests on small scale specimens. This phenomenon may be visualized in the plot of Fig. 13.
One reason for the inconsistencies between the predicted load and the experimental failure load may be due to the fact that the Wu and Niu and the ACI models were calibrated based on tests per- formed on prisms rather than on beam tests. The use of the prism tests means that these two models are applicable for type-1 IC deb- onding, where there are no other cracks between the crack where
(cited in [6]).
mm) f 0c (MPa)
Es (GPa)
fys (MPa)
As (mm2)
Reo (tension)
E0s (GPa)
f 0y (MPa)
A0s (mm2)
220 44.7 200 517 33 2–4.6 – – – 220 44.7 200 517 33 2–4.6 – – –
130 51.7 207 427 792 4–15.9 – – – 130 51.7 207 427 792 4–15.9 – – – 130 51.7 207 427 792 4–15.9 – – –
Pa) ta (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfrp (mm)
bfip (mm)
vexp (kN)
– C-W 186.00 1450 0.9 63 12.80 – C-W 186.00 1450 1.9 64 18.67
00 – C-W 23.00 3400 0.495 150 86.10 00 – C-W 23.00 3400 0.99 75 98.20 00 – C-W 23.00 3400 0.495 150 79.30
Table B.1 Database of beams failed by intermediate crack induced debonding. Type of test: f.p.b.t. = four point bending test; c.b.t. = cantilever beam test; 3.p.b.t = three point bending test. Bonacci and Maalej [46], Garden et al. [36], Rahimi and Hutchinson [10], Saadatmesh and Ehsani [42], Triantafillou and Plevris [16], Yao et al. [47].
b (mm)
h (mm)
a (mm)
B (mm)
L (mm)
d (mm)
d0
(mm) f 0c (MPa)
Es (GPa)
fvs (MPa)
As (mm)
E0s (GPa)
f 0y (MPa)
A0s (mm)
ta (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfip (mm)
bfrp (mm)
Vexp (kN)
Type of test
Bonacci and Maalej (2000)
B2 270 400 101 1300 3650 341 54 22.6 201 484 900 199 507 142 C-W 230.00 3400 0.165 250 148 f.p.b.t
Garden et al. (1998) C4u, 1.0
100 100 632 587 587 84 16 51.2 215 350 85 215 350 57 2.0 C-P 111.00 1414 0.82 67 15.43 t.p.b.t.
C5u, 1.0
100 100 817 772 772 84 16 51.2 215 350 85 215 350 57 2.0 C-P 111.00 1414 0.82 67 11.33 t.p.b.t.
Al 150 300 0 1065 2130 250 – 51.7 207 427 792 207 – – C-W 230.00 3400 0.165 150 72.8 t.p.b.t. A2 150 300 0 1065 2130 250 – 51.7 207 427 792 207 – – C-W 230.00 3400 0.33 150 84.9 t.p.b.t. A7 150 300 0 1065 2130 250 – 51.7 207 427 792 207 – – C-W 230.00 3400 0.33 75 86.1 t.p.b.t. Cl 150 300 0 1065 2130 250 – 51.7 207 427 792 207 – – C-W 230.00 3400 0.165 150 77.2 t.p.b.t. B3u, 1.0
100 100 20 340 900 84 16 43.2 215 350 85 215 350 57 2.0 C-P 111.00 1414 0.82 67 17 f.p.b.t.
B4u, 1.0
100 100 20 400 900 84 16 43.2 215 350 85 215 350 57 2.0 C-P 111.00 1414 0.82 67 17.25 f.p.b.t.
B5u, 1.0
100 100 20 400 900 84 16 43.2 215 350 85 215 350 57 2.0 C-P 111.00 1414 0.82 67 17.3 f.p.b.t.
Blu, 4.5
145 230 40 1525 4400 205 25 37.6 220 556 226 220 556 101 2.0 C-P 115.00 1284 1.28 90 30 f.p.b.t.
Rahiml and Hutchinson (2001)
B3 200 150 85 750 2100 120 30 49.2 210 460 157 210 460 157 2.0 C-P 127.00 1532 0.4 150 27.6 f.p.b.t. B4 200 150 85 750 2100 120 30 49.2 210 460 157 210 460 157 2.0 C-P 127.00 1532 0.4 150 26.3 f.p.b.t. B5 200 150 85 750 2100 120 30 49.2 210 460 157 210 460 157 2.0 C-P 127.00 1532 1.2 150 34.9 f.p.b.t. B6 200 150 85 750 2100 120 30 49.2 210 460 157 210 460 157 2.0 C-P 127.00 1532 1.2 150 34.8 f.p.b.t. B7 200 150 85 750 2100 120 30 49.2 210 460 157 210 460 157 2.0 G-P 36.00 1074 1.8 150 29.6 f.p.b.t. B8 200 150 85 750 2100 120 30 49.2 210 460 157 210 460 157 2.0 G-P 36.00 1074 1.8 150 30.8 f.p.b.t.
Saadatmanesh and Ehsani (1991)
E 205 455 155 1983 4575 400 55 35.0 200 200 456 253 1.5 G-P 37.23 400 6 152 32.5 f.p.b.t.
Triantaflllou and Plevris (1992)
4 76 127 75 458 1220 111 – 44.7 200 517 33 200 – – 2.0 C-P 186.00 1450 0.65 63.2 14.8 f.p.b.t. 5 76 127 75 458 1220 111 – 44.7 200 517 33 200 – – 2.0 C-P 186.00 1450 0.65 63.2 15.3 f.p.b.t. 6 76 127 75 458 1220 111 – 44.7 200 517 33 200 – – 2.0 C-P 186.00 1450 0.9 63.3 14 f.p.b.t. 7 76 127 75 458 1220 111 – 44.7 200 517 33 200 – – 2.0 C-P 186.00 1450 0.9 63.3 12.8 f.p.b.t. 8 76 127 75 458 1220 111 – 44.7 200 517 33 200 – – 2.0 C-P 186.00 1450 1.9 63.9 18.7 f.p.b.t.
Yao et al. (2002) CP1 301.5 150.5 100 1000 1100 117.4 – 27.0 208 343 314 208 – – 1.0 C-P 165.00 2800 1.2 50 19.95 c.b.t. CP2 303.6 151.9 100 1000 1100 111.3 – 37.7 208 343 314 208 – – 1.0 C-P 165.00 2800 1.2 50 17.58 c.b.t. CP3 302.7 150 100 1000 1100 108.2 – 12.6 208 343 157 208 – – 1.0 C-P 165.00 2800 1.2 50 13.31 c.b.t. CP5 304 149 100 1000 1100 117.4 – 25.6 210 355 157 210 – – 1.0 C-P 165.00 2800 1.2 50 10 c.b.t. CS1 303 150.8 100 1000 1100 115.3 – 21.4 208 343 157 208 – – 0.5 C-W 271.00 3720 0.165 50 8.51 c.b.t. GS1 302 151.2 100 1000 1100 117.9 – 22.6 208 343 157 208 – – 0.3 G-W 20.50 269 1.27 89.7 10 c.b.t.
A .M
. C
eci et
a l./C
o n
stru ctio
n a
n d
B u
ild in
g M
a teria
ls 2
7 (2
0 1
2 )
4 9
0 –
5 2
0 5
1 3
Table B.2 Database of beams failed by intermediate crack induced debonding. Type of test: f.p.b.t. = four point bending test; c.b.t. = cantilever beam test; 3.p.b.t = three point bending test. Beber et al. (as cited in [3]), Benjamin (as cited in [3]), Bonacci and Maalej [46], Chan et al. (as cited in [3]), Chan and Li (as cited in [3]), Delaney (as cited in [3]), Esfahani et al. [34], Gao et al. [48], Kishi et al. (as cited in [3]).
b (mm)
h (mm)
a (mm)
B (mm)
L (mm)
d (mm)
d0
(mm) f 0c (MPa)
Es (GPa)
fvs (MPa)
As (mm)
E0s (GPa)
f 0y (MPa)
A0s (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfip (mm)
bfrp (mm)
Vexp (kN)
Type of test
Beber et al. (1999) VR5 120 250 75 783 2349 214 34 33.6 200 565 157 200 565 57 C- 230.0 3400 0.44 120 51.1 f.p.b.t. VR6 120 250 75 783 2349 214 34 33.6 200 565 157 200 565 57 C- 230.0 3400 0.44 120 50.3 f.p.b.t. VR7 120 250 75 783 2349 214 34 33.6 200 565 157 200 565 57 C- 230.0 3400 0.77 120 62.1 f.p.b.t. VR8 120 250 75 783 2349 214 34 33.6 200 565 157 200 565 57 C- 230.0 3400 0.77 120 62 f.p.b.t. VR9 120 250 75 783 2349 214 34 33.6 200 565 157 200 565 57 C- 230.0 3400 1.1 120 64.8 f.p.b.t. VR10 120 250 75 783 2349 214 34 33.6 200 565 157 200 565 57 C- 230.0 3400 1.1 120 68.5 f.p.b.t.
Benjamin (2005) Li 152 254 – 2269 4537 229 25 23.3 200 429 398 200 429 157 C- 155.1 2792 1.4 25 39.9 3.p.b.t. HI 152 254 – 2269 4537 229 25 23.3 200 429 398 200 429 157 C- 155.1 2792 1.4 25 37.7 3.p.b.t. L2 152 254 – 2269 4537 229 25 23.3 200 429 398 200 429 157 C- 155.1 2792 1.4 51 44.3 3.p.b.t. L2x1 152 254 – 2269 4537 229 25 23.3 200 429 398 200 429 157 C- 155.1 2792 1.4 51 45.5 3.p.b.t. H2 152 254 – 2269 4537 229 25 23.3 200 429 398 200 429 157 C- 155.1 2792 1.4 51 43.5 3.p.b.t. H2x1 152 254 – 2269 4537 229 25 23.3 200 429 398 200 429 157 C- 155.1 2792 1.4 51 45.1 3.p.b.t. L4 152 254 – 2269 4537 229 25 23.3 200 429 398 200 429 157 C- 155.1 2792 1.4 102 51.8 3.p.b.t. H4 152 254 – 2269 4537 229 25 23.3 200 429 398 200 429 157 C- 155.1 2792 1.4 102 49.2 3.p.b.t.
Bonacci and Maalej (2000)
B2 270 400 101 1300 3650 350.2 44.8 22.6 201 485 900 201 485 143 C- 230.0 3400 0.3 250 148 f.p.b.t.
Chan et al. (2001) B2 250 470 50 1600 4600 430 40 42.4 200 505 628 200 505 402 C- 181.0 3180 1.2 150 142.5 f.p.b.t. B3 250 470 50 1600 4600 430 40 42.4 200 505 943 200 505 402 C- 181.0 3180 1.2 150 176 f.p.b.t. B6 250 470 50 1600 4600 430 40 42.4 200 505 628 200 505 402 C- 181.0 3180 1.2 150 129 f.p.b.t. B8 250 470 50 1600 4600 430 40 42.4 200 505 1257 200 505 402 C- 181.0 3180 1.2 150 220 f.p.b.t.
Chan and Li (2000) S6-50-0 330 100 – 850 2500 76 – 53.4 200 677 113 200 – – C- 165.0 2940.0 1.2 50 14.9 f.p.b.t. S8-50-0 330 100 – 850 2500 76 – 53.4 200 653 201 200 – – C- 165.0 2940.0 1.2 50 17.9 f.p.b.t. S8-50- 0F
330 100 – 850 2500 76 – 53.4 200 653 201 200 – – C- 165.0 2940.0 1.2 50 16.45 f.p.b.t.
Delaney (2006) R_UC_C1 150 200 50 820 1800 160 40 49.1 190 477 266 190 477 266 C- 50.5 817 1.4 150 44.4 f.p.b.t. R_UC_C2 150 200 50 820 1800 160 40 50.1 190 477 266 190 477 266 C- 50.5 817 1.4 150 49.5 f.p.b.t. R_UC_C3 150 200 50 820 1800 160 40 50.2 190 477 266 190 477 266 C- 50.5 817 1.4 150 45.3 f.p.b.t. R_UC_C4 150 200 50 820 1800 160 40 50.4 190 477 266 190 477 266 C- 50.5 817 1.4 150 48.5 f.p.b.t.
Esfahani et al. (2006)
11-20D- 1L:
150 200 – 600 1600 162 25 24.1 200 350 628 200 365 157 C-W 237.0 2845 0.176 150 54.455 f.p.b.t.
Gao et al. (2004) AO 150 200 150 500 1500 162 27 35.7 200 531 157 200 531 101 C- 235.0 4200 0.2 75 40.35 f.p.b.t. A10 150 200 150 500 1500 162 27 35.7 200 531 157 200 531 101 C- 235.0 4200 0.2 75 39.35 f.p.b.t. A20 150 200 150 500 1500 162 27 35.7 200 531 157 200 531 101 C- 235.0 4200 0.2 75 43.95 f.p.b.t.
Klshi et al. (1998) A200-1 150 250 50 1050 2600 210 40 24.8 206 378 402 206 378 402 A- 126.5 2480 0.1 130 37 f.p.b.t. A200-2 150 250 50 1050 2600 210 40 24.8 206 378 402 206 378 402 A- 126.5 2480 0.1 130 38 f.p.b.t. A415-1 150 250 50 1050 2600 210 40 24.8 206 378 402 206 378 402 A- 126.5 2480 0.3 130 41.7 f.p.b.t. A623-1 150 250 50 1050 2600 210 40 24.8 206 378 402 206 378 402 A- 126.5 2480 0.4 130 39.5 f.p.b.t.
5 1
4 A
.M .
C eci
et a
l./C o
n stru
ctio n
a n
d B
u ild
in g
M a
teria ls
2 7
(2 0
1 2
) 4
9 0
– 5
2 0
Table B.3 Database of beams failed by intermediate crack induced debonding. Type of test: f.p.b.t. = four point bending test; c.b.t. = cantilever beam test; 3.p.b.t = three point bending tes Kishi et al. (as cited in [3]), Kishi et al. (as cited in [3]), Kotynia (as cited in [3]), Kurihashi et al. (as cited in [3]), Kurihashi et al. (as cited in [3]), Leung (as cited in [3]).
b (mm)
h (mm)
a (mm)
B (mm)
L (mm)
d (mm)
d0
(mm) f 0c (MPa)
Es (GPa)
fvs (MPa)
As (mm)
E0s (GPa)
f 0y (MPa)
A0s (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfip (mm)
bfrp (mm)
Vexp (kN)
Type of test
Kishi et al. (1998)
A623-2 150 250 50 1050 2600 210 40 24.8 206 378 402 206 378 402 A- 126.5 2480 0.4 130 40.25 f.p.b.t. C300-1 150 250 50 1050 2600 210 40 24.8 206 378 402 206 378 402 C- 230.5 4070 0.2 130 39.6 f.p.b.t. C300-2 150 250 50 1050 2600 210 40 24.8 206 378 402 206 378 402 C- 230.5 4070 0.2 130 37.5 f.p.b.t. C445-1 150 250 50 1050 2600 210 40 24.8 206 378 402 206 378 402 C- 230.5 4070 0.2 130 42 f.p.b.t. C445-2 150 250 50 1050 2600 210 40 24.8 206 378 402 206 378 402 C- 230.5 4070 0.2 130 41.4 f.p.b.t.
Kishi et al. (2003)
A-250- 1
150 250 100 1050 2600 210 40 29.6 210 406 402 210 406 402 A- 118.0 2060 0.3 130 42.1 f.p.b.t.
A-400- 2
150 400 100 1050 2600 360 40 29.6 210 406 402 210 406 402 A- 118.0 2060 0.6 130 80 f.p.b.t.
Kotynia (2005) B-08/S1 150 300 150 800 3000 270 30 33.8 195 490 339 195 490 157 C- 172.0 2915 1.2 80 90 f.p.b.t. BF-04/ 0.5S
150 300 150 1500 3000 270 30 33.0 199 421 157 199 421 157 C- 172.0 2915 1.2 40 48 3.p.b.t.
BF-06/S 150 300 150 1500 3000 270 30 32.5 195 490 226 195 490 157 C- 172.0 2915 1.2 80 86 3.p.b.t. B-08/M 150 300 75 1400 4200 270 30 37.3 220 436 339 220 436 157 C- 220.0 2742 1.4 120 70 f.p.b.t. B-08/S2 150 300 75 1400 4200 270 30 32.3 220 436 339 220 436 157 C- 172.0 2915 1.2 50 47 f.p.b.t. B-083m 150 300 75 1400 4200 270 30 34.4 220 436 339 220 436 157 C- 170.0 2915 0.4 150 46 f.p.b.t.
Kurihashi et al. (1999)
BO-A 150 250 100 1100 2200 200 50 23.9 206 364 266 206 364 266 A- 126.5 2480 0.3 80 56.1 3.p.b.t. B40-A 150 250 100 1100 2600 200 50 23.9 206 364 266 206 364 266 A- 126.5 2480 0.3 80 26.15 f.p.b.t. BO-C 150 250 100 1100 2200 200 50 23.9 206 364 266 206 364 266 C- 126.5 4070 0.2 80 55.1 3.p.b.t.
Kurihashi et al. (2000)
R7-2 150 250 100 1450 3400 210 40 28.2 206 378 402 206 378 402 A- 126.5 2480 0.6 130 34.95 f.p.b.t. R6-2 150 250 100 1260 3020 210 40 28.2 206 378 402 206 378 402 A- 126.5 2480 0.6 130 41.3 f.p.b.t. R5-2 150 250 100 1050 2600 210 40 28.2 206 378 402 206 378 402 A- 126.5 2480 0.6 130 46.5 f.p.b.t. R4-2 150 250 100 840 2180 210 40 28.2 206 378 402 206 378 402 A- 126.5 2480 0.6 130 58.6 f.p.b.t. R3-2 150 250 100 650 1800 210 40 28.2 206 378 402 206 378 402 A- 126.5 2480 0.6 130 77.55 f.p.b.t.
Leung (2004) B11 300 800 800 2400 7200 740 60 41.5 200 526 2513 200 526 1030 C- 235.0 4200 0.9 300 508.8 f.p.b.t. B12 300 800 800 2400 7200 740 60 41.5 200 526 2513 200 526 1030 C- 235.0 4200 0.9 300 516.5 f.p.b.t. B21 150 400 400 1200 3600 370 30 41.5 200 535 603 200 535 226 C- 235.0 4200 0.4 150 137.2 f.p.b.t. B22 150 400 400 1200 3600 370 30 41.5 200 535 603 200 535 226 C- 235.0 4200 0.4 150 136.25 f.p.b.t. B31 75 200 200 600 1800 170 30 41.5 200 599 157 200 599 101 C- 235.0 4200 0.2 75 32.1 f.p.b.t. B32 75 200 200 600 1800 170 30 41.5 200 599 157 200 599 101 C- 235.0 4200 0.2 75 32.15 f.p.b.t. B41 75 200 200 600 1800 185 15 41.5 200 599 157 200 599 101 C- 235.0 4200 0.2 75 34.8 f.p.b.t. B42 75 200 200 600 1800 185 15 41.5 200 599 157 200 599 101 C- 235.0 4200 0.2 75 37.85 f.p.b.t. NB1-8 300 800 60 2400 7200 740 60 29.0 200 519 2513 200 519 1030 C- 235.0 4200 0.9 300 512 f.p.b.t. NB1-16 300 800 60 2400 7200 740 60 29.0 200 519 2513 200 519 1030 C- 235.0 4200 1.8 300 548.5 f.p.b.t. NB2-2 150 400 30 1200 3600 370 30 29.0 200 521 603 200 521 226 C- 235.0 4200 0.2 150 108.1 f.p.b.t. NB2-4 150 400 30 1200 3600 370 30 29.0 200 521 603 200 521 226 C- 235.0 4200 0.4 150 119.55 f.n.b.t.
A .M
. C
eci et
a l./C
o n
stru ctio
n a
n d
B u
ild in
g M
a teria
ls 2
7 (2
0 1
2 )
4 9
0 –
5 2
0 5
1 5
t.
Table B.4 Database of beams failed by intermediate crack induced debonding. Type of test: f.p.b.t. = four point bending test; c.b.t. = cantilever beam test; 3.p.b.t = three point bending test. Leung (as cited in [3]), Maalej and Leong (as cited in [3]), Maeda et al. (as cited in [3]), M’Bazaa et al. (as cited in [3]), Mikami et al. (as cited in [3]), Niu et al. [49].
b (mm)
h (mm)
a (mm)
B (mm)
L (mm)
d (mm)
d0
(mm) f 0c (MPa)
Es (GPa)
fvs (MPa)
As (mm)
E0s (GPa)
f 0y (MPa)
A0s (mm)
Type (–)
Efrp (GPa)
ffrp (MPa)
tfip (mm)
bfrp (mm)
Vexp (kN)
Type of test
Leung (2004) NB2- 6
150 400 30 1200 3600 370 30 29.0 200 521 603 200 521 226 C- 235.0 4200 0.7 150 127.6 f.p.b.t.
NB2- 8
150 400 30 1200 3600 370 30 29.0 200 521 603 200 521 226 C- 235.0 4200 0.9 150 137.95 f.p.b.t.
NB3- 2
75 200 15 600 1800 185 15 29.0 200 599 157 200 599 101 C- 235.0 4200 0.2 75 34.45 f.p.b.t.
NB3- 4
75 200 15 600 1800 185 15 29.0 200 599 157 200 599 101 C- 235.0 4200 0.4 75 37.2 f.p.b.t.
Maalej and Leong (2005)
A3 115 146 25 500 1500 120 26 42.8 180 547 236 180 547 157 C- 235.0 3550 0.2 108 38.75 f.p.b.t. A4 115 146 25 500 1500 120 26 42.8 180 547 236 180 547 157 C- 235.0 3550 0.2 108 37.75 f.p.b.t. A5 115 146 25 500 1500 120 26 42.8 180 547 236 180 547 157 C- 235.0 3550 0.3 108 43.7 f.p.b.t. A6 115 146 25 500 1500 120 26 42.8 180 547 236 180 547 157 C- 235.0 3550 0.3 108 42.9 f.p.b.t. B3 230 292 50 1000 3000 240 52 42.8 183 544 943 183 544 628 C- 235.0 3550 0.3 216 131.75 f.p.b.t. B4 230 292 50 1000 3000 240 52 42.8 183 544 943 183 544 628 C- 235.0 3550 0.3 216 130.15 f.p.b.t. B5 230 292 50 1000 3000 240 52 42.8 183 544 943 183 544 628 C- 235.0 3550 0.7 216 147.35 f.p.b.t. B6 230 292 50 1000 3000 240 52 42.8 183 544 943 183 544 628 C- 235.0 3550 0.7 216 142.15 f.p.b.t. C3 368 467.2 80 1600 4800 384 83.2 42.4 181 552 2413 181 552 1609 C- 235.0 3550 0.5 368 326.45 f.p.b.t. C4 368 467.2 80 1600 4800 384 83.2 42.4 181 552 2413 181 552 1609 C- 235.0 3550 0.5 368 334.65 f.p.b.t.
Maeda et al. (2001) SP-C 200 200 30 750 1800 165 35 35.0 200 360 266 200 360 266 C- 236.0 4120 0.2 200 39.15 f.p.b.t. SP- C2
200 200 30 750 1800 165 35 35.0 200 360 266 200 360 266 C- 236.0 4120 0.3 200 54.5 f.p.b.t.
M’Bazaa et al. (1996)
P111 200 300 50 1000 3000 240 – 44.3 200 439 157 200 – – C- 82.0 0.9 167 49.9 f.p.b.t.
Mikami et al. (1999)
A- 140
150 250 100 1500 3000 200 50 23.9 200 364 266 200 364 266 C- 126.5 2480 0.3 80 40.2 3.p.b.t.
Niu et al. (2006) Al 960 203 475 2100 4200 168 – 31.6 192 452 861 192 – – C- 184.0 2446 1.3 200 127.8 3.p.b.t. A2 960 203 475 2100 4200 168 – 33.4 192 452 861 192 – – C- 195.0 2384 1.2 200 130.4 3.p.b.t. A3 960 203 475 2100 4200 168 – 35.2 192 452 861 192 – – C- 80.4 724 1.4 300 102.7 3.p.b.t. A4 960 203 475 2100 4200 168 – 34.4 192 452 861 192 – – C- 108.5 859 2.6 300 133.7 3.p.b.t. A5 960 203 475 2100 4200 168 – 35.9 192 452 861 192 – – C- 108.5 859 2.6 200 107.4 3.p.b.t. A6 960 203 475 2100 4200 168 – 35.1 192 452 861 192 – – C- 80.4 724 1.4 200 93.7 3.p.b.t. Bl 960 203 475 1600 4200 168 – 35.2 192 452 861 192 – – C- 184.0 2446 1.3 200 71.85 f.p.b.t. B2 960 203 475 1600 4200 168 – 34.5 192 452 861 192 – – C- 80.4 724 1.4 300 56.7 f.p.b.t. B3 960 203 475 1600 4200 168 – 34.7 192 452 861 192 – – C- 80.4 724 1.4 200 54.15 f.p.b.t. C2 960 203 475 2100 4200 168 – 33.3 196 446 896 196 – – C- 184.0 2446 1.3 200 133.8 3.p.b.t. C3 960 203 475 2100 4200 168 – 34.1 196 446 896 196 – – C- 80.4 724 1.4 300 107.2 3.p.b.t.
5 1
6 A
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et a
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a n
d B
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ble B.5 tabase of beams failed by intermediate crack induced debonding. Type of test: f.p.b.t. = four point bending test; c.b.t. = cantilever beam test; 3.p.b.t = three point bending test. N et al. [49], Seim et al. [50], Spadea et al. [44], Takahashi d Sato (as cited in [3]), Takeo et al. (as cited in [3]), Teng and Yao [23], Wu et al. (1999, 2000) (as cited in [3]), Yao et al. [47].
b (mm)
h (mm)
a (mm)
B (mm)
L (mm)
d (mm)
d0
(mm) f 0c (MPa)
Es (GPa)
fvs (MPa)
As (mm)
E0s (GPa)
f 0y (MPa)
A0s (mm)
Type (–)
Efrp (GP
ffrp (MPa)
tfip (mm)
bfrp (mm)
Vexp (kN)
Type of test
Niu et al. (2006) C4 960 203 475 2100 4200 168 – 34.5 196 446 896 196 – – C- 80 724 1.4 200 90.5 3.p.b.t.
Seimetal. (2001) S11 480 102 100 1015 2030 81 – 33.2 205 462 214 205 – – C- 198 2270 1.2 100 40.8 3.p.b.t. S12 480 102 100 1015 2030 81 – 33.2 205 462 214 205 – – C- 198 2270 1.2 100 42.5 3.p.b.t. S5 480 102 100 1015 2030 81 – 33.2 205 462 214 205 – – C- 198 2270 1.2 100 43.2 3.p.b.t. S1m 480 102 285 1015 2030 81 – 33.2 205 462 214 205 – – C- 198 2270 1.2 100 41.9 3.p.b.t. C12 480 102 100 1015 2030 81 – 33.2 205 462 214 205 – – G- 63 675 1.1 480 80.8 3.p.b.t. C21 480 102 100 1015 2030 81 – 33.2 205 462 214 205 – – G- 91 724 1.2 480 71.3 3.p.b.t.
Spadea et al. (1998) A1.1 140 300 50 1800 4800 261 39 27.4 200 435 402 200 435 402 G- 152 2300 1.2 80 43.4 f.p.b.t. A3.1 140 300 50 1800 4800 263 37 28.5 200 435 402 200 435 402 C- 152 2300 1.2 80 37.4 f.p.b.t.
Takahashl and Sato (2003)
Fl 200 300 50 700 1600 250 50 35.8 200 371 573 200 371 63 C- 230 3480 0.2 200 113.5 f.p.b.t. F2 200 300 50 700 1600 250 50 40.2 200 371 573 200 371 63 C- 230 3480 0.3 200 122 f.p.b.t. F3 200 300 50 700 1600 250 50 39.0 200 371 573 200 371 63 C- 230 3480 0.5 200 135 f.p.b.t. F5 200 300 50 700 1600 250 50 50.3 200 371 573 200 371 63 C- 230 3480 0.3 200 139 f.p.b.t. F6 200 300 50 700 1600 250 50 49.5 200 371 573 200 371 63 C- 230 3480 0.5 200 155.5 f.p.b.t.
Takeo et al. (1999) No.2 160 260 70 1000 2000 225 35 31.3 200 356 266 200 356 266 C- 230 3480 0.2 140 33.85 3.p.b.t. No.3 160 260 70 800 2000 225 35 31.3 200 356 266 200 356 266 C- 230 3480 0.2 140 38.35 f.p.b.t. No.4 160 260 70 700 2000 225 35 31.3 200 356 266 200 356 266 C- 230 3480 0.2 140 43.5 f.p.b.t. No.5 160 260 70 550 2000 225 35 39.0 200 356 266 200 356 266 C- 230 3480 0.2 140 66 f.p.b.t. No.6 160 260 70 1000 2000 225 35 39.0 200 356 266 200 356 266 C- 230 3480 0.2 140 78.6 3.p.b.t. No.7 160 260 70 1000 2000 225 35 39.0 200 356 266 200 356 266 C- 230 3480 0.2 140 85.6 3.p.b.t.
Teng and Yao (2007)
CS- W50
150.6 255.3 50 500 1500 222.8 32.5 32.8 199 536 157.08 199 536 157.08 C-W 256 4114 2.01 50 71.3 f.p.b.t.
GS 151.1 252.2 50 500 1500 217.7 34.5 32.3 199 536 157.08 199 536 157.08 G-W 22 351 1.67 148 82 f.p.b.t.
Wu et al. (1999) H-s CFRP
150 200 50 600 1800 150 50 33.8 210 390 402 210 390 266 C- 230 4200 0.3 150 68.25 f.p.b.t.
H-m CFRP
150 200 50 600 1800 150 50 33.8 210 390 402 210 390 266 C- 290 4000 0.3 150 78.45 f.p.b.t.
Wu et al. (2000) RC-1 150 200 50 900 1800 160 40 30.2 210 360 402 210 360 266 C- 230 3200 0.1 140 65 3.p.b.t. RC-2 150 200 50 900 1800 160 40 30.2 210 360 402 210 360 266 C- 230 3200 0.1 140 68.9 3.p.b.t. RCS-1 150 200 50 900 1800 160 40 34.6 210 360 402 210 360 266 C- 230 3200 0.222 140 73.5 3.p.b.t.
Yao et al. (2005) CP4 304.5 150.3 100 1000 1100 120.2 – 46.2 208 343 157 208 – – C- 165 2800 1.2 50 13.5 c.b.t. II-1 303 153 100 1000 1100 117.5 – 25.6 208 349 157 208 – – C- 257 4519 0.2 30 7.2 c.b.t. I-2 305 149 100 1000 1100 116.5 – 25.3 208 332 157 208 – – C- 257 4519 0.2 50 8.4 c.b.t. II-3 305 150 100 1000 1100 117.5 – 30.2 208 332 157 208 – – C- 257 4519 0.2 70 8.9 c.b.t. II-4 302 150 100 1000 1100 118.7 – 21.9 208 332 157 208 – – C- 257 4519 0.2 90 10.2 c.b.t. II-8 203.5 152 100 1000 1100 114.5 _ 23.8 208 364 157 208 – – C- 257 4519 0.2 50 8.4 c.b.t.
A .M
. C
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Ta Da an
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a)
.4
.0
.0
.0
.0
.8
.5
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
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.0
.0
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Table B.6 Database of beams failed by intermediate crack induced debonding. Type of test: f.p.b.t. = four point bending test; c.b.t. = cantilever beam test; 3.p.b.t = three point bending tes Yao et al. [47], Zaniç et al. (as cited in [3]), Zhang et al. (as cited in [3]).
b (mm)
h (mm)
a (mm)
B (mm)
L (mm)
d (mm)
d0
(mm) f 0c (MPa)
Es (GPa)
fvs (MPa)
As (mm)
E0s (GPa)
f 0y (MPa)
A0s (mm)
Type (–)
Efrp (GP
ffrp (MPa)
tfip (mm)
bfrp (mm)
Vexp (kN)
Type of test
Yao et al. (2005)
II-9 320 151 100 1000 1100 117 – 22 2 208 332 157 208 – – C- 257 4519 0.2 30 6.9 c.b.t. III-l 203 155 100 1000 2000 121 – 22.5 208 346 157 208 – - C- 257 4519 0.2 50 15 3.p.b.t. III-2 199 156.5 100 1000 2000 122.5 – 21.2 210 373 157 210 – – C- 257 4519 0.2 100 21.4 3.p.b.t. III-4 150.1 153.5 100 1000 2000 122 – 22.4 206 351 157 206 – – C- 257 4519 0.2 50 18.4 3.p.b.t.
Zamiç et al. (1999)
1 200 300 100 960 2900 270 30 25.0 205 450 339 205 450 226 C- 150 2400 1.2 50 58.4 f.p.b.t. 2 800 120 100 960 2900 105 15 25.0 205 450 339 205 450 156 C- 150 2400 1.2 100 31.5 f.p.b.t.
Zhang et al. (2005)
A-l 150 340 100 1200 3000 300 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 63.35 f.p.b.t. A-2 150 340 100 1200 3000 300 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 63.5 f.p.b.t. A-3 150 340 100 1200 3000 300 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 63.1 f.p.b.t. A-4 150 340 100 1200 3000 300 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 65.8 f.p.b.t. A-5 150 340 100 1200 3000 300 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 62.15 f.p.b.t. A-6 150 340 100 1200 3000 300 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 62.1 f.p.b.t. B-2 150 250 100 1050 2600 210 40 31.5 210 407 402 210 407 402 C- 230 3400 0.2 130 40.45 f.p.b.t. B-3 150 250 100 1050 2600 210 40 31.5 210 407 402 210 407 402 A- 118 2060 0.3 130 42.1 f.p.b.t. B-4 150 250 100 1050 2600 210 40 31.5 210 407 402 210 407 402 A- 78 2350 0.4 130 41.05 f.p.b.t. B-6 150 400 100 1050 2600 360 40 31.5 210 407 402 210 407 402 C- 230 3400 0.3 130 78.15 f.p.b.t. B-7 150 400 100 1050 2600 360 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 79.6 f.p.b.t. B-8 150 400 100 1050 2600 360 40 31.5 210 407 402 210 407 402 A- 78 2350 0.8 130 78.1 f.p.b.t. C-l 150 235 100 650 1800 210 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 74.95 f.p.b.t. C-2 150 250 100 650 1800 210 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 75.95 f.p.b.t. C-4 150 235 100 1050 2600 210 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 45.25 f.p.b.t. C-5 150 250 100 1050 2600 210 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 47.2 f.p.b.t. C-6 150 270 100 1050 2600 205 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 48.5 f.p.b.t. C-7 150 235 100 1450 3500 210 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 34.4 f.p.b.t. C-8 150 250 100 1450 3500 210 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 34 f.p.b.t. C-9 150 270 100 1450 3500 205 40 31.5 210 407 402 210 407 402 A- 118 2060 0.6 130 35.4 f.p.b.t.
5 1
8 A
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C eci
et a
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(2 0
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) 4
9 0
– 5
2 0
t.
a)
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
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.0
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.0
.5
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.0
.0
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.0
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A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520 519
the delamination process initiates and the end of the FRP sheet. In prism tests, the tension at the end of the FRP sheet is zero, which is not the case when there are other cracks in between the initiating crack and the end of the FRP sheet. Also, the effect of the curvature in the beam is ignored in the prism tests. While the Casas and Pascual model takes these factors into account, the Wu and Niu fracture mechanics-based model considers only type-1 IC debond- ing. Similarly, the ACI model is based on the bond-strength model proposed by Chen and Teng, which was calibrated with a large data base of shear tests, and verified with a limited number of tests of RC beams in flexure. However, a significant number of additional tests have been used in the present analysis. This may explain why the ACI and Wu and Niu models over-predict the resistance of beams in IC debonding where a combination of type-1 and type-2 IC debonding is observed.
As expected for all IC models, the inclusion of the additional data set increases the COV associated with the point estimation of the bias by a significant amount. For the Casas and Pascual model one reason for the increase in the COV is due to the possible differences between the assumed resin properties and the real values which are not known. The COV of the Casas model increases from 18% to a very high 65%, while the Wu and Niu COV increases from 32% to 46%. The COV associated with the ACI bias also increases from 29% with the limited data set to 55% with the full data set. Fig. 13 shows the plot for the ACI comparison with the full data set. The larger range of the loads that cause failure is reflected by the larger scale used. The increase in the COV with the larger database may be due to the scale effects when the models are developed based on small scale speci- mens as well as the preponderance of type-2 debonding in the addi- tional beam tests included.
Similar observations to those noted above for the bias can be made for the regression coefficients. The trends in the regression standard error are also similar to those observed for the COV.
6. Conclusions
In this paper, two experimental databases were assembled to study the debonding failure mechanism of concrete beams rein- forced in flexure using FRP sheets. One database is for beams that failed due to end debonding and the second database is for beams that failed due to intermediate-crack induced debonding. The data- base for beams that failed by end debonding includes 34 testing programs, consisting of 161 tests performed on beams of various dimensions. The 184 beams that failed in intermediate crack in- duced debonding were collected from 37 different experimental investigations. The databases assembled in this study build up on the data bases previously assembled by Smith and Teng [6]and Col- otti [19].
The two databases were used to evaluate the suitability of exist- ing analytical models for designing FRP strengthening schemes that resist debonding or for predicting the debonding failure mode. The goal of the analysis is to asses the applicability of existing models for calibrating design criteria and proposing reliability-based safety factors which would produce uniform levels of safety during the de- sign of FRP strengthening schemes for concrete beams in bending. Twelve models were investigated for end debonding and three models for intermediate crack induced debonding. Based on the comparative study, the following conclusions can be drawn:
1. Many models were verified or calibrated to match the results of specific databases and may not produce similar results when the test conditions or scales are different than those of the tests that generated the models. For example, the Wu and Niu model [3] was found to over-predict the test results reported by other investigators.
2. The objective of many model authors was not necessarily to predict correctly the load of failure, but to provide a model that will lead to safe lower bounds on the failure loads for design purposes. For example, this is the approach taken by Smith and Teng [6] and Teng and Yao [22] whose models show large values for the bias of the model which gives the average ratio of the experimental results to the analytical results. Also, the ACI model for IC debonding was developed to prevent this mode of failure and not to predict it. However, even when the average bias for the design equation may exceed 1.0 by a signif- icant margin, the high variability in the test results may show that in many cases, the proposed equations may overpredict the load carrying capacity of FRP strengthened beams. There- fore, it is important to calibrate design equations for FRP deb- onding using structural reliability criteria that ensure that the design equations produce acceptable levels of safety that are consistent with those of other structural failure modes.
3. Colotti et al. proposed a model [19] based on strength of mate- rials criteria to not only predict the failure load but also the mode of failure of strengthened RC beams and came closest to providing a predictive model rather than a safe design model.
4. The design models which gave the lowest coefficients of varia- tion (COV) while showing consistent results for end debonding for both prepeg and wet lay-up installations are the Smith and Teng [6] and the Casas and Pascual model [27]. The Casas and Pascual model takes into consideration the interaction between FRP, the resin and the concrete which all other models except for Ziraba [26] ignored.
5. One clear advantage of the Casas and Pascual model [27] is that it can be used for end debonding and also for intermediate crack-induced debonding.
6. The results show that many models give good predictions for wet lay-up installations but few models give the same level of accuracy for prepeg plates. Very few models take into account the difference in behavior due to the installation process.
7. Most models ignored the effect of the FRP-concrete interface and did not take the resin properties into account although recent studies have shown that the debdonding process does initiate at the interface.
8. As previously reported in [27], it is noted that the scale effect is very important for the debonding mode of failure and that more tests need to be executed on full scale beams to verify the con- sistency of the current models for all pertinent scale levels.
The conclusions presented in this paper provide a statistical analysis of the response of FRP flexurally strengthened beams and, therefore, they are the first step on the way to developing a set of reliability-based partial safety factors to use during the de- sign of FRP strengthening schemes for bridge decks and beams. This will be the subject of a companion paper.
Acknowledgments
The financial support provided by the Spanish Ministry of Edu- cation through the Research Project BIA2010-16332 is greatly acknowledged. The third author also acknowledges the financial support provided by the Spanish Ministry of Education during his sabbatical leave at the Technical University of Catalonia (UPC) un- der the scholarship SAB2009-0164.
Appendix A. Database of beams failed by end debonding
See Tables A.1–A.6.
520 A.M. Ceci et al. / Construction and Building Materials 27 (2012) 490–520
Appendix B. Database of beams failed by intermediate crack induced debonding
See Tables B.1–B.6.
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- Statistical analysis of existing models for flexural strengthening of concrete bridge beams using FRP sheets
- 1 Introduction
- 2 Experimental database
- 3 Review of models for debonding of FRP-strengthened RC beams
- 3.1 Oehlers’ model
- 3.2 Smith and Teng’s model
- 3.3 Teng and Yao’s model
- 3.4 Jansze’s model
- 3.5 Ahmed and van Germert’s model
- 3.6 Colotti et al.’s model
- 3.7 Raoof and Zhang’s model
- 3.8 Wang and Ling’s model
- 3.9 Raoof and Hassanen’s models
- 3.10 Ziraba et al. models
- 3.11 Wu and Niu model
- 3.12 Casas and Pascual’s model
- 3.13 ACI 440.2R-08
- 4 Analysis of end debonding models
- 5 Analysis of IC induced debonding strength models
- 6 Conclusions
- Acknowledgments
- Appendix A Database of beams failed by end debonding
- Appendix B Database of beams failed by intermediate crack induced debonding
- References
HT120815 Readings/Modeling of IC Debonding of FRP-Strengthened Concrete Flexural Members.pdf
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Modeling of IC Debonding of FRP-Strengthened Concrete Flexural Members
Owen Rosenboom, M.ASCE1; and Sami Rizkalla, F.ASCE2
Abstract: The presence of a fiber-reinforced polymer �FRP� strengthening material bonded to the tension face of a reinforced concrete beam will restrict but not prevent the opening of intermediate flexural cracks due to applied loading. Test results indicate that displace- ments at the toe of flexural cracks create stress concentrations at the interface of the FRP laminate and the beam, leading to the development of localized interface cracks that, typically, propagate, under the effect of the load, to join the original flexural cracks and cause delamination of the FRP system. This type of FRP delamination is commonly termed intermediate crack �IC� debonding. In this paper the analytical models published in the literature are reviewed and it was found that these models do not correlate well with measured experimental results. This paper proposes an analytical model that characterizes the interface shear stress based on two distinct sources: �1� the change in the applied moments along the length of the member and �2� stress concentrations at the intermediate cracks. The proposed model is compared to an experimental database and shown to predict extremely well most of the test results reported by other researchers. A parametric study, performed using the proposed model, indicates that the model varies with several important variables that are not captured by most of the existing models.
DOI: 10.1061/�ASCE�1090-0268�2008�12:2�168�
CE Database subject headings: Concrete, reinforced; Concrete, prestressed; Fiber reinforced polymers; Analytical techniques; Bonding.
Introduction
The effectiveness of a fiber-reinforced polymer �FRP� strengthen- ing material bonded to the tension side of a flexural member is highly dependent on the bond stresses between the adherents and the member. Transfer of tension forces results in stresses that are a function of the applied loading conditions, as well as the geom- etry, configuration, and stiffness of the adherents and the adhe- sive. For reinforced/prestressed concrete, the distribution of bond stresses is more complex as a result of flexural and shear cracking disrupting the continuity of the FRP system. Bond stresses are induced due to the change of the internal moments along the length of the beam and by transfer of forces across cracks and at plate-end �Neubauer and Rostásy 1999�. Bond failure, or debond- ing, usually occurs rapidly and can be initiated in several loca- tions along the strengthened member. At the plate curtailment point, cracks due to stress concentrations may form as a result of the abrupt termination of the strengthening plate, or due to the influence of beam curvature on the material stiffness mismatch. This type of debonding is called plate-end �PE� debonding. For long-span flexural members, the stress concentrations due to the
1Research Associate, Dept. of Civil and Structural Engineering, Hong Kong Polytechnic Univ., Hong Kong, China.
2Distinguished Professor, Dept. of Civil Engineering, North Carolina State Univ., Raleigh, NC 27695. E-mail: sami�[email protected].
Note. Discussion open until September 1, 2008. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and pos- sible publication on September 6, 2006; approved on January 17, 2007. This paper is part of the Journal of Composites for Construction, Vol. 12, No. 2, April 1, 2008. ©ASCE, ISSN 1090-0268/2008/2-168–179/
$25.00.
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opening of flexural cracks are, typically, larger than the stress concentrations at the plate end, and debonding advances from the intermediate cracks �IC� towards the support �IC debonding�.
The first analytical models to describe the IC debonding pro- cess resulted from observations of the behavior of single lap-shear and double lap-shear specimens, which isolate a portion of a plated concrete beam with one flexural crack �Bizindavyi and Neale 1999; Maeda et al. 1997�. Several researchers have derived expressions to predict the ultimate load of single lap-shear con- crete specimens bonded with FRP based on the fracture energy of the concrete. The materials are usually assumed to be homoge- neous and linear elastic, the adhesive layer is assumed to be of negligible thickness and acts only as a medium to transfer the Mode II shearing loading, and the FRP plate and adhesive are assumed to be of uniform thickness. The solution depends on the relationship of interfacial shear stress to slip behavior of a concrete–FRP bonded joint, of which there have been several proposed relationships: linearly ascending �Täljsten 1994�; lin- early ascending and descending �Yuan et al. 2001; Brosens 2001; Chen and Teng 2001; Ulaga et al. 2003; Oehlers et al. 2006�, using the power function �Brosens 2001�; or bilinear allowing for localized debonding �Leung and Tung 2001�. Analytical methods exploring the presence of multiple flexural cracks along the length of the member have also been explored using a fracture-based approach �Chen et al. 2005� and using relationships closely tied to the stiffness of the adhesive �Harmon et al. 2003�.
Mechanics principles can be used to derive the shear stress in the FRP–concrete interface assuming a perfect bond �Sebastian 2001�. A discontinuous interfacial shear stress model has been proposed assuming the concrete remains elastic and using bilinear relationships for longitudinal steel reinforcement �Wang and Ling 1998�. A similar approach was also introduced which proposes
design equations against bond failure utilized estimates of the
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internal lever arm and assumed equal tensile strains in the FRP and internal steel �Matthys 2000�. Smeared-crack finite-element models have been used to develop design equations to predict IC debonding based on mechanics and fracture theories �Teng et al. 2004�. National code documents provide design guidelines on IC debonding, based on fracture approaches �Ye et al. 2005; FIB 2001; Concrete Society 2004; Oehlers et al. 2006� and empirical relationships �ACI 2002�. This paper reviews the applicability of the various models reported in the literature and clearly identifies the need to develop a new analytical that accurately predicts the IC debonding strain of FRP-strengthened reinforced and pre- stressed concrete beams. A review of the various models from the national codes can be found elsewhere �Rosenboom 2006�.
Assessment of Current Models
In order to assess the IC debonding analytical models available in the literature, a database was constructed from 51 beams or slabs. In the database 47 beams failed due to IC debonding and four failed due to FRP rupture. The beams or slabs represent a wide cross section of shapes and sizes, with depths varying from 150 mm up to 825 mm and shear span-to-depth ratios varying from 2.65 to 10.04. The steel reinforcement ratio varies from 0.34 to 2.7%. Three different FRP materials are found in the database: carbon FRP, aramid FRP, and glass FRP, which have been in- stalled using both the wet lay-up method and through externally bonding a precured laminate using structural adhesive. The prop- erties of the FRP vary significantly and represent both the lami- nate and fiber properties for wet lay-up systems. The beams or slabs were taken from 18 different literature sources. These sources, along with the full details of the database are given else- where �Rosenboom 2006�. An assessment of the existing models from the literature was performed against the IC debonding data- base. Not every model was assessed, and only those models with clear failure criteria were examined. The models were followed exactly as described in the relevant literature except the follow- ing: �1� a FRP rupture check was performed whether the model explicitly called for one or not; and �2� the initial strain on the beam soffit due to the effect of dead load was included. A width factor �kb� was included where advised by the model, and this is discussed at the end of this section. An assessment of the analyti- cal models from the national code documents is provided in Rosenboom �2006�.
Models from the Literature
The empirical model by Maeda et al. �1997� was compared to the assembled IC debonding database. Regression analysis of test re- sults obtained from double lap-shear specimens provided estima- tion of maximum strains in FRP at debonding failure. Two factors within the test setup helped in providing realistic results: �1� the presence of a layer of vinyl tape next to the “crack”; and �2� the use of a double lap-shear configuration. Both of these factors have inhibited the formation of a concrete tooth in the specimen at failure which may significantly alter the behavior of the lap-shear specimen. The model tends to overestimate the debonding strain as the axial stiffness of the FRP decreases. The experimental ver- sus predicted debonding strain is shown in Fig. 1. Matthys �2000� identified a failure criterion to be checked called “transfer of forces,” where the derivative of the tensile envelope due to ap- plied loading was determined and compared to the shear strength
of the concrete. Two simple design equations were presented to
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determine the maximum shear force that could cause debonding before or after steel yielding, yet all the beams in the database failed after steel yielding. Although the predicted shear forces show good correlation to the experimental shear force, this is mainly due to the large disparity between the sizes of the beams in the database. The correlation could also be deceiving since a significant increase in debonding strain is not proportional to in- creases in applied shear force. An analytical model proposed by Leung and Tung �2001� was assessed using the IC debonding database. One of the benefits of the model is its capability to predict the debonding strain at the main flexural crack at any various unbonded distances near the crack due to interfacial cracking. The value of acceptable localized debonding around the main flexural crack was assumed to be in the range of 25% of the height of the cross section of the beams. The experimental versus predicted debonding strains using the Leung and Tung �2001� model are shown in Fig. 2. The model is clearly underestimating the strain at debonding.
The model of Harmon et al. �2003� was assessed against the IC debonding database. The model takes into account the flexural crack spacing, and calculates the maximum force that can be de- veloped in the FRP through an iterative procedure. One of the important variables in the estimation of the force in FRP at the critical crack location is the effective bond length, Leff, which is equal to
Fig. 1. Experimental versus predicted debonding strains using model of Maeda et al. �1997�
Fig. 2. Experimental versus predicted debonding strains using model of Leung and Tung �2001�
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Leff = �Eftftb Ga
�1�
where Ef and tf = elastic modulus and thickness of the FRP mate- rial; tb = thickness of the bond �or adhesive� layer; and Ga = shear modulus of the adhesive. The effective bond length calculated using Eq. �1� is much less than the calculated value using other models �e.g., Chen and Teng 2001; Oehlers and Seracino 2004�. Fig. 3 shows the correlation between the shear modulus of the adhesive and the effective bond length for various values of Eftftb values �shown as EA in the plot�. Also shown in Fig. 3 is the value of Leff obtained using the Chen and Teng �2001� model using a concrete compressive strength of 33 MPa. In the Harmon et al. �2003� model the value of FRP force at the critical crack for IC debonding failure is heavily dependent on the value for effec- tive bond length.
The fracture-based model of Ulaga et al. �2003� was derived from an experimental program on double lap-shear specimens and assuming a linearly descending interface shear stress versus slip relationship. Similar to the other fracture based models, which are derived from test results on lap-shear specimens, the mean value of the model is conservative for the IC debonding database. Teng et al. �2004� developed a set of equations to predict the IC deb- onding resistance based on mechanics and fracture-based behav- ior. The calculation of one parameter in the model, the distance from the loaded end to the end of the cracked region �Lee�, was calculated using the following equation:
Lee = a − Mcr Mdb
a + s �2�
where a = shear span; s = distance from the center of the support to the FRP termination point; and Mcr and Mdb = cracking moment and nominal moment at the predicted debonding strain of the FRP-strengthened section. Since Mdb can only be calculated once assuming a debonding strain, the model becomes iterative. Simi- lar to conclusions proposed in the paper, the use of the more complicated mean model is not warranted since the design model has similar correlation. The experimental versus predicted deb- onding strains using the Teng et al. �2004� mean model are shown in Fig. 4 to overestimate the debonding strain and provide poor correlation with the experimental database. The fracture-based model was proposed by Chen et al. �2005� with a linearly de- scending shear stress versus slip relationship and assumed mul- tiple flexural cracks to predict IC debonding. The model was
Fig. 3. Adhesive shear modulus versus the effective bond length for Harmon et al. �2003�
derived from the behavior of a single lap-shear specimen having
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force applied to the FRP laminate from two directions, which simulates the behavior of the bonded joint between two flexural cracks. Two sets of equations are presented, one that ignores the deformation in the concrete and the other equation that includes it. The equations that include the deformation in the concrete layer do not match well the behavior of the measured values of the flexural members included in the database, and have less cor- relation and are more conservative than the equations ignoring the concrete deformation. The ratio of the applied load on the FRP on either side of the concrete block ��� was assumed to be 0.8, a value that was used in the design example presented in the paper. The experimental versus predicted debonding strains ignoring the deformation in the concrete is shown in Fig. 5. It should be noted that the equations developed by Chen et al. �2005� were derived from small-scale specimens, however, still compare well to the large scale specimens included in the database and are not overly conservative like earlier models �e.g., Chen and Teng 2001� as can be seen in the statistical analysis discussed later. This is most likely due to the more realistic boundary and loading conditions assumed in the derivation of the model, especially the nature of the applied load to both sides of the FRP laminate.
Fig. 4. Experimental versus predicted debonding strains using mean model of Teng et al. �2004�
Fig. 5. Experimental versus predicted debonding strains using model of Chen et al. �2005�
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Width Effect
Many researchers have found that the width of the FRP plate has an effect on the shear stress distribution, and that increases in the width of the laminate are not proportional to increases in failure load �Brosens 2001; Chen and Teng 2001�. Two possible justifi- cations exist for the width effect: the size effect theory from frac- ture mechanics and the spreading out of forces in the concrete �Brosens 2001�. Four different width factors were found in the literature and were assessed against the IC debonding database. A generalized equation for the width factor �kb� can be written as
kb = �b��1 − bfbc �2 +
bf �
�3�
where bf = width of the FRP laminate; bc = width of the concrete surface; and �b, �1, and �2 = empirical constants and were origi- nally derived to be set equal to 1.0, 2.0, and 1.0, respectively �Brosens 2001�. The value of � is set equal to bc in some models, and set equal to 400 mm in others. Table 1 summarizes the four different width factors considered.
The beams in the IC debonding database were analyzed using the width factors described above and the IC debonding model of Leung and Tung �2001�, which was assessed earlier. The applica- tion of the width factors kb1 and kb2 do not provide for any better correlation and make the model more conservative compared to the experimental results. The application of the width factor kb3 from the Concrete Society �2004� and Fédération Internationale du Béton �FIB 2001� also does not improve the correlation and has an adverse effect producing a less conservative prediction. The experimental versus predicted debonding strains for the origi- nal model, and after application of the four different width factors is shown in Fig. 6. The model of Chen and Teng �2001� was analyzed in a similar manner and the same effect was observed. An additional size effect that should be acknowledged is the ef- fect of the extra epoxy which is adjacent to the edge of the FRP laminate. A slight increase in strength is predicted due to the activation of concrete outside of the nominal dimensions of the FRP laminate. In experimental work, where small widths of FRP laminates are commonly used, this effect will be more pro- nounced than in field applications. Since the experimental work provides an upper bound width factor relationship, the width fac- tor models of kb1 or kb2 would be preferable to kb3. Both of these factors, however, deeply penalize the FRP configuration when approaching unity. It is not recommended to use width factors since there is little evidence of improvement of experimental to predicted correlation. However, if they are used, the relationship
Table 1. Width Factor Summary
Width factor Model
kb1 Chen and Teng �2001�; Brosens �2001�
kb2 Chinese code—Ye et al. �2005�; Teng et al. �2004�
kb3 FIB �2001�; Concrete Society �2004�
kb4 Proposed a
aWidth factors are not recommended. If used, the proposed equation sho
shown as kb4 in Table 1 is recommended.
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Proposed Analytical Model
The analytical models presented in the literature do not provide a good correlation to the collected database for IC debonding fail- ures. Therefore, this paper proposes a new analytical model based on mechanics and calibrated by the experimental database of IC debonding failures. Various failure criteria were examined in the construction of the model, and a check for possible rupture of FRP before debonding is also given. The initial strain in the beam soffit has been incorporated into the carbon FRP �CFRP� strain during calculation of the FRP system contribution to sectional strength. This strain is normally an additive quantity for pre- stressed concrete members and subtractive for reinforced concrete members. Considering a plated section with perfect bond along the plate-to-concrete interface the interface shear stress ��w� can be evaluated as
�w�x� = d
dx �Kp�x��p�x�� �4�
where d / dx��p�x�� = change in plate strain along the length of beam x; and Kp = axial stiffness of the plating material per unit width. For a FRP-plated concrete member with constant FRP con- figuration throughout the length of the beam Kp = nEftf. Using traditional equilibrium and compatibility conditions along with the assumption that plane sections remain plane after deforma- tion, an envelope of the axial strain in the FRP material can be determined for any given loading condition. The tensile strain in the internal steel reinforcement can also be calculated using the same approach and it can be determined at any given section after yielding of the steel.
�b �1 �2
� �mm� �1
1.0 2.0 1.0 bc No
1.0 2.25 1.25 400 No
1.06 2.0 1.0 bc Yes
1.0 2.0 1.0 bc No
used.
Fig. 6. Experimental versus predicted debonding strains using model of Leung and Tung �2001� and several width factors
uld be
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Along with interface shear stress due to the applied loading, there exist normal �or peeling� stresses throughout the bonded length. At the plate termination point the peeling stresses result from a stiffness mismatch between the FRP and the concrete and cause an outward force. A short distance away from the plate end, the peeling stresses due to applied loading become very small and occur in the opposite direction as clamping forces due to beam curvature. For this reason, the peeling stresses due to the applied loading away from the plate end can be ignored in most cases, and controlled at the plate end by using end anchorages. Since the peeling stresses will not significantly affect the behavior away from the supports, there exists only forward shear mode �Mode II� crack deformation on the FRP-to-concrete interface due to the applied loading. With the assumption of perfect bond, failure due to debonding will occur when the interface shear stress reaches the shear strength of the interface. Since the shear strength of the structural adhesive is usually greater than that of the concrete, failure will occur along the concrete interface.
FRP-plated regular reinforced and prestressed concrete beams will exhibit flexural behavior when the shear span-to-depth �a / d� ratio is approximately 2.5 or greater, except in rare cases such as when there is exceptionally high prestress force. When flexural cracking occurs, the perfect bond assumptions are no longer valid at the location of the crack. At the toes of the flexural cracks stress concentrations form another set of cracking along the FRP- to-concrete interface, usually within the weak concrete layer. The stress concentrations at the intermediate cracks occur in two di- rections: �1� shear stress along the interface; and �2� peeling stresses due to aggregate interlock along the interface crack. As mentioned previously the normal stresses due to applied load are “clamping” stresses. These are in the opposite direction from the peeling stresses developed from stress concentrations, and are small in magnitude of both types of peeling stresses therefore they are disregarded in the current analysis. It is also possible to have wide crack openings due to flexure-shear cracks away from the maximum moment region, which could lead to high peeling
Fig. 7. Interfacial st
stresses. It is assumed that the beam being strengthened in flexure
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has sufficient shear capacity to handle the higher loads and large shear crack deformations will not control the failure.
The interface shear stress at the toes of the flexural cracks due to stress concentration ��sc� is related to the fracture energy of the weakest material at the interface. With quality workmanship and critical selection of an acceptable externally bonded FRP system, failure will propagate initially along the concrete interface. The profile of the shear stress due to stress concentration around the toe of a flexural crack is similar to a single lap-shear test, and can be approximated using Yuan et al. �2001� equations. As will be shown later, it is the magnitude of the interface shear stress which is of prime importance and this is not predicted using these equations.
The shear stress at the FRP-to-concrete interface ��i� is in- duced from two sources: the applied loading ��w� and stress con- centrations at the toes of flexural cracks ��sc�, a philosophy that first appeared in Teng et al. �2004�. For a distance x from the support
�i�x� = �w�x� + �sc�x� �5�
As x increases along the length of a plated beam, the interface shear stress due to applied loading becomes larger proportional to the change in applied moment at the section. Alternatively, �sc is both additive and subtractive on either side of each flexural crack due to equilibrium of forces. The value will be maximum in high moment regions where the crack opening displacement has the greatest magnitude. A schematic of the applied moment, tensile force in FRP, and interface shear stress distribution is shown in Fig. 7 for the loading configuration shown.
The interface shear stress due to applied loading ��w� can be determined from a cracked section analysis along the length of the beam. A moment-curvature analysis of the plated section can be used to determine the tensile strain profile of the CFRP, from which the interface shear stress can be calculated from Eq. �4�. In Sebastian �2001�, equations are developed that predict the inter-
in plated RC beam
resses
face shear stress due to the applied loading along the length of a
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beam. Sebastian �2001� showed that an assumption of perfect bond showed little error with experimental results, especially when coupled with smeared crack tension stiffening. A tensile strain envelope for one of the girders tested in Rosenboom �2006� is shown in Fig. 8. The experimentally measured strain values are shown, along with three separate prediction methods: �1� the cracked section analysis program Response 2000 �Bentz 2000�; �2� a flexural model described in Rosenboom �2006�; and �3� the proposed predictive method that is discussed below. Note: for all of the analytical methods used, the strain envelope was created with the maximum value of tensile strain equal to the experimen- tally determined value. From Fig. 8 several conclusions can be drawn. The maximum change in tensile strain, and similarly the maximum interface shear stress, occurs at or near the length along the beam at which yielding of the internal steel occurs �in this case at approximately 3,200 mm from supports�. The analysis also indicated that the predictions made from the flexural model,
Fig. 8. Experimental versus predicted tensile strain for girder EB1SB �adapted from Rosenboom 2006�
Fig. 9. Proposed interface shea
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which is quite comprehensive, and the proposed method, which is relatively simple, correlate reasonably well with the measured values.
Therefore, it is proposed that the maximum interface shear stress due to applied loading ��wmax� be determined from the fol- lowing equation, which is related to the increase of applied mo- ment from the yielding moment �My� to the debonding moment �Mdb�. The equation predicts the maximum interface shear stress as in the region along the beam from the location of first yielding of the prestressing strands to location of debonding moment as
�wmax = nEftf �db − �f @y
a − xy �6�
where nEftf = axial stiffness of FRP material per unit width; �db = strain in the FRP at IC debonding failure at a moment of Mdb; �f @y = tensile strain in the FRP at first yielding of internal tensile steel at a moment of My; and xy = the distance from the support to the location of first yielding of internal tensile steel. For three and four point bending, xy is equal to
xy = a My Mdb
�7�
where a = shear span of the beam and is equal to the distance from the support to the section of maximum moment. For unsymmetri- cal loading, the shorter distance should be used. The distance xy can also be found easily for beams with other loading scenarios by considering the shape of the moment diagram. For example, for beams with uniform distributed loads, the distance xy can be determined as
xy = − L2
8Mdb �− 4Mdb
L + �� 4Mdb
L �2 − 16� Mdb
L2 �My� �8�
Using equations similar to Eq. �8�, the interface shear stress due to applied loading can be calculated for the region between the supports and the location of flexural cracking �xcr�, and the region
s versus length along member
r stres
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between the instance of first flexural cracking and yielding of the internal tensile steel as shown in Fig. 9.
The total interface shear stress was compared to a criterion for failure. Since the majority of the bond stresses at the interface are from Mode II type loading, it is assumed that the failure criteria will be the shear strength of concrete. The concrete shear strength adopted in the proposed model is based on �cmax = 1.8
*� f t�� where f t� = tensile strength of concrete and can be assumed equal to 0.63� f c��
0.5 from Matthys �2000�. Although this failure criterion gives higher values of the shear strength of concrete compared to many other models, it is believed that the shear strength of the FRP-to-concrete interface has a higher resistance to shear than plain concrete. The initial failure plane of beams which fail by intermediate crack debonding is at the FRP–concrete interface within the concrete surface. If sufficient surface preparation has been applied to open the pores of the concrete and expose the aggregates, the structural epoxy material will normally penetrate into the interface layer, making it able to resist more interface shear stress due to the higher shear modulus of the adhesive com- pared to the concrete. The analytical model was calibrated from a database of experimental intermediate crack debonding failures. The parameter that was calibrated was the maximum interface shear stress due to stress concentration ��scmax�. This value was calibrated for two separate purposes: �1� for the creation of an analytical model that closely represents the experimentally ob- served behavior �mean model�, and �2� an analytical model which is conservative and can be used in design �design model�.
When the maximum interface shear strength due to applied loading ��wmax� was calculated using the experimentally measured debonding strain for the beams in the database, it was determined that �scmax calculated in this manner had no correlation to the strength of the concrete. Test results by the authors and others suggest that good correlation is found between the interface shear stress due to stress concentration and the moment ratio My / Mdb. This is a result of the larger flexural crack opening displacement occurring as a result of having an applied moment much larger than the moment to cause yielding of the internal tensile steel.
The proposed equation for the maximum interface shear stress due to stress concentration ��scmax�, which gives the best correla- tion between the analytical model and the experimental database was found to be
�scmax = 2.15�1.1 − My Mdb
��f c� �9� For design purposes, the following conservative equation may be used, which provides a probability of exceedance of 5%
�scmax = 3�1.1 − My Mdb
��f c� �10� The experimental versus predicted debonding strains for the pro- posed mean and design analytical models are shown in Figs. 10 and 11, respectively. Figs. 10 and 11 provide evidence of the validity of the mean model to predict the test results and the conservatism of the design model.
In many of the beams collected in the experimental database, the observed failure mode was due to rupture of FRP and not IC debonding. The measured value of maximum strain near midspan prior to rupture was lower than that determined from FRP tensile tests, due to the presence of stress concentrations at the toes of the flexural cracks. Therefore, it is believed that the strain due to these stress concentrations ��sc� caused rupture at a value of ten-
sile strain assuming perfect bond ��db� lower than the ultimate
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rupture strain found during material testing ��u�. As a result, the proposed model requires checking possible rupture of FRP due to stress concentrations at flexural cracks must be performed by comparing the summation of the strain and debonding ��db� and the strain due to stress concentration ��sc� to the ultimate rupture strain of the FRP material ��u� as follows: �db + �sc � �u. For sim- plicity, the equation proposed by Teng et al. �2004� is adopted in the model. Assuming that the surface distribution of interface shear stress on one side of a flexural crack at midspan has a fractional value of 0.5, an equation for the rupture check can be derived as follows:
�db + 0.114 �scmax �nEftf
� �u �11�
For design, �u in the above equation should be reduced by an environmental reduction factor as proposed in ACI Committee 440 �ACI 2002�.
The following is the recommended design procedure using the proposed model: 1. Calculate the moment resistance corresponding to first yield-
ing of the tensile steel reinforcement, My and the correspond- ing strain level in the FRP material ��f @y�.
2. Assume a value for the strain in CFRP at failure due to intermediate crack debonding ��db�.
3. Calculate the nominal moment resistance of the section �Mdb� at debonding failure with the strain assumed in Step 2.
Fig. 10. Experimental versus predicted debonding strains for proposed mean model
Fig. 11. Experimental versus predicted debonding strains for proposed design model
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4. Determine the maximum interface shear stress due to the increase of the load from the yielding stage to the assumed failure stage, �wmax from Eq. �6�.
5. Determine the maximum interface shear stress due to stress concentration ��scmax� using Eq. �10�.
6. Calculate the total interface shear stress ��i� using Eq. �5�. 7. Revise the value of IC debonding strain until �i is equal to
the failure criterion ��cmax�, which is related to the tensile strength of concrete as �cmax = 1.8
*�0.63� f c�� 0.5�.
8. Using the final value of strain in the CFRP after iteration ��db�, calculate the maximum strain in the CFRP due to applied loading and stress concentrations ��scmax� using Eq. �11�.
9. If �scmax is greater than �u then failure will be due to rupture of the CFRP, and the nominal moment should be recalculated using the ultimate strain in the CFRP. �u is the design rupture strain of the FRP material, after application of appropriate environmental reduction factors like the ones provided in ACI Committee 440 �ACI 2002�.
Table 2. Results of Statistical Modeling Exercise
Analytical model
Mean �pred/exp�
Standard deviation
Maeda et al. �1997� 0.87 0.414
Matthys �2000� 1.27 0.703
Chen and Teng �2001� 0.41 0.168
Leung and Tung �2001� 0.72 0.268
Harmon et al. �2003� 0.21 0.149
Ulaga et al. �2003� 0.42 0.172
Oehlers and Seracino �2004� 1.07 0.482
Teng et al. �2004� 1.25 0.405
Chen et al. �2005� 0.81 0.306
Proposed model 1.00 0.181
Fig. 12. Normal distributions for
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Statistical Analysis
The proposed model as well as most of the analytical models discussed in this paper were statistically evaluated for comparison purposes. For each case, the mean � � and standard deviation � � was determined for the variable y = �predicted IC debonding strain� / �experimental IC debonding strain�. The sample size in this statistical analysis is based on the 51 beams that failed due to IC debonding and included in the database as described in detail in Rosenboom �2006�. The normal distribution was applied to the random variable x, using two tests �the Chi-squared and Kolmogorov–Smirnov� to determine the goodness of fit. The re- sults of the statistical analysis are shown in Table 2. If the model did not pass the goodness of fit test, the corresponding cell has bold typeface. The majority of the models in the literature were conservative when calculated against an experimental database of beams and slabs of diverse sizes. The proposed mean model gives a mean value of 1.0, a correlation coefficient �r2� of 76.3% and a standard deviation of 0.181. Fig. 12 shows the variable y which
KS test
Chi-squared test
Probability of exceedance
Correlation coefficient
�r2�
.19 92.4 0.378 0.240
.15 58.1 0.650 0.592
.09 48.8 0.000 0.144
.07 41.5 0.157 0.387
.23 6,494 0.000 0.040
.16 44.4 0.000 0.250
.15 31.1 0.557 0.184
.07 51.9 0.732 0.262
.17 44.3 0.272 0.293
.12 33.4 0.508 0.763
ed model and models in literature
0
0
0
0
0 0 0
0
0
0
propos
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represents the ratio of the predicted debonding strain to the ex- perimental debonding strain versus the normal distribution for the analytical models analyzed. There were several models which did not meet the 95% confidence level for either the Chi-squared or Kolmogorov–Smirnov �KS� test. The model proposed by Harmon et al. �2003� did not match a normal distribution and was ex- cluded in Fig. 12.
Parametric Study
A parametric study was conducted using the proposed mean ana- lytical model to predict intermediate crack debonding. Two types of concrete systems were examined: a reinforced concrete beam, and a prestressed concrete bridge girder. Various parameters were examined within the range of values found in the IC debonding database formulated in Rosenboom �2006�, or within a range of values typically encountered in the field. The proposed mean model was examined in each case and was compared to the model by Teng et al. �2004�. The prestressed concrete bridge girder ex- amined in the parametric study was the girder EB1SB, tested by Rosenboom �2006�. The reinforced concrete beam examined was beam B-08S. As a reference point, the experimentally measured IC debonding strain corresponding to the appropriate parameter is shown as a point in each plot.
Applied Loading
The effect of the applied loading on the IC debonding resistance can be shown either by varying the shear span under three or four-point bending or by using different loading scenarios such as a uniformly distributed load. As discussed previously, there is a greater probability of the FRP system failing by plate-end deb- onding once the shear span to depth ratio is below approximately 2.5. The study indicated that for beams loaded in three and four- point bending, the debonding resistance decreases as the shear span-to-depth ratio �a / d� decreases as shown in Fig. 13 for the prestressed concrete bridge girder. A similar plot can also be ob- tained for the reinforced concrete system. The figure also shows that the predicted resistance using the Teng et al. �2004� model provides a lower bound for low shear span to depth ratios, which gives conservative results as the s / d ratio is increased. Since the
Fig. 13. Predicted debonding strain versus shear span-to-depth ratio for prestressed concrete system
proposed analytical model for IC debonding is a function of the
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slope of the tensile strain in the CFRP strengthening material, for beams loaded using three or four-point bending the slope of this envelope is high near the point load. For structures loaded by uniformly distributed loads, the slope of the tensile envelope is less, so the debonding resistance in these cases would be greater. In the plots presented in the following sections the debonding resistance, assuming a uniform distributed load, is plotted along with the three or four-point bending resistance for comparison. In each case, the resistance assuming a uniform distributed load is higher.
Concrete Properties
Shear cracks during IC debonding propagate along the FRP-to- concrete interface along the concrete surface. Since the shear strength of the concrete is a function of the compressive strength, as the compressive strength of the concrete increases, the IC deb- onding resistance will increase. In both the proposed model and the model by Teng et al. �2004� this trend is applicable. The predicted debonding strain versus the concrete strength for the prestressed concrete system is shown in Fig. 14. For very low concrete strengths, the failure mode in the proposed model begins to transition between IC debonding and crushing of concrete. The predicted debonding strain versus the concrete strength for the reinforced concrete system is shown in Fig. 15. The model of Teng et al. �2004� describes the behavior of reinforced concrete better than prestressed concrete since it was calibrated with this type of system.
FRP Properties
The FRP axial stiffness per unit width �nEftf� was examined as one of the parameters in the parametric study for the two types of structural systems. The strengthened systems were evaluated at FRP stiffnesses corresponding approximately to the range of val- ues encountered in the IC debonding database: ranging from 10 to 500 kN / mm. This encompasses a wide range of FRP types including glass, aramid, and carbon of high, medium, and low modulus of elasticity values. At low values of FRP stiffness, the likely mode of failure is FRP rupture for long span structures. With higher values of stiffness, the behavior becomes asymptotic to a minimum value of debonding strain, which is dependent on multiple factors. The predicted debonding strain versus the FRP
Fig. 14. Predicted debonding strain versus concrete strength for prestressed concrete system
axial stiffness per unit width is shown in Fig. 16 for the reinforced
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concrete system. Similar to other parameters investigated, the model by Teng et al. �2004� gives better predictions for the rein- forced concrete system; for the prestressed concrete system evalu- ated, the model predicts FRP rupture only with very low values of FRP stiffness. It should be noted that the rupture strain shown is for each of the FRP systems used for the girders examined and may vary if FRP material with different moduli of elasticity are examined.
Internal Steel Properties
The tensile steel reinforcement ratio has a significant effect on the debonding resistance due to its relationship with the yield strength and the ultimate strength of the section. This relationship is not captured by the model of Teng et al. �2004�, where the strain at debonding is constant regardless of internal steel reinforcing ratio. At low levels of internal steel reinforcing ratio, the interface shear stress due to applied loading is low; however, the shear stress due to stress concentration is high. This is mainly a result of the low value of the ratio My / Mdb. As the internal steel reinforcement ratio is increased, two behaviors can occur. Behavior 1: the ratio of My / Mdb can approach unity and the predicted debonding strain will reduce, or Behavior 2: the FRP approaches rupture before the ratio of My / Mdb approaches unity. This is illustrated in Fig. 17, where the predicted debonding strain is shown for the reinforced
Fig. 15. Predicted debonding strain versus concrete strength for reinforced concrete system
Fig. 16. Predicted debonding strain versus FRP axial stiffness for reinforced concrete system
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concrete system versus the internal steel reinforcing ratio. In Fig. 17, for the beam loaded with a uniformly distributed load, Behav- ior 2 from above occurs; and for the beam loaded in four-point bending, Behavior 1 occurs. It should be noted that the maximum internal steel reinforcement ratio considered in the reinforced concrete system is 2%, approximately equal to the maximum limit prescribed in ACI Committee 318 �ACI 2005�. It is possible to calculate the interface shear stress due to applied load if the predicted moment at debonding �Mdb� is lower than the moment at yielding of the internal steel. This can be done through the calculation of a different interface shear stress block from the cracking moment as evidenced in Fig. 9. This can be done using the cracking moment and the moment at yielding. This was not done in the parametric study, mainly because this behavior was not observed in the IC debonding database, where the range of predicted My / Mdb ratios for the mean model was between 0.64 and 0.9. The two different types of behavior discussed above are also observed in the parametric study of the prestressed concrete system. However, since the FRP axial stiffness is relatively low for this system, the FRP material ruptures before significant re- duction of the predicted debonding strain has occurred due to Behavior 2 discussed above. The ratio of My / Mdb predicted from the mean model for girder EB1SB was 0.66, one of the lower values observed in the IC debonding database. However, since the stiffness of the prestressed concrete girder after yielding of the prestressing strands is greater than that of a reinforced concrete beam, the interface shear stress due to the applied loading does not increase as rapidly as in the case of a reinforced concrete beam.
Level of Prestress
By increasing the effective force in the prestressing strands two main effects may occur: �1� the initial compressive strain in the soffit �prior to strengthening� becomes larger; and �2� the sec- tional moment at which the prestressing strands yield becomes smaller. The first behavior results in a beneficial effect, as the initial compressive strain can be added to the IC debonding strain. The second behavior has the opposite effect, as the interface shear stress due to applied loading becomes larger when the sectional moment at yield is reduced. For the properties of the girder ex- amined, the second behavior controls the relationship and the pre- dicted debonding strain reduces as the effective prestressing force
Fig. 17. Predicted debonding strain versus internal steel reinforcing ratio for reinforced concrete system
is increased. The equation by Teng et al. �2004� does not vary
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with changes in the effective prestress force, and gives conserva- tive values of predicted IC debonding strain. The predicted debonding strain versus the ratio of effective prestress force to ultimate strength of the prestressing strands � f pe / f pu� is shown in Fig. 18.
Design Example
A rectangular reinforced concrete beam with a concrete compres- sive strength of 34.5 MPa is 305 mm wide by 610 mm deep and is reinforced by three 24.8 mm diameter steel bars with a yielding strength of 414 MPa located at a distance 546 mm from the ex- treme compressive fiber. It is proposed to strengthen the 7,310 mm long simply supported beam with two 305 mm wide carbon FRP plies extended to a point near the supports. The ulti- mate tensile strength of the FRP material is 621 MPa, the modu- lus of elasticity is 3,7000 MPa and the thickness is 1.0 mm. The beam is loaded with a uniformly distributed load. The proposed design model described in this paper is used for the design with environmental reduction factors from ACI Committee 440 �ACI 2002� for CFRP with interior exposure.
The existing state of strain on the soffit was determined to be 0.00061 mm / mm. Through an iterative process and ACI Commit- tee 440 �ACI 2002� stress block factors for concrete, the moment at first yielding of the internal steel was found to be 389.8 kN m. By assuming a value of debonding strain of 0.0102 mm / mm, the debonding moment was determined to be 516.4 kN m. The interface shear stress due to the applied loading was found using Eqs. �6� and �8� to be 0.35 MPa. The interface shear stress due to stress concentration was found using Eq. �10� to be 6.11 MPa. The summation of the interface shear stress due to stress concen- tration and due to applied loading was determined to be 6.46 MPa, which is less than the shear strength of concrete failure criterion �cmax = 1.8
*�0.63� f c�� 0.5� determined as 6.66 MPa. Upon
revision of the assumed debonding strain, the failure criterion was matched when the debonding strain was set equal to 0.0109 mm / mm. The final value of strain in the CFRP after itera- tion was used to calculate the maximum strain in the CFRP due to the applied loading and stress concentrations using Eq. �11�. Since this value was less than the ultimate rupture strain of the CFRP material after application of the environmental reduction
Fig. 18. Predicted debonding strain versus effective prestressing force ratio for prestressed concrete system
factors, the predicted failure is IC debonding. Using a strength
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reduction factor of 0.90, the nominal moment capacity of the strengthened section was 464.8 kN m.
Conclusions
This paper proposes a new analytical model which accurately predicts the intermediate crack debonding strain for reinforced and prestressed concrete members flexurally strengthened with FRP materials. Several conclusions from the research can be made: 1. Since the majority of the current analytical models were
derived using specific boundary conditions, loading configu- rations, and test results from single and double lap-shear experiments, many of the models analyzed were conservative in nature and did not correlate well with the database.
2. From experimental observations and analytical modeling, it was found that the interface shear stress along the length of the strengthened member is directly related to two distinct sources: the applied loading and stress concentrations at the toes of flexural cracks.
3. From various analyses of the strengthened reinforced con- crete member, it was found that the interface shear stress corresponding to the load increment from My to Mdb, which can be easily calculated, compares well to more complex analyses and is useful in design.
4. Various width factors were analyzed in the construction of the analytical model and were found not to improve the cor- relation to the IC debonding database.
5. A parametric study was completed that showed the proposed analytical model varies with shear span-to-depth ratio, longi- tudinal reinforcement ratio, prestress force, and several other variables that are not captured in the current models from the literature. Future experimental and analytical research on IC debonding should consider different loading configurations.
Acknowledgments
The writers would like to thank the generous contributions re- ceived from Paul Zia, Mina Dawood, Anthony Miller, and Catrina Walter. The North Carolina Department of Transportation funded much of this research and should be acknowledged. The writers also thank the helpful and thoughtful comments provided by the anonymous reviewers.
Notation
The following symbols are used in this paper: Ef � modulus of elasticity of FRP material; Ga � shear modulus of adhesive; Kp � axial stiffness of plating material per unit width; L � length of beam;
Lee � distance from loaded end to end of cracked region; Leff � effective bonded length; Mcr � flexural cracking moment of strengthened section; Mdb � nominal moment capacity at intermediate crack �IC�
debonding; My � moment at first yielding of internal tensile steel;
a � shear span; bc � width of concrete surface;
bf � width of FRP laminate;
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d � distance from extreme compressive fiber to centroid of tensile reinforcing steel;
f b� � concrete tensile strength; f c� � concrete compressive strength;
f pe � effective prestress force; f pu � ultimate tensile strength of prestressing strand;
h � height of section; kbi � width factor; ldb � unbonded distance near flexural crack due to
interfacial cracking; n � number of layers of FRP; r2 � correlation coefficient; s � distance from center of supports to FRP termination
point; tf � thickness of one layer of FRP material; tb � thickness of adhesive �bond� layer; x � distance along beam from left support;
xcr � distance from support to location of first flexural cracking of concrete;
xy � distance from support to location of first yielding of internal tensile steel;
y � random variable in statistical analysis; �b � calibration factor used in width factor; � � ratio of applied load to the FRP on either side of
concrete block; �db � tensile strain in FRP at failure due to IC debonding;
�f @y � tensile strain in FRP at first yielding of internal tensile steel reinforcing;
�sc � tensile strain in FRP due to stress concentration; �u � ultimate rupture strain of FRP material after
application of environmental reduction factor; � � width of concrete empirical constant used in width
factor; �cmax � shear strength of concrete failure criterion;
�i � interface shear stress; �sc � interface shear stress due to stress concentration;
�scmax � maximum interface shear stress due to stress concentration;
�w � interface shear stress due to applied load; �1 � calibration factor used in width factor; and �2 � calibration factor used in width factor.
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Ye, L. P., Lu, X. Z., and Chen, J. F. �2005�. “Design proposals for the debonding strength of FRP strengthened RC beams in the Chinese design code.” Proc., Int. Symp. on Bond Behavior of FRP in Struc- tures (BBFS 2005), Hong Kong.
Yuan, H., Wu, Z., and Yoshizawa, H. �2001�. “Theoretical solutions on interfacial stress transfer of externally bonded steel/composite lami-
nates.” J. Struct. Mech. Earthquake Eng., 675, 27–39.
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, 12(2): 168-179
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IP-0 56
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esign guidance for strengthening concrete structures using fi bre com
posite m aterials
Design guidance for strengthening concrete structures using fibre composite materials
This Report provides guidance for structural designers on strengthening concrete buildings and bridges by bonding fibre composite polymers (FRPs) to the surface or embedded in the concrete and covers multiple applications as well as guidance on the advantages and disadvantages of FRPs over similar materials. This relatively new technique is proving to be much quicker and more cost-effective than techniques using steel plates.
This third edition explains the design approach in detail and discusses workmanship, installation, inspection and maintenance as well as covering a number of changes brought about by the introduction of Eurocode 2, additional research findings and further experience of the use of the materials.
CCIP-056 Published May 2012 © The Concrete Society Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey, GU17 9AB Tel: +44 (0)1276 607140 Fax: +44 (0)1276 607141 www.concrete.org.uk
A cement and concrete industry publication
Report of a Concrete Society Working Party
Technical Report No. 55
Design guidance for strengthening concrete structures using fibre composite materials Third Edition
The C oncrete Society Technical R
eport N o.55
TR55 - cover.indd 1 17/05/2012 10:20:53
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A cement and concrete industry publication
Acknowledgements The work of preparing this Report was funded by the following organisations:
BASF Construction Chemicals Fyfe (Asia) Fyfe (Europe) Highways Agency Network Rail
The Concrete Society is grateful to the following for providing photographs for inclusion in the Report:
Concrete Repairs Ltd Cornwall County Council Fyfe Europe Halcrow Makers Uk Ltd Maunsell Structural Plastics Sika Ltd
Published by The Concrete Society
CCIP- 056 Published May 2012 ISBN 978-1-904482-70-3 © The Concrete Society
The Concrete Society Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey GU17 9AB Tel: +44 (0)1276 607140 Fax: +44 (0)1276 607141 www.concrete.org.uk
CCIP publications are produced by The Concrete Society (www.concrete.org.uk) on behalf of the Cement and Concrete Industry Publications Forum – an industry initiative to publish technical guidance in support of concrete design and construction.
CCIP publications are available from the Concrete Bookshop at www.concretebookshop.com Tel: +44 (0)7004 607777
All advice or information from The Concrete Society is intended for those who will evaluate the significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information is accepted by The Concrete Society or its subcontractors, suppliers or advisors. Readers should note that publications are subject to revision from time to time and should therefore ensure that they are in possession of the latest version.
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Design guidance for strengthening concrete structures using fibre composite materials, Third Edition
Contents
Members of the working party v 1. Introduction 1
2. Background 4 2.1 Assessment of structures to be strengthened 4 2.2 Strengthening solutions 7 2.3 Advantages and disadvantages of fibre composite strengthening 8 2.4 Design life 12 2.5 Economics 13 2.6 Level of strengthening 16
3. Material types and properties 17 3.1 Fibres 17 3.2 Fabrics 20 3.3 Plates 20 3.4 Rods and strips 21 3.5 Preformed shells for column confinement 21 3.6 Specials 22 3.7 Adhesives and laminating resins 23 3.8 Environmental aspects and health and safety 26 3.9 Choice of materials for design 26
4. Review of applications 33 4.1 Buildings 33 4.2 Bridges 37 4.3 Other structures 45
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5. Structural design of strengthened members 48 5.1 Symbols 48 5.2 Overview of available design guidance 52 5.3 Basis of design 52 5.4 Mechanical properties of materials 55 5.5 Partial safety factors for loads 57 5.6 Partial factors for material properties 57 5.7 Accidental actions 61
6. Strengthening members in flexure 70 6.1 General 70 6.2 Moment capacity 71 6.3 FRP separation failure 74 6.4 Flexural strengthening with near-surface-mounted reinforcement 84 6.5 Flexural strengthening plate location 90 6.6 Thick and multi-layer laminates 90 6.7 Statically indeterminate structures 91 6.8 Fatigue 93 6.9 Serviceability 94 6.10 Strengthening prestressed structures 97 6.11 Flexural strengthening design flow charts 100
7. Shear strengthening 104 7.1 Introduction 104 7.2 FRP strengthening design procedure 105 7.3 Spacing of FRP strips 108 7.4 Additional longitudinal FRP 109 7.5 Near-surface-mounted reinforcement for shear strengthening 110 7.6 Deep embedment bars for shear strengthening 111 7.7 Surface-mounted shear strengthening design flow chart 113
8. Strengthening axially-loaded members 115 8.1 Introduction 115 8.2 Compression in circular columns 116 8.3 Stress–strain model for concrete in FRP-confined circular sections 122 8.4 Combined axial compression and flexure 123
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8.5 Strengthening columns with non-circular cross-section 128 8.6 Other stress/strain conditions 134 8.7 Shear strengthening circular columns 135 8.8 Serviceability 137 8.9 Column design flow charts 138
9. Emerging technologies 144 9.1 Prestressing using FRP composites 144 9.2 FRP anchorage techniques 148 9.3 Bolted plate anchors 149 9.4 Prestressed NSM bars 149 9.5 NSM bars for shear strengthening 149 9.6 FRP anchor systems 150 9.7 Steel-reinforced polymers 150 9.8 Prestressed carbon FRP straps for shear strengthening 150 9.9 Mechanical fastening techniques 151 9.10 Strengthening for torsion 151 9.11 Inorganic adhesives 151
10. Workmanship and installation 153 10.1 Overview of requirements 153 10.2 Evaluation of concrete condition 154 10.3 Concrete preparation 155 10.4 Material conformity 157 10.5 Storage of materials 158 10.6 Site conditions 158 10.7 Mixing and application of adhesive 158 10.8 Assembly and visual inspection 162 10.9 Control samples 164 10.10 Non-destructive tests 167 10.11 Application of overcoatings 167 10.12 Identification/warning signs 168 10.13 Records 169
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11. Long-term inspection and monitoring 170 11.1 Inspection and monitoring regime 170 11.2 Frequency of inspections 171 11.3 Routine visual inspection 171 11.4 Detailed inspection 172 11.5 Maintenance 172
References 173 Appendix A. Glossary of terms 184 Appendix B. Tasks and responsibilities of installers and supervisors 186 B1 Installer role and responsibilities 187 B2 Supervisor role and responsibilities 187
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Members of the Working Party
Full Member Brian Bell Network Rail (Chairman) James Broughton Oxford Brookes University Lee Canning Mouchel John Clarke The Concrete Society (Secretary) Antony Darby University of Bath John Drewett Concrete Repairs Will Duckett Gifford Neil Farmer Tony Gee and Partners Chris Gallivan BASF Construction Chemicals Richard Hill Arup Nicholas Hooper Oxford Brookes University Tim Ibell University of Bath Christoforos Kolyvas Fyfe Europe Sam Luke Mouchel Martin Richardson Sika Wendel Sebastian University of Bristol Jon Shave Parsons Brinkerhoff Ian Smith Tony Gee & Partners Tim Stratford University of Edinburgh Pierfrancesco Valerio Highways Agency
Corresponding Members Jeslin Quek Fyfe Asia
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1. Introduction Fibre composites have been successfully used for many years in the aerospace and automotive industries. They are also used in construction – for example, for structural elements, particularly in aggressive environments such as chemical plants, and for cladding. This Report does not consider such applications but deals only with the strengthening of concrete structures with fibre composite materials bonded on the surface or embedded in the concrete.
There are a number of situations where the load-carrying capacity of a structure in service may need to be increased, such as change of loading or use, or where the structure has been damaged. In the past, strength would be increased by casting additional reinforced concrete, dowelling in additional reinforcement or adding structural steel – see for example the Concrete Bridge Development Group report Enhancing the capacity of concrete bridges(1). The technique of strengthening concrete structures by bonding steel plates to the surface of the tension zone with adhesives and bolts was developed in the 1960s. Since about the late 1980s the use of fibre-reinforced polymers (generally known as FRPs) in this application has been developing rapidly.
FRP materials have many advantages over steel plates in this application and they can be used in situations where it would be impossible or impractical to use steel: for instance, they can be formed in place into complicated shapes. FRPs are lighter in weight than steel plates of equivalent strength or stiffness. This makes installation much simpler and quicker and in most circumstances eliminates the need for temporary support for the plates while the adhesive gains strength. Unlike steel plates, fibre composites do not require the installation of bolts in the anchorage zones. FRPs can also be easily cut to length on site.
Some types of fibre are also available in the form of fabrics, which can be bonded to the concrete surface. The chief advantage of fabrics over plates is that they can be wrapped round curved surfaces, for example around columns or completely surrounding the sides and soffits of beams.
A sketch showing a wide range of strengthening applications to a hypothetical structure is shown in Figure 1. Clearly not all structures are suitable for strengthening using fibre composites. A major limitation will be when the concrete strength is low or where there are ongoing corrosion or other durability problems. The amount of strengthening that can be applied will often be limited by the problem of failure being induced elsewhere in the structure.
Flexural and shear strengthening can be achieved by bonding pultruded strips or rods into slots cut in the cover region of the concrete. This application is termed near-surface- mounted (NSM) reinforcement. Shear strengthening can also be achieved by FRP rods bonded into holes drilled vertically through the web.
Introduction 1
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1 Introduction
Figure 1 Different types of structural strengthening, applied to beams, slabs, walls and columns.
An appreciable number of structures in the UK and elsewhere have been strengthened using FRP materials. It is estimated that several hundred structures have been strengthened in the UK to date, with the amounts of fibre composite material involved ranging from a few metres (or square metres) for a small job to several kilometres on a major one.
There was little independent guidance on how the design of strengthening works should be carried out until the First Edition of Concrete Society Technical Report 55, Design guidance for strengthening concrete structures using fibre composite materials, was published in 2000(2). Subsequently, guidance documents have been published in various countries, including the USA(3) and Canada(4). In addition, in 2002 the Canadian Standards Association published the first national code for strengthening with FRP(5). In the light of these guidance documents and ongoing research, a Second Edition of TR55 was published in 2004(6). In the UK, the Highways Agency published guidance for strengthening bridges using FRP(7,8).
Following the publication of the First Edition of TR55, The Concrete Society published Technical Report 57, Strengthening concrete structures using fibre composite materials: acceptance, inspection and monitoring(9) in 2003, which covers the vitally important topics of inspection and maintenance.
Materials and techniques are developing, as is the range of applications. Hence it was thought necessary to produce this Third Edition of TR55. A number of the changes are matters of detail, brought about by the introduction of Eurocode 2(10), additional research findings and further experience of the use of the materials. However, significant changes or additions have been made in some areas, as follows: � Material and system selection guidance. � The treatment of partial safety factors in the design process has been modified; factors
are now applied to the FRP strains rather than the stresses. � Extreme loadings including the performance of strengthened members in fire.
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� A more systematic and comprehensive approach to separation failure. � Design of members in flexure, to give a more rational approach that is closer to that
used for reinforced concrete. � Design of members in shear, to provide a less empirical approach, allowing wider and
more confident application of the technique. � Column design, to provide a more unified approach for axial and combined axial and
flexural strengthening. A more detailed approach has been developed for the strengthening of rectangular columns.
� Flow charts for flexure, separation, shear and column design. � Additional guidance for the technique of NSM reinforcement. � Design guidance for the new technique of deep embedment bars for shear strengthening. � Overview of emerging technologies, such as the use of prestressed composites,
mechanical anchorage systems and alternatives to the adhesives currently used.
The guidance in this Report is not specific to any particular type of FRP material or any particular strengthening technique. It covers the use both of manufactured composite materials bonded on or near the concrete surface, or embedded in the concrete, and composites formed in situ on the surface. However, the Report is biased towards materials and techniques readily available in the UK construction industry; it should be noted that other places worldwide may favour different approaches or have different drivers.
The Report deals mainly with the design of strengthened members, i.e. beams, slabs and columns. Other aspects, such as currently available materials, appropriate application techniques and current uses, are described briefly. It is intended to cover the principles involved, not the detailed approaches that are applicable to individual materials and techniques. Further details of material properties and techniques can be obtained from materials suppliers and from specialist designers and contractors. The important topics of inspection and maintenance are covered briefly in this Report; more detailed coverage is given in Concrete Society Technical Report 57(9), which should be read in parallel with this Report. Reference is made to specific parts of Technical Report 57 (abbreviated to TR57) where appropriate.
The Report is specifically concerned with strengthening concrete structures. Fibre composites have been successfully used to strengthen metallic and other structures – see CIRIA C595(11). The basic principles of this Report will still be applicable but the detailed design recommendations will not apply.
To help readers unfamiliar with composites, a glossary of terms is given in Appendix A.
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2 Background
2. Background A concrete structure may need strengthening for many reasons. Examples include: � To increase live-load capacity, e.g. of a bridge subject to increased vehicle loads or a
building the use of which is to change from residential to commercial. � To add reinforcement to a member that has been underdesigned or wrongly constructed. � To improve seismic resistance, either by providing more confinement to increase the
strain capacity of the concrete, or by improving continuity between members. � To replace or supplement reinforcement, e.g. damaged by impact or lost due to corrosion.
(This will only be practical if the cause of the damage is identified and treated.) � To provide replacement reinforcement following structural alterations, e.g. around holes
cut through floor slabs for lift or stair installation or through walls to accommodate new services.
In most cases it is only practical to increase the live-load capacity of a structure. However, in some situations it may be possible to relieve dead load, by jacking and propping, prior to the application of the additional reinforcement. In these cases, the additional reinforcement will play its part in carry ing the structure’s dead load. Prestressing techniques using composite materials have been developed that also help to carry part of the dead load. This approach is not covered in detail in the design sections of this Report.
Three basic principles underlie the strengthening of concrete structures using fibre composite materials, which are the same irrespective of the type of structure: � Increase the bending moment capacity of beams and slabs by adding fibre composite
materials to the tensile face. � Increase the shear capacity of beams by adding fibre composite materials to the sides
in the shear tensile zone or by the addition of embedded FRP bars. � Increase the axial and shear capacity of columns by wrapping fibre composite materials
around the perimeter.
These forms of strengthening can also be used to increase the seismic performance of structures by improving the ductility of elements in addition to their strength.
The decision to strengthen a structure will come at the end of what may be a prolonged assessment process. This is illustrated, in outline only, in Figure 2. The process is independent of structure type and should be based on rigorous criteria and sound engineering judgement. The assessment process will usually involve some investigation of the condition of the structure or some reanalysis and study of the background issues. Guidance may be obtained from documents such as Concrete Society Technical Report 54, Diagnosis of deterioration in concrete structures(12), and the Institution of Structural Engineers’ Appraisal of existing struc tures(13). In all cases an experienced engineer should be part of the assessment team.
2.1 Assessment of structures to be
strengthened
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Background 2
The process will usually be aimed at providing answers to some or all of the following questions: � Has the condition or load-carrying capacity of the structure decreased significantly? � Has the loading changed significantly? � Is the concrete of adequate quality and strength to make strengthening a feasible option?
This applies to the structure overall and not just to the surface or surfaces to which the FRP is to be bonded. It is suggested that the minimum concrete strength should be 20MPa and the pull-off strength of the surface in the zone to be strengthened should be 1.5MPa.
� What are the risks to the public, to commerce and to the structure of taking no action? � What are the cost implications of strengthening, including direct costs, future costs
and the cost of disruption while the work is carried out? � What are the cost implications of demolition and rebuilding, including direct costs,
future costs, costs associated with loss of use of the structure and disruption while the work is carried out?
� What is the anticipated future life of the structure in its present form? � Will inspection and maintenance be possible? � How would strengthening works affect local infrastructure, commerce, safety and the
environment? � What is the age of the structure and is it of historical importance? � What parties and authorities would be required to approve the works? � Are there any programming or funding constraints?
By addressing these issues, decisions about the appropriate action for a particular structure can be made. In some cases, strengthening will not be a sensible option, unless other remedial work is also carried out. Examples are structures with significant materials problems, such as high chloride content leading to severe reinforcement corrosion. In general it will not be appropriate to strengthen a deteriorated structure unless the cause of the deterioration (e.g. chloride ingress) has been addressed and, where possible, mitigated. In some cases it may be preferable to re-analyse the structural capacity, possibly leading to downgrading in function.
The general principles for protection and repair of concrete structures (including FRP plate bonding) are outlined in Part 9 of BS EN 1504(14).
Once it has been decided that strengthening is a realistic option and that the structure is suitable for strengthening, the next step is to identify an appropriate strengthening scheme. The feasibility study should include consideration of the points listed above in relation to possible schemes – such issues as whole-life costs of the various options and careful assessment of the residual life and strength of the structure. The risks associated with each option should be assessed during the feasibility study. This assessment should compare the possible higher risks associated with newer techniques with those of older, tried and tested, methods. However, the benefits of newer techniques can outweigh perceived disadvantages: the risks associated with premature failure are low if strengthening is to be provided only for an appropriate proportion of the live-load case.
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2 Background
STRUCTURAL ASSESSMENT FLOWCHART
CONSTRUCTION PROCESS
IN SERVICE MANAGEMENT
Construction records
Periodic inspection and testing
Special inspection structural
assessments (if necessary)
Benchmark inspection
Deterioration
Change of use
Change of standards
External factors or accident
Continue inspections
Monitoring and other interim
measures
Consider remedial options
Not deficient Deficient
Figure 2 Flow chart of assessment process.
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Background 2
Strengthening solutions considered in a feasibility study can range from repair of a damaged structure in order to restore its original strength to adding elements to increase its capacity.
All solutions are, to a greater or lesser extent, project-specific but some general approaches are commonly used. Repair typically involves crack injection and/or breaking out damaged areas and reinstating with cementitious repair mortars or flowing concrete. As stated above, this approach is used where the aim is to restore the original strength of a structure.
The most common traditional techniques for strengthening are as follows: � Increase the reinforced concrete cross-section. Approval authorities and owners of
structures usually readily accept this solution as it has a proven track record. However, loading restrictions are required while the concrete cures to an acceptable strength. This restriction may be critical in some instances, for example where a bridge closure would lead to unacceptable disruption.
� Add prestressing to relieve dead load. Similar to increasing the cross-section, this technique has a proven track record and gains ready acceptance. Loading restrictions may be required during installation, which may not be acceptable. This technique requires the existing structure to be capable of withstanding high local pre stressing forces.
� Add material to provide confinement of the concrete in compression members. This can be achieved by installing in-situ reinforced concrete or prefabricated steel collars. The use of collars is the most common technique where space permits. With in-situ reinforced concrete collars, loading restrictions on the structure are required while the concrete gains strength.
� Shear strengthening. This can be achieved by installing external steel straps to beams.
Fibre composite strengthening is seen as a viable alternative to some of these traditional methods because of the speed and ease of installation and the ease with which the material can be cut to shape and bent to fit slightly curved surfaces. Fibre composites are particularly attractive in locations where space does not allow a significant increase in cross-section or where the installation time is critical. Columns can be strengthened by wrapping with fibre composite material, to increase their axial capacity and their resistance to bending and shear.
An alternative to externally bonded plates and fabrics is the use of Near Surface Mounted reinforcement (NSM), which has benefits where the exposed concrete surface is to be trafficked or otherwise exposed to potential damage. In the UK this technique has been applied to car park decks, and overseas to jetties and dockside structures that are subjected to loads from the movement of shipping containers. Under the European Sustainable Bridges project a redundant bridge in Örnsköldsvik, Sweden was strengthened with NSM and later demolished as a full-scale trial – see Elfgren et al.(15). The technique is also applicable where the surface of the concrete is undulating, or if there is excessive laitance or a thin layer of poor-quality concrete near the surface. Installation is more costly than for externally bonded reinforcement, due to the need to cut the slots and a slightly more complicated method for surface preparation. De Lorenzis et al.(16) briefly reviewed applications of NSM and cited examples of strengthening vertical elements and soffits as well as the more normal top surfaces. Usually the technique would only be used where externally bonded reinforcement is not a good technical solution, for example where the FRP might be damaged by traffic.
2.2 Strengthening solutions
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2 Background
A method of strengthening reinforced or prestressed beams in shear that has been demonstrated by laboratory testing to be effective is the use of deep embedded FRP bars. Holes are drilled vertically through the entire depth of the web, usually from the soffit to minimise disruption. The bars are then fixed into the holes with resin to provide additional shear resistance. Round bars should be used with adequate surface finish to ensure good bond. Testing has shown that carbon FRP bars should be used as they have sufficient tensile capacity to ensure full bond capacity is obtained and the failure is ductile – see Valerio et al.(17). The concept is similar to the use of stainless steel threaded bar for such applications but the FRP alternative eliminates the possibility of galvanic corrosion of the carbon steel reinforcement in close proximity to the stainless steel bars. This technique has the further benefits that no surface preparation of beam webs is required in beam-and-slab situations and the webs need not be accessible. This is very useful in situations where precast beams are closely spaced. The approach could also be used for strengthening slabs in punching shear around columns. The method has been shown to be feasible, preventing shear failure in laboratory tests and instead forcing a ductile flexural failure to occur – see Valerio(18). However, for many real-life scenarios the practicalities of drilling such holes whilst avoiding the existing steel reinforcement should not be underestimated”.
One of the benefits of FRP strengthening in terms of whole-life costs (or more correctly remaining-life costs) is the expected low cost of future maintenance and the reduced disruption due to shorter time on site. As with all strengthening schemes, there is the environmental advantage of retaining the existing structure as against replacement.
Overall, the advantages of fibre composites tend to outweigh the perceived disadvantage of a relatively limited track record and the reluctance of some approval authorities and owners of structures to adopt new materials.
Fibre composite strengthening techniques have a number of advantages and disadvantages when compared with more traditional approaches.
Fibre composite strengthening materials have higher ultimate strength and lower density than steel. When taken together, these two properties lead to fibre composites having a strength to weight ratio significantly higher than steel plate in some cases, although it is generally not possible to use this fully.
The lower weight makes handling and installation significantly easier than steel. This is particularly important when installing material in cramped locations. Figure 3 shows carbon fibre plates being installed in a rail tunnel.
2.3 Advantages and disadvantages of fibre
composite strengthening
2.3.1 Advantages
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Background 2
Figure 3 Installing fibre composite plates in a rail
tunnel.
Work on soffits of bridges and building floor slabs can often be carried out from man- access platforms rather than full scaffolding. Steel plate requires heavy lifting gear and must be held in place while the adhesive gains strength. Bolts must be fitted through the steel plate into the parent concrete to support the plate while the adhesive cures and to reduce the effects of peeling at the ends. When applying FRP plate or sheet material, pressure is applied to the surface using a roller to remove entrapped air and excess adhesive. It may be left unsupported. In general, no bolts are required; in fact, the majority of FRP strengthening material is uniaxial (i.e. all the fibres are aligned in one direction) and the use of bolts would seriously weaken the material unless additional cover plates are bonded on, or the plates are designed with, a proportion of fibres in the transverse direction. Fibre composite materials are available in very long lengths while steel plate is generally limited to 6m. The availability of long lengths and the flexibility of the material (see Figure 4) also simplify installation: � Laps and joints are not required. � Within limits, the material can take up irregularities in the shape of the concrete surface. � The material can follow a curved profile; steel plate would have to be pre-bent to the
required radius. � The material can be readily installed behind existing services (see Figure 5). � Overlapping, required when strengthening in two directions, is not a problem because
the material is thin (see Figure 6) but care must be taken with the application process in the region of the overlaps.
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2 Background
Figure 4 Installing FRP plate, showing the flexibility of
the material.
Figure 5 FRP plate installed behind existing services.
Figure 6 Overlapped carbon FRP plates on Dudley Port
Bridge, West Midlands.
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Background 2
The materials – fibres and resins – are durable if correctly specified, and require little maintenance. If they are damaged in service, it is relatively simple to repair them, by adding an additional layer.
The use of fibre composites does not significantly increase the weight of the structure or the dimensions of the member. The latter may be particularly important for bridges and other structures with limited headroom and for tunnels.
In terms of environmental impact and sustainability, studies have shown that the energy required to produce FRP materials is less than that for conventional materials. Due to their light weight, the transport of FRP materials has minimal environmental impact.
In combination, these various factors lead to a significantly simpler and quicker strengthening process than when using steel plate. This is particularly important for bridges because of the high costs of lane closures and possession times on major highways and railway lines.
The main disadvantage of externally strengthening structures with fibre composite materials is the risk of fire, vandalism or accidental damage, unless the strengthening is protected. A particular concern for bridges over roads is the risk of soffit reinforcement being hit by over-height vehicles (‘bridge bashing’). However, strengthening using plates is generally provided to carry additional live load and the ability of the unstrengthened structure to carry its own self-weight is unimpaired (see also Section 2.6 ). Damage to the plate strengthening material only reduces the overall factor of safety and is unlikely to lead to collapse. An additional cause of damage is that from following trades, such as drilling through FRP to fix brackets etc.
As detailed later, workmanship is critical to the success of a fibre composite strengthening scheme. Thus a further cause for concern is the difficulty of ensuring that the work is carried out correctly. In the UK a certification scheme for operatives and supervisors involved with the application and inspection of fibre composite plates in the strengthening of concrete buildings and civil engineering structures has been proposed and is currently being developed by TWI under their Certification Scheme for Personnel (CSWIP). This is a comprehensive scheme which provides for the examination and certification of individuals seeking to demonstrate their knowledge and/or competence in their field of operation. CSWIP certificates are generally well recognised by many different national bodies, including authorities, owners of plant and structures, and purchasers. An NVQ (National Vocational Qualification) Level 2 for installation of FRP is being developed.
Problems with the adhesive layer will not generally be visible from the surface. Similarly, it is difficult to assess the presence of voids in wet lay-up systems and thus there is uncertainty as to the properties that have been achieved.
2.3.2 Disadvantages
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2 Background
Currently the properties of FRP materials used in FRP strengthening schemes are not covered by British or International Standards. However, the adhesives are covered by Part 4 of BS EN 1504(14). In addition, the Classification and Assessment of Composite Materials Systems for Use in the Civil Infrastructure (CompClass) project, led by Oxford Brookes University, has developed a classification scheme for adhesives and laminating resins – see Section 3.9.6. Further information may be obtained from the website www.compclass.org.uk.
Experience of the long-term durability of fibre composites is limited, although some installations have been in service for a number of years. This may be a disadvantage for structures for which a very long design life is required (see Section 2.4) but can be overcome by appropriate monitoring (see Chapter 11 ) and as detailed in TR57(9). A means of long- term evaluation of the bonded strengthening system is included within the CompClass Classification Scheme.
Strengthening against one mode of failure (e.g. bending) may increase the probability of occurrence of another mode (e.g. shear). Strengthening may also alter the characteristics of a failure, so for example a beam that previously had a ductile flexural failure may become brittle in flexure. These factors must be considered in the design process.
A perceived disadvantage of using FRP for strengthening is the relatively high cost of the materials. However, comparisons should be made on the basis of the complete strengthening exercise (see Section 2.6), taking into account ‘hidden’ costs such as delays and disruptions to the users of the structure. However, installation can require large areas of the concrete surface to be prepared, particularly with fabrics, which can be labour-intensive and may be noisy and produce dust, so FRP strengthening may still cause some disruption.
A disadvantage in the eyes of many clients will be the lack of experience of the techniques and suitably qualified staff to carry out the work, but this can be overcome by using suitably experienced designers and contractors.
The Highways Agency documents BD 84/02, Strengthening of concrete bridge supports for vehicle impact using fibre reinforced polymers(7), and BD 85/08, Strengthening highway structures using externally bonded fibre reinforced polymer(8), use 30 years for the design life of a fibre composite strengthening system. This figure is considered reasonable, based on current experience of the adhesives used in steel plate bonding. There is considerable experience of the use of adhesives in other applications, such as marine structures, which would suggest a design life of at least 40 years. Wholly fibre composite structures such as the West Mill Bridge (see Canning and Luke(19)) have been designed for significantly longer lives and BD 90/05, Design of FRP bridges and highway structures(20), specifies a design life of 120 years.
2.4 Design life
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Background 2
Ideally, the design life for the strengthening system should be related to the remaining life of the structure and should take into account the future plans for the structure. In many cases, if a mature structure is to be strengthened, a 40-year life for a strengthening system may well be appropriate. However, this may not be the case for structures with long design lives, such as bridges and nuclear structures. Here, it may be necessary to accept a strengthening system with a design life less than the anticipated remaining life of the structure, on the understanding that the life of the strengthening system will be reassessed at a future date.
Due to the relative lack of long-term experience of the performance of fibre composite strengthening systems, regular inspection and maintenance regimes should be instigated – see Chapter 5 of TR57(9). This is particularly important for buildings, which, unlike bridges, are not generally subjected to any form of routine inspection. Where practical, additional material should be installed, which could be removed at a later stage for testing if required. This approach has been adopted on a number of structures including the Barnes Bridge in Manchester and the John Hart Bridge in British Columbia – see Section 4.2. It may be possible to incorporate some form of monitoring system in the fibre composite.
In their 2010 paper reviewing the use of FRP for strengthening road and rail bridges in the UK, Loudon and Bell(21) noted that ‘few real in-service issues have manifested themselves on any of the concrete FRP strengthening schemes completed by either the Highways Agency or Network Rail to date’.
The relative economics of the use of fibre composites and other strengthening systems depends on the circumstances. Many factors are involved, and it is necessary to compare costs both in the short and long term. The latter may be difficult to quantify as the lifetime behaviour can only be estimated fairly crudely. In many cases the alternative may be demolition and replacement of the structure, with the consequent disruption.
Factors such as the cost of access for installation and the required possession time should be taken into account as they can have a significant influence. High closure costs are often incurred by highway and railway works. These will vary significantly depending on a range of factors, including the location, the season and the time of day. However, they will not take into account the social costs of disruption. As an example, upgrading of a major highway in New York City had to be carried out at night as there was a requirement for the road to be fully open during the day. The penalty for failure to reopen the carriageway in the morning was $30,000 per hour, with a penalty of $20,000 per day for overrun of the complete project(22).
2.5 Economics
2.5.1 Installation
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2 Background
Studies carried out for Railtrack (now Network Rail) have indicated that strengthening with FRP materials will be approximately 30% cheaper than the equivalent strengthening using steel plate. The use of FRP for column strengthening on one UK highway bridge halved the cost, as well as shortening the contract duration and significantly reducing the need for lane closures.
Loss of revenue can be significant when a structure is understrength and hence cannot be used to its full capacity. It was reported that the Trenchard Street car park in Bristol was losing £1 million per year in lost sales prior to strengthening.
In Florida, the beam–column connections in a parking garage were strengthened by bonding carbon fibre sheet material to the sides of the beams – see Kliger(23). It was estimated that the adhesively bonded repair was 35% cheaper than the conventional method, which would have involved dowelling in additional steel reinforcement and encasing the joint with additional concrete.
In Edmonton, Canada, carbon FRP composite sheet material was applied to the soffits and sides of a bridge, to improve its shear resistance – see Alexander and Cheng(24). The cost was reported as $70,500 for strengthening the complete bridge. A conventional external stirrup system was estimated to cost some $100,000. Thus the bonded solution showed approximately 30% saving in costs, due chiefly to the fact that the work was carried out from below the bridge and avoided the traffic closures that would have been required for the conventional system.
Beams of the Maryland Street Bridge in Winnipeg, Canada, were strengthened with vertical and horizontal sheets of carbon fibre to increase the shear capacity. It was estimated that the cost was about 70% of the conventional approach, which would have involved removing parts of the bridge deck, installing post-tensioned external shear stirrups and casting additional concrete round the beams. This comparison was on the basis of direct costs and did not consider factors such as traffic delays.
A 30-year-old processing tower in Qatar was strengthened with 3500m of carbon FRP plate. Several options were considered but the material was chosen because of the speed of installation. The plant was shut down for 25 days to allow the work to be undertaken, but the contract was actually completed in 20 days. This enabled production to restart earlier than planned, which was clearly of great benefit to the operators of the plant – see Luke et al.(25).
Hooks and Cooper(26) give two examples of significant cost savings. The crossheads of a 1950s bridge in New York were strengthened in flexure and shear using carbon FRP plates, at a cost of $18,000. It was estimated that conventional repair would have cost $150,000. Concrete box beams in Kentucky were strengthened at a cost of $105,000, when replacement of the structure would have cost $450,000.
Some economic considerations for particular applications are reported in later chapters of this Report. Unfortunately, the information is largely qualitative, but can be used for guidance when investigating the economics of a situation.
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Background 2
The technique of whole-life costing can play an important part in making decisions on when and how to repair or strengthen concrete structures. This is recognised in Part 9 of BS EN 1504(14), which lists among the factors to be considered when choosing between repair options: � The number and cost of repair cycles acceptable during the design life of the concrete
structure. � The cost and funding of the alternative protection or repair options, including future
maintenance and access costs.
The whole-life cost of a repair or strengthening solution is the sum of the initial (installation) cost and the future (maintenance) costs over the remaining life of the structure. To permit meaningful comparisons to be made, future costs are discounted to present-day value. To carry out a life-cycle cost analysis requires an understanding of: � Deterioration processes as they relate to the particular structure or different parts of
the structure. � Repair and strengthening methods and their durability. � Costs of repair or strengthening and maintenance activities. � Indirect costs due to loss of service. � The owner’s requirements for the serviceability and service life of the structure.
In many cases, the basic data to permit reasonable assessments of the various elements that make up the whole-life cost are not available. Nonetheless, it can be appreciated that strengthening using fibre composites can be competitive in whole-life cost comparisons because both installation and maintenance costs are usually lower than those of competing techniques and possession times are shorter.
Prolonging the useful life of structures that will still be required for a long time into the future (e.g. road or rail bridges) becomes an attractive proposition in whole-life cost terms. This is because, if replacement can be delayed for many years, the cost at present-day value is considerably reduced. For example, if a discount rate of 8% is assumed, a cost of £1,000,000 at year 20 has a present-day value of only £200,000. It can be more economic, in whole-life cost terms, to strengthen now and replace in 20 years, than to replace now.
One factor which is difficult to take into account in whole-life costing is the time until the structure becomes obsolete. This may happen for physical, economic, functional, technological, social or legal reasons. This uncertainty can lead to the lowest initial cost option being favoured on the basis that there is little to be gained from additional spending now, if the structure is unlikely to be required in its present form in ten years.
2.5.2 Whole-life costing
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2 Background
A key factor in the choice of strengthening system will be the level of strengthening (i.e. the maximum increase in load capacity) that can be achieved. Strengthening against one mode of failure (e.g. bending) may increase the probability of occurrence of another mode (e.g. shear). Strengthening may also alter the characteristics of a failure; so, for example, a beam that previously had a ductile flexural failure may become brittle in flexure. This must be considered in the design process. In addition, the design must explicitly consider the risks associated with any possible partial or complete failure of the strengthening, due for example to fire, vandalism or accidental damage. Due to the lack of long-term experience of fibre composite strengthening, some clients are recommending that the approach should only be used to increase the factor of safety against collapse. In other words, failure of the composite will not lead to the collapse of the structure.
2.6 Level of strengthening
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Material types and properties 3
3. Material types and properties Fibre composites are formed from high-performance fibres combined with an appropriate resin. Epoxies are generally used, but some development has been carried out on inorganic cement-based matrices – see for example Balaguru and Toutanji(27). For strengthening applications, the composite may be preformed into plates or panels and bonded to the concrete. The most common example is composite plates bonded to the soffits of beams or slabs. Alternatively, the fibres may be combined with the resin in situ as part of the application process, such as in the wrapping of columns. The mechanical properties of fibre composites are chiefly controlled by the type, amount, orientation and distribution of fibres in the cross-section. The role of the resin is to transfer stresses to and from the fibres and also to provide some protection from the environment.
This chapter provides a general introduction to the fibres and resins used for strengthening. For further information on the properties and behaviour of composites, the reader should consult standard textbooks, such as An introduction to composite materials(28) and Composite materials: engineering and science(29). CompClass (see Section 3.9.6) includes details on the various testing methods and recommended standards for establishing properties for both design and quality control (QC) purposes. Reinforcing systems that have been evaluated according to the Classification Scheme that includes pultruded plates, cured prepreg (pre- impregnated) and fabric systems will have established data on bulk tensile performance, moisture uptake, glass transition temperature, thermal expansion, shrinkage, lap shear strength and pull-off strength, possibly including long-term evaluation.
The fibres most commonly used for strengthening applications are glass, carbon or aramid. (Aramids are better known by the trade names Kevlar® and Twaron.) More recently, basalt fibres have been introduced. Each is a family of fibre types in general, with individual fibre types within the families that may vary.
Typical values for the properties of fibres are given in Table 1. It should be noted that these values are for the plain fibres alone, not woven fabrics nor for the resulting fibre composites. The strength and modulus for manufactured composites, see Sections 3.3 to 3.6, will be significantly lower. The values in Table 1 should only be taken as indicative; where necessary, actual values should be obtained from the manufacturer. (Section 5.4.2 gives details of the approach to determining the characteristic strength and the required number of tests.) The fibres all have a linear elastic response up to ultimate load, with no significant yielding.
3.1 Fibres
3.1.1 Properties
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Table 1 Typical dry fibre properties.
3.1.2 Performance of different types of fibre
The selection of the type of fibre to use in a particular application will depend on many factors: the type of structure, the expected loading, the environmental conditions, and so on. Some information is given in this section; further advice can be obtained from the suppliers of strengthening materials. Throughout, the comments refer to the performance of the fibre itself; in most situations this will be modified by the resin or adhesive.
Chemical resistance Carbon and aramid fibres are resistant to most forms of chemical attack. Many types of glass fibre, including the widely used E glass, are attacked by alkalis (pH greater than about 11) but not by acids. Alkali-resistant (AR) glass fibres are specially formulated for use in highly alkaline environments. Aramids absorb much more water than either of the other two fibres, which can cause problems with the resin–fibre interface. There is some evidence to suggest that, in the presence of salts, fracture of all types of fibre can occur due to the formation of angular crystals.
Resistance to ultraviolet light Glass and carbon fibres are not affected by ultraviolet (UV) light. Aramid fibres change colour under UV light and the strength is reduced. However, when embedded in a resin matrix this degradation only occurs near the outer surface and there is little effect on the overall mechanical properties. (Direct exposure to sunlight can embrittle all resins and a protective paint is normally recommended if direct exposure is likely.)
Electrical conductivity Aramid and glass fibres are non-conducting and hence are suitable for use close to power lines, electrified railway lines and communications facilities. As carbon fibres conduct electricity they should be electrically isolated from any steel to prevent the establishment of a galvanic cell. In general the resin will be sufficient for this, but where there is a particular risk it is recommended that a glass fibre sheet be additionally included as the outermost layer of the FRP strengthening system.
Fibre Tensile strength (MPa)
Modulus of elasticity (GPa)
Elongation (%)
Specific density
Carbon: high strength* Carbon: high modulus* Carbon: ultra-high modulus†
4300–4900 2740–5490 2600–4020
230–240 294–329 540–640
1.9–2.1 0.7–1.9 0.4–0.8
1.8 1.78–1.81 1.91–2.12
Aramid: high strength and high modulus‡
3200–3600 124–130 2.4 1.44
Glass 2400–3500 70–85 3.5–4.7 2.6
Basalt 4100–4800 90–110 3.2 2.6–2.8 * Based on polyacrylonitrile precursor. † Based on pitch precursor. ‡ Aramids with the same strength but a lower modulus are available but are not used in structural strength ening applications.
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Designers should also be alert to the possibility of carbon fibres within an FRP attracting induced currents when placed close to an AC (alternating current) electricity supply. Whilst no experimental work appears to have been carried out in this area, it is theoretically possible that induced currents within a carbon FRP could lead to unacceptable heating of an ambient cure adhesive, as it has been shown that the conducting properties of carbon fibre can be used to pass an electric current to achieve a higher adhesive cure temperature.
For UK railway applications it is a requirement that any conducting material that could become live due to induced currents or short circuits from traction power sources must be electrically connected to the return conductor. For metallic structures this is normally achieved by attaching an electrical bond between the return conductor and the structure. Due to the distributed nature of carbon fibres within the adhesive matrix of a carbon FRP it is virtually impossible to guarantee that every single fibre can be connected to the return conductor by an electrical bond. Hence Network Rail will not permit the use of carbon FRP in close proximity to its AC overhead electrification systems; however, carbon FRP is permitted where DC (direct current) electrification systems are present.
Care is needed when handling or cutting carbon FRP close to electrical equipment due to the risk of short circuit by airborne particles (see Section 3.8.2 on health and safety). In addition, when used close to power lines etc., steps must be taken to ensure that, in the unlikely event of adhesive failure, the composite does not come into contact with the electrical source.
Compressive strength The compressive strengths of carbon and glass fibres are close to their tensile strengths; that of aramid is significantly lower.
Stiffness The elastic modulus of carbon fibre is similar to, or significantly greater than, that of steel. The stiffness of aramid is lower, and that of glass significantly lower.
Impact resistance Performance of fibres during impact is highly dependent on the elastic strain energy generated and absorbed. Fibres combining high strength with high elongation (tensile strength greater than 3500MPa and elongation greater than 2%) are most suitable for applications where impact resistance is important. Selected grades of carbon, aramid and glass fibre can meet these requirements.
Fire Carbon fibres are relatively insensitive to elevated temperatures, but start to oxidise in air above 650ºC (see Maluk et al.(30)). Glass and aramid fibres have more significant strength deterioration at high temperatures, and aramid fibres are not normally used above 200ºC (see Bisby et al.(31)). However, the fire performance of a composite is generally not dominated by the fibres but by the matrix resin or the bonding adhesive (see Section 3.7).
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Fabrics are available in two basic forms: � Sheet material. The fibres are generally in a unidirectional arrangement, although biaxial
and triaxial arrangements are available. They may be on a removable backing sheet or in the form of a woven or stitched cloth.
� Prepreg material. This consists of fibres pre-impregnated with resin, which are cured, once in place, by the application of heat or by other means.
The selection of the appropriate form of fabric will depend on the application.
The properties of the sheet materials depend on the amount and type of fibre used. An additional consideration is the arrangement of the fibres; parallel lay gives unidirectional properties while a woven fabric has bidirectional properties. In woven fabrics, the fibres may be engineered to provide different properties in different directions, with perhaps 70% of the fibres being in the ‘strong’ direction and 30% in the transverse direction. It should be noted that kinking of the fibres in the woven material significantly reduces the strength and stiffness. In addition, the fibre direction need not align with component main axes – fabrics may be formed with equal amounts of fibres in two perpendicular directions, and used in an element at ±45º to the longitudinal axis.
The thickness of the material will depend on the type and arrangement of the fibre. Fabrics are available in various widths to suit the particular application.
Unidirectional plates are usually formed by the pultrusion process. Fibres, in the form of continuous rovings, are drawn off in a carefully controlled pattern through a resin bath, which impregnates the fibre bundle. They are then pulled through a die, which consolidates the fibre–resin combination and forms the required shape. The die is heated which sets and cures the resin, allowing the completed composite to be drawn off by reciprocating clamps or a tension device. The process enables a high proportion of fibres (generally about 65%) to be incorporated in the cross-section. Hence, in the longitudinal direction, relatively high strength and stiffness are achieved, approximately 65% of the relevant figures in Table 3.1. As most of, if not all, the fibres are in the longitudinal direction, the transverse strength will be very low.
Plates formed by pultrusion are 1–4mm thick and are supplied in a variety of widths, typically between 50 and 150mm. (It should be noted that, while plate properties and dimensions of plates can be tailored to suit the particular application, it will generally be more economic to use stock sizes.) Carbon is the most widely used fibre for strengthening applications although glass is used in some applications. As pultrusion is a continuous process, very long lengths of material are available. Thinner material is provided in the form of a coil, with a diameter of about 1m, as shown in Figure 7. It can be easily cut to length on site using a simple guillotine – see Figure 8.
3.2 Fabrics
3.3 Plates
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Right Figure 7 Coil of carbon FRP plate.
Far right Figure 8 Cutting carbon FRP plate on site.
Plates can also be produced using the prepreg process, which is widely used to produce components for the aerospace and automotive industries. Typically plates have a fibre volume fraction of 55% and can incorporate 10% off-axis fibres (usually glass aligned at an angle of ±45° to the longitudinal axis) to improve the handling strength. Lengths up to 12m can be produced, with the width and thickness being tailored to the particular application. Widths up to 1.25m have been produced and thicknesses up to 30mm. Other forms of manufacture, such as resin infusion, are sometimes used but these are generally less attractive commercially.
As near-surface-mounted material is installed within the cover region of the concrete, the diameter of the rod, or maximum possible dimension of the cross-section of the strip, is limited. Most experimentation to date has used circular bars of diameters in the range 7–16mm, or rectangular strips of thickness less than 2mm. Initial UK applications have used carbon FRP bar with a circular cross-section of less than 10mm diameter.
Development work on deep embedded bars for shear strengthening has been carried out on rods with diameters between 6 and 9mm.
Preformed shells have been used to strengthen columns on a number of structures. (It should be noted that the basic principles of strengthening columns given in Chapter 8 are applicable, but strengthening with shells is a more complex design process.) There have been a number of applications in North America but only one in the UK to date. For a circular column, the most appropriate manufacturing process is probably filament winding. Resin-impregnated fibres are wound round a mandrel, in the pattern required to give the necessary hoop and longitudinal properties. Once fully cured, the cylindrical shell is removed from the mandrel and cut longitudinally so that it can be bonded round the column. Alternatively, shells can be formed, by hand lay-up or other processes, on the inside or outside of a suitable mould.
3.4 Rods and strips
3.5 Preformed shells for column confinement
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3 Material types and properties
In general, the internal diameter of the shell should be close to that of the external diameter of the column, to keep the increase in the overall diameter to a minimum. Typically, shells are installed with a clearance of between 50 and 150mm from the concrete surface, with the annulus later filled with an expansive grout. This will induce a permanent tensile stress in the composite and compression in the concrete. It will be necessary to check that the stress in the FRP is low enough to avoid the risk of stress rupture.
The strength and stiffness of the shell in the hoop and vertical directions will depend on the type and proportion of fibres in the cross-section and on the method of manufacture of the composite. They will be significantly lower than the values in Table 1. The performance of the shell is highly dependent on the efficiency of the connection between the component FRP units.
Due to the cost of fabricating mandrels or moulds, this approach is only likely to be cost- effective when a large number of identical columns are being strengthened, such as in multi-span bridges or multi-storey buildings.
Prefabricated carbon FRP plates formed into an ‘L’ shape may be used as an external link to provide shear reinforcement on beams, with the lower leg of the ‘L’ providing anchorage for the vertical portion, which requires embedment into the soffit of the slab to provide anchorage at the opposite end – see Figure 9. There have been various applications of this type in Germany and Denmark but, at the time of writing, only one in the UK.
3.6 Specials
Figure 9 Shear reinforcement straps.
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Material types and properties 3
Research into the performance of these anchorages and full-scale testing of the applied system have been carried out by the Swiss Federal Laboratories for Materials Testing and Research (EMPA)(32). Beams specifically designed for high shear stresses were statically tested to failure with different shear reinforcements. Additional beams were tested to investigate the load-bearing behaviour of a preloaded and subsequently strengthened beam and another subjected to 5 million cycles at a high load level and subsequent failure.
The main findings were that the ‘L’-shaped plates can increase the shear failure load, enabling the structure to bear significantly higher live loads. Furthermore, the brittle shear failure mode can be changed to a ductile failure through the yielding of the internal flexural reinforcement. The plates can also be used to improve behaviour in the serviceability limit state by reducing shear deformations, the strains in the internal steel stirrups and the crack widths.
The same type of unit could be used to provide anchorage at the top of the beam, at the interface with the slab or at beam–column connections.
General information on adhesives may be found in publications such as Adhesives in civil engineering(33) and the Institution of Structural Engineers’ A guide to the structural use of adhesives(34). They are also covered in Part 4 of BS EN 1504(14). The adhesives most commonly used with concrete are epoxies (usually solvent-free two-pack materials which cure at ambient temperature). Generally the adhesives should be procured from the same supplier as the plates or fabrics, to ensure that the materials are compatible.
The adhesives that are sometimes considered as alternatives to epoxies have certain drawbacks: � Polyester adhesives have high curing shrinkage, high coefficient of thermal expansion,
can be subject to alkaline hydrolysis, and are difficult to bond to when hardened. � Vinyl ester adhesives are subject to curing shrinkage, and the bond is badly affected by
moisture. � Polyurethane adhesives have high curing shrinkage, can be affected by moisture and
are difficult to bond to.
The selection of the type of adhesive to be used in a particular application is governed by various factors, including the environment and the required speed of fabrication. Advice should be obtained from the adhesive manufacturer.
Due to concerns over the performance of organic adhesives at elevated temperatures, there has been some development work on, and limited applications of, inorganic adhesives – see Section 9.11.
3.7 Adhesives and laminating resins
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Ambient cure epoxies for bonding or laminating FRP strengthening generally have a glass transition temperature (Tg) quoted between 50ºC and 65ºC. The term glass transition generally relates to a temperature region over which a polymer transforms from a solid (glassy) form to that of a less stiff (rubbery) state. In more practical terms, this can be translated as the temperature region over which an adhesive’s ability to sustain load is reduced significantly. Current design guidance stipulates the Tg of an adhesive (and, if included, primer, saturant or matrix) should be at least 15°C above its maximum operating temperature.
Part 4 of BS EN 1504(14) gives a glass transition temperature performance requirement of ≥ 40°C when the adhesive is tested to BS EN 12614(35). This Standard covers two different test methods: differential scanning calorimetry (DSC) and differential thermal analysis (DTA).
Another method used to determine the glass transition temperature is dynamic mechanical thermal analysis (DMTA) – see Part 1 of ISO 6721(36). Figure 10 shows a typical structural epoxy adhesive’s bulk characteristic DMTA plot, which includes the variation in stiffness (storage modulus) plotted against temperature. This is determined according to Part 5 of ISO 6721(36) using the DMTA method. Other data, such as loss modulus and tan delta, are also provided and can be used as additional information regarding the adhesive’s (viscoelastic) behaviour with respect to temperature.
3.7.1 Elevated temperature characteristics
Figure 10 Illustration of the variation in stiffness
(storage modulus and loss modulus) and tan delta plotted against temperature for a typical
structural epoxy adhesive. With permission of Joining Technology Research Centre (JTRC),
Oxford Brookes University (2011)
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Material types and properties 3
As mentioned above, in order to satisfy the design guidance, a singular, well-defined characteristic value of Tg is required. To illustrate the importance of this, Figure 10 shows three different conventions using the DMTA method, whereby the peak of tan delta, peak of loss modulus or the point of inflection along the storage modulus plot can, and have, all be used to provide a singular value of Tg. Experimental evaluation of a typical construction epoxy can therefore demonstrate significant variation in Tg depending upon the chosen method and convention (as much as 25°C) – see the National Physical Laboratory’s Measurement Good Practice Guide No. 62(37) and Ludwig et al.(38). This is an important detail for design purposes. In the example provided in Figure 10, using the peak of loss modulus to define the Tg produces a design with a more conservative upper temperature limit (i.e. 56 – 15 = 41°C), whilst using peak tan delta allows for a higher limit (i.e. 66 – 15 = 51°C). For the same example, it is also worth noting the comparative drop in stiffness of the bulk adhesive at these two temperatures.
It is essential for the designer to specify which Standard test method and convention has been used, or is preferred, to define an appropriate value of Tg for the proposed application.
Similarly, when QC testing the adhesive to ensure, among other things, that it has been mixed thoroughly on site and in the correct proportions, it is particularly important to use the same test method and convention that was used to establish the governing acceptance criteria, i.e. if BS EN 1264(35) is quoted on the manufactures data sheet then the same standard must be used for the QC acceptance otherwise there is a real danger that the on-site QC testing might not pass.
In special circumstances, such as bonding FRP material to the top surface of a bridge deck which is to receive hot bituminous surfacing, the adhesive may be heated significantly. This may post-cure the adhesive with no adverse effects. However, under certain circumstances, this may require the selection of an epoxy with a higher glass transition temperature. As a matter of caution it is recommended that the adhesive’s mechanical performance be reaffirmed, as certain means employed to increase the temperature resistance of an adhesive can often have an adverse effect on certain mechanical properties, e.g. reduced strain to failure. Advice should be sought from the supplier.
Most organic resins are combustible and generate toxic smoke on burning. Where fire is a significant design consideration, such as in tunnels and confined spaces, the adhesive selected should be one that releases a minimum amount of toxic gases – see also Section 5.7.1. Owners may have their own standards for the approval of materials (e.g. Fire safety performance of materials used in the Underground(39)). Advice should be sought from the supplier.
Adhesives are generally specified on the basis that the concrete surface is maintained in a dry condition during the strengthening work and is in a normal atmospheric exposure situation in service. Where the concrete surface cannot be kept dry during the work or where, for example, the surface is submerged, or sometimes submerged, in service, adhesives with special properties may be required and specialist advice should be obtained from adhesive manufacturers.
3.7.2 Determination of glass transition temperature
3.7.3 Other operating environment considerations
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3 Material types and properties
Where the strengthening is exposed to significant ultraviolet light, protective paints, which must be compatible with the adhesive, will generally be required to prevent the exposed epoxy resin in a fabric system degrading. Guidance should be sought from the supplier of the strengthen ing system.
For porous surfaces, a priming coat may be required, which must be compatible with the adhesive. As indicated in Section 10.3.1, the quality of the surface should be assessed after priming by pull-off tests; tests have shown that correctly specified primers can increase the pull-off strength by about 10%.
Designers should consider all environmental aspects, including the eventual disposal of the materials used.
Aramid, glass, carbon and basalt fibres are all non-toxic and inert, and are not considered to be hazardous as waste. For landfill disposal, they do not contain any substance that could leach out to contaminate the groundwater or the air. The most commonly used adhesive and matrix materials, when fully cured, are also substantially inert at normal ambient temperatures and so are not normally hazardous. However, incineration of matrix and adhesive materials may not be an appropriate disposal method unless special care is taken. In addition, incineration of carbon materials may release fine electrically conductive particles into the air.
Various approaches are being developed for recycling composites, mainly involving grinding the material to form a filler in new composites.
All fibres, when encapsulated in cured matrix or adhesive, present negligible risk to human health in normal use. However, care must be taken when cutting all composites because fine fibre particles may irritate skin, eyes and mucous membranes.
In addition, care must be taken when handling resins; also, some systems require use of solvents during plate installation. Suitable protective clothing should be worn. Reference should be made to the COSHH Regulations(40) and to the manufacturer’s data sheets. See also Section 10.1.
Presently (2011), in most concrete flexural strengthening projects, the chosen system involves the use of carbon FRP pultruded plates, bonded to the concrete structure through adhesive.
3.8 Environmental aspects and health and safety
3.8.1 Environmental aspects
3.8.2 Health and safety
3.9 Choice of materials for design
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Material types and properties 3
Plates are most commonly used because: � Minor unevenness in the surface can easily be bridged by the adhesive layer of a plate
system. � Less surface area of concrete needs to be prepared than would be the case if wider, but
thinner, wet lay-up sheets were used. � Plates are usually easier to install than sheets. � Pultruded plates contain more fibres than a wet lay-up sheet of similar cross-section.
However, there are specific instances where the use of wet lay-up sheets is preferred over the use of plates for flexural strengthening, often due to the lowering of longitudinal shear stress in the adhesive layer due to the sheets being thinner than plates. In particular, one might consider the use of wet lay-up sheets under the following circumstances: � High demand on longitudinal shear stress within the adhesive layer, particularly in
short-span situations. � Poor-quality substrate material, so that longitudinal shear capacity is low. � Requirement for a special anchorage system. � Strengthening around a corner. � Transportation of discrete plates is difficult. � Shallow structure requiring low levels of strengthening distributed over a large area.
The working practices of the installer may dictate whether a plate or wet lay-up system is used. From the point of view of the environment, some plates must be wiped down with a solvent prior to installation, whereas sheets require no such chemical preparation. On the other hand, the adhesive associated with plates does not drip or flow, whereas wet lay-up adhesive may drip and leak away from the working area if a spillage occurs.
While quality control needs to be particularly high during installation of either plate or wet lay-up systems, it is fair to say that quality control needs to be even higher for wet lay-up in order to minimise unevenness, misalignment, lamination defects, voids and crimping.
In situations where wet lay-up sheets are used to strengthen structures in shear, as much of the perimeter of the element should be wrapped as possible, so that the use of sheets is preferred over that of plates under such circumstances. Such applications might mean U-wrapping a beam, for instance, rather than merely adhering sheets to the sides of the beam. Further, in such circumstances, practicality of detailing means that the U-wrap will lead to sheets aligned vertically, rather than inclined sheets.
The following situations lend themselves to consideration of NSM systems for strengthening: � The strengthened surface of the structure is trafficked or susceptible to damage. � A thin layer of poor-quality or loose concrete exists on the surface to be strengthened,
but the rest of the substrate is of high strength. � The surface is very uneven. � Where there is limited headroom (although installing NSM overhead can be difficult).
3.9.1 Plates versus wet lay-up sheet systems
3.9.2 Near Surface Mounted (NSM) systems
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Particular care should be taken to prevent damage to existing reinforcing bars when cutting the required slots. It would be unwise to use NSM in a situation where the depth of cover was low.
While NSM has been proven to be practical and of real benefit in niche applications, its relative cost against the more conventional plate or sheet systems should be considered, together with the level of NSM experience in the industry, and the availability and quality of trained NSM installers.
Deep embedded bars may be considered for shear strengthening where there is limited access to the beam sides and only one face of the structural member is available. Due consideration should be given to the practicality of drilling such holes whilst avoiding the existing steel reinforcement.
To date, most concrete strengthening applications involving composites have used a carbon system, mainly due to high installed stiffness and strength requirements. Further, such carbon systems are usually less expensive than other systems due to less material being required, the area of surface preparation being small and the time of installation being short, all of which maximise the advantages of FRP strengthening over conventional approaches. This is also reflected in the level of worldwide research and testing, which focuses heavily on carbon. Therefore, it seems sensible that a carbon strengthening system should be considered initially due to confidence and knowledge in its use, although various reasons may sway the choice towards other materials instead. Such circumstances where other materials (aramid, glass or basalt) should be considered include the following: � Strengthening against blast. Much research has been carried out into the use of aramid
and carbon systems for such strengthening, so that the knowledge base is high. � Electromagnetically inert material is required, perhaps near to overhead electrification
on railway lines or radio/radar installations. � Robustness and/or toughness of the material are particularly important design criteria.
Under such circumstances, aramid might be considered (although a protective top layer over structural layers of carbon can be used, e.g. an abrasion-resistant layer on a car park column).
� Low-level strengthening required, so that relatively low-cost glass could be considered, placed in substantially thicker layers than the equivalent carbon.
� Wrapping of columns in the hoop direction to enhance confinement in the event of seismic actions. Under such circumstances, glass could be considered.
3.9.3 Deep embedded FRP bars for shear strengthening
3 Material types and properties
3.9.4 Specific composite material
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Material types and properties 3
When using carbon systems, it is usual to use ‘standard’ modulus fibres. Such materials are normally adequate for the majority of strengthening schemes. Higher stiffness materials (usually denoted HM for ‘high modulus’) are substantially more expensive than the equivalent standard modulus materials, so that good reasons for their use are usually required. Such reasons might include the following: � High strains cannot be induced into the carbon FRP, so that high stiffness fibres are required. � The quantity of standard modulus carbon fibre required for a particular stiffness is excessive.
Outside the area of concrete strengthening, it is usual to strengthen iron and steel structures using very high-modulus carbon FRP plates due to the otherwise large quantities of standard- modulus carbon FRP that would be required.
When compliance with the conditions of Annex ZA of Part 4 of BS EN 1504(14) is achieved, an EC certificate of conformity is drawn up which entitles the manufacturer to affix the CE marking. This covers structural bonding products for bonded plate reinforcement in buildings and civil engineering works (i.e. the adhesive in FRP systems).
The adhesive needs to meet the requirements for: � bond/adhesion strength � shear strength � shrinkage/expansion � workability � modulus of elasticity � coefficient of thermal expansion � glass transition temperature � reaction to fire � durability � dangerous substances.
Part 4 of BS EN 1504 sets out the test methods and the requirements. It also covers special applications where the strengthened structure may be subjected to dynamic loading. It is suggested that, within Europe, only adhesives with the appropriate CE marking are used for plate bonding.
CompClass was undertaken to develop a performance-based classification and qualification scheme, in line with CEN strategies and Eurocodes dealing with the use and application of materials associated with the rehabilitation and upgrade of civil structures. Although the primary focus of the project was metallic strengthening using FRP plates, much of the guidance is also applicable to concrete structures. CompClass enables engineers and specifiers to select materials systems on the basis of performance requirements, preventing substitution or use of inappropriate materials components of the system. It also provides the impetus for manufacturers and suppliers of FRP, resins, adhesives and related products to further develop materials that satisfy a broad range of requirements.
3.9.5 Stiffness issues
3.9.6 CE marking
3.9.7 CompClass
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Clients and designers should, therefore, consider specifing a repair system that has been evaluated according to the Classification Scheme, to ensure the most appropriate and compatible materials are used. The values from the Classification Scheme are also used to inform the design of repair or strengthening, including suitable quality assurance procedures. This is facilitated by the implementation of the Qualification Scheme, which provides the framework for the various stages where material data interface with the proposed job, and includes materials selection, design inputs, quality control test requirements and associated acceptance criteria.
Qualification The purpose of developing a qualification scheme is to identify the stages in the process of design and installation where material properties are involved.
3 Material types and properties
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Figure 11 Qualification flow chart.
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Material types and properties 3
The qualification scheme for stiffness/strengthening applications consists of 15 steps ranging from initial material selection through to final inspection checks. An interactive flow chart depicting the qualification scheme and detailing the 15 individual steps in the scheme that provide guidance on test methods, their interpretation and acceptance criteria, can be found at www.compclass.org.uk. A report detailing a variety of case studies is also provided so that the user can understand how the Qualification Scheme approach is applied to a strengthening application.
Classification Materials tested in accordance with the Classification Scheme enable designers to select the most appropriate and compatible systems for the application. The information provided includes all individual components of a reinforcing system, such as primers, adhesives, laminating resins, fibre pre-forms and pre-formed FRP composites. The Classification Scheme consists of a suite of tests that demonstrate the material’s working characteristics, cured bulk properties and, importantly, durability.
Each classified product provides data for: � a preliminary materials selection in the design process � characteristic values for detailed design � selection of appropriate QC test methods � definition of appropriate acceptance criteria.
An example of a Product Specification document evaluated under the classification scheme is given in Figure 12.
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3 Material types and properties
Product Specification Application: Flexural Plate Bonding Classification Reference: PB/1/CI/S [OBU A 001]
Test House
Supplier: xxxx (Name) Product: xxxx (Name) xxxx (Primer) xxxx (Reinf.) xxxx (Primer) Batch Numbers: 1077xxxx (Resin & Hardener)
1077xxxx (Resin & Hardener) 020921-xx-x 1070xxxx
Material Classification: Structural Epoxy Adhesive System
Performance Group
Performance Characteristic Test Method Description
Short term** values SD
C ha
ra ct
er is
tic
va lu
e
A cc
ep ta
nc e
va lu
e
Application to vertical surfaces EN 1799
Maximum sag flow (at 23°C) 1 mm (at 12)
n/a n/a n/a
Application to horizontal surfaces EN 1799 Maximum sag flow Not tested
n/a n/a n/a
Storage life - Maximum storage time 1 year n/a n/a n/a
Workable (pot) life ISO 9514 Maximum time from mixing 40 mins n/a n/a n/a
Open time EN 12189 Maximum time for use 30 mins n/a n/a n/a
Working Characteristics
Cure BS EN 59 Time to cure (Shore D Hardness) 82 (24hrs) 84 (7 days)
1.1 0.4
n/a ! 77 ! 82
Moisture resistance ISO 62 Water uptake Not tested n/a n/a n/a
Shrinkage EN 12617 Shrinkage 0.13 % n/a n/a n/a
ISO 6721 Glass transition temperature 60 °C 0.6 59 ! 57 ± 5 Temperature dependence
ISO 11359-2 Coefficient of thermal expansion 26 x10 -6 °C-1 1.5 23 n/a
Tensile Modulus 9 GPa 1.3 6 " 14 ! 3
Cured Bulk Properties
Bulk performance ISO 527 Tensile Strength 34 MPa 3.8 26 ! 18
Env1 10 MPa (100% A) 0.4 9 ! 8
(>75% A) ASTM D 5868 Tensile Lap shear (failure mode) Env2 No change n/a n/a n/a
Env1 15 MPa (5% S, 95% A) 0.8 13 ! 11
(>71% A)
Adhesion to: FRP (Carbodur)
EN 1542 Pull-off (failure mode) Env2 16 MPa (10% S, 90% A)
n/a n/a n/a
Surface Preparation*: Solvent wiped with Sika Thinner until no discolouration was visible on a white cloth.
Env1 353 J/m 2
(100% P) *** *** n/a
ASTM D 3762 Wedge cleavage (failure mode) Env2 218 J/m
2
(100% P) n/a n/a n/a
Env1 16 MPa (No change) 1.5 13 ! 10
(>75% P)
Adhesion to: Cast Iron (with Primer)
EN 1542 Pull-off (failure mode) Env2 No change n/a n/a n/a
Substrate Properties: Historic Grey Cast Iron (Flexural modulus ~60GPa, Flexural strength ~236MPa) Surface Preparation*:
Gritblasted to SA 2.5. Loose debris was removed with a filtered air blast. Icosit EG1 primer applied with roller
Adhesion & Durability
Key to failure modes:
Adhesive: Cohesive failure within adhesive Primer: Cohesive failure within primer Interfacial: Apparent adhesion failure Substrate: Cohesive failure within substrate
Note: *Handling, mixing and application of products was carried out to manufacturer’s recommendations **All short term testing (Env1) was performed at ambient temperatures (23°C and 50%RH). All specimens subject to Env2 were submerged in de-ionised water for 28days at 23°C *** More replicates required to obtained SD and Characteristic values
Sheet No. 003 - Draft
Figure 12 Example Product Specification Document for
a structural adhesive product.
01/05/12
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4. Review of applications A large number of structures in the UK have been strengthened with FRP and there are numerous examples of the use of the technique worldwide. Details of representative examples of strengthening with FRP are given in subsequent sections.
Fibre composites have been used for strengthening a wide range of buildings, either to make good structural deficiency or as part of structural alterations.
Additional load capacity Carbon FRP plates were bonded to the soffit of the concrete trough slab which formed the roof of Normanby College, part of King’s College Hospital in London, to strengthen it sufficiently to carry an additional floor – see Parker(41). It was suggested that the conventional strengthening approach using steel plates would not have been possible because of the problems of inserting bolts into the soffits of the thin ribs. The work was carried out in 1996 and was one of the first uses of FRP for strengthening in the UK. A recent inspection (in 2010) indicated that the strengthening was still performing satisfactorily.
Similarly in 1997 the main beams supporting the floors in a factory in Tutbury were strengthened using carbon fibre plates to increase the flexural capacity by 30% to cater for the installation of new plant and processing equipment – see Taylor et al.(42). The work was carried out with minimum disruption to the factory operations.
Structural alterations As part of the refurbishment of Allders Department Store in Croydon, new escalators were required. This necessitated cutting holes up to 10m × 6m in the 300mm-thick flat slab and strengthening the adjacent slabs. After considering various options, carbon fibre plate bonding was selected as it minimised disruption to the operation of the store. The same approach was used at the company’s store in Portsmouth, where new stairwells were constructed – see Gold and Martin(43).
Due to changing ownership and tenants’ requirements, major alterations were required to the structure of parts of the Westfield shopping and leisure complex in west London before initial occupation – see Gaskill(44). These included the formation of large penetrations (typically 1.9m × 4.2m) through the existing slabs. Carbon FRP plates were bonded to both the top and soffit of the slabs around the perimeters of the openings. (In addition, areas of the floor were strengthened with carbon FRP plates to carry the increased loading.) In areas where it was not possible to provide adequate anchorage, such as at the edges of the floors and around the cores, the plates were mechanically anchored by means of an 8mm-thick transverse FRP plate bolted to the concrete.
Review of applications 4
4.1 Buildings
4.1.1 Beams and slabs
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4 Review of applications
The refurbishment of the Cripps Building in St John’s College, Cambridge, included the addition of bathrooms – see Williams(45). Carbon fibre plates were used to strengthen the floor slabs around the larger openings required for additional services.
Eberhardt et al.(46) described alterations carried out to a casino in Atlantic City, USA, which involved the removal of an existing floor to create a new double-height concourse. This resulted in the internal columns having a significantly increased unsupported length, with associated potential buckling problems. Space limitations excluded the traditional approach of casting additional concrete round the columns. Carbon fibre sheets were bonded vertically over the full height of the columns, which were then wrapped with carbon fibre, to improve both the buckling resistance and the axial load capacity.
Figure 13 shows carbon fibre plates installed around a hole cut through a slab to allow additional services to pass through.
In addition there have been situations where the floor slab has been strengthened with carbon fibre sheet material rather than plates, such as the Beyer Building, Manchester University, where openings were formed for new air-conditioning ducts.
At Wormsley Library, Oxfordshire, the installation of new services required the removal of a load-bearing wall. The concrete slab above was strengthened with carbon fibre plate to carry the resulting increase in dead and live loading – see Gold and Martin(43).
Chacos(47) reported that some of the main beams in a car park in Cleveland, Ohio, required modification to increase the headroom. This required the removal of as much as 270mm of concrete from the soffits in some areas and the installation of new prestressing strands. Carbon fibre near-surface-mounted rods were installed in the top of the slab near the columns to help achieve the required moment capacity.
Due to a design error, the simply supported beams of a warehouse in Belgium were understrength and had insufficient bearing at the intermediate supports. To improve the performance they were made continuous using a combination of carbon fibre sheet and steel plate – see Ignoul et al.(48).
Figure 13 Strengthening around hole cut through slab.
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Review of applications 4
Insufficient reinforcement Carbon FRP plates have been used to strengthen balcony slabs in Germany to overcome problems of deflections caused by insufficient steel reinforcement – see Steiner(49). The same approach has been used in Italy.
The shear capacity of the ends of precast prestressed double-tee beams in a multi-storey car park at Pittsburgh International Airport was strengthened using carbon fibre sheet – see Blaszak(50).
Near-surface-mounted reinforcement has been used to improve the seismic resistance of a number of concrete shear walls in buildings in Turkey. The approach has also been used for seismic upgrading in Italy and the USA.
Incorrectly located reinforcement During casting, the top reinforcement in the cantilever slabs of a car park in Bristol had been depressed, resulting in a cover of up to 95mm, significantly reducing the strength. Carbon fibre near-surface-mounted rods were installed to a depth of about 20mm to reinstate the strength – see Farmer(51).
Structural damage In Italy, carbon fibre strips have been bonded in two directions to both faces of a prestressed double-curvature concrete shell roof structure. The structure had been damaged, resulting in the loss of some prestress; conventional repair techniques were deemed not to be appropriate. Similarly, the concrete shell roof of a 1950s warehouse in Antwerp was repaired with carbon FRP plates following severe damage due to a fork-lift truck hitting one of the supporting columns. Carbon fibre strips were also used to strengthen the main roof beams of an exhibition building, increasing both the flexural and shear capacity. The ground-floor beams of a residential building, which had been damaged by an earthquake, were repaired with carbon fibre sheets wrapped round and bonded to the concrete.
Fire damage A number of prestressed concrete beams in a multi-storey car park in Orpington were damaged due to a vehicle fire. Following repairs to the concrete, the beams were strengthened with carbon FRP plates. After strengthening, the beams were load tested and insulation boards fitted to provide one-hour fire protection. Similar work was undertaken at a retail premises in Portsmouth, using a combination of carbon FRP plate and wrapping.
Donnelly(52) reported that a major fire at a factory in Jakarta, Indonesia, severely deteriorated the concrete and steel strength. Carbon and glass fabrics were used to provide additional flexural and shear capacity to the damaged elements.
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Repair Dortzbach(53) described repairs to the steel–concrete composite slab of a car park in Chicago, USA, which, due to the effects of de-icing salts, had suffered severe corrosion damage both to the steel decking and the top continuity steel over the supports. As part of the repair, carbon fibre plates were bonded to the top surface of the slab over the supports. As some of the existing cracks were about 3mm wide, the plates were debonded on either side of the support to reduce the peak stresses.
Corrosion induced by de-icing salts had seriously weakened the decks of a car park in Liverpool, UK. After making good the damaged concrete, the slabs were strengthened using near-surface-mounted carbon fibre composite rods – see Farmer(51).
Wrapping a column with fibre composite significantly increases the structural capacity. This is most effective on circular columns but is significantly less effective for square or rectangular columns. Much work has been carried out in Japan and the USA with the aim of developing cost-effective retrofitting to increase the seismic resistance of columns.
Additional load capacity Aramid fibre sheets were used to strengthen the main columns of a seven-level car park in Manchester so that two further storeys could be added, providing an additional 300 car parking spaces – see Russell and Lomax(54) and Russell and Modi(55). The material was chosen in preference to conventional approaches, such as casting an additional layer of concrete round the columns, because of the speed of installation and the minimal increase in the column dimensions.
Insufficient reinforcement Newly constructed circular columns for a multi-storey building in Dublin were found to have insufficient links. They were strengthened by wrapping with carbon fibre sheet. This approach caused minimal disruption to the construction programme.
Incorrect detailing During remedial work on a multi-storey car park in west London, it was found that the links in the columns were located inside the main bars rather than outside. To rectify this fault, all 400 columns were wrapped with carbon fibre sheet in discrete bands, replicating the links.
Insufficient design Excessive ground movements and floor loadings led to the shear failure of newly constructed square columns in the basement car park of a hotel in Dublin. After repairing the shear failure, the columns were strengthened by wrapping them with carbon fibre sheet. The approach was found to be quicker than traditional strengthening methods.
Lim et al.(56) reported that late in the construction of a multi-storey building in Singapore, the intended use of the podium structure was changed, requiring the structural members to be strengthened. Fibre-composite wrapping of the columns was chosen as this offered the least disruption.
4 Review of applications
4.1.2 Columns
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Review of applications 4
Additional seismic capacity Corneliu et al.(57) give details of the upgrading of the reinforced concrete frame of a brewery in Romania to bring it into line with current seismic requirements. Some beams were strengthened with carbon FRP and columns wrapped with carbon sheet material.
In Canada, glass FRP shells have been bonded to the surface of damaged columns to improve their load-carrying capacity.
In Japan and the USA, columns have been strengthened following earthquake damage by wrapping them with carbon FRP, in the form either of thin strips or sheets. Similarly, columns have been strengthened by wrapping them with aramid fibre tape, bonded to the surface.
Donnelly(52) gives brief details of the wrapping of the columns in a clinic building in Armenia to upgrade their seismic performance.
In Florida, the beam–column connections in the parking garage of the Palm Beach Hilton hotel have been strengthened by bonding carbon fibre sheet material to the sides of the beams – see Kliger(22). This approach was chosen in preference to the conventional solution of increasing the size of the connection by dowelling-in additional steel reinforcement and encasing the joint with additional concrete. It was estimated that the adhesively bonded repair was 35% cheaper than the conventional method.
Donnelly(52) described bi-directional glass fabric applied to the beam–slab connections of a clinic building in Armenia to upgrade their seismic performance.
In 1997, pultruded carbon fibre plates were installed for the first time in an operating nuclear power station in the UK – see Garden(58). The plates, of only 1m length, were bonded in several locations across structural cracks in reinforced concrete walls. The objective was to restore the original reinforcement contribution of the embedded reinforcing bars, which had yielded due to widening of the cracks. The length of the composite plates, and their cross-sectional dimensions, were tailored to suit the substrate material properties and anticipated design loads in the walls.
Trials in the UK and the USA have demonstrated that aramid fibres bonded to the faces of concrete walls can significantly increase their blast resistance.
Fibre composite strengthening techniques have been widely used on bridges, both in the UK and elsewhere, since the 1990s.
4.1.3 Connections
4.1.4 Walls
4.2 Bridges
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Above Figure 14 Underpass, Great Missenden.
Above right Figure 15 Applying carbon fibre sheet to Greenbridge
Subway, Swindon.
Additional load capacity In 1997, a small concrete underpass beneath the A413 at Great Missenden in Buckinghamshire (Figure 14) was strengthened with carbon fibre composite plates(59). The alternative would have been the complete reconstruction of the bridge, with consequent major traffic delays and disruption.
The late 1960s Greenbridge Subway in Swindon was strengthened with carbon fibre fabric to increase its flexural capacity to that required for current traffic loadings; Figure 15 shows the material being applied. Carbon fibre plates were used to strengthen the soffit of the River Gardens Bridge in Hounslow to increase the live-load capacity and allow heavy vehicles into an industrial estate – see Barton(60). Two bridges in Crawley were strengthened with carbon fibre plates applied to the soffits to increase the load capacity, as was the bridge carrying the A16 over the Haven Waterway in Boston, Lincolnshire.
Carbon fibre plates have been applied to the top surfaces of several bridges to increase the transverse bending capacity. Luke and Canning(61) described the strengthening of the cantilevers of a slip road onto the M1 motorway, which was required after the installation of improved parapets. Due to the different geometries, carbon FRP plate was applied to one cantilever and carbon fibre sheet material to the other.
Both the bridge deck and the cross-heads of the A71 Williamston Interchange Bridge in West Lothian were found to be understrength. They were strengthened with two widths of carbon FRP, which caused minimal disruption to traffic.
The Glade Bridge (Figure 16) carries an access road over the railway between Leatherhead and Bookham in Surrey. The precast concrete slabs were strengthened using carbon fibre plates to upgrade the capacity from 5 to 17 tonnes(62). This was the first bridge in the UK over a railway strengthened using carbon fibre plates. As the electrical supply is ‘third rail’ there were no concerns about the electrical conductivity of the material – see Section 3.1.2.
4.2.1 Beams and slabs
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Figure 16 Strengthening of Glade Bridge.
In the UK there has been limited use of FRP for strengthening concrete bridges carrying railway tracks. Luke and Canning(61) reported that carbon FRP plates were used to strengthen the soffit of the St Michael’s Road Bridge in Widnes which carries two tracks. Work was carried out during possessions to minimise any effects of live loads on the adhesive bond. Loudon and Bell(20) described the strengthening of Mill’s Hill Bridge in Rochdale, which carries the railway over the M62 motorway. Carbon FRP plates were used to increase the transverse moment of resistance. As indicated earlier, the soffit of a redundant railway bridge in Örnsköldsvik, Sweden was strengthened with NSM and the bridge was later demolished as a full-scale trial under the European Sustainable Bridges project – see Elfgren et al.(15). The strengthening was carried out so that the deck failed in shear rather than flexure. The results indicated that the technique had increased the load capacity by around 50%.
The soffit of the Parkhouse Bridge, Helhoughton, Norfolk was strengthened using near- surface-mounted reinforcement. Two sizes of carbon FRP bars were used, namely 16mm and 20mm, both with a peel ply finish. The reason for using NSM rather than carbon FRP plates was due to concern that material floating in the river might hit the plates and remove them. This would appear to be one of the first situations in which NSM has been installed overhead.
Woven carbon fibre mats have been bonded directly to the soffit of a bridge over the A10 motorway in France to strengthen it(63). This appears to be the first application of carbon fibre mats in Europe.
In Canada, carbon fibre sheets were applied to the soffits and sides of the Clearwater Creek Bridge near Edmonton, Alberta to improve the shear resistance – see Alexander and Cheng(23). This is a three-span highway bridge with a length of about 18m. Hutchinson(64) reported that four beams of the Maryland Street Bridge in Winnipeg were also strengthened with vertical and horizontal sheets of carbon fibre to increase the shear capacity by 36%.
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The alternative would have been to remove parts of the bridge deck, install post-tensioned external shear stirrups and cast additional concrete round the beams. The work was carried out without interrupting the traffic on the bridge and was estimated to cost about 70% of the conventional approach. This comparison was based on direct costs and did not consider factors such as traffic delays.
Hutchinson also reported that the ends of 64 beams of the John Hart Bridge in Prince George, British Columbia were strengthened with diagonal sheets of carbon fibre, to increase the shear capacity by about 20%. In addition to the areas that required strengthening, carbon fibre sheet was applied to non-critical locations. These may be removed at a later date to determine the long-term performance.
Herman(65) described the strengthening work carried out on the precast prestressed box beams of two bridges in Ohio, USA. The self-weight of the structures was minimised by removing the asphalt road surface before any work was carried out. Prestressed carbon FRP plates were used to strengthen the box beams, to reduce crack widths in the concrete and to relieve some of the stresses in the reinforcement under service loads. After stressing, the plates were bonded to the soffits of the box beams. Some additional unstressed FRP plates were also installed to improve the flexural capacity of the box beams.
Fujita et al.(66) reported that prestressed carbon FRP plates were used to strengthen a 30-year- old two-span box girder bridge in Japan. Load tests were carried out before and after the bridge was strengthened, which showed that deflections were reduced by 30% or more.
Ehsani(67) reported briefly on a newly completed highway bridge in the USA which was found to contain only half of the required reinforcement. The deficiency was made up by bonding carbon fibre fabric to the soffit of the bridge.
Additional seismic capacity Kim et al.(68) reported that the piers of the Portage Creek Bridge in Victoria were upgraded by wrapping with five layers of glass fibre sheet material. Strain gauges and accelerometers were installed to monitor the enhanced seismic behaviour.
Repair following damage to the structure There have been a number of examples of strengthening being required following impact from an over-height vehicle. For example, the edge of the slab of the Devonshire Place Bridge in Skipton, Yorkshire was repaired with carbon plate following damage to one of the tendons – see Taylor et al.(69) and Smith(70). The edge beam of a bridge in Crawley, West Sussex, that had been struck by a vehicle, was strengthened with carbon fabric, as was the edge beam of a bridge over the M45 motorway.
Luke and Canning(61) described repairs carried out on the 29-span Theydon Bois Viaduct, Essex following corrosion of the main reinforcement. While most of the spans were propped during repairs to relieve part of the load, this was not possible for the one span that crossed a railway line. Multiple factory bonded carbon FRP plates were bonded to the top surface over the supports to increase the hogging capacity.
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The soffits of some of the beams of the Ibach Bridge, near Lucerne in Switzerland, were repaired with carbon FRP plates following damage to a prestressing tendon – see Meier et al.(71). Similarly, repair work to the soffits of beams has been carried out in Italy (see Nanni(72)) to repair the damage caused by vehicle impact, the carbon plates being used to provide some additional shear capacity as well as increasing the flexural capacity. A beam on Interstate Highway 95 at West Palm Beach, Florida was also strengthened using carbon fibre sheet after it was struck by a truck, causing twisting and longitudinal cracking.
Kim et al.(73) described the use of prestressed carbon FRP sheets for strengthening the outer beams of a bridge in Winnipeg, which had been severely damaged by successive vehicle impacts resulting in rupture of the prestressing cables. The repair increased the capacity of the damaged beams by about 20%, returning them to their original design capacity.
Insufficient reinforcement A bridge over the M3 motorway was found to have inadequate transverse flexural capacity due to insufficient transverse reinforcement. This was rectified by the use of carbon FRP plates bonded to the soffit. Similarly, in the USA, a bridge to the north of Wilmington, Delaware, USA had developed longitudinal cracks because of insufficient transverse reinforcement in the bottom of the precast box-beams. They were repaired with carbon fibre sheet – see Meier(74).
Uddin et al.(75) give details of work carried out on the beams of a bridge in Huntsville, Alabama, USA which had cracked shortly after construction. The beams were strengthened using longitudinal carbon fibre sheets and sheets wrapping fully around the webs. Application was by vacuum-assisted resin infusion. The authors concluded that the costs of the technique were similar to those of conventional hand lay-up.
Incorrect reinforcement detailing The top surface of Haversham Bridge in Milton Keynes was strengthened using carbon fibre plates to increase the hogging capacity. (Figure 17 shows a similar strengthening job in Switzerland.) The plates were provided because the top steel had insufficient lap lengths and anchorage for the increased loading requirements. Carbon plates were chosen in preference to steel plates because of the improved durability and the absence of the bolts required with steel – see Taylor et al.(69), Luke(76) and Soudain(77). When installed on the top surface of a deck slab, the composites are protected by the running surface during normal operation. However, there is some concern that they may be susceptible to damage when the surface is planed off prior to resurfacing.
The soffit of the Barnes Bridge, which carries the A34 over the M60 Manchester Outer Ring Road, was found to have inadequate laps in the reinforcement during an assessment of its ability to carry 40-tonne vehicles – see Sadka(78). It was strengthened with carbon FRP plate of three different sizes.
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Figure 17 Strengthening the top surface of a bridge in
Switzerland using carbon fibre plates.
Figure 18 and 19 Column wrapping.
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In this section, the applications are grouped according to the type of strengthening material used. The materials are generally applied by hand (see Figures 18 and 19) although specialist machines have been developed for large structures. The machine is clamped around the column and a carrier head revolves around the column, laying down a continuous fibre tape under tension. The machine is gradually raised round the column, as the required thickness of fibre is installed.
Wrapping with fabrics The first trial application of FRP for the wrapping of columns was carried out on the Bible Christian Bridge over the A30 Bodmin Bypass in Cornwall – see Figure 20. Three different systems were applied to the 6m-high 800mm-diameter columns. The materials were glass, carbon and aramid, in either sheet or ribbon form. The concrete surface was first cleaned and repaired then generally impregnated with an epoxy resin before application of the first layer of fibre. In each case, several layers of the fabric were applied vertically, to increase the flexural capacity, as well as in the hoop direction to increase the shear capacity – see Parker(41) and Lynch and Duckett(79).
Columns of the approach spans of the A92 Tay Road Bridge, which was constructed in the mid-1960s, were wrapped with aramid fibre sheet to improve their vehicle impact resistance – see Drewett(80). Keble(81) described the application of aramid fibre sheet to strengthen the columns of bridges on the M6 motorway in Cumbria. The fibres were principally in the vertical direction to improve the flexural capacity with additional fibres in the hoop direction to improve the shear capacity and localised concrete bursting in the event of vehicle impact. Similar work was carried out on the Patchway Viaduct on the A38 – see Richardson(82). As part of the installation, additional bands of aramid were installed above the area to be strengthened that included deliberate defects. Trials were subsequently carried out to assess the effectiveness of thermography in locating the defects.
Carbon sheet for wrapping columns was developed in Japan and has been widely used for strengthening bridges, particularly to improve their seismic resistance(83). The approach has been approved by the California Department of Transportation since the early 1990s(22).
4.2.2 Columns
Figure 20 Bible Christian Bridge, Cornwall.
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Cercone(84) reported that the piers of a railway bridge over a major highway in New York State were wrapped with a water-cured prepreg glass fabric. This appears to be the first use of a water-cured material. It is not clear whether the wrapping provided additional strength or was mainly to protect the concrete, which had suffered severe damage; the bridge was described as ‘structurally sound’.
In Canada, repairs were carried out in August 1996 at Saint-Étienne-de-Bolton, Québec, where nine columns of a bridge over Highway 10 were repaired, five with glass fibre and four with carbon fibre, supplied by three different companies – see Neale(85) and Neale and Labossière(86). The circular columns are 6m high, with a diameter of 760mm. The work was backed up by laboratory studies, including the behaviour of the wrapping materials under wet–dry and freeze–thaw cycles.
In Montreal, one of the main piers of the Champlain Bridge over the St Lawrence River was wrapped in October 1996. A total of nine layers of glass fibre wrap were installed to give a thickness of 10mm, both to strengthen the concrete and to protect it from ice damage. The column is 1.37m in diameter. To reduce the problems associated with working over water, the fibre sheets were pre-impregnated with resin and wrapped round a roller on land. They were then installed on the pier by simply rolling out while the resin was still wet – see Neale and Labossière(86,87). This technique should not be confused with the use of a prepreg part-cured material.
Combined plates and wrapping The reinforcement in circular columns of a bridge in Poland was heavily corroded. After repair of the concrete, the area of longitudinal reinforcement was found to be insufficient and the links needed to be reinstated. The repaired columns were strengthened longitudinally with carbon FRP plates and then wrapped with carbon sheet – see Siwowski(88).
Expansive grout combined with fabric Neale and Labossière(87) reported that, as part of the repair of the Leslie Street Bridge in Toronto, Canada, an expansive mortar was cast round a deteriorated column. The repair was wrapped with a plastic sheet, followed by a glass fibre wrap. As the mortar continued to expand it tensioned the glass fibre, putting the parent concrete into biaxial compression.
Preformed shells Various types of prefabricated glass fibre composite shell are being developed in the USA, including the full-height ‘Hardcore’ system, as used on the Santa Monica Freeway in Los Angeles and the segmental ‘Clockspring’ system – see Roberts(89). Preformed shells were used to strengthen columns on the New Jersey Turnpike, which had heights between 3 and 4.5m(90). The shells were installed with a clearance of 50–150mm from the concrete surface, which was later filled with grout. In some locations the lower end of the shell was below water. Possibly the largest application to date has been the Yolo Causeway, west of Sacramento, California, where 3000 columns were wrapped with glass fibre reinforced preformed shells – see Karbhari and Seible(91). The first application in the UK was on the A19 on Tyneside, where 24 columns were strengthened with glass FRP shells – see Kendall(92) and Pinzelli(93). The original columns were tapered, but the shells were of uniform diameter throughout. Thus the thickness of the annulus filled with grout increased from the bottom of the column to the top.
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There has been limited use of composites to improve the continuity of bridges. Meier et al.(71) reported that the joints in the Katten busch Bridge in Germany were strengthened in 1986 by bonding a large number of glass FRP composite plates across them. The plates were 3.2m long, 150mm wide and 30mm thick.
While the majority of strengthening schemes using fibre composites have been applied to buildings or bridges, the techniques have also been applied to a range of other structures, as outlined in this section.
In Japan, deteriorated concrete chimneys have been strengthened by means of carbon or aramid fibre tapes bonded to the surface, generally to increase the seismic resistance but also to increase the resistance to wind and thermal loading – see Okamoto(94). Dial(95) reported that chimneys at a former cement plant in San Antonio, Texas were wrapped in glass FRP to increase their flexural and shear capacities and to improve their appearance when the plant was converted into a retail and entertainment complex.
Donnelly(52) described the strengthening of four telecommunications towers in Brazil which were wrapped with a combination of carbon and bidirectional glass fabrics. Fibre composites were chosen in preference to the steel jackets that were originally proposed because they would apply little additional weight to the foundations.
Trials are planned for near-surface-mounted reinforcement strengthening on the chimneys of a disused power station in London. In addition a cathodic protection system will be installed to protect the steel reinforcement. Hence aramid FRP rods have been selected for the NSM because they are non-conducting.
Carbon fibre sheets have been used in a number of highway tunnels and railway tunnels to repair cracks in concrete linings and also to increase the strength. Fukuyama et al.(96) reported that there were approximately 25 such applications in Japan in 1996.
A large-diameter water chamber forming part of the Frontenac Hydroelectric Power Plant in Sherbrooke, Quebec, Canada was strengthened in 1998 with glass FRP on both the inside and the outside faces. This was an environment with very high humidity and the strengthening was made more complicated by water seeping through the highly porous concrete – see Neale(97).
Deller(98) described the application of unidirectional carbon fibre sheet material to strengthen the central wall of a twin-bore tunnel in Leeds, which was found to be vulnerable to vehicle impact. Up to eight layers of fabric were applied to achieve the required level of strengthening, with successive layers set at 90° to each other.
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4.2.3 Continuity
4.3.2 Tunnels
4.3 Other structures
4.3.1 Towers and chimneys
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Various lighthouses in the North Sea have been strengthened with carbon fibre sheet material. The alternative, steel bands, lifted into position using a helicopter, would have been a more expensive option.
The deck of the 29-span Langstone Bridge, which connects Hayling Island near Portsmouth to the mainland, was strengthened with carbon fibre plates to enable to bridge to carry 40-tonne vehicles – see Berry(99).
Following the construction of a new pier at the Humber Sea Terminal, part of the approach span required strengthening. Carbon fibre plates were bonded to the underside of the approach ramp – see Deane(100).
The US Navy has carried out trials on various composite materials for strengthening concrete piers – see Phair(101). Gee(102) reported that piles in the tidal zone were wrapped using an epoxy specially formulated for use under water and the strengthened area then protected with a layer of plastic sheet until the resin had fully cured. The supporting columns of various piers and other coastal structures in California have been strengthened by wrapping with carbon fibre. In some cases the strengthening extended below ground level. At Fort Mason in San Francisco, 245 submerged reinforced concrete foundation piers were retrofitted for seismic confinement using a combination of systems.
De Lorenzis et al.(15) reported that the top surface of Pier 12 at the San Diego Naval Station, California, USA was strengthened with NSM to take additional loads from vehicles and mobile cranes. The work was also reported by Odello(103) who additionally noted that preformed glass fibre shells were used to strengthen the piles of Pier 12, with the annulus filled with grout.
Vertical and horizontal bands of aramid FRP were used to strengthen the cooling towers of West Burton Power Station in Nottinghamshire(104). Aramid was chosen because of its abrasion resistance. The turbine support units at Torness Power Station were strengthened using carbon fibre sheet.
In Japan, concrete electricity transmission poles have been strengthened using carbon fibre sheet material. In Montreal, Canada, laboratory trials have been carried out on railway sleepers strengthened with polyester fabric – see El-Hacha et al.(105). A 30-year-old processing tower in Qatar was strengthened with 3500m of carbon FRP plate. Several options were considered but the material was chosen because of the speed of installation – see Luke et al.(24).
Walsh(106) reported that a number of reinforced concrete silos, each about 15m in diameter and 32m high, for the temporary storage of coal at a mine in New South Wales, Australia, developed vertical cracks after a short time in service. Post-tensioned cables were subsequently installed to control the cracking but after 25 years they were starting to fail due to corrosion. The cables were gradually removed, areas of defective concrete repaired and carbon FRP plates installed on the outer surface, both vertically and horizontally. The latter were continuous around the perimeter.
4.3.3 Marine/coastal structures
4.3.4 Miscellaneous structures
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FRP composite systems can provide solutions for the strengthening of masonry. The dynamic properties of the existing structure remain unchanged because there is minimal addition of weight, and stiffness changes may be engineered case by case.
FRP composites used for flexural and/or shear strengthening of masonry structures are similar to those used for strengthening of concrete elements. A number of research projects have demonstrated the effectiveness of FRP composites to improve the structural performance of masonry walls, particularly in situations of high slenderness – see Tumialan et al.(107). Available literature shows that walls strengthened with FRP in the laboratory usually fail due to debonding of the laminates.
An alternative to FRP laminates is the use of near-surface-mounted (NSM) FRP bars. In this way, FRP bars have been used successfully to increase the flexural strength of concrete masonry walls. FRP systems can also be used to improve the performance (strength or pseudo-ductility) of masonry walls subject to in-plane loads – see Gergely and Young(108). Strengthening by FRP structural repointing (insertion of small-diameter FRP bars in the bed joints) can also increase shear capacity and provide pseudo-ductility to walls.
4.3.5 Concrete masonry walls
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5 Structural design of strengthened members
5. Structural design of strengthened members This chapter deals with the general principles of strengthening with fibre composites while specific design aspects, e.g. strengthening members in flexure, are covered in subsequent chapters.
The following symbols are used in this Report: Ac gross cross-sectional area of concrete section Af area of FRP Afa additional longitudinal FRP strengthening area required due to shear Afw area of FRP for shear As area of longitudinal steel in compression Ast area of longitudinal tension steel $sw cross-sectional area of steel shear reinforcement Au-wrap area of U-wrap anchorage required to prevent peeling due to shear cracks a major dimension of elliptical column av shear span b width of section ba width of adhesive layer bbarperim perimeter of NSM FRP bar bf width of FRP laminate bnotchperim effective perimeter of NSM groove Cd serviceability criteria c minor dimension of elliptical column D diameter of circular column Deqv equivalent diameter for elliptical column d effective depth of section db diameter of deep embedded bars df effective depth of FRP shear reinforcement Ec,eff effective modulus of elasticity of concrete Ecm secant modulus of elasticity of concrete Ed design action Efd design elastic modulus of FRP Efi,d design action in fire Efk characteristic elastic modulus of FRP Es modulus of elasticity of steel (200GPa) E2 slope of linear portion of confined concrete stress–strain curve e prestressing tendon eccentricity ei nominal eccentricity of load on column e2 lateral deflection due to second-order effects for slender columns
5.1 Symbols
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fat characteristic adhesive tensile strength fc0 unconfined concrete compressive strength fcc confined concrete axial compressive stress fccd design confined concrete compressive strength fci cylinder strength determined from core test fck characteristic compressive cylinder strength of concrete fctk characteristic tensile strength of concrete (ideally derived from in-situ pull-off tests) fc,WCS worst credible strength of concrete ffd design tensile strength of FRP ffk characteristic tensile strength of FRP ffm mean tensile strength of FRP fp,0.1k prestressing steel proof stress fyd design yield strength of longitudinal reinforcement fyk characteristic yield strength of reinforcement fywd design yield strength of shear reinforcement fywk characteristic yield strength of shear reinforcement G permanent action g depth from neutral axis to extreme tension fibre h overall depth of section hc cross-sectional dimension of column for slenderness calculation Ic second moment of area of uncracked concrete section Icc second moment of area of unstrengthened concrete equivalent transformed
cracked section Ics second moment of area of strengthened concrete equivalent transformed
cracked section Itrans second moment of area of concrete equivalent transformed prestressed
concrete section, including FRP kb bond force factor ke confinement effectiveness factor kn number of standard deviations to be subtracted from mean strength to
determine characteristic strength lb,max deep embedded bar anchorage length lnsm anchorage length provided for NSM bar lnsm,max anchorage length for NSM bar required to generate Tnsm,max lt anchorage length provided lt, max maximum anchorage length corresponding to Tk,max lU-wrap minimum length of U-wrap to extend up side faces of a beam for anchorage l0 effective length of column Madd additional required moment capacity Madd,service additional moments under service loading conditions after strengthening Mapplied applied moment in column MEd design ultimate moment MEdG design moment due to permanent loads Mexisting moment at time of strengthening My moment in strengthened section at steel yield M2 nominal second-order moment in slender columns
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N ultimate axial load on column N0 theoretical axial capacity of column under concentric loading nbars number of NSM bars crossing a 45° shear plane nc number of core tests ne number of effective axial reinforcing bars nnsm number of NSM bars in a section ns factor for anchorage of shear strengthening Pm,t prestressing force Q variable action Rc corner radius of rectangular column r radius of gyration s spacing of steel stirrups sb spacing of deep embedded bars sd standard deviation sf spacing of FRP strips snsm spacing between NSM bars Tk characteristic bond failure force Tk,max ultimate bond failure force Tnsm characteristic anchorage force for NSM Tnsm,ad characteristic adhesive bond failure force Tnsm,lim limit of maximum achievable anchorage force for NSM Tnsm,max maximum NSM anchorage force tf thickness of FRP laminate Vadd shear force additional to that present at time of strengthening VEd shear force due to ultimate loads Vf shear resistance contribution from FRP VRd,c shear resistance of member without shear reinforcement VRd,crack capacity of member to resist formation of critical shear cracks leading to
debonding VRd,max maximum allowable shear resistance of member VRd,s shear strength of concrete section including shear reinforcement VRd,s,f shear capacity of strengthened section Vs shear resistance contribution from steel reinforcement Vu ultimate shear capacity weff width over which deep embedded bars effectively carry shear x depth of neutral axis of FRP-strengthened member x distance to centroid of FRP in tension from neutral axis yt,b distance from centroid of unstrengthened beam to top and bottom ytrans,t,b distance from centroid of strengthened beam to top and bottom z lever arm zf lever arm between longitudinal FRP and centroid of compression force Df modular ratio of FRP to concrete E angle between the principal fibres of the FRP and a line perpendicular to the
longitudinal axis of the member JA partial safety factor for adhesive JC partial safety factor for concrete
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JFRP,E partial safety factor for modulus of elasticity of FRP JFRP,m partial safety factor for manufacture of FRP JFRP,mE design partial safety factor for modulus of elasticity of FRP JFRP,mf design partial safety factor for strength of FRP JFRP,mε design partial safety factor for strain of FRP JFRP,ε partial safety factor for strain of FRP JS partial safety factor for steel 'Fsteel additional longitudinal tensile force in steel associated with shear 'Ftd additional longitudinal tensile force associated with shear 'x length along beam between positions of maximum moment and moment at
first yield of the steel 'y short length along FRP for longitudinal shear stress calculation 'Vf change in stress in NSM over length 'y Hc2 axial strain in unconfined concrete at peak stress Hcc confined concrete axial strain Hcc,max maximum concrete stress in confined rectangular columns Hccu confined concrete ultimate axial strain Hcu2 and Hcu3 maximum concrete strain limits defined in Table 3.1 of BS EN 1992-1-1 Hfd design ultimate strain of FRP Hfd,longi maximum allowable tensile strain in longitudinal FRP on columns Hfe effective FRP strain Hfk characteristic failure strain of FRP Hfmax FRP strain at maximum design moment Hfse effective strain in the FRP for shear strengthening Hh,debond strain at which FRP wrap debonds Hh,rup hoop rupture strain for FRP Hmt maximum FRP strain in the yield zone Hsv,eff effective strain in shear stirrups Ht position of transition region between parabola and straight line for confined
concrete Hy yield strain of steel Kfi reduction factor during fire T angle between compression strut and axis perpendicular to shear force O slenderness ratio Ocrit critical slenderness ratio for strengthened section Olim limiting slenderness ratio for unstrengthened section UH confinement strain ratio UN confinement stiffness ratio Vconc,t,b maximum concrete stresses at top and bottom of prestressed section Vf stress in FRP due to bending Vf, max FRP stress at maximum design moment Vfy FRP stress at steel yield Vs stress in steel due to bending W longitudinal shear stress Wad maximum longitudinal shear stress at adhesive–FRP interface for NSM Wb average bond strength for deep embedded bars
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Wconc maximum longitudinal shear stress at concrete–adhesive interface for NSM Wlim,c limiting longitudinal shear stress in concrete Wlim,y limiting longitudinal shear stress in yield zone Wm mean longitudinal shear stress in yield zone Wsc local longitudinal shear stress at crack positions Wt total longitudinal shear stress in yield zone M creep coefficient Mef effective creep coefficient \L creep multiplier
Since the publication of the second edition of this Technical Report, a number of new national and international guidelines, dealing specifically with the design of externally strengthened concrete structures, have been introduced or revised. The American Concrete Institute has published a design standard, ACI 440.2R-08(3), which has significantly developed from their previous design guideline, ACI 440.2R-02. The Fédération Internationale du Béton (fib) task group 9.3 is preparing a second edition of Bulletin 14(109) (originally published in 2001) aiming to update, improve and refine the Bulletin. Design software is available based on the fib equations e.g from www.sika.com. A guideline has been produced by the Italian National Research Council (CNR DT/200)(110), and there are codes or guidelines in preparation in Hong Kong, China and Australia.
Other guidelines have previously been developed by the Japan Society of Civil Engineers(111), the ISIS Canada Research Network(4), and by Täljsten in Sweden(112).
In the UK, other relevant publications are provided by the Highways Agency. The Agency’s design guide BD 84/02(7) provides advice on strengthening concrete bridge supports using FRP while BD 85/08(8) gives further guidance on using FRPs for strengthening highway structures. The Construction Industry Research and Information Association (CIRIA) has published a report on the use of composites in construction(113) and guidelines on strengthening metallic structures using FRPs(11). Advice on the design of adhesively bonded joints, for fibre composite materials, is given in the EUROCOMP design code and handbook(114).
Chapters 5 to 8 of this Report provide the necessary guidance for engineers to carry out the design of non-prestressed FRP strengthening systems for concrete structures. The guidance has been written to be used in conjunction with the Eurocodes for structural design as appropriate, in particular BS EN 1990 Basis of structural design(115), BS EN 1991 for Actions on structures(116), and BS EN 1992 Design of concrete structures(10). This Report refers to the respective Eurocodes using the BS prefix to indicate the UK implementation of the standards to be used with the respective UK National Annexes and has been prepared with reference to the revisions current at the time of publication. For projects outside the UK, the National Annexes for the country where the project is located should be used.
5.2 Overview of available design guidance
5.3 Basis of design
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It is important to recognise that the basis of strengthening using FRP differs from the design of conventional steel reinforced concrete structures in a number of important respects. These include the elastic-brittle behaviour of FRP materials and the bond behaviour at the interface with the existing structure.
The strengthening will generally be carried out following a detailed appraisal, to identify the need for strengthening. The methodology and standards used to carry out the appraisal are often different from the design standards. When the structure is a bridge, in the UK, reference should be made to the Highways Agency standard BD 44 The assessment of concrete highway bridges and structures(117), which is broadly based on the approaches that were in Part 4 of BS 5400(118) (now withdrawn), but modified for existing structures, including the possibility of using lower partial safety factors and worst credible strengths based on material testing. For buildings, the Institution of Structural Engineers Appraisal of existing structures(13) also suggests lower partial safety factors, but appropriate equations have not been developed, although the approaches adopted by BD 44 should be equally applicable to other types of structure.
The design of FRP strengthening systems should be based on limit state principles. The aim of limit state design is the achievement of an acceptable probability that the structure being strengthened will perform satisfactorily during its design life. This involves checking that the structure does not reach a limit state during its intended life, which may render it unfit for use.
The types of limit states to be satisfied by structures are set out in BS EN 1990(115). Limit states fall into two categories: ultimate limit state (ULS) and serviceability limit state (SLS). Ultimate limit states are related to safety and typically include mechanisms that cause partial or complete collapse of the structure, while serviceability limit states correspond to the durability, appearance or proper performance of the structure. The rules for satisfying particular limit states relevant to concrete structures are set out in BS EN 1992. These verifications will still be relevant for FRP-strengthened structures, taking account of the behaviour of the concrete and the steel reinforcement. In addition, there are further verifications that are associated with the behaviour of the FRP materials and the interface with the concrete, as set out in this Report.
Examples of ultimate and serviceability limit states relevant to FRP strengthening systems are given in Table 2.
Ultimate Serviceability
Structural strength Bending Shear Compression Anchorage–plate separation FRP stress rupture Fatigue Fire
Deflection Concrete crack widths Stress limitations Vibration
Table 2 Limit states relevant to FRP strengthening
systems.
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The design of FRP strengthening systems is mainly concentrated on the ULS of strength (see Chapters 6 to 8). This includes checks for bending, shear and compression, conditions normally associated with reinforced concrete design, as well as checks for plate separation that are particular to FRP-strengthened structures. Since structural strengthening invariably increases the stiffness of flexural members, which in turn increases the risk of brittle failure, a check on ductility will also be necessary (see Section 6.2.4 Design resistance moment of FRP-strengthened beam).
Fatigue and stress rupture are prevented by limiting design stresses, determined in accordance with Sections 6.8 and 6.9.3 respectively.
Service loads should not cause damage or adversely affect the appearance or functioning of strengthened structures. For many concrete structures an explicit deflection check is required according to BS EN 1992. Strengthening with FRP materials will reduce live load deflections due to an increase in stiffness; nevertheless, the increase in section stiffness due to the strengthening will typically be proportionally less significant than the increase in section strength, and the magnitude of the loading will often have increased in line with the section strength. For this reason it will generally be necessary to check the deflection of the strengthened structure against the appropriate limits.
Vibration checks are also generally required for new structures although it is unlikely that the installation of FRP strengthening would cause vibration problems in a structure. Generally it may be acceptable to omit vibration checks for the design of FRP-strengthened structures except in cases where vibration has been identified as a problem or where there is a particular concern due to change of use, loading, or changes in natural frequency.
For concrete structures, BS EN 1992 requires checks to be made for stress limits and crack widths at the serviceability limit state. Generally, FRP-strengthened structures should experience closely spaced narrow cracks in the concrete, provided that good bond exists between the FRP and the concrete substrate. However, where problems are anticipated, the designer should take steps to ensure that the design crack widths in the concrete do not exceed the limits given in BS EN 1992. It is also important that, in order to ensure yielding does not occur under service loads, the steel reinforcement stress does not exceed the serviceability limits in BS EN 1992. BS EN 1992 also has stress limitations for the concrete in compression, although for buildings in the UK, reference may be made to PD 6687-1(119), which includes a recommendation that it may not be necessary to check the concrete compressive stress limit at SLS.
Much of the testing work that has been carried out has confirmed that carbon FRP retains its chemical and physical properties when exposed to conditions typical of those relevant to concrete construction in the UK. However, other materials are less stable when exposed to moisture or ultraviolet radiation, and consideration must therefore be given to the use of protective coating systems.
For buildings and other structures where fire design is required, it is important to check the structural performance under fire conditions at ULS. This aspect is discussed further in Section 5.7.1.
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5.4 Mechanical properties of materials
An accurate knowledge of the properties of the materials in the original structure and of the fibre composite system are required in the design process.
The strength of concrete is expressed as a 28-day compressive cylinder strength, fck, while reinforcement strength is expressed as a yield strength, fyk.
The values of the material strengths should be either a characteristic strength (based on the strength below which no more than 5% of all possible test values would be expected to fall), or a worst credible strength. The worst credible strength is the worst value of the strength that the designer realistically believes could occur, and is typically derived based on material testing on the structure. Guidance on estimating the worst credible stress is provided in BD 44/95(117), which includes the following formula for the worst credible concrete compressive strength:
fc,WCS = i = 1 ( 100 - 20 ) Equation 5.1 100nc √nc where fci = the cylinder strengths determined from each core test nc = the number of core tests.
If the worst credible strength is used, a lower partial factor for material strength may be applied to determine the design strength (see Section 5.6.2).
The values of the characteristic strengths of the concrete and steel may be taken from the original design drawings where these are available. If characteristic concrete cube strengths are given, these may be converted to a characteristic cylinder strength based on Table 3.1 of BS EN 1992-1-1. If characteristic material strengths are unknown then material testing should be considered to derive the worst credible strength. Concrete Society Technical Report 70(120) provides guidance on the properties of historical steel reinforcement. For modern structures the reinforcement may be assumed to have a characteristic yield strength of 250MPa for mild steel and 460MPa for high yield steel.
The mean 28-day modulus of elasticity of the concrete Ecm may be derived from Table 3.1 of BS EN 1992-1-1.
The modulus of elasticity of steel reinforcement Es may be assumed to be 200GPa.
5.4.1 Properties of concrete and steel reinforcement
nc
Σ fci
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The mechanical properties of FRP materials depend principally on the type and percentage of fibre used. These aspects are likely to vary between competing composite products, and since there is currently no agreed standard specification for their manufacture, all design must be based on the actual properties obtained from the manufacturer, who should supply either characteristic values or mean values and standard deviations.
The normally available mechanical properties of FRP are tensile strength, modulus of elasticity and elongation at failure. For fabric materials, the mechanical properties may be measured directly on samples, which may be assumed to be representative of the material applied to the structure. The properties of plates should be determined on representative samples. For wet lay-up systems, test samples should be prepared under the same conditions that the composite is applied to the actual concrete. Fully cured samples may then be tested to give an indication of the in-situ properties. The mechanical properties of other manufactured composites, such as shells, should be determined by the manufacturer from tests on coupons. Five per cent characteristic values for material properties may generally be assumed to be equal to the mean value minus kn times the standard deviation, where kn is taken from Table D1 of BS EN 1990. This value depends upon the number of samples taken.
Thus, the 5% characteristic tensile strength of FRP, ffk, is related to the mean tensile strength, ffm, by:
ffk = ffm – kn sd Equation 5.2
where sd is the standard deviation. It is recommended that a minimum of eight samples be taken, in which case kn can be taken as 2.0. For design purposes, actual properties may be obtained from the manufacturer. As test methods vary, the information should detail the basis for the information (e.g. frequency of testing, standard deviation). Characteristic rather than mean values should be used for final design purposes.
It is important that the adhesive or laminating resin being used is compatible with the laminate or fibre. Ideally, to ensure compatibility, all the components of the system (including any priming or top coating materials) should be from a single supplier. The comments in Section 5.4.2 regarding the information on FRP are equally applicable to adhesives although it is rare for the adhesive strength to be a critical design parameter when strengthening concrete structures.
5.4.2 Properties of FRP
5.4.3 Properties of adhesives and laminating resins
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The equations developed for the design of FRP strengthening systems given in Chapters 6 to 8 are based on the parabola-rectangle stress–strain relationship for concrete in compression and the relationship for reinforcing steel described in Section 6.2.4, which gives the reason for adopting this relationship. Alternative, more exact stress–strain curves, such as those given in BS EN 1992(10), may be used in analysis.
Unlike steel reinforcement, all FRP has a linear elastic response to failure, with no, or very limited, yielding. Woven fabrics have a degree of non-linearity but this may be ignored for design purposes.
For the ultimate and serviceability limit states, the design loading will normally be obtained based on the actions as described in BS EN 1991 combined with the partial factors and combination factors defined in BS EN 1990 using the rules for combination as given in BS EN 1990.
Prior to strengthening, the designer will need to assess the probable effect of an accidental loss of strengthening effectiveness resulting from fire, vandalism, or impact. Guidance on structural fire design is given in BS EN 1991-1-2 and BS EN 1992-1-2. See also Sections 5.7 and 6.2.2 of this Report.
The initial strains in the structure at the time of strengthening should be calculated with partial factors for loads set to unity, for both ultimate and serviceability limit state verifications (e.g. see item (a) of Section 6.2.5). These calculations should be based on the actions on the structure at the time of strengthening, which may be assumed to be consistent with the quasi-permanent combination of actions, as defined in BS EN 1990, unless the imposed loading is controlled to specified design limits during installation.
The characteristic material properties (see Section 5.4) are divided by appropriate partial safety factors from Tables 3 to 5 to give the values to be used in design at the ultimate limit state. These tables do not cover fire design.
The partial safety factors for FRP are intended to take into account the uncertainties associated with the material itself and with its use in the structure. Guidance on developing project-specific partial safety factors can be found in the CIRIA report on FRP composites in construction(113). However, in most situations and in the absence of independent field testing of material properties as installed, the partial safety factors given in the following sections may be used.
5.4.4 Stress–strain curves
5.5 Partial safety factors for loads
5.6 Partial factors for material properties
5.6.1 Background
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The magnitude of the partial safety factors applied to the FRP will depend on the type of fibre and the stage in the manufacturing process at which the test samples are taken (see Section 5.6.3). The partial safety factors are intended to take into account changes in material properties with time. In this respect they differ from the factors applied to traditional construction materials such as steel and concrete, whose properties are assumed not to change with time.
The design strength of the steel and concrete may be determined based on the partial factors in Table 3. If worst credible strengths are used (see Section 5.4.1) the values of the partial factors may be reduced according to Table 3. The values in Table 3 are derived from BS EN 1992-1-1 and BD 44/95(117).
Partitial safety factor
Design situations Value for use with Concrete (γC)
Reinforcement and prestressing steel (γS)
Persistent and transient Characteristic strength 1.5 1.15
Worst credible strength 1.2 1.10 (or 1.05 if measured steel depths are used)
Accidental Characteristic strength or worst credible strength
1.2 1.0
In most practical design situations the limiting factor governing the failure of an FRP- strengthened structure is the strain in the FRP (e.g. anchorage, separation failure) although rarely ultimate strain. It is therefore the stiffness of the FRP that is of importance. Although durability tests in laboratory conditions on unloaded glass and carbon FRP composites have shown that there is little significant degradation of the modulus of elasticity under long-term (10,000h) environmental exposures such as salt water, high alkalinity, humidity and freeze–thaw (see for example Steckel(121)), the modulus of elasticity of FRP may change with time under load and may vary according to the method of manufacture and application. In particular, lack of straightness of fibres can significantly affect the stiffness. In addition, the accuracy with which the properties are obtained from test samples is dependent upon the method of manufacture. Therefore, it is necessary to apply partial safety factors relating to both material type and method of manufacture to the characteristic modulus of elasticity, Efk, of FRP in arriving at the design strength of structures strengthened with external reinforcement:
Efd = Efk/JFRP,mE Equation 5.3
where JFRP,mE = JFRP,E × JFRP,m Equation 5.4
5.6.2 Design strength of steel and concrete
Table 3 Partial factors for concrete and steel
reinforcement and prestress.
5.6.3 Design modulus of elasticity of FRP
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Recommended partial safety factors for modulus of elasticity are given in Table 4 and partial safety factors for method of manufacture and application can be taken from Table 5.
Material Factor of safety, JFRP,E Carbon FRP Aramid FRP AR glass FRP E-glass FRP Basalt FRP
1.1 1.1 1.6 1.8 1.8
Type of system (and method of application or manufacture)
Additional partial safety factor, JFRP,m
Plates Pultruded Prepreg Preformed
1.05 1.05 1.1
Sheets or tapes Machine-controlled application Vacuum infusion Wet lay-up
1.05 1.1 1.2
Prefabricated (factory-made) shells Filament winding Resin transfer moulding Hand lay-up Hand-held spray application
1.05 1.1 1.2 1.5
It is also possible in some situations that the ultimate strain in the FRP may govern failure of a strengthened structure (e.g. shear strengthening or ultimate strain of confined concrete) although, typically, other strain limits are reached first. Durability tests on unloaded specimens of glass and carbon composites have demonstrated significant long-term ultimate strain reductions, particularly due to exposure to humidity (see Steckel(121)). As for the material partial safety factor for modulus of elasticity, the partial safety factor for ultimate strain is also related to both material type and route of manufacture and application. Thus, the design strain is given by:
Hfd = Hfk/JFRP,mH Equation 5.5
where JFRP,mH = JFRP,H × JFRP,m Equation 5.6
Recommended partial safety factors for ultimate strain are given in Table 6 and partial safety factors for manufacture method can, again, be taken from Table 5.
Material Partial safety factor, JFRP,ε Carbon FRP Aramid FRP AR glass FRP E-glass FRP Basalt FRP
1.25 1.35 1.85 1.95 1.95
Table 4 Partial safety factors for Young’s modulus at
the ultimate limit state (all design situations).
Table 5 Recommended values of additional partial
safety factors, to be applied to manufactured composites, based on Clarke(114).
5.6.4 Design ultimate strain of FRP
Table 6 Partial safety factor for strain at the ultimate
limit state (all design situations).
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In some instances the ultimate tensile strength of the FRP is required during the design of a strengthened structure (e.g. ultimate flexural strength, although actual failure is likely to be due to separation of the FRP from the concrete, which, in general, is related to FRP strain). In such cases, the design strength can be derived from the design modulus of elasticity, Efd, and the design strain, Hfd:
ffd = Efd Hfd Equation 5.7
Hence, given the partial safety factors acting on the modulus of elasticity and the ultimate strain of the FRP, the partial safety factors acting on the strength of the material are as follows:
JFRP,mf = JFRP,mE × JFRP,mε = JFRP,E × JFRP,ε × (JFRP,m) 2 Equation 5.8
So the design strength is given by:
ffd = ffk/JFRP,mf Equation 5.9
Figure 21 shows the relationship between design stress and strain and the partial material safety factors.
5 Structural design of strengthened members
5.6.5 Design ultimate strength of FRP
εfk εfd
ffd
ffk
E fk
E fd
Stress
Strain
Figure 21 Assumed stress–strain behaviour for FRP.
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In general, the ultimate behaviour of a strengthened section will be governed by the strength of the concrete and not by the strength of the adhesive, provided the following are satisfied: � All the materials used are in accordance with recognised standards. � The material properties are checked on samples made on site. � The in-service temperature does not differ significantly from that at which the test
samples were made and cured. � The work is carried out by suitably experienced staff, in accordance with the advice in
Chapter 10. � Detailed and proven method statements and specifications are used. � The structure is ‘fail-safe’, i.e. failure of the strengthening will not lead to failure of the
structure (see Section 6.2.2).
Where there is a need to consider adhesive strength, an approach for determining appropriate partial safety factors may be found in A guide to the structural use of adhesives(34).
It should be noted that cyclic strains applied to an adhesive during the curing period, for example due to traffic loading on a bridge under repair, may lead to a change in the properties of the adhesive. These changes may be up to 32% reduction in the strength of the fully cured material (see Section 6.9.4).
As a general recommendation, the stress in the adhesive should be kept below 25% of the short-term strength, which equates to the recommended minimum material partial safety factor of JA = 4.0.
For many types of structures, accidental actions, e.g. fire or impact, will be a major design consideration.
The FRP materials used for structural strengthening degrade at elevated temperatures. Carbon fibres are relatively insensitive to elevated temperature (Section 3.1); however, the mechanical and bond performance of polymers degrade at temperatures approaching the glass transition temperature (see for example Bisby et al.(31) and Stratford et al.(122)). The glass transition temperature of a typical ambient cure epoxy bonding adhesive is 50–65°C (Section 3.7.1).
However, fire is an accidental design situation for which the partial factors for actions and materials are reduced (see BS EN 1990(115)). Consequently, in many cases the unstrengthened structure will have adequate resistance even if the FRP strengthening is rendered completely ineffective during fire. The following example outlines an appropriate approach to demonstrate the adequacy of a reinforced concrete slab strengthened in flexure with an externally bonded FRP strengthening system. A similar approach could be used for shear strengthening or axial strengthening of columns.
5.6.6 Adhesive
5.7 Accidental actions
5.7.1 Designing FRP strengthening for fire
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Checking the fire resistance of the existing slab The schematic timeline in Figure 22 shows the different design resistances that are used in the fire design of FRP strengthening. By way of explanation, consider for example a floor slab with permanent load G and imposed load Q:
1. Before strengthening, the bending resistance of the slab is sufficient to carry the loads 1.35G + 1.5Q.
2. The slab is strengthened to carry an additional 50% imposed load. Hence, after strengthening, the slab is designed to resist a load of:
1.35G + 1.5 (1.5Q)
The design action under this load condition is Ed.
3. The required resistance of the slab in fire is defined by the reduction factor Kfi, which is the ratio of the design actions in fire (Efi,d) to the design actions at ambient temperature (Ed) (see BS EN 1991-1-2(116)):
Efi,d = Kfi Ed
Section 2.4.2 of BS EN 1992-1-2 should be used to calculate Kfi. Using the default value of Kfi = 0.7 gives a required load to be resisted in fire of:
0.7 x {1.35G + 1.5 (1.5Q)}
4. In a typical floor slab, G ≈ Q, so in this case the required design resistance in fire ≈ 2.52G. (In this case, the required design resistance is similar to the serviceability design effect, Cd, for the strengthened structure, but this will not always be the case.)
5. The required resistance in fire (2.52G) is less than the resistance of the unstrengthened slab (2.85G) under ambient conditions. However, in a fire, the resistance of the unstrengthened slab is reduced. Therefore, the resistance of the unstrengthened slab must be established in fire conditions if it is assumed that the FRP strengthening system is rendered structurally ineffective during the fire due to heating well above its glass transition temperature.
The resistance of the existing structure (without FRP) during a fire should be checked using one of the methods described in BS EN 1992-1-2(10), such as the 500°C isotherm method or the zone model described in Annex B of BS EN 1991-1-2. The structure must resist exposure to the standard temperature–time fire curve for the required resistance period – see BS EN 1992-1-2, as indicated in Figure 22.
Note that the tabulated data in BS EN 1992-1-2 Section 5 are empirical and assume Kfi = 0.7; that is, the required resistance in fire is 70% of the unstrengthened resistance of the structure. This is unlikely to be the case for an FRP-strengthened structure. Consequently, it is not sufficient to only check the section geometry and cover to satisfy fire design requirements.
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Figure 22 Schematic timeline showing the design
resistances of a strengthened structure before and during a fire.
Improving load resistance in fire using protection systems If the existing member alone cannot meet the required fire resistance, fire protection can be applied. This fire protection improves the fire endurance of the existing member by insulating the concrete and reinforcing steel from the fire and thus delaying their degradation. An insulation system that remains in place during a fire can thus be used to increase the fire resistance period of a member without a strength contribution from the FRP, and this has been demonstrated in full-scale loaded fire tests of insulated FRP-strengthened concrete elements (see Kodur et al.(123)).
The BS EN 1992-1-2(10) methods (e.g. the 500ºC isotherm method) can be used to determine the fire resistance of an insulated concrete member. However, a thermal analysis will be required to determine the temperature profile through the concrete section at the required fire resistance period because of the presence of the supplemental insulation (the temperature profiles in Annex A of BS EN 1992-1-2 are for direct exposure of the concrete surface to the standard fire). In general, a specialist consultant should be employed for this heat transfer analysis.
The fire protection system must stay in place throughout the required fire resistance period. Suitable fire protection systems include fire protection boards or spray-applied fire protection systems. Further information should be obtained from a supplier of fire protection systems, who will provide the thermal properties of their materials for design.
Note that, in general, the fire protection is not intended to enable the FRP strengthening to remain active during a fire. Rather, it is provided to improve the resistance of the unstrengthened structure to fire. Any system designed to allow the FRP strengthening to carry load during a fire must be tested according to the methods described in BS EN 13501(124).
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Other reaction to fire considerations FRP-strengthened members must comply with the appropriate flame spread requirements, and requirements governing smoke and toxic fume generation, particularly in enclosed locations such as tunnels or buildings (see for example Fire safety performance of materials used in the Underground(39)). Coatings and insulation systems (see for example Bisby et al.(125), Kodur et al.(126) and Williams et al.(127)) can be used to limit smoke generation and flame spread.
Seismic loading will not be a major loading case for most UK structures (other than nuclear facilities). However, globally, the issue of seismic loading is highly significant. Where structures are found to be deficient under seismic loading, the use of FRPs for retrofit is a possible solution, although this does not mean other options should not be considered. BS EN 1998-3(128) provides guidance on assessing structures for seismic resistance and guidance on seismic retrofit. Amongst other retrofit solutions described in Annex A of BS EN 1998-3(128) (including concrete and steel jacketing) is a section devoted to FRP plating and wrapping. This gives a more detailed treatment of the subject but it should be noted that this Annex is for information only. It should also be noted that the detailed design procedures described in BS EN 1998-3 do not necessarily directly conform to the approaches described in this Report, as these are primarily intended for non-dynamic load conditions.
There are several reasons why a structure might be deficient under seismic loading. Considering framed structures, the main deficiencies are: � Inadequate transverse reinforcement leading to shear failure. � Poor concrete confinement in plastic hinge regions. � Lack of resistance against buckling of longitudinal compression reinforcement within
hinge regions. � Inadequate lap splices between lengths of longitudinal steel.
The overall aim of seismic retrofit, therefore, is to improve any deficient aspects leading to ductile behaviour, preventing brittle modes of behaviour. This leads to a deformable structure with the ability to absorb earthquake energy, helping prevent collapse. Seismic loading primarily consists of lateral inertial forces, rather than locally loading elements, and acts globally on a structure. It is therefore important that any retrofit strategy does not locally increase the stiffness of a structure otherwise load will be attracted to the stiffened region, increasing the potential for local failure. Consequently, the design solution should increase ductility and increase resistance against brittle failure (e.g. shear) without increasing stiffness.
Preventing brittle failure mechanisms Shear failure is a primary brittle mechanism to be avoided. This can be achieved in columns by fully wrapping them in areas of high shear. Beams can be strengthened in shear, using U-wrapping, or full wrapping if practical. The design methods described in Chapter 7 may be used to ascertain strengthening required for a given shear action.
5 Structural design of strengthened members
5.7.2 Seismic loading
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Where longitudinal steel is lapped, there must be sufficient bond for the lap-splice to transfer the load. Debonding of the splice will occur when longitudinal cracks develop in the concrete cover due to dilation stresses caused by high lap bond stresses during bending. This will lead to cover spalling and rapid loss in flexural capacity. This can be again be prevented by wrapping members transversely with FRP, resisting lateral tensile stresses in the concrete cover and confining the concrete, hence, enhancing the lap bond capacity.
Buckling of longitudinal steel in compression, as a plastic hinge forms, may occur when links are too widely spaced for this extreme load condition. The steel will burst through the concrete cover. FRP wrapping of columns in hinge regions (usually at the ends of the columns) helps prevent this type of reinforcement buckling.
Increasing ductility The overall capacity of the structure depends upon the plastic deformation capacity of each resisting element. This deformation capacity is conveniently related to ductility, one definition of which is the ultimate curvature divided by the yield curvature. Ultimate curvature, and hence ductility in columns, is usually limited by the ability of the concrete in compression to reach large strains. Wrapping columns with FRP will again improve this behaviour, confining the concrete so as to allow it to reach higher strains than normal.
Due to the difficulties in confining compression zones in beams (due to floor slabs, for instance, preventing full wrapping), it should be ensured that any plastic hinges form in the columns rather than in the beams. Thus, this hierarchal behaviour must be maintained following strengthening by ensuring that the flexural capacity of the columns is not increased significantly by the wrapping solution.
It is therefore recommended that a low confinement stiffness ratio, Uκ, of around 0.01 (see Section 8.2) be used so as to allow these high strains to be achieved without increasing concrete strength significantly. However, even with no strength increase, the increased strain capacity will inevitably still lead to a small increase in flexural capacity, so it should be checked that this does not increase beyond the flexural strength of the beams (which will probably have lower ductility).
It is only necessary to increase this ductility in regions where high moment exists, typically at the column ends, rather than along the full length of the column. Shear forces associated with design of the strengthened columns should be checked. It should be noted, however, that wrapping to provide low confining stiffness for increasing ductility may be incompatible with providing sufficient shear enhancement or lap splice confinement if it is necessary to provide this in the same location.
Longitudinal FRP is not generally considered for seismic retrofit (e.g. to increase flexural strength) for two reasons. First, the maximum moments will usually occur at the beam– column connection locations where it is difficult to anchor the longitudinal FRP. Second, and more importantly, the addition of longitudinal FRP is likely to reduce ductility since it will limit the ability of the steel to yield due to the elastic stress–strain nature of the FRP.
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Strengthening beam–column joints using FRP is extremely difficult due to the practicality of providing adequate jacketing. It is recommended that such strengthening be attempted only after carrying out testing on suitably constructed specimens under representative cyclical load conditions.
Instances involving vehicle impact with structures, particularly bridge piers, have the potential to cause significant social and economic consequences. A bridge column impacted by a vehicle requires the strength to withstand the impact and ductility to dissipate the energy. It is estimated that during a vehicle impact up to 80% of the energy is dissipated through crushing of the vehicle. Given these requirements, the application of longitudinal and transverse FRP provides good possibilities for enhancing a column’s response.
The success of enhancing a column’s impact response with longitudinal and transverse FRP was demonstrated in a study by the Highways Agency on circular columns. Longitudinal FRP was used to provide enhancement to the moment capacity and transverse FRP was used to increase the shear capacity. The ductility of the member is further enhanced by the confinement provided by the transverse hoop wraps, which allows the compression concrete to attain a much higher strain prior to failure. Detailing issues may play an important role in designing retrofit systems. Preventing the possibility of direct shear failure may require the retrofitting system to be continued over the interface between the column and the bridge deck, although in practice this may be difficult to achieve.
The Highways Agency study demonstrated that columns retrofitted for impact loads were at least as effective as those designed for quasi-static loads. Design guidelines prepared by the Highways Agency (see BD 84/02(7)) for strengthening bridge support structures with FRP suggest that designs can be carried out to resist the equivalent static loads given in BD 48/93(129). In some circumstances it may be necessary to carry out a full dynamic analysis. However, the conservatism of the loading equivalent static method normally negates this. Furthermore, the strengthening guidelines developed by the Highways Agency do not include dynamically enhanced material properties, therefore design solutions are likely to be conservative.
Tests on rectangular columns strengthened with aramid FRP carried out by Suter et al.(130) have shown the effectiveness of applying longitudinal FRP followed by hoop wrapping in increasing the flexural capacity and hence the energy-absorbing capacity of columns under equivalent static loading. This method is highly effective since debonding of the longitudinal FRP is prevented by the hoop wraps. It is also claimed in the Highways Agency design document BD 84/02 that this technique allows the compressive strength of the FRP to be used in design (loading is transient and therefore creep effects which usually prevent use of compression FRP are negated). The work carried out by Suter et al.(130) considered the use of aramid FRP due to its high toughness although other materials may be equally suitable for alternative reasons.
5 Structural design of strengthened members
5.7.3 Impact loading
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Structural design of strengthened members 5
Under certain circumstances impact resistance may become important in buildings, for example falling weights on slabs and beams. Tests by Tang and Saadatmanesh(131) demonstrated the effectiveness of strengthening reinforced concrete beams with carbon FRP and aramid FRP in both the compression and tension faces. When compared with an unretrofitted beam, it was shown that the FRP increased the stiffness of the members and reduced the peak and residual displacements along with the width of cracks. In this research carbon FRP- strengthened beams were demonstrated to perform better than aramid FRP-strengthened ones.
Therefore, for the purposes of strengthening columns against impact, the following is recommended: � Conservative equivalent static loading should be used to ascertain flexural and shear
demand. � Shear strength enhancement to achieve the shear resistance (if necessary) can be
calculated according to the methods in Chapter 7 (for rectangular columns) and 8 (for circular columns).
� Flexural strength enhancement can be achieved through adding longitudinal FRP (see Chapters 6 and 8). This enhancement will typically not be achieved at the top and bottoms of the column because of difficulties in providing adequate anchorage.
� FRP in compression may be considered in design but only for circular columns and only in conjunction with transverse wrapping. Compression FRP should always be neglected in rectangular or square columns.
� Increase in strain capacity of concrete columns wrapped transversely may be considered in calculating flexural capacity, but concrete strength enhancement should be neglected (i.e. provide low confinement stiffness Uκ = 0.01; see Chapter 8).
When mitigating the effects of blast loads the fundamental concern for designers is to ensure the structure retains its integrity to avoid progressive collapse, prevent injuries to the inhabitants from flying debris created by the spalling of the concrete and dissipate the blast energy in a ductile manner. FRPs have been demonstrated to be effective in strengthening a number of different structural elements (including columns, slabs and walls) against explosive loads. Carbon FRP has generally been used in this application owing to its high strength and stiffness. However, the toughness of aramid FRP is a desirable property for this application and a hybrid carbon/aramid FRP may be best suited (see Crawford et al.(132)).
Blast loads provide a unique design situation due to the extremely high overpressures and very short duration of load application. The extremely high overpressures cause the member impacted by the blast to deform extremely rapidly. This high rate of straining causes the material properties to change, with reinforced concrete showing significant increases in strength. Analysis of existing structures subjected to blast loads is typically carried out using either simplified analytical methods or through complex finite-element models. These models should account for the enhancement of material properties due to the high strain rate response.
5.7.4 Blast loading
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5 Structural design of strengthened members
Column strengthening for blast Load-bearing columns around the perimeter of a structure are a primary component in preventing structural collapse in the event of blast loading. However, it has also been shown in dynamic tests that, as the rate of loading increases, the potential for shear failure becomes greater (see Fu et al.(133)) leading to loss of load-bearing capacity. Maintaining the structural integrity of these columns by designing for robustness is therefore the main concern when retrofitting against blast loads.
Tests demonstrate that the application of as few as two layers of sheet carbon FRP wrapped in the transverse direction can increase the shear capacity enough to prevent a brittle shear failure. The confinement provided by the FRP also allows the concrete in compression to sustain a much higher strain prior to failure, therefore dissipating significantly more energy in a ductile manner. In blast situations, attempting to strengthen a column in flexure by applying longitudinal FRP is not recommended due to the possibility of spalling of the concrete on the tension face due to the blast shock wave through the concrete, even if transverse wraps are provided.
In addition to conventional shear failure, where a shear crack forms diagonally across the column, direct shear failure can occur. Direct shear failure is a pure shear phenomenon where a shear plane forms transversely across the column cross-section, usually directly across the top or bottom of the column, where it meets the beams or foundations. The direct shear strength is usually significantly higher than the conventional diagonal shear strength and is not considered in conventional design situations. However, direct shear failure has been observed in blast tests on columns, particularly when heavily strengthened to prevent diagonal shear failure. It is not practical to increase the direct shear strength by FRP retrofit and therefore this will limit the degree of flexural and diagonal shear strengthening which can be achieved.
An additional and valuable side effect of wrapping columns with FRP is that they do not suffer explosive spalling so the potential for injuries from flying debris is reduced.
One final consideration applies where columns are strengthened against blast in seismic zones. The retrofit systems for columns may increase the stiffness of the member. As retrofit systems for blast loads are typically only applied to perimeter columns, if the building were subjected to a seismic event, these columns would attract a disproportionate amount of the load and may thus collapse. Clearly this is of low concern in the UK but highlights important issues that engineers must consider when designing retrofit systems.
In situations where deliberate vandalism is considered to be a potential problem (primarily in an urban environment), there are a number of possible actions that can be taken. First, the FRP may be physically protected, by providing some form of barrier that limits accessibility (either to the surface of the strengthened structure or around the structure as a whole).
5.7.5 Vandalism
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Structural design of strengthened members 5
Second, a form of strengthening which is inherently resistant to physical attack, such as NSM, may be chosen. Third, frequent inspection or monitoring should be carried out so that any damage resulting from vandalism can be quickly remedied. However, it is not possible for these measures to prevent damage from a determined attack. It is therefore necessary for the unstrengthened structure to be able to satisfactorily carry the serviceability limit state loading using the frequent combination of actions as defined in BS EN 1990(115).
Accidental damage may also occur due to subsequent works on a structure, for example contractors drilling through FRP or removing protective coatings without realising the structural implications. This can be avoided by making contractors aware that the FRP should not be interfered with. This may be achieved by application of some form of printed warning, either directly to the FRP or in close proximity if the finish of the FRP is important, and by inclusion of appropriate information in structure management records. Further guidance and suggested warning signs can be found in Section 10.12 below and in The Concrete Society’s Technical Report 57(9).
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6 Strengthening members in flexure
6. Strengthening members in flexure The flexural strength of reinforced concrete beams and slabs can be increased by bonding FRP to the tension faces of the members, as shown in Figure 23.
For members strengthened in flexure, the following should be considered: � maximum moment � risk of peeling failure at the ends of the FRP � risk of debonding of the FRP and the concrete substrate � shear capacity of the section � ductility of the strengthened member � compliance with relevant serviceability limit states, e.g. stress limitations, cracking,
deflection, fatigue, creep-rupture.
6.1 General
Flexural strengthening
Shear strengthening
Figure 23 Strengthening beams and slabs with FRP.
In addition, this design guidance is dependent on the following assumptions: � No slip between the FRP strengthening and the substrate (i.e. plane sections remain
plane). This assumption places limits on adhesive thickness, adhesive shear modulus and FRP composite in-plane shear rigidity.
� Inter-laminar shear strength of the FRP strengthening is greater than the adhesive bond shear strength. This should be covered in the specification by specifying the type of resins that are acceptable, limits on fibre volume fraction and elastic modulus of the FRP strengthening.
� The substrate quality is such that it will not reduce the effectiveness of the FRP strengthening. Therefore the actual condition must be established and taken into account in design together with likely future deterioration which may be indicated by chloride levels, existing cracks, moisture and half-cell potential of the concrete substrate. The specification should also outline clearly the allowable minimum compressive and tensile strengths of the concrete to ensure a proper bond and long-term durability. Tests to determine these properties (e.g. pull-off tests) should be outlined in the specification.
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Strengthening members in flexure 6
� The surface preparation of the concrete substrate is sufficient to achieve the required level of bond strength required in the design.
� The installation methods and specification are as detailed in Chapter 10.
The section should normally be designed such that yielding of the steel reinforcement precedes both compressive failure of the concrete and tensile failure of the FRP.
In cases where the FRP will theoretically reach its design tensile strain before the concrete crushes, failure normally occurs due to plate separation rather than plate rupture and the stress and strain limits to prevent debonding, discussed in Section 6.3.3, will frequently govern the design. In some cases the concrete will crush before the FRP reaches its design tensile strain (see Section 6.2.4). However, provided that the steel strain at failure is sufficiently large, this should not result in brittle failure of the strengthened member.
Design ultimate moment capacity should normally be determined by linear elastic methods. If there is evidence of local yielding taking place, the results of an elastic analysis need to be applied with care. Since members undergoing strengthening will usually be steel reinforced, some redistribution of elastic moments may occur under ultimate limit state conditions. Section 6.7 gives further guidance on the extent of this redistribution.
The ultimate bending resistance of the existing section should be calculated by conventional concrete design methods, such as those in BS EN 1992. However, care should be taken where the structure contains materials or details that are outside the scope of current design requirements. If the material properties are unknown they should be estimated giving due regard to the age of the structure (see Sections 5.4 to 5.6).
The section should only be considered for strengthening if the ultimate resistance of the unstrengthened (existing) section is at least as great as the effects arising from the serviceability limit state loading using the frequent combination of actions as defined in BS EN 1990. This indicates that even in the event of removal of the FRP strengthening by some unforeseen event, catastrophic collapse of the structure is unlikely.
An initial but potentially non-conservative estimate of the FRP requirement for the section can be obtained by assuming that the position of the neutral axis remains approximately equal to that of the unstrengthened section. The approximate area of FRP required, Af, can therefore be obtained by dividing the required additional moment capacity of the beam, Madd, by the product of the steel lever arm, z, and the design stress in the FRP (given by εfe Efd) as follows:
6.2 Moment capacity
6.2.1 Introduction
6.2.2 Requirements of the existing section
6.2.3 Preliminary design
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Af = Madd/εfe Efd z Equation 6.1
where εfe = the lesser of εfk/JFRP,mε (the design ultimate strain of FRP) and a strain of 0.008 (a
value which typically results in separation failure, according to empirical evidence, but see Section 6.3.3 for more detailed consideration of separation)
Efd = design modulus of elasticity of FRP, Efk/JFRP,mE z = steel lever arm.
This calculation becomes a less reliable predictor of the FRP area required if the existing section is already heavily reinforced, or if the section is doubly reinforced. In any event, it is always necessary to proceed with the detailed design method rather than rely on this initial estimate.
When analysing a cross-section to determine its ultimate moment of resistance, the following assumptions should be made: � The strain distribution in the concrete in compression and the strains in the reinforcement,
whether in tension or compression, are derived from the assumption that plane sections remain plane and that no longitudinal slip occurs between or within the components of the section.
� The stresses in the concrete in compression are derived from the stress–strain curves in Section 3.1.7 of BS EN 1992-1-1 with the maximum strain at failure limited to εcu2 or εcu3 depending on the stress–strain diagram used – see BS EN 1992-1-1, Table 3.1.
� The tensile strength of the concrete is ignored. � The stresses in the steel reinforcement are derived from the stress–strain curves in
Section 3.2 of BS EN 1992-1-1 (Figure 24). � The strains in the cross-section should take into account the strains present in the
existing structure at the time of application of the FRP reinforcement. The calculation of this initial strain may be based on the SLS loading under the quasi-permanent combination of actions, or alternatively based on constraints to the loading during installation where these are reliably controlled.
� The stresses in the FRP reinforcement are derived from the assumption that the FRP has a linear elastic characteristic until rupture.
� Separation failure will occur when the FRP longitudinal shear stress reaches the limits in Section 6.3.3.
� FRP rupture will occur when the FRP strain exceeds the rupture strain (see Section 6.3.3).
In addition, if the ultimate moment of resistance, calculated in accordance with this clause, is less than 1.15 times the required value, the section should be proportioned such that the strain at the centroid of the tensile steel reinforcement is not less than 0.002 + fyk/(EsJS).
6 Strengthening members in flexure
6.2.4 Design resistance moment of FRP-strengthened
beam
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Strengthening members in flexure 6
stress
strain
f /yk gs
E s =200 GPa
Figure 24 Idealised stress–strain curve for reinforcing
steel in the design of strengthened beams in flexure.
Allowance should also be made for the requirements of additional tensile capacity (to carry the tensile forces arising from the truss analogy for resisting shear) if significant shear and bending moment coincide. (See also Chapter 7 on shear.)
The following example design method illustrates the process for determining the ultimate bending resistance. a) Calculate the initial strains in the structure at the time of strengthening (which in this
example are based on the SLS loading under the quasi-permanent combination of actions). The concrete modulus of elasticity should be modified to account for the duration of the loads and the effects of creep (see Section 3.1.4 of BS EN 1992-1-1). In this example the quasi-permanent combination is being considered and so it is reasonable to assume a long-term value of the concrete modulus of elasticity after creep has occurred, i.e. Ecm/(1+φef), where φef is the effective creep coefficient (see Sections 3.1.4 and 5.8.4 of BS EN 1992-1-1).
b) Calculate the loads to be applied to the structure at ULS for the appropriate design situation (which in this example is the persistent design situation). From a structural analysis determine the shear forces and bending moments at the section considered.
c) Estimate an area of longitudinal FRP for the design (see Section 6.2.3). d) Initially assume a value for the maximum compressive strain in the concrete of εcu2 or
εcu3 depending on the stress–strain diagram used – see BS EN 1992-1-1. e) Assume an initial neutral axis position. f) Adopting the assumptions described in Section 6.2.4 calculate the forces in the component
parts of the cross-section. The strain used to calculate the force in the FRP should be evaluated by subtracting the initial strain in the concrete at the position of the FRP at the time of strengthening (calculated in step (a)) from the strain at the position of the FRP from the assumed linear strain profile (dependent on the assumed neutral axis position and maximum concrete strain in steps (d) and (e)).
g) Iteratively adjust the assumed neutral axis position until step (f) results in zero net axial force present in the section (i.e. ‘force balance’ is achieved).
h) Check the calculated stresses and strains against the following criteria: � The concrete maximum compressive strain should not exceed εcu2 or εcu3 depending
on the stress–strain diagram used. � The FRP maximum longitudinal shear stress should not exceed the limits calculated
in accordance with Section 6.3.3.
6.2.5 Example design method
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� The strain in the FRP, according to Section 6.3.3, is less than the ultimate design strain capacity of the FRP.
If the FRP tensile strain or shear stress exceeds these limits then the maximum strain in the FRP should be reduced and the process should be repeated from step (e) to achieve axial equilibrium. If this is the case, the concrete will not reach its limiting strain (εcu2 or εcu3) since the maximum FRP strain will govern design. The maximum strain in the concrete will be governed by the strain in the FRP and the neutral axis depth. The force in concrete can be calculated from either of the stress–strain diagrams in BS EN 1992-1-1, namely Figures 3.3 or 3.4, but with an appropriately truncated strain limit. Do not use a rectangular stress block, since this is only valid if the concrete reaches its ultimate strain.
i) The bending resistance of the section may then be calculated based on the moment of the forces in the section. If the bending resistance exceeds the applied moment and the steel reinforcement strain exceeds 0.002 + fyk/(EsJS), or the bending resistance exceeds 1.15 times the applied moment, then the design is adequate in bending. Otherwise it may be necessary to increase the amount of FRP and repeat the above process from step (d).
For sections with shear reinforcement or shear strengthening, it is necessary to assess whether there is sufficient longitudinal reinforcement (steel or FRP) to carry the additional tension forces associated with shear. This may be achieved in accordance with Section 7.4, either by extending the FRP by an appropriate length or by providing additional FRP.
The behaviour of the interface between the FRP and the concrete surface is crucial to the performance of the strengthened structure.
In an analysis of results from tests on 127 reinforced concrete beams (23 different studies) with externally bonded FRP reinforcement, Bonacci and Maalej(134) observed that 63% of the beams were reported to have failed by failure of the FRP-to-concrete interface, causing the FRP to separate from the concrete, with consequent loss of FRP-to-concrete composite action. This is in agreement with other studies which show that such separation of the FRP from the concrete is the most prevalent failure mode of FRP strengthened beams. It is therefore essential to address such failure modes in the design of FRP strengthening schemes. Figure 25 illustrates typical FRP separation failure modes observed in tests.
FRP separation, owing to its importance, remains a subject that stimulates considerable research. A number of initiation mechanisms have been identified and advances are continually being made in understanding these mechanisms. The design approaches given below combine appreciation of the underlying mechanics, theoretical analysis and calibration of equations against experimental data.
Work on steel plate bonding has shown that separation failures tend to initiate from the ends of the plates. To address this, limitations on plate aspect ratio are incorporated in the Highways Agency Advice Note on steel plate bonding, BA 30/94(135), together with requirements for bolting. Early work on FRP separation failures similarly focused on the ends of the plates. However, for FRP strengthening schemes, experimental evidence now shows that
6.3 FRP separation failure
6.3.1 Background
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Strengthening members in flexure 6
anchorage zone anchorage zone zone requiring strengthening
Original moment capacity
Required moment capacity, MEd
steel yield zone
Moment at which steel yields, My
Moments due to ultimate loading
(A) surface irregularities
(B) shear crack induced
separation
(C) longitudinal shear stresses in yield zone
Additional moment to be carried, Madd
(D) FRP rupture
(E) longitudinal shear stresses
outside yield zone (F) anchorage
failure
(a) Possible FRP failure modes:
(c) Longitudinal shear stresses at FRP-concrete interface (for UDL):
Shear stresses due to stress gradient i FRP, τm
n
Shear stresses
in elastic region
Shear stresses
in yield zone
Shear stresses in anchorage
zone
Additional shear stresses due to cracking, τsc
(b) Bending moments:
Increase in shear stress due to FRP termination
Figure 25 Possible failure modes and development of
longitudinal shear stresses for FRP- strengthened beam.
Note that the bending moment diagram and longitudinal shear stresses are dependent upon the
exact loading and support conditions.
separation can also initiate from flexural cracks in the span, shear cracks or concave irregularities in the surface profile, and that all of these cases need to be taken into account in the design. Importantly, research has also shown that externally bonded FRP strengthening can be highly effective without the need for bolting or the use of other mechanical fixings.
It has been shown that increasing the area of FRP bonded to the concrete and reducing the FRP thickness reduces the likelihood of separation failure modes.
The bond behaviour of externally bonded FRP differs markedly from that of embedded steel reinforcement. Experiments have shown that the longitudinal shear stress that can be transferred between the FRP and the concrete is not independent of the bonded length, as typically assumed for embedded steel reinforcement. Thus, whilst it is possible to anchor steel reinforcement by providing an anchorage length beyond which the full strength of the reinforcement can be developed, this is not typically the case for externally bonded FRP. This aspect of the behaviour of externally bonded FRP greatly influences, and adds complexity to, the design of strengthening schemes.
6.3.2 Bond behaviour
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In tests on the anchorage of FRP externally bonded to concrete, it has been found that beyond a limiting bonded length, of the order of 50–300mm, there is no further increase in the ultimate anchorage load capacity with increased bonded length. Furthermore, this ultimate anchorage capacity can be very much less than the ultimate tensile capacity of the FRP.
Such behaviour is shown in the work of Neubauer and Rostasy(136). Based upon their model, Denton et al.(137) have investigated the ratio of the strain when FRP separation occurs to the ultimate FRP strain capacity for varying anchorage lengths and a range of different FRP plate thicknesses. For all the cases considered, the maximum force that can be developed in the FRP anchorage is less than 25% of the ultimate FRP capacity.
Experimental studies have, however, shown that the FRP force that can be developed in the span of strengthened beams can be very much greater than the FRP anchorage capacity. These findings indicate that, provided there is a gradual build-up of stress outside the anchorage region, it is possible for the FRP to sustain stresses in excess of the anchorage capacity without separation failure occurring. Importantly, it seems that this gradual build-up of FRP stress relies on some flexural cracking of the concrete as the ultimate limit state is approached. Thus, particular care is required in cases where the FRP is bonded to concrete that is not expected to crack at the ultimate limit state, for example because of changes in section properties or the presence of prestress.
With reference to Figure 25, the design procedure to account for FRP separation failures first requires two structure-dependent conditions to be checked, namely that failure will not be initiated by either (A) irregularities in the concrete surface profile or (B) shear cracking. Provided these are satisfied, four further design-specific criteria must be considered relating to (C) the longitudinal shear stress between the FRP and the concrete in the steel yield zone, (D) rupture of the FRP, (E) longitudinal shear stresses outside of the yield zone and (F) the stresses developed in the anchorage region.
(A) Surface irregularity induced FRP separation Concave irregularities in the profile of the surface to which the FRP is bonded will lead to the development of transverse tensile stresses in the adhesive and surface concrete as the FRP attempts to straighten under load. Such transverse tensile stresses can promote the initiation of FRP separation failure.
It is usually the case during strengthening works that the surface to which FRP will be bonded is concavely curved to some extent. Such unevenness is sometimes relatively local, perhaps due to formwork being flexible during casting, or alternatively it could also be more global, for example when the entire soffit of a structure is curved.
Through testing (see Eshwar et al.(138) and Porter et al.(139)), it has been found that concave curvature can significantly affect the degree of strengthening achieved. The work of Eshwar et al.(138) suggests that the extent over which the concave curvature exists may affect the significance of such concavity, and it seems that the behaviour of strengthened members is more sensitive to global than local curvature.
6.3.3 Design procedure
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Therefore it is advised that if the soffit of a concrete structure to be strengthened is globally concave, reference should be made to specialist literature(138,139), and specialist advice sought.
If undulations in the concrete are local with a smoothly varying profile, the influence of curvature may be disregarded in the design provided over any 1m length, any concavity in the FRP profile, as installed, does not exceed 3mm in depth. Fabric-based systems tend to closely follow the profile of the concrete to which they are bonded and it is therefore essential that the specification for such schemes requires the concrete surface to which the FRP will be bonded to have only smooth variations in profile with a maximum unevenness of 3mm in 1m. For plate-based systems, the FRP tends not to follow the profile of the concrete so closely and therefore greater unevenness in the concrete profile, up to 5mm in 1m, may be acceptable provided the FRP, once installed, has a smooth variation in profile with a maximum unevenness of 3mm in 1m. In such cases, the difference in the concrete and FRP profile must be taken up in the adhesive.
(B) Shear-crack-induced FRP separation The presence of shear cracks can lead to a tendency for a step to develop in the tension face of the member to which the FRP is bonded. This can result in the development of sizable transverse tensile stresses in the adhesive and the surface concrete, leading to the initiation of FRP separation failure. Moreover, shear cracks at the end of an FRP laminate can result in concrete cover separation failure. It is therefore necessary to consider shear-crack- induced separation within the FRP anchorage zone.
This type of failure may occur if the design shear force, VEd, exceeds the capacity of the section to resist formation of significant shear cracks, VRd,crack. This resistance is a combination of the shear strength of the concrete without stirrups, VRd,c, together with an effective contribution from any stirrups which might be present, VS,eff (see Teng and Yao(140)). However, experimental studies (see Ibell et al.(141)) have shown that shear cracking will have initiated at or before 67% of the ultimate design shear capacity of the section.
Where the shear plane under consideration lies within a shear span of 2d from the support, shear enhancement is allowed when calculating VRd,c provided that the internal longitudinal steel reinforcement is fully anchored. However, if shear enhancement is included, then the effective contribution from stirrups, VS,eff, should be neglected, as should any load reduction factor β (defined in Section 6.2.2 of BS EN 1991-1).
Therefore, the capacity of the strengthened section to resist shear crack formation can be calculated according to the following conditions: � VRd,crack should be no greater than VRd,c+VS,eff. � For members with shear reinforcement but no shear strengthening, VRd,crack should be
no greater than 0.67VRd,s. � For members with shear strengthening, VRd,crack should be no greater than 0.67VRd,s,f. � However, in all cases, VRd,crack need not be taken as less than (2d/av)VRd,c where av
<2d, or VRd,c where av ≥2d.
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where VRd,c = shear strength of the concrete section without shear reinforcement, calculated
according to Section 6.2.2 of BS EN 1992-1-1 VRd,s = shear strength of the concrete section including shear reinforcement, calculated
according to Section 6.2.3 of BS EN 1992-1-1, assuming a variable angle truss analogy. If shear strengthening is included, VRd,S can be replaced with VRd,S,f
VS,eff = the effective shear resistance from steel shear reinforcement (see Equation 6.2 below)
av = shear span (distance from edge of the support to the section under consideration). For av ≤ 0.5d, a value of 0.5d should be used
d = effective depth of the section.
Here, the effective shear resistance from the steel, VS,eff, is typically significantly lower than the maximum shear resistance which would be calculated if the steel stirrups yielded. To ensure cracking is limited, cotθ (where θ is the assumed angle of the compressive strut in the truss analogy) should be taken as 1.0 when calculating VS,eff, resulting in an effective resistance provided by the steel stirrups given by:
VS,eff = d AswEsεsv,eff Equation 6.2
s
where the effective strain in shear stirrups is:
εsv,eff = 10–5 ≤ ε y Equation 6.3
Efd tf 1.3
√ αflex αw ( Ecm ) (d ) and
αflex = I cs - I cc
I cc
αw = b
≤ 3 bf
where Icc = second moment of area of unstrengthened, concrete equivalent transformed
cracked section Ics = second moment of area of strengthened, concrete equivalent transformed
cracked section d = effective depth of the concrete section s = spacing of steel stirrups b = width of concrete section bf = width of FRP tf = thickness of FRP Asw = cross-sectional area of steel shear reinforcement Es = Young’s modulus of steel Ecm = Young’s modulus of concrete Efd = design Young’s modulus of FRP
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As a conservative lower bound, an effective strain of εsv,eff = 0.00025 can be assumed. If VRd,crack is less than VEd at the section being considered, it can be assumed that shear crack induced debonding will be initiated. Anchorage of the FRP may be possible in the affected region using U-wrapping.
U-wrap anchorage Transverse U-wrap FRP can be applied over the longitudinal FRP, extending up the side faces of the beam to anchor the longitudinal FRP in the anchorage region, as indicated in Figure 26. The corners of the beam which the U-wrap wraps around should be rounded to a minimum 25mm radius. The following equation can be used to calculate the area of FRP required:
AU-wrap = 0.5 Af σfmax Equation 6.4
Efd εfe
where Au-wrap = cross-sectional area of U-wrap anchorage on each side face of the beam required to
prevent shear crack induced cover separation/peeling. This should be distributed over the entire anchorage length of the FRP so as to be equal to lttf (anchorage length × thickness of U-wrap FRP)
σfmax = maximum stress in the longitudinal FRP (at position of maximum moment (MPa). This is calculated in the check for longitudinal shear stress failure in the yield zone
Af = cross-sectional area of longitudinal FRP Efd = design modulus of elasticity of U-wrap FRP (GPa) εfe = effective strain in U-wrap FRP according to the following equation:
fctk εfe = 0.5 √ Efdtf ≤ 0.004 Equation 6.5
where fctk = characteristic tensile strength of the concrete (MPa) tf = thickness of the U-wrap FRP (mm).
The U-wrap should extend up the side faces of the beam, perpendicular to the longitudinal FRP, by a minimum length of
lU-wrap = 0.7 √
Efdtf (mm). fctk
Strengthening members in flexure 6
≥ lU wrap Af
Cross-sectional area, AU-wrap= l ttf
Figure 26 U-wrap anchorage.
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(C) Longitudinal shear stress in the yield zone The longitudinal shear stress must be checked where any changes in section properties occur. It should also be checked at positions where there are discontinuities in shear force, such as at the positions of point loads. Importantly, longitudinal shear should be checked in yield zones.
The longitudinal shear stress is directly proportional to the rate of change of the axial stress in the FRP. In elastic zones, increase in moment along the plated beam is shared by the steel and FRP reinforcements on the tension side of the neutral axis, so the axial force gradient along the FRP (and hence the longitudinal shear stress) can be low or moderate. Along yield zones, however, the steel has limited (if any) ability to carry increased axial stress beyond the yield stress in response to increasing moment along the beam. Thus, increasing moment along yield zones is resisted almost exclusively by the FRP on the tension side of the neutral axis. The result is higher stress gradients along the FRP, and so higher longitudinal shear stresses, in proceeding from elastic zones to yield zones along FRP-strengthened RC members, as shown in Figure 25c. These yield-zone longitudinal shear stresses can be exacerbated by local effects at the positions of flexural cracks, which can open quite widely due to yield of the embedded steel.
There are two key sources of longitudinal shear in the FRP-to-concrete connection within yield zones. One source is the change in section moment along the yield zone. The other source is the stress concentrating effect near flexural cracks in the concrete beam within the yield zone. The method described below for assessing longitudinal shear in yield zones is based on the approach of Rosenboom and Rizkalla(142). This design approach is based upon data from tests on several FRP-strengthened specimens for which the ratio My/MEd (the ratio of the moment capacity of the strengthened section when the steel first yields to that of the strengthened beam at failure) varied from 0.64 to 0.9. The approach combines longitudinal shear stresses from the two above sources and compares the overall stress to a limiting shear stress for the concrete, as that is most commonly the weakest of the three materials (concrete, adhesive, FRP) at the connection. The approach assumes perfect bond, plane sections remaining plane (i.e. a linear strain distribution), zero strength for concrete in flexural tension, and that the tensile strength of the concrete is lower than the tensile strength of the adhesive.
1) Determine My, the moment at which the steel first yields in the FRP-strengthened RC section (taking into account strains already in the concrete section prior to strengthening). Also determine σfy, the associated nominal stress in the FRP.
2) Determine MEd, the maximum design moment in the FRP-strengthened RC beam within the yield zone. Determine σfmax, the associated stress in the FRP and the corresponding strain, εfmax (again, taking into account the strains already in concrete section prior to strengthening). The FRP strain, εfmax, should typically be a maximum of 0.008.
3) For the applied loading, determine the distance Δx along the beam between the sections of first yield moment (My) and maximum moment (MEd) within the yield zone.
4) Calculate τm, the mean longitudinal shear stress due to the gradient of the nominal axial stress in the FRP between the minimum and maximum moment locations along the yield zone – using the following expression:
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τm = tf [ σfmax - σfy ] Δx Equation 6.6
where tf = thickness of the FRP
5) Calculate τsc, the additional longitudinal shear stress due to stress concentration at the positions of flexural cracks in the yield zone, using the following expression:
τsc = 7.8 [1.1 - My ] fctk MEd Equation 6.7
where fctk = characteristic tensile strength of concrete (MPa) which should ideally be
obtained from pull-off tests on the actual concrete, otherwise calculated from the concrete cylinder strength according to BS EN 1992.
6) Determine τt, the total combined maximum longitudinal shear stress within the yield zone:
τt = τm + τsc Equation 6.8
7) This must be less than τlim,y, the limiting longitudinal shear stress in the yield zone according to:
τt ≤ τlim,y = 4.5 fctk Equation 6.9
JC
where JC = material partial safety factor for concrete.
(D) Strain in the FRP It is rare that rupture governs failure in surface-mounted FRP strengthening schemes, but nevertheless should be checked. The maximum strain in the FRP will occur as a result of bending stresses together with localised strain increases at crack locations. This total maximum strain in the FRP in the yield zone, εmt, can be calculated according to:
εmt = εfmax + 0.114 τsc Equation 6.10
�Efdtf where τsc = shear stress due to stress concentrations, as calculated in Equation 6.7, in MPa tf = thickness of the FRP, in mm Efd = design modulus of elasticity for the FRP, in MPa. εfmax = FRP strain corresponding to maximum moment calculated from sectional
analysis (step 2 when calculating the maximum longitudinal shear stress).
This increase in strain due to cracks may lead to rupture of the FRP. Therefore, the maximum strain in the FRP must be less than the design rupture strain of the FRP, i.e. εmt ≤ εfd.
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(E) Longitudinal shear stress near ends of FRP For surface-mounted reinforcement, when both the original section and the applied FRP are prismatic and do not taper along their length, assuming the concrete and steel reinforcement to behave linear-elastically (i.e. outside the region where the reinforcement has yielded, as shown in Figure 27), the longitudinal shear stress, τ, can be calculated using the expression:
τ = Vadd αf Af (h – x) / Ics ba Equation 6.11
where Vadd = difference between the ultimate shear force and the applied shear force when
the strengthening is installed αf = short-term modular ratio of FRP to concrete = Efd /Ecm Af = area of FRP plate x = depth of neutral axis of strengthened section Ics = second moment of area of strengthened concrete equivalent cracked section ba = width of adhesive layer h = total depth of the section.
This expression is suitable for calculating the longitudinal shear stress near to the plate ends in the elastic region between the yield zone and the anchorage zone, as shown in Figure 27, where the shear force acting on the strengthened portion of the member will be at its greatest. Equation 6.11 may be used in this position provided both the concrete in compression and steel reinforcement are still behaving approximately elastically. This calculation assumes no local increase in shear stress due to cracking, therefore the longitudinal shear stress should be limited to a maximum of:
τlim,c = 0.8 f ctk Equation 6.12
γ
C
where fctk = characteristic concrete tensile strength, which in the absence of test values can
be calculated using BS EN 1992 γC = material partial safety factor for concrete.
The longitudinal shear stress need not however be checked within lt,max of the end of the plate (the anchorage region), where lt.max is determined in accordance with Equation 6.14.
(F) Anchorage design In addition to maintaining low longitudinal shear stresses, adequate FRP end anchorage must be provided. Due to the combination of increased longitudinal shear as a result of the FRP terminating and normal stresses resulting in peeling, simple shear stress calculations are not appropriate in the anchorage zones. Work on end anchorage lengths has been carried out by a number of authors. The recommended approach is based upon the model proposed by Neubauer and Rostasy(136).
Figure 27 illustrates the model. As also described above, it can be seen that the characteristic bond failure force, Tk, increases with increasing anchorage length, lt, but that there is a threshold anchorage length, lt,max, above which no increase in the bond failure force is possible.
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Anchorage length f t
l t, max
T k, max
C ha
ra ct
er is
ti c
bo nd
fa ilu
re fo
rc e
F k
Figure 27 Characteristic bond failure force vs anchorage
length.
The maximum ultimate bond force, Tk,max, and the corresponding maximum anchorage length, lt,max, needed to activate this bond force can be calculated using the following expressions:
Tk, max = 0.5k b b f √ (Efd tf fctk) (N) Equation 6.13
lt,max = 0.7 √ (Efd tf /fctk) (mm) Equation 6.14
where kb = 1.06√ [(2 – bf /b) / (1 + bf /400)] ≥ 1.0 Equation 6.15 bf = width of FRP laminate (mm) b = beam width (or plate spacing for solid slab) (mm) tf = FRP thickness (mm) Efd = design elastic modulus of the FRP (MPa) fctk = characteristic tensile strength of concrete (MPa) Ideally fctk should be obtained from pull-off tests on the actual concrete, otherwise
calculated from the concrete strength according to BS EN 1992.
It is recommended that, where the FRP is curtailed in the span, a minimum anchorage length of 500mm should be provided. In situations where it is not possible to provide an anchorage length in excess of lt,max, the bond force will be less than Tk,max and may be calculated using the following expression:
Tk = (Tk, max lt /lt, max) (2 – lt /lt, max) (N) Equation 6.16
where lt = anchorage length provided (lt < lt,max).
The anchorage design should be undertaken by determining the point in the span where the FRP is no longer required, as indicated in Figure 27. From a sectional analysis, in accordance with the approach described in Section 6.2, the force that will be developed in the FRP if it is bonded to the member at this point should then be determined.
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It is important to recognise that, although the FRP may not be required at this point, the fact that it is bonded to the concrete will nevertheless mean that some force will be developed in it. The resulting FRP force should be checked to ensure that it is less than the ultimate anchorage capacity, Tk, and if so, an acceptable anchorage design will result from extending the FRP by an anchorage length beyond this point. If this condition is not satisfied then the FRP should be extended further towards the support or consideration given to using a thinner but wider FRP laminate. Alternatively, consideration may be given to using an anchorage device, provided that its capacity has been proved by testing.
Flexural strengthening can be achieved by bonding pultruded strips or rods into slots cut in the surface of the concrete. This application is termed near-surface-mounted (NSM) reinforcement, and has benefits where the exposed concrete surface is to be trafficked or otherwise exposed to potential damage. The technique is also applicable where the surface of the concrete is undulating, or if there is excessive laitance or a thin layer of poor-quality concrete near the surface. The method also results in an increased bond area, which helps to delay the onset of debonding-type failure. Installation is more costly than for externally bonded reinforcement, due to the need to cut the slots and prepare the bond surface. Usually the technique would only be used where externally bonded reinforcement is not a good technical solution.
Other than for FRP curtailment (see Section 6.4.3), the basis for design of NSM schemes is substantially the same as for surface-mounted flexural strengthening. Appropriate allowance must be made for the fact that the FRP reinforcement is located within the concrete cover of the section, and will therefore be strained slightly less than the surface of the concrete. Flexural design methods and limits should otherwise be as for surface- mounted reinforcement (see Section 6.2).
Material details and compatibility should be in accordance with the manufacturer’s recommendations. Complete systems should be adopted, since details, such as the preparation of the surface after the groove has been cut, depend upon the adhesive used. For example, clean dry surfaces are normally required but primers may be necessary before certain adhesives are applied to the concrete. The type and thickness of adhesive to be used should be in accordance with the manufacturer’s recommendations. Since this may also be affected by the location and orientation of the groove and specific requirements of the structure (e.g. environmental exposure, service conditions such as elevated temperatures), this should be discussed with the manufacturer early in the design process.
6.4 Flexural strengthening with near-surface-mounted
reinforcement
6.4.1 Design basis
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6.4.2 Bond behaviour Curtailment and anchorage of NSM FRP differs from that of surface-mounted FRP. The adhesive is a thicker block than the thin layer used for surface-mounted strips. The interface area between FRP and adhesive is potentially much smaller than that between adhesive and concrete. Furthermore, the practicalities of surface preparation are likely to result in different qualities of preparation on the sides of the slots than on the bottom of the slot. For these reasons, some of the debonding criteria used for surface-mounted plates are not applicable to anchorage of NSM rods.
There are more variable factors for NSM applications than for surface-mounted strips and plates. The key factors include bar size and shape, bar material, bar surface preparation (deformed or sand coated), slot size, shape and surface preparation, bonding agent (epoxy or cementitious material), strength of concrete and location of existing bars. The effects of these factors have been noted experimentally and are still being actively researched.
Most experiments to date have been performed on NSM bars with circular or rectangular cross-section. Circular bar diameters range between 7 and 16mm while strips are usually rectangular in shape of thickness less than 2mm. Most tests on NSM bars have used carbon or glass FRP bars (see Hassan and Rizkalla(143) and De Lorenzis and Nanni(144)). Tests have shown that higher average bond stresses are obtained from bars made from carbon than those made from glass(144), probably due to the higher stiffness of carbon.
To improve the bond capacity, NSM bars have either a prepared surface (by grit-blasting, abrasion or peel-ply) or a deformed surface, with ribs similar to deformed steel bars or spiral surface deformations, or bonded sand (or similar) particles, as a result of the method of manufacture. De Lorenzis and Nanni(144) observed that deformed bars perform better in terms of bond than grit-blasted bars. Although it might seem reasonable to use square bars within what is inevitably a rectangular slot cut into the concrete cover, square bars have received little attention. This is perhaps due to the lack of appropriate bars which are commercially available. It has been seen that surface texture is important in developing bond and while round and rectangular (in the form of plate) bars are commonly provided with surface texture, square bars, where available at all, generally are not. Furthermore, there is little advantage in using square bars compared with circular bars, with only a small increase in surface area to cross-sectional area ratio. However, it is acceptable to use square bars if desired.
The size and shape of the groove into which the bar is placed affect the mode of failure of the anchorage of an NSM bar. It should be noted that other factors such as strength and thickness of the adhesive surrounding the bar interact with the size (depth and width) to determine the mode of failure.
Although cement-based adhesive materials can be used to fill the grooves and surround the bar, experimentation has shown that this gives lower average bond strengths than epoxy adhesives, which have higher tensile strengths. Expansive cement-based mortars should be avoided since the expansion can introduce cracks and weaken the bond (see De Lorenzis et al.(145)). Furthermore, most of the existing experimental results on NSM techniques have been obtained using epoxy adhesives.
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Due to the experimental results noted above, and reflecting the bars currently available in the UK market, guidance is presented here for use of rectangular strips or circular bars used in NSM schemes using epoxy adhesives. Other combinations of bar shape and/or adhesive and bar materials should have designs verified by specific testing.
Both pull-out tests and beam tests have indicated that the ultimate load carried by NSM bars increases with increasing bond length. As for surface-mounted strips, there is a limit to this length beyond which any further length increase does not enhance the bond strength (see Hassan and Rizkalla(143) and Perera et al.(146)). However, the strength arising from this limit is a much higher proportion of the FRP capacity than is the case for surface-mounted strips, and is correspondingly less likely to be a limiting design factor.
There are a number of modes of failure associated with NSM bars, all of which have been observed in tests: � Adhesive splitting failure: splitting of the adhesive cover surrounding the bar as a result
of high tensile stresses that are initiated at the FRP bar–epoxy adhesive interface. This is usually a result of a thick adhesive layer leading to substantially lower stresses at the adhesive–concrete interface compared to the adhesive bar interface.
� Concrete splitting failure: splitting of the concrete surrounding the adhesive as a result of concrete at the interface reaching its tensile strength. This mode normally occurs when the adhesive strength is much higher than the surrounding concrete.
� FRP outer fibre debonding: when the FRP bar has a strong mechanical bond with the adhesive (i.e. highly deformed surface), it is possible for the outer layer of the FRP to debond from the inner core of the FRP, leading to failure, particularly when the adhesive strength is high.
� Tensile rupture of the FRP bar: where a high ratio of perimeter to cross-sectional area exists (e.g. for a thin rectangular bar) the bond area and hence bond capacity is high relative to the strength of the bar. In such situations FRP rupture can occur, this being a limiting behaviour, should the other failure mechanisms be prevented.
� Concrete cover separation: where bond strength is high, relative to the strength of the concrete, and bar capacity is low, it is possible for the cover concrete to fail by separation at the level of the internal steel reinforcement. This is a second limiting condition, should all other failure mechanisms be prevented. Many bond pull-out tests have not observed this type of failure, but it is common in beam-type bond tests where internal steel reinforcement exists.
The splitting and debonding modes of failure are generally accompanied by pull-out of the NSM bar along the interface where the failure is initiated. Mixed-mode failure involving a combination of modes has also been reported (see Hassan and Rizkalla(143), De Lorenzis and Nanni(144) and Perera et al.(147)).
The tensile rupture of the FRP and concrete cover separation can be thought of as the two limiting cases for failure so that, even if the other modes of failure can be avoided, one of these two limiting conditions will govern the full strength achievable.
6.4.3 Modes of failure
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Shear-crack induced separation, surface irregularity induced separation and longitudinal shear stress limits should be checked in a similar way to that for surface-mounted FRP (see Section 6.3). The longitudinal shear stress should be checked in the steel yield zone both between the NSM adhesive and the concrete and between the NSM reinforcement and the adhesive. Under ultimate limit state loading, the distribution of shear stress within the yield zone (i.e. between My and MEd), between the NSM reinforcement and the concrete, should be determined according to:
τconc = Af [ Δσf ] Equation 6.17 bnotchperim Δy
where τconc = longitudinal shear stress at the adhesive–concrete interface Af = area of NSM reinforcement Δy = short length along beam Δσf = change in stress in the NSM reinforcement over the length Δy bnotchperim = effective perimeter of groove in the concrete cover.
The value of Δy used should be chosen to be appropriately small so as to generate the shear stress profile within the yield zone, allowing the maximum shear stress to be identified. For a rectangular groove, the effective perimeter of groove, bnotchperim, would normally be the minimum width plus the minimum depth, i.e. only half each side of the groove is counted since the groove sides cannot normally be prepared to as high a standard as an exposed face. If special methods and particular care are used on the sides of the groove, it may be appropriate to increase the useful perimeter to the width plus twice the depth, i.e. the gross perimeter of the groove. If there is a layer of weak laitance near the surface of the concrete, the value for the depth should be reduced appropriately.
The maximum calculated shear stress should be less than the limiting value:
τlim,c = 0.8 fctk Equation 6.18
JC
where fctk = characteristic concrete tensile strength, which in the absence of test values can
be calculated according to BS EN 1992.
In a similar manner, the shear stress between the NSM reinforcement and the adhesive should be determined according to:
τad = Af [ Δσf ] Equation 6.19 bbarperim Δy
where bbarperim = effective perimeter NSM reinforcement.
6.4.4 NSM separation failure design
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The calculated maximum shear stress should be less than the limiting value given by:
τad,lim = 0.8 fat Equation 6.18
JA
where fat = characteristic adhesive design tensile strength (may be taken from manufacturer’s
data) JA = partial safety factor for adhesive (see Section 5.6.6).
In checking irregularity, the profile of the as-installed bars should be considered, since NSM bars may be appropriate for an undulating surface if this is corrected by the groove-cutting process.
In view of the number of different failure modes possible, an approach based upon an analogy with the Neubauer and Rostatsy(136) anchorage model for external strengthening is suggested. The guidelines are presented assuming the following design recommendations: � Epoxy adhesive is used to bond bars into grooves with a minimum thickness of 2mm
around the full perimeter of the NSM bar. � Grooves should have a maximum width equal to the width of the NSM bar plus 8mm. � The NSM bar must have suitable surface properties, provided by the manufacturer
(e.g. peel-ply, sand coating or a deformed surface), to provide sufficient bond. Smooth bars should not be used.
� Grooves are cut such that the installed bar is straight. � Existing structural metallic reinforcement does not intersect the groove. � Where grooves are spaced on the structure, the clear spacing between grooves should
be at least the width of the groove and not less than 3 times the largest dimension of the bar cross-section. The same distance should be allowed to the edge of the structure.
� Grooves should have a surface preparation that provides a rough gripping surface for bonding (i.e. not simply diamond sawn).
� Maximum cross-sectional dimension of NSM bars should be 16mm.
For conditions outside these criteria, specialist advice should be sought. Detailed analysis as described in the references may be required to confirm anchorage, or it may be appropriate to undertake testing to confirm the assumed performance.
To avoid concrete splitting failure, the maximum ultimate anchorage force, Tnsm,max and corresponding maximum anchorage length lnsm,max can be calculated from the following expressions:
Tnsm,max = 10bnotchperim � Efd Af fctk Equation 6.21
lnsm,max = 0.135bnotchperim � Efd Af Equation 6.22
fctk
6.4.5 Anchorage design
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where Tnsm,max = maximum NSM anchorage force (N) lnsm,max = anchorage length required to generate Tnsm,max (mm) Efd = design FRP modulus of elasticity (GPa) Af = area of FRP (mm2) bnotchperim = effective perimeter of notch (mm) (making allowance for surface preparation
and/or weak laitance layer) fctk = concrete characteristic tensile strength (MPa).
In situations where the maximum anchorage length is not possible or necessary (i.e. lnsm < lnsm,max), the anchorage force generated by a shorter length can be assessed from:
Tnsm = Tnsm,max lnsm ( 2 - lnsm ) Equation 6.23 lnsm,max lnsm,max
where Tnsm = characteristic anchorage force for NSM lnsm = anchorage length provided for NSM.
However, two further limits on maximum capacity apply. To prevent failures in the adhesive layer, the force should be limited to:
Tnsm,ad = 0.3 fat bbarperim lnsm Equation 6.24
where Tnsm,ad = characteristic adhesive bond failure force (N) lnsm = anchorage length provided (mm) bbarperim = effective perimeter of bar (mm) fat = adhesive tensile strength (MPa).
Further, to prevent concrete cover separation or tensile failures:
Tnsm,lim = 38 � b
Efd Af fctk ≤ Af ffd Equation 6.25
nnsm
where Tnsm,lim = limiting maximum achievable anchorage force (N) b = width of concrete section at location of NSM bars (mm) nnsm = number of NSM bars provided (MPa) ffd = design strength of NSM bar (MPa) Efd = design FRP modulus of elasticity (GPa) Af = area of FRP (mm2).
In the case of strengthening a slab, the term b/nnsm should be replaced with the spacing between NSM bars. It should be noted that the concrete cover separation limit is independent of anchorage length. It is usually only critical when anchorage length is relatively long.
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Flexural strengthening is usually achieved by bonding plates (or fabric) to the tensile face of the member being strengthened (e.g. the soffit of a sagging simply supported beam). This achieves maximum efficiency in use of material, since the FRP is subjected to the maximum possible tensile strain. However, in certain situations it may be appropriate to bond plates to other parts of the section.
If this is undertaken, there is reduced utilisation of the FRP as it is less highly strained since it is located nearer to the neutral axis of the section. Other issues must also be considered. Most significantly, if it is proposed to bond the FRP to the sides of the beam, the strip will now be subjected to bending about its strong axis, in which it may have significant flexural stiffness. Although this may make a small additional contribution to the flexural stiffness of the section as a whole, the most significant effect is that debonding of the FRP may be precipitated, since in addition to tensile peeling and longitudinal shear stress, the adhesive interface is now also subject to transverse shear stresses. There has been no significant research with plates in this orientation. If this arrangement is considered, the adequacy of the design should be confirmed by testing, unless the beam is very deep and therefore the differential strain between the edges of the plate is relatively small.
The FRP strengthening systems available in the UK are generally pultruded plates of less than 2mm thick (1.2mm and 1.4mm are the most common) and fabrics with an effective thickness of between 0.1mm and 0.3mm.
Some manufacturers can supply thicker plates, either manufactured in a single process or by bonding together previously manufactured pultruded plates to produce a thicker laminate. In addition, it is possible to bond plates in stacks on site. Fabrics are laminated onto the structure by applying successive layers of resin and fabric until the required thickness (and hence strength) is obtained.
However, there are limitations to the thickness of FRP that can be usefully employed. Frequently, the prevention of a debonding failure of the FRP from the concrete will limit the thickness, since stacking two laminates will almost double the longitudinal shear stresses in the FRP–concrete adhesive bond.
Additional layers increase the number of potential failure modes, since failure can occur in the adhesive between layers and exacerbates potential failure within the FRP. If the stacked layers are not of the same length (which is normal, in order to reduce stress concentrations in the curtailment zone), there are also additional anchorage zones that must be checked for debonding.
While it is preferable not to stack pultruded plates, in some situations (e.g. T beams with narrow webs that have insufficient width of soffit to accommodate the required areas of FRP) it may be the only way that a suitable scheme can be detailed.
6 Strengthening members in flexure
6.5 Flexural strengthening plate location
6.6 Thick and multi-layer laminates
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In these situations stacking of plates in-situ, or use of thicker laminated plates may be appropriate if the following conditions are met: � The plates are intended by the manufacturer for such use, and have sufficient inter-
laminar strength that they will not suffer internal shear failures. � The plates that are bonded to both sides have suitable preparation to both faces; some
plates incorporating peel-ply are manufactured with this on only one face, and would not be suitable for stacking without further preparation work.
� Peeling failure is checked at the curtailment of every plate, and allowance is made in the design calculations for the non-prismatic section.
� The construction sequence is carefully specified to ensure that bonding subsequent plates does not disturb or damage the bond of the lower plates.
For stacks of plates formed in-situ, the stack should not normally be more than two high. There is some limited UK experience with stacks three high, but in this case specialist advice should be sought. For stacks formed by the manufacturer under factory conditions, higher stacks may be possible. Testing may be necessary to demonstrate the performance of the stack, but it is unlikely that greater than 5mm thickness will be useful, due to the limits of the bond strength to the concrete.
When fabrics are used, multiple plies can be overlaid to achieve the necessary strength of the FRP component. The same overall limitations apply, but these limits will normally be reached when many plies are installed. If large numbers of plies are overlaid, it is likely to be the achievable quality workmanship that limits the design, and a trial installation should be considered in order to demonstrate that a void-free laminate can be produced under the site conditions relevant to the particular project.
It should be noted that the general implicit assumption throughout this report is that the FRP (either plates or fabrics) carry only tensile loads. However, as they become thicker, bending stresses are induced in the plate as a beam deforms under load. Such additional stress is unlikely to be significant in terms of increasing overall stresses in the FRP but may have consequences at the ends of the FRP, i.e. in the anchorage zone, leading to significantly higher peeling stresses. Furthermore, the greater the eccentricity of the FRP from the face of the beam, the greater the peeling stresses. This may lead to premature failure not captured by the anchorage models provided in this guidance.
The approaches given for designing flexural strengthening schemes demonstrate that prediction of FRP separation failure requires consideration of moments. In a statically determinate structure, the moments depend only on the type and position of the loading along the span and the span itself. However, in a statically indeterminate structure, the flexural stiffness distribution along the structure specific to the load level under consideration, along with boundary conditions such as differential settlement, will also influence the moment distribution along the structure under a defined load.
6.7 Statically indeterminate structures
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For conventional under-reinforced concrete structures, the lower bound theorem of plasticity enables the design process to avoid the need to consider actual stiffness distribution and differential settlement at the ultimate limit state. With FRP present, however, this theorem may not be applicable, so it is prudent to consider the stiffness profile and boundary influences in analyses to determine the range of possible moment conditions under ultimate loads. This can be particularly important for anchorage, where small changes in the position of the point of contraflexure near FRP curtailment due to changes of stiffness distribution or settlement can significantly alter the actual anchorage length. Similarly, longitudinal shear stresses are significantly affected by changes in moment.
Under service loading on a bridge, note that change of differential settlement patterns and of stiffness distributions as traffic travels along the bridge can continuously alter the bond stresses in curtailment zones. It is prudent to establish the range (including sign) of these bond stresses via an influence line approach, as this range may have significant implications for fatigue of the bond.
Moment redistribution in any continuous concrete structure relies on adequate rotation capacity of critical sections (see for example Mattock(148)). If a structure displays ductility, it will also display rotation capacity. However, if a structure displays rotation capacity, it will not automatically display ductility (see Ibell and Silva(149)). This is important in the context of FRP-strengthened concrete structures because research has shown that ductility is usually limited in such structures (see Burgoyne(150)), even though adequate levels of rotation capacity often exist (see for example Casadei et al.(151) and El-Refaie et al.(152)).
Tests on continuous beams (see for example Corden et al.(153) and Ashour et al.(154)) have shown that while limited ductility and some redistribution into strengthened regions is feasible, the amount of redistribution is not significant. Concrete cover separation often occurs, due to increased shear demand associated with both the strengthening itself and redistribution, despite anchoring in compression regions of the concrete, thus limiting the amount of redistribution available.
Furthermore, in order to demonstrate adequate ductility, limits on neutral axis depth are conventionally used. This is related to moment–curvature relationships. In the case of FRP- strengthened beams the horizontal moment–rotation plateau typical of conventional reinforced concrete is not exhibited, nor is concrete crushing always the limiting behaviour. Therefore, defining a neutral axis depth limit is not an appropriate way of defining ductility and redistribution limits in a strengthened beam (see Oehlers et al.(155)).
With the above in mind, it is recommended that redistribution is only allowed into an FRP-strengthened region, up to a maximum of 15% and then only if sufficient ductility and rotation capacity can be demonstrated. Associated shear demands on the beam itself and at the concrete–FRP interface must also be investigated. In individual FRP-strengthened regions the beneficial effects of redistribution should be ignored, i.e. redistribution is not allowed out of FRP-strengthened regions.
6.7.1 Redistribution
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In structures that require additional resistance in both hogging and sagging regions, it can be possible in some cases to use redistribution out of the hogging zone and only strengthen the sagging zones with FRP. For structures where such an approach is not possible and it is proposed to use FRP to strengthen both hogging and sagging zones, care should be taken to account for the gradual evolution of cracking in the structure and the implications on the distribution of structural effects. For example, in some cases where concrete cracking is expected in the hogging zone first, it can be possible to design the FRP in the hogging zone based on the moments determined from an elastic analysis with uncracked properties, and to design the FRP in the sagging zones based on bending moments determined from an elastic analysis assuming the concrete is cracked in the hogging regions only.
Fatigue damage has been shown not to be significant if the FRP-plated RC member is exposed to typical service load ranges (between 30 and 60% of the load required to induce first yield), but remarkable damage can occur if the load range exceeds 60% of the load at first yield (see Kim and Heffernan(156)). For that reason, care is advised in designing FRP strengthening when the new service loads are significantly higher than they were for the original structure. Part 2 of EN 13894(157) may be considered for specific projects where the strengthened structure may be subjected to dynamic loading after hardening.
In such cases, for both FRP-strengthened and unstrengthened RC beams under fatigue loading, tests show that failure most commonly occurs by fracture of the main steel reinforcement in peak moment zones. Fatigue failure of steel is linked to the stress range in the material, so it is recommended that the stress range in the steel reinforcement is limited in order to extend the fatigue lives of FRP-plated RC beams. In so doing, the stress ranges and fatigue cycles already experienced prior to FRP-plating must be accounted for. BS EN 1992 Section 6.8 describes how fatigue damage to steel reinforcement due to multiple cycles with variable amplitudes can be accounted for, as well as describing appropriate combinations of actions.
FRP materials themselves possess excellent fatigue resistance, so fatigue failure of the FRP has rarely been observed in tests, prior to that of the embedded steel. However, the FRP- to-concrete bond underpins the composite action that leads to the reduction of stress within the steel reinforcement. Local loss of FRP–concrete bond initiated at positions of peak moment (e.g. due to bond stress concentrations at crack positions) may lead to higher stresses developing in the steel reinforcement as the number of load cycles increases.
The designer should therefore consider the effect of repeated variable loading on the structure, including the FRP. A simplified method for the fatigue verification of FRP is to consider the FLM3 load model in BS EN 1991-2 and ensure that the stress range in the FRP does not exceed the values in Table 7.
Material Stress range (%) Carbon FRP Aramid FRP Glass FRP Basalt FRP
80 70 30 30
6.8 Fatigue
Table 7 Maximum stress ranges within FRP as a
proportion of the design ultimate strength (%).
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Wherever possible, lap splices of FRP plates should be avoided in regions where the fatigue stress range is high. In addition, lap splices in adjacent plates should be staggered and alternated to avoid the concentration of lap splices in a single region.
Research has shown that the fatigue life of a lap splice is dependent, among other factors, on the length of the lap. Therefore, the minimum length of any lap splice should be 300mm or the manufacturer’s minimum recommended lap splice length, whichever is the greater.
Concrete Society Technical Report 57(9) provides guidance on the acceptable limits of delamination and voids in an adhesive bond.
The causes of any existing cracking in the concrete substrate should be ascertained, and resolved if possible, prior to installation of the FRP strengthening system. Any such cracks should be repaired prior to installation of the FRP strengthening system, for example by resin injection; all materials used should be compatible with the FRP strengthening system.
Normally, crack widths will not be excessive providing the FRP strengthening system has been properly installed. Where necessary, crack widths at service loads should be checked against design limits such as those required in BS EN 1992 and the corresponding National Annex. This method can be adapted for FRP-strengthened structures simply by calculating the strain in the tension steel, using a suitable effective modulus of elasticity for concrete, and determining crack width under permanent load and variable load separately. The FRP strengthening can be taken into account by using the transformed area of the FRP laminate in calculating the strain in the tension steel under variable loading (unless the construction sequence is such that the FRP laminate will be subject to permanent loads, for example where surface finishes are applied over the FRP laminate). The second moment of area of the section should be determined assuming that the effective modulus of elasticity for concrete is adjusted to take account of creep as follows:
Ec,eff = ( 1 ) Ecm Equation 6.26 1 + φef
where φef = effective creep coefficient = φψL φ = creep coefficient (see Section 3.1.4 of EN 1992-1-1) ψL = creep multiplier, which may be assumed to be 1.0 in the quasi-permanent
combination of actions. In general, ψL may be assumed to be MEd,G/MEd where MEd,G is the design moment due to permanent loads and MEd is the total design moment.
6.8.1 Lap splices of FRP plates
6.8.2 Delaminations/voids
6.9 Serviceability
6.9.1 Crack widths
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It is worth noting that the true cracking behaviour is not as straightforward as suggested here. This is because, when the FRP strengthening system is placed on the surface, the crack spacing is defined by the load on the unstrengthened structure. The crack width due to live load would be significantly reduced due to the presence of the FRP strengthening. However, only a limited amount of experimental and theoretical work defining the extent of this reduction in crack width has been carried out. In the interim, therefore, the procedure outlined above is recommended, which will provide a conservative estimate.
Where a wet lay-up FRP strengthening system is used to fully cover the concrete surface, the durability of the concrete structure may be significantly improved in the region of the FRP strengthening. However, additional appropriate construction details, for example to prevent the build-up of moisture in the substrate adjacent to the wet lay-up FRP strengthening, should also be considered.
Deflections due to the design loading should not exceed the limits recommended in BS EN 1992. In addition, the SLS stresses in the steel reinforcement at the characteristic combination of actions should not exceed the relevant design limits in BS EN 1992-1-1. For guidance regarding the applicability of the concrete stress limitation in BS EN 1992 see PD 6687 Clause 2.1.5 for buildings and Clause 8.1.1 of PD 6687-2(158) for bridges. The stresses may be determined from a sectional analysis using the effective tensile modulus for concrete as given in Equation 6.26.
Rupture of the FRP may occur at service loads due to sustained stresses in the material. Applications where sustained stresses may be present in the FRP include: � Temporary dead load removal by jacking, followed by FRP strengthening. � Physical removal of dead load, followed by FRP strengthening and then reinstatement
of dead load.
It is therefore recommended that if, under the characteristic combination of actions, the FRP carries a sustained stress, then this sustained FRP stress should not exceed the values given in Table 8.
Material Maximum stress (%) Carbon FRP Aramid FRP Glass FRP Basalt FRP
65 40 45 35
One of the great benefits of using FRP for retrofit strengthening is the ease, speed and short period of time required for the works. In order to maximise these benefits during the strengthening of concrete bridges, it is clearly desirable that traffic be allowed to flow over the bridge during the works.
6.9.2 Deflections and material stresses
6.9.3 Stress rupture
Table 8 Maximum stress in FRP under service loads to avoid stress rupture as a proportion of design
strength (%).
6.9.4 Strengthening under non-static live load
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The obvious caveat to strengthening under live load is the effect that intermittent loading has on the curing process in the adhesive. Hejll et al.(159) have carried out laboratory tests on concrete bridge girders strengthened under static conditions and under simulated live-load conditions, in which a load causing 60% of the yield strain in the steel reinforcement was applied cyclically every 108 seconds. Their tests showed that there was effectively no difference in ultimate capacity and behaviour between bonded systems (either laminate or NSM) that had been installed under static or under simulated live-load conditions. What is more, the level of strengthening was 80–150% of the original capacity of the unstrengthened bridge girders, adding confidence to their claim that traffic need not be stopped during FRP strengthening works on bridges.
This tends to confirm work by Barnes and Mays(160) who conducted tests on strengthened beams with a 1Hz cyclic load during curing of between 20 and 170 microstrain. Their research showed that for strengthening concrete beams under live load there was no effect on the ultimate strength. This was because failure in their test specimens was due to the concrete cover pulling off, rather than failure of the adhesive.
However, tests by Darby et al.(161) have demonstrated that there is a residual compressive strain within the FRP due to the relative slip between the FRP and concrete during intermittent live loading as the adhesive cures and hardens. This residual compressive strain is equal to half the strain in the concrete soffit at full live load. This is unlikely to have any significant effect upon ultimate flexural capacity, since the failure of the FRP bond is largely independent of the initial strain state. There is a potential effect on serviceability limit state behaviour in the form of deflections and crack widths, which are likely to be slightly larger than they would be if the initial strain in the FRP was zero under dead load conditions. This residual compressive strain could be evaluated and considered in serviceability calculations if substantial intermittent live load is allowed to occur during adhesive curing.
Tests by Barnes and Mays, designed to investigate failure in the adhesive itself, showed a significant reduction in strength if the adhesive interface governed. It is therefore recommended that the strength of the adhesive be reduced in accordance with Table 9. If this reduced adhesive strength is less than the design strength of the concrete, then the live load during adhesive curing should be restricted. This should be taken into account when calculating achievable anchorage force in NSM strengthened structures.
Live load strains at FRP–concrete interface during curing (10–6)
Reduction in tensile bond strength of adhesive (%)
20 50 100 150 200
10 12 16 22 32
Part 1 of BS EN 13894(157) may be considered for specific projects where the strengthened structure may be subjected to dynamic loading during cure.
Table 9 Reduction in strength of adhesive for given
live-load strains at FRP–concrete interface (%).
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Many of the same principles outlined in the previous sections of this chapter can be applied to the strengthening of prestressed concrete structures. However, note that serviceability issues govern prestressed design whereas these guidelines focus predominantly upon ultimate limit state. There are a number of supplementary matters to consider when strengthening a prestressed structure, such as: � The need to accurately assess current and future stress states. � The sensitivity of the strengthened section to the initial stress state compared to that
of an uncracked reinforced concrete section. � The lower ductility of prestressing tendons compared with reinforcing steel. � Different anchorage behaviour due to reduced cracking preventing the full generation
of anchorage force.
Bearing the above points in mind, the design of a strengthening scheme for a prestressed beam can follow largely the same procedure as strengthening a reinforced concrete beam. The following sections give more detail about the above considerations for incorporating into the design procedure.
Prestressed concrete sections are generally designed to serviceability limit states. If the beam is to carry an increased load after strengthening then it is possible that the concrete is overstressed under the SLS characteristic loads, either in compression or tension. These stresses are usually calculated based upon an assumed uncracked section, although if present, some cracking can be allowed for (see Clause 7.1(2) of BS EN 1991-1-1). These stresses are based on the concrete section alone, with the prestressing tendons providing an applied force. Any non-prestressed reinforcement (i.e. in a partially prestressed section) can be considered using a transformed section approach. If FRP strengthening is added to the section then this can be considered as part of a transformed section, allowing for the concrete already being stressed at the time of strengthening due to any loading existing at that time, typically the dead load and the prestressing force. Assuming a tendon below the centroidal axis to resist bending, the stress in the bottom of the section will be given by superposition of the stresses before and after strengthening, assuming elastic behaviour:
σconc,t,b = Pm,t +
Pm,t eyt,b ± Mexisting yt,b ±
Madd,service ytrans,t,b Equation 6.27 Ac Ic Ic Itrans
where σconc,t,b = maximum concrete stresses (tensile or compressive) in the top and bottom
of the section Pm,t = prestressing force in the section at the time of strengthening, accounting for
losses Ac = area of concrete section e = eccentricity of prestressing tendon from existing centroidal axis yt,b = distance from existing centroidal axis to top or bottom of the section Ic = second moment of area of concrete section Mexisting = moment at section, existing at time of strengthening Madd,service = additional moments applied after strengthening, meeting SLS load combinations
6.10 Strengthening prestressed structures
6.10.1 Serviceability limit state criteria
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ytrans,t,b = distance from new centroidal axis (for transformed section) to top or bottom of the section
Itrans = second moment of area of section including FRP, using a transformed section approach with a modular ratio for the FRP of αf = Efd/Ecm
where Ecm = secant modulus of elasticity of concrete (see BS EN 1992) Efd = design Young’s modulus of FRP.
For the appropriate serviceability load combinations, the maximum compressive and tensile stresses should be checked against the appropriate stress limits as defined by BS EN 1992-1-1, Section 7.2. If the concrete exceeds the tensile stress limit under the increased load then either the amount of FRP should be increased to prevent this, or the section second moment of area should be adjusted to reflect this assuming a cracked section in the tension zone, if this is allowable. However, BS EN 1992 also prescribes decompression limits (depending upon exposure class), to ensure that the tendon always lies within the compression zone, and crack widths. The strengthened structure must also meet these limits. This can be established by examining the stress distributions given by Equation 6.27 above, bearing in mind the change in position of the centroidal axis after strengthening.
Steel tendon rupture High-tensile prestressing steel has an assumed bilinear stress–strain curve with a characteristic 0.1% proof stress, fp,0.1k, used instead of a characteristic yield strength due to the rather ill-defined yield point. Clause 3.3.6(7) of BS EN 1992-1-1 allows two possible models for high-tensile prestressing steel: one which is initially elastic followed by perfectly plastic behaviour, and an alternative model which allows a post-yield increase in strength due to strain hardening (as shown in BS EN 1992-1-1, Figure 3.10). BS EN 1992 imposes a limit on the maximum allowable strain for the alternative model. Although there is no strain limit imposed if the elastic perfectly plastic model is used, it would seem pragmatic to calculate the maximum strain in the steel under any increased load, particularly since high-tensile prestressing steel is usually more brittle than high-yield reinforcing steel and a greater proportion of the strain capacity is taken up in the elastic zone, due to higher yield strength. It is likely that debonding of the FRP will occur before any steel strain limit is reached. However, if there is concern regarding the strains in the prestressing steel then the alternative stress–strain model should be used (allowing strain hardening) and the ultimate strain should be limited as described in Clause 3.3.6(7) of BS EN 1992-1-1. This can be done using conventional sectional analysis, to calculate the neutral axis position, with due regard to the initial soffit strain at the time of strengthening for the FRP, and taking initial prestressing strains (after losses) into account in the prestressing steel.
Anchorage It should be noted from the discussion on anchorage in Section 6.3.3 that beyond a certain anchorage length, the force in the FRP which leads to failure does not increase (Figure 28). This anchorage length corresponds to the length of the FRP beyond the cracked region of the beam.
6.10.2 Ultimate limit state criteria
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It is widely accepted that concrete cracking is the essential action required to develop higher forces in the FRP since shear stresses at the FRP–concrete interface can build up between cracks to allow an increment in FRP force to be generated. However, for prestressed beams, even at the ultimate limit state, cracking may be less extensive than in reinforced concrete beams, especially in the low moment regions, where the FRP will be anchored. This lack of cracking has been shown to limit the capacity of a strengthened beam, with the flexural capacity of the section limited by the maximum force which can be sustained by the FRP at the edge of the cracked region, i.e. the anchorage force, Tk, according to Equation 6.10 (see Darby et al.(162)), as indicated in Figure 6.5. This is slightly conservative, since the stress states are not necessarily the same, but is a reasonable simplification of behaviour. Therefore this moment capacity, limited by the anchorage force in the FRP, should be compared to the moment at this position where cracking occurs. This position can be established through an elastic analysis of the section, similar to that in Equation 6.24, but relating to ULS design (factored) loads rather than SLS characteristic combinations. This may be an iterative procedure if the tendon is curved since the eccentricity of the tendon will alter depending upon the position of the section along the length of the beam. This moment capacity should be checked in addition to the capacity at the maximum moment location and the lower value will govern the achievable capacity.
T k
T k
l t
Figure 28 Anchorage-type behaviour in uncracked region, limiting achievable force in FRP.
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�
�� � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
Calculate the loads at the ultimate condition and hence determine the shear and moments in the section
Assume an initial strain in concrete � εcu2 or εcu3
Calculate moment of resistance due to compressive and tensile forces
At the section under consideration, determine the moments, and hence
strains, in the concrete, which exist at the time of strengthening
Calculate compressive and tensile forces in cross-section based upon
assumed linear strain profile where the strain in the FRP takes the initial strain in the concrete into account. Subtract
Asa from As if appropriate
Assume a neutral axis position
Are compressive and tensile forces in
equilibrium? Adjust position of neutral axis
Yes
No
(Continued)
Estimate the area of FRP strengthening required according to Eqn 6.1
6 Strengthening members in flexure
6.11 Flexural strengthening design flow charts 6.11.1 Flow chart for required area of FRP
(Continued) (Continued)
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� �
�� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
Is moment of resistance � total ultimate
moment?
Increase assumed compressive strain in concrete (� εcu2 or εcu3)
No
Yes
Yes
Is moment of resistance >
1.15 × ultimate moment? No �
Is tensile strain in tensile steel >
0.002 + Iyk/�(sγS �?
Design complete �
Check aspects of anchorage and separation failure (see separation
failure flow chart)
Check if additional longitudinal FRP is required for additional force due to
increased shear demand
Does strain in FRP
exceed design ultimate strain (see separation failure
flow chart)?
No
Yes
Yes
No
Do longitudinal shear
stresses result in debonding? (Vee 6.11.2)
No
Yes Adjust quantity or configuration of tensile FRP�
(Continued from previous page)
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6 Strengthening members in flexure
6.11.2 Flow chart for separation failure of surface-mounted reinforcement
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Strengthening members in flexure 6
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7 Shear strengthening
7. Shear strengthening Externally bonded FRP laminates and fabrics can be used to increase the shear strength of reinforced concrete beams and columns.
FRP may be bonded to the concrete in various configurations. Ideally FRP should be wrapped around the whole perimeter of the member (fully wrapped). Alternatively, it can be applied only to the sides of the member (side-only) or to the sides and the tension face of the member (U-wrapped). Figure 29 shows examples of possible FRP shear strengthening configurations. This chapter focuses on rectangular beams and columns. Guidance on strengthening of circular columns in shear is included in Section 8.7 of Chapter 8.
7.1 Introduction
Figure 29 Shear reinforcement configurations.
The orientation of the FRP fibres can affect the performance of the strengthening system. Theoretically, fibres that are inclined to resist the formation of shear cracks can be more effective than fibres aligned perpendicular to the longitudinal axis of the member. However, if the shear force direction can reverse, or if the FRP is partially or fully wrapped around the beam, systems with fibres aligned perpendicular to the longitudinal axis of the member are more convenient and are typically used in practice.
In understanding the behaviour of FRP strengthening in shear, it is important to recognise that the bond behaviour of FRP differs markedly from conventional embedded steel reinforcement. As discussed in Section 6.3, it has been found in tests on the anchorage of externally bonded FRP that beyond a limiting bonded length, no further increase in the ultimate anchorage load-capacity occurs with increasing bonded length. This maximum anchorage capacity can be very much less than the ultimate tensile capacity of the FRP. The contribution that the FRP makes to the shear capacity can therefore be governed by separation of the FRP from the concrete, and it is not sufficient to assume that fracture of the FRP will occur. Such separation is typically associated with the propagation of a failure plane in the concrete close to the surface.
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Shear strengthening 7
Side-only or U-wrapped members will be more prone to separation failures than fully wrapped members. Full wrapping is therefore preferable and should always be used when it is feasible. However, it is generally not practicable for beams because the top of the beam is inaccessible. In most cases it will be possible to fully wrap columns. It is recommended that where FRP wraps around a corner, the concrete should be rounded to a minimum radius of 25mm to prevent premature rupture of the FRP.
The behaviour of reinforced concrete in shear is complex. Furthermore, considerably less research has been undertaken into FRP shear strengthening than flexural strengthening. It is therefore appropriate at present to adopt a cautious design procedure for shear strengthening. The design procedure given is based upon that proposed by Denton et al.(137). In developing their proposals, they reviewed numerous alternative design approaches and provide a detailed justification for their proposed method.
The majority of experimental testing of reinforced concrete members strengthened in shear has used carbon rather than aramid or glass fibre. Although the underlying principles should be common to all materials, the design procedure presented below is best suited to designs using carbon FRP. The approach should be conservative if applied to aramid or glass FRP, and in some cases may be significantly so.
As with flexural strengthening, the assumptions made in the design should be reflected in the installation work on site. It is therefore important to consider the issues outlined in Section 6.1 in developing the design for shear.
The approach for calculating the ultimate shear resistance of a section including normal steel shear reinforcement and strengthened with external FRP shear reinforcement is based on an extension of the method in Clause 6.2.3 of BS EN 1992-1-1.
The method for the design resistance of an unstrengthened reinforced concrete section allows the truss angle to be chosen by the designer to be either at the lower limit of 21.8° (cot θ = 2.5) or increased if desired up to a maximum value of 45° (cot θ = 1). When FRP shear reinforcement is introduced, this typically has the effect of steepening the effective truss angle at ULS. This effect can be modelled using the principle of superposition, considering the total effect to be the superposition of two truss systems, one relating to the steel reinforcement, with a truss angle θ limited to be between 21.8° and 45° (i.e. 1 < cot θ < 2.5), and another associated with the FRP, with a truss angle equal to 45°. The shear resistance is found by superposing these systems, and limiting the stresses in the steel, concrete and FRP to ensure that they do not exceed their design values. This is equivalent to considering a single truss system with a truss angle that is a weighted mean of the truss angles for the steel and FRP systems.
This approach results in the following expression for shear resistance:
VRd,s,f = Asw zfywd cot θ +
Afw ( df – ns lt,max cos β ) Efdεfse (sin β + cos β) Equation 7.1 s sf 3
7.2 FRP strengthening design procedure
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7 Shear strengthening
The corresponding maximum shear resistance (relating to an inclined compression failure in the concrete) may be taken to be VRd,max as given in Clause 6.2.3 of BS EN 1992-1-1 (this expression for maximum shear resistance is conservative, as it is based on the truss angle for the steel component, rather than a weighted mean of the truss angles for the steel and FRP components, which would give a higher value).
where Asw = cross-sectional area of steel shear reinforcement s = longitudinal spacing of the steel shear reinforcement stirrups z = lever arm between the longitudinal steel reinforcement and the centroid of the
compression in the section fywd = design yield strength of the steel shear reinforcement θ = angle between the concrete compression strut and the beam axis perpendicular
to the shear force Afw = area of FRP (mm2) for shear strengthening measured perpendicular to the
direction of the fibres. When FRP laminates are applied symmetrically on both sides of a beam, Afs is the sum of the areas of both laminates, i.e. Afs = 2bf tf
sf = longitudinal spacing of the FRP laminates used for shear strengthening (mm). For continuous FRP sheet, sf is taken as 1.0
df = effective depth of the FRP strengthening, measured from the top of the FRP shear strengthening to the steel tension reinforcement (mm)
ns = 0 for a fully wrapped beam, = 1.0 when FRP is bonded continuously to the sides and bottom of a beam
(U-wrapped) and = 2.0 when it is bonded to only the sides of a beam lt,max = anchorage length required to develop full anchorage capacity (see Section 6.3) β = angle between the principal fibres of the FRP and a line perpendicular to the
longitudinal axis of the member. β is positive when the principal fibres of the FRP are rotated away from the direction in which a shear crack will form
Efd = design tensile modulus of the FRP laminate (MPa) (see Section 5.6.3) εfse = effective strain in the FRP for shear strengthening bf = width of the FRP laminate (mm) measured perpendicular to the direction of the
fibres. For continuous FRP sheet, bf is taken as cos β tf = thickness of the FRP laminate (mm).
The notation is illustrated in Figure 30.
bf sf hd
Af = 2bftf
FRP laminates on both sides
β
Figure 30 General notation for shear strengthening.
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Shear strengthening 7
The effective strain in the FRP, εfse, accounts for the variation in strain in the FRP along the shear crack when the ultimate limit state is reached. It should be taken as the minimum of:
(i) εfd/2
(ii) 0.5 � fctk Efd tf
(iii) 0.004
where fctk = characteristic tensile strength of the concrete (MPa) εfd = design ultimate strain capacity of FRP (see Section 5.6.4).
The first strain limit of half the ultimate strain capacity represents the average FRP strain when fracture of the FRP occurs. Alternative limits have been suggested for this condition. Chen and Teng(163) propose half the ultimate strain capacity, whilst Taljsten(112) proposes 0.6 times the ultimate strain capacity. It appears that Täljsten’s limit applies when the behaviour of the member is predominantly elastic and that Chen and Teng’s limit is more suitable when the behaviour of a member is characterised by rigid body movements of the regions of the member either side of a shear crack. The lower of the two values has been adopted.
The second strain limit corresponds to debonding of the FRP, and is based on Neubauer and Rostasy’s anchorage model, as described in Section 6.3. In other design approaches, FRP separation has been considered primarily for FRP bonded either to the sides of beams or to the sides and the tension face of beams. Here it is recognised that this condition should also be applied to fully wrapped beams to ensure that the integrity of the concrete is maintained. For small beams such an approach may be conservative, but importantly it should be safe for the cases most frequently encountered in practice.
The final 0.004 strain limit was proposed in early design methods to ensure that the concrete integrity is maintained. This convenient rule of thumb appears to have limited rational justification and, as is shown by Denton et al.(137), does not necessarily prevent the development of wide cracks. It is retained because it seems sensibly cautious to do so.
Equation 7.1 is only valid when the steel reinforcement yields before failure or separation of the FRP. It may generally be assumed that this will occur as long as:
fywk < εfse Es
where fywk = characteristic yield strength of the steel shear reinforcement Es = Young’s modulus of the steel shear reinforcement.
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7 Shear strengthening
Figure 31 Typical variation in ultimate strain capacity
with bonded length (after Neubauer and Rostasy(136)).
100
0.05
0.1
0.15
0.2
0.25
0 0
200
Bonded length (mm)
Parabolic curve
t f = 0.5mm
t f = 1mm
t f = 1.5mm
300 400 500 600
Efd = 230GPa ε fd = 0.015 fctm = 3MPa
In Equation 7.1, the effective depth is reduced by a length equal to (ns/3)lt,max cos β. This adjustment accounts for the reduction in force that can be sustained by the FRP in the anchorage regions. The Neubauer and Rostasy anchorage model, as described in Section 6.3, assumes a parabolic variation of stress with distance (see Figure 31). The force corresponding to the area under the stress curve in the anchorage region is therefore only 2/3 of the maximum stress multiplied by the anchorage length. This reduction in the FRP contribution can be modelled by subtracting (ns/3)lt,max from the effective depth, as in Equation 7.1. The adjustment is made at the top for U-wrapped beams (ns = 1.0) and at the top and bottom for beams with FRP bonded only to the sides (ns = 2.0). No adjustment is necessary for fully wrapped beams (ns = 0). If the FRP at the top of a U-wrapped configuration is anchored and the system is shown by testing to provide full anchorage (preventing premature end peeling) then n can be reduced from 1.0 to 0.
As in the case of steel shear reinforcement, the centre-to-centre spacing of strips of FRP should not be so wide as to allow the full formation of a diagonal crack without intercepting a strip. In addition, Equation 7.1 is based on the approximation that the FRP contribution to the shear resistance is distributed across the whole crack, rather than in discrete locations, which becomes invalid at large strip spacings. For these reasons, if strips are used, their centre-to-centre should not exceed the least of:
(i) 0.8df (ii) df – (ns/3)lt,max cos β (iii) bf + df /4
where the variables are as defined after Equation 7.1.
Alternatively, the contribution of FRP strips to shear capacity may be evaluated with a rigorous analysis, accounting for the critical location for a shear crack and the effect of anchorage of the FRP strips. If this approach is used, the limits on strip spacing in items (i)–(iii) need not apply.
7.3 Spacing of FRP strips
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Shear strengthening 7
Using the truss analogy it can be shown that beam and column elements subjected to a shear force will experience longitudinal tensile forces (i.e. forces along the length of the element), additional to those due to bending. Additional longitudinal reinforcement may therefore be required when strengthening for shear.
For members where longitudinal FRP is required for bending resistance, the tension forces due to shear may be taken into account by simply extending the longitudinal FRP required for bending by a distance of 0.5zf cot θ beyond where it is no longer needed for flexure, and ensuring the FRP is adequately anchored beyond this position. zf is the lever arm between the longitudinal FRP and the centroid of the compression force in the section. This method is valid near positions where the shear force changes sign (e.g. mid-span sagging zones or internal supports of continuous beams), and where the steel reinforcement also extends the same distance 0.5zf cot θ beyond the point under consideration and is fully anchored.
Alternatively, the additional tension force in the longitudinal reinforcement associated with shear forces ΔFtd may be calculated directly (see Clause 6.2.3(7) of BS EN 1992-1-1). If the steel reinforcement has sufficient residual capacity Ast(fyd – σs) to resist the force ΔFtd then no additional longitudinal FRP is required. Otherwise, the area of longitudinal FRP calculated for bending should be increased by an area Afa, where:
Afa = ΔFtd – Ast (fyd – σs) Equation 7.2
σf
where Ast = area of longitudinal steel tension reinforcement σs = stress in the steel reinforcement due to bending σf = stress in the FRP due to bending fyd = design yield strength of the longitudinal steel tension reinforcement.
However, at locations where the shear force changes sign, the total tension force carried by the steel and the FRP does not need to exceed that required for flexure alone at the position of maximum moment (see Clause 6.2.3(7) of BS EN 1992-1-1).
Clearly these approaches are not relevant when no longitudinal FRP is present for bending. In this case, the ultimate bending capacity of the member should be re-evaluated assuming the area of each longitudinal reinforcing bar between the tension face and the mid-depth of the section is reduced by an amount equal to:
ΔFtd Equation 7.3 ne fyd
where ne = total number of effective longitudinal reinforcing bars between the tension face
and the mid-depth of the section.
Any shortfall in bending capacity should be compensated for by providing longitudinal FRP reinforcement.
7.4 Additional longitudinal FRP
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The use of NSM reinforcement for shear strengthening has been demonstrated, amongst others, by Rizzo and De Lorenzis(164). The NSM bars are mounted in slots cut into the sides of the beam to be strengthened. Due to the high degree of bond, failure may occur by separation of the cover concrete. In the following design methodology it is assumed that: � NSM bars are perpendicular to the longitudinal axis of the member, in line with the
shear forces acting on the section. � NSM bars have either surface deformations, a peel ply or sand coating (smooth bars
should not be used). � FRP bar diameters are between 8 and 14mm if circular bars are used. � The width of rectangular/square bars/strips is a minimum of 1mm and a maximum of
16mm. � Grooves are square or rectangular in cross-section and between 4 and 8mm larger in
dimension (depth and width) than the relevant dimensions (diameter or width/depth) of the NSM bar.
� Epoxy adhesive is used to fix the NSM reinforcement into the grooves. � Concrete characteristic cylinder strength is between 20 and 50 MPa.
For shear strengthening using NSM bars mounted to the sides of a beam, a similar approach of combining the contribution from the steel (assuming a variable angle truss) and that from the NSM bars (assuming a 45° truss) can be performed. However, since full anchorage lengths for NSM bars are significantly longer than for surface-mounted FRP, it is quite feasible that the maximum anchorage length of the NSM bars, lnsm, max, is always longer than the anchorage provided either side of the 45° shear plane, lnsm. Therefore it is suggested that the contribution from the NSM bars be calculated from the sum of the achievable force in each bar (both sides of the beam), which will be limited by anchorage failure, concrete cover failure or FRP rupture. Hence, the capacity is:
VRd,s,f = Asw zfywd cot θ +
Σ
Tnsm
Equation 7.4 s nbars
where nbars = number of bars which cross the 45° shear plane (typically equal to df/snsm on
each side of the beam) Tnsm = achievable anchorage force in each NSM bar across the 45° shear plane.
Other variables are as defined for Equation 7.1.
Tnsm for each bar is the lower of: (i) Tnsm,max = 10bnotchperim � Efd Af fctk (for lnsm ≥ lnsm,max) where
lnsm,max = 0.135bnotchperim
� Efd Af
fctk
7 Shear strengthening
7.5 Near-surface-mounted reinforcement for shear
strengthening
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Shear strengthening 7
(ii) Tnsm = Tnsm,max lnsm ( 2 – lnsm ) (for lnsm < lnsm, max) lnsm,max lnsm,max
(iii) Tnsm,ad = 0.3 fat bbarperim lnsm
(iv) Tnsm = 38 � snsm Efd Af fctk where snsm = spacing between NSM bars
(v) Tnsm = 0.004 Efd Af
(vi) Tnsm = εfd Efd Af
2
Here, lnsm is the shorter of the lengths of the NSM bar under consideration, either side of the 45° shear plane under consideration. Other parameters are as defined in Section 6.4.5.
Maximum spacing for NSM bars, centre to centre, should not exceed 0.75df. Minimum clear spacing between grooves should be at least the width of the groove and not less than three times the largest dimension of the bar cross-section.
Full details on the development of the deep embedment technique (described in Section 2.2) can be found in Valerio et al.(16). Much testing has been carried out on both FRP (carbon, aramid and glass) and steel bars bonded into concrete with various resins. Unlike the typically triangular bond–slip response observed for externally bonded reinforcement, deep embedded bars exhibit a ductile response, post peak, with a sustained bond stress for values of slip well over 3mm. The bond is so effective that for longer anchorage lengths the FRP bars, whose tensile capacity is lowest, can rupture in tension. To ensure full bond capacity is attained, it is therefore recommended that CFRP bars are used.
In the following it is assumed that: � Epoxy adhesive is used to bond the FRP bars into the holes. � The bar diameter, db, is a maximum of 12mm and a minimum of 6mm. � The hole diameter is 3mm larger than the bar diameter (resulting in an average
adhesive thickness of 1.5mm). � The bar surface is deformed or has a surface coating (i.e. not smooth). � The maximum spacing, sb, for deep embedment bars does not exceed 0.75hf where h
is the strengthened depth of the element (i.e. length of the bars). � The deep embedded bars are insterted perpendicular to the longitudinal axis, in line
with the applied shear forces.
7.6 Deep embedment bars for shear strengthening
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7 Shear strengthening
As for surface-mounted reinforcement, there is an anchorage length, beyond which no increase in capacity can be achieved. This anchorage length is given by the equation:
lb,max = εfse Efd Af Equation 7.5
( πdb τb ) JA where τb = average bond stress over the length of the anchor. From test results, this can
conservatively be taken as 15MPa in the absence of any other test data on the actual bars and resin to be used
εfse = limiting effective strain in the FRP which, based on experimental evidence collected on strain measurements of deep embedded bars at failure, can be taken conservatively as 0.004
Efd = design Young’s modulus of the FRP bar JA = partial safety factor for adhesive (see Section 5.6.6) db = deep embedded FRP bar diameter Af = bar cross-sectional area.
For shorter anchorage lengths (i.e. near the ends of a shear crack) the force which can be generated in the bar is lower and can conservatively be neglected. Therefore, assuming a 45° truss angle for the FRP contribution to the shear strength, the effective width over which the deep embedment bars will act, weff, should be taken as:
weff = (h - 2lb,max) Equation 7.6
where h = the strengthened depth of the structure lb,max = anchorage length according to Equation 7.5.
Due to the ductility of the bond–slip response of the deep embedment system, it is possible to rely on a sustained value of the bond stress even for large crack widths (and therefore, large slips) allowing any steel stirrups to yield before the bond capacity of the FRP bars is overcome. Therefore, the contribution from the embedded bars (based upon a 45° truss analogy) can be added to the steel stirrup contribution (calculated in accordance with BS EN 1992, based upon a variable angle truss) to give the full shear capacity:
VRd,s,f = Vs + Vf = Asw zfywd cot θ +
εfse Efd Af weff
Equation 7.7 s sb
where sb = spacing of the deep embedded bars. Other variables are as defined for Equations 7.1 and 7.5.
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Shear strengthening 7
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7 Shear strengthening
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Strengthening axially-loaded members 8
8. Strengthening axially-loaded members Concrete columns in existing structures such as bridges and buildings may require upgrading to enhance the following properties: � axial load capacity � flexural capacity � shear capacity � ductility.
Increased axial load capacity, for example, may be needed for compression required to carry higher loads than originally envisaged or where the loading requirements have changed. Enhanced flexural strength may be required for bridge supports that: � are not capable of fully sustaining design loads from heavy vehicle impact � have insufficient lap lengths � have incorrect termination of longitudinal reinforcement.
Some columns designed to older codes may be incapable of withstanding the large horizontal displacement that occurs between member ends during an earthquake. They may therefore require ductility enhancement in order to hold the cover concrete in place and prevent buckling of longitudinal reinforcement under axial load. Shear strength must also be considered in any proposed column upgrading.
Where a deficiency exists, upgrading can be achieved by bonding layers of hoop FRP (i.e. fibres wrapped around the column, oriented perpendicular to the longitudinal axis) and possibly also longitudinal FRP (i.e. fibres oriented parallel to the longitudinal axis of the column) to the column perimeter.
Bonding hoop FRP to the column surface enhances axial load capacity and ductility of columns. The hoop FRP resists lateral expansion due to the axial loading, resulting in a confining stress to the concrete core, delaying rupture of the concrete and thereby enhancing both the ultimate compressive strength and the ultimate compressive strain of the concrete. This process is significantly more efficient with circular than with square or rectangular columns. This is because, with the latter, the confining action is mostly concentrated at the corners. Measures for, and limitations of, strengthening columns of non-circular cross-section are discussed in Section 8.5.
Bonding longitudinal FRP to the column surface enhances the flexural strength of the member, usually in conjunction with hoop wrapping, which should be placed over the longitudinal FRP. Hoop FRP may prevent buckling of the longitudinal fibres, potentially enabling them to contribute in compression. However, this contribution has been shown to be small and should therefore be neglected.
8.1 Introduction
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Column strengthening is normally carried out using fabric, which may be applied dry or be pre-impregnated with an epoxy resin. The use of preformed shells made from a range of fibre types, including glass and carbon, is another option. However, at present, most of the studies that have been carried out using FRP shells have concentrated on their potential for new construction, where the FRP acts both as permanent formwork to the wet concrete and as external reinforcement, rather than in repair or strengthening work.
The following sections deal with design of columns for enhanced compressive strength, flexural strength, shear strength and ductility. It should be noted that the basic principles of strengthening columns given in this chapter are applicable also to strengthening with shells. However, this is a more complex design process that includes aspects such as the performance of the grout annulus and is beyond the scope of this Report.
In designing a column strengthening scheme, using hoop FRP to confine concrete in compression and thus increase capacity, the following should be considered: � Tensile rupture of the FRP. � Failure of the FRP jacket at lap joints. � Shear capacity of the column. � Compliance with relevant serviceability limit states, such as axial shortening, lateral
deformation, loss of strengthening effectiveness, fatigue, creep rupture, creep buckling, and second-order effects.
� Concrete limiting strain.
In addition, other limiting conditions or behaviours might need to be considered. These will be discussed in the following sections.
In the design of strengthened columns, it is necessary to consider the effect of the confinement provided by the FRP on the performance of the concrete.
Concrete in circular columns confined by hoop FRP displays an approximately bilinear stress–strain response, as shown in Figure 32. Initially, the behaviour is similar to that of plain concrete since the FRP exerts a limited confining pressure on the concrete. However, as the axial stress increases, the rate of lateral deformation of the concrete also increases, which results in a concomitant reduction in stiffness of the concrete. Once the concrete reaches the strain relating to peak stress for unconfined concrete, typically 0.002, the material becomes highly fissured and the confinement provided by the FRP is fully activated. At this stage, the stress–strain response becomes approximately linear with a slope dependent upon the stiffness of the hoop FRP. However, if confinement stiffness is low, the resulting stress–strain behaviour may have a descending branch (as shown by the dotted line in Figure 32), such that the peak load is higher than the ultimate load at peak axial strain. The confinement levels which cause this type of behaviour and the resulting maximum failure strength and corresponding strain will now be discussed.
8 Strengthening axially-loaded members
8.2 Compression in circular columns
8.2.1 Background
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Strengthening axially-loaded members 8
Stiff confinement (ascending branch)
Unconfined concrete
Low stiffness confinement (descending branch)
Axial strain, ε c A
xi al
c om
pr es
si ve
s tr
es s,
f c
fccd
ε ccu
Figure 32 Idealised stress–strain curves for FRP-
confined concrete.
It should be noted that, unlike flexural strengthening, initial strain conditions are largely unimportant in confinement of columns since, provided that the column is wrapped under normal service load conditions, the concrete will be behaving elastically. As discussed above, the FRP wrap is ineffective under these conditions and only starts to strain and provide confinement once the concrete exceeds its elastic limit. This implies that it can only increase ultimate limit state capacity not capacity under normal service loading. Thus, service loading conditions should be assessed, according to the recommendations in Section 8.8.
Several authors have proposed models that attempt to predict the compressive behaviour of confined concrete. Most of these formulations were founded on the pioneering work of Richart et al.(165) on hydrostatically triaxially confined concrete. This showed that both axial strength and ductility of concrete increases with increasing confinement pressure.
FRP confined concrete is somewhat different, in that the confinement pressure constantly increases with axial load and ultimate capacity is usually governed by failure of the FRP rather than of the concrete itself. Generally, therefore, it is assumed that compression members strengthened by hoop wrapping will fail if the circumferential stress in the composite exceeds its rupture stress capacity.
However, this would suggest that irrespective of the stiffness of the FRP confinement, if the ultimate strength of the FRP is the same, the ultimate capacity of the strengthened section will be the same. However, the stiffness of the confinement has also been shown to influence the section capacity significantly.
It is therefore recommended that the following model be used, based upon the work of Teng et al.(166). The two factors contributing to the confined behaviour are confinement rupture strain capacity (and by implication, strength) and confinement stiffness.
8.2.2 Confinement under concentric axial load
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These are written in non-dimensionalised form as stiffness ratio, ρK, and strain ratio, ρE:
ρK = 2Efd tf Equation 8.1
(0.85 fck) D εc2 where fck = characteristic concrete cylinder strength εc2 = axial strain in unconfined concrete at peak stress = 0.002 for fck < 50MPa (according to BS EN 1992) = 0.002 + 0.000085(fck – 50)0.53 for fck > 50MPa (according to BS EN 1992) D = column diameter Efd = design Young’s modulus of the FRP tf = total thickness of the FRP wrap
and
ρε = εh,rup Equation 8.2
εc2
where εh,rup = hoop rupture strain of the confining jacket.
In Equation 8.2, the hoop rupture strain, εh,rup, of the FRP jacket has been shown to be less than the ultimate tensile strain of the FRP if it were tested in pure uniaxial tension. There are a number of possible reasons for this lower strain capacity when used for confinement, such as a biaxial stress state, stress discontinuity at overlap regions and stress concentrations due to concrete fracture. However, as a lower bound, from many tests where FRP strain has been measured (see Lam and Teng(167)) a value of 60% of the ultimate strain capacity is recommended:
εh,rup = 0.6εfd Equation 8.3
The increase in strength due to confinement is written as a function of stiffness so that:
fccd = 1 + 5.25(ρK – 0.01)ρε when ρK ≥ 0.01 Equation 8.4 fc0
where fccd = confined concrete strength fc0 = unconfined concrete strength = 0.85fck/JC
The confinement stiffness, ρK ≥ 0.01, represents the stiffness at which the confinement results in a non-descending branch to failure. Therefore, peak stress occurs at the ultimate strain in such a situation. Where the confinement stiffness is low, ρK < 0.01, these equations are not valid and should not be used for design since strength reduces as strain increases beyond a certain point.
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The corresponding axial strain at rupture is required to calculate the stress–strain curve described in Section 8.4. As already stated, the behaviour of confined concrete depends not only on the confining pressure but also the stiffness of the confining FRP (see Samaan et al.(168). As a result, ultimate strains are different for different confining FRP materials, even when the confining pressure is the same. Using the same two non-dimensionalised parameters as for the strength prediction, ρε and ρK, Teng et al.(166) have developed an empirical equation for ultimate concrete strain, εccu, that takes into account the stiffness of the FRP as follows:
εccu = 1.75 + 6.5 ρK0.8 ρε1.45 Equation 8.5 εc2
The first term on the right-hand side, 1.75, ensures that Equation 8.5 converges to predict a value of 0.0035 for εccu when no FRP confinement is provided (i.e. the value of ultimate strain for unconfined concrete according to BS EN 1992 for concrete strengths fck < 50MPa). Again, this fits available data with reasonable accuracy, although there is generally a wider scatter in results from test to test compared to the strength (since the slope of the ascending branch is usually relatively low such that variation in ultimate strain makes little difference to ultimate strength). However, it should be noted that at concrete compressive strains of over approximately 0.01, the concrete will have been crushed and lost all cohesion, resulting in the possibility of shear failure. It is therefore recommended that if the ultimate strain, εccu, is greater than 0.01, then the failure stress, fccd, should be taken as the value of fcc corresponding to the value of εcc = 0.01 from the stress–strain curve (as defined in Section 8.3), rather than the failure stress at rupture of the FRP.
In order to calculate the theoretical axial capacity of a reinforced concrete circular column, under perfectly concentric loading, the above equations can be used to evaluate the concrete strength. Note that material partial safety factors have already been applied to the equations (as well as the factor 0.85 which converts cylinder strength into compressive strength). Therefore the theoretical capacity, N0, of the column under idealised concentric loading conditions is given by:
N0 = Ac,net fccd + As fyk/JS Equation 8.6
where Ac,net = net area of concrete = Ac – As As = area of longitudinal steel in compression fyk = characteristic yield strength of longitudinal steel JS = material partial safety factor for steel fccd = confined concrete strength as determined above.
Just as for unstrengthened columns, generally, even under concentric load conditions, some small nominal moment will exist due to either loads not being applied exactly concentrically or due to initial imperfections in the straightness of the column.
Strengthening axially-loaded members 8
8.2.3 Effect of imperfections
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8 Strengthening axially-loaded members
The initial eccentricity should therefore be taken as the larger of:
ei = hc/30 ei = 20mm and ei = l0/400
where hc = relevant cross-sectional dimension of column (width, breadth, diameter)(mm) l0 = effective length of the column which depends upon restraint conditions, as
detailed in BS EN 1992 (mm).
This first-order effect should be dealt with by considering the small additional moment, Nei, in the design process (see Section 8.4 for combined compression and bending). It has been observed from tests that the effect of this eccentricity has a greater effect on the reduction in capacity of strengthened columns compared with unstrengthened columns and therefore must not be ignored.
The slenderness of a column relates to its potential for buckling and second-order effects determining the capacity of the section rather than concrete crushing. Due to the reduced stiffness of the concrete section once loading exceeds the unconfined concrete strength, the critical slenderness between short and slender behaviour is not the same as for unstrengthened columns.
The slenderness ratio of a column is defined as:
λ = l0 Equation 8.7
r
where l0 = effective length of the column (mm)
r = radius of gyration = r = ��Ic Equation 8.8 Ac
Ic = second moment of area of the uncracked concrete section Ac = gross cross-sectional area of the concrete.
To account for non-linear behaviour of a strengthened column, it is suggested (based on Teng and Jiang(169)) that the critical slenderness ratio is taken as:
λcrit = λlim Equation 8.9
fccd (1 + 0.06 ρε) fc0
where ρε = the strain ratio,
ε h,rup
ε c2
λlim = the limiting slenderness for the unconfined column, according to BS EN 1992-1-1 Section 5.8.3.1.
The ratio fccd /fc0 can be calculated from Equation 8.4.
8.2.4 Slenderness
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Strengthening axially-loaded members 8
Thus, a high degree of confinement leads to a lower critical slenderness ratio, since confinement substantially increases load capacity without significantly increasing flexural stiffness.
If a strengthened column is found to be slender, i.e. λ > λcrit, according to Equation 8.9, the column should be designed with an additional nominal second-order moment, M2, based upon estimated lateral deflection of the column curvature at the ultimate limit state. This is in addition to any first-order moments due to the eccentricity of any applied loading and initial out of straightness (see Section 8.2.3), which should be combined in accordance with Section 5.8.8.2 of BS EN 1992. The following is based on the EN 1992-1-1 nominal curvature method:
M2 = Ne2 Equation 8.10
where N = applied axial load e2 = peak second-order lateral deflection given by:
e2 = Kr Kφ 1 l02 Equation 8.11
ro 10
where
Kr = ( nu –n ) ≤ 1.0 nu – 0.4 Kφ = 1 + βφef
φef = effective creep coefficient, according to EN 1992-1-1 Section 5.8.4 β = 0.35 + fck/200 – λ/150
nu = ( 1 – As fyd ) Ac fccd
n = ( N ) Ac fccd
1 =
( fyd ) ro Es 0.45d d = effective depth of the column section fyd = design yield strength of the longitudinal steel already existing in the section Es = Young’s modulus for reinforcing steel (200GPa).
Equation 8.11 assumes a constant cross-section for the member and it can be assumed that the second-order moment, M2, varies sinusoidally (or parabolically) over the effective length of the member. It will be conservative to take Kr as 1.0, although perhaps overly conservative in situations where strengthening is being considered, leading to unnecessary additional capacity requirements or impractical designs.
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8 Strengthening axially-loaded members
In situations where the column is loaded in combined bending and compression or where serviceability requirements limit capacity, the full stress–strain behaviour is required. While a large number of researchers have developed theoretical stress–strain models validated by experimental testing, the model developed by Lam and Teng(167) captures the main aspects of the behaviour of FRP-confined circular concrete columns in a simple form which reflects the behaviour generally observed. The model has been verified against available test data.
The model is made up of two parts: an initially parabolic section, similar to that of unconfined concrete, followed by a straight line section, the slope of which is dependent upon the level of confinement. The initial slope of the parabolic section is the same as that for unconfined concrete. The parabola and straight line meet at the same slope and the projection of the linear portion intercepts the stress axis at the unconfined strength, fc0, as shown in Figure 33. The model converges to a stress–strain model similar to that in BS EN 1992 for the unconfined case. The model is defined as follows:
for 0 ≤ εcc ≤ εt:
fcc = Ecmεcc – (Ecm – E2)2εcc2/4fc0 Equation 8.12
and for εt ≤ εcc ≤ εccu:
fcc = fc0 + E2εcc (ρK ≥ 0.01) Equation 8.13
where εt = position of transition region between parabola and straight line = 2fc0 /(Ecm – E2) Equation 8.14 E2 = slope of linear portion of confined stress–strain curve = (fccd – fc0)/εccu Equation 8.15 Ecm = modulus of elasticity of concrete according to BS EN 1992 εcc = confined concrete axial strain fcc = confined concrete axial compressive stress εccu = confined concrete ultimate axial strain (given by Equation 8.5) fccd = confined concrete ultimate strength (given by Equation 8.4) fc0 = unconfined concrete compressive strength = 0.85fck/JC
The values of the ultimate design failure stress, fccd, and ultimate compressive failure strain, εccu, of the concrete define the end point and, hence, the slope of the ascending branch of the model. These are the values defined in Section 8.2.2.
As previously stated, this is valid only for the case when ρK ≥ 0.01 (increasing strength to failure, as shown in Figure 33) and should not be used when ρK < 0.01. The resulting stress– strain behaviour, as defined by Equations 8.12 and 8.13, can be used for evaluating concrete stresses for any concrete strain, in particular for situations where the strain across the confined concrete section varies. Methods for analysing sections under combined axial and flexural loads are detailed in Section 8.4.
8.3 Stress–strain model for concrete in FRP-confined
circular sections
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Strengthening axially-loaded members 8
Unconfined concrete
Well confined concrete (ρκ >0.01)
1 E2
fc0
fccd
fcc
εcc εccu ε t 0.0035
Ecm
Poorly confined concrete (ρκ <0.01)
Figure 33 Stress–strain model.
It should also be noted that Equations 8.12 and 8.13 are both calibrated against test results obtained by subjecting cylindrical specimens to substantially concentric compression. In most practical situations, columns are subject to both axial load and flexure, either due to load eccentricity or applied moments. In particular, columns in bridge structures can be loaded horizontally as a result of vehicle impact. In this case, the column must sustain a combination of axial load and bending moment. Methods for analysing sections under combined axial and flexural loads are detailed in the following section.
Bonding longitudinal FRP overwrapped with hoop FRP to column surfaces can enhance the flexural strength of columns.
The main benefit of the longitudinal FRP is to increase the flexural strength of the member, and the requirement of the design is to determine the thickness of longitudinal FRP fibre required to resist the combined design axial load and moment. The hoop wrapping confines the concrete, increasing its compressive strength and strain to failure. This can significantly improve the efficiency of the strengthening design by increasing the strain that can develop in the longitudinal FRP. It should be remembered, however, that flexural enhancement can only be achieved within the span of the column. It cannot be achieved by bonded FRP alone at connections to beams or footings. This may preclude this strengthening solution if highest moments occur at the column ends unless sufficient anchorage of the longitudinal FRP can be provided.
Therefore, the design of compression members which are also subject to flexure (which is all compressive members, if nominal eccentricities are considered) should, in addition to the criteria listed in Section 8.1, consider the following: � At critical points the combination of maximum moment and coexistent axial load. � The risk of debonding. � The risk of anchorage failure. � The shear capacity of the column – see Section 8.7.
8.4 Combined axial compression and flexure
8.4.1 Background
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8 Strengthening axially-loaded members
To calculate the maximum moment and coexistent axial load capacity of an FRP- strengthened column of circular cross-section, the following assumptions can be made: � Sections that are plane before bending remain plane after bending. � Slip does not take place between the FRP and the concrete. � Longitudinal fibres are placed in a layer of even thickness all round the column. � The stress–strain response for unconfined concrete follows the idealised curve for
concrete presented in current codes and standards, with JC = 1.5. � The maximum allowable compressive strain in the concrete is 0.01 or εccu, whichever is less. � The stress–strain response for steel reinforcement follows the idealised curves
presented in current codes and standards, with JS = 1.15. � FRP has a linear elastic response to failure in tension. � The tensile strength of the concrete is ignored. � Confinement provided by any existing hoop steel is ignored. � Longitudinal FRP in compression is neglected.
It is suggested that analysis of the capacity of columns under combined axial and flexural loading be established through developing interaction diagrams. It should be noted however, that the interaction diagrams may be different depending upon whether or not longitudinal FRP is provided to increase flexural capacity. Figure 34 shows the form of the two possible interaction diagram shapes. If there is no longitudinal FRP, the interaction diagram has a maximum moment occurring at a balance point, where the tension steel yields at the same time as the concrete crushes. After this point the force in the steel cannot increase further, regardless of strain, so the moment capacity starts to drop with further reduction in neutral axis depth. Conversely, if longitudinal FRP is included, then even if the steel has yielded, the force in the longitudinal FRP will still increase with increasing strain due to the neutral axis depth reducing. Therefore there is the possibility that the moment capacity still increases, although this will depend upon the relative ratio of steel to FRP in the tension zone.
8.4.2 Moment capacity with axial load
N
M
εccu
εccu
εccu
εccu
0.0035 0.0035
Point 1 (N0)
Point 2
Point 3
Point 4
(Possible balance point corresponding to rupture or debonding of longitudinal FRP)
ε> εfd,longi
(εfd,longi)
ε<εfd,longi
With longitudinal FRP
Without longitudinal FRP
eccentricity ei+e2
Figure 34 Interaction diagrams with and without
longitudinal FRP.
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Strengthening axially-loaded members 8
A simplified method adapted from the approach suggested by Rocca et al.(170) is proposed, whereby four points on the curve are determined: 1. The point on the axial load axis corresponding to zero moment. 2. The point corresponding to a neutral axis depth x = D. 3. The balance point where the tension steel yields at the same time that the concrete
reaches its maximum strain. 4. The point on the moment axis representing zero axial force.
These points can be joined to form an approximate interaction diagram for design with relatively little effort, although the process is best performed computationally. Once the balance point is reached, the strength of the section is governed by either rupture/debonding of the longitudinal FRP, or by yielding of the reinforcement. The increase in concrete strength plays little part and therefore can be ignored from Point 3 to Point 4. It is suggested that if the loading is such that steel will yield in tension, confinement for increased load capacity should not be considered as a strengthening solution.
Once quantities of longitudinal and hoop FRP have been chosen, the general procedure is as follows:
Point 1. This represents a uniform strain across the section, equal to the ultimate axial strain capacity of the confined concrete, εccu, providing the full concentrically loaded axial capacity. This can be calculated as follows: a) Calculate maximum confined strength, fccd, and corresponding strain, εccu, according to
Equations 8.4 and 8.5. b) Calculate axial capacity, N0, according to Equation 8.6.
Note that this capacity is not achievable in reality due to the nominal moment caused by the combination of initial eccentricities, ei, and slenderness effects, e2.
Point 2. This represents a compressive strain distribution from zero to εccu across the section. a) Establish the stress–strain relationships using Equations 8.12 and 8.13. b) Calculate the forces due to the concrete. For a circular section, the concrete force is most
easily found using a layered approach, i.e. by subdividing the section into a number of horizontal layers, parallel to the axis of bending, and calculating the compressive force contribution of the concrete, i.e. the area of the layer multiplied by average concrete stress in the layer (dependent on the average strain through the stress–strain relationship found in step (a)). Compressive forces due to existing steel reinforcement can be added separately. Any FRP in compression should be ignored.
c) Hence, calculate the axial load, N, and the corresponding ultimate moment capacity, M.
Point 3. This point is assumed to give the maximum moment capacity of the section if steel yielding dominates behaviour. The strain distribution should be taken between a tensile strain at a value of εy appropriate to yield of the longitudinal steel in the section at the position of the outermost steel, and the concrete compressive strain capacity εccu at the edge of the concrete in compression. The procedure is identical to that described for Point 2 above except that some of the reinforcing steel, and longitudinal FRP if provided, will be in tension.
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The forces in the longitudinal FRP in tension are again best calculated using a layered approach, i.e. the tensile force in the longitudinal FRP in each layer multiplied by the corresponding layer average strain multiplied by the design Young’s modulus, Efd.
Thus there will be compressive forces in the confined concrete and some of the steel, while tensile forces will exist in the rest of the steel and some of the longitudinal FRP. Axial load, N, and moment, M, can then be calculated as before.
Point 4. This corresponds to the behaviour under pure moment (zero axial load) and, as such, the neutral axis depth will have to be iterated until longitudinal forces in the materials are in equilibrium. However, it also corresponds to behaviour where the effect of concrete confinement is negligible and therefore the concrete strain capacity is limited to a maximum of 0.0035 and the concrete strength to fc0.
If there is no longitudinal FRP then the strain profile is governed by the 0.0035 concrete compressive strain and the neutral axis depth (which defines the strain in the steel). This neutral axis depth can be iterated until equilibrium of the longitudinal forces is reached, from which the moment capacity can be calculated. This will be exactly the same as for the unconfined column.
If, on the other hand, longitudinal FRP is present, then there are two possibilities which govern behaviour. The strain profile is, again, governed by the neutral axis depth and the 0.0035 concrete compressive strain. Provided the strain in the FRP required for equilibrium of the forces is less than or equal to the maximum design strain for the FRP, the fully strengthened section can be utilised. However, there is a possibility that the maximum FRP strain required for equilibrium is greater than the maximum allowable strain of the longitudinal FRP, εfd,longi, which should be taken as the lesser of either the design ultimate strain of the FRP or the debonding strain, as discussed in Section 8.4.3 below. In this situation the longitudinal FRP will have ruptured or debonded and the capacity should be calculated neglecting the longitudinal FRP, i.e. the unstrengthened capacity (in reality some of the FRP will still be understressed in tension, but unacceptable failure will have occurred). In this case there will be a balance point at a lower curvature (less steep strain profile) where the FRP ruptures or debonds at the same time that the concrete crushes (i.e. a strain profile going from εfd,longi in tension to εccu in compression). This point should also be calculated, in a similar way as for Point 3, since it represents the maximum moment capacity of the section, with a coexistent axial load.
Once these four (or five, if rupture/debonding of longitudinal FRP occurs) points have been established, the interaction diagram can be approximated by joining them with straight lines. Limiting the maximum usable axial force to that corresponding to the moment given by an eccentricity, ei, as defined in Section 8.2.3, the combined moment and axial load capacity of the column can be established. If unsuitable, the level of concrete confinement and/or longitudinal FRP can be modified.
8 Strengthening axially-loaded members L i c e n s e d c o p y : a t k i n s , A t k i n s P l c , 0 7 / 0 7 / 2 0 1 3 , U n c o n t r o l l e d C o p y , © C o n c r e t e S o c i e t y
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Strengthening axially-loaded members 8
If the column in question is slender, as defined by Equation 8.9, an additional moment should be included in the design as defined by Equation 8.10. This second-order moment, Ne2, should be added to the existing first-order nominal moment, Nei, (if concentrically loaded) or the applied moment, Mapplied, to provide the full moment, which should be used in design.
The work by Cuninghame et al.(171) appears to show that the provision of hoop wrapping over the longitudinal fibres can prevent end peeling type debonding failure. However, it is possible that longitudinal shear stress type debonding may occur locally. While not necessarily leading to complete debonding of the longitudinal FRP, it should be conservatively assumed that lack of shear transfer occurs once the shear stresses exceed the value defined in Section 6.3.3 (for externally bonded FRP) or Section 6.4.4 (for NSM). Alternatively, a conservative strain limit in the longitudinal FRP of 0.006 may be assumed to prevent debonding provided that the column is also transversely wrapped with FRP.
The longitudinal FRP can fail at the base and/or top of columns and at cut-off points. Anchoring the FRP by extending beyond the point at which it is theoretically no longer required can prevent this. The same anchorage limits as discussed in Section 6.3.3 (for externally bonded FRP) or Section 6.4.5 (NSM) could be provided. However, as discussed previously, this is often not possible since highest moments may occur at the beam–column intersections and/or at the foundation level where it is not feasible to provide sufficient anchorage length. In such situations, the longitudinal wrapping may be enclosed within a collar constructed of steel or concrete, although the efficacy of this solution should be assessed by testing.
Failure of the FRP jacket can occur at lap joints due to debonding, if the lap length is inadequate. This type of failure is brittle and can be avoided simply by providing an adequate lap length. The actual length of overlap required is likely to vary between strengthening systems and so it is recommended that individual manufacturers are consulted. Where considered necessary, independent testing should be carried out.
When two or more plies of FRP are applied to a column, the lap joints should be arranged so they are staggered evenly around the column perimeter, as shown in Figure 35. The minimum overlap for fabric materials, in the direction of the fibres, should be in accordance with the manufacturer’s recommendations to achieve a ‘full-strength’ lap, but not less than 200mm.
8.4.3 Debonding
8.4.4 Anchorage
8.4.5 Lap joint failure
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8 Strengthening axially-loaded members
Figure 35 Laps in columns.
column Lap to be determined column
Confining non-circular columns is generally less efficient than confining circular columns.
With square columns, confinement is concentrated at the corners rather than around the entire perimeter and thus the level of confinement varies throughout the cross-section, with much of the section having low levels of confinement. Research on both small and large columns (see Darby et al.(172) and Toutanji et al.(173)) has shown that the maximum achievable increase in compressive stress for FRP confined square columns with reasonable levels of rounding of corners is about 50%, compared with up to 200% for circular columns. The efficiency decreases further with columns of rectangular cross-section.
The following analysis method allows the effects of debonding, FRP rupture and variation in strain across the cross-section to be taken into account. Whilst theoretically the model can be applied to any size square and rectangular columns, there is little benefit to using it in the following situations: � When the aspect ratio is greater than 1:1.5 for rectangular columns. � When the corners have radii less than 20mm. � When load eccentricity is such that the steel yields in tension.
8.5 Strengthening columns with non-circular cross-
section 8.5.1 Square and rectangular
column cross-sections
Figure 36 Rectangular column dimensions.
h
Rc
b
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Strengthening axially-loaded members 8
With reference to Figure 36, the recommended analysis method is as follows.
As has been discussed for circular columns, the maximum strain which can be achieved in the hoop wrap of FRP before rupture occurs is less than the ultimate strain in the FRP when loaded under uniaxial conditions. In the case of circular columns only 60% of the full design strain can be mobilised. For rectangular columns with rounded corners the rupture strain decreases as the ratio of the corner radius to side length decreases. Given a maximum limiting rupture strain of 0.6εfd for a circular column (2Rc/h = 1) and a minimum strain of 0.14εfd when no radius is provided (2Rc/h = 0), then the rupture strain in the FRP, εh,rup, is given by the relationship (see Barrington et al.(174)):
εh,rup = εfd [ 0.46 ( 2Rc ) + 0.14 ] Equation 8.16 h where h = length of long side Rc = radius of corner.
Typically, for practical corner radii, rupture strains will lie between about 25 and 40% of the design strain capacity of the FRP when applied to square or rectangular columns.
A simplified, conservative approach to calculating the capacity of a confined rectangular column, based upon Darby et al.(172) and Karam and Tabbara(175), is recommended as follows. Rather than explicitly define an effectively confined area, as done in many models, this assumes a simpler average confining stress approach together with equilibrium models to derive an effectiveness factor:
ke = Rc ( 1 + b ) Equation 8.17 b h
where b = short side length h = long side length (see Figure 36).
For a circular column, ke = 1 and for a square column ke = 2Rc/b.
The confined strength of a rectangular column is given by:
fccd = 1 + 5.25 (keρk – 0.01) ρε when ρk ≥ 0.01
Equation 8.18 fc0 ke
where, in this case:
ρk = Efd tf Equation 8.19
(0.85 fck ) Rc εc2
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8 Strengthening axially-loaded members
and
ρε = εh,rup Equation 8.20
εc2
where parameters are as defined in Section 8.2.2.
These equations are only valid for cases where the confinement has sufficient stiffness
(ρK ≥ 0.01
) ke
to result in an increase in strength capacity to failure, otherwise this approach
should not be used.
Slenderness and nominal eccentricity Nominal load eccentricity or out-of-straightness and slenderness effects should be considered, as discussed previously in Sections 8.2.3 and 8.2.4. This generally means that an interaction diagram should be produced (at least a partial interaction diagram) even when considering columns with a nominally concentric load.
Rectangular columns with combined bending and axial load As for circular columns, the FRP hoop confinement can be used to help increase flexural capacity as well as axial capacity by confining the concrete in compression. The addition of longitudinal fibres can be also be used to provide additional tensile strength, but additional compressive strength from longitudinal FRP should be ignored. The approach to design is similar to that for circular columns, by creating a simplified interaction diagram.
There are, however, important differences to consider for rectangular columns. First, in reality, the confinement stresses vary throughout the cross-section, even under concentric loading conditions. For simplicity an average confining stress approach is assumed for design. This approximation leads to a conservative estimate of the concrete contribution to capacity when loads are eccentric.
Axial strain
NA
εcc,max = 0.001
ε h,rup
ε h,rup
Hoop FRP strain
ε h,rup
Corner confining force
Shear stress, τ
Figure 37 Effects of eccentric loads on confining
stresses; neutral axis within the section.
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Strengthening axially-loaded members 8
Potentially more important is that, when loads are eccentric, the stress in the FRP along the side faces reduces approximately linearly from the corner towards the neutral axis position, as indicated in Figure 37. This reduction in stress in the hoop FRP leads to the development of shear stresses between the FRP and concrete along the sides which, if large enough, will lead to debonding. This may limit the confining force that can be generated at the corners and, hence, the capacity of the section. Furthermore, the concrete is in a biaxial state of stress leading to reduced shear capacity. Therefore, the limiting shear stress is defined as:
τlim,c = 0.8 fctk Equation 8.21
Jc
where fctk = characteristic concrete tensile strength, which in the absence of test values can
be calculated using BS EN 1992.
Once debonding occurs, the stiffness of the confinement reduces significantly, leading to ineffective strength enhancement. Therefore, if shear stresses exceed this value, then the rupture strain at the corners, εh,rup, should be replaced by the value at which debonding occurs, εh,debond.
Using a similar approach to that for circular columns, the interaction diagram should be constructed as follows.
Find the following four points on the interaction diagram: 1. The point on the axial load axis corresponding to zero moment. 2. The point corresponding to neutral axis depth = h (or b if bending about the minor axis). 3. The balance point where the tension steel yields at the same time that the concrete
reaches its maximum strain. 4. The point on the moment axis representing zero axial force.
As for circular columns, beyond Point 3 the increase in concrete strength plays little part and therefore can be neglected from Point 3 to Point 4.
Once quantities of longitudinal and hoop FRP have been chosen, the general procedure is as follows.
Point 1. This represents idealised concentric loading and can therefore be calculated according to Equations 8.18 and 8.6.
Point 2. This represents a compressive strain distribution from zero to the maximum confined concrete strain, εcc, max, across the section. Due to the lack of theoretical models for predicting maximum achievable strains in rectangular columns, a value of εcc, max = 0.01 is recommended (this is lower than typically seen in practice but is a limit which maintains concrete integrity).
The hoop FRP in this situation is able to reach its rupture strain on the compression side, but is effectively unstressed on the edge with zero axial strain.
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The maximum strength can be calculated, using Equation 8.18, which will occur close to the face of the column where maximum axial strain exists. Due to the variation in stress in the FRP along the sides, debonding may occur. The shear stress is given by:
τ = tf Efd εh,rup ≤ τlim,c
Equation 8.22
(h – 2Rc)
If this limit is not satisfied, then εh,rup in Equation 8.20 should be limited to a value which achieves this limit, that is:
εh,rup = εh,debond = τlim,c (h –2Rc) Equation 8.23
tf Efd
If bending is about the minor axis, the side dimension h should be replaced by b, the smaller side dimension, in Equations 8.22 and 8.23.
Due to the linear variation in axial strain, a stress–strain model will be required: a) Establish the stress–strain relationships using Equations 8.12 and 8.13. b) Calculate the forces due to the concrete. For a rectangular section, due to the rectangular
geometry of the section an equivalent bilinear approximation for the stress–strain graph can be used in conjunction with the section width to calculate the forces in the concrete (based upon the conservatively assumed ‘smeared’ confinement behaviour). Compressive forces due to existing steel reinforcement can be added separately. Any FRP in compression should be ignored.
c) Hence, calculate the axial load, N, and the corresponding ultimate moment capacity, M.
Point 3. This point is assumed to give the maximum moment capacity of the section if steel yielding dominates behaviour.
The strain distribution should be taken between a tensile strain equal to the yield strain, εy, appropriate to the steel in the section, at the position of the steel furthest from the neutral axis, and a concrete compressive strain of 0.01 at the edge of the concrete in compression furthest from the neutral axis. The procedure is identical to that described for Point 2 above except that some of the steel, and longitudinal FRP if provided, will be in tension. The forces in the longitudinal FRP in tension can easily be calculated without the need for a layered approach.
The longitudinal shear stress between the FRP and concrete will be even higher than for Point 2 and should again be checked:
τ = tf Efd εh,rup ≤ τlim,c
Equation 8.24
(x – Rc)
where x is the neutral axis depth for this particular strain distribution.
If the shear stress is greater than the limiting value then the hoop strain should be limited to:
εh,rup = εh,debond = τlim,c (x –Rc) Equation 8.25
tf Efd
The resulting moment and axial load can then be calculated.
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Strengthening axially-loaded members 8
Point 4. This corresponds to the behaviour under pure moment (zero axial load) and, as such, the neutral axis depth will have to be iterated until longitudinal forces in the materials are in equilibrium. However, it also corresponds to behaviour where the concrete confinement has negligible effect and therefore the concrete strain capacity can conservatively be limited to a maximum of 0.0035 and the concrete strength to fc0. As for circular columns, if there is no longitudinal FRP, this point is the same as for an unstrengthened column. If, on the other hand, longitudinal FRP is present, then the possibility of rupture or debonding of the longitudinal FRP should be investigated. The maximum allowable strain of any longitudinal FRP, εfd,longi, should be taken as the lesser of either the design ultimate strain of the FRP or the debonding strain, as discussed in Section 8.4.3. If this is exceeded, Point 4 is calculated neglecting any longitudinal FRP. The balance point, given by a linear strain distribution from where FRP ruptures/debonds (maximum tensile strain = εfd,longi), to where the concrete reaches a confined compressive strain limit of 0.01, should also be found.
Once these four (or five, if rupture/debonding of longitudinal FRP occurs) points have been established, the interaction diagram can be approximated by joining them with straight lines. The maximum usable axial force should be limited to that corresponding to the moment given by an initial eccentricity as defined in Section 8.2.3, and additional second- order effects should be considered in design, should the column be deemed slender, as defined in Section 8.2.4.
Confinement efficiency can be improved by rounding the corners of the column or by casting circular or oval concrete rings around the column perimeter. However, it should be noted that the confined strength of oval columns reduces as the aspect ratio increases. Following a similar approach to that described for circular and rectangular columns, an empirically derived effectiveness factor (see Teng and Lam(176)) applicable for columns with aspect ratio of up to 2.5 is given as:
ke = ( c ) 2
Equation 8.26 a
where a and c are the major and minor cross-sectional dimensions respectively.
Thus, using Equation 8.4, the confined strength of an elliptical column is given by:
fccd = 1 + 5.25 (keρk – 0.01) ρε when ρk ≥ 0.01
Equation 8.27 fc0 ke
where, in this case:
ρk = 2Efd tf Equation 8.28
(0.85 fck ) Deqv εc2
8.5.2 Elliptical columns
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8 Strengthening axially-loaded members
where the equivalent circular diameter column dimension (based upon an equivalent circular column defined as one with the same volumetric FRP ratio as the elliptic column) is given by:
Deqv = 2ac
Equation 8.29 1.5 (a + c) – � ac
and
ρε = εh,rup Equation 8.30
εc2
where
εh,rup = 0.6 εfd
All other parameters are as defined in Section 8.2.2.
This model should be used with caution, since it calibrated against a small number of concentrically loaded specimens. The greatest aspect ratio tested was 5/2.
Rectangular carbon fibre jackets are also reported to provide sufficient confinement and bar buckling restraint to achieve high flexural displacement ductility levels -see Seible et al.(177). Perhaps an alternative approach may be to use preformed circular FRP shells and fill the intervening space with grout. Other methods may also be employed in order to improve the efficiency of confined rectangular columns. Where it is difficult to shape corners to a radius of at least 15mm, significant stress concentrations may occur resulting in premature failure of the FRP. In such situations it has been suggested that additional localised wrap reinforcement be provided at the corners prior to the application of the continuous layers, thus reducing corner stresses - see Campione et al.(178). It has been suggested that internal FRP ties can be used through the width of the section to increase confinement where side lengths are large - see Tan(179). It may be beneficial to incorporate additional longitudinal FRP in a wrapping scheme to reduce the likelihood of bursting failures. The design of strengthening schemes that use any of these systems should be verified by independent testing.
Lack of ductility is largely an issue for compression members that are located in seismic regions. Upgrading normally involves confining the concrete at column ends (where bending moments are greatest) with hoop FRP. To ensure that column bar buckling does not control the flexural failure mode, additional checks on the transverse reinforcement ratio need to be performed, particularly for slender columns where MEd/VEdD > 4, in which MEd and VEd are the maximum column moment and shear respectively - see Priestley et al.(180). Ductility enhancement may increase the risk of shear failure both at column ends and column centres, and the risk of flexural failure due to lap splice debonding at the junction between the footing and column base - see Seible et al.(177).
8.5.3 Preformed shells
8.6 Other stress/strain conditions
8.6.1 Ductility
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Strengthening axially-loaded members 8
For bridges the designer should consider the effect of repeated live loading on the fatigue strength of the FRP. Checks for fatigue should be carried out in accordance with the recommendations in EN 1992-1-1. The stress range in the FRP should be limited to the appropriate values given in Table 7of this Report.
Rupture of the FRP may occur at service loads due to the sustained stresses that exist in the material. This type of failure can be avoided simply by limiting the stress level in the FRP. It is therefore recommended that the stress in the FRP under service loads should not exceed the values given in Table 8 of this Report.
The presence of hoop FRP can increase the shear strength of concrete columns. Guidance on shear strengthening of square or rectangular beams and columns is included in Chapter 7. The guidelines included in this current section relate to circular columns.
The maximum shear strength of the section should be determined in accordance with Section 7.2. This capacity gives the upper limit on the degree of strengthening that can be achieved.
The ultimate shear capacity of an FRP-strengthened column can be expressed as:
Vu = Vs + Vf Equation 8.31
where Vf = contribution from the FRP to the shear capacity Vs = contribution from the steel to the shear capacity Vu = ultimate shear capacity of FRP-strengthened section.
As described in Section 7.2, the steel stirrup contribution can be determined using the variable angle truss design approach of EN 1992-2-2. Additional guidance on applying this design approach for evaluating the capacity of circular columns is given by Orr et al.(181). As described in Chapter 7, the additional capacity provided by the transverse FRP, Vf, is conservatively based upon a 45° truss analogy.
For rectangular or square sections it is important to take account of debonding of the FRP in the design of shear strengthening, even if the member is fully wrapped. However, for circular members, the significance of debonding is reduced because the development of tensile stresses in the hoop FRP tends to improve the bond behaviour by providing a lateral confining pressure. Therefore, for continuous hoop FRP wrapped around a circular column with fibres aligned perpendicular to the longitudinal axis of the member, Vf is given by:
Vf = (π/2) tf d Efd εfse Equation 8.32
8.6.2 Fatigue
8.6.3 Stress rupture
8.7 Shear strengthening circular columns
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8 Strengthening axially-loaded members
where the effective strain in the FRP, εfse, should be taken as the lesser of:
(i) εfd/2
(ii) 0.004
and εfd = design ultimate strain capacity of FRP d = effective depth (dis tance from the extreme com pression fibre to the centroid of
the tension reinforcement) Efd = design tensile modulus of the FRP tf = thickness of the FRP.
As discussed in Section 7.4, additional longitudinal reinforcement may be required when strengthening for shear. Section 7.4 also outlines how the area of this reinforcement can be determined. However, this approach is not directly transferable to a circular column, since the longitudinal FRP (and steel) is distributed around the section. Therefore, once the additional longitudinal force, ΔFtd, has been calculated, the contribution to carrying this force from the tension steel, ΔFsteel, can be calculated using a lower bound approach as suggested in Orr et al.(181). Any additional force not carried by the steel must be carried by the longitudinal FRP. The force in this FRP will be proportional to the distance from the neutral axis. Thus the additional force is given by:
ΔFtd = ΔFsteel + Afa ffd x
Equation 8.33 g
and, hence:
Afa = (ΔFtd – ΔFsteel) Equation 8.34
(ffd x ) g where ΔFtd = calculated additional tensile force due to shear ΔFsteel = achievable contribution from longitudinal steel Afa = the area of the FRP on the tension side of the column (i.e. the length of the
perimeter of the portion of the column in tension multiplied by the FRP thickness) g = depth from neutral axis to extreme tension fibre x = distance from neutral axis to centroid of FRP in tension (i.e. centroid of the
perimeter of the column on the tension side of the neutral axis) ffd = design tensile strength of the FRP.
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Strengthening axially-loaded members 8
Axial shortening due to projected load increases will give rise to lateral deformation of compression members. This deformation, if excessive, may cause problems of appearance, damage to brittle finishes and/or loss of structural efficiency. Also, at service loads the maximum compressive strain in the concrete should not be excessive otherwise loss of confining pressure due to accidental damage, fire, vandalism, etc., may result in brittle collapse, because the concrete is fissured. To prevent the possibility of either problem arising, it is recommended that the axial compressive stress of the concrete should not exceed 0.6fck under characteristic loads. Similarly, to prevent yielding of steel, the maximum stress (compressive or tensile) in the steel under characteristic loading conditions should be limited to 0.8fyk. These stresses can be calculated using appropriate elastic analysis techniques. The effect of hoop FRP should be ignored under this condition but longitudinal FRP in tension may be included.
8.8 Serviceability
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8 Strengthening axially-loaded members
8.9 Column design flow charts 8.9.1 Stress–strain behaviour of FRP confined circular concrete columns
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Strengthening axially-loaded members 8
8.9.2 Stress–strain behaviour of FRP confined concrete rectangular/square columns
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8 Strengthening axially-loaded members
8.9.3 Column strengthening – combined axial load, N, and moment, M
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Strengthening axially-loaded members 8
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8.9.4 N–M interaction diagram for circular and square/rectangular columns
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No
Define linear strain distribution from εccu in compression to zero on the opposite edge of
the column
Yes
Is longitudinal FRP provided?
No
Calculate 10 (axial load corresponding to zero moment, according to Eqn 8.6)
Define a linear strain profile with maximum concrete strain of 0.0035
Assuming maximum strength of concrete = Ic0 (the unconfined
strength), calculate forces in concrete and steel and iterate neutral axis
depth until in equilibrium
Define a linear strain profile with maximum concrete strain of 0.0035
Assuming maximum strength of concrete = Ic0 (the unconfined strength), calculate
forces in concrete, steel and longitudinal FRP in tension and iterate neutral axis depth
until in equilibrium
Is maximum strain in
longitudinal FRP < debonding or rupture strain?
Yes
Calculate 00, the point on the moment axis corresponding to zero axial load
Longitudinal FRP ineffective. Calculate 00
assuming zero contribution from FRP
For the proposed FRP strengthening, evaluate the stress–strain behaviour of
confined concrete (see appropriate confined concrete stress–strain flow charts)
For the strain distribution, calculate the shear stress, τ, between FRP
and concrete on the side faces (Eqn 8.22 or 8.24 as appropriate)
No Is
column circular in cross- section?
Yes
8 Strengthening axially-loaded members
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Strengthening axially-loaded members 8
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9 Emerging technologies
9. Emerging technologies This chapter describes a number of technologies that are being developed for strengthening concrete structures. Some have already been used on site while others are still at the laboratory stage.
The use of prestressed FRP composites for flexural strengthening of concrete structures has been developing over recent years, and a number of proprietary FRP systems are now available commercially. However, design guidance in this area is still developing, and as such it is advisable to seek specialist advice for the design of prestressed FRP composite strengthening systems.
There are many reasons for strengthening of concrete structures using prestressed FRP composites: � Increasing live load capacity. � Reducing dead load deflections (i.e. mobilising locked-in stresses). � Reducing crack widths and delaying the onset of cracking. � Reducing serviceability problems such as excessive deflection, cracking of the concrete
and tensile steel stresses at serviceability. � Improving fatigue strength by reducing tensile steel stresses. � Regaining prestressed conditions in the concrete that may be lost by damage to the
original prestressing tendons or other effects.
However, if the concrete stress at the serviceability limit state is high, prestressing with FRP composites will not provide a significant increase in the serviceability load.
For some prestressing systems, no reliance on an adhesive bond is required, which can be advantageous where very low or very high service temperatures are present (or there is a significant fire risk) and could significantly reduce the performance of the adhesive, or where the surface quality of the concrete is inadequate for adhesive bonding.
The use of prestressed FRP composite strengthening systems may not be appropriate, or at least will require more detailed planning and risk assessment, where there are limited available installation periods (e.g. within railway possessions or in structures where there is a continuous industrial process), significant risk of vandalism, or exposure to a highly aggressive environment that would affect the long-term properties of the FRP composite.
It has also been suggested that the use of prestressed FRP composites can increase shear capacity by a confining effect on the concrete (see Garden and Hollaway(182)), although this has not been investigated in great detail.
FRP composites generally exhibit superior durability and fatigue properties to those for steel. A number of types of FRP composite can be used to post-tension existing concrete structures: bonded or unbonded FRP composite plates or sheets, bonded FRP near-surface- mounted reinforcement and external FRP composite tendons.
9.1 Prestressing using FRP composites
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Prestressing allows a greater proportion of the FRP composite tensile strength to be utilised, and can therefore be more efficient than unstressed solutions. Carbon FRP composite is generally the most suited type for prestressing applications due to its superior creep and stress rupture properties compared to those of glass FRP and aramid FRP composite. It is advisable not to use glass FRP composites for prestressing, unless the prestressing force being applied is quite low, where stress rupture will not be an issue. Aramid FRP composites can be used instead of carbon FRP composites, their lower tensile elastic modulus being an advantage in achieving greater control of elongations in the prestressing process. However, as with glass FRP, aramid FRP can be susceptible to stress rupture, and therefore the prestress levels should be limited.
The basic principle of strengthening concrete structures by post-tensioning with FRP composites is similar to that for conventional post-tensioned concrete structures. A portion or all of the existing dead load in the concrete member is transferred to the FRP composite by creating a tensile force in the FRP prior to application, bonding and/or anchoring the FRP to the concrete substrate, and then releasing the prestress load. The bonded joint or mechanical anchors at the ends of the plate then transfer the prestress into the concrete member. The prestressed FRP composite carries both a portion of dead load, and also live load, in comparison to unstressed FRP strengthening where the FRP composite only carries a portion of live load.
The method of prestressing the FRP composite is crucial to the feasibility of a practical FRP prestressed strengthening application. The method can be described in a number of stages: 1. Application of tensile force to FRP composite. 2. Anchorage/bonding of FRP composite to concrete substrate. 3. Release of prestress into concrete member and redistribution of forces throughout section.
The method of jacking out the dead load deflection of a concrete member, or physically removing existing dead load temporarily, prior to the application of unstressed FRP composite is also essentially a prestressing solution as the FRP composite carries a portion of the dead load in addition to live load.
The ROBUST project demonstrated the benefits of prestressing the FRP prior to bonding to the concrete, on 1.0m and 4.5m beams in the laboratory, and with 18.0m beams in the field. Specially developed glass FRP end tabs were developed to enable the carbon FRP plate to be pulled, prior to anchoring the tabs into the concrete using resin anchors – see Hollaway and Leeming(183). However, the ROBUST project also illustrated the major disadvantage of this technique in that in order to mechanically anchor the ends of the plate to the concrete, a number of holes need to be drilled into the existing concrete. With the 18.0m beams in the field, so much of the existing reinforcement was cut during this drilling that the ‘strengthened’ beam ended up weaker than before strengthening works commenced.
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Anchorage of the prestressed FRP composite is a critical aspect of the application. Large shear stresses are present within the adhesive bond when the prestress in the FRP composite is released and transferred into the concrete member. Therefore, in most cases a mechanical anchorage at the ends of the FRP composite is required, although techniques are under development to avoid the need for bulky end anchorages.
A number of anchorage types have been developed, generally based on jacking the FRP composite plate through a steel anchorage and bolting through the plate (which is locally strengthened with steel or glass FRP end tabs to avoid failures due to stress concentrations around the bolt holes) into the anchorage and the concrete substrate. The plate is then cut and the transfer of prestress occurs via the bolted anchorage.
In Switzerland, a system has been developed whereby a carbon FRP plate is stretched over a set distance between two large wheels – see Stoecklin and Meier(184). The entire mechanical system is then lifted up to the soffit of the concrete and the laminate is bonded to the structure. This method overcomes many of the problems associated with successfully gripping the plate. Furthermore, this method also allows the problem of high longitudinal shear stress at the concrete–plate interface to be overcome. The longitudinal shear stresses originally led to anchorage failures in laboratory tests. However, a gradually anchored system was devised to reduce the longitudinal shear stresses and delay the onset of anchorage failure. Using this method, the plate is bonded to the concrete from the centre and then moving outwards in stages. As each portion of the plate is bonded to the concrete at successive stages, the prestressing force is slightly reduced to a nominal value at the end of the plate. In order to speed up the curing process, so that the step-wise technique is economic and practical, heating devices within each portion of the plate are used to reduce the adhesive bond curing time.
On transfer of the prestress to the concrete member, some losses occur in a similar manner to those for conventional prestressed post-tensioned structures. The losses in prestress in the short term are due to: � Elastic shortening of the concrete member. � Creep effects in the adhesive for systems with no mechanical anchorage. � ‘Drawing in’ within the anchorage system (if a mechanical anchorage is used).
The relaxation loss for prestressed FRP composite in comparison to high-strength steel is generally small.
The losses in prestress in the long term are essentially the same as those for post-tensioning with low relaxation steel, due to the reduction in elastic modulus of the concrete and shrinkage in the long term.
The ultimate load capacity of concrete members post-tensioned with FRP composites can be analysed based on conventional theory for reinforced concrete structures – see for example Hollaway and Leeming(183) and El-Hacha et al.(105) – but only if flexural failure is the dominant failure mode. The failure mode may be either concrete crushing or FRP composite rupture, depending on the degree of prestress applied to the FRP.
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Emerging technologies 9
Design checks are also required at the serviceability limit state. The level of prestress should be such that the following conditions are acceptable: � Tensile stress and cracking at the concrete edge away from the prestressed FRP
composite under dead and superimposed dead load, after transfer of the prestress. � Compressive stress in the concrete and dead, superimposed dead and live loading. � Tensile stress in the FRP composite under dead and superimposed dead load (for
durability and stress rupture), and live load (for fatigue).
The achievable prestress levels vary depending on the type of FRP composite used, based on their susceptibility to stress rupture. Carbon FRP composite is less susceptible to stress rupture and therefore the greatest degree of prestress can be achieved, followed by aramid FRP composite and glass FRP composite, which both exhibit stress rupture. As an indication, carbon FRP composite can typically be stressed up to 50% of the design tensile stress, aramid FRP composite up to 30% of the design tensile stress and glass FRP composite to only 15–20% of the design tensile stress. For prestressing systems where the adhesive bond is relied upon to transfer prestress forces, the permanent stress in the adhesive should be limited to 25% of the design strength to avoid creep and durability problems, as stated in Section 5.6.6.
A number of commercial prestressing systems are currently available, using the following methods of prestressing: � Stressing and anchoring of carbon FRP plates in a steel anchorage, placed in a recess in
the concrete, containing a base plate for force transfer (bonded and bolted to the concrete), tensioning plate for the hydraulic jack and levelling aids. The stressing process is undertaken in two stages with temporary and permanent anchorages.
� Stressing and anchoring in a steel and carbon FRP composite anchor block, placed in a recess in the concrete substrate. The steel anchorage is bonded and bolted to the concrete substrate. The prestressing operation is carried out in a single stage.
Some prestressing systems are designed such that plate failure would always occur prior to anchorage failure.
A number of reinforced concrete and conventionally prestressed and post-tensioned concrete structures have been strengthened using prestressed FRP composites throughout Europe, particularly in Germany and Switzerland. The first full-scale application of an FRP composite prestressing system in the field was on Lauterbridge, Gomadingen, Germany in October 1998. In this particular case, the prestressing system was installed to reduce crack widths, and increase the flexural strength and rigidity.
Herman(65) reported that prestressed FRP plates were used to strengthen two precast prestressed bridges in Ohio, USA (see Figure 38). Prestressing was used to reduce crack widths in the concrete box beams and to relieve some of the stresses in the reinforcement under service loads. After stressing, the plates were bonded to the soffits of the box beams.
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9 Emerging technologies
Figure 38 Stressing FRP plate on bridge in Ohio.
A number of existing concrete bridges have been strengthened using carbon FRP prestressing tendons or aramid FRP ropes – see Tjandra and Tan(185) and Keller(186). FRP tendons were chosen due to easy handling on site, small-diameter bundles allowing simple deviator detailing, and corrosion resistance. Anchorage systems for FRP tendons have been developed that allow full design strength of the tendon to be assumed, under both static and cyclic loading conditions – see Brown(187). Furthermore, research has shown that external FRP tendon prestressing systems allow substantial rotation to occur over supports in continuous spans near the ultimate limit state. Based on this research, it is possible for full moment redistribution to be assumed – see Araujo and Guimarães(188).
The use of transverse FRP U-wraps around the soffit of a beam is a common laboratory technique to anchor longitudinal FRP laminates – see De Lorenzis et al.(189). This technique has also been carried out in practice on many occasions, with satisfactory results being achieved – see Hutchinson and Rizkalla(190).
Another well-founded laboratory technique to anchor wet lay-up FRP laminates is to cut a transverse groove in the concrete, insert the end portion of the fabric into the groove and anchor into place (through resin) an FRP NSM bar. Again, this technique has also been used in practice, particularly where sufficient anchorage length for the FRP cannot be provided by bond alone. Examples where this technique is particularly useful include anchorage of U-wrap laminates for shear strengthening of T-beams – see Eshwar et al.(138) and anchorage of longitudinal laminates for flexural strengthening of members, which vary in cross-section near supports – see Denton(191).
9.2 FRP anchorage techniques
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Emerging technologies 9
Nurchi et al.(192) have assessed the enhancement of anchorage provided by bolting the ends of an FRP plate to concrete, in addition to adhesive. The primary use of the bolts is to prevent or delay the onset of debonding and concrete cover failure. However, the use of bolts requires multidirectional FRP in order to prevent longitudinal splitting failure of the FRP, and in order to provide sufficient bearing stiffness at the position of the bolts. The bolts, about 200mm in length, are fixed into pre-drilled holes using epoxy adhesive. An additional FRP reinforcement layer is added at the ends of the FRP plates to increase strength at these positions.
The results of their tests indicate that the use of bolts within the shear span of the beam significantly postpones debonding. Following debonding, they are still capable of anchoring the ends of the FRP so that it acts as an unbonded tension member, resulting in a less brittle mode of failure at the ultimate condition. The load capacity of the beam following debonding is reported to be at least equal to the capacity of the beam with the bond intact, although greater deflections occur.
One way in which the problem of high shear stress at the ends of prestressed FRP plates might be overcome is to use NSM bars instead. This is because they are bonded over most of their perimeter, leading to a spreading of longitudinal shear stress in comparison with the one-side-bonded laminate case. Research conducted in Sweden and in the USA has confirmed their suitability – see Nordin(193). Naturally, the main concern is how to prestress the NSM bars prior to insertion into the grooves. At present, this is being considered in some detail because of the potential for this form of strengthening.
As NSM bars offer potentially superior bond performance over plates or sheets, their use for shear strengthening has been attempted, with success. It has been found that the use of either glass or carbon FRP NSM bars increases shear resistance of concrete beams considerably. In particular, De Lorenzis and Nanni(194) have shown that, in the case of strengthening T-beams in shear, if it is possible to anchor the NSM bars into the compression flange, shear resistance is enhanced greatly. They have also shown that angling the NSM bars at approximately 45° (rather than placing them vertically) is advantageous. While such angled reinforcement is problematic for plates or sheets, it is relatively straightforward for the NSM case.
Further work on NSM applications for shear has been carried out by Rizzo and De Lorenzis(164) and by Bianco et al.(195). The authors note that failure can occur not only by debonding of the FRP from the concrete but also by the separation of the concrete cover from the main body of the beam, a failure mode which needs to be accounted for.
9.3 Bolted plate anchors
9.4 Prestressed NSM bars
9.5 NSM bars for shear strengthening
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9 Emerging technologies
In situations where FRP laminates need to be mechanically anchored because of insufficient bond length, there are various options already available. For instance, bolted steel plate anchor systems, may be used for FRP plates. Alternatively, FRP NSM bars may be used to anchor wet lay-up FRP laminates within slots.
Another anchorage system in the process of development has proved to be very effective in preliminary tests at the University of Missouri-Rolla, reported by Eshwar et al.(138). The anchors themselves consist of many glass fibres of overall length 150mm. They are dipped into resin to a depth of 75mm, and the resulting glass FRP portion (of approximate diameter 12mm) is allowed to cure. Holes 75mm deep and 200mm apart are drilled into the soffit of the concrete structure to be strengthened, and resin is inserted into each hole. The first layer of wet lay-up sheet is adhered to the surface of the concrete, following standard procedures. At each hole location, the glass FRP end of each anchor is inserted into the hole through the sheet (by locally realigning the sheet fibres to skirt around the anchor). The ‘dry’ end of each anchor is then fanned out over the surface of the first layer of sheet and fixed into place with resin. Subsequent layers of sheet are added above the fanned anchors so that, after curing, the fan anchor is located within the thickness of the FRP laminate. This enhances anchorage and bond behaviour.
The use of steel-reinforced polymer (SRP) materials has recently been considered in the USA – see Casadei and Nanni(196). Part of the motivation for use of this novel material is that discarded motor car tyres contain significant quantities of ‘hardwire’ steel strand, which can be used to make the SRP. This clearly has environmental benefits, which is advantageous. However, the thin steel strands are susceptible to corrosion. Various matrix materials have been looked at to protect and bind the steel strands. A cementitious grout presently appears to offer a good compromise between structural strength and a durable composite.
A parking garage in Indiana, USA, was recently condemned. Prior to its demolition, parts of it were strengthened using SRP, with encouraging results – see Casadei et al.(197, 198). The strengthened sections showed distinct improvement over the original sections in terms of capacity and ductility. Failure occurred by SRP peeling, in much the same way that might be expected to occur in the FRP situation. Casadei et al.(197) also report the use of SRP in trials on five bridges in Missouri, USA.
As it is difficult to anchor U-wraps around T-beam webs, slots could be drilled in the flange at regular intervals, and full strap-wrapping of the equivalent rectangular section carried out. Since local overstrain in bonded FRP at crack locations can lead to local failure, it would be best not to bond these straps to the concrete. Further, in order to resist shear crack openings (and hence enhance aggregate interlock effects), the straps should be prestressed.
9.6 FRP anchor systems
9.7 Steel-reinforced polymers
9.8 Prestressed carbon FRP straps for shear
strengthening
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Such a system has been developed for commercial use – see Kesse and Lees(199). The straps consist of five or ten individual carbon FRP tapes, heat-welded together in order to create continuity. The straps are prestressed using a patented system, and accurately machined wedges are inserted between strap and concrete in order to maintain the prestress. Results from tests show that shear strength is enhanced considerably through making use of a debonded, prestressed system.
Some of the limitations associated with FRP strengthening of concrete structures are the modest longitudinal shear strength of adhesives, the time taken to prepare the concrete surface and the brittle form of failure, which occurs when the FRP peels off under severe overload. The use of a mechanical bonding system might be an approach to addressing these problems.
Research carried out in the USA has shown the feasibility of using such a technique. Originally intended for extremely rapid strengthening of civilian concrete bridges to allow heavy military vehicles to pass, the technique is to mechanically fasten a pre-cured FRP laminate to the concrete soffit using power-driven bolts. No surface preparation of the soffit is required. The FRP is bidirectional in nature, to prevent longitudinal splitting. Bank(200) reported that preliminary tests carried out in Madison, Wisconsin, USA have shown the potential for this rapid form of construction, although integrity of the cover concrete following the power-driving activities has been shown to be crucial to successful implementation. Casadei et al.(197) also report briefly on the use of mechanically fastened laminates in trials on five bridges in Missouri, USA.
Limited tests have been conducted on torsional strengthening of concrete structures using FRP materials. Results published by Täljsten(201) show that such strengthening is possible and that FRP can contribute substantial torsional resistance. Preliminary indications are that the wrapping of the torsion element should be as full as possible, as the confinement that is created in this way is particularly beneficial in resisting torsion in a controlled, ductile manner.
Due to concerns over the performance of organic adhesives at elevated temperatures (e.g. fire) and, in some cases, degradation under ultraviolet radiation (leading to long- term durability problems), there are moves to develop inorganic adhesives, more akin to cement-based materials.
Kurtz and Balaguru(202) reported on various studies conducted on the mechanical properties of composite plates made with inorganic polymer in combination with carbon, glass and steel fabrics and sheets. The general conclusions were that the method of application is not dissimilar to that of organic resins and adhesives. The inorganic matrix appears compatible with glass and carbon, reporting properties of 650MPa, 550MPa and 30MPa for tension, flexure and shear respectively.
9.9 Mechanical fastening techniques
9.10 Strengthening for torsion
9.11 Inorganic adhesives
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The inorganic adhesives also displayed good adhesion to wood, concrete and steel, the latter reportedly exhibiting a shear strength of 15MPa. Katakalos and Papakonstantinou(203) have also reported improvements in the fatigue performance of RC beams reinforced with steel-reinforced inorganic polymers.
With regard to studies conducted on reinforced concrete beams strengthened with carbon fibre sheets, Toutanji and Deng(204) and Kurtz and Balaguru(202) arrived at similar conclusions on several points: � Inorganic and organic systems provided comparable performance with respect to the
increased capacity but displayed a higher post-yield stiffness increase per unit carbon area.
� The inorganic systems exhibited lower ultimate failure deflection (~25%) compared to the organic system.
� Organic and inorganic systems exhibit different failure modes. Compared to organic systems, which tend to fail by concrete delamination, the inorganic matrix reinforced beams failed, predominantly due to fibre rupture as a result of the development of microcracks in the carbon fibre sheets.
Toutanji and Deng(204) have reported tests on beams strengthened using ‘geopolymer’ adhesives consisting of alumina-silicate with a water-based alkali activator. Geopolymer concrete also exhibits a much smaller CO2 footprint than traditional Portland cements. Sumajouw and Rangan(205) studied geoploymer concrete used to make reinforced concrete beams and columns. The performance was comparable to traditional Portland cement beams and they were expected to perform significantly better at high temperatures. Balagaru(206) and Papakonstantinou and Balagaru(207) have reported geopolymers to be less permeable than concrete, thus slowing the flow of water through the weakened exterior surfaces, which would suggest that environmental effects on the system should be reduced. However, Nguyen Thang et al.(208) reported that when exposed to humid environments, geopolymer matrix–fibre-reinforced composites absorb moisture and undergo dilatational expansion. Hence, more research is needed to establish whether existing, or new formulations, using for example an alkoxide binder, actually improve environmental resistance.
Fibre-reinforced cementitious mortar (FRCM) systems are also available, that combine an open weave fibre fabric with a cement-based mortar – see Bisby et al.(209). These have improved mechanical performance at elevated temperature compared to fibre-reinforced polymer systems, and are particularly suitable where flame spread, toxic smoke production or combustion are of concern.
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10. Workmanship and installation The design guidance in Chapters 5 to 8 is only valid if the component materials used are in accordance with the specification and the installation is carried out correctly. This chapter is not intended to be a specification for strengthening with composites but gives background information on the standards of workmanship and the installation procedures required. The relevant British Standard is Part 10 of BS EN 1504(14). Further information on the requirements for inspection during the installation process, along with advice on the necessary records that need to be maintained, is given in Chapter 4 of Concrete Society Technical Report 57, Strengthening concrete structures using fibre composite materials: acceptance, inspection and monitoring(9), which should be read in parallel with this chapter.
The client should satisfy himself as to the competency of the contractor. All installations should comply with the requirements of the Health and Safety at Work etc. Act(210), the Control of Substances Hazardous to Health Regulations(40) and the Construction (Design and Management) Regulations(211). In addition, all materials must be used in accordance with the manufacturer’s requirements.
Only limited post-application inspection is possible, so the success of the application relies heavily on the quality of the workmanship. It is therefore crucial to the success of the installation that an experienced contractor, with suitably trained and supervised staff experienced in the technique, is appointed. The contractor should have quality assurance procedures in place, accredited and audited in accordance with BS EN ISO 9001(212). The contractor should have a proven track record in the installation of composites and, in the UK, should preferably be a member of the Concrete Repair Association. The contractor must be able to demonstrate competency and be approved for the application of the system. This approval may be obtained by providing evidence of the training of the operatives who will undertake the work and by documentary evidence of experience on similar projects. Alternatively, personnel may be trained under the Certification Scheme for Personnel (CSWIP). CSWIP certificates are generally well recognised by many different national bodies, including authorities, owners of plant and structures, and purchasers. Details of the specified tasks and responsibilities of installers and supervisors for FRP plates for strengthening structures are given in Appendix B.
It is strongly recommended that the following issues are taken into account when selecting a contractor: � The contractor should provide a full method statement and risk assessment for the works. � Operatives should be trained and qualified in application techniques by the
manufacturer of the system. � Personnel should be supplied with the correct personal protection equipment for use
when handling the materials. � The contractor should provide a safe means of access to the work location.
10.1 Overview of requirements
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� The contractor should maintain an environment suitable for the successful use of structural adhesives, bearing in mind the possible effects of low temperatures on the curing of adhesives.
� Procedures should be in place to minimise the risks to the workforce and to any other persons (especially children) who may be affected by the work.
� The methods and procedures should consider risks to the environment, including those from accidental spillage of uncured materials. This will be particularly relevant in sensitive working locations such as over watercourses.
The following sections give general guidance on the installation of plate and fabric materials, which are bonded to the surface of the concrete, and of near-surface-mounted and deep embedded material. The installation of shells around columns, which are generally bonded to the concrete by means of a secondary process such as grout injection, should be in accordance with the manufacturer’s requirements and are not covered here. For all materials and processes, quality assurance procedures should ensure that each stage is approved before starting the next stage. It is vitally important that the manufacturer’s recommendations are followed throughout.
The sequence of the subsections in this chapter follows the step-by-step procedures that would be followed on site by a competent contractor.
An investigation of the condition of the structure, see for example Concrete Society Technical Report 54, Diagnosis of deterioration in concrete structures(12), should be carried out prior to the decision to undertake strengthening. This will identify any deterioration processes (e.g. reinforcement corrosion due to the presence of chlorides) likely to affect the performance of the structure within its residual design life. Water movements through the structure will be particularly relevant if the works fully encapsulate a surface, such as may be the case with fabrics. The investigation should also include a thorough inspection of the concrete surfaces on which the bonding is to be carried out, a visual inspection, an assessment of the concrete strength (see Figure 39) to assess whether it is sufficient for strengthening to be carried out (see Section 2.2), chemical analysis and a sounding survey to identify defects.
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10.2 Evaluation of concrete condition
Figure 39 Use of pull-out test to determine concrete
strength.
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If defects are identified, repairs should be carried out using an appropriate concrete repair system in accordance with the requirements of BS EN 1504(14) and the manufacturer’s recommendations. Cementitious repairs should be cured for at least 28 days before undertaking bonding work. As indicated in Section 2.2, the cause of any deterioration should, as far as possible, be eliminated before the structure is strengthened.
Good preparation of the concrete surface is of paramount importance to the long-term success of the bonding and strengthening operation, though this is less crucial for fully wrapped systems.
Before adhesive is applied the concrete surface must be cleaned so that it is free of laitance, loose material, fungal or mould growth, oil or grease, corrosion products, previous coatings and, in the case of new concrete, mould release agents and curing membranes. The concrete substrate should be prepared in accordance with is Part 10 of BS EN 1504(14). Cracks wider than 0.1mm should be filled with compatible structural repair material.
It is important that the preparation process selected is such that it removes the surface layer to expose small particles of aggregate without causing microcracks or other damage in the substrate. The surface should not be polished or roughened excessively. Sharp edges, shutter marks or other irregularities should be removed to achieve a flat surface.
Mechanical impact methods such as needle gunning and bush hammering are very effective but are often too aggressive and produce a deeper texture in originally smooth concrete. In addition they may shatter aggregate particles, causing microcracks.
10.3 Concrete preparation
10.3.1 Concrete surface for plates and fabric
Figure 40 Surface grinding.
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Mechanical methods may be effective in removing deeply penetrated greases, oils and paints, but may remove an unacceptable depth of concrete. Washing techniques may be ineffective and can simply spread the contaminant further. In such instances the use of solvent-based and sodium hydroxide-based products in the form of a gel or poultice can be effective in drawing out the contaminants. Such products must be used with great care; if they are not thoroughly removed, debonding of the strengthening system may occur.
Wet grit-blasting or vacuum dry-blasting are commonly used because they reduce the dust created by ‘open’ dry-blasting which is unacceptable for health, safety and environmental reasons. However, wet techniques may create a water disposal problem and the concrete surface needs to be allowed to dry out to a degree that is suited to the intended adhesive.
Whichever method is adopted, it is always advisable to carry out trials to select and optimise the technique in conjunction with the material supplier.
The preparation of the surface should be to a standard such that the adhesive layer is of uniform thickness when the strengthening material is in place. Any steps in the surface should be removed and hollows filled with a suitable quick-setting repair mortar. Generally the flatness of the surface should be such that the gap under a 1m straight-edge does not exceed 5mm. The thickness of the adhesive layer is commonly between 2 and 5mm, depending on the material, although thickening to 10mm may be acceptable to accommodate local defects such as dislodged aggregate.
When fabric is to be wrapped round corners, e.g. round a square column or round the bottom of a beam, the corners should be rounded to a minimum radius of 15mm, or as recommended by the supplier, to avoid local damage to the fibres.
Minor imperfections in the concrete surface can be treated at this stage with epoxy materials which can be applied in thin layers and whose rapid strength gain permits over- bonding to be carried out after a short time. Some bonding systems require the use of a primer on completion of the surface preparation. This primer, which seals the surface, should be applied in strict accordance with the manufacturer’s instructions.
The final assessment for surface quality can take the form of a series of pull-off tests. (If a surface primer is used, the tests should be carried out on the primed surface.) Figure 41 shows a ‘dolly’ after being pulled off, with the concrete still adhering to it. A minimum of three tests per representative area should be carried out, as described in BS 1881: Part 207(213), to give an indication of the tensile strength of the substrate and the quality of the surface preparation. The concrete surface should be dry for normal applications. Where this is not possible, because of the nature of the structure, special consideration should be given to the adhesive to be employed.
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Figure 41 Pull-off specimen after removal from concrete
surface.
Before starting to form slots for near-surface-mounted reinforcement, a covermeter survey should be carried out to check the position and depth of the existing steel reinforcement in the area to be strengthened, to avoid damaging it. Slots are formed by making parallel cuts in the surface to the required depth, at an appropriate distance apart, and removing the intervening concrete using a chisel or similar. The slots should be cleaned, using a vacuum cleaner or high-pressure air, to remove any loose material but otherwise should not require any further preparation to ensure that the adhesive has adequate bond.
Holes are drilled vertically through the entire depth of the beam, usually from the soffit to minimise disruption. Care must be taken to avoid cutting through the existing steel reinforcement. The diameter of the hole should be 3mm greater than that of the bar.
The design process will involve certain assumptions about the properties of the FRP. It is therefore important that all materials are in accordance with the specification. FRP plates, rolls of fabric etc. should carry identification labels to indicate their type and grade. To ensure that materials are compatible, they are generally specified as part of a system, e.g. pultruded plate and adhesive. Materials should be marked and labelled in accordance with Part 8 of BS EN 1504(14). Using material systems tested according to CompClass requirements (see Section 3.9.7) will ensure appropriate information is available to identify a suitable system. Alternative materials should not be substituted without the approval of the specifier. Guidance on the approaches for ensuring conformity and on acceptance tests is given in TR 57(9), which includes a proforma for recording details of the materials used. The Report also includes guidance on permissible tolerances in pultruded plate geometry. The cleanliness of the FRP should be assessed in accordance with Part 10 of BS EN 1504.
10.3.2 Slots in concrete surface for near-surface-
mounted material
10.3.3 Drilling for deep embedment bars
10.4 Material conformity
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Thick fibre composite plates and near-surface-mounted reinforcement are usually delivered to site in the lengths required for installation. Thinner plates and fabrics are delivered in the form of a long roll, which can be cut easily to the required lengths at site. Materials should be stored at site in such a way that damage or contamination is avoided.
Adhesives should be stored in dry conditions in accordance with the manufacturer’s instructions, paying particular attention to the specified maximum and minimum storage temperatures. Adhesive and material delivery dates should be recorded and these items should be used in rotation.
Temperature, relative humidity and surface moisture at the time of installation can affect the performance of the FRP system and should be measured in accordance with Part 10 of BS EN 1504(14). It is necessary to maintain the appropriate environment in the work area during surface preparation, application of the adhesive and the subsequent curing period. Environmental control during surface preparation generally consists of a system to extract dust from the work area and the exclusion of any material that might contaminate the prepared surface. A clear access path should be maintained from the area where the adhesive is applied on the plates to the location of the concrete surface to which the plates are to be applied. This is to minimise the risk of contamination of the adhesive surface whilst the plate is being handled.
During the curing period it is necessary to maintain the temperature in the adhesive at an appropriate value and within specified limits. Exceeding the maximum specified temperature may result in a joint with poor long-term properties. Curing temperatures below the specified minimum may result in an adhesive with a low strength. Of equal importance is keeping the work dry.
Most strengthening work is carried out on ‘live’ buildings and structures. It is unlikely that vibration during curing of the adhesive or resin will have a significant effect on the performance of the strengthening system.
All equipment used for the mixing and application of the adhesive and materials should be kept clean and maintained in good operating condition. All operatives should be suitably trained in the use of such equipment.
The mixing and application of the adhesive should be strictly in accordance with the manufacturer’s instructions. (Figure 42 shows adhesive being mixed using a power tool with a suitable attachment.) In particular, the amounts of materials mixed at any one time should not exceed the specified amounts, as larger volumes will lead to higher temperatures being generated, which will reduce the pot life. Resin and hardener have to be mixed together in defined proportions or the properties of the cured adhesive will be impaired. Hence pre-batched quantities of resins and hardeners should be used.
10.5 Storage of materials
10.6 Site conditions
10.7 Mixing and application of adhesive
10.7.1 Mixing adhesive
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(Left) Figure 42 Mixing adhesive.
(Above) Figure 43 Application of adhesive to concrete surface.
The components should be thoroughly mixed together. Some adhesives are supplied with resin and hardener of different colours. This makes it easier to check that thorough mixing has been achieved.
The volume of adhesive mixed at one time must be such that it may be applied and the surfaces brought together within the pot life of the adhesive. Any adhesive remaining at the end of the specified pot life must be discarded.
Where the concrete surface is to be strengthened using FRP plates, the mixed adhesive is applied to the bonding area by hand, using plastering techniques – see Figure 43. The thickness of the adhesive should be maintained at 1–2mm.
Before installation, FRP plates should be checked visually for signs of damage, such as cracks or delamination. The surface of the plate should be prepared immediately before application of the adhesive, in accordance with the manufacturer’s recommendations. This may involve light abrasion and cleaning with a solvent. Some materials are manufactured with an additional peel ply, which, on removal, exposes a clean surface with the appropriate roughness. This is the preferred approach since no additional treatment at site is required.
The adhesive layer should be applied to the plates to form a slightly convex profile across the plate. The extra thickness along the centreline helps to reduce the risk of void formation. A method of application is shown in Figure 44.
10.7.2 Application to substrate prior to plate
installation
10.7.3 Application to FRP plates
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Figure 44 Application of adhesive layer onto fibre
composite plate.
Where the concrete surface is to be strengthened using FRP fabric, the bonding adhesive is applied using a hand-held foam roller or brush. This should be evenly applied to saturate the concrete surface and promote adhesion of the fabric material.
Fabric can be readily cut to size using simple tools (see Figure 45). Dry fabric can be directly applied to the resin-saturated concrete surface without adhesive being applied to the fabric. For wet fabric, the resin is applied to the fabric before it is installed. This resin can be applied to the fabric using brushes or hand-held foam rollers (see Figure 46). Alternatively, a saturator machine may be used to impregnate the fibres with the epoxy (see Figure 47). An epoxy bath is formed by two heavy rollers. The dry fibre is passed through the epoxy and then through the gap in between the rollers. This gap is small enough to provide pressure to saturate the fibres. The gap is also set as a quality control measure to make sure that the correct fibre to epoxy ratio is achieved. The wet fibres are rolled as they come out of the saturator machine and brought to the required location for installation.
Alternatively, vacuum-assisted resin infusion can be used to form the composite in-situ – see, for example, Uddin et al.(75). In this technique, the fibres are applied to the structure dry, the area is sealed with a rubber sheet and a vacuum used to draw in the resin.
10.7.4 Application to substrate prior to fabric
installation
10.7.5 Application to FRP fabrics
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(Above left) Figure 45 Cutting fabric.
(Above) Figure 46 Applying resin using roller.
(Left) Figure 47 Machine for impregnation of fabric.
When near-surface-mounted reinforcement is installed on the top surface on a member, adhesive is simply poured into the slot to a depth equal to approximately the eventual mid-section of the NSM rod or strip. The adhesive needs to be sufficiently fluid to flow into the slot without entrapping air. For installation overhead or on vertical surfaces, a stiffer adhesive is required which will not ‘slump’ significantly. Installation will be by means of an adhesive ‘gun’.
10.7.6 Inserting adhesive into slots for near-surface-
mounted reinforcement
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The FRP material must be correctly installed to ensure the long-term performance of the strengthening system.
Immediately after application of the adhesive, the fibre composite plate should be brought into contact with the concrete substrate. There is sufficient ‘grab’ in the adhesive to hold the fibre composite material in position, and no other temporary support is usually needed.
Even pressure is applied by roller (as shown in Figure 48), starting at one end along the longitudinal centreline and working outwards to expel excess adhesive at the edges and to produce an even glue line. A final adhesive thickness of 1.5–2mm is ideal in most cases. Excess adhesive is removed using scrapers, cloths and solvents.
Where it is necessary for plates to be lapped, the length of the overlap, in the direction of the fibres, should be determined by the designer, but should not be less than 200mm. Chapter 6 gives more detailed information on lap lengths. The spacing of FRP plates on the soffit or top surface of a slab should not exceed 0.2 × span or 5 × slab thickness.
Immediately after assembly, the joint should be inspected. The aim is to check that a continuous and uniform layer of adhesive is visible. In some situations the soundness of the installed adhesive layer can be checked by tapping the composite with a small object such as the edge of a coin. Voids or gaps give a characteristic sound. Further information is given in Section 4.3 of TR 57(9). If defects are found, techniques such as vacuum filling with a suitable resin or plate overlapping could be used as a repair. Further information is given in Section 6.2 of TR 57.
10.8 Assembly and visual inspection
10.8.1 Installation of FRP plates
Figure 48 Installing FRP plates, using a roller to apply
pressure.
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The dry fabric is wrapped tightly over the concrete substrate, avoiding any wrinkles. Figure 49 shows fabric being wrapped round an arched member and Figure 50 shows the wrapping of a column. After application, the fabric is rolled to force the adhesive through the fibres and to expel any air (see Figure 51). If required, further layers of fabric can be applied in a similar fashion, making sure that each successive layer is fully saturated with resin. Finally, a layer of epoxy adhesive may be applied to encapsulate and protect the composite material. Alternatively, the fabric can be impregnated with resin, i.e. wet fabric, and then wrapped around the member. As before, the surface should be rolled to remove wrinkles and to expel air.
The minimum overlap for fabric materials, in the direction of the fibres, should be in accordance with the manufacturer’s recommendations, but should not be less than 200mm. The fib guide(109) suggests a maximum of five layers in a given direction. However, some suppliers suggest that more layers may be used. CALTRANS (the California Department of Transportation) permits up to 14 layers. Advice should be sought from the supplier.
(Above) Figure 49 Wrapping fabric round an arched member.
(Above right) Figure 50 Wrapping fabric round column.
(Right) Figure 51 Rolling fabric to consolidate layers.
10.8.2 Installation of FRP fabrics
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The near-surface-mounted reinforcement is placed in the slot which is partly filled with adhesive. The reinforcement is pressed into the adhesive to the correct depth. The remaining void in the slot is then filled with further adhesive (taking care to avoid trapping air) and finished flush with the concrete surface.
The holes drilled vertically through the web are filled by injecting an appropriate non-sag epoxy adhesive. The FRP rods, of the same length as the depth of the structural member to be strengthened, are inserted fully into the hole by hand ensuring that excess epoxy is squeezed out from the bottom. The initial adhesion between the very light FRP bar and the epoxy eliminates the need for temporary support.
Testing of the basic materials of the strengthening system (e.g. plates, adhesive) will not generally be necessary as they are deemed to be covered by the manufacturer’s quality control. However, some clients may require tests to be carried out on samples obtained from each batch of adhesive and on the composite materials for testing by an independent laboratory to confirm the properties of the materials used. These tests should be in accordance with agreed national or international standards (such as Part 8 of BS EN 1504(14)), as detailed in Appendix B of TR 57(9).
The importance of good quality control specimens cannot be overstated. If any of the quality control (QC) tests do not pass the relevant acceptance criteria the job cannot/ should not be signed off until the designer has (a) reassessed the design taking into account the deficient values or (b) some form of remedial action has been carried out. It is important, therefore, that the QC test requirements are carefully considered prior to the commencement of any works, particularly any testing that involves the production of QC test specimens for independent offsite evaluation. This includes obtaining and preparing any bulk resin casting moulds well in advance of any on-site construction.
The most common off-site QC tests are: � Bulk adhesive dumbbell tests to obtain tensile properties. � Bulk adhesive prisms for the measurement of flexural modulus. � Bulk adhesive prisms for the measurement of adhesive glass transition temperature. � Overlap joints (single or double) to obtain cured joint strength and failure mode.
A number (or suite) of tests is required in case one set of QC specimens produces a failure. This reduces the risk of failing a job due to the manufacture of substandard QC specimens. Cast bulk adhesive specimens are easily manufactured if the appropriate moulds are available, as for example the mould set shown in Figure 52. The mould is then left to cure on-site, subject to the same site conditions, for a minimum of five days before sending on to the independent test house for evaluation.
10.8.3 Installation of near- surface-mounted
reinforcement
10.8.4 Installation of deep embedment bars
10.9 Control samples
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Figure 52 Bulk adhesive mould equipment.
Figure 53 shows a single lap shear coupon and how it is constructed on-site. Note, it is typical to bond actual-size FRP plates together, in a manner that is closely related to the actual site use of fibre composite plates. The overriding concern is to bond the two plates together using the same procedure as that used to bond the plates to the concrete substrate, and generally in accordance with the manufacturer’s recommendations. These are then sent to an independent test house where they are machined to the appropriate Test Standard dimensions and end-tabbed. The testing of the QC samples is normally performed using a standard universal testing machine and can, relatively easily, be performed at different temperatures if required. Compatibility of fibre, or composite, and adhesive can be tested. The double lap shear test, shown in Figure 54, can also be used in a similar manner if deemed more appropriate, e.g. thick FRP plates (>5mm).
Figure 53 Single lap shear test specimen preparation
and finished end-tabbed joint.
Figure 54 Double lap shear test specimen.
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Additionally, pull-off tests should be performed to check the adhesion of the adhesive to the substrate (though always performed on-site by a supervised/qualified contractor). With all of these tests it is of paramount importance to note the mode of failure. This is just as critical as the resulting shear strength of the joint. To help clarify this, it should be remembered that these types of tests are equally a measure of workmanship and not solely performance, providing a measure of the correct application of the adhesive and appropriate surface preparation.
QC procedures for the FRP plate material are not normally necessary and a simple Material Conformity Note, supplied by the manufacturer, will suffice. If dry-fibre resin infusion or wet lay-up materials are used, then it may be necessary/wise to perform additional QC tests on the cured bulk material. Tensile tests can be machined from large flat coupons, cured under site conditions and sent for testing. However, this can produce highly variable results due to difficulties in obtaining the correct resin content. In cases like this a more suitable test method has been proposed which measures the glass transition temperature. This gives a measurement of the state of cure, which is performed in the same way as that for the adhesive mentioned earlier, and a much more consistent evaluation of the consolidation of the composite and hence its performance.
All of the above tests, except for the double lap shear, conform to those listed in the Classification Scheme, and as such any QC specimens will therefore be evaluated under the same test conditions as the ones used to obtain the design values. This is vital for fair comparison against acceptance criteria. Acceptance criteria are used to define the allowable values (typical minimum) that should be attained from either on-site or offsite QC testing.
The QC protocols for carrying out the QC testing can be accessed at www.compclass.org. uk. Acceptance values will vary according to the materials being used and are, therefore, linked to the Product Specification documentation provided by the Classification Scheme. QC testing performed on-site is generally undertaken by the contractor or subcontractor. Offsite testing is always carried out by an independent test house. If any QC sample data sets fail the acceptance criteria, the non-conformance steps listed in the classification scheme documentation should be followed.
When the deep embedment technique is used for shear strengthening, pull-out tests – see Valerio et al.(16) should be carried out on sample FRP bars embedded into concrete specimens to assess the bond capacity of the system, which can be detrimentally affected by the presence of major voids due to poor installation or by poor compatibility between the surface finish of the FRP bar and the adhesive used.
BS EN 1504(14) is the product standard for materials for the repair and protection of concrete. It details the required properties of the materials and the tests that are required to demonstrate conformity. Guidance may be found in Concrete Society Technical Report 69, Repair of concrete structures with reference to BS EN 1504(214).
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Various non-destructive tests may be used to inspect a completed and cured bond for surface bonded materials as described in Part 10 of BS EN 1504(14). However, there is no regime of non-destructive testing that can guarantee the soundness of an application. Full details of available tests are given in TR 57(9). The most common is acoustic sounding (hammer tapping). Thermography may be used to survey large areas; laboratory trials, see for example Lai et al.(215) and Hu(216), have shown good agreement between predicted and measured defects. Other methods, such as ultrasonic testing, are being developed. However, there are currently no non-destructive methods that are capable of detecting poor adhesion, which might lead to failure of the joint in the long term. To provide assurance about long- term performance, additional pull-off dollies could be installed at the time of strengthening. Pull-off tests could be performed on these at various times in the future to monitor the adhesion between the adhesive and the substrate. Similarly, additional double-lap shear test specimens could be prepared at the time of strengthening, placed securely on site, and tested at various times in the future to monitor the adhesion between the FRP material and the adhesive.
Some documents, such as TR 57(9) and ACI 440.2(3), suggest the extent of delamination that may be acceptable. However, the acceptable extent will be very dependent on the type of strengthening and the location in the structure. For example, an area of delamination in the wrapping of a column will probably have a limited effect on the performance while delamination of a plate on the soffit of a beam, particularly at points of high adhesive longitudinal shear, will have a significant effect.
Currently there are no techniques for inspecting NSM strengthening systems after installation, apart from a visual check for major voids.
For major structures, it may be appropriate to install instrumentation prior to the strengthening. Measurements of the difference in the response of the structure under a load test before and after strengthening can be compared with predictions and the instrumentation used to monitor changes with time.
When overcoatings are to be applied, these should be compatible with the underlying composite material and approved for use by the manufacturer. These over-coatings may be applied for the following reasons: � Fire protection. Regulations may require the application of an overcoat layer, which
has been tested on the fully cured composite system. � Protection against vandalism or accidental damage. Where the FRP material may be
vulnerable to damage, it may be encapsulated in a cementitious or epoxy mortar, either spray- or hand-applied.
� Appearance. A cosmetic overcoating can be applied to the composite material to match the existing structure.
� Protection against ultraviolet radiation. The manufacturer should be consulted for advice on the UV resistance of the FRP. If the manufacturer recommends UV protection, a cementitious, or other, overcoating can be applied.
10.10 Non-destructive tests
10.11 Application of overcoatings
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� Reducing solar gain. In exposed situations the FRP could be painted white or shrouded to reduce solar gain and the consequent temperature rise.
� Other reasons. In certain circumstances the FRP material may be encapsulated by other structural finishes or, on bridge decks, covered by the waterproofing.
Figure 55 shows a sprayed mortar overcoat being applied to FRP plates on the soffit of Dudley Port Bridge.
There may be a risk that the fibre composite will be damaged by other work carried out on the structure. For example, holes drilled though to take the fixings for a false ceiling would seriously affect the capacity of the fibre composite; due to stress concentrations around the hole, drilling will lead to a loss in strength equivalent to a reduction in section of two or three hole diameters. When FRP is bonded to the upper surface of a member and covered by a surfacing with a limited life, removal of the surfacing may lead to damage of the FRP. In such cases suitable identification/warning plates or other markings should be fixed on or adjacent to the composite (see Figures 56 and 57). Where an overcoating layer is applied, the plates should, where possible, be placed on the exposed surface.
Figure 55 Spray application of mortar overcoating.
10.12 Identification/ warning signs
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Figure 56 Example of warning printed on carbon fibre
plate.
Figure 57 Examples of proposed warning plates fixed to
structure adjacent to strengthened area.
Detailed records should be kept of the work carried out. Details of the records that should be kept, along with suggested proformas and checklists, are given in TR 57(9). Some of this information will also be required under the CDM Regulations, and should be added to the Health and Safety File, which should also include details of any future inspection and testing regime that is considered appropriate.
10.13 Records
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11 Long-term inspection and monitoring
11. Long-term inspection and monitoring Full details of the requirements for inspecting and monitoring structures strengthened with FRP are given in TR57, Strengthening concrete structures using fibre composite materials: acceptance, inspection and monitoring(9), which includes checklists for the aspects to be considered at various stages and a standard proforma for recording inspection data. The following sections summarise the information in TR57, which should be read in parallel with this document.
As with all structural elements there will be a need to check the fibre composite strengthening system as part of the regular inspection and monitoring of the structure. Such inspections are already carried out for bridges, with general (visual) inspections annually and detailed inspections every six years or so. However, buildings are rarely inspected on a regular basis, inspections often being carried out only when there is a change of use or of ownership. It is strongly recommended that all building owners should instigate a regular inspection regime for strengthened elements.
In the UK, information on the materials used in the strengthening should be included in the Health and Safety File for the structure. This File should also include details of any initial faults in the fibre composite strengthening, such as minor areas of delamination, and should indicate those regions of the strengthening that are critical, such as anchorage zones. The structural engin eer responsible for designing the strengthening should indicate the action to be taken in the event of any likely forms of damage to the composite material. An example of this might be damage to fibre composite material on the soffit of a bridge following impact by an overheight vehicle. The action to be taken will be specific to the particular structure as it will depend on the amount of damage and the extent to which the structure has been strengthened. Hence no general guidance can be given in this Report.
It is strongly recommended that additional samples of the fibre composite material should be bonded to the structure away from the region to be strengthened. (This approach has been adopted on a number of structures including the Barnes Bridge in Manchester and the John Hart Bridge in British Columbia – see Section 4.2.) Additionally, or alternatively, FRP can be bonded to concrete samples, such as short beams, which can be stored on or adjacent to the structure. Samples can be inspected and tested as part of the inspection regime. To aid inspection, some or all of the samples should not be covered with any protective layer. They should thus indicate a lower bound to the performance of the composites bonded to the main structure. Details should be included in the Health and Safety File along with recommendations for the frequency of testing.
Finally, the Health and Safety File should include details of any instrumentation that was installed as part of the strengthening exercise, along with any data obtained before and after strengthening.
11.1 Inspection and monitoring regime
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The intervals between inspections recommended below, taken from Chapter 1 of TR57, should only be taken as a guide. Structures in aggressive environments will require more frequent inspection. Special structures may require a special inspection regime, the frequency and extent of which being determined by a risk assessment.
The recommended intervals for routine visual inspection are as follows:
Bridges Every year
Buildings Every year
Other structures Depends on the use of the structure but ideally every year
In the absence of other guidance, detailed inspections should be carried out at intervals as follows:
Bridges At least every six years
Buildings At change of occupancy or change of use, when structural work or refurbishment is carried out on the building, but at intervals not exceeding ten years
Other structures Depending on the use of the structure but at least every ten years
Detailed inspections should be carried out more frequently in the first few years after installation, to give the owner of the structure confidence that the strengthening has been carried out satisfactorily.
Information on routine visual inspection is given in Section 5.2 of TR57(9). The surface of the fibre composite should be inspected for signs of crazing, cracking or delamination, which would indicate some level of overall deterioration. The composite should be inspected for local damage, for example caused by impact or abrasion. In addition, of course, the inspection should look for signs of the deterioration of the concrete structure itself, such as additional cracking or corrosion.
Where the composite has been covered with overcoating, it will not be possible to directly inspect the composite. Damage to the protective layer will suggest the possibility of damage of the composite. In general, it will not be appropriate to remove the protective layer as this may cause damage to the fibre composite. Thus any inspection of the composite will have to be limited to the control samples.
Identification/warning labels (see Section 10.12 and Figures 56 and 57) should be checked and missing ones should be replaced. This is particularly important where there is the likelihood of future work that could damage the fibre composite material, such as the installation of fixings for services.
11.2 Frequency of inspections
11.2.1 Routine, visual inspection
11.2.2 Detailed inspection with testing
11.3 Routine visual inspection
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The fibre composite may have been covered by paint or other form of protective layer, e.g. for protection from ultraviolet light, which will have a limited life. It will be necessary to check the condition of this layer and to replace it when required, in accordance with the supplier’s recommendations, with a material that is compatible with the fibre composite.
Information on detailed inspection and testing is given in Section 5.3 of TR57(9). De-bonding of the fibre composite material from the concrete may be determined by tapping or thermo- graphy, as indicated in Section 10.10. However, there are currently no simple, non-destructive tests that can be used to assess the condition of the adhesive. This is best determined by carrying out pull-off tests on the control specimens at regular intervals. These tests should be carried out as part of the detailed inspection, though there may be a requirement to test samples more frequently, at least during the early period after the strengthening.
Instrumentation may have been installed as part of the assessment process, for example to measure strains due to live loading on the structure. In addition, instrumentation may have been installed on the structure at the time of strengthening, to enable the response to be compared with that predicted. Such instrumentation can be used to indicate changes in the response. If significant changes are observed, it will be necessary to identify whether they are due to changes in the strengthening system (such as delamination) or due to overall changes in the concrete structure (such as additional cracking or corrosion) so that appropriate action can be taken. It will be necessary for the structure to be reanalysed by a structural engineer to determine what remedial action may be required.
When local areas of damaged composite are identified, they may be repaired by techniques such as vacuum filling with a suitable resin (taking care not to further damage the material) or plate overlapping. When major damage is identified, such as peeling and de-bonding of large areas, it may be necessary to remove the defective material and adhesive. The defective material should be removed over a sufficiently large area such that material on the periphery is fully bonded. The concrete surface should then be prepared again and further FRP installed. It will be necessary to provide an adequate overlap between the new and old material at the periphery of the repaired area. Where these repair techniques are used, it is crucial to check the compatibility of the repair material with the materials already in place. In addition to compatibility, the repair material must have similar characteristics to the material in place. Such characteristics include fibre orientation, volume fraction, strength, stiffness and overall thickness. Some additional information on repair is given in Section 6.2 of TR57.
The nature of FRP materials means that they should need little or no maintenance while in service. However, as indicated in Section 2.3 of TR57, moisture is one of the most damaging elements and so all gutters, drains etc. must be kept clear of debris, so that rainwater is carried off the structure and away from the FRP. If any cleaning is carried out near the FRP, it must be checked that any solvents used will not cause damage. Cleaning techniques such as water jetting or grit blasting are not appropriate as they are likely to cause damage to the FRP.
11.4 Detailed inspection
11.5 Maintenance
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204. TOUTANJI, H and DENG, Y. Comparisons between organic and inorganic matrices for RC beams strengthened with carbon fibre sheets, Journal of Composites for Construction, Vol. 11, No. 5, 2007,
pp. 507–513.
205. SUMAJOUW, M and RANGAN, B. Low-calcium fly ash-based geopolymer concrete: reinforced beams and columns, Research Report GC3, Faculty of Engineering, Curtin University of Technology, Perth, Australia, 2006.
206. BALAGARU, PN. High strength composites for infrastructure: current and future directions for research, Proceedings of the 13th International Offshore and Polar Engineering Conference, Honolulu, Hawaii, 2003, pp. 2251–2259.
207. PAPAKONSTANTINOU, PN and BALAGARU P. Geoploymer protective coatings for concrete, Proceedings of the International SAMPE Symposium and Exhibition, Baltimore, USA, Infrastructure 3 Session, 7 June 2007.
208. NGUYEN THANG, X, KROISOVÁ, D, LOUDA, P, BORTNOVSKY, O, PROKOPCÁKOVÁ, P, ZDOBINSKÁ, P and KEJZLAR, P. Moisture and chemical resistant of geopolymer composites, Proceedings of the 7th International Conference, TEXSCI 2010, Liberec, Czech Republic, 6–8 September 2010.
209. BISBY, LA, STRATFORD, TJ, SMITH, J and HALPIN, S. FRP versus fibre reinforced cementitious mortar strengthening systems at elevated temperature, Proceedings of the 10th International Symposium on Fiber Reinforced Polymer Reinforcement for Reinforced Concrete Structures (FRPRCS-10), Tampa, Florida, USA, 2–4 March 2011.
210. THE STATIONERY OFFICE. Health and Safety at Work etc. Act, The Stationery Office, London, 1994.
211. THE STATIONERY OFFICE. The Construction (Design and Management) Regulations, SI 2007/320, The Stationery Office, London, 2007.
212. BRITISH STANDARDS INSTITUTION, BS EN ISO 9001. Quality management systems, BSI, London, 2008.
213. BRITISH STANDARDS INSTITUTION, BS 1881: Part 207. Recommendations for the assessment of concrete strength by near-to-surface test, BSI, London, 1992.
214. THE CONCRETE SOCIETY. Repair of concrete structures with reference to BS EN 1504, Technical Report 69, The Concrete Society, Camberley, 2009.
215. LAI, WL, KOU, SC, POON, CS, TANG, WF and LAI, CC. Characterization of the deterioration of externally bonded CFRP–concrete composites using quantitative infrared thermography, Cement and Concrete Composites, Vol. 32, Issue 9, October 2010, pp. 740–746.
216. HU, CW. Fabric integrity evaluation of structural materials using infrared thermography, PhD Thesis, University of Glamorgan, Treforest, 2002.
217. BRITISH STANDARDS INSTITUTION, BS EN 923. Adhesives – terms and definitions, BSI, London, 1998.
218. AMERICAN SOCIETY FOR TESTING AND MATERIALS, ASTM D 907. Standard terminology of adhesives, ASTM, West Conshohocken, Pennsylvania, USA.
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Appendix A
Appendix A. Glossary of terms As many readers of this Report may be unfamiliar with fibre composites and with adhesive technology, many of the terms used are defined below. A more extensive glossary of adhesive terms is given in BS EN 923(217) and ASTM D 907(218).
ADHESIVE: A polymeric material which is capable of holding two materials together by surface attachment.
ARAMID: A manufactured fibre in which the fibre-forming substance consists of a long- chain synthetic aromatic poly amide.
BASALT FIBRE: Fibres produced by melting basalt rock which is then extruded through fine nozzles to form a continuous filament.
BOND: The adhesion of one surface to another, with the use of an adhesive or bonding agent.
CARBON FIBRE: Fibres produced by the pyrolysis of organic precursor fibres such as rayon, polyacrylonitrile (PAN) or pitch in an inert atmosphere. The term is often used interchangeably with graphite; however, carbon fibres and graphite fibres differ in the temperature at which the fibres are made and heat-treated, and the carbon content.
COMPOSITE OR COMPOSITE MATERIAL: A combination of high-modulus, high- strength and high-aspect-ratio fibre reinforcing material encapsulated by and acting in concert with a polymeric matrix.
CURE: To change the properties of an adhesive irreversibly by chemical reaction into a more stable condition and to develop the desired properties.
EPOXY RESINS: Resins which may be of widely different structures but which are characterised by the reaction of the epoxy group to form a cross-linked hard resin.
FABRIC, NON-WOVEN: A textile structure produced by bonding or interlocking of fibres, or both, accomplished by mechanical, chemical, thermal or solvent means and combinations thereof.
FABRIC, WOVEN: A generic material construction consisting of interlaced yarns or fibres, usually a planar structure.
FILAMENT WINDING: A reinforced plastics process that employs a series of continuous resin-impregnated fibres applied to a mandrel in a predetermined geometrical relationship under controlled tension.
FILLER: A relatively inert substance added to an adhesive to alter its physical, mechanical, thermal, electrical or other properties or to lower the cost.
FRP: Fibre-reinforced plastics (or polymers).
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Appendix A
GLASS FIBRE: A fibre spun from an inorganic product of fusion which has cooled to a rigid condition without crystall ising.
GLASS TRANSITION TEMPERATURE (Tg): The approximate temperature at which a polymeric adhesive changes from a relatively stiff and brittle material to a viscous material.
HAND LAY-UP: A process in which resin and reinforcement are applied either to a mould or to a working surface and successive layers built up by hand.
HARDENER: The curing agent or catalyst, which promotes chemical cross-linking with the resin in two-component adhesive systems.
LAMINATE: A layer of fibre composite, either preformed or formed in-situ.
NSM: Near-surface-mounted reinforcement.
PEEL PLY: The outside layer of a reinforced plastic material, which is removed to aid bonding.
PLATE: Preformed prismatic FRP element, formed by pultrusion or manufacturing process, generally with all the fibres arranged in the longitudinal direction.
POLYMERIC: Adjective describing a material (most commonly organic) composed of molecules characterised by the repetition of one or more types of simple units.
POT LIFE: The period of time during which a multi-part adhesive can be used after mixing the components. (Note: The pot life varies with the volume and temperature of the mixed adhesive and the ambient temperature. The term ‘pot life’ is also used for the application of hot-melt adhesives for the period for which an adhesive, ready for use, remains usable when kept at normal operating temperature.)
PREPREG: Reinforcing fibres in sheet or roll form impregnated with resin and stored for use.
PRIMER: Material used to protect a surface prior to the application of the adhesive, improve adhesion and/or improve the durability or to stabilise/protect the substrate.
PULTRUSION: A continuous process for the manufacture of composite profiles by pulling layers of fibres, impregnated with a thermoset resin, through a heated die, thus forming the ultimate shape of the profile.
RESIN: The reactive polymer base in adhesive and prepreg matrix systems.
SUBSTRATE: The material of the adherend adjacent to the adhesive layer.
Tg: See Glass transition temperature.
THERMOSET: A resin that is substantially infusible and insoluble after being cured.
UHM: Ultra-high modulus.
WET LAY-UP: A method of making a reinforced product by applying a liquid resin system while the reinforcement is put in place, layer by layer.
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Appendix B
Appendix B. Tasks and responsibilities of installers and supervisors for FRP plates for strengthening structures according to CSWIP (the Certification Scheme for Personnel)
Operational step* Activities Supervisor Installer
Design and specification Materials selection
Design by Engineer in association with client
Method statement(s) Contractor develops methods to satisfy requirements of specification documents ✔
Site activities prior to installation of strengthening system
Install plant/equipment ✔ ✔
Erect access and sheeting ✔
Start bonding record ✔
Site inspection of materials and conformance with specification ✔ ✔
Site trials ✔
Surface preparation Prepare surface(s) ✔
Apply surface repair coatings (if applicable) ✔ ✔
QC tests – mechanical assessment of surface condition ✔ ✔
Application of strengthening system Preparation of materials ✔
Application of primers, adhesives, etc. ✔
Application of composite material(s) ✔
Finishing ✔
QC test specimens ✔ ✔
Witness plates (if applicable) ✔ ✔
Provision of particular curing conditions ✔ ✔
Bonding records ✔ ✔
Inspection ✔
Final QA checks, inspection and approval Inspection ✔
Propose repair methods (if applicable) ✔
Remedial works (if applicable) Materials removal ✔
Materials reinstatement ✔
QC test specimens ✔ ✔
Bonding records ✔
Inspection ✔
Finishing, maintenance and monitoring Apply finishing coatings and paints ✔
Signage ✔
Inspection ✔
* Adapted from CompClass Project.
Table B1 FRP strengthening of structures: identification
of the different roles of installers and supervisors.
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187
Appendix B
The installer, following the instructions provided in the Method Statement, is primarily responsible for initial substrate preparation prior to application of the strengthening system, mixing and application of the adhesive and strengthening system, appropriate QC test specimen preparation and final finishing procedures.
The supervisor is responsible for the production of the Method Statement, based on initial information provided by the designer, inspection and sign-off of all materials and equipment to be used, supervising adequate substrate surface preparation prior to installation of the strengthening system, supervision of the application of the strengthening system, supervision of fabrication of QC specimens and final inspection of the finished installation.
B1 Installer role and responsibilities
B2 Supervisor role and responsibilities
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Fibre Reinforced Polymer (FRP) composites have been used for over 30 years. In civil engineering applications, FRP has proven itself in fabric roof structures, internal concrete reinforcement, deck gratings, and most of all as externally bonded reinforcement. FRP materials are successful in all of these applications because they exhibit low creep and compared with steel, are thinner, lighter, and have 10 times more tensile strength. BASF’s MBrace® Composite Strengthening System, an externally bonded FRP reinforcement system for concrete and masonry structures, has proven itself in the field by exhibiting all of these properties. MBrace® Advantages: * Lightweight * Easy to conceal * Low installation time * Highly durable, non-corrosive * High strength, high stiffness * Forms around complex surface shapes * Can be installed in areas with limited access BASF plc, Construction Chemicals 19 Broad Ground Road, Lakeside,Redditch B98 8YP T: 01527 512255 www.basf-cc.co.uk
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Concrete Repairs Ltd began installing FRP strengthening systems in 19 9 4 and has since completed over 50 0 commercial contracts both in the UK , Europe and the Middle East. We have installed more than 50 kilometres of unstressed and pre - stressed plates to strengthen all t ypes and sizes of concrete, steel and cast iron structures including buildings, bridges and power stations. CRL is an Approved Contractor for all the leading material suppliers and in addition to installation provides a comprehensive design ser vice, of ten incorporating custom - made f ibre composites to meet unique strengthening requirements.
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�ŽŶƚĂĐƚ�Antony Darby, Tim Ibell or Peter Walker at: �ĞƉĂƌƚŵĞŶƚ�ŽĨ��ƌĐŚŝƚĞĐƚƵƌĞ�ĂŶĚ��ŝǀŝů��ŶŐŝŶĞĞƌŝŶŐ hŶŝǀĞƌƐŝƚLJ�ŽĨ��ĂƚŚ �ĂƚŚ���Ϯ�ϳ�z dĞů͗�нϰϰ�;ϬͿϭϮϮϱ�ϯϴϱϯϵϰ� �ŵĂŝů͗�ĂĐĞΛďĂƚŚ͘ĂĐ͘ƵŬ www.bath.ac.uk/ace/BRE-Welcome/
The BRE centre for innovative construction materials
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QUALITY CONTROL AND MATERIALS TESTING The Joining Technology Research Centre (JTRC) at Oxford Brookes is recognised as one of the leading independent Test Houses in the UK today providing Quality Control (QC) and Materials testing for bonded composite strengthening of civil structures.
With over 30 years of experience in adhesive technology JTRC has had significant input into many design and workmanship guides, including the COMPCLASS scheme for classification and qualification of site- prepared composite and adhesive materials. For more details visit www.compclass.org.uk
JTRC also undertakes consultancy and short- and long-term research contracts in most areas of adhesion, adhesive bonding, sealant technology and failure analysis.
Contact us for a preliminary discussion of your requirements, including hire of equipment for making suitable QC test specimens.
Joining Technology Research Centre Oxford Brookes University, Wheatley Campus Wheatley, Oxford OX33 1HX, United Kingdom
Email: [email protected] Tel: +44 (0) 1865 48 3553/3504 Fax: +44 (0) 1865 484179 Web: http://mems.brookes.ac.uk/research/ mechanical-engineering/jtrc
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Sika Structural Strengthening Solutions Sika provide state-of-the-art strengthening systems based on carbon fibre technology and other composite materials for concrete, metallic and masonry structures, including:
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C C
IP-0 56
D
esign guidance for strengthening concrete structures using fi bre com
posite m aterials
Design guidance for strengthening concrete structures using fibre composite materials
This Report provides guidance for structural designers on strengthening concrete buildings and bridges by bonding fibre composite polymers (FRPs) to the surface or embedded in the concrete and covers multiple applications as well as guidance on the advantages and disadvantages of FRPs over similar materials. This relatively new technique is proving to be much quicker and more cost-effective than techniques using steel plates.
This third edition explains the design approach in detail and discusses workmanship, installation, inspection and maintenance as well as covering a number of changes brought about by the introduction of Eurocode 2, additional research findings and further experience of the use of the materials.
CCIP-056 Published May 2012 © The Concrete Society Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey, GU17 9AB Tel: +44 (0)1276 607140 Fax: +44 (0)1276 607141 www.concrete.org.uk
A cement and concrete industry publication
Report of a Concrete Society Working Party
Technical Report No. 55
Design guidance for strengthening concrete structures using fibre composite materials Third Edition
The C oncrete Society Technical R
eport N o.55
TR55 - cover.indd 1 17/05/2012 10:20:53
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