writing an objectives on a lab report

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OAKLAND UNIVERSITY School of Engineering and Computer Science

ME 361 Mechanics of Materials

Laboratory 2

DETERMINATION OF BENDING MOMENTS IN BEAMS

UNDER TRANSVERSE LOADING

1. Objective To determine moments in a beam under transverse loading and then compare the results with

theoretically calculated values.

2. Reference

2.1 Class Notes

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2.2 Mechanics of Materials, 4th Ed., by Beer and Johnson, Mc Graw-Hill, Inc., 2005.

3. Apparatus/Materials

3.1 As simply supported (supported by knife edges) rectangular beam with strain gauges mounted

at various locations.

3.2 Weights and hangers

3.3 VISHAY strain gauge Indicators.

4. Procedure

The rectangular Aluminum beam has to be located between to knife-edges for the beam to be

simply supported. Several strain gauges are mounted at pre–set locations (cannot be changed) along

the length of the beam. There are three weight hangers that can be moved to any location along the

length of the beam. Transverse load to be applied to the beam have to be hung from these three

hangers.

In this experiment, at least two loading conditions must be considered. For each loading condition,

all the three weight hangers must be used.

4.1 Arrange beam supports (knife edges) A and B (this will be done by lab instructor). Strain

gauges are delicate, so be careful in handling the beam with strain gauges so as not to

damage strain gauges and terminals.

4.2 Measure and record the distance between both knife-edges A and B of the supports; this will be the overall length L (see Fig 1).

4.3 Measure and record the distances from the support A to each strain gauge. For example, with the number 10, 8 and 6. This will be the length L10, L8, L6 (see Fig 1).

4.4 Select three strain gauge locations at which you plan to take the strain measurements. Connect the strain indicators to the gauges.

4.5 Calibrate and balance each strain indicator following the steps introduced in lab 1.

4.6 Place the three weight hangers at selected locations (all three weight hangers should be used). Measure the length La, Lb, Lc as shown in Fig 1.

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4.7 Add weights not exceeding the maximum value. The maximum weight recommended at each location is 6 lbs. Record values of the individual loads corresponding to their locations.

4.8 Record the strain gauge readings at the selected points on the beam. 4.9 Repeat steps 4.5 and 4.6 for the same loading condition. Record the strain gauge readings. 4.10 Repeat until the strains from all possible strain gauge locations are recorded for this loading

condition.

4.11 Repeat steps 4.5 to 4.11 for different loading condition. Be sure to use different loads at different location.

5. Parameters:

E = Modulus of elasticity of Aluminum = 10.16 × 106 psi

b = Beam Width = 1.5 in

t = Beam thickness = 0.5 in

 = Strain gauge readings (Note: Strain gauge readings are in  values)

Gauge factor = 2.10 ± 0.05

6. Calculations 6.1 Calculate the theoretical bending moments at each strain gauge position. Be sure to enter the

correct values for lengths (always measured from support A).

6.2 Plot the theoretical bending moment diagram. 6.3 Calculate the experimental bending moment for each strain gauge position from the strain

gauge output using the formula

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2 tb

EM ii

  

where the subscripts i correspond to the gauge numbers

6.4 On the same plot developed in 6.2 from theory, plot the experimental values of M calculated in 6.3. Provide percentage error observed between theoretical and experimental values.

7. Questions (Answers to be included as part of discussion) 7.1 Consider a case where the thickness of the beam is greater than the width. If the beam width

was 0.5 in and the thickness was 1.5 in, would you expect larger or smaller moments?

Explain.

7.2 Why is there a discrepancy between the theoretical and experimental results observed? List and explain the reasons briefly. Also in the experiment you may find a larger discrepancy

between the theoretical and experimental results, explain the reasons.

7.3 Where does the maximum strain in the beam occur for each case? Explain if there is any relationship to the type of loading you subjected the beam to.

7.4 In a few words, explain how this experiment can be used to design beams just from the strain data obtained. Note: The strains observed in this experiment are all normal strains acting

normal to the cross section of the beam.

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SAMPLE OF EXPERIMENTAL DATA

La=17.75 in, Lb=47.75 in, Lc=55.25 in, L=69.75 in Load

Conditions

Gauge 1*

0o

Gauge 2

0o

Gauge 3

0o

Gauge 4

0o …

Gauge 9

0o

Gauge 10

0o

Wa=0, Wb=0,

Wc=0 εo =0 ε- εo 634 ε- εo -563 ε- εo 449 ε- εo 48 ε- εo 953 ε- εo

Wa=2 lbs,

Wb=4 lbs,

Wc=0 lbs

33 33 697 63 -463 100 568 120 168 120 994 41

*Only Gauge 1 is balanced here; At other gauges there is εi=ε- εo

Experimental bending moment at each strain gauge position:

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2 tb

EM ii

  

Theoretical bending-moment at each strain gauge position can be obtained by calculating bending-

moment M(xi) or by drawing bending-moment diagrams.