review the thesis

Proceedings of the Institution of Civil Engineers Structures and Buildings 163 June 2010 Issue SB3 Pages 151–164 doi: 10.1680/stbu.2010.163.3.151

Paper 800013 Received 24/01/2008 Accepted: 07/09/2009

Keywords: failures/stress analysis/ structural frameworks

Robert Mark Lawson SCI Professor of Construction Systems, University of Surrey, Guildford, UK

Jane Richards Technical Director, WSP Cantor Seinuk, London, UK

Modular design for high-rise buildings

R. M. Lawson BSc (Eng), PhD, CEng, MICE, MIStructE, MASCE, ACGI and J. Richards BSc, CEng, MICE

Modular construction is widely used for residential

buildings of four to eight storeys and there is pressure

to extend this relatively new form of construction to 12

storeys or more. This paper reviews recent modular

technologies, and also presents load tests and the

analysis of light steel modular walls in compression. A

design method for high-rise modular applications is

presented taking account of second-order effects and

installation tolerances. For the modular walls tested, it

was found that the plasterboard and external sheathing

boards effectively prevent minor axis buckling of the

C sections, so that failure occurred either by major axis

buckling or local crushing of the section. In all cases, the

results of the tests on 75 mm and 100 mm deep 3

1.6 mm thick C sections exceeded the design resistance

to BS 5950-5 by 10 to 40%. However, an eccentricity of

20 mm in load application reduced the failure load by 18

to 36% owing to local crushing of the C section. Tension

tests on typical connections between the modules and

corridors gave a failure load of 40 kN, which is adequate

to transfer wind forces to a braced core and also to

provide tying action in the event of loss of support to

one corner of a module. Corner posts provide enhanced

compression resistance but their buckling resistance is

dependent on the sway stiffness of the wall panel. It is

also shown that the notional horizontal force approach

for steel structures presented in BS 5950-1 should be

increased for modular construction.

1. INTRODUCTION

Modular construction comprises prefabricated room-sized

volumetric units that are normally fully fitted out in

manufacture and are installed on site as load-bearing ‘building

blocks’. Their primary advantages are

(a) economy of scale in manufacturing of multiple repeated

units

(b) speed of installation on site

(c) improved quality and accuracy in manufacture.

Potentially, modular buildings can also be dismantled and

reused, thereby effectively maintaining their asset value. The

current range of applications of modular construction is in

cellular-type buildings, such as hotels, student residences,

Ministry of Defence (MoD) accommodation and social housing,

where the module size is compatible with manufacturing and

transportation requirements. The current application of

modular construction of all types is reviewed in a recent Steel

Construction Institute Publication 348 (Lawson, 2007). A paper

in The Structural Engineer (Lawson et al., 2005) describes the

mixed use of modules, panels and steel frames to create more

adaptable building forms.

There are two generic forms of modular construction, which

affect their range of application: load-bearing modules in

which loads are transferred through the side walls of the

modules – see Figure 1; and corner-supported modules in

which loads are transferred by way of edge beams to corner

posts – see Figure 2.

In the first case, the compression resistance of the walls

(comprising light steel C sections generally at 300 to 600 mm

spacing) is crucial. Current heights of modular buildings for

this type of construction are typically limited to four to eight

storeys, depending on the particular modular system and the

size and spacing of the C sections used.

In the second case, the compression resistance of the corner

posts is the controlling factor and for this reason, square hollow

sections (SHS) are often used owing to their high buckling

resistance. Building heights are limited only by the size of the

SHS that may be used for a given module size (150 3 150 3

12.5 SHS is the maximum sensible size of these posts).

Figure 1. Partially open-sided module with load-bearing walls (courtesy PCKO Architects)

Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards 151

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Resistance to horizontal forces, such as wind loads and

robustness to accidental actions, becomes increasingly

important with the scale and height of the building. The

strategies employed to ensure adequate stability of modular

assemblies, as a function of the building height, are

(a) diaphragm action of boards or bracing within the walls of

the modules – suitable for four to six-storey buildings

(b) separate braced structure using hot-rolled steel members

located in the lifts and stair area or in the end gables –

suitable for six to ten storeys

(c) reinforced concrete or steel-plated core – suitable for taller

buildings.

Modules are tied at their corners so that structurally they act

together to transfer wind loads and to provide for alternative

load paths in the event of one module being severely damaged.

This is the scenario presented in Approved document A of the

Building Regulations (HMSO, 2006), which leads to minimum

tying force requirements. A recent paper (Lawson et al., 2008)

reviews the robustness requirements for modular construction

based on a ‘localisation of damage’ route. Modules or load-

bearing elements are removed individually to assess the ability

of the rest of the assembly to support the applied loads at the

accidental limit state.

For taller buildings, questions of compression resistance and

overall stability require a deeper understanding of the

behaviour of the light steel C sections in load-bearing walls

and of the robust performance of connections between the

modules. A further issue in the design of modular construction

is that of installation and manufacturing tolerances, which

cause eccentricities in the compression load path and also lead

to additional horizontal forces applied to the modules. This is

considered later in the paper in the context of design to BS

5950-1 (BSI, 2000), which is the standard for structural

steelwork in buildings.

2. HIGH-RISE BUILDING FORMS USING MODULAR

CONSTRUCTION

Modular construction is conventionally used for cellular

buildings up to eight storeys high where the walls are load-

bearing and resist shear forces owing to wind. However, there

is pressure to extend this technology to high-rise buildings by

using additional concrete cores or structural frames to provide

stability and robustness.

One technique is to cluster modules around a core without a

separate structure in which the modules are designed to resist

compression and the core provides overall stability. This

concept has been used on a major project called Paragon in

west London, shown in Figure 3, in which the modules were

constructed with load-bearing corner posts (a paper on this

project was presented in The Structural Engineer (Cartz and

Crosby, 2007).

The building form may be elongated laterally provided that

wind loads can be transferred to the core. This can be achieved

by using in-plane trusses placed within the corridors, or by

consideration of the structural interaction between the modules

and their attachment to the core. Various alternative high-rise

building forms in which modules are clustered around a core

are presented in Figure 4.

An adaptation of this technology is to design a ‘podium’ or

platform structure on which the modules are placed. In this

way, more open space can be provided for retail or commercial

use or below-ground car parking. Support beams should align

with the walls of the modules and columns are typically

arranged on a 6 to 8 m grid (7.2 m is optimum for car parking),

as shown in Figure 5.

For the modular system covered by the tests reported in this

Figure 2. Open-sided module with corner and intermediate posts supported by a structural frame (courtesy Yorkon and Joule Engineers)

Figure 3. Modular building stabilised by a concrete core (courtesy Caledonian Building Systems)

152 Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards

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paper, three building projects have been completed to date

based on the enhanced modular technology. Bond Street,

Bristol is a 12-storey student residence and commercial

building in which six to ten storeys of modules sit on a two-

storey steel-framed podium (see Figure 6). The 400 bedroom

modules are 2.7 m external width, but approximately

100 modules are combined in pairs to form ‘premium’ studios

consisting of two rooms. The kitchen modules are 3.6 m

external width. Stability is provided by four braced steel cores,

into which some modules are placed (Figure 7).

A second building, Pitwines in Poole, is an eight-storey student

residence comprising approximately 300 modules. Both

buildings use lightweight cladding attached to the walls of the

modules and comprise terracotta tiles or insulated render

cladding. The nature of the student residential sector is that the

construction period is often less than 12 months, and the

installation of modules is generally carried out in the January

to March period for a September completion. A further project

using this technology has been completed in east London and

another is under way in north London. This last project is

shown under construction in Figure 8.

Another modular manufacturer has developed a system using

1B2P

2B4P

2B4P

2B4P

1B2P

2B4P

9 9

0 0

9 9

0 0

330033006000 6000 12001200

1 2

0 0

2B4P 2B4P

1B2P 1B2P

3B6P

1B2P 1B2P

9 9

0 0

24001200 120060006000

6 6

0 0

6 6

0 0

(a)

(b)

Figure 4. Typical high-rise building forms using modules and concrete cores (courtesy HTA Architects) (2B4P means a two-bedroom, four-person apartment for example): (a) option 1A; (b) option 2B

2·8 m Modules

Core for stairs/lifts

300 mm

3–3·6 m

300 mm

4·5 m

Spa n of

12– 18 m

6 m

Figure 5. Modules supported by cellular beams acting as a podium

Figure 6. Twelve-storey modular student residence at Bond Street, Bristol (courtesy Unite Modular Solutions)

Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards 153

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SHS corner posts and a concrete floor with perimeter parallel

flange channel (PFC) steel sections. This has been used in eight

to eleven residential buildings, such as the one shown in Figure

9, and construction of taller buildings is in progress. In this

form of heavier modular construction, the effect of

construction tolerances on the forces acting on the corner posts

is much more important –see section 6.4.

3. DESIGN OF

MODULAR WALLS TO

BS 5950-5

Light steel walls and floors in

modular construction are

currently designed to

BS 5950-5 (BSI, 1998), but

interpretation of this standard

is required to take account of

the practical aspects of the

constructional system. In

modular systems with load-

bearing walls, the light steel

C sections in the walls are

subject to potentially

complex loading and

restraint conditions. In most cases, these conditions are as

outlined below.

(a) Axial load is transferred by way of direct wall–wall

bearing, taking into account eccentricities in manufacture

and installation of the modules, which causes additional

build-up of moments and accentuates the local bearing

stresses at the base of the wall.

(b) Loading from the floors and ceilings is taken as applied at

the face of the wall (at an eccentricity of half the wall

width), which causes additional local moments.

(c) Restraint is provided at the floor and ceiling positions so

that the effective height of the wall may be taken as its

clear internal height.

(d) Two layers of plasterboard or similar boards are attached to

the internal face of the wall by screws at not more than

300 mm spacing and provide up to 90 min fire resistance.

(e) Cement particle board (CPB) or oriented strand board (OSB)

are often attached to the exterior of the wall for weather-

tightness of the module and to provide some diaphragm

action. In production, boards may be fixed air-driven pins

enhanced by glued joints.

( f ) In taller modular buildings, second-order (P�˜) effects may occur owing to sway and other eccentricities that are

often neglected in the design of low-rise buildings

The effects of axial loading and eccentricity can be taken into

account in the design of compression members to BS 5950-5

(BSI, 1998), but the stabilising effect of the boards on local and

overall buckling is largely unquantified. It is reasonable to

assume that boards fixed on both sides provide restraint in the

minor axis direction of the C section, but the stiffening effect

of the boards in the major axis (out-of-plane) direction is not

known, nor is the stabilising effect of boards attached only on

one side. This is the subject of the test programme described

below.

4. COMPRESSION TESTS ON MODULAR WALLS

The following tests were carried out to verify the structural

action of the load-bearing walls in a typical modular system.

Two series of tests were carried out: one series on 75 mm

deep 3 45 mm wide 3 1.6 mm thick C sections at the Building

Research Establishment (BRE) and one series on 100 mm

deep 3 42 mm wide 3 1.6 mm thick C sections at the

University of Surrey.

Core 2

Core 4

Core 3

Core 1

Corridor Corridor

Corr idor

Separating wall

Premier room modules

Separating wall

Standard modules

Figure 7. Plan of modular building at Bond Street, Bristol showing the core positions

Figure 8. Eleven-storey modular student residence in north London under construction (courtesy Unite Modular Solutions)

Figure 9. Modular residential building, Wolverhampton (courtesy Vision Modular Structures)

154 Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards

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The tests were intended to establish the compression resistance

of the C sections, nominally placed at 300 mm spacing, taking

account of the restraining and stiffening effects of various

types of board. The sensitivity to eccentricities up to 20 mm

was also investigated, as this exceeds the maximum that may

be envisaged with good control on installation of modules in

practice.

The panels were loaded using a spreader beam and lateral

restraints in the form of PFC sections, and the test arrangement

is illustrated in Figure 10. The eccentricity in load application

was introduced by a 6 mm thick steel plate inserted at the base

of the wall.

The main variables were the type of boards that are attached

on one or both sides and the eccentricity in axial load.

Additional tests were included on taller walls to examine the

influence of slenderness. The boards were fixed using 2 mm

diameter air-driven nails at 200 mm centres, as used in

production of the wall panels. The boards were attached 2 mm

short of the web of the top and bottom track so that the boards

were not loaded directly.

OSB was attached externally and, in some tests, CPB was

included to assess the difference in restraint provided by the

two types of board. Two layers of 15 mm fire-resistant

plasterboard were used internally, as required for 90 min fire

resistance. In two of the tests,

this plasterboard was omitted.

The walls were first loaded up

to around 100 kN to represent

serviceability loading before

loading incrementally to

failure. Deflections were

recorded at the top of the wall

(vertically and horizontally)

and at mid-height

(horizontally). The test failure

loads are presented in Table 1.

The failure load generally

occurred at a relatively small

vertical displacement of less

than 5 mm.

A further series of tests was

carried out on 2300 mm

high 3 600 mm wide wall

panels, comprising three

100 mm deep C sections

with a mid-height noggin

built into the wall panel to

provide lateral restraint in

the minor axis.

Side B

Roller

Spreader 150 75 18

PFC � �

150 75 18 PFC

� �

2450 mm

11 mm OSB 2 15 mm plasterboard�

75 1·6 C�

Lateral restraint

Jack

Side A

Plate

150 75 18 PFC� �

1200 mm

150 75 18 PFC� �

(6 mm thick) Plate

Figure 10. Test arrangement for BRE wall compression tests

Wall test details Wall height: m Eccentricity of loading: mm

Failure load per C section: kN

Design resistance to BS 5950-5: kN

Model factor

75 3 45 3 1.6C: OSB boards on one side only

2.45 0 64 48 1.33

75 3 45 3 1.6C: Plasterboard on one side,

2.45 0 97 76 (inc. effect of boards) 1.27

OSB on the other 2.77 0 90 56 (inc. effect of boards) 1.61 2.45 10 79 56 (inc. effect of boards) 1.41

2.45 20 62 47 (crushing) 1.31

75 3 45 3 1.6C: Plasterboard on one side, CPB

2.45 0 96 76 (inc. effect of boards) 1.26

on the other 2.45 20 52 47 (crushing) 1.10 100 3 42 3 1.6C: Plasterboard on one side only

2.30 0 57 51 1.13

100 3 42 3 1.6C: CPB on one side only

2.30 0 70 61 1.14

Model factor ¼ Failure load/design resistance

Table 1. Failure loads of C section wall studs and comparison with BS 5950-5

Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards 155

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Two additional bending tests were carried out on wall panels

using 75 3 1.6 C sections subject to a line load at mid-span.

The purpose was to calculate the effective stiffness of the wall

panels in order to calculate the modified slenderness of the

C section for the compression resistance to major axis buckling.

The cases considered were

(a) OSB board on one side and two layers of plasterboard on

the other (OSB in compression)

(b) OSB board on one side with no plasterboard on the other

(OSB in compression).

The measured values of Ieff taking into account the stiffening

effects of composite action with the boards were

432 3 103 mm4 and 270 3 103 mm4 per C section respectively.

The calculated second moment of area of the bare C section

was 265 3 103 mm4. It follows that the effective inertia is

increased by 62% for boards fixed on both sides but by only

2% for OSB board on one side.

5. ANALYSIS OF WALL TESTS TO BS 5950-5

The light steel walls were analysed in accordance with

BS 5950-5 using measured section dimensions and steel

strengths. Composite action occurred owing to the additional

stiffness of the boards attached to both sides, which increase

the buckling resistance of the wall. The section properties of

the C sections were calculated for the case where the edge lips

are considered to be fully effective.

The strip steel was S350 grade supplied to BS EN 10327 (BSI,

2004b) and measured strengths were in the range 380–405

N/mm2. Calculated compression resistances to BS 5950-5 are

presented in Table 1. The model factor is the ratio of the test

failure load to the compression resistance to BS 5950-5, based

on measured material strengths and geometry.

The attachment of boards to both sides of the wall effectively

prevents minor axis buckling, even for the narrow wall panels

tested and so failure may occur in one of three modes

(a) crushing of the cross-section locally in compression, as in

Figure 11

(b) buckling of the wall in the major axis direction, as in

Figure 12

(c) delamination of the boards from the wall studs, leading to

loss of composite action.

The stiffening effect of the boards leads to a reduction in

slenderness and increase in buckling resistance. Using the

measured 62% increase in bending stiffness of the wall panel,

the effective slenderness of the bare C section is reduced by

22% owing to attachment of the OSB and plasterboards. For a

2.45 m wall panel, the slenderness in the major axis direction

was 79, and so the effective slenderness becomes

0.78 3 79 ¼ 62. This leads to a buckling strength of pc ¼ 263 N/mm2 according to Table 10 of BS 5950-5 when using a Q factor (effective area/gross area) of 0.88.

The calculated compression resistance was 67 kN, which is

approximately 70% of the test result of 97 kN. This suggests

that the buckling curve for cold-formed sections used in

BS 5950-5 is conservative. In addition, local buckling of the

Figure 11. Local crushing of C section in compression tests

Figure 12. Wall failure by overall buckling in pure compression

156 Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards

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flanges of C section may be reduced by the attachment of the

boards, which increases the effectiveness of the cross-section.

The eccentricity of load application using a plate below the

wall accentuates local crushing, as well as overall buckling.

The crushing resistance of the C section without consideration

of buckling is calculated from Aeff py. The reduced crushing

resistance owing to eccentric loading may be taken into

account by considering a reduced compression area, Aeff .

Because the buckling resistance is approximately 70% of the

crushing resistance, it follows that buckling will occur first

unless the crushing resistance is reduced by over 30%.

A 10 mm eccentricity caused a 19% reduction in load capacity

and a 20 mm eccentricity caused a 36% reduction in capacity.

However, in the tests, a 10 mm eccentricity did not reduce the

failure load below the theoretical buckling capacity.

The second series of tests on walls used 100 3 1.6C sections

with boards on one side only. These tests showed that minor

axis buckling is prevented by fixing to plasterboard for 1.6 mm

thick steel, but the increase in compression resistance relative

to BS 5950-5 was less than for the 75 mm deep sections. This is

attributable to the lower transverse bending stiffness of the

web of the deeper C section, which means that the unsupported

flange is only partially restrained.

6. STRUCTURAL ACTION OF GROUPS OF

MODULES

The structural behaviour of an assembly of modules is complex

because of the influence of the tolerances that are implicit in

the installation procedure, the multiple interconnections

between the modules and the way in which forces are

transferred to the stabilising elements such as vertical bracing

or core walls. The key factors to be taken into account in the

design of high-rise modular buildings are

(a) the influence of initial eccentricities and construction

tolerances on the additional forces and moments in the

walls of the modules

(b) application of the design standard for steelwork, BS 5950-1

to modular technology, using the notional horizontal load

approach

(c) second-order effects due to sway stability of the group of

modules, especially in the design of the corner columns

(d) mechanism of force transfer of horizontal loads to the

stabilising system, for example concrete cores

(e) robustness to accidental actions (also known as structural

integrity) for modular systems.

These aspects are now discussed in turn.

6.1. Influence of constructional tolerances

The National Structural Steelwork Specification for Building

Construction (NSSS) (BCSA, 2007) presents the permitted

tolerances of steel frames, in which the maximum out-of-

verticality of a single column is �H < height/600, but < 5 mm per storey. Furthermore, for steel-framed buildings of more

than ten storeys high, the maximum out of verticality over the

total building height is limited to 50 mm in the NSSS.

BS EN 1090-2 (BSI, 2008) concerns the execution of structures

and in it, the essential tolerances define the maximum

deviations that are permitted so as not to impair the overall

performance of a structure or member. BS EN 1090-2 Table

D.1.12, referring to multi-storey frames, differs from the NSSS

in that the cumulative error over n floors each of height h is

given by h ffiffiffi n

p =300. It follows that the permitted cumulative

deviation over n storeys is 10 ffiffiffi n

p mm (for h ¼ 3 m) to BS EN

1090-2.

These permitted deviations for steel frames may not, however,

reflect the practicalities involved in modular construction

because of the difficulties in precisely positioning one module

on another and in making suitable connections. For a single

module placed on another module, it is proposed that the

maximum out of alignment during installation may be taken as

12 mm in orthogonal plan directions relative to the top of the

module below. This alignment requires careful control on site,

especially in windy conditions.

For a vertical stack of modules, the cumulative positional error,

e, owing to installation can be partially corrected over the

building height. Using the same logic as in BS EN 1090-2, the

cumulative positional tolerance (in millimetres) may be taken

statistically as e < 12 ffiffiffi n

p , where n is the number of modules in

a vertical group. Typically, for n ¼ 10, the total cumulative positional tolerance that is permitted becomes approximately

40 mm, but this neglects the geometric tolerances in the

module manufacture.

An alternative simplified procedure that is easier to control on

site is to limit the cumulative positional tolerance to 5 mm per

module in orthogonal directions with a maximum of 50 mm

(for n ¼ 10), which is similar to the NSSS. However, it is considered that the maximum positional error of one module

on another may be taken as 12 mm (except at ground level

where a maximum of 5 mm should be achievable). This means

that at the first floor, the cumulative tolerance of 10 mm will

control, even if the first-floor module is 12 mm out of position

relative to the base module and the base module is positioned

at < �2 mm from datum.

Added to this positional error is the possibility of a systematic

manufacturing error in the geometry of the modules. For a

single module, the maximum permitted tolerance in geometry

may be taken as illustrated in Figure 13. However, over a large

number of modules, the average error in manufacture may be

taken as half of the permitted tolerance for a single module.

Therefore, the out of verticality of the corner posts may be

taken as h/1000, where h is the module height (typically 3 m).

To take account of manufacturing tolerances, the cumulative

out of verticality over the building height may be taken as

nh/1000, or approximately 3n mm. The total permitted out-

of-verticality �H over the building height, consisting of a stack of n modules vertically, is therefore a combination of

positional and geometric tolerances, approximately as

follows

�H < e þ nh=1000 ¼ 5n þ 3n ¼ 8n mm1

Using this simplified formula, it follows that �H ¼ 80 mm for

Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards 157

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n ¼ 10 storeys, which is equivalent to approximately h/350 per floor. This is 60% higher than the tolerance permitted for

structural steelwork and reflects the different installation and

connection methods between structural frames and a group of

modules.

It is recommended that the absolute out of verticality in

modular construction is limited to a maximum of 80 mm

relative to a ground datum, which will control for buildings of

ten or more storeys. This is achievable with good control on

installation. Adjustments in module position should be made

gradually rather than at a few positions, which would

otherwise add to local eccentricities. These adjustments can be

made by varying the cavity spacing between the modules. In

detailing, the cavity width should be at least equal to half of

the expected maximum tolerance, or as a simple rule, taken as

a minimum of 40 mm.

6.2. Application of notional horizontal forces in modular

construction

A way of assessing the sway stability of a group of modules is

by using the notional horizontal force approach given in clause

2.4.2.3 of BS 5950-1. For steel frames, this horizontal force

corresponds to 0.5% of the factored vertical load acting per

floor, and is used in the absence of wind loading. It represents

the minimum horizontal force that is used to assess the sway

stability of a frame. A further limit for the combination of

wind and vertical load is that the wind load should not be less

than 1% of the factored dead load acting horizontally. This

may control where the self-weight exceeds the imposed loading

on a floor.

BS EN 1993-1-1 Eurocode 3 clause 5.3.2 (BSI, 2004a) permits

an out-of-verticality of L/200 for a single column, but this is

reduced by a factor of 2/3 when considering the average over a

number of storeys (i.e. �H < L/300). The permitted out of verticality of a whole structure is obtained by multiplying this

value for a single column by a factor of f[0:5 [1 þ (1=m)]g0 :5

for m columns in a group horizontally. The result tends to

�H < L/420, which is higher than in the NSSS, but further requirement in the approach of Eurocode 3 is that this out of

verticality is considered in combination with wind loading

rather than as an alternative load case, as in BS 5950-1.

The combined eccentricity on a vertical assembly of modules

takes into account the effects of eccentricities of one module

placed on another, and the reducing compression forces on the

walls acting at the increased eccentricity with height. This effect

is illustrated in Figure 14. The walls of the module are unable to

resist high moments owing to these effects and so the equivalent

horizontal forces required for equilibrium are transferred as

shear forces in the ceiling, floors and end walls of the modules.

The total additional moment acting on the base module is

therefore given by an effective eccentricity ˜eff multiplied by the compression force in the base module, as follows

� h/500

h Bow /1000� hOut of verticality

/500� h

Datum position

Idealised dimensions Actual dimensions of module

Width tolerance

/500� h

Length tolerance /500� h

Figure 13. Permitted maximum geometric errors in manufacture of modules

P � � � � � �

1 2

1000 e h

�P

P

P

P P

P

∆3

∆2

∆1

h

P( 1)/n n�

P( 2)/n n�

P P

e1 M P� e

e3

e2

V

V 1:1000 1:1000

(a) (b)

Figure 14. Combined eccentricities acting on the ground-floor modules: (a) shear in end walls due to eccentric loading for a four-sided module; (b) transfer of eccentric loading to stabilising system for corner-supported modules

158 Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards

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Madd ¼ Pwall˜eff

¼ Pwall (n � 1)

n þ 2

(n � 2) n

þ 3 (n � 3)

n . . . þ

1

n

� �

3 (e þ h=1000)

2

where Pwall is the compression force at the base of the ground-

floor module ¼ nWu, n is the number of modules in a vertical assembly, e is the average positional eccentricity per module, h

is the module height (in mm), and Wu is the factored load

acting on each module.

As a good approximation, it is found that the following

formula holds for the effective eccentricity of the vertical stack

of modules as a function of n:

˜eff ¼ n � 1 6

� � 8n3

The effective base eccentricities are presented in Table 2 for

n ¼ 6 to 12 storeys and for a module height, h ¼ 3 m. This eccentricity may be converted to a notional horizontal force

applied at each floor level, which is expressed as a percentage

of the vertical load acting at each floor level, and is defined as

the force which causes the same equivalent moment in the base

module as the effective eccentricity in Equation 2. This

moment is given by

kWun 2 h=2 ¼ Pwall˜eff ¼ nWu˜eff4

where k is the proportion of the factored load acting on each

floor, and so

k ¼ 8(n � 1) 3h

� � or

n � 1 3n

� � 80

h

� � for n . 105

From Table 2, and using the tolerances defined above, it is

calculated that the notional horizontal force varies from 0.5% to

0.9%, when expressed as a percentage of the vertical load

applied to the module. It should be noted that k ¼ 0.5%, when the maximum tolerance is 50 mm, which agrees with BS 5950-1.

For modular construction, it is therefore recommended that the

notional horizontal force is taken as a minimum of 1% of the

factored vertical load acting on each module, which reflects the

higher tolerances that are permitted in modular construction. It

is used as the minimum horizontal load in assessing overall

sway stability of the structure, and it is proposed that it is used

in combination with wind forces.

As an example, for a module of 25 m2 floor area subject to

factored loading of 7 kN/m2, the notional horizontal force

acting in orthogonal directions is approximately 2 kN. For a

vertical stack of ten modules, the base shear is therefore 20 kN.

This shear force may be shared between the two walls of the

module in the direction under consideration. The notional force

may be compared with a wind load of up to 10 times this

magnitude acting as a shear on the longitudinal side façade of

the building, and so is still relatively small. The notional

horizontal force may, however, control when there are less

than 10 modules in a horizontal group.

If the modules are unable to resist the horizontal force required

for overall stability, the forces must be combined for a number

of modules on plan at each level and transferred to the

stabilising system. This may be the case for partially open-

sided modules.

6.3. Forces at module interconnections

The structural interactions within a group of modules are

complex. Horizontal forces may be transferred by tension and

compression forces in the ties at the corners of the modules by

utilising the diaphragm action of the base and ceiling of the

modules. Shear forces may be transferred through the

continuous corridor members rather than the corner

connections because of the potential articulation through the

bolts and connecting plates between the modules. These actions

are illustrated in Figure 15.

Where the corridor floor is used to transfer shear forces, the

connection of the modules to the corridor may be made by a

detail of the form of Figure 16. The extended plate is screw

fixed on site to the corridor members and is bolted to the re-

entrant corners between the modules so that it also acts as a tie

plate. This detail is not used to provide vertical support to the

corridor floor, which is supported on continuous angles

attached to corridor wall of the modules.

The forces in the tie connection in Figure 16 may be calculated

on the basis of the wind forces acting on the module. The

highest force occurs for an external pressure coefficient of

+0.85 and a negative internal pressure of �0.3. The wind force on one module is divided between two module-to-corridor

connections. For a wind pressure of 1.2 kN/m2, the force in this

connection is approximately 8 kN at working loads.

The shear attachment to the core is made both through the

corridor and also at the module adjacent to the core. This

Number of modules

Approx. building height: m

Cumulative out-of-verticality at top of building: mm

Effective eccentricity on base module – Simplified formula in

Equation 3: mm

Notional horizontal force Equation 5: %

n ¼ 6 16 48 5/6 3 48 ¼ 40 0.5 n ¼ 8 22 64 7/6 3 64 ¼ 75 0.7 n ¼ 10 27 80 9/6 3 80 ¼ 120 0.9 n ¼ 12 33 80 11/6 3 80 ¼ 147 0.9

Table 2. Summary of effective eccentricities and notional horizontal forces in modular construction as a function of building height

Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards 159

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connection force at the core is designed for the aggregate of

the module–corridor connection forces, which for a group of

three to four modules is 24 to 32 kN (factored loading ) or 18

to 24 kN as a working load.

6.4. Stability of corner posts in modular construction

Corner posts add to the compressive resistance of a wall and, if

they are included in the module, it is normal practice to

assume that all the applied vertical loads acting on the module

are resisted by the corner posts. These posts are usually in the

form of steel angle sections for low-rise applications, or SHSs

for taller buildings. The posts are effectively restrained from

buckling by the in-plane stiffness of the walls of the modules

to which they are connected, but this assumption may not be

valid for partially open-sided modules or for highly perforated

walls.

Consider the stability of the corner posts of a module when

restrained only by the in-plane stiffness of the walls of the

module, as illustrated in Figure 17. The posts are discontinuous

at the module–module connections and do not contribute to

the sway stiffness of the structure, but are restrained against

buckling in their height between the connection points.

The initial out of verticality of the corner post increases under

an axial load, P, in each post, which may be approximated by

strut buckling theory, according to

� ¼ �o

1 � 2P=Pcritð Þ 6

where P is the axial compression acting on one post; �o is the initial out of verticality and eccentricity of the corner post; Pcrit is the critical buckling resistance for sway stability of the

module.

From this simple shear failure mechanism, the work done in

Module

(a)

θ Tie

L

B

Tie in corridor

(b)

Forces in ties

Module

Figure 15. Force transfer between modules: (a) force transfer at corridor – bending action; (b) force transfer at corridor – pure shear

80

7030 gap

Bolt hole

Upper module

Lower module

(a)

(b)

Figure 16. Connection detail between the corridor cassette and modules: (a) sketch detail; (b) actual detail

160 Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards

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shear and compression may be equated, in order to determine

the critical buckling load, Pcrit, as follows

k˜2

2 ¼

2Pcritð Þ˜2 2h

or Pcrit ¼ 0:5kh7

where k is the shear stiffness of the wall panel.

As P approaches Pcrit, so the shear deflection of the wall panel

increases rapidly. Therefore, it is necessary to keep P well

below Pcrit to avoid instability effects. The eccentricity of load

causes both bending in the post and shear in the wall panel.

The shear stiffness of the wall can be estimated from shear

diaphragm tests and corresponds to the horizontal load at a

serviceability deflection of h/500, where h is the module height

in millimetres. This is achieved for a shear force of typically

(a) 10 kN for a 2.4 m wide wall panel with a window, or

approximately 4 kN/m width

(b) 20 kN for a 2.4 m wide unperforated panel, or

approximately 8 kN/m width.

In the case of a module with h ¼ 3 m and width of b ¼ 3.6 m, it follows that the typical shear stiffness of an end wall panel

with a window becomes

k ¼ 4 3 3:6 3 500

3:0 ¼ 2400 kN=m

Inserting this value of k in Equation 7 leads to a critical

buckling load owing to shear in the end wall of a module of

Pcrit ¼ 0:5 3 2400 3 3 ¼ 3600 kN

To check the stability of the corner post, it is recommended

that the eccentricity in load application is taken as the

maximum positional eccentricity of 12 mm when one module

is placed on another plus the maximum out of verticality in

manufacture of a single module (or h/500, as shown in Figure

13). For a 3 m high module, �o ¼ 12 + 6 ¼ 18 mm. These eccentricities are illustrated in Figure 18.

In addition, a local moment is transferred from the floor or

edge beam, which may act in the same sense as the positional

eccentricity. For a floor–wall junction, this shear load may be

assumed to act at the face of the wall studs (or a minimum of

50 mm). For a corner post, the shear load acts at the centre of

the bolt group, and a minimum eccentricity of 75 mm from the

centre of the post may be used. This local moment acts only on

individual modules and is not cumulative.

The additional moment acting on a corner post is calculated

from M ¼ P�, where � is given by Equation 6. For a wall, the effective eccentricity also includes the bow in the wall between

the corners (or h/1000, as shown in Figure 14).

For a corner post, the effective eccentricity is therefore given

by �o ¼ 18 + 75/n mm. For a load-bearing wall, the effective eccentricity is given by �o ¼ 21 + 50/n mm. For n ¼ 10, the effective eccentricities become approximately 25 mm in both

cases.

The stability of a corner post is then checked as

P=Pc þ M=Mc < 1:08

where P is the load acting at the top of the base module and Pc is the compression resistance of the post.

When the post is restrained against buckling in its height by

attachment to the adjacent walls, then the bending resistance

may be taken as Mc ¼ Mel, where Mel is the elastic bending resistance of the post. Elastic properties should be used in order

to take account of uncertainties in this simple linear interaction

method in Equation 8.

For an unsupported post (not restrained by the walls), the

compression resistance is given by Pc ¼ pcA, where pc is calculated from the minor axis slenderness of the post and Mc

B

P P

H

2P

∆ K

φ

Figure 17. Sway stability of the wall of a module for corner posts in compression

Pmax ( 1)n �

nPmax ( 1)n �

n

Wall of module

Floor

Floor

φ 0·002�

� /500h

Ceiling

Mfloor

Pmax Pmax b

w

h

Mfloor � 0·25 wbd

d

e

Figure 18. Illustration of eccentricity of forces applied to the walls or corner posts of a module

Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards 161

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is the bending resistance for lateral torsional buckling. The

interaction equation is also modified to take into account

bending in two directions, as in BS 5950-1.

As an example for a 7.2 m long 3 3.6 m wide module, with a

factored floor load of 7 kN/m2, the compression force acting at

the top corner of the ground-floor module in a 12-storey

building is approximately

P ¼ 7 3 7:2 3 3:6 3 (12 � 1)=4 ¼ 499 kN

Check the compression resistance of the corner posts using

100 3 100 3 10 SHS (in S355 steel), which are stabilised by

the walls of the modules: crushing resistance, Py ¼ 1239 kN, and bending resistance, Mel ¼ 32.8 kN m.

The out-of-plane displacement and its associated moment, M,

are obtained from Equation 6

�o ¼ 18 þ 75=n ¼ 25 mm

� ¼ 25

1 � 2 3 499=3600ð Þ ¼ 34 mm

M ¼ 499 3 0:034 ¼ 17:0 kN m

Using the linear combination of axial force and moment for

member stability

P=Pc þ M=Mel ¼ 499=1239 þ 17:0=32:8

¼ 0:40 þ 0:52 ¼ 0:92 , 1:0

It follows that the effect of eccentricity in installation and out

of verticality in manufacture is to reduce the compressive

resistance of a corner post by about 60%. It is also

recommended that for simple design, the effective eccentricity

of load acting on the corner post is taken as not less than

35 mm, which allows for a 40% magnification in sway from

the initial eccentricity of 25 mm.

6.5. Robustness to accidental damage

The ability of an assembly of modules to resist applied loads in

the event of serious damage to a module at a lower level is

dependent on the development of tie forces at the corners of

the modules. The loading at this so-called accidental limit state

is taken as the self-weight plus one third of the imposed load

all multiplied by a partial factor of safety of 1.05 to BS 5950-1.

To satisfy ‘robustness’ in the event of accidental damage to one

of the modules, the tie forces between the adjacent modules

may be established on the basis of a cantilever model, as

presented in a recent paper (Lawson et al., 2008). Assuming

that the worst case corresponds to loss of support to one side of

a corner module and that each module above is able to develop

tying forces equally, the tension force in the ties is given as

follows

T ¼ Wab

4h

� � 9

where Wa is the load acting on the module at the accidental

limit state, and b and h are the dimensions of narrow end of

the module.

Figure 19 shows the results of a finite-element analysis of a

module when one corner support is removed, which is a more

likely case than complete removal of one side wall. The applied

load is taken as 10 kN/m per wall for a heavyweight module

using the partial factors noted above. Torsional stiffness of the

module is developed by diaphragm action of the walls and

floor/ceiling. From this analysis, the maximum horizontal tying

force is equal to 26% of the total load applied to the module

(rather than 48% in the cantilever formula) and the maximum

vertical load is approximately 40% of the total load. It is

concluded that the minimum values of the horizontal tying

force, T, may be taken as 30 kN for lightweight modules (self-

weight , 3.5 kN/m2) or 50 kN for heavyweight modules (self-

weight , 6 kN/m2).

6.6. Module connection tests

As part of the development programme for the modular

supplier, tests on complete modules were carried out at the BRE

to assess the tensile resistance of the tie detail between the

corridor cassette and the corner of the module. The tie

connection is made at the re-entrant corner of the module.

The module was held in place at two corners and a tensile force

was applied at the top opposite corner causing pull-out of the

connecting bolt to the 4 mm thick corner angle manufactured

as part of the module. Forces within the module are transferred

by way of in-plane diaphragm action of the ceiling and walls.

A rigid corner gusset plate was attached across the junction

between the bottom track and the end wall stud, and the

tension force reached of 40 kN at failure corresponding to a

displacement of 10 mm. The gusset detail at a load level of

25 kN is shown in Figure 20. The load–deflection graph for

this test is shown in Figure 21.

27 kN

5 kN

1 kN

56 kN

27 kN

5 kN

1 kN

38 kN

38 kN 50 kN

38 kN

3·6 m

2·7 m

10 kN/m

10 kN/m

Deflected shape

7·2 m

32 mm vertically

Figure 19. Illustration of tie forces when support to one corner of a module is removed

162 Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards

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The test using a stiffening plate at the corner of the module

showed that this arrangement offers the best solution for the

module-to-corridor connection. The characteristic resistance of

this connection is taken as 20% less than the failure load of a

single test, or 0.8 3 40 ¼ 36 kN, which exceeds the calculated load of 24 kN for transfer of wind forces across three modules

to an adjacent core.

7. CONCLUSIONS

This paper presents the results of tests on light steel walls in

compression, which are used to demonstrate the extension of

modular construction up to 12 storeys high. The tests showed

that the stiffening effect of the fascia boards is very high and

that the compression resistance of the C sections is increased in

comparison to the bare steel section. These conclusions refer to

internal wall heights of 2.3 to 2.8 m using 75 mm to 100 mm

deep C sections.

(a) Minor axis buckling is effectively prevented by attachment

of various types of boards on one side only, provided the

steel thickness is not less than 1.6 mm.

(b) The test load capacities exceeded the design resistance to

BS 5950-5 by 10 to 40% due to the stiffening effects of the

attached boards.

(c) The effective bending stiffness of the bare steel sections is

increased by up to 62% due to the attachment of OSB and

CPB boards on both sides.

(d) The effect of 10 mm out-of-plane eccentricity in load

application reduces the failure load by 19%, and the effect

of 20 mm out-of-plane eccentricity accentuates local

crushing and reduces the failure load by 18 to 36%.

The tests on the module-to-module connections showed that a

tying force of 40 kN can be resisted. For robustness to

accidental actions, the minimum tying force between modules

should be taken as 30 kN for lightweight modules (self-weight

, 3.5 kN/m2) and 50 kN for heavyweight modules.

The effect of installation and geometric inaccuracies must be

taken into account in the design of modular buildings. It is

proposed that the maximum positional error is 12 mm for one

module placed on another. When combined with

manufacturing tolerances, it is proposed that the maximum out

of verticality should not exceed 8 mm per module in a vertical

group (or an absolute maximum of 80 mm) relative to ground

datum. Using these tolerances, the notional horizontal force

used to evaluate stability of a group of modules should be

taken as a minimum of 1% of the applied vertical load on the

modules, which acts in combination with wind loading but at

reduced load factors.

For modules designed with corner posts, it is shown that an

additional effect owing to the shear flexibility of the end walls

has to be taken into account when calculating the moments

acting on the posts due to sway effects. The minimum

eccentricity for design of the corner posts should not be less

than 35 mm taking account of second-order effects, and the

minimum eccentricity for design of load-bearing side walls

should not be less than 25 mm.

ACKNOWLEDGEMENTS

The structural testing at the Building Research Establishment

was funded by Unite Modular Systems Ltd as part of their

development strategy. The contribution of Dave Brooke and the

team in the Heavy Structures Lab at BRE is gratefully

acknowledged. Additional wall tests at the University of Surrey

were funded by Metek UK Ltd.

REFERENCES

BCSA (British Constructional Steelwork Association) (2007)

National Structural Steelwork Specification for Building

Construction, 5th edn. BCSA, London.

BSI (British Standards Institution) (1998) Structural Use of

Steelwork in Building. Code of Practice for Design of Cold

Formed Thin Gauge Sections. BSI, London, BS 5950: Part 5.

BSI (2000) Structural Use of Steelwork in Building. Code of

Figure 20. Tensile test on module with stiffening plate

�10·00

0·00

10·00

20·00

30·00

40·00

50·00

�5 0 5 10 15 20 25 30 Deflection mm

L o a d : kN

Figure 21. Load–displacement results for module test with stiffening plate. Unite module corner test 7

Structures and Buildings 163 Issue SB3 Modular design for high-rise buildings Lawson • Richards 163

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Practice for Design of Simple and Continuous Construction:

Hot Rolled Sections. BSI, London, BS 5950 Part 1.

BSI (2004a) Eurocode 3: Steel Structures – General Rules and

Rules for Buildings. BSI, London, BS EN 1993-1-1.

BSI (2004b) Specification For Continuously Hot-dip Zinc Coated

Structural Steel and Strip – Technical Delivery Conditions.

BSI, London.

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Structures. Part 2 Technical Requirements for Execution of

Steel Structures. BSI, London, BS EN 1090-2.

Cartz JP and Crosby M (2007) Building high-rise modular

homes. The Structural Engineer 85(l9): 20–21.

HMSO (2006) England and Wales Approved Document A.

HMSO, London

Lawson RM (2007) Building design using modules. The Steel

Construction Institute, London, Publication 348.

Lawson RM, Ogden RG, Pedreschi R, Popo-Ola S and Grubb J

(2005) Developments in pre-fabricated systems in light steel

and modular construction. The Structural Engineer 83(6):

28–35.

Lawson RM, Byfield M, Popo-Ola S and Grubb J (2008)

Robustness of light steel frames and modular construction.

Proceedings of the Institution of Civil Engineers, Buildings

and Structures 161(1): 3–16.

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