Performance of ceiling diaphragms in steel-framed domestic ... · plane behaviour of cold-formed steel-framed wall panels sheathed with fibre cement board”, Proceedings of the 22nd

Performance of Ceiling Diaphragms in Steel-Framed

Domestic Structures Subjected to Wind Loading

Ismail Saifullah

A thesis submitted in total fulfilment of the requirements of the degree of

Doctor of Philosophy

March 2016

Faculty of Science, Engineering and Technology

Swinburne University of Technology

Hawthorn, Victoria 3122

To My Parents

who trained me diligence in difficult situations

&

My Wife

who stood by me all the way throughout this journey

i

Abstract

In Australia, houses are typically one and two storey light framed structures and often

referred to as domestic structures. They are typically comprised of timber or steel

structural framing with plasterboard lining for the walls and ceilings, and brick veneer

exterior cladding. The roof cladding is either tiles or steel sheeting. The focus of this

research is on houses built with cold-formed steel frames. This research is a part of a

sustained research effort to make houses more affordable and safer. In particular it aims

to better understand the properties of the ceiling diaphragm to resist lateral loads.

The lateral loads generated due to wind and earthquake loads need to be transmitted to

the foundation through the structures. The ceiling and roof diaphragms play an

important role to distribute the lateral loads to the bracing walls. The International

Building Code (IBC, 2006) classifies diaphragms as either flexible or rigid depending

on the relative stiffness of the diaphragm to the walls. However, in Australian design

standards, there is no reference to the rigidity of the ceiling or roof diaphragms.

Therefore, rational assessment of the stiffness and strength of the horizontal diaphragms

is necessary to correctly design the lateral load resisting system.

The research presented in this thesis is focused on typical ceiling diaphragms found in

Australian houses. Such diaphragms are made of standard core plasterboard which is

screwed to ceiling battens which are in turn screwed to the bottom chord of the roof

trusses. In order to determine the strength and stiffness of such diaphragms both

experimental and analytical works were completed. The experimental work was

involved testing of full scale segments of diaphragms in different configurations.

Furthermore, testing of screw connections between the plasterboard and steel ceiling

batten was undertaken. These connections essentially transfer the in-plane shear load

between the plasterboard and ceiling framing.

Based on the experimental program it was found that testing of diaphragms in beam

configuration provides more realistic behaviour compared to the simpler cantilever

configuration. Indeed, such diaphragms can be represented by deep beams whose

behaviour is dominated by shear. Furthermore, the full scale testing of diaphragms

provided clear understanding of the failure modes and influence of boundary conditions

such as end walls on the overall performance. In all tests, the ultimate capacity of the

ii

diaphragms was limited by the failure of the connections between the plasterboard and

the ceiling battens. All the tests were undertaken under monotonic loading using

specially developed test rigs.

Detailed finite element (FE) modelling was undertaken to represent the behaviour and

ultimate capacity of ceiling diaphragms. The developed FE models included the

plasterboard, battens, truss bottom chords and associated connections. All the material

properties used were based on published data. The connections between the battens and

the bottom chords were considered to be pinned, while the connections between the

plasterboard and the battens were represented by non-linear springs whose properties

were obtained from the completed tests.

Remarkable agreement was achieved between the FE models and experimental results

for all ceiling specimens tested. The load-deflection curves, deformed shapes and failure

modes matched very well. Hence, the developed FE modelling technique was deemed

appropriate based on these validations.

The validated FE models were used to undertake a parametric study to cover a range of

typical diaphragm configurations and properties. These parameters included: diaphragm

aspect ratio; batten spacing; bottom chord spacing; different plasterboard to framing

connection patterns and strength; and different boundary conditions around the

plasterboard edges.

Based on the parametric studies it was found that the lateral performance of the

diaphragm can be increased with the addition of a limited number of extra screws. The

strength and stiffness of the diaphragm also increased considerably with the reduction

of the batten spacing. Moreover, longer ceilings (those with high aspect ratios) exhibit

greater flexural deformation and hence, failure occurred at a larger deflection compared

to shorter ceilings which have their deflection dominated by shear action. There was no

significant variation of strength due to changes of length.

A simplified mathematical model was developed for determining the deflection; and

hence, the stiffness of typical steel framed ceiling diaphragms used in Australia. This

model was verified against the experimental results as well as the FE model results.

Based on strength and serviceability limit states, a typical example for the development

of a design chart for maximum spacing between bracing walls is presented.

iii

Declaration

This is to certify that this thesis includes:

Contains no material which has been accepted for the award to the candidate of

any other degree or diploma, except where due reference is made in the text of

the examinable outcome;

To the best of the my knowledge, it contains no material previously published or

written by another person except where due reference is made in the text of the

examinable outcome; and

Where the work is based on joint research or publications, discloses the relative

contributions of the respective workers or authors.

Sincerely Yours

Ismail Saifullah

March 2016

iv

Preface

The following publications have been produced:

Saifullah, I., Gad, E., Shahi, R., Wilson, J., Lam N.T.K. and Watson K. (2014),

‘Ceiling diaphragm actions in cold formed steel-framed domestic structures’,

ASEC 2014-Structural Engineering in Australasia-World Standard, July 9-11,

Auckland, New Zealand.

Saifullah I., Gad E., Wilson J., Lam N.T.K. and Watson K. (2012), ‘Review of

diaphragm actions in domestic structures’, Australasian Conference on the

Mechanics of Structures and Materials, December 11-14, Sydney, Australia

Publications from second components of the entire research project:

Shahi, R., Lam, N., Saifullah, I., Gad, E., Wilson, J. and Watson, K. (2014),

‘Application of a new racking cyclic loading protocol on cold-formed steel-

framed wall panels’, Proceedings of the Structural Engineering in Australasia

ASEC 2014 Conference, Auckland, New Zealand, Paper No. 21.

Shahi, R., Lam, N., Saifullah, I., Gad, E., Wilson, J. and Watson, K. (2014), “In-

plane behaviour of cold-formed steel-framed wall panels sheathed with fibre

cement board”, Proceedings of the 22nd International Specialty Conference on

Cold-Formed Steel Structures, St. Louis, Missouri, USA, pp. 809-823. (This

paper had received a Wei-Wen Yu Student Scholar Award provided by the Wei-

Wen Yu Center for Cold-Formed Steel Structures)

Shahi, R., Lam, N., Gad, E., Saifullah, I., Wilson, J. and Watson, K. (2014),

“Incremental dynamic analysis for seismic assessment of cold-formed steel-

framed shear wall panel”, Proceedings of the Australian Earthquake

Engineering Society 2014 Conference, Victoria, Australia, Paper No. 31.

Shahi, R., Lam, N., Saifullah, I., Gad, E. and Wilson, J. (2013), “Realistic

modelling of cold-formed steel in domestic constructions for performance based

design”, Proceedings of the Australian Earthquake Engineering Society 2013

Conference, Tasmania, Australia, Paper No. 06.

http://acmsm.org/

http://acmsm.org/

v

Acknowledgements

It is a great pleasure to acknowledge my principal supervisors, Professor Emad Gad,

Chair, Department of Civil and Construction Engineering, Swinburne University of

Technology, Australia. Without his continuous advice, valuable guidance, consistent

encouragement, extra financial support and friendly discussions throughout my

research, my research would never have concluded. The continuous support and help

from my supervisor both technically and theoretically, particularly, experimental tests

and finite element modelling provide me the motivation to be continuously engaged in

my research despite of having several difficulties throughout the study.

I would like to express my profound gratitude to my co-supervisor Professor John

Wilson of Swinburne University of Technology, and Associate Professor Nelson Lam,

of the University of Melbourne for their valuable suggestions and encouragement. The

work described in this research is supported by the Australian Research Council (ARC)

Linkage Grant LP110100430. I would also like to thank the members of the project

team, Mr. Ken Watson and Les McGrath of the National Association of Steel-framed

Housing (NASH) for their input into this research. I am indebted to John Shayler,

Business Development Manager at Steel Frame Solutions who supplied test materials

used for the experimental work. The financial and technical support provided by NASH

members is also gratefully acknowledged. The contributions of NASH members who

supplied the materials are acknowledged.

I owe special thanks to the Smart Structures Laboratory Staff, Mr. Kia Rasekhi, Mr.

Graeme Burnett, Mr. Sanjeet Chandra, and Mr. Michael Culton who always assisted in

various ways while working in the laboratory. I would like to express a special thanks to

Mr. Rojit Shahi, my PhD colleague, who is also studying the lateral performance of

cold-formed steel-framed domestic structures at the University of Melbourne, for his

willingness to assist in every possible way.

My sincere love and deepest gratitude are to my beloved parents, brothers and sisters for

their unconditional love and continuous encouragement throughout the study. I would

like to express my gratitude to my wife for her support and patience throughout the

course of my study.

Finally, my greatest thank to the Almighty who has been always looking after me.

vi

Table of Contents

Abstract .............................................................................................................................. i

Declaration ....................................................................................................................... iii

Preface .............................................................................................................................. iv

Acknowledgements ........................................................................................................... v

List of Figures ................................................................................................................ xiv

List of Tables................................................................................................................. xxv

CHAPTER 1 ..................................................................................................................... 1

INTRODUCTION ............................................................................................................ 1

1.1 Background of the Research ............................................................................... 1

1.2 Research Aim and Objectives ............................................................................ 5

1.3 Outline of Thesis ................................................................................................ 6

CHAPTER 2 ..................................................................................................................... 8

LITERATURE REVIEW.................................................................................................. 8

2.1 Introduction ............................................................................................................. 8

2.2 Background on Cold-formed Steel .......................................................................... 8

2.3 Current Design Practices in Australia ................................................................... 10

2.4 Components of Steel-framed Domestic Structures ............................................... 11

2.4.1 Floor ................................................................................................................ 12

2.4.2 Walls ............................................................................................................... 12

2.4.3 Roof ................................................................................................................ 13

2.5 Behaviour of Light-framed Structures................................................................... 14

2.6 Diaphragm Analysis .............................................................................................. 22

vii

2.6.1 Diaphragm Stiffness ....................................................................................... 23

2.6.2 Diaphragm Classifications .............................................................................. 24

2.6.3 Continuous Diaphragms ................................................................................. 28

2.7 Bracing System of Diaphragm .............................................................................. 30

2.7.1 Roof Bracing ................................................................................................... 30

2.7.2 Wall Bracing ................................................................................................... 31

2.7.3 Floor and Subfloor Bracing ............................................................................ 31

2.7.4 Combination of Bracing Systems ................................................................... 32

2.7.5 Typical Location and Distribution of Bracing Walls ...................................... 33

2.8 Lateral Force Distribution Methods for Light-framed Structures ......................... 35

2.8.1 Tributary Area Method ................................................................................... 36

2.8.2 Simple and/or Continuous Beam Methods ..................................................... 37

2.8.3 Total Shear Method ........................................................................................ 38

2.8.4 Relative Stiffness Method without Torsion .................................................... 39

2.8.5 Rigid Beam on Elastic Foundation/ Relative Stiffness with Torsion ............. 39

2.8.6 Plate Method ................................................................................................... 41

2.8.7 Finite Element Method ................................................................................... 41

2.9 Performance of Light-framed Structures under Lateral Loads ............................. 41

2.10 Experimental Studies of Light-framed Structures ............................................... 43

2.10.1 Full-scale Structures ..................................................................................... 44

2.10.2 Roof and Ceiling Diaphragm ........................................................................ 47

2.11 Analytical Modelling ........................................................................................... 49

2.11.1 Full-scale Structures Modelling .................................................................... 50

viii

2.11.2 Ceiling and Roof diaphragm ......................................................................... 51

2.12 Summary and Research Needs ............................................................................ 52

CHAPTER 3 ................................................................................................................... 54

EXPERIMENTAL PROGRAM (PHASE I): SHEAR CONNECTION TESTS ............ 54

3.1 Introduction ........................................................................................................... 54

3.2 Overview of Experimental Program ...................................................................... 55

3.3 Test Methodology .................................................................................................. 56

3.3.1 Test Materials ................................................................................................. 61

3.3.2 Specimen Configurations and Fabrication ...................................................... 62

3.3.3 Test Equipment ............................................................................................... 65

3.3.4 Instrumentation ............................................................................................... 65

3.3.5 Loading ........................................................................................................... 68

3.4 Results and Discussion .......................................................................................... 68

3.4.1 Failure Mechanisms ........................................................................................ 73

3.4.2 Effect of Edge Distance .................................................................................. 76

3.4.3 Effect of Section Thickness ............................................................................ 79

3.4.4 Idealization of Load-Slip Behaviour for Sheathing-to-framing Connection .. 79

3.5 Summary and Conclusions .................................................................................... 81

CHAPTER 4 ................................................................................................................... 82

EXPERIMENTAL PROGRAM (PHASE II): FULL-SCALE TESTING OF CEILING

DIAPHRAGM IN CANTILEVER CONFIGURATION ............................................... 82

4.1 Introduction ........................................................................................................... 82

4.2 Experimental Arrangement ................................................................................... 82

ix

4.3 Testing Program .................................................................................................... 84

4.3.1 Test Set up ...................................................................................................... 84

4.3.2 Test Specimen ................................................................................................. 86

4.3.3 Instrumentation and Data Acquisition System ............................................... 91

4.3.4 Loading ........................................................................................................... 92

4.4 Results and Discussions ........................................................................................ 92

4.4.1 Loading Frame Friction .................................................................................. 92

4.4.2 Discussion of Test Results .............................................................................. 93

4.4.3 Estimation of Design Strength ...................................................................... 103

4.5 Summary and Conclusions .................................................................................. 104

CHAPTER 5 ................................................................................................................. 106

EXPERIMENTAL PROGRAM (PHASE III): FULL-SCALE TESTING OF CEILING

DIAPHRAGM IN BEAM CONFIGURATION ........................................................... 106

5.1 Introduction ......................................................................................................... 106

5.2 Scope of Testing .................................................................................................. 106

5.3 Testing Arrangement ........................................................................................... 107

5.4 Instrumentation and Loading ............................................................................... 115

5.5 Description of Tests ............................................................................................. 116

5.5.1 Beam Test Specimen #1 (5.4 m x 2.4 m diaphragm with 600 mm batten

spacing) .................................................................................................................. 116


spacing and effects of plasterboard bearing) ......................................................... 119



x


spacing) .................................................................................................................. 124



5.6 Results and Discussion ........................................................................................ 129

5.6.1 Frame Test .................................................................................................... 129


spacing) .................................................................................................................. 130






spacing) .................................................................................................................. 139



5.7 Load-deflection Behaviour of Tested Diaphragm ............................................... 147

5.7.1 Diaphragm Behaviour in Region I (linear portion of the curve) .................. 147

5.7.2 Diaphragm Behaviour in Region II (transition portion of the curve) ........... 148

5.7.3 Diaphragm Behaviour in Region III (inelastic portion of the curve) ........... 149


CHAPTER 6 ................................................................................................................. 152

ANALYTICAL MODELLING .................................................................................... 152

6.1 Introduction ......................................................................................................... 152

6.2 Finite Element Modelling Software .................................................................... 152

xi

6.3 Finite Element Modelling Strategy ..................................................................... 153

6.3.1 Representation of Structural Components .................................................... 153

6.3.2 Material and Sectional Properties ................................................................. 154

6.3.3 Plasterboard Screw Connections .................................................................. 155

6.3.4 Boundary Conditions .................................................................................... 156

6.4 Model Validation against Test Results ................................................................ 158

6.4.1 Validation of Model against Cantilever Test Results ................................... 158

6.4.2 Validation of FE Model against Beam Test Results ..................................... 160

6.4.2.1 Validation of Beam Test Specimen #1................................................... 161





6.5 Finite Element Modelling under Different Loading Configurations ................... 173

6.6 Parametric Studies ............................................................................................... 174

6.6.1 Investigation 1: Ceiling Diaphragms with Boundary Conditions ................. 174

6.6.1.1 Aspect ratio ............................................................................................ 174

6.6.1.2 Spacing of Plasterboard Screws ............................................................. 180

6.6.1.3 Gap Size ................................................................................................. 187

6.6.1.4 Batten Spacing ....................................................................................... 189

6.6.2 Investigation 2: Sensitivity of Isolated Ceiling Diaphragms ........................ 191

6.6.2.1 Aspect ratio ............................................................................................ 191

6.6.2.2 Spacing of Plasterboard Screws ............................................................. 195

6.6.2.3 Batten Spacing ....................................................................................... 201

6.6.2.4 Bottom Chord Spacing ........................................................................... 203

xii

6.6.3 Investigation 3: Sensitivity of Isolated Ceiling Diaphragms with Different

Structural Arrangements ........................................................................................ 204

6.6.3.1 Loading Directions ................................................................................. 205

6.6.3.2 Type of Testing Assembly ..................................................................... 206

6.6.3.3 Plasterboard Fixing to Different Structural Members ............................ 207

6.6.3.4 Properties of Plasterboard Screws .......................................................... 209


CHAPTER 7 ................................................................................................................. 215

LATERAL LOAD DISTRIBUTION AND INDUSTRIAL APPLICATIONS ........... 215

7.1 Introduction ......................................................................................................... 215

7.2 Simplified Mathematical Model to Predict Diaphragm Deflections ................... 215

7.2.1 Estimation of Deflection Equation Parameters under One-third Loading .... 219

7.2.2 Simplified Mathematical Model Validation against Test Results ................ 225

7.2.3 Simplified Mathematical Model Modification to Replicate Wind Load ...... 226

7.2.4 Sample Calculation of Diaphragm Deflection using Simplified Mathematical

Model ..................................................................................................................... 228

7.2.5 Simplified Mathematical Model Validation against Finite Element Model

Results .................................................................................................................... 230

7.3 Approximate FE model for diaphragm deflection............................................... 231

7.3.1 Deep Beam Model ........................................................................................ 231

7.3.2 Plate Element Model ..................................................................................... 233

7.4 Case study ............................................................................................................ 234

7.4.1 Maximum bracing wall spacing .................................................................... 236

7.4.2 Method 1: Total shear ................................................................................... 236

xiii

7.4.3 Method 2: Deep beam method ...................................................................... 237

7.4.4 Method 3: Plate method ................................................................................ 240

7.4.5 Diaphragm load distribution ......................................................................... 244

7.5 Design Charts for Industrial Applications ........................................................... 245


CHAPTER 8 ................................................................................................................. 250

CONCLUSIONS AND RECOMMENDATIONS ....................................................... 250

8.1 Conclusions ......................................................................................................... 250

8.2 Recommendations for Future Research .............................................................. 256

References ..................................................................................................................... 257

xiv

List of Figures

Figure 1.1: A photograph of light-framed cold-formed steel house construction in

Australia ............................................................................................................................ 2

Figure 1.2: A photo of completed residential structures made of cold formed steel in

Australia ............................................................................................................................ 2

Figure 2.1: Cold-formed steel sections used for structural framing (NASH, 2014) ......... 9

Figure 2.2: Various truss cross sections (NASH, 2009) ................................................... 9

Figure 2.3: Typical framing of steel-framed structures (NASH, 2014) .......................... 12

Figure 2.4: Typical wall framing system (NASH, 2009) ................................................ 13

Figure 2.5: Typical truss roof system (NASH, 2009) ..................................................... 14

Figure 2.6: Factors affecting strength and stiffness of ceiling diaphragms .................... 15

Figure 2.7: Factors affecting strength and stiffness of roof diaphragms ........................ 16

Figure 2.8: Transfer of racking load from ceiling and roof diaphragm to walls via the

cornice (Golledge et al., 1990) ........................................................................................ 20

Figure 2.9: Arrangement of wind forces on the surface of single storey building.......... 23

Figure 2.10: Determination of diaphragm flexibility (Florida Building Code

Commentary, 2007)......................................................................................................... 25

Figure 2.11: Schematic representation of rigid and flexible diaphragm ......................... 26

Figure 2.12: Ceiling diaphragm actions in two extreme conditions ............................... 27

Figure 2.13: Configurations of simplified continuous diaphragms ................................ 29

Figure 2.14: Various bracing systems (NASH, 2009) .................................................... 30

Figure 2.15: Illustration of the importance of deformation compatibility or ductility in

assessing the cumulative effects of different bracing types (NASH, 2009) ................... 32

Figure 2.16: Typical location and distribution of bracing walls ..................................... 34

xv

Figure 2.17: Plan view of various load distribution methods (Kasal et. al. 2004) .......... 36

Figure 3.1: Summary of the experimental testing of this study ..................................... 55

Figure 3.2: Test arrangement for lateral resistance of screws (ASTM D1761-12) ......... 57

Figure 3.3: Field shear connection test set-up to replicate connection with top-hat

section member (dimensions are in mm) ........................................................................ 58

Figure 3.4: Edge shear connection test set-up to replicate connection with top-hat


Figure 3.5: Field shear connection test setup to replicate connection with channel


Figure 3.6: Edge shear connection test setup to replicate connection with channel

section steel member (here Y designates edge distance 15 mm, 17 mm and 20 mm)

(dimensions are in mm) ................................................................................................... 61

Figure 3.7: Specimens of shear connections constructed by the author (a) field screw

connection specimens for top-hat sections, (b) edge screw connection specimens for

top- hat sections, and (c) field screw connection specimens for channel sections. ........ 64

Figure 3.8: Shear connection test set-up for plasterboard sheathing-to-top hat sections

(a) field screw tests, and (b) edge screw tests ................................................................. 66

Figure 3.9: Shear connection test set-up for plasterboard sheathing-to-channel section

(a) field screw tests, and (b) edge screw tests ................................................................. 67

Figure 3.10: The upper and lower bounds (red lines) of the field screw shear (sheathing-

to-top hat section) connection test results (for one screw) .............................................. 69

Figure 3.11: The upper and lower bounds (red lines) of the edge screw shear (sheathing-

to-top hat section) connection test results (for one screw) .............................................. 69

Figure 3.12: Load-slip behaviour of plasterboard sheathing-to-top hat section

connections under monotonic loading (for one screw). This figure shows measurements

from LDTs on both sides of the specimens. .................................................................... 70

xvi


connections under monotonic loading (mean values obtained for one screw) ............... 71

Figure 3.14: Load-slip behaviour of plasterboard sheathing-to-channel section

connections under monotonic loading (mean values obtained for one screw) ............... 71

Figure 3.15: Definition of tangent and secant stiffness under monotonic loading ......... 73

Figure 3.16: ‘Bulging’ of plasterboard happened as the screw head penetrated into the

plasterboard. .................................................................................................................... 74

Figure 3.17: Failure modes of plasteroard sheathing-to-top hat section connections

under monotonic loading (a) field screw, and (b) edge screw ........................................ 75

Figure 3.18: Failure modes of field screw connection tests of sheathing-to- channel

section framing connections under monotonic loading .................................................. 76


connections for different edge distances under monotonic loading (mean values

obtained for one screw) ................................................................................................... 77

Figure 3.20: Failure modes of plastebroard sheathing-to-channel section connections for

different edge distances under monotonic loading (a) 15 mm edge distance, (b) 17 mm

edge distance, and (c) 20 mm edge distance ................................................................... 78

Figure 3.21: Load-slip behaviour of plasterboard sheathing-to-framing (top hat and

channel sections) connections under monotonic loading (mean values obtained for one

screw) .............................................................................................................................. 79

Figure 3.22: Load-slip behaviour of sheathing-to-framing connection under monotonic

loading ............................................................................................................................. 80

Figure 4.1: Configuration of ceiling diaphragm testing systems (a) Cantilever/racking

test assembly, (b) beam test assembly............................................................................. 83

Figure 4.2 Test set-up and instrumentation for cantilever test ........................................ 84

Figure 4.3: Photograph of loading frame with ceiling bottom chords and ceiling battens

mounted on it. ................................................................................................................. 85

xvii

Figure 4.4 Ceiling panel configurations along with connection details .......................... 86

Figure 4.5: Photograph showing tested ceiling diaphragm assembly ............................. 87

Figure 4.6: Photograph showing steel casters to prevent the ceiling specimen from

moving out-of-plane. ....................................................................................................... 88

Figure 4.7: Photograph of specimen (after modification) using timber sections between

bottom chords to prevent twisting of bottom chords (a) front view of the specimen, (b)

holding the specimen from the back ............................................................................... 89

Figure 4.8: Photograph showing using stud sections along the length of specimens to

prevent twisting of bottom chords................................................................................... 90

Figure 4.9: Load vs. deflection curves of loading frame only ........................................ 92

Figure 4.10: Starting of the twisting of bottom chord sections at the load of 1.7 kN and

corresponding displacement of 35 mm. .......................................................................... 93

Figure 4.11: Separation of LDT from the contact of sections at the load of 2.0 kN and

with the corresponding displacement of 42 mm ............................................................. 94

Figure 4.12: Load vs. net-deflection curve of test specimen #1 ..................................... 95



Figure 4.15: Load-deflection behaviour of tested ceiling diaphragms under monotonic

loading ............................................................................................................................. 97

Figure 4.16: Tested ceiling diaphragm assembly showing numbering of screws and

battens ............................................................................................................................. 98

Figure 4.17: Failure modes of cantilever specimen: (a) tearing of plasterboard around

screws along batten 1; (b) pulling through of plasterboard; (c) view of plasterboard from

the back ......................................................................................................................... 100

Figure 4.18: Photograph showing plasterboard rotation as a single unit ...................... 101

Figure 4.19 Definition of the initial and the secant stiffness for monotonic tests ........ 102

xviii

Figure 5.1: Beam test configuration of ceiling diaphragm testing system .................... 107

Figure 5.2: Typical structural testing arrangement of diaphragm in beam configuration

....................................................................................................................................... 108

Figure 5.3: Fixing system of plasterboard to framing members ................................... 109

Figure 5.4: Details of pin support (a) Top view, (b) Side view .................................... 110

Figure 5.5: Details of roller support (a) Top view, (b) Side view ................................. 111

Figure 5.6: Lateral supports (a) pin support, (b) roller support .................................... 112

Figure 5.7: Details of one-third loading point (a) Top view, (b) Right side view, (c) Left

side view........................................................................................................................ 114

Figure 5.8: Mechanism of loading system .................................................................... 115

Figure 5.9: Structural ceiling diaphragm testing system for beam test specimen #1 .... 117

Figure 5.10: Bottom chords and ceiling battens on the test jig before placement of

plasterboard ................................................................................................................... 118

Figure 5.11: Complete set-up of beam test specimen #1 .............................................. 118

Figure 5.12: Effects of plasterboard bearing edges on the top plates of end walls ....... 119

Figure 5.13: Structural ceiling diaphragm beam testing arrangement for beam test

specimen #2 ................................................................................................................... 120

Figure 5.14: Beam test specimen (a) complete test set-up, (b) close-up view of the

system for study of top plate effects ............................................................................. 121


specimen #3 ................................................................................................................... 122


plasterboard ................................................................................................................... 123

Figure 5.17: Complete test set-up of beam test specimen #3 ........................................ 123

xix


specimen #4 ................................................................................................................... 124


plasterboard ................................................................................................................... 125

Figure 5.20: Details of connection system of ceiling batten overlapping ..................... 125

Figure 5.21: Test set-up (a) complete test specimen, (b) lateral restraint system at pin

support, (c) lateral restraint system at roller support .................................................... 127


specimen #5 ................................................................................................................... 128

Figure 5.23: Complete test set-up for beam test specimen #5 ...................................... 128

Figure 5.24: Load vs. net-deflection curve for the frame only (without plasterboard) . 130

Figure 5.25: Load vs. net-deflection curve for beam test specimen #1 ........................ 131

Figure 5.26: Failure mode of diaphragm for beam test specimen #1 (a) tear-out of

plasterboard at the left corner of diaphragm, (b) tear-out of plasterboard at the right

corner of diaphragm, (c) pulling out of plasterboard at the top left corner of diaphragm,

(d) pulling out of plasterboard at the top right corner of diaphragm, (e) pulling out of

plasterboard at the perimeter of diaphragm, (f) deformed shape of tilted screw .......... 132

Figure 5.27: Deformed shape of the test specimen showing the bending of battens and

translation of the plasterboard as a rigid body. ............................................................. 133





(d) pulling out of plasterboard at the top right corner of diaphragm, (e) plasterboard

bearing on both edge of diaphragm, (f) deformed shape of tilted screw, (g) considerable

bending of ceiling battens ............................................................................................. 136


xx




(d) pulling out of plasterboard at the middle left side of diaphragm, (e) pulling out of

plasterboard at the middle right side of diaphragm, (f) deformed shape of tilted screw

....................................................................................................................................... 138






plasterboard field screws, (f) deformed shape of tilted screw ...................................... 140





(d) deformed shape of tilted screw ................................................................................ 143

Figure 5.36: Definition of initial and the secant stiffness for beam test ....................... 145

Figure 5.37: Typical ceiling diaphragm assembly (showing numbering for explanation)

....................................................................................................................................... 146

Figure 5.38: Load-deflection behaviour of full-scale diaphragms under monotonic

loading ........................................................................................................................... 148

Figure 6.1: Typical input load-displacement curve for a COMBIN39 non-linear spring

element. ......................................................................................................................... 153

Figure 6.2: Typical load-displacement curve based on combining a tension and a

compression spring ....................................................................................................... 156

Figure 6.3: Effects of plasterboard bearing edges on the top plates of end walls ......... 157

Figure 6.4: Schematic diagram of plasterboard-bearing edge modelling ..................... 157

xxi

Figure 6.5: FE model developed in cantilever configuration ........................................ 159

Figure 6.6: Comparison between analytical and experimental results in cantilever

configuration for an isolated ceiling diaphragm ........................................................... 159

Figure 6.7: Deflected frame shape from the FE model ................................................. 160

Figure 6.8: Developed FE model for beam test specimen #1 ....................................... 162

Figure 6.9: Comparison between experimental and analytical results for beam test

specimen #1 ................................................................................................................... 162

Figure 6.10: Deflected shape for beam test specimen #1 .............................................. 163

Figure 6.11: FE model for beam test specimen #2........................................................ 164

Figure 6.12: Load-deflection curves comparison between the experimental and

analytical for beam test specimen #2 ............................................................................ 164




specimen #3 ................................................................................................................... 166



Figure 6.18: Load-deflection curves of experimental and analytical results for beam test

specimen #4 ................................................................................................................... 168




specimen #5 ................................................................................................................... 170


xxii

Figure 6.23: Load-deflection curves for different loading configurations (one-third point

load, mid-span load, and uniformly distributed load) ................................................... 173

Figure 6.24: Load-deflection behaviour for ceilings with different lengths with

boundary conditions ...................................................................................................... 176

Figure 6.25: Load-deflection behaviour for ceilings with different widths with boundary

conditions ...................................................................................................................... 178

Figure 6.26: Comparison of load-deflection curves (with and without boundary

conditions) for ceilings with different widths ............................................................... 180

Figure 6.27: Load-deflection behaviour for ceilings with different screw spacing along

each ceiling batten with boundary conditions ............................................................... 181

Figure 6.28: Different screw patterns used for ceiling diaphragms with boundary

conditions (all dimensions are in mm) .......................................................................... 185

Figure 6.29: Load-deflection curves for different additional plasterboard screw patterns

with boundary conditions .............................................................................................. 186

Figure 6.30: Load-deflection behaviour due to variation of gap size between the

plasterboard edge and end walls ................................................................................... 188

Figure 6.31: Effect of batten spacing on load-deflection behaviour with boundary

conditions ...................................................................................................................... 190

Figure 6.32: Load-deflection curves for isolated ceilings with different lengths ......... 192

Figure 6.33: Behaviour of isolated ceiling diaphragms with different widths .............. 194

Figure 6.34: Load-deflection behaviour for different screw spacing along each ceiling

batten for isolated ceiling diaphragms .......................................................................... 196

Figure 6.35: Different screw patterns used for isolated ceiling diaphragms (all

dimensions are in mm) .................................................................................................. 199

Figure 6.36: Load-deflection curves for different plasterboard screw patterns for

isolated ceiling diaphragms ........................................................................................... 200

xxiii

Figure 6.37: Effect of batten spacing on load-deflection behaviour for an isolated ceiling

diaphragm ...................................................................................................................... 202

Figure 6.38: Load-deflection behaviour of an isolated ceiling diaphragm with bottom

chord spacing ................................................................................................................ 204

Figure 6.39: Comparison of load-deflection behaviour between loading directions

parallel to batten and parallel to bottom chords ............................................................ 205

Figure 6.40: Comparison of load-deflection behaviour of frame only (without

plasterboard) between loading directions parallel to batten and parallel to bottom chords

....................................................................................................................................... 206

Figure 6.41: Capacity-deflection curves for cantilever and beam testing assemblies .. 207

Figure 6.42: Load-deflection curves for plasterboard-batten fixed and plasterboard-

bottom chord fixed diaphragms .................................................................................... 208

Figure 6.43: Load-deflection properties of field screws ............................................... 209

Figure 6.44: Load-deflection properties of edge screws ............................................... 210

Figure 6.45: Performance of ceiling diaphragms with different plasterboard-steel frame

connection capacities .................................................................................................... 210

Figure 7.1: Various components of diaphragm deflection ............................................ 218

Figure 7.2: Diaphragm subjected to one-third loading ................................................. 219

Figure 7.3: Application of parallel axis theorem for determination of moment of inertia

....................................................................................................................................... 220

Figure 7.4: Deformed shape of a plasterboard sheathing panel in shear ...................... 222

Figure 7.5: Deformed shape of a plasterboard sheathing panel .................................... 223

Figure 7.6: Plasterboard sheathing panel elongation with respect to panel diagonal ... 224

Figure 7.7: Comparison of diaphragm deflection between simplified mathematical

model and beam test results .......................................................................................... 226

Figure 7.8: Diaphragm configuration showing lateral load along chord direction ....... 228

xxiv

Figure 7.9: Average screw load-slip response (source: Chapter 3) .............................. 229


model and FEM results ................................................................................................. 230

Figure 7.11: Diaphragm model using deep beam analogy ............................................ 231

Figure 7.12: Diaphragm deformed shape using deep beam model ............................... 233

Figure 7.13: Building configuration showing lateral load resisting elements in long

direction......................................................................................................................... 234

Figure 7.15: Diaphragm model using deep beam element ............................................ 237

Figure 7.16: Diaphragm and bracing wall displacement using deep beam model........ 239

Figure 7.17: Diaphragm model using plate element method ........................................ 241

Figure 7.18: Diaphragm deformed shape from plate element model............................ 242

Figure 7.19: Diaphragm and bracing wall displacement .............................................. 242

Figure 7.20: Diaphragm load distribution to bracing walls .......................................... 244

Figure 7.21: Configurations of wind load to be resisted by various types of buildings 247

Figure 7.22: Maximum bracing wall spacing for wind class N3/C1 ............................ 248

xxv

List of Tables

Table 3.1 Basic test matrix for shear connection tests .................................................... 63

Table 3.2 Summary of monotonic test results for one screw .......................................... 72

Table 4.1 Matrix of test specimens under monotonic loading ........................................ 90

Table 4.2 Summary of test results of specimens subjected to monotonic loading ....... 102

Table 4.3 Summary of loads at serviceability displacement ......................................... 102

Table 5.1 Matrix of test specimens under monotonic loading ...................................... 129

Table 5.2 Summary of test results for specimens subjected to monotonic loading ...... 144

Table 6.1: Finite-element representation of structural components in ANSYS ........... 154

Table 6.2: Material properties used in the FE model .................................................... 154

Table 6.3: Real constants for materials used in the FE model ...................................... 155

Table 6.4: Basic test matrix of tested specimens in beam configuration ...................... 161

Table 6.5: Summary of experimental and analytical results under monotonic loading 172

Table 6.6: Parameters for different ceiling lengths with boundary conditions ............ 175

Table 6.7: Load-carrying capacity and stiffness of ceiling with different ceiling length

(i.e. aspect ratios) with boundary conditions ................................................................ 176

Table 6.8: Various parameters for different ceiling width with boundary conditions .. 177

Table 6.9: Load-carrying capacity and stiffness of ceilings with different widths with

boundary conditions ...................................................................................................... 179

Table 6.10: Parameters for varying screw spacing with boundary conditions ............ 181

Table 6.11: Load-carrying capacity and stiffness of ceilings with different screw spacing

with boundary conditions .............................................................................................. 182

Table 6.12: Parameters for various screw fixing patterns ............................................. 183

xxvi

Table 6.13: Load-carrying capacity and stiffness of ceilings with boundary conditions

for different screw patterns ........................................................................................... 186

Table 6.14: Parameters for varying gap sizes with boundary conditions .................... 187


for different gap sizes .................................................................................................... 188

Table 6.16: Parameters for varying batten spacing with boundary conditions ............ 189

Table 6.17: Load-carrying capacity and stiffness of ceilings for different ceiling batten

spacing with boundary conditions ................................................................................. 190

Table 6.18: Parameters for isolated ceiling diaphragms with different lengths ............ 191

Table 6.19: Load-carrying capacity and stiffness of ceilings with different ceiling

lengths (i.e. aspect ratios) for isolated ceiling diaphragms ........................................... 192

Table 6.20: Parameters for isolated ceiling diaphragms with different widths............. 193

Table 6.21: Load-carrying capacity and stiffness of ceilings with different widths for

isolated ceiling diaphragms ........................................................................................... 194

Table 6.22: Parameters for varying screw spacing for isolated ceiling diaphragms .... 195


for isolated ceiling diaphragms ..................................................................................... 196

Table 6.24: Parameters for various screw fixing patterns for isolated ceiling diaphragms

....................................................................................................................................... 197

Table 6.25: Load-carrying capacity and stiffness of ceilings with different screw fixing

patterns for isolated ceiling diaphragms ....................................................................... 201

Table 6.26: Parameters for varying batten spacing for isolated ceiling diaphragms ... 201



Table 6.28: Parameters for varying bottom chord spacing for isolated ceiling

diaphragms .................................................................................................................... 203

xxvii



Table 7.1: Validation of equivalent diaphragm stiffness (5.4 m x 2.4 m- 400 mm batten

spacing) using deep beam model .................................................................................. 232

Table 7.2: Equivalent diaphragm stiffness (GAs) for deep beam method .................... 238

Table 7.3: Bracing wall stiffness ................................................................................... 238

Table 7.4: Bracing wall strength and deflection check ................................................. 239

Table 7.5: Diaphragm deflection check ........................................................................ 240

Table 7.6: Equivalent diaphragm stiffness (Gts) for plate method ............................... 241

Table 7.7: Bracing wall stiffness ................................................................................... 241

Table 7.8: Bracing wall strength and deflection check ................................................. 243

Table 7.9: Diaphragm deflection check ........................................................................ 243

1

CHAPTER 1

INTRODUCTION

1.1 Background of the Research

In Australia, houses are usually one- and two-storey light-framed structures, often

referred to as domestic structures. People depend on these structures for safety against

extreme natural events, including cyclones and earthquakes.

In Australia, domestic structures typically comprise of timber or steel structural frames

which have plasterboard interior wall lining, plasterboard ceiling lining and brick veneer

exterior cladding. Steel sheets or tiles are generally used as roof cladding. The overall

response of a domestic structure due to lateral loading may be greatly influenced by

both structural and non-structural components (Saifullah et al. 2012). The effects of

non-structural components on the structural behaviour of a house are known as system

effects. The system effects play an important role in determining the performance of

domestic structures under wind and earthquake loading.

Until recently, technology and engineering design have played a small part in the

development of houses, particularly those made from timber. The design and

construction techniques have been developed based on tradition and trade experience.

Steel- and timber-framed domestic structures have the same structural form and are

constructed in a similar fashion. The focus of this research is on houses built with cold-

formed steel frames. Figure 1.1 shows a typical Australian residential structure with

cold-formed steel frame members. The complete construction of a house using cold-

formed steel frames is presented in Figure 1.2. It should be mentioned that light-framed

domestic structures are not only constructed in Australia, but also in many parts of the

world, including New Zealand, the USA, South Africa and Japan.

2

Figure 1.1: A photograph of light-framed cold-formed steel house construction in

Australia

Figure 1.2: A photo of completed residential structures made of cold formed steel in

Australia

3

In light-framed structures, the lateral loads generated from wind and earthquake events

are transmitted to the foundation through the structure. The ceiling and/or roof

diaphragm plays an important role in distributing the lateral loads to the bracing walls.

Walker (1978) stated that the lateral loads are generally transferred through a complex

interaction between the bracing walls, ceiling and/or roof structures, and floor

structures.

The stiffness of the ceiling and roof diaphragm is important in determining how the

lateral loads are distributed to the bracing walls. If the diaphragm is rigid the

distribution would be different from that based on a flexible diaphragm. According to

NEHRP (1997) and the International Building Code (2006), a diaphragm is considered

flexible when its deflection is equal to or greater than twice the deflection of the

resisting walls. In a flexible diaphragm, the lateral load may be distributed on the basis

of tributary areas, whereas the load is distributed in proportion to the stiffness of walls

in the case of a rigid diaphragm. Hence, the determination of strength and stiffness of

diaphragms is important for the safe and accurate distribution of lateral loads.

Approximately 150,000 new houses are built in Australia every year. In the 2007-2008

financial year the total value of such construction was more than $39 billion (ABS,

2008b). In terms of dollar value, house construction accounts for approximately 40% of

all construction work, making it one of the most important economic activities in

Australia. At an individual level, home ownership is a key element of the Australian

culture and having a safe home is paramount.

In Australia, the size of houses has increased significantly in the last 20 years. The

average size of houses has increased by approximately one third from approximately

180 m2 to 240 m2 (Australian Bureau of Statistics (ABS) 2008a). In addition, the

architectural floor layout has deviated considerably from houses which were built a few

decades earlier. Most modern homes have large open-plan areas with extensive

openings and large doors and windows. This is in contrast to earlier homes which

typically had more internal walls and partitions. Most of the historical performance data

are based on the earlier style homes which are smaller in size and more regular in

layout.

4

Australian design standards and codes of practice (e.g., Australian Standard AS1684

and NASH Standard, 2005) allow the designer of a house to rely on nominal walls

with lining to provide up to 50% of the total bracing requirements. These nominal walls

are typically plasterboard-lined walls which can be external (along the perimeter of the

structure) or internal partition walls. Furthermore, plasterboard ceilings are used to

transfer the lateral loads to the bracing walls. These design assumptions are supported

by findings from past research, which clearly demonstrated that plasterboard lining can

act as a stiff medium (Gad et al, 1999; Reardon and Mahenderan, 1988; Reardon, 1990).

However, in recent times there have been significant changes in the manufacturing of

plasterboard and the way it is installed in new houses. For example, modern

plasterboard is lighter, due to the addition of foaming agents in the gypsum.

Furthermore, the paper liner which provides most of the strength to the board is

of lower weight (grams per square meter).

Importantly, there is very limited data available on the strength and stiffness of ceiling

and roof diaphragms in steel-framed houses. Indeed, for timber-framed houses there is

also very limited information to allow a designer to determine the capacity of ceiling

diaphragms to transfer lateral loads. The only information available is that contained in

AS1684, which specifies the maximum distance between bracing walls which can be

spanned by the roof system. This span is limited to a maximum of 9 m, regardless of the

loading, roof geometries or material properties. Hence, if the clear spacing between

bracing walls in an open plan area is greater than 9 m, there is no guidance whatsoever.

Therefore, rational assessment of the stiffness and strength of horizontal diaphragms is

necessary to correctly design the lateral load-resisting system. The development of a

rational design method would allow Australian designers and manufacturers to develop

optimised systems rather than relying on extrapolation of historical empirical data. This

would be foster innovation in the important sector of industry in both Australia and

internationally. Without rational engineering design models and performance-based

design, domestic structures will not benefit from innovation and optimisation.

Furthermore, the true performance of these structures under extreme events will be

difficult to assess.

5

1.2 Research Aim and Objectives

The overall research program is broken up into two components. A research companion,

Rojit Shahi, PhD research student, The University of Melbourne, has focused on the

assessment of bracing walls which included development of a test method for

estimating the strength and stiffness of different bracing walls under both wind and

earthquake loading. The research presented in this thesis is focused on the behaviour of

ceiling diaphragm and how lateral loads from the ceiling would be distributed to the

bracing walls.

The International Building Code (IBC, 2006) classifies diaphragms as either flexible or

rigid, depending on the relative stiffness of the diaphragm to the walls. However, in

Australian design standards, there is no reference to the rigidity of the ceiling or roof

diaphragms. Therefore, the overall aim of this project is to quantify the strength and

stiffness of typical cold-formed steel-framed plasterboard lined ceiling diaphragms

subjected to monotonic loading to simulate wind loading conditions. The specific

objectives are:

Based on a critical literature review, identify the key factors which affect the

performance of diaphragms in residential structures. In addition, review previous

research to highlight methods for testing of diaphragms and relevant analytical

models which can be used to predict their behaviour.

Using experimental testing, identify the load-deflection behaviour of the critical

connections in ceiling diaphragms, i.e. the screws connecting the plasterboard to

the supporting ceiling frame. These connections are subjected to shear loading

and their behaviour may be dependent on the locations of the screws from the

edge of the plasterboard and the thickness of the steel supporting members.

Determine the strength and stiffness properties of typical ceiling diaphragms by

testing full-scale segments. The results of these tests will also be used to validate

analytical models developed in this thesis.

Develop and validate detailed analytical models for ceiling diaphragms which

can accommodate different geometries and material properties. The developed

model should predict the correct failure models, stiffness and strength of typical

ceiling diaphragms.

6

Develop a simplified mathematical model for predicting the stiffness of typical

ceiling diaphragms which can be used by engineers for design purposes. Further,

demonstrate the use of the developed mathematical model for determining the

distribution of lateral loads to bracing walls via the ceiling for a typical

structure.

1.3 Outline of Thesis

Chapter 1 provides the background and rationale of this research. The objectives,

significance and research methodology of this thesis are described in this chapter.

Chapter 2 presents a critical literature review of domestic structures under lateral loads.

The literature review is not limited to steel-framed structures but also to some extent

related to timber-framed structures. In this chapter, the factors which affect the lateral

behaviour of ceiling diaphragm are also summarised and discussed, the research gap is

identified, and recommendations for further research are reported.

Chapter 3 discusses the first phase of the experimental program, which consisted of

shear connection tests between plasterboard sheathing and cold-formed steel framing

members. The details of the apparatus, test specimen requirements and testing

procedure are described. Detailed observation of the failure mechanism of the

connection between the plasterboard and steel framing members through the connecting

screws is also presented in this chapter.

Chapter 4 presents the second phase of the experimental program. This chapter

describes the construction of three full-scale ceiling diaphragm specimens, the testing

methodologies adopted, including the selection of appropriate loading protocols, the

testing program and the testing facilities necessary to perform the tests. The results,

analyses and conclusions obtained from this phase of the experimental program are also

reported.

Chapter 5 describes the third phase of the experimental program conducted in this

research project. This chapter mainly focuses on the ceiling diaphragm actions in beam

configurations. Five full-scale tests have been conducted based on common ceiling

systems in cold-formed steel structures with different configurations to determine the

strength and stiffness of such diaphragms under monotonic loading.

7

Chapter 6 presents the analytical modelling for predicting the lateral load-deflection

behaviour of plasterboard-clad ceiling diaphragms. A description of the strategy of the

developed modelling is also reported in this chapter. This chapter also presents the

validation of the model against the experimental results. Extensive parametric studies

are also undertaken to observe the influence of various factors such as aspect ratio,

spacing of the plasterboard screws, effect of batten and bottom chord spacing, gap size

in corners and various loading configurations. The discussion and conclusions based on

the analytical modelling provide basic guidance to designers to assess the critical

parameters for steel-framed domestic constructions.

Chapter 7 describes the different methods for the distribution of the lateral load to the

bracing walls through the ceiling diaphragm. A method is recommended to distribute

the lateral loads to the bracing walls through the ceiling diaphragms. Design chart for

the maximum spacing of bracing walls in a typical wind scenario in Australian houses is

reported in this chapter.

Chapter 8 provides a summary and conclusions of this research project. Based on the

accomplished work, the recommendations for future research are also provided in this

chapter.

8

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

The lateral load-resisting system in light-framed structures usually comprises a ceiling

and/or roof diaphragm that transmits horizontal loads to vertical load-resisting elements.

The roof diaphragm is made of corrugated steel deck sheets which are fastened to each

other and to the supporting members, typically trusses. The ceiling diaphragm in

residential structures is made of plasterboard sheeting attached to ceiling battens, which

in turn are attached to the bottom chords of trusses.

This chapter discusses all of the factors which affect the lateral behaviour of ceiling and

roof diaphragms as well as relevant experimental and analytical research conducted in

different parts of the world.

2.2 Background on Cold-formed Steel

In building construction, cold-formed steel products are mainly used as structural

members, diaphragms, and coverings for roofs, walls and floors. Cold-formed steel

members are widely used in residential construction and pre-engineered metal buildings

for industrial, commercial and agricultural applications (Yu, 2000).

Cold-formed steel has numerous advantages over other construction materials,

including: (i) light weight, (ii) high strength and stiffness, (iii) fast and easy erection and

installation, (iv) dimensionally stable material, (v) no formwork needed, (vi) durable

material, (vii) economy in transportation and handling, (viii) non-combustible material,

(ix) recyclable nature and (x) energy efficiency.

Cold-formed steel section shapes are manufactured by press-braking blanks sheared

from sheets, cut lengths of coils or plates, or by roll forming cold- or hot-rolled coils or

sheets, and conducting forming operations at ambient room temperature, i.e., without

the addition of heat as required for hot-rolling (AS/NZS 4600:2005). Various shapes are

available for walls, floors, and roof diaphragms and coverings, as shown in Figures 2.1

and 2.2. Typical cold-formed steel members such as studs, track, purlins, girts and

angles are mainly used for carrying loads, while panels and decks constitute useful

surfaces such as floors, roofs and walls, in addition to resisting in-plane and out-of-

plane surface loads. Prefabricated cold-formed steel assemblies include roof trusses,

9

panelized walls or floors, and other prefabricated structural assemblies (Yu, 2000).

Hancock (1994) and Yu (1991) stated that the behaviour, characteristics and subsequent

design of cold-formed steel elements are greatly affected by local buckling, web

stiffening, and the characteristics and effect of openings.

Figure 2.1: Cold-formed steel sections used for structural framing (NASH, 2014)

(Figure is omited from the electronic version of thesis due to copyright issue)

Figure 2.2: Various truss cross sections (NASH, 2009) (Figure is omited from the

electronic version of thesis due to copyright issue)

Structural strength and stiffness are the main considerations in the design of structures.

Load-carrying panels and decks not only withstand loads normal to their surface, but

10

also act as shear diaphragms to resist forces in their own planes if they are adequately

interconnected to each other and to supporting members (Yu, 2000).

Paultre et al. (2004) reported that structural steel framing provides designers with an

extensive choice of economic systems for floor and roof construction. Steel framing can

attain longer spans more competently than other kinds of construction. This reduces the

number of columns and footings, thus increasing speed of assembly.

2.3 Current Design Practices in Australia

In Australia, there are material-based standards for the design of structures and loading

standards for the loadings applied to structures. Most research in Australia has been

based on timber-framed structures, and research on steel-framed domestic structures has

been a recent occurrence. Before 1993, there was no Australian Standard specifically for

the structural design of steel-framed domestic structures. The Cold-formed Steel

Structures Code (AS1538:1988) was generally used for the design of cold-formed steel

framing members. However, there was a lack of information regarding steel-framed

domestic structures. For that reason, the National Association of Steel-framed Housing

(NASH) published a design manual in collaboration with BHP Steel, the CSIRO and the

Australian Institute of Steel Construction (AISC) entitled "Structural Performance

Requirements for Domestic Steel Framing" (AISC, 1991). AISC (1991) was developed

to assist in the design and development of cold-formed steel framing for domestic

construction.

In 1993, Australian Standards published the Domestic Metal Framing Standard (AS

3623). This standard provides the performance requirements, in terms of structural

adequacy and serviceability, for the framing of domestic buildings of up to two storeys

in height and roof pitches of up to 35°. This standard was developed in accordance with

AS 4055 (Wind loads for housing) and the relevant parts of AS 1170 (Minimum design

loads on structures).

Bracing systems are designed to resist horizontal loads due to wind or earthquake.

Bracing elements are as evenly distributed practicably possible and are provided in two

orthogonal directions (AS 4055:2010).

According to AS 3623:1993, all external walls are required to resist wind loads normal

to their planes. Internal walls should be designed to resist some lateral loads, to allow,

11

among other things, for the effects of varying air pressure within a building, which can

impose significant loadings during high winds if doors and windows open or break. All

walls can be used to incorporate wall bracing elements to resist horizontal loads in

shear. For the design of the top wall plates, it is usually assumed that the roof/ceiling

system (for single-storey buildings or the upper storey of two-storey buildings) or the

floor/ceiling (for lower storeys) is sufficiently stiff to carry the horizontal wind loads.

The total roof system should perform as a single unit to resist both horizontal and

vertical loads. Roof trusses or rafters are normally used to resist vertical loads.

Horizontal loads are resisted by the roof bracing system (AS 3623:1993).

AS/NZS 4600:2005 provides designers of cold-formed steel structures with

specifications for cold-formed steel structural members used for load-carrying purposes

in buildings and other structures.

In NASH Part 2 (2014), it is stated that plasterboard lining can contribute up to 50% of

the bracing resistance. It also allows for the contribution of 0.75 kN/m for walls lined on

both sides and 0.45 kN/m for walls lined on one side only, which was found on the basis

of testing. This standard is used to provide the building industry with procedures that

can be used to determine, design or check construction details, and to determine

member sizes, and bracing and fixing requirements for steel-framed construction in

cyclonic and non-cyclonic areas.

In accordance with Australian Standard AS 1170.4 (2010), no specific earthquake

design is required for steel-framed houses (BCA Class 1a and 1b structures), subject to

the following conditions:

The hazard factor Z is less than or equal to 0.11 (kP = 1.0 for housing).

The frame has been designed to resist lateral wind forces in accordance with

NASH Standard Part 1.

2.4 Components of Steel-framed Domestic Structures

In Australia, the term “houses” refers to one- and two-storey light-framed structures,

often referred to as domestic structures. There are three major components in steel-

framed domestic structures: floor, walls and roof. Figure 2.3 shows the framing of

typical steel-framed domestic structures.

12

Figure 2.3: Typical framing of steel-framed structures (NASH, 2014) (Figure is omited

from the electronic version of thesis due to copyright issue)

2.4.1 Floor

A floor is a horizontal structural system mainly consisting of joists, girders and

sheathing. In addition to resisting gravity loads, floor systems are designed to: (i) resist

lateral forces consequential from wind and seismic forces and to transfer the loads to

supporting bracing walls through diaphragm action; (ii) avoid excess vibration, noise,

etc. and (iii) function as a thermal barrier (Breyer, 1988). There are generally two types

of floors used in steel-framed houses: slab on ground and suspended floors. The floor is

expected to act as a rigid diaphragm in its own plane. The sub-floor bracing is designed

to transfer the load from the floor diaphragm into the ground (NASH, 2009).

2.4.2 Walls

A wall is a vertical structural system that transfers gravity loads from the roof and floors

to the foundations. Walls also resist lateral loads generated due to wind and earthquakes

(NAHBRC, 2000). Figure 2.4 shows a typical steel-framed wall and its components.

13

Figure 2.4: Typical wall framing system (NASH, 2009) (Figure is omited from the


Structural wall sheathing distributes lateral loads to the wall framing and provides

lateral restraint to the wall studs (i.e., buckling resistance). Wall bracing is required for

each storey to transfer the horizontal shear forces due to wind and earthquakes to the

appropriate supports. These forces are vertically additive, i.e. the horizontal shear forces

become larger as they move closer to the foundation (NASH, 2009).

2.4.3 Roof

A roof is normally a sloping structural system that supports gravity and lateral loads and

transfers the loads to the walls. Commonly, roofs are made of trusses, as shown in

Figure 2.5. Members such as battens have an important role in providing lateral restraint

to the top and bottom chords of roof trusses (Saifullah et al. 2012). They also act in

conjunction with the rest of the ceiling system to provide a diaphragm which transfers

horizontal wind loads to the wall bracing system. The roof system should be adequately

anchored to the wall system below to enable this transfer of wind forces and also to

resist wind uplift (NASH, 2009). Depending on the shape of the roof, a variety of

trusses can be used in Australia, as shown in Figure 2.5.

14

Figure 2.5: Typical truss roof system (NASH, 2009) (Figure is omited from the


2.5 Behaviour of Light-framed Structures

In steel-framed domestic structures, the roof is considered to be the dominant mass

compared with the walls. Hence, under earthquake loading, the inertia forces generated

at the roof level are transferred to the foundation through the bracing walls (Gad, 1997).

The distribution of wind and earthquake loads from the roof to the walls depends on the

15

behaviour of the roof diaphragm. The lateral load distribution depends on the relative

flexibility of the bracing walls and ceiling/roof diaphragm.

There are several factors which affect the behaviour of ceiling/roof diaphragms. The

diaphragm action of the roof/ceiling system and its interaction and effect on loading the

shear walls in a domestic structure can be considered to fit within two extreme

scenarios: rigid diaphragm/flexible walls and flexible diaphragm/rigid walls (Williams,

1986). Phillips et al. (1993) tested a full-scale single-storey wooden house under both

symmetrical and non-symmetrical lateral loads at several stages of loading to assess the

structural response and load-sharing features. These researchers found that (i) the roof

diaphragm affects the distribution of lateral load to the shear walls of the building and

the roof diaphragm behaves almost like a rigid diaphragm; (ii) load distribution among

the shear walls is a function of wall stiffness and position within the building; and (iii)

the walls transverse to the loading direction carry little portion of the applied lateral

load.

Based on previous experimental and analytical studies, there are several factors which

affect the stiffness and strength of diaphragms. These factors have been collected and

are presented in Figures 2.6 and 2.7. Key factors are also discussed below.

Figure 2.6: Factors affecting strength and stiffness of ceiling diaphragms (Saifullah et

al. 2012)

16

Figure 2.7: Factors affecting strength and stiffness of roof diaphragms (Saifullah et al.

2012)

Nails or Screws

Anderson (1990) reported that when the working stress is exceeded, nails perform less

effectively than screws, because nails pierce the steel, leaving jagged edges and tears in

the sheet, while screws cut fairly smooth bearing surfaces into the sheeting. Nails in

thicker steel can give an equivalent performance to screws in 29-gauge steel

(Gebremedhin, 2007). Gebremedhin (2007) also stated that shear transfer through nail

connectors in 29-gauge steel may cause leaks as openings around the nails enlarge with

time and the stiffness of the roof diaphragm decreases due to these openings.

Length/size of Fasteners

Yu (2000) stated that when the fasteners are small in size or number, failure may occur

due to shearing or separation of the fasteners or by localized bearing or tearing of the

surrounding material. Niu (1996) concluded that the strength of diaphragm panels

fastened with 38.1 mm long wood-grip, self-drilling screws increased by 2.5 times in

17

comparison to the strength of a similar diaphragm panel fastened with 25.4 mm long

screws, but found no obvious difference in stiffness. Atherton (1981) performed cyclic

static tests on several ceiling diaphragms (4.9 m x 14.6 m) with waferboard and

particleboard sheathing and found that there is no substantial increase in stiffness or

ultimate load due to increasing the nail size from 8d to 10d.

Position of Fasteners

The shear strength of the connection of the fastener depends on the configuration of the

surrounding metal (Yu, 2000). Hausmann and Esmay (1975) found that the orientation

of screws through the valleys of a metal cladding profile contribute significant stiffness

to the diaphragm, rather than screws through the ribs. Anderson (1990) reported that

when the sheet-to-roof batten fasteners are placed next to the rib, compression buckling

behind the fastener is prevented.

Reardon (1989) stated that when metal sheeting is fastened to the roof and walls of a

post-frame building, large metal-clad wood frame diaphragms are formed, which

increase the rigidity of the building. According to Easley (1977), Luttrell (1991) and

Davies and Bryan (1982), stiffer and stronger diaphragms can be obtained if the

fasteners used to hold the sheeting to the lumber are located in the flats of the sheet

rather than in the ribs.

Sheathings/Claddings

In Australia, generally, the term cladding is used for the exterior, while lining is used to

cover the interior side of the frames. In Australia, plasterboard is normally used for the

interior side. Cladding, sheathing and lining are all terms used to provide enclosure and

possibly lateral bracing to the wall frames. In Australia, plasterboard is used for both

walls and ceilings. Ceiling and wall plasterboards are connected through the ceiling

cornices using glue.

Thickness of Sheathing

The cladding thickness is an important factor in assessing the performance of clad

frames under lateral loading. Miller and Pekoz (1994) reported that a thicker cladding

material increases the failure load per fastener. Increasing the thickness of the cladding

increases the load carrying capacity of the clad frame (Stewart et al, 1988). Atherton

18

(1981) revealed that the strength and stiffness of the diaphragm increases with

increasing the sheathing thickness from 7/16" (11 mm) to 5/8" (16 mm) or increasing

the number of nails.

Boot (2005) found that plywood thickness and nailing schedule along with blocking to a

lesser degree, to be the leading factors in determining the strength and stiffness of the

diaphragm. He also concluded that increased plywood thickness (without using longer

nails) and corner openings reduced strength but had little effect on stiffness, and

openings in the sheathing at normal intervals caused the specimens to be ineffective as

diaphragms.

Yu (2000) stated that when a continuous flat plate is welded directly to the supporting

frame, the failure load is nearly proportional to the material thickness. Nonetheless, in a

formed panel, the shear is transferred from the support beams to the shear-resisting

element through the vertical ribs of the panels, and the shear strength of such a

diaphragm can be increased by increasing of the material thickness, but not linearly.

Test results showed that diaphragms with thicker gauge sheathing provide more strength

and stiffness (Yu, 2000). Phillips et al. (1993) conducted static tests on a full-scale

timber house and found that the stiffness contributions from additional layers of

cladding are additive.

Orientation of Sheathing

Wolfe (1982) conducted experimental tests to determine the influence of the orientation

of gypsum board on timber panels and concluded that there is an average increase in

ultimate strength of 50% and an average increase in stiffness of 43% when panels are

oriented horizontally rather than vertically. Moreover, when the sheets are fixed

horizontally, the joints between the sheets are horizontal, which are easier to construct.

Atherton (1981) found that staggered panel patterns are slightly stiffer than stacked

patterns at ultimate loads, and load cycling has no effect on the ultimate strength of the

diaphragm. The staggered panel pattern layout permits additional contact, which helps

to increase the stiffness of a horizontal diaphragm (Applied Technology Council, 1981;

James and Bryant, 1984).

19

Size of Sheathing

Yu (2000) considered the effect of the sheet width within a panel, and concluded that

wider sheets are generally stronger and stiffer because there are fewer side laps. Yu

(2000) also stated that the height of panel has a considerable effect on the shear strength

of the diaphragm when a continuous flat plate element is not provided. The deeper

profile is more flexible than shallower sections. Therefore, the distortion of the panel,

particularly near the ends, is more prominent for deeper profiles. However, the height of

panels has slight or no effect on the shear strength of the diaphragm panels when a

continuous flat plate is connected to the supporting frame (Yu, 2000).

Aspect Ratio

Gebremedhin (2007) reported that diaphragm panels are strongest at resisting forces in

their longest direction. For wind gusting perpendicular to the long side of a post-frame

building, the largest effective diaphragms are the roof and end walls. When a building

has a small length (length-to-width ratio ≤ 3:1) with no supporting transverse walls

(shear walls), the horizontal wind forces are mostly distributed to the end walls by the

roof diaphragm. On the other hand, when a building is long (length-to-width ratio ≥

3:1), the roof and ceiling diaphragms need the transverse walls to effectively distribute

the in-plane loads (Gebremedhin, 2007).

Luttrell (1988) found that the stiffness of a diaphragm is highly dependent upon the

ceiling length; however, there is no effect on the shear strength. Yu (2000) considered

that shorter span panels provide higher shear strength than longer span panels.

However, test results showed that the failure load is not mainly sensitive to changes in

span (Yu, 2000).

Boot (2005) stated that when the top plate is continuous and sufficiently fastened down,

the outside walls can efficiently stiffen a diaphragm. The primary effect of walls on

diaphragms increased flexural stiffness because of the resistance of the top plate to the

tension forces developed through bending action (Boot, 2005).

Effect of Cornice

The ceiling cornice makes some contribution to load transfer and panel stiffness, as

it binds the wall and the ceiling cladding together (Saifullah et al. 2012). Reardon

20

(1990) conducted full- scale tests on Nu-Steel framed houses in order to observe the

importance of cornices. He recommended that, assuming rigid roof diaphragm action,

the ability of cornices to transfer shear loads from the ceiling diaphragm to the

wall systems becomes crucial. Reardon (1990) also found that when there is a ceiling

only, the addition of the cornice reduces the lateral displacements to about one tenth of

the original values, and the ceiling and cornice are able to provide a very stiff path for

load transfer. The mechanism of load transfer from the ceiling and roof to a wall parallel

to the applied load through the cornice was studied by Golledge et al. (1990) and is

shown in Figure 2.8.

Figure 2.8: Transfer of racking load from ceiling and roof diaphragm to walls via the

cornice (Golledge et al., 1990) (Figure is omited from the electronic version of thesis

due to copyright issue)

Gad (1997) found that the inclusion of set corners changed the force distribution in the

frame and the cladding. Consequently, the failure mode of walls with set corners was

substantially different from that of walls without set corners. For walls without set

corners, failure was due to screws tearing in the plasterboard along the top plate, and

panels with set corners failed due to plasterboard buckling out-of-plane and tearing

around the screws along the bottom plate (Gad, 1997).

21

The ceiling cornice also prevents out-of-plane buckling of wall plasterboard when a

wall with set corners is racked (Saifullah et al. 2012). Golledge et al. (1990) stated that

strengthening the wall plasterboard at the top by the cornice may force the out-of-plane

buckling to occur at the bottom. The skirting-boards may prevent this failure mode as

they strengthen the bottom of the plasterboard.

Fixing System

Walker et al. (1982) stated that systems in which the cladding is directly attached to the

ceiling joists appear to have better structural performance than those which utilize

battens, provided that other factors remain the same. This is more marked with

plasterboard systems than with versilux asbestos cement sheeting. The difference may

be due to the difference in behaviour between the systems, the plasterboard being

representative of systems where plastering along the joints causes the cladding to act as

a single sheet, and the versilux system being representative of systems where each

cladding sheet acts independently (Walker et al, 1982).

Walker and Gonano (1983) reported that the contributing factor to the relatively high

ultimate load capacity is the nogging between battens along the edges of the sheets,

which allows continuous nailing around the full perimeter of each sheet of cladding.

Nogging between the battens along the edges of the cladding and then fastening around

the full perimeter of each sheet can more than double the ultimate load capacity in the

case of ceilings clad with individually acting sheets. Due to the connection system

between the steel battens and the ceiling joists, the ultimate strength and stiffness is

increased (Walker and Gonano, 1981).

Boot (2005) found that foam adhesive and blocking is the most effective combination of

parameters to increase the shear stiffness and cyclic stiffness. Boot (2005) also reported

that the shear stiffness can be increased by construction techniques that serve to better

“interlock” sheathing panels into one large sheathing system against horizontal shear.

Since the overall diaphragm stiffness is typically related to shear stiffness, shear

stiffness increases will generally cause similar increases in overall diaphragm stiffness

(Boot, 2005).

Walker and Gonano (1983) reported that the influence of the adhesive is small due to

the adhesive joint failing at a relatively low load (due to the weakness of the paper

22

surface of the plasterboard). The presence of effective chord members causes a

significant increase in flexural stiffness. Proper splicing and sufficient fastening of the

overhanging edge of sheathing is significant to the performance of diaphragms (Boot,

2005).

Trusses and Roof Battens

White et al. (1977) concluded that diaphragm strength and stiffness are not affected by

the truss spacing within typical construction ranges if the roof batten details are not

changed. They also concluded that if intermediate stitch connectors are used, strength

and stiffness are not affected by the roof batten spacing (within typical ranges).

Anderson (1987) stated that panels with recessed roof battens decrease the stiffness of

the panel, and there is a reduction in the stiffness if roof battens are placed on edge

rather than flat. Moreover, placing roof battens flat is geometrically more stable than

placing them on edge. This type of construction decreases eccentricity between the

sheet and the rafter and, therefore, decreases the potential for twisting of roof battens

(Gebremedhin, 2007). Yu (2000) found that with decreasing roof batten spacing, the

shear strength of panels is increased, and the effect is more noticeable in thinner panels.

Boot (2005) established that there is little impact of spacing of roof battens on the

strength and stiffness of diaphragms. Boot (2005) stated that when roof trusses are used

in light-frame structures, the bottom chord of the roof truss serves as the frame member

of the ceiling diaphragm.

2.6 Diaphragm Analysis

Diaphragms can be used as elements of the structural system in order to resist lateral

loads generated due to wind and earthquake loads. For design purposes, wind loads are

considered as acting perpendicular to the surfaces under consideration. Since the present

research is mainly concerned with the design of plasterboard-sheathed steel-framed

diaphragms acting to resist lateral loads, only the horizontal components of the wind

loads acting on the building surfaces are considered. The configuration of the wind

loads acting on building surfaces is presented in Figure 2.9.

23

Figure 2.9: Arrangement of wind forces on the surface of single storey building

2.6.1 Diaphragm Stiffness

Diaphragms can be analysed using various methods, such as the girder analogy and the

truss analogy. However, the girder analogy is the most suitable method for the

estimation of diaphragm deflection for plasterboard-clad diaphragms. There are various

reasons for the estimation of diaphragm stiffness:

To control the deformation of the vertical supporting elements. ATC (1981)

reported that over-stressing of the vertical load-resisting systems (i.e. shear

walls) because of diaphragm deformation could lead to failure of the structure

within the permissible strength capacity of the diaphragm. Plasterboard-sheathed

steel-framed diaphragms can be used to resist the lateral loads generated due to

wind or earthquake loads, considering that the deflection of the diaphragm does

not exceed the allowable deflection (i.e. H/300 = 8 mm) of the attached

supporting resisting elements. “Allowable deflection” refers the amount of

deformation for which any component will maintain its structural integrity and

continue to support the designated wind load on the structure (IBC, 2006).

The behaviour of a structure under dynamic loads (for instance, loads generated

due to earthquake ground motion) depends on the natural period of the structure,

24

which is associated with the period of the diaphragm, and this period can be

obtained from the deformation behaviour of the diaphragm (ATC, 1981).

Therefore, it is essential to determine the stiffness of diaphragm.

Another reason for the determination of diaphragm stiffness is to evaluate the

lateral load distribution to the vertical load-resisting elements in a structure to

which the diaphragm is continuous over several vertical elements (ATC, 1981).

In most cases, a diaphragm is considered as a simply supported beam with

discontinuity. Hence, the load is distributed based on the tributary areas of the

diaphragm. However, this assumption is not valid for the situation where the

relative stiffness of both the diaphragm and the vertical elements of the lateral

load-resisting system are considered for load distribution (Phillips et al. 1993).

2.6.2 Diaphragm Classifications

A diaphragm can be defined as a structural system (usually horizontal) that acts to

transmit lateral forces to the vertical lateral resisting system (Saifullah et al. 2012). A

diaphragm structure is formed when a variety of vertical and horizontal elements are

accurately tied together for the arrangement of a structural unit. The behaviour of

diaphragms can be obtained by analytical studies as well as experimental testing.

According to Breyer et al. (2007) an appropriately designed and connected together

assembly functions as a horizontal beam that distributes loads to the vertical resisting

elements. It is important to consider diaphragm flexibility to develop a model for

distributing lateral loads to the bracing walls. In wood light-frame buildings, the

diaphragm is designated as either flexible or rigid for the purpose of lateral load

distribution (Breyer et al. 2007).

Phillips et al. (1993) found that the design procedures for light-framed housing normally

adopt the horizontal roof and ceiling diaphragms as flexible. Based on this assumption,

tributary area methods are used to estimate the lateral loads in the shear walls. There is

no recognition provided to consider the influence on the distribution of lateral loads of

the actual stiffness of the horizontal diaphragms or the interaction with the other

components of the structure. This over-simplification of the structural behaviour of

light-frame structures may result in inefficient designs or potential failures (Saifullah et

al. 2012).

25

It should be mentioned that in single-storey steel-framed domestic structures, there may

be up to two diaphragms. The first may be the roof diaphragm if it is metal-clad (e.g.

with colorbond) and the second is the ceiling diaphragm, if it is made of plasterboard

lining with positive fixing to the roof trusses.

Diaphragms can be classified as "rigid", "flexible", and "semi-rigid", based on the

relative rigidity between the diaphragm and bracing walls. According to IBC (2006), a

diaphragm is considered “rigid” when the lateral deformation of the diaphragm is less

than two times the average storey drift. The diaphragm is considered flexible if the

diaphragm deflection is greater than two times the average storey drift, as shown in

Figure 2.10. A diaphragm is considered semi-rigid when the diaphragm deflection and

the deflection of the vertical lateral load resisting elements are of the same order of

magnitude. The deflection in the plane of the diaphragm should not exceed the

allowable deflection of the supporting attached components.

Figure 2.10: Determination of diaphragm flexibility (Florida Building Code

Commentary, 2007) (Figure is omited from the electronic version of thesis due to

copyright issue)

Generally, if the vertical lateral resisting system comprises of light-framed members, it

can generate a rigid diaphragm on flexible supports. In the case of a rigid diaphragm,

the ceiling and/roof acts as a rigid beam spanning between the walls and results in equal

racking displacements in each of the walls (assuming no torsion). When the diaphragm

26

is rigid, the lateral load is distributed to the vertical resisting elements on the basis of the

relative stiffness of these vertical elements. If the walls have different racking stiffness,

the stiffer walls will carry more load than the more flexible walls. On the other hand, in

the case of flexible diaphragms, the lateral loads are distributed to the bracing walls

according to tributary areas, resulting in different racking deflections in walls of

different stiffness. Figure 2.11 illustrates these two cases. When there is irregular

stiffness and distribution at any level within the structure, torsional forces are developed

and this needs to be considered in the design of the structure. Torsional forces can also

be generated due to the arrangement of the vertical resisting system and can be

transferred through a rigid diaphragm. Furthermore, the additional loads on the vertical

resisting elements should be appropriately accounted for in the design of diaphragms

(ATC, 1981).

Figure 2.11: Schematic representation of rigid and flexible diaphragm (Saifullah et al.

2012)

The relative rigidities of the vertical and horizontal lateral load-resisting systems can

vary significantly. The diaphragm action of the roof/ceiling system and its interaction

and effect on loading of the bracing walls in a domestic structure can be considered to

fit within two extreme scenarios: a flexible diaphragm with infinite stiff vertical shear-

resisting elements, and flexible vertical elements with infinite rigid diaphragms. It

should be mentioned that both of these two extreme scenarios occur in most structures,

as presented in Figure 2.12 and the relative rigidities of the several components mainly

govern the lateral load distribution.

27

(a) Flexible diaphragms with stiff walls

(b) Rigid diaphragms with soft walls

Figure 2.12: Ceiling diaphragm actions in two extreme conditions

Barton (1997) stated that the rigid diaphragms/soft walls model is the less conservative

of the two with respect to strength limit states of the structure, since it has the potential

to produce higher loads in the stiffer walls for a given total load applied to the structure.

The soft diaphragms/rigid walls model is less conservative with respect to serviceability

limit states, since it has the potential to produce higher deflections in more flexible

28

walls for a given total load applied to the structure. Breyer et al. (2007) considered

timber roof diaphragms as flexible, while Paevere et al. (2003) stated that the roof and

ceiling diaphragm behave as a rigid diaphragm. Reardon (1990) tested a cold-formed

steel-framed house under simulated wind loads and concluded that both roofing and

ceiling acted as stiff diaphragms.

It should be noted that the relative stiffness between the diaphragm and walls is unlikely

to remain constant under loading. As lateral loads are imposed, the initial stiffness of

walls (including contributions from non-structural walls) may be quite high and then the

diaphragm could be considered flexible. As the lateral loads increase (particularly

beyond serviceability), the walls soften and the diaphragm may be considered rigid

compared to the walls. Foliente (1995a), Wang and Foliente (2006) also revealed that

the stiffness of light wood-framed shear walls degrades fairly quickly. In other words,

the stiffness of shear walls deviates from linearity soon after experiencing moderate

lateral displacements.

2.6.3 Continuous Diaphragms

The lateral load distribution to the vertical lateral resisting elements and the extent of

diaphragm continuity that generally exists in the analogous girder are subject to several

interpretations. It should be noted that when the diaphragm flanges are continuous, the

web should also be considered continuous and the diaphragm need to consider to some

extent of continuity. ATC (1981) reported that the web can be considered as continuous

even though the plasterboard sheathing is interrupted due to the vertical lateral resisting

elements (i.e. shear walls) where the diaphragm sheathing is connected to the vertical

elements in order to transfer the lateral loads to the element. The diaphragm sheathing is

connected on both sides of the vertical elements where fire-separation walls are used in

multi-storey structures or carried via the roof (ATC, 1981).

The girder analogy used for the estimation of diaphragm deflection is appropriate for

the determination of the lateral load distribution to the bracing walls. The diaphragm,

which acts as a continuous girder or beam supported on four walls, transfers some

portion of lateral load to each end wall and a significant portion of load to the middle

wall, where significant bending deformation is expected, as shown in Figure 2.13. The

distribution system is appropriate for simple supports where the shear deformation

predominates. However, it is conventional to design diaphragms for shear at the ends as

29

estimated for simple beams and shear at the centre as determined for full continuity of

the diaphragm (ATC, 1981). The comparison of wall stiffness with diaphragm stiffness

ensures the reasonability of the rigid supports.

It should be noted that structures with irregular configurations can result in continuous

diaphragms with different stiffness in the numerous portions of the diaphragms. When

the reactions of the walls are considered rigid, the lateral loads are distributed generally

parallel to that diaphragm with varying stiffness. Figure 2.13 illustrates the

configurations of continuous diaphragms. ATC (1981) reported that when the offsets of

the shear walls are extreme in structures, the continuity of the diaphragm is lost and in

that situation, simple beam distribution of loads should be executed. However, in order

to provide continuity in this irregular configuration, it is essential to extend the flanges

of the diaphragm at offsets into the nearby elements beyond the support (ATC, 1981).

Figure 2.13: Configurations of simplified continuous diaphragms

As the stiffness of plasterboard-sheathed steel-framed diaphragms is considerably

dependent on shear, the relative stiffness of diaphragm portions is closely associated

with the segment widths and very little affected due to the moment of inertia of the

flanges. A demanding analysis could use the ratio of inverse of deflections determined

using equal loads to assign the relative stiffness of several segments of the diaphragm

30

(ATC, 1981). It should be noted that the relative stiffness of the segments is normally

allocated according to their relative widths.

2.7 Bracing System of Diaphragm

NASH (2009) stated that bracing is provided primarily to enable the roof, wall and floor

systems to resist the wind and earthquake loads applied to the building. To transfer

these forces into the building’s foundations, the connections between systems must be

adequate. Horizontal wind forces on the external surfaces are transferred by horizontal

or near-horizontal diaphragms and bracing. Horizontal diaphragms transfer racking

forces to lower level diaphragms via the connections and vertical bracing (NASH,

2009).

There are different types of bracing, including wall bracing, roof bracing, floor and sub-

floor bracing. Figure 2.14 shows the various bracing systems of a steel-framed house.

Figure 2.14: Various bracing systems (NASH, 2009) (Figure is omited from the


2.7.1 Roof Bracing

NASH (2009) reported that roof bracing is important to ensure that the roof performs as

an integral unit and transmits the imposed loads to the supports. Bracing should be

31

provided at the top and bottom chords of roof trusses. Top chord bracing is necessary to

transfer horizontal wind loads to the supports where load is perpendicular to the span of

trusses. Wind and earthquake loads are transferred to the top chords by the roof battens.

Bottom chord bracing is used to provide restraint to the bottom chords of trusses when

they are in compression due to wind uplift or bending. In addition to supporting roof

cladding and transferring longitudinal wind loads, roof battens are designed to provide

lateral buckling restraint to the top chords of the roof trusses (NASH, 2009). NASH

(2009) also reported that a hip roof structure provides significant permanent bracing

capacity; and continuous ceiling systems with lining, such as correctly fixed

plasterboard, can be assumed to act as diaphragms.

2.7.2 Wall Bracing

Wall bracing is necessary for every storey to transmit the horizontal shear forces

developed due to wind and earthquakes to the supports. There are different types of wall

bracing systems, such as K bracing, cross bracing, sheet bracing, and portal frame

action.

According to NASH (2009), the capacity of sheet bracing is dependent on various

factors: (i) the type and thickness of the sheeting material; (ii) the type and number of

connectors used to fix the sheet to supporting members; and (iii) the location of the

connectors (e.g. edge connectors are more effective than those along intermediate

studs). Adham et al. (1990) studied the influence of cross-sectional area of strap braces

on the lateral performance of clad frames, and concluded that the lateral load-carrying

capacity and stiffness increased as the strap size increased, and the load-carrying

capacity increased by a similar ratio to the increase in the strap brace cross-sectional

area.

2.7.3 Floor and Subfloor Bracing

Roof and wall bracing systems are designed to transfer wind and earthquake loads to the

footings. The floor is expected to act as a rigid diaphragm in its own plane. The subfloor

bracing is designed to transfer the load from the floor diaphragm into the ground. Steel

posts placed into concrete footings can be used to transfer the racking forces to the

foundations. Where the column capacity is not adequate to resist the lateral load,

additional bracing or cross bracing may be considered. Unreinforced masonry walls

may be used to transfer racking forces in the subfloor region (NASH, 2009).

32

2.7.4 Combination of Bracing Systems

When different bracing systems are combined and the diaphragm is assumed to be rigid,

it is crucial to observe if their contributions are additive. There are several methods for

determining the distribution of lateral load to the bracing walls, including the tributary

area method, the simple beam method, the relative stiffness method, the total shear

method, and the plate elements method. Details of all of these methods are presented in

Section 2.8. NASH (2009) stated that for the total shear method, all elements should

have compatible deformation capacity or sufficient ductility. The NASH (2009)

illustration of this is shown in Figure 2.15, which indicates the racking load versus

deflection relationships for three different types of wall bracing systems. In this figure,

Fx, Fy and Fz are the ultimate capacities of bracing types X, Y and Z, respectively. If

the roof and/or ceiling diaphragms are assumed to be rigid, the ultimate capacities (Fx,

Fy and Fz) cannot be cumulative, as bracing type X achieves its ultimate capacity at a

deflection value (Δ1) below that of types Y and Z. Similarly, for bracing types Y and Z,

the ultimate capacities are only cumulative if the building is designed or assessed at

deflection Δ2. However, at higher levels of deflection, for example Δ3, the contribution

of bracing type Y is limited, and the ultimate capacities (Fy and Fz) are not cumulative.

Figure 2.15: Illustration of the importance of deformation compatibility or ductility in

assessing the cumulative effects of different bracing types (NASH, 2009)

33

Wolfe (1982) conducted static tests on light-framed domestic timber structures to

examine the effect of combining either of three bracing systems (diagonal wood let-in

compression bracing, wood let-in tension bracing and metal strap bracing) with gypsum

wallboard cladding. Wolfe (1982) suggested that a parallel spring model could be used

to predict the combined effects of bracing and cladding. This model assumes that the

stiffness of each wall is equal to the sum of the stiffness of each contributing element.

Wolfe used the secant modulus as the stiffness. He proposed the following parallel

spring model:

Ri = Δi (K1, i + K2, i + ….. + Kn,i)

where,

Ri = composite resistance at displacement Δi

Kn,i = secant modulus from the racking load-displacement curve of component ‘n’ at

displacement Δi.

Wolfe (1982) used this spring model to predict the load-displacement of composite

walls based on the independent load-displacement behaviour of the components. Wolfe

(1982) concluded that the contributions from the cladding and the bracing system are

additive, and the proposed parallel spring model produced satisfactory estimates of

composite wall performance, based on the load-displacement curves of the individual

components.

2.7.5 Typical Location and Distribution of Bracing Walls

The location of the bracing walls ought to be roughly consistently distributed and they

should be placed in every direction to represent the wind loading, as illustrated in Figure

2.16. It should be mentioned that “ceiling depth” refers to the width of the building

parallel to the wind loading direction, as shown in Figure 2.16. It is recommended to

provide bracing initially in external walls as well as at the corners of the buildings

where possible (AS 1684:2010). However, where it is not possible to provide bracing in

external walls due to openings or identical circumstances, it is suggested to provide a

structural diaphragm ceiling that is able to transmit the racking loads to the designated

bracing walls that can carry the loads. Otherwise, wall frames can be designed for portal

action (AS 1684:2010).

34

(a) Right angle to long direction

(b) Right angle to short direction

Figure 2.16: Typical location and distribution of bracing walls

35

2.8 Lateral Force Distribution Methods for Light-framed Structures

The lateral loads generated due to extreme wind or earthquakes on the whole structure

are distributed to the lateral force-resisting system of the structure. In order to design

light-frame structures for wind and earthquake loads, it is necessary to design lateral

load-resisting elements, such as a combination of bracing walls and diaphragms and

their connections, to transfer the loads to the building’s foundations. Light-frame

structures can be defined as an assembly of numerous components or sub-assemblies

with monotonous members (for instance, walls, floors and roof systems) connected by

inter-component connections such as bolts, metal straps or exclusive connectors,

making a three-dimensional extremely indeterminate structural system (Kasal et al.,

2004). Therefore, the design of individual sub-systems and components is greatly

dependent on the precision and trustworthiness of the methods used to distribute

structural loads to the several components of the structure.

According to Kasal et al. (2004), if the load sharing and distribution is not done

properly, it will result in either over-conservative (i.e. uneconomical) or under-

conservative (less safe) structures. Hence, if the load distribution is not anticipated

appropriately, it is possible to have an ‘‘engineered’’ structure that is potentially less

safe than the one that has not been ‘engineered’ (Paevere, 2001), or in other words, it

can be stated that an engineered structure can produce a false sense of confidence of

safety and performance (Kasal et al., 2004). It should be mentioned that UBC (1997)

classified structures into two categories such as (i) engineered structures which include

light-frame structures of unusual size, shape or split level, and (ii) non-engineered or

conventional structures that include structures of one-, two- or three stories, single-

family houses’ apartments. Non-engineered structures are constructed using the

“general construction requirements” as well as the “conventional construction

requirements’’ (NAHBRC, 2000). Cobeen (1997) and Foliente (1998) mentioned that if

performance-based methods are to be successfully applied in the design and assessment

of light-frame structures, more accurate and reliable lateral load distribution methods

need to be developed, based on a detailed understanding of the structural behaviour.

Kasal et al. (2004) describes various lateral load distribution methods, as presented in

Figure 2.17.

36

Figure 2.17: Plan view of various load distribution methods (Kasal et. al. 2004) (Figure

is omited from the electronic version of thesis due to copyright issue)

2.8.1 Tributary Area Method

The tributary area method is probably the most widespread approach used to distribute

lateral loads to shear walls. The wind or earthquake loads on various components of the

lateral load-resisting system are distributed based on the tributary areas of the geometry

of the structures. In this method, it is assumed that a horizontal diaphragm is considered

flexible (i.e. comparatively flexible with respect to the shear walls) and it distributes

lateral loads based on the tributary areas rather than the stiffness of the supporting

bracing walls, as illustrated in Figure 2.17(a). When the diaphragm is considered as

considerably rigid compared to the shear walls, and the shear walls have approximately

equal stiffness, the reactions of the shear walls will be roughly equivalent. If this

hypothesis is correct, the interior and exterior shear wall would be over-designed and

under-designed respectively using the tributary area method (NAHBRC 2000).

According to the NAHBRC (2000), diaphragm flexibility mainly depends on its

construction system and its aspect ratio (span-width ratio). Long-narrow diaphragms

37

exhibit more flexibility than short-wide diaphragms in bending along their long

dimension i.e. rectangular diaphragms are comparatively stiffer in one loading direction

while reasonably flexible in the other. Likewise, longer shear walls with few openings

are stiffer than narrow shear wall portions (Kasal et al. 2004).

Kasal et al. (2004) reported that in seismic design, tributary areas are related to uniform

area weights (i.e., dead loads) allocated to the structure systems (i.e., roof, walls, and

floors) that produce the inertial seismic load during lateral ground motion of the

structure. In contrast, in wind design, the lateral component of the wind load acting on

the exterior surfaces of the structure is considered as a tributary area.

According to Kasal et al. (2004), the tributary area method can be presented as a series

of flexible beams on rigid supports. Kasal and Leichti (1992) found that this method

can provide erroneous results for particular plan arrangements and can deliver both

conservative and non-conservative results. Kasal and Leichti (1992) also determined

that, if the structure is considered as a flexible beam on rigid supports, the forces in the

shear wall may be over-predicted by 130% or under-predicted by 60% using the

tributary area method. The tributary area method is appropriate in situations where the

layout of the shear walls is normally symmetrical in terms of spacing and they have

similar strength and stiffness characteristics. The main advantages of the tributary area

method compared to other methods are its ease and applicability to simple structural

arrangements (NAHBRC, 2000).

Phillips et al. (1993) stated that no load sharing between the shear walls is considered in

a flexible diaphragm. Hence, the lateral load distributions to every shear wall are

calculated based on their tributary areas. Phillips et al. (1993) also revealed that when a

structure is non-symmetrical and possesses variances in stiffness between nearby shear

walls, the tributary areas method is not appropriate. This is because the ceiling/roof

diaphragm will distribute a significant portion of the applied load to the stiffer walls of

the structure. In the case of a rigid diaphragm, the lateral load distribution is estimated

based on the relative stiffness of the shear walls (Phillips et al. 1993).

2.8.2 Simple and/or Continuous Beam Methods

The simple and/or continuous beam methods are a subgroup of the tributary area

method. In defining the lateral load distribution to the shear walls, the roof

38

configuration is not considered in both the simple and continuous beam methods, while

the arrangement of the roof and the wall elevations are considered in the tributary area

method. According to Kasal et al. (2004), the simple beam method (Figure 2.17(c))

represents the structure as a consideration of a sequence of simple beams loaded by

means of uniformly distributed load which is equivalent to the total wind load divided

by the length of the structure. In contrast, the continuous beam method (shown in Figure

2.17(e)) models the structure as a beam continuous over several simple supports with a

uniform distribution load that is equivalent to the total wind load divided by the length

of the structure. The continuous beam method can be analysed using analysis method

including the moment distribution method, the slope deflection method, the force

method, and the stiffness method.

2.8.3 Total Shear Method

This method is the second most common and easiest method. The method indicates that

the total shear resistance in all the shear walls needs to add up to the total applied shear

(Kasal et al. 2004). In the total shear method (as shown in Figure 2.17g), the total storey

shear developed on a specified floor level is distributed in every orthogonal direction of

loading. The amount of shear wall is then distributed consistently in the level based on

the designer’s judgment. In order to avoid inequalities of possible loading or stiffness,

the total shear method provides worthy judgment to the distribution of the shear wall

(NAHBRC, 2000).

NAHBRC (2000) stated that in seismic design, loading discrepancies can be produced if

the mass distribution of the building is not uniform, and in the case of wind design,

loading discrepancies occur if the building’s surface area is not uniform (i.e., taller walls

or steeper roof sections provide larger lateral wind loads). In both conditions,

discrepancies are generated if the centre of resistance does not coincide either with the

centre of mass (seismic design) or the resultant force centre of the exterior surface

pressures (wind design). Kasal et al. (2004) stated that the shear forces are distributed

consistently to the lateral resisting shear walls according to their stiffness or location.

After all, the accuracy of this method is dependent on the designer’s judgement;

otherwise, the method would provide poor results under severe seismic or wind events.

This method takes into account neither the distribution of wind load to each bracing

wall nor the deflection check of bracing walls. These shortcomings are taken into

39

account in other methods, such as the deep beam method, the relative stiffness method

and the plate method, which are described below.

2.8.4 Relative Stiffness Method without Torsion

This method is the contrary of the tributary area method. In this method, it is assumed

that the horizontal diaphragm is stiff compared to the shear walls, and the lateral loads

on the structure are distributed to the shear walls based on their relative stiffness (refer

to Figure 2.17.b). Several methods are available for the estimation of wall stiffness,

such as the perforated shear wall method and the segmented shear wall method. The

stiff diaphragm rotates to some extent to distribute lateral loads to all shear walls of the

structure, but not only to shear walls parallel to an expected loading direction

(NAHBRC, 2000). Therefore, the relative stiffness method considers torsional load

distribution and direct shear load distribution.

Klingner (2010) stated that plan torsion can be ignored when the structure has a

reasonable plan length of walls in every major plan direction. This method provides

reasonably precise results with less effort, and is therefore relatively cost-effective for

design. Although the method is conceptually precise and relatively more difficult than

the tributary area and total shear methods, its limitations in terms of reasonably defining

the actual stiffness of shear walls and diaphragms means that its relevance to real

structural behaviour is uncertain (NAHBRC 2000).

It is recommended that the eccentricity between the centre of mass and centre of rigidity

should be taken into account when assessing the forces acting in the various elements of

the lateral load-resisting system of structures. Nowadays, the inelastic torsional

response of building structures can be examined using a static three-dimensional push-

over analysis. However, the point of application of the lateral load is assumed to be

located at the centre of mass, which may not be representative of the conditions under

dynamic loading (Tremblay et al. 2000).

2.8.5 Rigid Beam on Elastic Foundation/ Relative Stiffness with Torsion

This method is similar to the relative stiffness method, with the consideration of

torsional effects. Kasal et al. (2004) stated that in this method, the structure is

characterized by a rigid beam on elastic foundations. In a linear elastic foundation, the

displacement is a linear function of the applied load. In this method, the shear walls can

40

be denoted by linear springs subjected to smaller amount loads and their corresponding

response. NAHBRC (2000) reported that the relative stiffness method is the only

available preference when it is necessary to consider the torsional load distribution to

exhibit the lateral stability of an unevenly braced structure or to fulfil the building code

requirements. The structure is efficiently represented as a rigid beam on linear springs

where the rotation of the structure is considered, as presented in Figure 2.17(d).

However, this method is not appropriate where strong nonlinear behaviour of the system

is expected to occur, for instance, the building may be loaded well beyond its elastic

limit under earthquake loading (Kasal et al. 2004).

Klingner (2010) stated that a torsional moment is produced when the centre of gravity

of the lateral loads does not coincide with the centre of rigidity of the lateral load-

resisting elements, providing the diaphragm is adequately rigid to transfer torsion.

When the structure’s centre of gravity and the centre of rigidity of the shear walls do not

coincide, a torsional component of shear will occur in addition to the direct shear force

(Phillips et. al 1993). The magnitude of the torsional moment generated that must be

distributed to the lateral load-resisting elements through a diaphragm is determined by

the sum of the moments produced due to the physical eccentricity of the translational

loads at the level of the diaphragm from the centre of rigidity of the resisting elements.

The torsional distribution through rigid diaphragms to the lateral load-resisting elements

is assigned in proportion to the stiffness of the walls and the distance from the centre of

rigidity. However, flexible diaphragms should not be used for torsional distribution

(Klingner, 2010).

NAHBRC (2000) reported that the torsional discrepancies in any structure may be

responsible for the comparatively better performance of particular light-framed

structures when one side is weaker (i.e. lower stiffness and lower strength) compared to

the other three sides of the structure. This situation normally occurs because of the

aesthetic aspiration and functional necessity for additional openings on the front of a

structure. Nevertheless, a torsional behaviour in under-design (i.e. “weak” or “soft”

storey) may cause devastation to a structure and create a severe risk to life (NAHBRC,

2000).

41

2.8.6 Plate Method

In this method, plate elements are used to model the diaphragm for distributing wind

load to the bracing walls. The plate method may be used for multi-storey structure

analysis and stochastic analysis, due to its simplicity. Kasal et al. (2004) stated that in

plate method, the structure can be modelled as a simplified two- or three-dimensional

structure that can capture the contribution of transverse wall stiffness in order to observe

the complete behaviour of the structure (refer to Figure 2.17(h)).

In the plate model, the plate represents the diaphragm, and the spring represents the

shear walls. It should be mentioned that the stiffness of the shear walls can be

represented by either linear or nonlinear springs. Generally, the stiffness in the plate

model is governed by the plate thickness and material properties (Kasal et. al. 2004).

Therefore, estimation of the load-deflection behaviour of the springs which represent

shear walls and plate stiffness (i.e., the diaphragm stiffness), and the location of the

vertical mass centre that expresses the floor elevations are essential in the plate method

analysis.

2.8.7 Finite Element Method

Kasal et al. (2004) reported that finite element modelling can capture the behaviour of a

whole structure according to the properties of materials as well as connections in the

structure (see Figure 2.17.i). This method can be used to observe the behaviour of steel-

framed structures under both static and dynamic loads. Finite element modelling can

also be used to conduct sensitivity analysis, and to produce inputs for further simpler

models. According to Klingner (2010), most computer programs developed for the

analysis of structures assume that floor diaphragms are rigid in their own planes. Every

floor level has three horizontal degrees of freedom (two horizontal displacements and

rotation about a vertical axis). This method (while rational for frame structures whose

floors are rigid in their own planes compared to the vertical frames), is not accurate for

wall structures whose horizontal diaphragms are usually almost as rigid as their vertical

walls (Klingner, 2010).

2.9 Performance of Light-framed Structures under Lateral Loads

Kasal and Leichti (1992) stated that the capability of a light frame structure to resist

wind loads mainly depends on the diaphragm’s shear strength. They also stated that the

proportion of transfer of the load is a function of the building geometry, wall stiffness

42

and the inter-component connections. The shear force transferred via each wall can be

calculated based on a series of simple beam analyses. A method that incorporates wall

stiffness for the distribution of the reaction forces is required (Kasal et. al. 1992).

Kasal et al. (1994) studied a three-dimensional nonlinear finite element model of a light-

frame wood building in order to determine the internal forces due to wind pressure in

shear walls. They compared the results with existing design procedures and found that

approximately one-half of the loads are transmitted directly to the foundation and

simple and continuous beam models lead to inaccurate results in calculating the internal

forces in the shear walls. They also proposed and analysed both linear and nonlinear

models with the consideration of the roof diaphragm as a rigid beam on elastic supports,

and verified their finite element model with the experimental results. They concluded

that the rigid beam analogy is an appropriate method when the shear stiffness of the

walls is known.

Henderson et al. (2006) noted that the most commonly observed building failures due to

cyclone Larry (March, 2006) included: widespread failure of roller doors, often

accompanied by loss of wall or roof panels; loss of struts, ridge members and connected

rafters when struts were not tied down; and structural component failure of under-

designed cold-formed steel sheds and garages. More than half a billion dollars was lost

due to damage to domestic and commercial buildings. Henderson et al. (2006) also

reported that another tropical cyclone Winifred crossed the same area of the North

Queensland coast in February 1986. The most common failure in older houses was loss

of roof cladding, often with battens attached.

Boughton et al. (2011) reported that tropical cyclone Yasi had wind speeds equivalent

to 55% to 90% of typical housing’s ultimate limit state. They concluded that normally

less than 3% of all post-80s houses in the worst-affected areas suffered substantial roof

damage, more than 12% of the pre-80s houses experienced considerable roof damage,

and more than 20% of the pre-80s houses in some towns had substantial roof loss.

Boughton et al. (2011) identified the main reasons for the worse performance of pre-80s

houses and indicated that the tie-down systems which were used during construction do

not satisfy the present requirements.

43

Cyclone Amy, which struck in 1980, caused considerable damage to the mining town of

Goldsworthy. Three weeks later another cyclone, Dean, crossed the coast of Port

Hedland in Western Australia. At least sixteen houses suffered extensive damage during

cyclone Amy, and a further four during cyclone Dean. Such damage usually meant loss

of roof structure and loss of some walls. Both cyclones demonstrated the need for

sufficient fasteners to be provided in the roof structure (Reardon, 1980).

Reardon and Oliver (1982) found that about 50% of industrial and commercial

buildings had significant damage, mainly loss of roof sheeting and damage to roof

structure. There were some cases where walls were damaged also, due to the loss of

lateral bracing provided by the roof structure. Investigations of some of the damaged

buildings revealed that few cyclone precautions were included in the construction of

houses. Generally, concrete block houses performed better than timber-framed houses

(Reardon and Oliver, 1982).

Boughton and Reardon (1984) noted that the Northern Territory town of Borroloola was

battered on 23 March 1984 by high winds known as cyclone Kathy. The cause of the

damage for some buildings was a complete lack of design for high winds, and this

seemed more prevalent in the temporary buildings. They also observed that many roof

sheeting failures originated near edges or corners where no attention had been given to

the high localised uplift pressures in those areas.

Boughton and Falck (2007) discovered that due to cyclone George, the damage of major

parts of the roof structure was the worst structural damage. Structural damage occurred

due to reasons including the deterioration of older structural elements, and the failure of

non-structural elements such as flashings and trims. Henderson and Leitch (2005)

surveyed the damage due to cyclone Ingrid and found that where failures were

observed, the damage was attributed to inadequate, missing or corroded structural

components, and corrosion of components initiated failure in many cases.

2.10 Experimental Studies of Light-framed Structures

The overall structural behaviour of a house is not only dependent on the behaviour of

individual elements and sub-systems in isolation, but also on their interactions. Without

considering the whole structural system, it is very difficult to identify which

components lead in determining the overall behaviour of the structure. In domestic

44

structures, both the structural and non-structural components affect the structure's

behaviour. This section reviews several experimental studies conducted in the United

States, Australia, and Japan on full-scale light-framed houses and diaphragms.

2.10.1 Full-scale Structures

Tuomi and McCutcheon (1974) conducted test on a full-scale house under simulated

wind loads to determine the structural response of a conventional wood-frame house to

simulated wind loads. They observed that the first failure occurred at the sole plate of

the loaded wall at a pressure of 3000 Pa (63 psf). At a pressure of 5900 Pa, the house

slid off the sill plate and testing was terminated. The failure pressure was equivalent to

that caused by a wind velocity of 98 m/s. They concluded that the stiffness of the wall

sheathing is sufficient to cause the loaded wall to act as a plate, resulting in

approximately three-eighths of the total windward wall force being resisted by each of

the end shear walls. This fraction of lateral loads resistance would likely change for a

longer house with interior partitions, which would act as intermediate shear walls.

Tuomi and McCutcheon (1974) also conducted wood-framed house testing with the

application of transverse loads without uplift. The researchers found that there was no

failure until the lateral load reached the “equivalent” of a 98 m/s wind event without the

inclusion of uplift loads.

The Cyclone Testing Station has tested different configurations of light-frame houses

(single-storey timber-framed brick veneer houses tested by Reardon 1986; a two-storey

split steel timber-framed brick veneer house by Reardon and Mahendran 1988; and a

single-storey light gauge steel-framed brick veneer house by Reardon 1990) to examine

the response under the design level of wind loadings. They also conducted wind tunnel

tests to determine appropriate load distributions. Their studies focussed on the necessity

of the interactions of the component and the effect of the boundary conditions and non-

structural components.

In Australia, Reardon and Henderson (1996) conducted destructive testing on a house

and concluded that conventional residential construction (only marginally different from

that in the United States) is capable to resist about 2.4 times its projected design wind

load without failure of the structure.

45

Fischer et al. (2001) conducted a shake table test of a house with plan dimensions of

4.9m x 6.1m to observe the seismic performance under different levels of seismic

shaking and for different structural configurations. They concluded that a fully

engineered timber-framed house has better seismic performance than a conventionally

constructed house. These tests were conducted to assess the contributions of different

elements to the response and the researchers found that non-structural wall finishes

considerably stiffen the structure and reduce the response level.

Filiatrault et al. (2004) performed shake table testing of a full-scale two-storey wood-

framed house model and concluded that wall linings have a positive effect on the

dynamic response of the structure. Filiatrault et al. (2010) also conducted shake table

testing of a two-storey full-scale light-framed wood structure to decide the dynamic

characteristics and the seismic performance of the test building under several base input

intensities. The building was tested with and without interior (gypsum wallboard) and

exterior (stucco) wall claddings. They found that the fixing of gypsum wallboard to the

interior surfaces, and exterior stucco of structural wood-sheathed walls significantly

enhanced the seismic performance of the structure. Shake table test results provided

evidence for the significant influence of wall finish materials on the behaviour of lateral

load-resisting systems in light-frame wood construction.

Sugiyama et al. (1988) completed lateral tests on a full-scale Japanese conventional

wood-frame house in order to study the effect on racking resistance of transverse walls.

These researchers found that transverse walls make only a minor contribution to lateral

resistance.

Boughton and Reardon (1982) conducted tests on a full-scale house under simulated

high wind loads. They concluded that the roof assembly had adequate in-plane strength

to distribute the lateral load to the shear walls. Based on the stiffness test results, they

concluded that approximately 60% of the lateral load was transmitted to the shear walls

through the roof sheathing and ceiling systems, and the remainder was transmitted

directly to the internal shear walls or was resisted by the windward wall.

Stewart et al. (1988) tested two homes under simulated wind loading to investigate the

effect of transverse walls on racking resistance and the interaction between the roof

diaphragm and the shear walls. They found that the roof system was stiffer than the

46

shear walls, so that the system could be approximately modelled as a stiff beam on

elastic foundations. Richins et al. (2000) also conducted a series of tests under simulated

design-level wind loads. They applied distributed loads and concentrated loads at the

ceiling level and measured the global displacements of the house and reactions in the

tie-down straps. They concluded that the racking and slip displacements were small

under design-level wind loads.

Reardon (1987; 1989) conducted whole-house testing in Australia and concluded that

about 75% deflection (i.e., drift) of a wall reduces due to the addition of interior ceiling

finishes. He also found that the addition of the cornice trim to cover or dress the wall-

ceiling joint reduces the deflection of the same wall by another 60% (roughly 16% of

the original deflection).

Reardon (1987) tested a brick veneer house under simulated cyclone wind conditions

and studied the diaphragm action of the ceiling and roofing materials. They found that

the house was very strong in resisting horizontal wind forces, but inadequate to resist

the applied cyclic uplift wind forces. He also concluded that (i) fatigue cracks due to

cyclic loading can severely weaken light gauge metal straps used in construction joints

of houses in cyclone-prone areas; (ii) a ceiling can act as a very efficient diaphragm in

distributing horizontal wind forces, (iii) normal internal wall cladding provides a much

stiffer wall bracing medium than conventional cross-bracing; (iv) light metal tiles can

provide some bracing diaphragm action; (v) uncracked single leaf brickwork can resist

the design loads without requiring much support from the timber frame; (vi) the

ultimate strength of the brick veneer was adequate, and dependent upon the buckling

strength of the brick ties; and (vii) return walls in the brickwork provide a considerable

stiffening effect against lateral wind forces.

Boughton (1984) provided a brief outline of the procedure used to test a complete house

designed and built in accordance with the current building regulations for houses in

cyclone-prone areas. He demonstrated mechanisms of load transfer, load sharing

between the elements in the house and areas of weakness or excessive strength. He

concluded that (i) roof, ceiling and floor diaphragms functioned as highly effective

diaphragms to transmit lateral forces to the top of vertical bracing elements; (ii) the

house structure above floor level has great reserves of strength to resist lateral loads in

spite of severe debris damage to load-carrying walls; (iii) at working loads, all walls

47

within the house function well within their elastic range to carry lateral loads from top

plate level to floor level.

Ohashi and Sakamoto (1988) conducted tests on a two-storey building with two

partition walls in every storey and found that the structure performed as a nonlinear

system with degrading stiffness. The load-deflection curves were similar to those

reported by Chou (1987) for single nail connections, and concluded that there is a robust

influence of connections on the overall behaviour of the structure.

2.10.2 Roof and Ceiling Diaphragm

Estimation of ceiling or roof diaphragm stiffness is important for determining the

distribution of lateral load to the shear walls. However, very little research has been

conducted in this area to date.

Tremblay et al. (2004) conducted an experiment to study the response of steel roof deck

diaphragms (made of corrugated steel deck panels) for low-rise steel buildings under

seismic loading. They observed that (i) diaphragms constructed with screwed side lap

fasteners and nailed deck-to-frame connectors showed a pinched hysteretic behaviour,

but could withstand large inelastic deformation cycles with limited strength

degradation; (ii) the systems that included welding with washer connections possess

higher shear resistance and less pinching, but the strength reduces quickly after reaching

the peak load, and therefore, the systems ought to be designed for limited inelastic

response; (iii) deck systems with button punched side laps and frame welds without

washers exhibited a brittle response and must be designed to resist elastic response

under severe earthquake motions; and (iv) the inelastic response increases with the

decreased spacing of the fasteners. Samples built with an interior overlap joint showed

extensive warping of the cross-section, primarily due to the shorter panel length.

Turnbull et al. (1982) performed tests on three farm building ceilings under simulated

wind loads: (i) conventional, 7.5mm sheathing of Douglas fir plywood nailed directly to

trusses spaced at 600 mm and plyclips at panel edges mid-span between trusses; (ii)

improved plywood diaphragm, 7.5-mm sheathing Douglas fir nailed along four edges to

a 1200 x 1200-mm grid under trusses spaced at 1200 mm; and (iii) screwed sheet steel

diaphragm, power-screwed under trusses spaced at 1200 mm. They found that the

screwed steel ceiling is about 2.4 times stiffer than the plywood ceiling and 1.6 times

48

stiffer than the improved plywood ceiling up to 12 mm deflection. The screwed steel

ceiling provides higher stiffness, probably due to the better connection stiffness along

the full perimeter of each steel sheet. Turnbull et al. (1982) also concluded that with a

typical 2.4 m stud wall height and 0.64 KN/ m2 wind pressure; the conventional

plywood ceiling would be safe to a ceiling length/width ratio (L/W) up to 3.67, the

improved plywood ceiling to 6.04, and the screwed steel ceiling to 5.35.

Carradine et al. (2002) conducted tests of timber frame and structural insulated panels

(SIP) roof systems to establish procedures for integrating the substantial in-plane

strength and stiffness of SIPs within the lateral load design of timber-framed and SlP

buildings. From their primary studies it has been reported that timber-framed structures

do not have the structural integrity to resist lateral loads for code-compliant designs

without including diaphragm action. They concluded that the ultimate shear capacity

and shear stiffness of the diaphragm increases with the increase of the screw diameter or

decreased spacing of the screws.

Mastrogiuseppea et al. (2008) studied the effect of non-structural roofing components

on the dynamic properties of single-storey steel buildings, particularly on the roof

diaphragm properties. They found that gypsum board is the stiffest element of the non-

structural components, and there is a higher influence on the in-plane force-deformation

behaviour of the steel roof deck diaphragm. There is very little effect due to the other

non-structural elements, either due to their low in-plane shear stiffness or the lack of a

direct connection to the steel deck. Finite element modelling showed that the stiffness of

the steel diaphragm increases with the increase of the thickness of the steel roof deck

panels as well as closer spacing of the connections.

Kunnath et al. (1994) presented a comprehensive experimental, analytical, and

parametric study to observe the performance of gypsum-roof structures under severe

earthquake excitations. They provided some recommendations for strengthening

gypsum roof diaphragms: (i) diaphragm spans may be reduced by adding vertically-

oriented lateral load-resisting elements consisting of shear walls or steel bracings; (ii)

the ends of the gypsum diaphragm (where the shear stresses are the highest) can be

strengthened by the addition of another layer of gypsum and mesh reinforcement; and

(iii) place horizontal bracings below and in the plane of the diaphragm as a substitute

49

shear-resisting element so that the bracing is stiff enough to control gypsum drift to

within prescribed strain levels.

Falk and Itani (1987) tested three floor, three ceiling, and four wall diaphragms ranging

in size from 8 x 24 ft to 16 x 28 ft to investigate the effects of typical sheathing

materials such as plywood and gypsum wallboard, as well as the effect of a stairwell

opening in one floor diaphragm and door and window openings in two walls. They

concluded as follows: (i) diaphragm stiffness decreases with increasing diaphragm

displacement and consequently decreased natural frequency; and (ii) the presence of

openings usually generates lower damping ratios than identical diaphragms without

openings.

In Australia, Boughton and Reardon (1984) tested a house with fibre cement exterior

cladding and plasterboard interior finishes and found that the roof and ceiling

diaphragm is stiff and the diaphragm rigidly distributes the lateral loads to the walls.

These researchers recommended that the house has adequate capacity to resist a design

wind speed of 65 m/s. Reardon (1989) observed the effect of various sheathing

materials on the diaphragm action of house elements and concluded that the stiffness of

the house is enhanced significantly when the wall or the roof sheathing is included in

the model.

2.11 Analytical Modelling

Analytical modelling is important to extend the usefulness of experimental results and

to predict the structural behaviour of the entire building its sub-assemblies under

different loading conditions. In analytical modelling, the physical relationships between

individual components and entire buildings are included. Analytical and experimental

studies of light-framed structures are also important to develop a design procedure. The

analysis of light-framed structures under lateral loads is a difficult task, due to several

degrees of nonlinearity (e.g. material nonlinearities, nonlinear joints and connections,

and discontinuities between adjacent elements), the complex nature of the connections

and fasteners, and the wide variability in material properties and construction

techniques.

50

2.11.1 Full-scale Structures Modelling

Yoon and Gupta (1991) developed a program to analyse the Tuomi-McCutcheon (1974)

house to compute factors of safety against possible failure modes, such as buckling

of sheathing panels and slippage of the connecting nails. The experimental results of

the Tuomi-McCutcheon house were compared with those of Yoon and Gupta (1991)

and good agreement between the two results was found.

Schmidt and Moody (1989) extended the Tuomi-McCutcheon (1978) model for the

analysis of shear walls by including the nonlinear behaviour of the fasteners. They used

the model to predict the response of 3-dimensional wood-frame structures subjected to

lateral loading. The main assumption of their 3-D model was that the ceiling and roof

diaphragms were sufficiently rigid, such that the shear walls in each storey can be

combined into a three-degrees-of-freedom system: two horizontal translations and one

rotation. The model was validated using the experimental results from the full-scale

house tested by Tuomi and McCutcheon (1974) and Boughton and Reardon (1984) and

reasonable agreement was found. They also found that the analytical results differed

from the experimental results in the cases where the building was loaded with an

eccentric point load. This may be due to the oversimplification of the model that

neglects the out-of-plane stiffness of the walls, the slippage of inter-component

connections and the shear stiffness of areas above and below the openings, and the

assumption of rigid ceiling and roof diaphragms.

Kasal et al. (2004) and Kasal et al. (1994) developed a nonlinear 3-D finite element

model of complete wood-frame structures and used the model in the analysis of the full-

scale house tested by Philips (1990). Their model was designed as an assembly of

substructures (walls, roof, and floors) joined by inter-component connections. Using the

ANSYS software, they developed two 3-D finite element models: a coarse and a refined

mesh of the house tested by Philips (1990). They observed that when only two adjacent

walls out of the four were loaded, the model did not yield accurate results for the

unloaded walls. This inaccuracy may be due to the transfer of forces through the roof

diaphragm and inter-component connections. Their results also indicated that there was

no significant difference between the response of the coarse and refined meshes and that

the distribution of loads among the shear walls depends on the combination of shear

wall stiffness, roof diaphragm action, and inter-component connection stiffness.

51

2.11.2 Ceiling and Roof diaphragm

Schmidt and Moody (1989) developed a simple 3-D model using rigid ceiling

diaphragms and nonlinear shear walls to predict the behaviour of light-frame buildings

under lateral load and derived an exponential function for the monotonic load-slip

connection. The model was compared with Tuomi and McCutcheon’s (1974) and

Boughton and Reardon’s (1984) test results and reasonable agreement was found.

In a 3-D truss model, Ge (1991) applied nonlinear diagonal springs in order to substitute

the shear behaviour of diaphragm elements due to static or pseudo-static lateral loads in

a light-framed structure. The model was validated using the experimental results of

Tuomi and McCutcheon (1974), Boughton and Reardon (1984), and Reardon and

Boughton (1985). Ge (1991) found satisfactory agreement for symmetrically-loaded

buildings, but for asymmetrically-loaded constructions, agreement was not supported

appropriately.

Kataoka (1989) developed a nonlinear three-dimensional finite element model for full-

scale structural analysis. In his model, nonlinear springs were used in order to model

inter-component connections and the shear resistance of walls. Kataoka (1989) also

modelled the building as a three-dimensional framed with nonlinear diagonals and

nonlinear member connections. However, bending stiffness of the wall was not included

in the model. He found good agreement between the analytical and experimental results.

Falk and Itani (1989) described a two-dimensional finite element model to signify the

distribution and stiffness of the nails that secure sheathing to framing in a wood

diaphragm. The load-displacement results obtained by Falk and Itani (1989) showed

that the diaphragm stiffness increases with the increasing properties of the nails. They

also concluded that nail spacing had a larger effect on diaphragm stiffness than nail

modulus. There was a very dramatic effect on diaphragm stiffness due to the variance of

perimeter nail spacing, but changing field nail spacing did not affect diaphragm stiffness

to the identical range. Falk and Itani (1989) also investigated the effect of blocking on

the standard ceiling diaphragm stiffness and found that diaphragm stiffness increased

due to blocking. They also found that extra nails that secure the sheathing to the

blocking and frame action provide an identical effect on diaphragm stiffness.

52

Collins et al. (2005) presented a nonlinear three-dimensional finite element model

which is capable of static and dynamic analysis and compared the model with the

results of an experiment on a full-scale asymmetric light-framed building. The model

was validated based on global and local responses using measures of energy dissipation,

displacement, and load. They showed that the energy dissipation, hysteretic response,

load sharing between the walls, and the torsional response were estimated reasonably

well.

Foschi (1977) presented a formulation for the structural analysis of wood diaphragms

that is executed in the SADT program and integrates the basic features of wood

structural assemblies such as orthotropic plate action and nonlinear connection

behaviour. The model provided estimates for diaphragm deformations and was capable

of providing approximations for ultimate loads based on connection yielding.

Itani and Cheung (1984) developed a finite element model to predict the static load-

deflection behaviour of sheathed wood diaphragms under racking loads and found that

the properties of nailed joints are the controlling factor for the performance of sheathed

diaphragms.

2.12 Summary and Research Needs

This chapter has discussed the main components in domestic structures, the factors

which affect the lateral behaviour of houses and ceiling and roof diaphragms, and

presented current practice in Australia. The critical factors which require research

have been identified as follows:

Several experimental studies and analytical modelling have been conducted for

the determination of the strength and stiffness of shear walls. However, very few

studies have been undertaken on the determination of the strength and stiffness

of ceiling and/or roof diaphragms in cold-formed steel houses. Determination of

diaphragm stiffness is essential in the design of light-framed structures in order

to estimate the predicted deflection and thereby classify the diaphragm as rigid

or flexible. This classification controls the method of load distribution from the

diaphragm to the resisting walls. The ability to calculate accurately diaphragm

stiffness and hence, deflections will improve the safety and economy of

diaphragms and structures.

53

Shear connection tests are essential to determine the load-displacement

behaviour of the connections between plasterboard and the steel framing

members. The values of the load-displacement curves can be used as the input

parameters for the development of analytical modelling. The proposed model

will be validated against experimental data.

54

CHAPTER 3

EXPERIMENTAL PROGRAM (PHASE I): SHEAR CONNECTION TESTS

3.1 Introduction

The experimental program comprised of three stages. The first stage was a series of

tests including shear connection tests between plasterboard sheathing and cold-formed

steel framing members as well as loading on the edge of plasterboard to determine its

bearing capacity. Figure 3.1 shows the complete experimental program in this research

project. The second stage involved full-scale ceiling diaphragm tests in cantilever

configuration, and the third stage involved full-scale ceiling diaphragm tests in beam

configurations.

In this chapter, the results of the first phase of the experimental program, i.e. individual

connections between plasterboard sheathing and cold-formed steel framing members,

are discussed. The connection between the steel framing members (ceiling battens or

bottom chords of trusses) and the plasterboard sheathing is made using screws. The

strength and stiffness of screwed steel-framed ceiling diaphragms are mainly governed

by the strength and stiffness of the connections between the steel framing members and

the plasterboard sheathing, rather than the members’ properties themselves. Since

screws are responsible for the transfer of the forces to the framing members from the

plasterboard, it is crucial to observe their performance in shear connection tests. These

tests assist understanding of the basic behaviour of these components and help to

provide understanding of the behaviour of a complete ceiling diaphragm.

Virtually all investigations of shear connection tests have focused on monotonic static

loading testing. Inexpensive test methods have been performed to replicate

representative tests in order to determine the parameters defining the load-displacement

curves for the connections between cold-formed steel framing members and

plasterboard sheathing. The objective of the shear connection tests was to determine the

upper and lower bounds of the load-displacement curves for typical framing-to-

plasterboard connections in ceiling diaphragms. The results of the connection tests were

used as the input parameters in the development of analytical models to predict the full-

sized ceiling diaphragm performance, as described in Chapter 6. The methods used in

testing, specimen configuration, specimen fabrication, instrumentation, and the data

55

acquisition system applied for these tests are discussed in detail in this chapter. The

results and conclusions drawn from phase I are also reported in this chapter.

3.2 Overview of Experimental Program

The test loading protocol implemented in this testing program concentrated on lateral

wind loading rather than earthquake loading. This is simply because the governing

lateral load for Australian houses is wind load. Therefore, only static monotonic loading

protocols were applied.

Figure 3.1: Summary of the experimental testing of this study

Research experience has demonstrated that the entire behaviour of a diaphragm is

mainly governed by the behaviour of the sheathing-to-framing connections (Foliente

1995b). In addition, to illustrate the measured response of diaphragms, the responses of

individual connections between plasterboard sheathing and cold-formed steel framing

members were determined through shear connection testing. Shear connection testing of

specimens also permits a range of connection arrangements, materials, and loading

protocols to be undertaken. Furthermore, shear connection tests are less expensive and

faster to complete, compared to the testing of full-scale diaphragms.

A number of parameters influence the response of sheathing-to-framing connections,

such as the fastener type and diameter, the framing member thickness, the type and

thickness of sheathing/cladding, and the applied loading. In Australia, as typical steel-

56

framed houses have plasterboard ceilings which are attached to steel ceiling battens

(typically top-hat sections) using a specific type of screw, only these materials and

products were covered by the test program. In addition, for situations where the

plasterboard is connected directly to the bottom chord of trusses (typically ‘C’ sections),

additional shear connection tests were performed for plasterboard to channel sections.

3.3 Test Methodology

There is no prescribed standard testing method for shear connection tests between

plasterboard and cold-formed steel framing members. However, a number of efforts

were completed to obtain the most representative configurations. Shear connection tests

can be used to determine the shearing strength of connections between plasterboard

sheathing and steel framing material. As stated previously, shear connection tests are

often accepted by investigators to quantify the load-slip behaviour of shear connections

for the development of analytical modelling.

Currently, only the Standard Test Methods for Mechanical Fasteners in Wood (ASTM

D1761-12) provide a standard test method for shear connections to evaluate the

resistance to lateral movement offered by a single nail or screw in wood members. The

test set-up of ASTM D1761-12 is shown in Figure 3.2. However, this test set-up method

has lost favour with academics due to loading eccentricity. As a result, many

investigators have developed substitute testing procedures in efforts to improve ASTM

D1761-12.

The present common shear connection tests have been developed for wood-based

materials, which makes them inappropriate for connections between plasterboard and

steel framing. The reasons are that plasterboard is weaker in compression and it would

be crushed when the plasterboard is gripped firmly or when it is put in bearing.

Therefore, an alternative test set-up has been developed to obtain the load-slip

behaviour of connections between plasterboard and supporting steel frame and this new

method was applied in the experimental program of this research project.

57

Figure 3.2: Test arrangement for lateral resistance of screws (ASTM D1761-12) (Figure

is omitted from the electronic version of thesis due to copyright issue)

An alternative test configuration for testing plasterboard-to-steel frame connection is

depicted in Figures 3.3 to 3.6. In this set-up, a field shear connection test set-up

replicates the shear connections away from the edges, while the edge shear connection

test set-up replicates the shear connections where the screw under shear moves towards

a plasterboard edge. In this set-up, it is not necessary to clamp or support (bearing) the

plasterboard specimens on the testing machine. As an alternative, the channel sections

provide gripping areas for the testing machine. As a consequence, the risks related to the

crushing of the plasterboard specimens and slipping due to inadequate clamping can be

disregarded.

58

Figure 3.3: Field shear connection test set-up to replicate connection with top-hat

section member (dimensions are in mm)

Screws under testing

59

Figure 3.4: Edge shear connection test set-up to replicate connection with top-hat



60

Figure 3.5: Field shear connection test setup to replicate connection with channel



61

Figure 3.6: Edge shear connection test setup to replicate connection with channel

section steel member (here Y designates edge distance 15 mm, 17 mm and 20 mm)

(dimensions are in mm)

A number of tests were performed on shear testing of screw connections between the

plasterboard and top-hat sections as well as channel sections. The objectives of these

tests were to determine the load-displacement behaviour of these connections under

monotonic loading.

3.3.1 Test Materials

The materials used in this study are typical of those used in the construction of cold-

formed steel-framed domestic structures in Australia. The steel sections used in this

research were provided by role persons who are members of NASH and their products

are representative of typical sections used.


62

Framing

Two types of cold-formed steel framing are used, depending on the system of ceiling

diaphragm construction used. These two framing members include top-hat22 section

(0.42 mm thickness) and 90 x 40 x 0.75 mm channel “C’’ sections manufactured by

BlueScope Pty Ltd. In the Australian construction industry, generally top-hat sections

are used as battens for ceilings, roofing, cladding and lining support and as joists for

flooring support. Channel “C” sections are used as truss bottom chords and ceiling

joists. The structural grade of both of the steels is G550. The dimensions and properties

of various steel top-hat sections and steel lipped and unlipped C-sections are available

in NASH Standard Part-2 (2014).

Sheathing

Plasterboard was used as a sheathing material in this study. The sheathing used in this

study was 10 mm thick plasterboard manufactured by Boral Plasterboard Pty. Ltd. This

plasterboard is manufactured to comply with AS/NZS 2588.

Screws

In Australia, screws are typically used to attach the plasterboard to the steel members.

The screws used in this study were 6G-18 x 25 mm bugle-head needle-point,

manufactured by Buildex Pty Ltd. These screws are typically used to fix plasterboard to

steel up to about 0.8 mm thick.

3.3.2 Specimen Configurations and Fabrication

A total of 24 plasterboard specimens were tested as outlined in Table 3.1. Out of the

twenty four tests, ten tests were performed for top-hat sections and the remaining 14 for

‘C’ section connections. Specimens for shear connections for both top-hat and channel

section members prior to testing are shown in Figure 3.7.

In a typical construction, the recommended minimum distance between a screw and the

edge of plasterboard ceiling varies from 15 mm to 22 mm, as described in the Gyprock

Ceiling System Installation Guide (2008) and the Gyprock Residential Installation

Guide (2010). Therefore, 20 mm edge distance is considered to be the typical edge

distance.

63

Table 3.1 Basic test matrix for shear connection tests

Connection

type

Number of

specimens

Screw distance from

plasterboard edge (mm) Specimen designation

Field screw 5 60 Field screw-top hat sections

Edge screw 5 20 Edge screw-top hat sections

Field screw 5 60 Field screw-channel sections

Edge screw 3 15 Edge screw-channel sections



(a)

64

(b)

(c)

Figure 3.7: Specimens of shear connections constructed by the author (a) field screw

connection specimens for top-hat sections, (b) edge screw connection specimens for

top- hat sections, and (c) field screw connection specimens for channel sections.

65

As shown in Figure 3.3, for edge screw tests, the shear load was resisted by one screw

on each side of the specimen; hence the load per screw is half of the applied load. On

the other hand, for field screw tests, the applied load was divided by 2 screws on each

side of the specimen; hence the load per screw is a quarter of the total applied load.

In all tests, the screws were driven until the screw heads were flush with the sheathing

surface. It should be noted that to prevent the variable of overdriven screws, care was

taken to ensure the face of the plasterboard specimens was not penetrated by the screw

head.

3.3.3 Test Equipment

All tests were performed in the Smart Structures Laboratory at Swinburne University of

Technology, Hawthorn, Australia. An MTS hydraulic testing machine was used to

perform shear connection tests under monotonic loading using the displacement-

controlled approach. Loads were measured by the universal testing machine.

Displacements were measured using linear differential transformers (LDTs). The

specimens were subjected to tension, which in turn subjected the screw connections to

shear.

3.3.4 Instrumentation

The instrumentation and measurements of the shear connection tests conducted in Phase

I were relatively simple compared to those of the full-scale ceiling diaphragm cantilever

tests and the full-scale ceiling diaphragm beam tests. In the specimens with top-hat

sections, four LDTs were attached to the sides of the specimens to measure the relative

movement (slip) of the fastener between the framing members and the plasterboard

sheathing (shown in Figure 3.8). Two LDTs were attached to the sides of specimens

with channel sections to measure connection slip, as shown in Figure 3.9.

The data acquisition system for the shear connection tests included National Instruments

data acquisition hardware and Lab view software. Six channels were recorded during

the testing with top-hat sections: the load, machine displacement, and four LDTs.

During the testing with channel sections only two LDTs were used in addition to load

and machine displacement. The data were analysed using commercial spreadsheet

software.

66

(a) Field screw

(b) Edge screw

Figure 3.8: Shear connection test set-up for plasterboard sheathing-to-top hat sections

(a) field screw tests, and (b) edge screw tests

6G-18 x 25 mm bugle head needle point

LDT

Plasterboard

LDT

Edge screw (6G-18 x 25 mm bugle head needle point)

Top hat sections

Specimen clamped to universal testing machine

67

(a)

(b)

Figure 3.9: Shear connection test set-up for plasterboard sheathing-to-channel section

(a) field screw tests, and (b) edge screw tests

Edge screw (6G-18 x 25 mm bugle head needle point)

Channel sections

LDT

Plasterboard

6G-18 x 25 mm bugle head needle point

68

3.3.5 Loading

The loading adopted for these shear connection tests was monotonic. The loading was

displacement-controlled. The specimens were loaded in tension, following a ramp

loading pattern. The load and displacement readings were recorded directly from the

testing machine at one-second time intervals. The test specimens were pulled at the rate

of 1 mm/min. Each specimen was tested until failure so that sufficient data could be

gathered to obtain the load-slip curves. Crucial data achieved from these tests were

ultimate load and displacement. One of the essential aspects of the test is that there was

no eccentricity on the connection under testing. The results of the tests conducted in

Phase I are presented in Section 3.4.

3.4 Results and Discussion

This section presents the results of the shear connection tests. All of the plasterboard

specimens were tested along the machine direction. Liew (2003) stated that for

specimens loaded along the machine direction and across the machine direction, the

difference between their ultimate loads was only 1.2% and recommended that the

loading direction of the specimen was not critical for the connection test. In order to

ensure consistency, all of the tested specimens were prepared from a single sheet.

The load-slip curves from the field screw shear connection tests show some scatter, as

shown in Figure 3.10. This is attributed to inconsistent construction quality. Therefore,

the upper and lower bounds of these curves were fitted using multiple linear curves, to

contain the range of these load-slip curves in order to develop the analytical models in

Chapter 6. The load-slip curves achieved from the edge shear connection tests also

showed some inconsistency. Again, due to the variability of the load-slip curves, the

upper and lower bounds were fitted using multiple linear curves, as presented in Figure

3.11.

Unlike the plasterboard-to-framing connections in the field, edge screw connections

show different failure modes (tear out) of plasterboard where the screws move towards

the plasterboard edge. Small movement towards the edge failed the plasterboard

specimens. It should be noted that for edge screw connections, the specimens failed at a

smaller displacement and did not achieve maximum capacity when compared to field

screws.

69

Figure 3.10: The upper and lower bounds (red lines) of the field screw shear (sheathing-

to-top hat section) connection test results (for one screw)

Figure 3.11: The upper and lower bounds (red lines) of the edge screw shear (sheathing-

to-top hat section) connection test results (for one screw)

70

From the load-displacement curve results, it is clear that the quality of the construction

of the tested specimen was maintained. The reasons for variation in quality of the

construction of the tested specimen are: (i) screws are over-driven, (ii) screws are not

driven at a right angle to the plasterboard; (iii) screws ream a hole in the plasterboard

before screwing into the steel.

Figure 3.12 shows the measurement of the movement of plasterboard relative to the

framing on both sides of the specimens using LDTs, which indicates good consistency.

The typical load-slip curves obtained from the plasterboard -to-top hat section shear

connection tests for both field screws and edge screws are presented in Figure 3.13. The

values are presented for one screw. The load-slip behaviour of plasterboard -to-channel

section connections is presented in Figure 3.14. The complete details of the results from

the entire series of the tests conducted are reported in Table 3.2. Further details of the

utilisation of these test data in the analytical modelling are discussed in Chapter 6.


connections under monotonic loading (for one screw). This figure shows measurements

from LDTs on both sides of the specimens.

71


connections under monotonic loading (mean values obtained for one screw)


connections under monotonic loading (mean values obtained for one screw)

72

Three parameters were used to compare load–displacement results: the ultimate load,

displacement at ultimate load; and initial (tangent) stiffness. The ultimate load provides

the capacity of the connection, the displacement at the ultimate load provides a sense of

the capacity of the connection to deform, and the tangent stiffness provides the

relationship between load and displacement in the initial response. From Table 3.2, it

can be seen that there is a notable difference in the ultimate loads between the field

specimens and edge specimens. The definitions of tangent and secant stiffness under

monotonic loading are shown in Figure 3.15.

Table 3.2 Summary of monotonic test results for one screw

Specimen

Edge

distance

(mm)

Mean

ultimate

load

(kN)

Average

displacement

at ultimate

load (mm)

Average

tangent

stiffness

(kN/mm)

Average

secant

stiffness

(kN/mm)

Failure

mode

Field screw:

top- hat

sections

60 0.44 6.7 0.17 0.07 Bearing and

tilting of

screw

Edge screw:

top- hat

sections

20 0.38 4.7 0.15 0.08 Plasterboard

tearing

Field screw:

channel

sections

60 0.60 6.9 0.75 0.09 Bearing and

tilting of

screw

Edge screw:

channel

sections

15 0.41 1.9 0.73 0.22 Plasterboard

tearing

Edge screw:

channel

sections

17 0.46 2.4 0.72 0.20 Plasterboard

tearing

Edge screw:

channel

sections

20 0.52 3.3 0.70 0.16 Plasterboard

tearing

73

Figure 3.15: Definition of tangent and secant stiffness under monotonic loading

As expected, field screws had higher strength than edge screws. Further, the greater the

edge distances, the higher the strength. For both the top-hat sections and channel

sections, for a 20 mm edge distance the ultimate strength was approximately 85% that

of field screws.

Top-hat sections exhibited lower strength than the channel sections by about 25%. This

is attributed to the lower base metal thickness of the top-hat section compared to the

channel section. This is similar to connections between cold-formed steel plates, where

the lower thickness end plate produces lower strength compared to thicker plates.

3.4.1 Failure Mechanisms

During the shear connection tests, it was observed that the initial load transmission

involved the screw shank bearing on the gypsum and the linerboard. This bearing lead

to the initial crushing of the gypsum and tearing of the linerboard, followed by tilting of

the screw and the consequent penetration of the screw head into the plasterboard. As a

result, ‘bulging’ of the plasterboard in bearing was observed. This in turn caused the

plasterboard to ride over the tilted screw, resulting in the ‘bulge’ enlarging more, as

74

shown in Figure 3.16, to a position where the linerboard might no longer engage. It

should be noted that the ultimate load and corresponding displacement are governed by

the properties of the plasterboard, the screws and the steel framing members.

Figure 3.16: ‘Bulging’ of plasterboard happened as the screw head penetrated into the

plasterboard.

Field connection screws for both the sheathing-to-top hat section and sheathing-to-

channel section showed a failure mode with plasterboard bearing as well as screw tilting

and its head piercing the sheathing material (as shown in Figure 3.17a and Figure 3.18

respectively). The failure mode for edge connections was tearing out of the sheathing

material from its edge (shown in Figure 3.17b). Although significant scatter exists in the

test results, some basic findings are immediately clear: the initial stiffness of both edge

and field connections are similar, whereas the capacity of edge connections (in terms of

load and displacement) is lower than that of field connections. Mean values of load and

deflection from identical specimens are plotted in Figure 3.19, which demonstrates a

failure mode (tearing of board) for specimens with edge distances of 15 mm, 17 mm

and 20 mm and failure modes of plasterboard bearing and screw tilting for specimens

with edge distances of 60 mm. Important parameters obtained from each load-deflection

Bulging

75

curves, including tangent and secant stiffness (refer to Figure 3.15), peak strength, and

deflection at peak strength, are provided in Table 3.2.

(a) Field screw

(b) Edge screw

Figure 3.17: Failure modes of plasteroard sheathing-to-top hat section connections

under monotonic loading (a) field screw, and (b) edge screw

76

Figure 3.18: Failure modes of field screw connection tests of sheathing-to- channel

section framing connections under monotonic loading

3.4.2 Effect of Edge Distance

The effect of edge distance on the specimens in the shear connection tests is

demonstrated in Figure 3.19. All of the specimens failed by tear-out of plasterboard

edges, as shown in Figure 3.20. For specimens with 20 mm edge distance, the

plasterboard developed the load required to tear the gypsum ahead of the screw and

keep that constant load until finally tearing through the edge of the plasterboard.

Therefore, the deformation of the specimen up to failure is a function of the edge

distance. The edge shear connections with 15 mm, 17 mm and 20 mm edge distance

reached their ultimate loads at relatively small displacements compared to the field

screw shear connections. At an edge distance of 15 mm, the shear capacity of the

plasterboard in tearing is not totally involved before the failure spreads to the edge of

the board. Edge distance is significant in determining both the strength and deformation

capacity of screws connected to plasterboard.

77


connections for different edge distances under monotonic loading (mean values

obtained for one screw)

(a) Edge distance-15 mm

78

(b) Edge distance-17 mm

(c) Edge distance-20 mm

Figure 3.20: Failure modes of plastebroard sheathing-to-channel section connections for

different edge distances under monotonic loading (a) 15 mm edge distance, (b) 17 mm

edge distance, and (c) 20 mm edge distance

79

3.4.3 Effect of Section Thickness

Figure 3.21 shows the response of sheathing-to-framing (top hat and channel section)

connections under monotonic loading. From Figure 3.21, it can be seen that that the

ultimate capacity of the plasterboard-to-channel section is approximately 35% higher

than the ultimate capacity of the plasterboard-to-top hat section for both field screw and

edge screw tests. Moreover, the initial stiffness of the connection to channel section is

almost 4 times that of the connection with the top-hat section, as shown in Table 3.2.

However, the failure mechanisms for both sheathing-to-framing connections are the

same (i.e. plasterboard bearing and tilting of screw in field screw connections, and

tearing of plasterboard in edge screw connections tests).

Figure 3.21: Load-slip behaviour of plasterboard sheathing-to-framing (top hat and

channel sections) connections under monotonic loading (mean values obtained for one

screw)

3.4.4 Idealization of Load-Slip Behaviour for Sheathing-to-framing Connection

The process for the idealization of plasterboard sheathing-to-steel framing connection

behaviour is requires idealization of the load-displacement curve under monotonic

loading. A typical monotonic behaviour of a plasterboard-to-framing connection is

80

shown in Figure 3.22. The figure also shows the segments of data used to determine

each of the parameters. From the load-slip curves shown in Figure 3.22, it can be stated

that the shapes of the curves are characterised by a realistically linear segment followed

by a transition to plastic behaviour. The load at which plastic behaviour starts; and the

deflection at failure are greatly influenced by the geometry of the test. This was

observed during the failures of the shear connections. The load-displacement behaviour

of the connections between the plasterboard and framing, particularly the deflection at

failure, is a function of the orientation of loading on the fastener, as described by

Walker et al. (1982).

Figure 3.22: Load-slip behaviour of sheathing-to-framing connection under monotonic

loading

The load-slip curve can be illustrated using three regions. In Region I (initial stiffness),

the behaviour is initially linear (i.e. the increase of load is proportional to the

corresponding increase of displacement). In this region, the sheathing, framing material,

and screws are fundamentally elastic. In Region II (secondary stiffness), non-linear

behaviour characterizes the curve. The non-linearity occurs as sheathing screws start to

tilt. In Region III (tertiary stiffness), the load capacity of the specimen decreases with

81

increasing displacement. This region can be approached using a negative linear

relationship.

3.5 Summary and Conclusions

This chapter has discussed the first phase of the experimental program, the shear

connection tests. The details of the test set-up, test specimens and testing procedure are

described. Since the failure mechanism of shear connection is the foundation for the

evaluation of plasterboard performance, a detailed analysis of shear connection failure

mechanisms is presented. Detailed observation of the failure mechanism of the

connection between the plasterboard and steel framing members through the connecting

screws is also presented. The key findings can be summarised as follows:

For all the edge screw shear connection tests, the failure mode for edge

connections was tearing out of the sheathing material from its edge.

Field screw shear connections showed failure modes of plasterboard bearing as

well as screw tilting and the screw head piercing the sheathing material.

Edge shear connections with 20 mm edge distance achieved approximately 85%

of the ultimate loads of the field screws with the same plasterboard and steel

member

Edge shear connections with 15 mm, 17 mm and 20 mm edge distances reached

their ultimate loads at relatively small displacements compared to the field screw

shear connections.

The ultimate capacity of the plasterboard-to-channel section connection is

approximately 35% higher than that of the plasterboard -to-top hat section for

both field screw and edge screw tests. The initial stiffness of the connection to

the channel section is almost 4 times that of the connection with the top-hat

section. This is due to the greater thickness of the channel sections.

82

CHAPTER 4

EXPERIMENTAL PROGRAM (PHASE II): FULL-SCALE TESTING OF CEILING DIAPHRAGM IN CANTILEVER CONFIGURATION

4.1 Introduction

It is essential to conduct full-scale testing in order to develop understanding of the

behaviour and response of steel-framed domestic structures under lateral loading (e.g.

wind and earthquake loads). Experimental test results are also crucial to validate

analytical models.

This chapter presents the second phase of the experimental program, the testing of a

segment of a ceiling diaphragm as a cantilever wall in racking. The details of the test

specimens, test methods, instrumentation and data acquisition system are reported. The

results, analyses and conclusions obtained from this phase of the experimental program

are also reported.

4.2 Experimental Arrangement

The most common method for determining the in-plane strength and stiffness of ceiling

diaphragms is laboratory testing of full-scale diaphragm segments. Construction and

testing procedures for such assemblies are available in the ASTM E455-04 ‘Standard

Test Method for Static Load Testing of Framed Floor or Roof Diaphragm Constructions

for Buildings’. There are two different configurations for testing the diaphragm

assembly, namely: a cantilever set-up; and a simple beam set-up as shown in Figure 4.1.

In the cantilever set-up, the diaphragm is essentially tested in racking as a shear wall,

while in the beam set-up the diaphragm is tested as a deep beam in bending (Saifullah et

al. 2014). Both set-ups were employed in this research and the results for two

configurations are reported here. This chapter describes the ceiling diaphragm tests in

cantilever assembly, and the ceiling diaphragm tests in beam configuration are

illustrated in Chapter 5.

The diaphragm test assembly is almost identical to the typical ceiling diaphragm

construction of the steel-framed domestic structures in Australia. The sizes of the

specimens are restricted, due to the testing facilities available in the Smart Structures

Laboratory at Swinburne University of Technology.

83

(a) Cantilever test

(b) Beam test

Figure 4.1: Configuration of ceiling diaphragm testing systems (a) Cantilever/racking

test assembly, (b) beam test assembly

84

4.3 Testing Program

In organizing the experimental testing program, it was desired that the test specimen

should resemble what is used in practice and as large as could be suitably fitted within

the laboratory facilities. Specimens with a height of 2.25 m and width of 2.4 m were

chosen to fit within the available test rig. The ceiling was made out of standard full-

scale components and made to resemble a ceiling of a small room within a domestic

structure.

4.3.1 Test Set up

Ceiling diaphragm tests in the cantilever test assembly (shown in Figure 4.1) are

illustrated. It should be noted that the cantilever test requires less space in the laboratory

compared to the simple beam test assembly. An experimental test set-up for racking

tests is shown in Figure 4.2. The ceiling panel was placed in vertical position and was

mounted on a loading frame.

Figure 4.2 Test set-up and instrumentation for cantilever test

In the cantilever test set-up, the two end vertical members experience tension and compression (push-pull) forces generated by the horizontal racking force. The tension

85

member needs to be restrained from unrealistic uplift otherwise premature failure may occur. Such restraints would be totally artificial and hard to practically replicate a ceiling system, unlike shear or bracing walls. Given that the purpose of this test was to obtain the shear resistance of a ceiling panel, a loading frame (parallelogram) was developed to apply the racking load which would also resist the tension and compression forces, negating the need to provide supplementary restraints to the ceiling members.

The loading frame, shown in Figure 4.3, was made of hot rolled steel channel sections

with two horizontal members (top and bottom) and three vertical members. All

members were connected to each other with a single bolt to allow free rotation (i.e., all

members were truly pin connected). The bottom of the frame was anchored to the

concrete floor of the Smart Structures Laboratory using M20 threaded rods spaced at

500 mm centres. The top of the frame was restrained in the out-of-plane direction for

stability.

Figure 4.3: Photograph of loading frame with ceiling bottom chords and ceiling battens

mounted on it.

Loading frame

Bottom chord

Ceiling batten

86

4.3.2 Test Specimen

In this stage, tests of three full-scale ceiling diaphragms in cantilever tests were conducted. All the tests had the same dimensions. All plasterboard sheets and framing members had the same properties. The plasterboard screws were 6G-18 x 25 mm plasterboard screws. It should be noted that adhesive was not used on these diaphragm specimens.

To maintain consistency with the specimens of the shear connection tests described in Chapter 3, the same plasterboard type was used for the cantilever tests. Similar to the ceiling battens used in the shear connection tests in Chapter 3, the ceiling battens were made of G550 Top-hat 22 cold-formed steel sections manufactured by BlueScope Pty. Ltd. The three ceiling diaphragms specimens were fixed according to the provisions stated in the Gyprock Ceiling System Installation Guide (2008) and the Gyprock Residential Installation Guide (2010).

A typical detail of the ceiling panel configuration associated with its cold-formed steel

frame members is shown in Figure 4.4. The test specimen simulated a section of a

typical plasterboard ceiling, whereby the plasterboard is attached to battens which in

turn are fixed to the bottom chords of roof trusses.

Figure 4.4 Ceiling panel configurations along with connection details

87

Hence, the first step in making the specimen was to attach the bottom chords (G550 90

x 40 x 0.75 mm lipped channel sections) to the loading frame using M16 bolts. The

bottom chords were placed at 750 mm centres. The ceiling battens (G550 standard Top-

hat 22 sections) were attached to the bottom chords at 600 mm spacing using double

Buildex 10 gauge self-drilling hex head screws at each joint (as per normal

construction). The plasterboard sheets (one 2400 x 1200 x 10 mm and the other 2400 x

1350 x 10 mm) manufactured by Boral Plasterboard Pty. Ltd. were fixed to the battens

using Buildex 6G-18 x 25 mm bugle-head needle-point screws at 300 mm centres along

each batten. For these specimens, the plasterboard sheets were fixed horizontally

(perpendicular) to the ceiling battens. The plasterboard sheets were butt-jointed using

typical construction details. The overall dimensions of the test specimen were 2250mm

high x 2400mm in length. The tested ceiling diaphragm assembly is shown in Figure

4.5. Two props were used in the top of the frame in order to prevent the loading frame

from moving out-of-plane. The details of this provision are shown in Figure 4.6. Grease

was placed under the steel casters to minimise friction so that little load was carried to

the support wall.

Figure 4.5: Photograph showing tested ceiling diaphragm assembly

Plasterboard screw

Prop for supporting steel casters

Loading frame

Support wall

Hydraulic actuator

Bottom chord

Butt joint

88

Figure 4.6: Photograph showing steel casters to prevent the ceiling specimen from

moving out-of-plane.

During loading, it was noted that the bottom chord members started to twist gradually

(see Figure 4.10) with the increase of the load, but with no damage to the tested

specimen. This phenomenon is illustrated in detail in Section 4.4. The load was released

to recover the problem. The testing arrangement was modified to eliminate the

unrealistic twisting of the bottom chord sections. The ends of the bottom chords were

blocked using timber sections (for specimen #1 and specimen #2) and stud sections (for

specimen 3) to prevent section twisting. The front and back of the overall test set-up

using timber sections are shown in Figure 4.7. Moreover, Figure 4.8 shows the overall

test set-up using stud sections to prevent twisting of the bottom chords.

Steel casters

89

(a)

Figure 4.7: Photograph of specimen (after modification) using timber sections between

bottom chords to prevent twisting of bottom chords (a) front view of the specimen, (b)

holding the specimen from the back

Timber sections

90

Figure 4.8: Photograph showing using stud sections along the length of specimens to

prevent twisting of bottom chords

Table 4.1 shows the basic test matrix of all specimens. It should be mentioned that all of

the three specimens were tested under monotonic loading.

Table 4.1 Matrix of test specimens under monotonic loading

Specimen Dimensions

(mm x mm)

Batten

spacing

(mm)

Bottom chord

spacing (mm)

Loading

direction

to failure

End restraint

to prevent

twisting

Specimen #1 2250 x 2400 600 750 Pushing Timber

sections

Specimen #2 2250 x 2400 600 750 Pulling Timber

sections

Specimen #3 2250 x 2400 600 750 Pulling Stud sections

Stud sections

91

4.3.3 Instrumentation and Data Acquisition System

The instrumentation used in these experiments is shown in Figure 4.2. The hydraulic

actuator contained the internal load cell as well as a displacement transducer that

supplied information on the resisting force and applied displacement, respectively.

Four linear differential transformers (LDTs) were used to measure displacements, as

shown in Figure 4.2. One transformer (LDT #4) was mounted on the bottom chords at

the top-right end (opposite end of actuator position) of the specimen to measure top

horizontal displacements. Two LDTs (LDT #1 and LDT#2) were positioned at the

bottom of each end bottom chord to determine the uplift. LDT#3 was placed at the

bottom to measure the horizontal displacements of the bottom chords. It should be noted

that the transducers were positioned relatively close to the upper portions of the bottom

chords, where they were assumed to bend most under lateral load. All transducers

provided additional information that provided comprehensive monitoring of the ceiling

diaphragm performance while conducting the test. All measurements were logged

continuously during the test using a computer-based data-logger.

The deflections measured at the above-mentioned four locations (shown in Figure 4.4) are indicated as D1, D2, D3 and D4. The net-deflection can be obtained by Equation 4.1 as follows:

Δnet = D4- D3-(a/b)*(D1+ D2) (4.1)

where,

Δnet = Net racking displacement of the ceiling specimen

D4 = Horizontal in-plane displacement at the top of the ceiling panel measured by LDT #4

D3 = Horizontal in-plane displacement at the bottom of the ceiling panel measured by LDT #3

D1 and D2 = Vertical displacement at the bottom of the ceiling panel measured by LDT #1 and LDT#2 respectively.

a = Length of the ceiling (perpendicular to the loading direction)

b = Depth of the ceiling (parallel to the loading direction)

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4.3.4 Loading

Only monotonic loading conditions were applied for the cantilever test. All tests were

performed in the displacement-controlled method. The specimens were loaded at the

rate of 2 mm/min. All the three ceiling specimens were pulled and pushed to accomplish

a complete cycle at serviceability displacement (usually equal to height/300 which is

approximately 8 mm for a 2250 mm length ceiling) before they were pulled to failure.

4.4 Results and Discussions

4.4.1 Loading Frame Friction

While the loading frame was assumed to be a mechanism without a lateral strength, an

initial racking test was performed on the loading frame only (i.e., without the ceiling) to

ensure that it had very little in-plane stiffness. The frame used in the test panel was

loaded in three different stages. In the first stage, the frame was pulled at the rate of 3

mm/min up to 8 mm, and then pushed at the same rate up to 8 mm. In the second stage,

the frame was pulled up to 45 mm and then pushed up to 45 mm at 3 mm/min. In the

final stage, to observe the effect of loading rate on the behaviour of the frame, the frame

was loaded at the rate of 10 mm/min up to the displacement of 45 mm in the pulling

direction and then the pushing direction up to 45 mm. The resulting load vs. deflection

curves of the loading frame are shown in Figure 4.9.

Figure 4.9: Load vs. deflection curves of loading frame only

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It can be seen that the maximum load restraint of the frame due to friction was

approximately 0.2 kN. It is also observed that there are no significant differences of

magnitude of load with the application of load at different rates.

4.4.2 Discussion of Test Results

For specimen #1, it was observed that the bottom chord members started to twist at a

load of 1.7 kN with the corresponding deflection of 35 mm (shown in Figure 4.10).

With the increase of the load, the bottom chords were twisted gradually. At a load of 2.0

kN and corresponding deflection of 42 mm, LDT lost the contact from steel sections

(shown in Figure 4.11), but no damage to the specimen was observed. The load was

released to resolve this problem. The testing arrangement was modified to remove the

twisting of the bottom chord sections. The ends of the bottom chords were blocked

using timber sections (for specimen #1 and specimen #2) and stud sections (for

specimen #3) to prevent unrealistic section twisting, as described in Section 4.3.

Figure 4.10: Starting of the twisting of bottom chord sections at the load of 1.7 kN and

corresponding displacement of 35 mm.

94

Figure 4.11: Separation of LDT from the contact of sections at the load of 2.0 kN and

with the corresponding displacement of 42 mm

After modification using timber members to prevent twisting of the bottom chord

sections, specimen #1 was again pushed and pulled to accomplish a complete cycle at

serviceability displacement (8 mm) and the specimen failed in applying loading by

pushing. In order to investigate the variation in results due to specimen failure between

pushing and pulling, the researcher performed testing of specimen #2 by applying

loading in pulling direction until failure. The resulting load versus net deflection curves

for specimen #1 and specimen #2 are shown in Figure 4.12 and Figure 4.13

respectively.

Specimen #3 was modified using stud sections in order to prevent twisting of the

bottom chord sections. The specimen was pulled and pushed to accomplish a complete

cycle at serviceability displacement (8 mm) and the specimen failed in applying loading

in the pulling direction. The resulting load versus net deflection curve for the specimens

is shown in Figure 4.14. It should be noted that the initial loading cycle (±8 mm)

represents serviceability loading before the diaphragm specimens were loaded to failure.

The resulting ultimate loads and their corresponding displacements of the three

specimens are listed in Table 4.2. It should be noted that the maximum load capacity of

the frame due to friction was approximately 0.2 kN and this value was deducted from

the test results. Specific numbering of members and plasterboard screws is also shown

in Figure 4.15 to aid the explanation of the failure mode.

95

Figure 4.12: Load vs. net-deflection curve of test specimen #1


96


From Figure 4.12 to Figure 4.14 it can be observed that the shape of the load -

deflection curves of the tested ceiling diaphragms are similar to those obtained in shear

connection tests (described in Chapter 3) between the plasterboard sheathing and steel

framing members.

The basic characteristic of these load-deflection curves is initially linear, as presented in

Figure 4.15. In the linear portion, the deflections adjacent to the screws are predicted to

be proportional to the load on the screws. Since the load carried by individual screw is

proportional to the displacement of the screw for all screws, the load on the ceiling

diaphragm is proportional to the displacement of the ceiling diaphragm.

97

Figure 4.15: Load-deflection behaviour of tested ceiling diaphragms under monotonic

loading

With the increase of the force in the diaphragm, the screws near the corner of the

diaphragm approach their transition state. Therefore, the force carried by these screws is

smaller than the linear behaviour. As a result, the overall behaviour of the diaphragm is

no longer linear behaviour. With further increase of applied displacement on the

diaphragm, screws at the corners of the tension diagonal fail, with the failure mode

shown in Figure 4.17. Significant load redistribution takes place and this ceiling panel

behaviour diverges considerably from the linear behaviour. At this stage, other

connections adjacent the tension diagonal corners also move into their transition state.

However, they can withstand load for much higher deflections due to these connections,

as shown in Figure 4.12 to Figure 4.14.

With further increases in load, more connections transfer to the transition state of their

load-deflection curve, resulting the deflection of the diaphragm as an entire to be

considerably higher than the linear behaviour. Considerable redistribution of the load

occurs, and screws near the centre of the plasterboard, which have a large plastic region

in their load-deflection curve, carry greater loads.

98

It should be noted that the load-deflection behaviour of screw connections is dependent

on the edge distance of the plasterboard sheathing as well as the orientation of loads on

the screws. The failure of individual screw connections was by pulling through the

plasterboard sheathing or tearing away from the plasterboard through an edge.

The failure modes of all three ceiling diaphragm specimens were quite similar. The

failure modes observed during the cantilever test of the ceiling panels were associated

with the connections of the plasterboard with the ceiling battens. When the specimens

were loaded to failure in pushing directions (specimen #1), the specimen suddenly lost

load capacity past this load due to failure of the plasterboard screw connections along

batten 1 (refer to Figure 4.16). Upon failure of the plasterboard screws along batten 1,

the majority of the remaining racking capacity was resisted by the screws along batten

2, which eventually failed in the same manner as for batten 1. Similarly, following the

failure of the screw connections along batten 2, the screw connections along batten 3

failed. This unzipping effect along the three battens (1, 2 and 3) is manifested in Figure

4.12, Figure 4.13 and Figure 4.14, respectively.

Figure 4.16: Tested ceiling diaphragm assembly showing numbering of screws and

battens

99

However, when the specimens were loaded to failure in pulling directions, the specimen

lost load capacity due to failure of the plasterboard screw connections along batten 5

(refer to Figure 4.16). Upon failure of the plasterboard screws along batten 5, the screws

along batten 4 failed in the same manner as for batten 5, followed by the failure of the

screw connections along batten 3. The failure of screw connections in all three

specimens was in the form of tearing of the plasterboard around the screw heads and

pull-through of the plasterboard. Figure 4.17 shows the failure mode of specimen #3.

(a)

(b)

100

(c)

Figure 4.17: Failure modes of cantilever specimen: (a) tearing of plasterboard around

screws along batten 1; (b) pulling through of plasterboard; (c) view of plasterboard from

the back

There was no relative movement observed between the individual plasterboard sheets

and no cracks were observed in all three specimens. The entire plasterboard lining

rotated as a single unit, as shown in Figure 4.18, rather than two plasterboard sheets

rotating individually, signifying that the butt joint between the two plasterboard sheets

almost in the middle of the ceiling diaphragm is sufficiently strong so that both

plasterboard sheets acted as a single continuous diaphragm. Further, no relative

displacement was observed between the ceiling battens and the bottom chords. No

damage was observed for the bottom chords or ceiling battens.

101

Figure 4.18: Photograph showing plasterboard rotation as a single unit

Table 4.2 is a summary of test results under monotonic loading. In Table 4.2, the

ultimate load is considered as the peak load, and the definition of the initial and the

secant stiffness is presented in Figure 4.19. The initial stiffness can be calculated by

dividing the load at the tangent to the deflection at that load. For instance, in case of

specimen #1, the load at tangent is 3.1 kN and the deflection at that load is 10.6 mm.

Therefore, the initial stiffness is 3.1/10.6 = 0.29 kN/mm. From Table 4.2, it can be

observed from the full-scale ceiling diaphragm cantilever test results that the ultimate

load of the ceiling diaphragm with the pulling test is close (with only 10% variation) to

that of specimens with the pushing test. Moreover, the ultimate load and failure

mechanisms of the ceiling diaphragm with stud sections is very similar to that of the

specimens with timber sections to avoid unrealistic twisting of the bottom chord

sections, although there is minor variation in initial and secant stiffness. Considering the

limited number of full-scale ceiling diaphragm cantilever tests performed in this

research, the coefficient of variation (CoV) of approximately 5.5% between these tests

reflects excellent agreement between the test results.

102

Table 4.2 Summary of test results of specimens subjected to monotonic loading

Test No Ultimate

load (kN)

Displacement at

ultimate load (mm)

Initial stiffness

(kN/mm)

Secant stiffness

(kN/mm)

1 4.3 20 0.29 0.22

2 3.9 19 0.30 0.21

3 4.3 24 0.31 0.18

Average 4.2 21 0.3 0.2

Coefficient of

variation 5.5% 12.6% 3.3% 9.3%

Table 4.3 Summary of loads at serviceability displacement

Test No Load (kN)

+ 8 mm -8 mm

1 2.1 -1.8

2 1.9 -1.6

3 2.3 -1.7

Figure 4.19 Definition of the initial and the secant stiffness for monotonic tests

103

From Table 4.2 and Table 4.3, it can be seen that the ultimate loads of specimens were

approximately 40% to 50% higher than the loads at serviceability displacement (±8

mm). Hence, potentially different design values for strength and serviceability can be

provided for such diaphragms.

4.4.3 Estimation of Design Strength

The maximum load that could be supported by the specimen was 4.2 kN. The design

load can be obtained as the ultimate load divided by a sampling factor of 1.93 (as

recommended in the NASH Standard, Residential and Low-rise Steel Framing, Part 1:

Design Criteria 2005, Amendment C: 2011 for three tests) and is expressed as force per

unit depth. The design stiffness can be obtained by dividing the design load on the total

ceiling depth (width of the building parallel to the wind loading direction) to the

deflection measured at that design load. The stiffness is considered at design load

because of the nature of the non-linear elastic load-deflection curve.

According to the NASH standard (Residential and Low-rise Steel Framing, Part 1:

Design Criteria 2005, Amendment C: March 2011), the design value (Rd) must satisfy

either:

Rd = (Rmin / kt-min) or Rd = (Rave / kt-ave)

where,

Rmin = minimum value of the test results;

kt-min = sampling factor

Rave = average value of the test results

kt-ave = sampling factor

According to the NASH standard (Residential and Low-rise Steel Framing, Part 1:

Design Criteria 2005), the value of the coefficient of variation of structural

characteristics (ksc) must be not less than 20% for assembly strength, and 10% for

assembly stiffness, unless a comprehensive test program is used to establish ksc. Based

on the results, the average value of the ultimate load is 4.2 kN. The sampling factor for

use with the average value of three test results = 1.93. The width of the diaphragm is 2.4

104

m. Therefore, the design strength of the tested diaphragm is calculated to be 0.9 kN/m

and is expressed as force per metre depth (i.e., 4.2 kN/2.4m/1.93). The design load is

2.2 kN and the deflection at that load would be 7.3 mm, based on the average tangent

stiffness.


The second phase of the experimental program conducted in this research project has

been reported in this chapter. This chapter discusses the results for specimens of ceiling

diaphragms under raking/cantilever testing under monotonic loading. This chapter also

describes the construction of three full-scale ceiling diaphragms specimens, the testing

methodologies including the selection of loading protocols, the testing program and the

testing facilities necessary to perform the tests. Descriptions of the behaviour of the

tested specimens, failure mechanisms, assessment of diaphragm parameters and

conclusions drawn from the experimental tests are also presented in this chapter.

These cantilever tests have highlighted the important aspects of the behaviour,

performance, and load-sharing characteristics of the main components in steel-framed

domestic structures. Additional findings from the test results and analyses are

summarised as follows:

The maximum load capacity of the loading frame due to friction was

approximately 0.2 kN. It is also observed that there are no significant differences

between the magnitudes of frictional resistance with the application of load at

different rates.

For all specimens the ultimate failure mode was found to be the same. In all

cases, the plasterboard connections failed at the locations where maximum

relative movement between the plasterboard and battens occurred.

The failure of screw connections in all three specimens was in the form of

tearing of plasterboard around the screw heads and pull-through of the

plasterboard.

In all specimens, no relative movement was observed between the individual

plasterboard sheets. The entire plasterboard lining rotated as a single unit rather

than two plasterboard sheets rotating individually. However, these movements

are not typically practical in a full-scale house test, because the plasterboard

105

sheathing is allowed 10 mm maximum movement in lateral directions due to

providing the cornices, skirting boards and top plates of end walls, as discussed

in Chapter 5.

In all three specimens, no relative displacement was observed between the

ceiling battens and the bottom chords.

There was no damage to the bottom chords or ceiling battens.

There was limited variation (approximately 5.5%) between the results from the

three test specimens, indicating excellent agreement between these test results.

The average ultimate racking load was 4.2 kN, which is equivalent to 1.8 kN/m.

Based on three specimens and a maximum co-efficient of variation (CoV) of

structural characteristics 20%, the corresponding design capacity would be 0.9

kN/m.

While the failure mode was as expected, the specimens seemed to have lower stiffness.

Therefore, to ensure that the performance of the ceiling specimen is not highly

influenced by the test set-up, an alternative beam setup was considered, as discussed in

Chapter 5.

Having gained understanding and knowledge of the behaviour of ceiling diaphragm

specimens under racking load, analytical models were developed to predict the lateral

load-deflection behaviour of plasterboard-clad ceiling diaphragms typically found in

light steel-framed domestic structures in Australia. The details of these analytical

models are presented in Chapter 6.

106

CHAPTER 5

EXPERIMENTAL PROGRAM (PHASE III): FULL-SCALE TESTING OF CEILING DIAPHRAGM IN BEAM CONFIGURATION

5.1 Introduction

The third phase of the experimental program conducted in this research project is

reported in this chapter. In the beam configuration tests reported in this chapter, the

ceiling is assumed to act as a simply-supported deep beam spanning between bracing

walls. This set-up is close to the actual action of a ceiling; however, it is more

demanding in terms of testing due to the larger space and more complex loading and

measurement system required (Saifullah et al. 2014). Five full-scale tests were

conducted based on common ceiling systems in cold-formed steel structures.

The aim of this testing was to determine the strength and stiffness of typical cold-

formed steel-framed ceiling diaphragm specimens under various configurations

subjected to monotonic loading conditions. The purpose of these beam tests was also to

validate analytical models to predict the behaviour of domestic structures and identify

the contributions of the various elements of diaphragms under lateral loads.

This chapter describes the construction of full-scale ceiling diaphragm specimens, the

testing methodologies, instrumentation and data acquisition system, and the testing

facility necessary to conduct the tests. Descriptions of the behaviour of the tested

specimens, the failure mechanisms, and conclusions drawn from the experimental tests

are also presented in this chapter.

5.2 Scope of Testing

Full-scale diaphragm tests in beam configuration were conducted to observe the

strength and stiffness of the diaphragm. In organizing the experimental testing program,

it was desired that the dimensions of tested specimens be similar to those which would

be used in practice and as large as could be fitted within the laboratory facilities. Some

tests were performed at the Smart Structures Laboratory at Swinburne University of

Technology, Hawthorn, Australia. These types of diaphragm constructions occupy large

spaces. Because of the limited space in the Smart Structures Laboratory, the rest of the

tests were performed at the Wantirna campus of Swinburne University of Technology.

107

Of the five full-scale tests, the dimensions of the diaphragm for three specimens were

5.4 m x 2.4 m with varying batten spacing and consideration of the effects of the

plasterboard bearing on the top plates of end walls. Two specimens (8.1m x 2.4 m) with

the same batten and bottom chord spacing were constructed with the high aspect ratio

3.4. The only difference between these two is with/without consideration of the effects

of the plasterboard bearing on the top plates of the end walls. The test parameters

examined for the effects of diaphragm strength and stiffness include spacing of battens,

and with/without effects of plasterboard bearing on the top plate of the end walls. The

ceiling was made out of standard full-scale components to resemble a ceiling in one

room of a steel-framed domestic structure. All the materials used for these tests were

identical to those used for the cantilever tests (i.e., the same bottom chord section,

battens, plasterboard and screws). The construction details were also identical.

Specimens were subjected to monotonic loading by a manually controlled hydraulic

jack with load cell. Load and deflection values were recorded using a computer data

acquisition system.

5.3 Testing Arrangement

Figure 5.1 shows the ceiling diaphragm testing system in beam configuration. In this

system, load is applied at one-third distance of the diaphragm.

Figure 5.1: Beam test configuration of ceiling diaphragm testing system

The diagrammatic view in Figure 5.2 shows all of the components of the test apparatus,

including the support frame, the reaction frame, and the load distribution spreader beam.

108

To maintain consistency with the specimens in the cantilever tests (described in Chapter

4) and the shear connection tests (described in Chapter 3), the same plasterboard was

used for the beam tests. Similarly, the same ceiling battens as those used in the shear

connection tests and cantilever tests were used for the beam tests. The ceiling battens

were made of G550 Top-hat 22 cold-formed steel sections manufactured by BlueScope

Pty. Ltd. All of the ceiling diaphragms specimens were fixed in accordance with the

construction details provided in the Gyprock Ceiling System Installation Guide (2008)

and the Gyprock Residential Installation Guide (2010).

Figure 5.2: Typical structural testing arrangement of diaphragm in beam configuration

The framework consisted of ceiling battens running along the panel’s sides which were

connected to bottom chord members. The ceiling battens were top-hat 22 sections,

while the bottom chord members were 90 x 40 x 0.75 mm lipped channel sections. The

ceiling battens were connected to the bottom chord members using double Buildex self-

drilling hex head screws. Figure 5.3 shows the fixing system of plasterboard to the

ceiling battens which were in turn screwed to the bottom chord members.

109

Figure 5.3: Fixing system of plasterboard to framing members

The panels were tested in the horizontal plane as beams spanning over the length. The

panels were constructed in such a way that one end of the test specimen was pinned and

the other end was a roller, as shown in Figure 5.2. Figures 5.4 and 5.5 show the

connection details of the bottom chord members with the pin support (designated as ‘A’

in Figure 5.2) and roller support (designated as ‘B’ in Figure 5.2). The universal column

(250UC89.5) steel channel sections were fixed securely to the laboratory floor using

M20 bolt threaded rods at 1000 mm spacing. This support frame has the same function

as in the cantilever tests by transferring the loads out of the diaphragm at each end. The

support structure also serves to hold the specimens at the appropriate elevation/position

for the point loading from the hydraulic cylinder. Some steel stands were also

positioned on the laboratory floor under the specimen to hold the interior of the

specimen at a suitable elevation. Bottom chords members were connected only at the

two corner support structures at the opposite side of the loaded diaphragm to represent

pin support and roller support. The rest of the support structures were placed to hold the

specimen at the correct elevation so that there was no friction between the bottom chord

members and support structures. Lateral supports were provided at both pin support and

roller support positions, as illustrated in Figure 5.6.

110

(a)

(b)

Figure 5.4: Details of pin support (a) Top view, (b) Side view

6 No.

M10 bolt

Washers

Bottom chord

111

(a)

(b)

Figure 5.5: Details of roller support (a) Top view, (b) Side view

6 No.

M10 bolt

Washers

Bottom chord

50 mm slotted holes

112

(a)

(b)

Figure 5.6: Lateral supports (a) pin support, (b) roller support

113

The specimens were loaded parallel to the direction of the bottom chord members and

the loads were applied to the bottom chord members. Loads were applied at one-third

point systems through the spreader beam, as shown in Figure 5.2. Figure 5.7 shows the

connection details of both one-third loading systems (designated as “C”) in Figure 5.2.

The connections between the spreader beam and web members and between the web

members and supports were made in such a way that no failure occurred in any

connections or framing members.

A manually controlled hydraulic jack with ±100 mm stroke was used to apply the load,

and a load cell with 20 kN capacity was attached to the hydraulic jack. Figure 5.8 shows

the details of the mechanism of the loading arrangement of the tested diaphragm. The

hydraulic cylinder was connected to the spreader beam at the centre of the specimen

using a 24 mm threaded rod.

(a)

Steel angle section

4 No.

M12 bolts

Spreader beam

Bottom chord

114

(b)

(c)

Figure 5.7: Details of one-third loading point (a) Top view, (b) Right side view, (c) Left

side view

Bottom chord

8 No. M8 bolts

115

Figure 5.8: Mechanism of loading system

5.4 Instrumentation and Loading

The deflections of the panel were measured using linear variable displacement

transducers (LVDTs) and a photogrammetry system. Prior to the start of the

experimental program, calibration testing was conducted on the instruments used in this

research to quantify the level of accuracy of the instruments.

A typical layout of displacement transducers on the tested ceiling diaphragm and the

reaction frame is shown in Figure 5.2. Deflections were measured at four locations on

the diaphragm specimens. The deflections were measured at both support locations as

well as both loading points (as shown in Figure 5.2) and indicated as D1, D2, D3 and D4.

The net deflection can be obtained using Equation 5.1 as follows:

Δnet = (D2 + D3-D1- D2) (5.1)

where,

Δnet = Net displacement of the ceiling specimen

D1 = Horizontal in-plane displacement of the ceiling panel at pin support point measured by LVDT #1

D2 and D3 = Horizontal in-plane displacement of the ceiling panel at one-third loading point measured by LVDT #2 and LVDT #3 respectively.

Spreader beam

Hydraulic jack

Hydraulic pump

Load cell

Threaded rod

116

D4 = Horizontal in-plane displacement of the ceiling panel at roller support point measured by LVDT #4

As shown in Figure 5.2, the diaphragm was tested using two equal-point loads applied

symmetrically along the depth of the diaphragm i.e. at one-third points. The load was

applied using a hydraulic cylinder in displacement control mode.

5.5 Description of Tests

Different sizes of panel were tested. Some panels were 5.4 m long and 2.4 m wide,

while others panels were 8.1 m long and 2.4 m wide. In the 5.4 m long panels, there

were no splices in the ceiling battens, while there were splices in the ceiling battens in

the 8.1 m long panels. The splices were made according to the construction details in

Australia. In a typical construction, the recommended edge distance (typically 20 mm)

of corner screws of the diaphragm varies from 15 mm to 22 mm, as described in the

Gyprock Ceiling System Installation Guide (2008) and the Gyprock Residential

Installation Guide (2010). Therefore, plasterboard screws were provided at the typical

edge distance of 20 mm along the perimeter of the diaphragm. Plasterboard sheathing

was used as necessary to complete the desired ceiling panel configuration. Only screw

configurations using 6G-18 x 25 mm plasterboard screws were adopted for these ceiling

diaphragm specimens. Although the size of the tested panels was small, the construction

of the tested diaphragm specimen is representative of those constructed in practice in

Australian steel-framed domestic structures. In this research, adhesive was not used to

connect the plasterboard sheathing with the battens. However, some tests should be

conducted in future to observe the effect of adhesive.


spacing)

Figure 5.9 shows a diagrammatic view of the beam testing arrangement for beam test

specimen #1. The size of the tested specimen was 5400 mm long and 2400 mm wide.

The spacing of the bottom chord members was 900 mm and the spacing of the ceiling

battens was 600 mm.

The cladding consisted of four 2400 x 1350 x 10 mm Gypsum plasterboard sheets

manufactured by Boral Plasterboard Pty. Ltd which were screwed to the ceiling battens.

The plasterboard sheets were placed perpendicular to the ceiling battens using Buildex

6G-8 x 25 mm bugle-head needle-point screws at 270 mm spacing along each ceiling

117

batten as per the construction system described in the Gyprock Ceiling System

Installation Guide (2008). The ceiling battens were attached to the bottom chord

members using two Buildex 10G x 20 mm hex head self-drilling tek screws at each

joint. Figure 5.10 shows the bottom chords and ceiling battens on the test jig before

placement of the plasterboard. The recessed joints between the plasterboard sheets were

butt-jointed using the procedure recommended by the manufacturer. The details of the

application of the Gyprock tape and coating system in recessed joints is described in the

Gyprock Ceiling System Installation Guide (2008). The different stages of the

preparation of specimens for testing are shown in Figures 5.10 and 5.11. Figure 5.11

shows the complete set-up of beam test specimen #1. The dark spots on the plasterboard

are reflective photogrammetry targets.

Figure 5.9: Structural ceiling diaphragm testing system for beam test specimen #1

118


plasterboard

Figure 5.11: Complete set-up of beam test specimen #1

Ceiling batten Bottom

chord

Spreader beam

Plasterboard

Ceiling batten Bottom

chord

Edge screw

119


spacing and effects of plasterboard bearing)

The beam set-up was further enhanced to consider the effects of the top plates of end

walls supporting the roof trusses (Figure 5.12). These top plates provide further bending

resistance to the ceiling diaphragm and also provide bearing areas for the plasterboard

ceiling as it translates in the direction of an end wall (Saifullah et al. 2014). These

effects are considered in this test. The Gyprock Residential Installation Guide (2010)

recommends that the size of the gap should not exceed the thickness of the plasterboard

(10 mm in this case). Therefore, the gap size of approximately 10 mm was adopted in

this testing.

Figure 5.12: Effects of plasterboard bearing edges on the top plates of end walls

Figure 5.13 shows a diagrammatic view of the beam testing arrangement for beam test

specimen #2 considering the effects of plasterboard bearing edges on top plates of end

walls. The size of the test specimen was 5400 mm long and 2400 mm wide. The spacing

of bottom chord members was 900 mm and the spacing of the ceiling battens was 600

mm.

120


specimen #2

The complete set-up of this experiment is shown in Figure 5.14. The top plate, as shown

in Figure 5.14(b), was screwed to the bottom chords of the diaphragm to replicate the

flanges of the top plates of end walls.

The cladding consisted of four 2400 x 1350 x 10 mm plasterboard sheets manufactured

by Boral Plasterboard Pty. Ltd. The plasterboard sheets were placed perpendicular to the

ceiling battens using Buildex 6G-8 x 25 mm bugle-head needle-point screws at 270 mm

spacing along each ceiling batten as per the construction system recommended in the

Gyprock Ceiling System Installation Guide (2008). The ceiling battens were attached to

the bottom chord members using two Buildex 10G x 20 mm self-drilling hex head

screws at each joint. The recessed joints between the plasterboard sheets were jointed

using Gyprock Easy Tape and Coating, as recommended by the manufacturer.

121

(a)

Figure 5.14: Beam test specimen (a) complete test set-up, (b) close-up view of the

system for study of top plate effects

Top plates

10 mm gap

600 mm

Ceiling battens

Bottom chord

122



In Australia, the spacing of the batten in the construction system may vary from region

to region. Most of the construction systems use 450 mm spacing of the battens instead

of 600 mm. Therefore, the author conducted three additional tests with changing batten

spacings and aspect ratios. In this test series, the size of the test specimen was 5400 mm

long and 2400 mm wide. The spacing of bottom chord members was 900 mm.

However, the spacing of the ceiling battens was 400 mm to maintain equal spacing

between them, as shown in Figure 5.15.


specimen #3

To maintain consistency, the cladding consisted of four 2400 x 1350 x 10 mm

plasterboard sheets manufactured by Boral Plasterboard Pty. Ltd. The plasterboard

sheets were placed perpendicular to the ceiling battens using Buildex 6G-8 x 25 mm

bugle-head needle-point screws at 270 mm spacing along each ceiling batten. The

ceiling battens were attached to the bottom chord members using two Buildex 10G x 20

mm self-drilling hex head screws at each joint. Figure 5.16 shows the bottom chords

and ceiling battens on the test jig before placement of the plasterboard. The complete

test set-up is shown in Figure 5.17. The test was performed at the Wantirna campus of

Swinburne University of Technology.

123


plasterboard

Figure 5.17: Complete test set-up of beam test specimen #3

400 mm

Bottom chord Ceiling batten

Top plate

Direction of loading

Direction of loading

124


spacing)

In this set-up, the length of the diaphragm was increased from 5400 mm to 8100 mm.

However, the width of the diaphragm remained the same i.e. 2400 mm. The spacing of

bottom chord members was 900 mm, while spacing of the ceiling battens was 400 mm.

The aspect ratio of this tested diaphragm is 3.4 (i.e. 8100/2400 = 3.4). The main concern

of this diaphragm testing was to observe the effect of aspect ratio on the strength and

stiffness of the diaphragm. The testing arrangement for this diaphragm set-up is shown

in Figure 5.18. This test was performed without consideration of the effects of

plasterboard bearing on top plates of end walls. However, beam test specimen #5 was

tested with the consideration of the effects plasterboard bearing on top plates of end

walls on the same diaphragm. All plasterboard and other fixing details are the same as

for beam test specimen #3.


specimen #4

It should be noted that the maximum length of the ceiling batten available in the market

is 6.1 m. However, the length of the tested specimen was 8.1 m. Therefore, it was

necessary to use at least two ceiling battens to prepare a specimen of the desired length.

In this ceiling diaphragm, the ceiling battens were spliced. According to the

manufacturer’s guidelines, the minimum length of the batten overlap should be 40 mm,

and the overlap of the batten must be spliced at a ceiling member. The circle in Figure

125

5.19 indicates the location of the batten overlapping at the bottom chord members. The

joint between two ceiling battens was made along the ceiling batten using four 10G self-

drilling hex head screws. Figure 5.20 shows the details of the construction system of the

batten overlapping.


plasterboard

Figure 5.20: Details of connection system of ceiling batten overlapping

Figure 5.21 shows the complete test set-up of this specimen. The diaphragm was also

restrained at two corners where the pin support (as shown in Figure 5.21(b)) and roller

support was located (as shown in Figure 5.21 (c)). The lateral restraint steel section was

Ceiling batten

Bottom chord

Roller support

Lateral restraint

Location of batten splice

400 mm

Spreader beam

Hydraulic jack

126

anchored securely to the floor of the laboratory using M16 anchored bolts, as shown in

Figure 5.21(b) and Figure 5.21(c).

(a)

(b)

Roller support

900 mm

Pin support

Pin support

Lateral restraint

127

(c)

Figure 5.21: Test set-up (a) complete test specimen, (b) lateral restraint system at pin

support, (c) lateral restraint system at roller support



In this test set-up, the effect of plasterboard bearing on the top plates of end walls was

considered. Figure 5.22 shows the diagrammatic view of the beam testing arrangement

for the specimen. The size of the test specimen was 8100 mm long and 2400 mm wide.

The spacing of bottom chord members was 900 mm and the spacing of the ceiling

battens was 400 mm. The complete set-up of this experiment is shown in Figure 5.23.

The top plate, as shown in Figure 5.23, was screwed to the bottom chords of the

diaphragm to replicate the flanges of the top plates of end walls. All plasterboard and

fixing details are similar to those for beam test specimen #4.

Roller support

128


specimen #5

Figure 5.23: Complete test set-up for beam test specimen #5

Table 5.1 shows the basic test matrix of all specimens. It should be mentioned that all of

the five specimens were tested under monotonic loading.

Top plate

10 mm gap

400 mm

129

Table 5.1 Matrix of test specimens under monotonic loading

Specimen

designation

Length

(m)

Width

(m)

Aspect

ratio

Batten

spacing

(mm)

Bottom

chord

spacing

(mm)

Batten

splice

Boundary

conditions

Beam test

specimen #1 5.4 2.4 2.25 600 900

No

batten

splice

No

plasterboard

bearing

Beam test

specimen #2 5.4 2.4 2.25 600 900

No

batten

splice

Plasterboard

bearing on

top plates

Beam test

specimen #3 5.4 2.4 2.25 400 900

No

batten

splice

Plasterboard

bearing on

top plates

Beam test

specimen #4 8.1 2.4 3.38 400 900

Batten

splice

No

plasterboard

bearing

Beam test

specimen #5 8.1 2.4 3.38 400 900

Batten

splice

Plasterboard

bearing on

top plates

5.6 Results and Discussion

This section reports the results from the full-scale diaphragm tests in beam

configuration. These test results are analysed and discussed in detail.

5.6.1 Frame Test

The author performed the frame test to measure the strength and stiffness of the steel

frame only without plasterboard. Figure 5.24 shows the load-deflection behaviour of the

tested frame only. It can be observed that the frame itself carries negligible load and has

negligible stiffness.

130

Figure 5.24: Load vs. net-deflection curve for the frame only (without plasterboard)

In the load-deflection curve, the ‘load’ refers to the total applied load at the panel. The

‘net-deflection’ refers to the adjusted deflection (based on displacement measured at

four locations of the panel from the bottom chord members of the diaphragm) using the

equation mentioned in instrumentation and data acquisition system (see Section 5.4).


spacing)

The test panel was loaded in increments up to failure, and the load-deflection behaviour

of the tested ceiling diaphragm is shown in Figure 5.25. Failure occurred at the load of

7.4 kN as result of tear-out of plasterboard at the left and right corners of the diaphragm,

as shown in Figure 5.26(a) and Figure 5.26(b) respectively. Failure also occurred as a

result of the plasterboard screws pulling through the cladding at both the top left and top

right corner of the diaphragm, as shown in Figure 5.26(c) and Figure 5.26(d)

respectively. Figure 5.26(e) shows plasterboard screws pulling though the cladding

along the perimeter of the diaphragm. The deformed shape of the screws, as shown in

Figure 5.26(f), occurred in the locations where tearing of plasterboard edges as well as

pulling out of plasterboard were seen. The rest of the screws remained undeformed.

131

Figure 5.25: Load vs. net-deflection curve for beam test specimen #1

(a)

(b)

132

(c)

(d)

(e)

(f)





plasterboard at the perimeter of diaphragm, (f) deformed shape of tilted screw

There was no relative movement between the individual plasterboard sheets. The whole

cladding system translated as a single unit. No relative displacement was observed

between the ceiling battens and the bottom chords. However, considerable bending of

the ceiling battens was observed. No damage was observed to the bottom chords. Some

local buckling of the bottom chord members observed during the test was recoverable

after the termination of the test.

133

The overall deformed shape of the beam test specimen #1 is illustrated in Figure 5.27,

which shows bending of the battens and translation of the plasterboard as a rigid body.

The dashed lines in Figure 5.27 indicate the original position of the plasterboard.

Figure 5.27: Deformed shape of the test specimen showing the bending of battens and

translation of the plasterboard as a rigid body.



The presence of top plates on end walls leads to another mode of load transfer

mechanism from the steel frame to the plasterboard. Without top plates on end walls, all

the racking loads are transferred through the screws connecting the plasterboard to the

ceiling battens via shear action. The top plates of end walls transfer some of the racking

loads through bearing on the plasterboard edges. When there is a gap between the

plasterboard and the top plates of the end walls, the racking load is initially transferred

to the plasterboard via the screws until the ceiling battens start to deform relative to the

plasterboard as the screws tear and are pulled into it. With the increase of this relative

movement, the gap closes and the top plates of end walls bear against the plasterboard

edges at the flanges of the end studs, as shown in Figure 5.29(e). This ultimately leads

Battens Chords

Plasterboard

134

to bearing of the plasterboard edges at both corners of the diaphragm. The load-

deflection behaviour of the tested ceiling diaphragm is shown in Figure 5.28.


Failure occurred at the load of 12.4 kN as a result of tear-out of plasterboard at the left

and right corners of diaphragm, as shown in Figure 5.29(a) and Figure 5.29(b)

respectively. Failure also occurred as a result of the plasterboard screws pulling through

the cladding at both the top left and top right corner of the diaphragm, as shown in

Figure 5.29(c) and Figure 5.29(d) respectively. The deformed shape of the screws, as

shown in Figure 5.29(f), occurred in the locations of tearing of plasterboard edges as

well as pulling out of plasterboard. The rest of the screws remained undeformed.

135

(a)

(b)

(c)

(d)

(e)

(f)

136

(g)




(d) pulling out of plasterboard at the top right corner of diaphragm, (e) plasterboard

bearing on both edge of diaphragm, (f) deformed shape of tilted screw, (g) considerable

bending of ceiling battens




the ceiling battens was observed, as shown in Figure 5.29(g). No damage to the bottom

chords was observed. Some local buckling of the bottom chord members was

recoverable after the termination of the test.



The load-deflection behaviour of the tested ceiling diaphragm is shown in Figure 5.30.


and right corners of the diaphragm, as shown in Figure 5.31(a) and Figure 5.31(b)

respectively. With the increase of the relative movement of plasterboard, the gap closes

and the top plates of the end walls bear against the plasterboard edges at the flanges of

the end studs, as shown in Figure 5.31(c). This ultimately leads to bearing of the

plasterboard edges at both corners of the diaphragm.

137


Failure also occurred as a result of the plasterboard field screws pulling through the

cladding at both sides of the diaphragm, as shown in Figure 5.31(d) and Figure 5.31(e).

(a)

(b)

138

(c)

(d)

(e)

(f)




(d) pulling out of plasterboard at the middle left side of diaphragm, (e) pulling out of

plasterboard at the middle right side of diaphragm, (f) deformed shape of tilted screw




the ceiling battens was observed. No damage to the bottom chords was observed. Some

local buckling of the bottom chord members was recoverable after the termination of

the test.

139


spacing)

The load-deflection behaviour of the tested ceiling diaphragm is shown in Figure 5.32.


and right corners of the diaphragm, as shown in Figure 5.33(a) and Figure 5.33(b)

respectively. Failure also occurred as a result of the plasterboard screws pulling through

the cladding at both the top left and top right corners of the diaphragm, as shown in

Figure 5.33(c) and Figure 5.33(d) respectively. The deformed shape of the screws is

shown in Figure 5.33(f). The rest of the screws remained undeformed.


140

(a)

(b)

(c)

(d)

(e)

(f)



141



plasterboard field screws, (f) deformed shape of tilted screw



between the ceiling battens and the bottom chords. However, there was considerable

bending of the ceiling battens. No damage to the bottom chords was observed. Some


the test.



With the increase of the relative movement of plasterboard to the ceiling batten, the gap

closes and the top plates of the end walls bear against the plasterboard edges at the

flanges of the end studs. This ultimately leads to loading of the plasterboard edges at

both corners of the diaphragm. The load-deflection behaviour for the tested ceiling

diaphragm is shown in Figure 5.34. Failure occurred at the load of 12.8 kN as a result of

tear-out of plasterboard at the left and right corners of the diaphragm, as shown in

Figure 5.35(a) and Figure 5.35(b) respectively.

Failure occurred as a result of the plasterboard screws pulling through the cladding at

both the top corners of the diaphragm, as shown in Figure 5.35(c). The deformed shape

of the screws, as shown in Figure 5.35(d), occurred in the locations of tearing of

plasterboard edges as well as pulling out of plasterboard. The rest of the screws

remained undeformed.

142


(a)

(b)

143

(c)

(d)




(d) deformed shape of tilted screw

No relative movement occurred between the individual plasterboard sheets. The whole



the ceiling battens was observed. No damage to the bottom chords was observed. Some


the test.

The observed load-deflection behaviour of full-scale diaphragms is similar in form,

although there is variation in magnitude. These variations were also observed in the

results of the plasterboard sheathing-to-steel framing connections. The variation of the

performance of the diaphragms is possibly due to the following reasons (i) some screws

may have been over-driven; (ii) some screws may not have been driven at a right angle

to the plasterboard.

Table 5.2 shows a summary of the test results. In Table 5.2, the ultimate load is

considered as the peak load resisted by every specimen during testing. The maximum

deflection at ultimate load and strength of the diaphragms are tabulated in column 3 and

column 4 respectively. Column 5 shows the initial or tangent stiffness at the linear

portion of the load-deflection curve, whereas the secant stiffness measured at ultimate

144

load is presented in column 6. The secant stiffness per unit depth is calculated by

dividing the total load by the displacement at ultimate load and width of diaphragm. The

definitions of initial and secant stiffness are presented in Figure 5.36.

Table 5.2 Summary of test results for specimens subjected to monotonic loading

Specimen

designation

Ultimate

load (kN)

Displacement

at ultimate

load (mm)

Strength

per unit

depth

(kN/m)

Initial

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m)

Beam test

specimen #1 7.5 18.0 1.56 0.28 0.18

Beam test

specimen #2 12.5 26.0 2.60 0.27 0.20

Beam test

specimen #3 12.6 24.5 2.63 0.41 0.21

Beam test

specimen #4 10.8 25.0 2.25 0.29 0.18

Beam test

specimen #5 12.8 29.0 2.67 0.30 0.18

145

Figure 5.36: Definition of initial and the secant stiffness for beam test

From Table 5.2, it can be observed that there is significant variation of strength and

stiffness due to changes of spacing of battens. The strength of the diaphragm with

boundary conditions (i.e. considering the effects of plasterboard bearing on top plates)

is approximately 20% higher than the strength of the diaphragm without boundary

conditions. However, the stiffness of the diaphragm with boundary conditions is very

similar to that of the diaphragm without boundary conditions. The stiffness of the

diaphragm decreases with the increase of aspect ratio (length/width ratio). The stiffness

of the diaphragm with an aspect ratio of 3.4 (i.e. 8.1m/2.4) is approximately 35% lower

than that of the diaphragm with an aspect ratio 2.3 (i.e. 5.4m/2.4m). However, ultimate

strength does not change significantly due to variation of the aspect ratio of the

diaphragm. Only, stiffness changes due to variation of aspect ratio. This effect is

discussed in more detail in Chapter 6.

Figure 5.37 shows the assembly of the tested ceiling diaphragm with the numbering of

screw lines and bottom chord members. Most of the damage which occurred in the

diaphragm was in both corners of the plasterboard sheathing panels at pin support and

roller support locations. Sheathing failure was caused by the screws at the corners of the

146

diaphragm and along the diaphragm perimeter pulling through the plasterboard

sheathing. In all specimens, failure occurred as a result of tear-out of plasterboard edges

at both corners of the specimen. Tear-out of plasterboard edges also occurred at the first

three bottom corner screws from the left corner (i.e. line 1, line 2 and line 3) and the

right corner (i.e. line 22, line 23 and line 24) of the diaphragm (refer to Figure 5.37).

Failure also occurred due to field screws pulling out simultaneously through the

plasterboard along line 1, line 2 and line 3 between bottom chord 1 and bottom chord 2

as well as field screws pulling out along line 22, line 23 and line 24 between bottom

chord 6 and bottom chord 7. Therefore, it can be stated that failure occurred between

the first two bottom corners where the shear force is maximum. The screws along line 1,

line 2 and line 3 in the left side and along line 22, line 23 and line 24 in the right side (as

shown in Figure 5.37) also deformed at the same time. The rest of the screws remained

essentially undeformed.

Figure 5.37: Typical ceiling diaphragm assembly (showing numbering for explanation)

It should be noted that the cladding came into contact with the top plates before failure

of the screws had occurred. The movement of ceiling battens provided bearing of the

cladding against the top plates prior to the failure of the cladding screws.

In tests 1, 2, and 3, the ceiling battens were continuous. However, it is common to have

joints in ceiling battens and bottom chord members. In tests 4 and 5, the ceiling battens

147

were spliced as per construction systems in Australia, as depicted in Section 5.5. Based

on the experimental results, no significant effect on the strength of the diaphragm was

observed due to the splicing of ceiling battens.

Ceiling diaphragm testing was conducted on panels incorporating ceiling battens. The

diaphragm arrangement was similar to that for the cantilever testing. An increase of

stiffness was observed in the beam tests. The reason is that the ceiling battens are

perpendicular to the loading direction and there is no tendency for the battens to slide,

as occurred in the cantilever test. Based on the test results, it is clear that the strength of

the diaphragm increases with the increase of the number of screws in the panel.

Clearances were provided between the plasterboard and top plates to ensure that the

plasterboard did not bear against the top plate. The clearance that was provided between

the plasterboard and top plates was 10 mm. If the clearances had been kept very small,

higher ultimate loads could have been obtained and the failure modes of the cladding

screws would have been inhibited. The failure modes which occurred in this case would

be due to tension in the joints between the plasterboard sheets or buckling of the

cladding sheets. The plasterboard bearing against the top plate would have prevented

cladding screw failure.

5.7 Load-deflection Behaviour of Tested Diaphragm

From the observed load-deflection behaviour of all beam test specimens, it can be stated

that the load-deflection curves of the tested ceiling diaphragms were of a similar shape

to those obtained in shear connection tests (described in Chapter 3), as well as cantilever

tests (described in Chapter 4). The load-deflection behaviour showed highly non-linear,

softening and inelastic characteristics.The curve exhibited three identical regions: linear,

transition and inelastic, as depicted in Figure 5.38.

5.7.1 Diaphragm Behaviour in Region I (linear portion of the curve)

The behaviour is initially linear, (i.e. the increase of load is proportional to the

corresponding increase of deflection). In this region, the sheathing, framing material,

and screws are fundamentally elastic. In this region, the deflections near the screws are

predicted to be proportional to the load on the screws. Since the load carried by an

individual screw is proportional to the deflection of the screw for all screws, the load on

148

the total ceiling diaphragm is proportional to the deflection of the total ceiling

diaphragm.

Figure 5.38: Load-deflection behaviour of full-scale diaphragms under monotonic

loading

5.7.2 Diaphragm Behaviour in Region II (transition portion of the curve)

A non–linear behaviour of the curve is observed in region II. The non–linearity of the

curve occurs due to the plasterboard starting to tear/pull and/or the screw connections

starting to tilt. With the increase of the load in the diaphragm, the screws near the corner

of the diaphragm approach their transition state. Therefore, the load carried by these

screws is smaller than that of those in the linear behaviour and causes the load to

separate from these screws. As a result, the overall behaviour of the diaphragm changes

from linear behaviour. It continues until a nearly plastic plateau is reached and a closely

linear load-displacement relationship is achieved. With further increase of the load in

the diaphragm, substantial load redistribution takes place and the ceiling panel

behaviour diverges significantly from linear behaviour. At this stage, other connections

adjacent to the corners also move into their transition state. However, they can

withstand load for much higher deflections.

149

5.7.3 Diaphragm Behaviour in Region III (inelastic portion of the curve)

With further increases in load, more connections transfer into the transition portion,

resulting in the deflection of the diaphragm as an entire to be significantly higher than

the linear behaviour. Significant redistribution of the load occurs, and screws near the

centre of the plasterboard which have a big plastic region in their load-deflection curve

carry greater loads than linear behaviour. The load-deflection behaviour at the ultimate

loads above the transition region is determined essentially by the screws in the plastic

behaviour region. However, the load-deflection behaviour of screws in this region is not

only a function of the properties of the materials used, but also the edge distance of the

plasterboard sheet and the orientation of loads on the screws. The failure of individual

screws by pulling through the plasterboard sheathing or tearing away from the

plasterboard through an edge causes the load on the residual screws to change in

magnitude as well as direction. As a result, the load-deflection behaviour for a certain

screw deviates due to load redistribution as the test proceeds. At the failure location,

the failure of one screw and the consequent load redistribution result in overloading of

all residual screws along that edge. Therefore, screws along the edge fail at the same

time, resulting in a drop in load-carrying capacity. The carrying capacity of the

diaphragm decreases with further increase of deflection.


It is essential to conduct full-scale ceiling diaphragm testing in beam configuration in

order to gain a complete understanding of the performance of steel-framed domestic

structures under lateral loading. Experimental test results are also essential to validate

the analytical models. While the cantilever set-up is simpler from an experimentation

point of view, the beam analogy is a more realistic representation of how a ceiling spans

between bracing walls. Therefore, a complete beam testing program was arranged and

developed to recognize and quantify the most important factors that affect the strength

and stiffness of the ceiling diaphragm.

This chapter has presented the details of the test specimens, test methods, and

instrumentation and the data acquisition system engaged for full-scale ceiling

diaphragm in beam assembly has been reported. The results, analyses and conclusions

obtained from this phase of the experimental program were also reported. The test

results focussed on the behaviour of the ceiling diaphragm under in-plane lateral loads

150

generated due to wind. Based on the results presented for five specimens, the following

remarks can be made:

For all tested diaphragms, the ultimate failure mode was found to be the same.

In all diaphragms, the plasterboard connections failed at the locations where

maximum relative movement between the plasterboard and battens occurred.

In all specimens, failure occurred as result of tear-out of plasterboard edges at

the corners of the specimen. Tear-out of plasterboard edges also occurred at the

first three bottom corner screws from the left and right corners of the diaphragm.

The top plates of the end walls supporting the roof trusses provided further

bending resistance to the ceiling diaphragm and also provided bearing area for

the plasterboard ceiling as it translates in the direction of an end wall.

The strength of a diaphragm with boundary conditions (i.e. considering the

effects of plasterboard bearing on top plates) is approximately 20% higher than

that of a diaphragm without boundary conditions. However, the stiffness of a

diaphragm with boundary conditions is almost the same as that of a diaphragm

without boundary conditions.

The stiffness of the diaphragm decreases with the increase of aspect ratio

(length/width ratio). The stiffness of a diaphragm with an aspect ratio of 3.4 is

approximately 35% lower than that of a diaphragm with an aspect ratio 2.3.

However, the strength does not change significantly due to variation of the

aspect ratio.

The load-deflection curves of all the ceiling diaphragms tested in beam

configuration were of a similar shape to those obtained in cantilever tests.

In all specimens, no relative displacement was observed between the ceiling

battens and the bottom chords. However, considerable bending of the ceiling

battens was observed.

No damage observed to the bottom chords was observed. Some local buckling of

the bottom chord members was recoverable after the termination of the test.

No relative movement occurred between the individual plasterboard sheets. The

movement of the plasterboard relative to the frame was only in the loading

direction. The whole cladding system translated as a single unit.

151

There is no significant effect on the strength of the diaphragm due to splicing of

ceiling battens.

It is important to develop analytical models of the structural behaviour of the ceiling

diaphragm. It is also essential to observe the three-dimensional behaviour of the

structural response under in-plane loading. The analytical modelling is described in

detail in Chapter 6. As mentioned in Chapter 2, there are several factors that affect the

strength and stiffness of the diaphragm. Therefore, it is crucial to conduct parametric

studies with varying parameters in order to observe the behaviour of the diaphragm.

With the understanding and knowledge of the behaviour of the tested ceiling diaphragm

in beam configuration under a one-third loading system, analytical models have been

developed to predict the performance of plasterboard-clad ceiling diaphragms typically

found in light steel-framed domestic structures in Australia. The details of these

parametric studies are described in Chapter 6.

152

CHAPTER 6

ANALYTICAL MODELLING

6.1 Introduction

Analytical modelling is essential to complete the knowledge achieved from

experimental analyses, particularly in performing parametric analyses. The aim of this

chapter is to amalgamate the experimental test results reported in Chapter 4 and Chapter

5, and to utilise them to develop analytical models of plasterboard-clad steel-framed

ceiling diaphragms.

This chapter includes brief explanations of the assumptions considered in developing

the model, and presents analytical models under monotonic load for predicting the

lateral load-displacement behaviour of plasterboard-clad ceiling diaphragms. This

chapter presents the validation of the finite element (FE) models against the results of

the experiments. Parametric studies are also performed to determine the sensitivity of

FE models subjected to different configurations.

6.2 Finite Element Modelling Software

ANSYS (version 12.1) software was used for the analytical modelling. The reason for

choosing ANSYS is that it has an extensive library of elements and can consider

different types of non-linearity. The response of a structure or a component can vary

unduly with the applied loads due to the non-linearity of the structure. ANSYS covers

various types of non-linearity, such as material non-linearity, geometric non-linearity,

element non-linearity and non-linear buckling (SASI, 2014). In this research, element

non-linearity is only used in the model development of the ceiling diaphragm of steel-

framed domestic structures. In the ANSYS program, typical non-linear elements include

contact surface elements, interface elements, spring elements, and tension-only or

compression-only elements.

In the modelling of ceiling diaphragms of domestic structures as presented here, non-

linear spring elements were used comprehensively. This non-linear spring element is

unidirectional with a non-linear generalized load-displacement capability. The element

possesses a single degree of freedom. The input load-displacement curve has portions

with either positive or negative slopes, as presented in Figure 6.1. In the input load-

displacement curve, the unloading curve is parallel to the initial slope.

153

Figure 6.1: Typical input load-displacement curve for a COMBIN39 non-linear spring

element.

6.3 Finite Element Modelling Strategy

The modelling program conducted on the steel ceiling diaphragm systems had two

stages: (i) validation of the FE models compared with the experimental test results, as

described in Chapter 4 and Chapter 5, and (ii) the undertaking of parametric studies. A

complete description of each of the models is provided later in this chapter. The loading

functions used for the FE model analyses include racking loading, one-third loading and

uniformly-distributed loading.

6.3.1 Representation of Structural Components

Table 6.1 shows the finite-element representation of structural components. The choice

of element was based on the assumption that the non-linear behaviour of ceiling

diaphragms is predominantly attributable to the sheathing-to-framing connections.

Linear elements were used to represent the frame and sheathing members.

154

Table 6.1: Finite-element representation of structural components in ANSYS

Structural Component Finite-Element Representation Element Designation

Bottom chord Beam element: 2-node BEAM3

Ceiling batten Beam element: 2-node BEAM3

Sheathing (Plasterboard) Plane element: 8-node plain

stress PLANE82

Sheathing (Plasterboard)-

to- framing (Ceiling batten)

connections

Spring element: 2-nodes,

Nonlinear (X, Y and Z direction) COMBIN39

Plasterboard bearing to top

plates

Spring element: 2-nodes,

Nonlinear (Y direction only) COMBIN39

In addition to the information in Table 6.1, pin connections and roller connections were

used to model the bottom chord connections to the support structures using bolts.

6.3.2 Material and Sectional Properties

Two different types of material were used in the finite element (FE) model: cold-formed

steel, and plasterboard sheathing. All materials were defined to be linear elastic and

isotropic. Table 6.2 shows the material properties used in the FE model. The structural

grade of the cold-formed steel was G550 MPa, and the shear modulus of plasterboard

ranged from 180 MPa to 270 MPa, based on the tests conducted by Telue (2001). In this

research, the shear modulus of plasterboard sheathing was taken 180 MPa for the

development of FE models.

Table 6.2: Material properties used in the FE model

Material Name Elements Modulus of

Elasticity (MPa) Poisson’s ratio

Cold-formed steel Battens, Bottom chord 200000 0.3

Plasterboard Cladding/sheathing 450 MPa 0.25

155

Table 6.3 shows the sectional properties (real constants) used in the FE model. The real

constants for the consideration of the bearing of plasterboard on the top plates of the end

walls were obtained from the crushing capacity of plasterboard conducted by Gad

(1997).

Table 6.3: Real constants for materials used in the FE model

Elements Thickness

(mm)

Second moment of

Inertia (mm4) Area

(mm2)

Ix Iy

Bottom chord 0.75 17.13 x 104 2.53 x 104 133

Battens 0.42 15000 3500 42

Sheathing/cladding 10 - - -

6.3.3 Plasterboard Screw Connections

The plasterboard screws were modelled as non-linear spring elements (Combin39).

Each screw was modelled by three springs, with two springs acting in two orthogonal

directions (one for the horizontal (X) direction, one for the vertical (Y) direction) within

the plane of the plasterboard and the third acting in the out-of-plane direction (i.e.in the

Z direction). These spring elements possessed different load-slip characteristics,

depending on the position of the screw (field screw and edge screw) being modelled.

The values used to define the load-slip curves of the non-linear spring elements were

obtained from the shear connection tests presented in Chapter 3.

The reason for choosing three springs is to enable modelling of the slack/gap

development among the plasterboard and the screw under monotonic loading. Figure

6.2 shows the typical load-displacement curve based on combining a tension and a

compression spring.

156

Figure 6.2: Typical load-displacement curve based on combining a tension and a

compression spring

6.3.4 Boundary Conditions

The behaviour of the diaphragm changes due to the existence of the boundary

conditions (i.e. end walls, cornices). The cornice strengthens the diaphragm. The

cornice is generally glued to both the ceiling and the wall. The existence of the end

walls generates transfer of the load from the frame to the plasterboard. Without end

walls, all the racking forces are transferred ideally through the screws which connect the

plasterboard to the ceiling battens. When there is a gap between the plasterboard and the

end walls, as shown in Figure 6.2, the force is transferred initially to the plasterboard

through the screws until the plasterboard travels far enough to start bearing on the top

plate of the end walls.

157

Figure 6.3: Effects of plasterboard bearing edges on the top plates of end walls

In practice, there is a 10 mm gap between the ceiling diaphragm and the end walls. In

order to model the bearing of the plasterboard against the end walls, non-linear springs

were connected along the plasterboard edges to accommodate this action, as presented

in Figure 6.4. All of the springs worked in compression only. The springs included the

initial slackness (gap) and had the load-displacement characteristics of plasterboard

crushing along the edge. Therefore, in the FE model, the top plates of the end walls

were attached to the bottom chord members on which the springs were also connected.

Figure 6.4: Schematic diagram of plasterboard-bearing edge modelling

158

Gad (1997) conducted a number of tests on crushing small segments of plasterboard

along the edge. The load-displacement behaviour for plasterboard crushing was

obtained from those tests. In this test, Gad (1997) loaded small portions of plasterboard

in compression along the edge to obtain experimentally the crushing capacity of

plasterboard and the corresponding load-deflection behaviour. The plasterboard edge

was actually loaded against the flange of a stud section as would happen in a real wall.

6.4 Model Validation against Test Results

6.4.1 Validation of Model against Cantilever Test Results

The model was verified with the experimental cantilever test results. The experimental

set-up comprised of a single steel ceiling diaphragm frame measuring 2400 x 2225 mm

with batten spacing of 600 mm and bottom chord spacing of 750 mm. It was clad with

standard 10 mm plasterboard laid horizontally. The plasterboard was fixed to the frame

by 6 gauge x 18 mm long bugle-head needle-point screws. The screw spacing was at

300 mm centres along the ceiling battens.

The FE model was created to the same construction details, except for the supporting

loading frame details. Figure 6.5 represents the modelling strategy of the isolated

ceiling diaphragm in cantilever configuration. In the experiment, the racking and uplift

displacements were measured. For the experimental results, the horizontal component of

uplift was deducted from the total racking deflection to find the net racking

displacement. In the FE model, uplift was eliminated; hence the total displacement was

the same as the net racking displacement.

To validate the modelling strategies, the FE model was subjected to increasing

displacement in pulling directions along the top bottom chord members, as illustrated in

Figure 6.5. The application of the displacement was consistent with the experimental

set-up. The obtained load-deflection curve from FE model was plotted against the

experimental results, as shown in Figure 6.6.

159

Figure 6.5: FE model developed in cantilever configuration

Figure 6.6: Comparison between analytical and experimental results in cantilever

configuration for an isolated ceiling diaphragm

160

From Figure 6.6, it is clear that there is good agreement between the analytical FE

model and the experimental results. The deflected shape and failure mode obtained in

the FE model were similar to those observed in the experiment, where the battens

showed a significant bending at the bottom, as presented in Figure 6.7. The plasterboard

screw connections also failed at the same locations as observed during the experiment.

Figure 6.7: Deflected frame shape from the FE model

6.4.2 Validation of FE Model against Beam Test Results

The FE modelling was verified against tests conducted in beam configurations with

boundary conditions (i.e. bearing of plasterboard on end walls) and without boundary

conditions (i.e. isolated ceiling). The isolated ceiling diaphragm model represents the

lower bound of lateral strength. In the FE model, the displacement was applied at one-

third distance of the diaphragm along the bottom chord members to be consistent with

the experimental set-up. Table 6.4 shows the basic matrix of the tested specimens in

beam configuration.

Batten

Bottom chord

161

Table 6.4: Basic test matrix of tested specimens in beam configuration

Designation Length

(m)

Width

(m)

Screw

spacing

(m)

Batten

spacing

(mm)

Bottom

chord

spacing

(mm)

Boundary

condition

Beam test

specimen #1 5.4 2.4 270 600 900 No boundary

Beam test

specimen #2 5.4 2.4 270 600 900

Plasterboard

bearing on top

plate

Beam test

specimen #3 5.4 2.4 270 400 900

Plasterboard

bearing on top

plate

Beam test

specimen #4 8.1 2.4 270 400 900 No boundary

Beam test

specimen #5 8.1 2.4 270 400 900

Plasterboard

bearing on top

plate

6.4.2.1 Validation of Beam Test Specimen #1

Figure 6.8 shows the FE model developed for this diaphragm. The diaphragm was

restrained at two corners simulating pin support and roller support as per the test set-up.

The comparisons of the experimental and analytical load-deflection curves are presented

in Figure 6.9.

The analytical results show higher initial stiffness. This can be attributed to variation in

the screw fixing. For example, in the experiment, all screws may not have been fixed at

right angles to the plasterboard and some screws may have been over-driven into the

plasterboard.

162

Figure 6.8: Developed FE model for beam test specimen #1


specimen #1

163

The deflected shape of the diaphragm obtained from the FE model is almost the same as

that observed in the experiment, where the ceiling battens showed a significant bending

at the ends of the diaphragm, as illustrated in Figure 6.10. The maximum relative

movement between the plasterboard and frame occurred at both ends of the diaphragm,

which was also observed in the experiment. Moreover, failure of the screw connections

also occurred at the same locations as those observed during the test.

Figure 6.10: Deflected shape for beam test specimen #1


The top plates of end walls provide bearing areas for the plasterboard ceiling as it

translates in the direction of an end wall. Using the same modelling technique and the

same elements as described earlier, a model was constructed for a single isolated

diaphragm panel (i.e. with corner effects). The construction details are same as those in

diaphragm test #1, as described in the previous section. However, the effects of

plasterboard bearing on the top plates of the flanges of end walls are considered in this

model. Figure 6.11 presents the developed FE model with the addition of consideration

of the plasterboard bearing on top plates of end walls. In this model, the top plates of the

end walls were connected with the bottom chord members using the coupling strategy in

ANSYS. The experimental and analytical results are presented in Figure 6.12. The

behaviour of the diaphragm in the FE model showed very good consistency with the

experimental results.

164

Figure 6.11: FE model for beam test specimen #2

Figure 6.12: Load-deflection curves comparison between the experimental and

analytical for beam test specimen #2

165

The deflection behaviour obtained from the FE model nearly followed that observed in

the experiment, where the ceiling battens showed considerable bending, as presented in

Figure 6.13. The maximum relative movement between the plasterboard and frame

occurred at both ends of the diaphragm, which was also observed in the experiment.

Moreover, failure of the screw connections also occurred at the same locations as those

observed during the test. The bearing of the plasterboard edges also occurred at almost

the same location as that observed in the experiment from both ends of the diaphragm.

Refer to Figure 6.13.



In this test, the size of the test specimen was 5400 mm long and 2400 mm wide. The

spacing of the bottom chord members was 900 mm. However, the spacing of the ceiling

battens was kept at 400 mm. The test and corresponding model also included the

bearing effect of plasterboard on the end wall, as shown in Figure 6.14.

Figure 6.15 presents the comparison of load-deflection curves between experimental

and analytical results for beam test specimen #3. The FE model behaviour of the

diaphragm matched closely, with excellent agreement with the experimental results.

166



specimen #3

The deflected shape of the diaphragm obtained from the FE model is nearly identical to

that observed in the experiment, where the ceiling battens showed significant bending at

167

both ends of the diaphragm as well as maximum relative movement between the

plasterboard and the ceiling battens at both ends, as illustrated in Figure 6.16. Moreover,

the locations of failure of the screw connections in the FE model were observed in the

same places as in the experiment. The plasterboard bearing action occurred at both ends

of the ceiling diaphragm, similar to that observed in the experiment.



In this test, the length of the diaphragm was changed from 5400 mm to 8100 mm.

However, the width of the diaphragm remained the same i.e. 2400 mm. The spacing of

the bottom chord members was 900 mm, while spacing of the ceiling battens was 400

mm. This test was performed without consideration of the effects of the top plates of the

end walls. The developed FE model for 8.1m x 2.4 m diaphragm without boundary

conditions is presented in Figure 6.17. The analytical FE model matched the

experimental load-deflection curve with good agreement, as shown in Figure 6.18.

168


Figure 6.18: Load-deflection curves of experimental and analytical results for beam test

specimen #4

169

The deflected shape and failure observed in the FE model were similar to those

observed during the experimental test, where maximum relative movement between the

plasterboard and frame occurred at both ends of the diaphragm. Significant bending of

ceiling battens at both ends of the diaphragm was also observed, as depicted in Figure

6.19. Furthermore, the locations of the failure of the screw connections were also

occurred in the same places as observed in the experiment.



The construction specification of the diaphragm in test #5 was similar to the ceiling

diaphragm of test #4. In this test set-up, the effect of the top plates of the end walls was

considered. Figure 6.20 shows the developed FE model for 8.1m x 2.4 m diaphragm,

taking into consideration the effects of end walls. Very good agreement was found

between the load-deflection behaviour in both the experimental and analytical studies,

as illustrated in Figure 6.21.

170



specimen #5

The deflected shape of the diaphragm obtained from the FE model was similar to that

experienced in the experiment, where the ceiling battens showed significant bending at

171

both ends of the diaphragm, as illustrated in Figure 6.22. The maximum relative

movement between the plasterboard and ceiling battens also occurred at both ends,

which is similar to the behaviour observed in the experiment. The bearing of

plasterboard edges occurred at both ends of the ceiling diaphragm, similar to that

observed in the experiment. In addition, the failure of the screw connections observed in

the FE model was at the same locations as those observed during the test.


Table 6.5 shows a summary of the comparison between experimental and finite element

model results under monotonic loading. In Table 6.5, column 1 represents diaphragm

configurations, and column 2 and column 3 shows the maximum force observed from

the experiment and the FE model of the diaphragm, respectively. The ultimate load was

considered as the peak load resisted by every specimen. Column 4, column 8 and

column 12 show the ratio of experimental results and analytical results for ultimate

load, initial stiffness and secant stiffness respectively. The initial or tangent stiffness at

the linear portion of the load-deflection curve for both experimental and analytical

results is presented in columns 6 and 7 respectively. The secant stiffness measured at

ultimate load for the experiment and the FE model are presented in columns 10 and 11

respectively. The accuracy of the FE model with respect to the experimental testing in

terms of ultimate load, initial stiffness and secant stiffness are presented in column 5,

column 9 and column 13 respectively. The definitions of initial and secant stiffness

were presented in Chapter 5.

172

Table 6.5: Summary of experimental and analytical results under monotonic loading

Specimen

designation

Ultimate load (kN) Initial stiffness (kN/mm) Secant stiffness (kN/mm)

Exp FEM Exp/

FEM

% difference

w. r. to Exp Exp FEM Exp/

FEM

% difference

w. r. to Exp Exp FEM Exp/

FEM

% difference

w. r. to Exp

Cantilever

configuration 3.9 3.7 1.05 5.1 0.30 0.29 1.03 3.3 0.21 0.20 1.05 4.8

Beam configuration

Beam test specimen #1

7.5 7.3 1.03 2.7 0.68 0.74 0.92 -8.8 0.41 0.46 0.90 -12.2

Beam test specimen # 2

12.5 12.4 1.01 0.8 0.66 0.73 0.90 -10.6 0.48 0.47 1.02 2.1


12.6 12.8 0.98 -1.6 0.98 0.94 1.04 4.1 0.51 0.52 0.98 -2.0


10.8 10.6 1.02 1.9 0.69 0.71 0.97 -2.9 0.43 0.48 0.90 -11.6


12.8 13.0 0.98 -1.6 0.71 0.72 0.98 -1.4 0.44 0.42 1.05 4.5

173

6.5 Finite Element Modelling under Different Loading Configurations

An FE model was developed to understand the performance of the ceiling diaphragm

subjected to different types of lateral loading (i.e. wind loads) namely, one-third point

loading, mid-span loading, and uniformly distributed loading. The analysis was

performed in order to find whether there is any significant variation due to these loading

configurations. The length and width of the diaphragm was 5.4 m, and the spacing of

the ceiling battens and bottom chords was 450 mm and 900 mm respectively. The

plasterboard screws were fixed at 270 mm c/c along all ceiling battens. The load-

deflection curves for all the loading configurations are depicted in Figure 6.23.

Figure 6.23: Load-deflection curves for different loading configurations (one-third point

load, mid-span load, and uniformly distributed load)

From Figure 6.23, it can be seen that the ultimate capacity of the ceiling diaphragm is

quite similar for all loading configurations. However, uniform loading provides

moderately higher stiffness than the one-third point loading configuration, and the mid-

span loading system shows lower stiffness than all of the other loading configurations.

174

6.6 Parametric Studies

There are several factors that affect the strength and stiffness of the ceiling diaphragm.

The performance of plasterboard-clad ceiling diaphragms was investigated further in the

finite element (FE) model by varying a number of the parameters which affect the

strength and stiffness of the diaphragm.

6.6.1 Investigation 1: Ceiling Diaphragms with Boundary Conditions

This investigation focused on the behaviour of ceiling diaphragms with the plasterboard

bearing on the flanges of the top plates of the end walls. The performance of

diaphragms was conducted under uniformly-distributed loading, which represents wind

loads. The parameters that were changed in this investigation include ceiling length,

ceiling width, spacing of plasterboard screws, gap size between the plasterboard edge

and end walls, and spacing of ceiling battens.

6.6.1.1 Aspect ratio

Ceiling length

The ceiling length was considered as 5.4 m, 8.1 m, 13.5 m and 16.2 m, while

maintaining the same width of 4.05 m, i.e. the corresponding aspect ratios are 1.33, 2,

3.33 and 4. The spacing of the ceiling battens and bottom chord members were kept at

450 mm and 900 mm respectively. Screws were fixed at 270 mm spacing along each

batten. The gap size between the plasterboard edge and the top plate of end wall was

kept at 10 mm. All the other parameters were kept the same. The aim of this

investigation was to observe the limits of extrapolation of the experimental results.

Generally, different ceiling diaphragm sizes were tested in different configurations, as

discussed in Chapter 5. Table 6.6 shows the parameters considered in this study.

175

Table 6.6: Parameters for different ceiling lengths with boundary conditions

Model

Designation

Length

(m)

Width

(m)

Aspect

ratio

Screw

spacing

(mm)

Batten

spacing

(mm)

Bottom

chord

spacing

(mm)

Gap

size

(mm)

FEM #A 5.4 4.05 1.33 270 450 900 10

FEM #B 8.1 4.05 2 270 450 900 10

FEM #C 13.5 4.05 3.33 270 450 900 10

FEM #D 16.2 4.05 4 270 450 900 10

Figure 6.24 shows the load-deflection curves obtained from the analysis of four ceiling

lengths. Longer ceilings (those with high aspect ratios) exhibit greater flexural

deformation and failure therefore occurs at a larger deflection compared to shorter

ceilings which have their deflection dominated by shear action.

L=5.4 m

W=4.05 m

AR=1.33 AR=2

AR=3.33 AR=4

L=8.1 m

L=13.5 m L=16.2 m

W=4.05 m

W=4.05 m W=4.05 m

FEM #A FEM #B

FEM #C FEM #D

176

Figure 6.24: Load-deflection behaviour for ceilings with different lengths with

boundary conditions

Table 6.7 shows the lateral load-carrying capacity and stiffness per unit width for each

diaphragm. There is no significant variation of ultimate strength due to changes of

length. However, the stiffness decreases with the increase of the ceiling length (i.e.

aspect ratio).

Table 6.7: Load-carrying capacity and stiffness of ceiling with different ceiling length

(i.e. aspect ratios) with boundary conditions

Model

Designation

Total

ultimate load

(kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m)

FEM #A 18.1 2.23 0.54 0.20

FEM #B 17.9 2.21 0.40 0.17

FEM #C 18.2 2.25 0.32 0.15

FEM #D 18.3 2.26 0.22 0.15

177

Ceiling width

The ceiling width was considered as 4.05 m, 5.4 m, 6.3m, 7.2 m and 10.8 m, while

maintaining the same length of 5.4 m, i.e. the corresponding aspect ratios are 1.33, 1,

0.86, 0.75 and 0.5. The spacings of the ceiling battens and bottom chord members were

kept at 450 mm and 900 mm respectively. Screws were fixed at 270 mm spacing along

each batten, and a 10 mm gap was kept between the edge of the plasterboard and the top

plates of the end walls. All the other parameters were kept the same. Table 6.8 shows

the parameters of diaphragm analysis for the five models considered and their

designations.

Table 6.8: Various parameters for different ceiling width with boundary conditions

Model

Designation

Length

(m)

Width

(m)

Aspect

ratio

Screw

spacing

(mm)

Batten

spacing

(mm)

Bottom

chord

spacing

(mm)

Gap

size

(mm)

FEM #E 5.4 4.05 1.33 270 450 900 10

FEM #F 5.4 5.4 1.00 270 450 900 10

FEM #G 5.4 6.3 0.86 270 450 900 10

FEM #H 5.4 7.2 0.75 270 450 900 10

FEM #I 5.4 10.8 0.50 270 450 900 10

Figure 6.25 shows the load-deflection curves obtained from the FE model of the above-

mentioned models. Similar to earlier finding, ceilings with higher aspect ratios fail at

higher displacement.

178

Figure 6.25: Load-deflection behaviour for ceilings with different widths with boundary

conditions

The lateral load-carrying capacity per unit width for each diaphragm is shown in Table

6.9. The capacity is not constant; it decreases with the increase of the width. However,

the tangent stiffness decreases with the increase of the ceiling width, whereas the secant

stiffness is not monotonic, as shown in Table 6.9. Figure 6.26 illustrates the comparison

of load-deflection behaviour with boundary conditions (i.e. effects of top plates on end

walls) and without boundary conditions for ceilings with different widths. A model

designation with a single letter (for example, FEM #I) indicates diaphragm analysis

with the consideration of the boundary conditions; whereas a double letter model

designation (i.e. FEM #II) indicates the corresponding diaphragm without boundary

conditions.

179

Table 6.9: Load-carrying capacity and stiffness of ceilings with different widths with

boundary conditions

Model

Designation

Total

ultimate load

(kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m)

FEM #E 18.1 2.23 0.53 0.20

FEM #F 21.1 1.95 0.46 0.17

FEM #G 23.1 1.83 0.45 0.22

FEM #H 25.8 1.79 0.45 0.22

FEM #I 37.7 1.75 0.34 0.23

From Figure 6.26 it is observed that the effect of boundary condition (i.e. effects of

plasterboard bearing on top plates on end walls) becomes less significant with the

increase of ceiling width. The boundary condition has a significant effect on strength of

diaphragm up to ceiling width of 7 m. However, here is no significant variation of the

strength due to the consideration of the top plate's effect (i.e. model FEM #H and FEM

#HH) when the ceiling width exceeds 7 m, as illustrated in Figure 6.26. Moreover, there

is no variation of the initial stiffness observed due to the influence of the boundary

conditions (i.e. effects of top plates of end walls) compared with the diaphragm without

boundary conditions.

180

Figure 6.26: Comparison of load-deflection curves (with and without boundary

conditions) for ceilings with different widths

6.6.1.2 Spacing of Plasterboard Screws

As mentioned in literature review, the number of screws connecting the plasterboard to

the steel frame members has a substantial effect on the ultimate load-carrying capacity

of the ceiling diaphragm. From the experiments conducted on isolated ceiling

diaphragms in this research, it has been observed that the screws along the ceiling

battens are most critical. Nevertheless, to date no research has been performed on

ceiling diaphragms with end walls to evaluate the effect of plasterboard screw spacing

on the ultimate load capacity and stiffness of the diaphragm. The length and width of

the ceiling for this investigation was 10.8 m and 5.4 m respectively, while the spacing

of batten and bottom chord was 450 mm and 1200 mm respectively. Table 6.10 shows

the five models with varying screw spacing along each batten. The resulting load-

deflection curves for these models are depicted in Figure 6.27. The strength and

stiffness of the diaphragm increases significantly with the decrease of the plasterboard

screw spacing, as indicated in Table 6.11.

181

Table 6.10: Parameters for varying screw spacing with boundary conditions

Model

Designation

Length

(m)

Width

(m)

Aspect

ratio

Batten

spacing

(mm)

Bottom

chord

spacing

(mm)

Gap

size

(mm)

Screw

spacing

(mm)

FEM #J 10.8 5.4 2 450 1200 10 300

FEM #K 10.8 5.4 2 450 1200 10 100

FEM #L 10.8 5.4 2 450 1200 10 150

FEM #M 10.8 5.4 2 450 1200 10 200

FEM #N 10.8 5.4 2 450 1200 10 400

Figure 6.27: Load-deflection behaviour for ceilings with different screw spacing along

each ceiling batten with boundary conditions

182


with boundary conditions

Model

Designation

Total

ultimate load

(kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m)

FEM #J 19.9 1.84 0.34 0.13

FEM #K 34.8 3.22 0.44 0.30

FEM #L 28.0 2.59 0.40 0.18

FEM #M 24.5 2.27 0.36 0.16

FEM #N 16.9 1.56 0.31 0.11

It should be noted that the maximum shear occurs in both ends of the diaphragm. The

shear decreases gradually from the end to the middle. Basically, no significant shear

develops in the middle of the diaphragm.

Seven screw fixing patterns (as shown in Figure 6.28) were investigated to observe the

behaviour of the diaphragm. Table 6.12 depicts the basic matrix of this investigation.

FEM #P is used as a reference model for this sensitivity analysis. The load-deflection

behaviour for different additional plasterboard screw fixing patterns with boundary

conditions is presented in Figure 6.29. Table 6.13 shows the load-carrying capacity and

stiffness of ceilings with boundary conditions for different screw patterns.

183

Table 6.12: Parameters for various screw fixing patterns

Model

Designation

Length

(m)

Width

(m)

Screw

spacing

(mm)

Batten

spacing

(mm)

Bottom

chord

spacing

(mm)

Gap

size

(mm)

Additional

screws (from

both ends)

along each

batten (refer

Fig. 6.27)

FEM #P 10.8 5.4 300 450 1200 10 Fig. 6.27(a)

FEM #Q 10.8 5.4 300 450 1200 10 Fig. 6.27(b)

FEM #R 10.8 5.4 300 450 1200 10 Fig. 6.27(c)

FEM #S 10.8 5.4 300 450 1200 10 Fig. 6.27(d)

FEM #T 10.8 5.4 300 450 1200 10 Fig. 6.27(e)

FEM #U 10.8 5.4 300 450 1200 10 Fig. 6.27(f)

FEM #V 10.8 5.4 300 450 1200 10 Fig. 6.27(g)

(a) FEM #P 300 300

184

(b) FEM #Q

(c) FEM #R

(d) FEM #S

150 300 300 150 150 150

300 300 4@150 4@150

6@150 6@150

185

(e) FEM #T

(f) FEM #U

(g) FEM #V

Figure 6.28: Different screw patterns used for ceiling diaphragms with boundary

conditions (all dimensions are in mm)

300

6@100

300 3@100 3@100

300 300

9@100 9@100

6@100

186

Figure 6.29: Load-deflection curves for different additional plasterboard screw patterns

with boundary conditions


for different screw patterns

Model

Designation

Total ultimate

load (kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant stiffness

per unit depth

(kN/mm/m)

FEM #P 19.9 1.84 0.34 0.13

FEM #Q 25.3 2.34 0.37 0.28

FEM #R 27.4 2.54 0.37 0.18

FEM #S 27.5 2.55 0.37 0.18

FEM #T 33.2 3.07 0.41 0.30

FEM #U 34.2 3.17 0.41 0.29

FEM #V 34.4 3.19 0.41 0.29

187

From Table 6.13, it can be observed that adding a single screw at both end sides along

each batten of the ceiling (FEM #Q) at 150 mm screw spacing provides approximately

30% higher strength and about 10% and 20% higher tangent stiffness and secant

stiffness respectively compared to standard ceiling construction systems (FEM #P).

Moreover, the strength and stiffness increases with the addition of another single screw

on both sides of diaphragm (FEM #R) along each batten. However, no variation of

strength and stiffness of the diaphragm were observed in the case of ceiling FEM #R and

ceiling FEM #S. In the case of ceiling FEM #T, the addition of two screws along each

batten at 100 mm spacing at both end sides provides about 70% higher strength,

approximately 20% higher tangent stiffness and about 35% higher secant stiffness than

ceiling FEM #P. There is a slight increase of strength and stiffness of ceilings (FEM #U,

FEM #V) due to the further addition of another two and four screw along each batten at

both end sides, as presented in Table 6.13. It can be concluded that the ultimate load-

carrying capacity is more affected by the addition of screws along each batten at corners

only rather than increasing the number of screws along the entire panel.

6.6.1.3 Gap Size

For this investigation, the length of the ceiling was 10.8m, while the ceiling width was

5.4, i.e. the aspect ratio for this analysis is 2. The spacing of the battens and bottom

chords was kept 450 mm and 1200 mm respectively. Plasterboard screws were placed at

300 mm c/c along the battens. Five scenarios were investigated as presented in Table

6.14. The gap size was changed from 10 mm to 0 mm (i.e. no gap). Figure 6.30 depicts

the resulting load-deflection curves from the analysis of these five models.

Table 6.14: Parameters for varying gap sizes with boundary conditions

Model

Designation

Length

(m)

Width

(m)

Aspect

ratio

Batten

spacing

(mm)

Bottom

chord

spacing

(mm)

Screw

spacing

(mm)

Gap

size

(mm)

FEM #W 10.8 5.4 2 450 1200 300 10

FEM #X 10.8 5.4 2 450 1200 300 8

FEM #Y 10.8 5.4 2 450 1200 300 5

FEM #Z 10.8 5.4 2 450 1200 300 3

FEM #Z/ 10.8 5.4 2 450 1200 300 no gap

188

Figure 6.30: Load-deflection behaviour due to variation of gap size between the

plasterboard edge and end walls

Results showed that there is a significant impact on the ultimate capacity of the

diaphragm due to changes in the gap size. The ultimate capacity of the ceiling increases

with the decrease of the gap size, as shown in Table 6.15.


for different gap sizes

Model

Designation

Total ultimate

load (kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m) FEM #W 19.9 1.84 0.34 0.13

FEM #X 20.6 1.91 0.34 0.16

FEM #Y 23.0 2.13 0.34 0.18

FEM #Z 24.1 2.23 0.34 0.19

FEM #Z/ 25.3 2.34 0.35 0.24

189

From Table 6.15, it can be seen that the ultimate capacity of the ceiling with no gap size

is approximately 30% higher than that of the ceiling with a 10 mm gap. It also shows

higher secant stiffness when there is no gap, followed by 3 mm, 5 mm, 8 mm and 10

mm gap size. The bend in the curve for ceilings with gap sizes was a consequence of

tilting and failure of the screw connections between the corner and first bottom chord

members along the ceiling battens, as well as transfer of the load to the plasterboard

edge. However, this distinctive mechanism was not observed in ceilings with no gap, 3

mm gap and 5 mm gap. It occurred due to the earlier bearing action on the plasterboard

edge and therefore followed a constant load direction with the loading on the screws.

Therefore, there was a seamless transition from the loading on the screws to the loading

on the plasterboard edge for 0 mm and 5 mm gaps.

6.6.1.4 Batten Spacing

Two models were investigated (as shown in Table 6.16) in order to observe the

behaviour of the ceiling due to change of the ceiling batten spacing (450 mm and 600

mm). For this investigation, the length of ceiling was 10.8m, while the ceiling width

was 5.4. The spacing of the bottom chords was 1200 mm. Plasterboard screws were

placed at 300 mm along the battens. The resulting load-deflection curves are presented

in Figure 6.31. Table 6.17 shows the load-carrying capacity and stiffness of ceiling

diaphragms subjected to different ceiling batten spacing.

Table 6.16: Parameters for varying batten spacing with boundary conditions

Model

Designation

Length

(m)

Width

(m)

Aspect

ratio

Bottom

chord

spacing

(mm)

Screw

spacing

(mm)

Gap

size

(mm)

Batten

spacing

(mm)

FEM #A/ 10.8 5.4 2 1200 300 10 450

FEM #B/ 10.8 5.4 2 1200 300 10 600

190

Figure 6.31: Effect of batten spacing on load-deflection behaviour with boundary

conditions

Table 6.17: Load-carrying capacity and stiffness of ceilings for different ceiling batten

spacing with boundary conditions

Model

Designation

Total

ultimate load

(kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m) FEM #A/ 19.9 1.84 0.34 0.13

FEM #B/ 16.2 1.50 0.30 0.11

Table 6.17 illustrates that there is a moderate impact on the strength and stiffness of the

diaphragm due to increased batten spacing from 450 mm to 600 mm. The capacity of

the ceiling with 450 mm spacing is about 20% higher than that of the ceiling with 600

mm batten spacing. Since the plasterboard screws are fixed along the ceiling battens,

the number of screws increases with the increase of the number of ceiling battens. As

191

mentioned earlier, the capacity of the diaphragm is mainly dependent on the number of

plasterboard screws used in the construction of the ceiling diaphragm.

6.6.2 Investigation 2: Sensitivity of Isolated Ceiling Diaphragms

Although isolated ceilings are not representative of the behaviour of typical ceilings in

actual domestic steel structures, they are discussed here to provide a complete picture of

the behaviour and performance of ceiling diaphragms. The parameters that were

investigated included aspect ratio, ceiling length, ceiling width, spacing of plasterboard

screws, spacing of ceiling battens and spacing of bottom chords.

6.6.2.1 Aspect ratio

Ceiling length

In this investigation, four ceilings with two different lengths were studied. The ceiling

lengths were 5.4 m, 8.1 m, 13.5 m, 16.2 m, while the width of the ceiling was kept at

4.05 m. Therefore, the aspect ratios are 1.33, 2, 3.33, and 4.0 respectively. Table 6.18

shows the parameters considered to demonstrate the behaviour of the ceiling diaphragm

due to change of length. The load-deflection curves obtained from the FE analysis are

shown in Figure 6.32.

Table 6.18: Parameters for isolated ceiling diaphragms with different lengths

Model

Designation

Length

(m)

Width

(m)

Aspect

ratio

Screw

spacing

(mm)

Batten

spacing

(mm)

Bottom

chord

spacing

(mm)

FEM #AA 5.4 4.05 1.33 270 450 900

FEM #BB 8.1 4.05 2 270 450 900

FEM #CC 13.5 4.05 3.33 270 450 900

FEM #DD 16.2 4.05 4 270 450 900

192

Figure 6.32: Load-deflection curves for isolated ceilings with different lengths

Table 6.19 shows that the stiffness decreases with the increase of the ceiling length (i.e.

aspect ratio). Longer ceilings (those with high aspect ratios) exhibit greater flexural

deformation, and hence failure occurs at a larger deflection compared to shorter ceilings

which have their deflection dominated by shear action. For the aspect ratios 1.33, 2,

3.33, 4, the load-carrying capacity is similar.

Table 6.19: Load-carrying capacity and stiffness of ceilings with different ceiling

lengths (i.e. aspect ratios) for isolated ceiling diaphragms

Model

Designation

Total

ultimate load

(kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m) FEM #AA 14.6 1.80 0.53 0.30

FEM #BB 14.7 1.81 0.40 0.25

FEM #CC 14.9 1.84 0.30 0.22

FEM #DD 14.9 1.84 0.22 0.17

193

Ceiling width

The ceiling width was considered as 4.05 m, 5.4 m, 6.3 m, 7.2 m and 10.8 m, while

maintaining the same length of 5.4 m, i.e. the corresponding aspect ratios are 1.33, 1,

0.86, 0.75 and 0.5. The spacings of the ceiling battens and bottom chord members were

kept 450 mm and 900 mm respectively, as listed in Table 6.20. The aim of this

investigation was to observe the effect of ceiling width on the strength and stiffness of

diaphragms for isolated ceilings.

Table 6.20: Parameters for isolated ceiling diaphragms with different widths

Model

Designation

Length

(m)

Width

(m)

Aspect

ratio

Screw

spacing

(mm)

Batten

spacing

(mm)

Bottom

chord

spacing

(mm) FEM #EE 5.4 4.05 1.33 270 450 900

FEM #FF 5.4 5.4 1.00 270 450 900

FEM #GG 5.4 6.3 0.86 270 450 900

FEM #HH 5.4 7.2 0.75 270 450 900

FEM #II 5.4 10.8 0.50 270 450 900

Figure 6.33 depicts the load-deflection behaviour for different widths of the diaphragm.

In order to develop the relationship between the ceiling width and capacity, the ultimate

strength per unit width for each ceiling was estimated against ceiling width, as

presented in Table 6.21. The stiffness of the diaphragm increases with the increase of

the diaphragm width.

194

Figure 6.33: Behaviour of isolated ceiling diaphragms with different widths

The total strength of the ceilings is strongly dependent on the ceiling width, as presented

in Table 6.21. The capacity per unit width decreases slightly with the increase of the

width. According to the FE model results, extrapolation of the load-carrying capacities

of a ceiling with an aspect ratio of 1 would be considered reasonable for typical

geometries where no boundary effects are considered.

Table 6.21: Load-carrying capacity and stiffness of ceilings with different widths for

isolated ceiling diaphragms

Model

Designation

Total ultimate

load (kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m) FEM #EE 14.6 1.80 0.53 0.30

FEM #FF 19.1 1.77 0.53 0.28

FEM #GG 22.2 1.76 0.52 0.27

FEM #HH 25.2 1.75 0.49 0.27

FEM #II 37.4 1.73 0.41 0.25

195

6.6.2.2 Spacing of Plasterboard Screws

The length and width of the ceiling for this investigation was 10.8 m and 5.4 m

respectively. The spacing of battens and bottom chords were 450 mm and 1200 mm

respectively. In order to investigate the sensitivity of ceiling diaphragms to plasterboard

screw spacing, five different screws spacings (as shown in Table 6.22) were considered.

The spacing of screws was fixed along each batten at 100 mm, 150 mm, 200 mm, 300

mm and 400 mm. The resulting load-deflection curves for these models are depicted in

Figure 6.34.

Table 6.22: Parameters for varying screw spacing for isolated ceiling diaphragms

Model

Designation

Length

(m)

Width

(m)

Aspect

ratio

Batten

spacing

(mm)

Bottom

chord

spacing

(mm)

Screw

spacing

(mm)

FEM #JJ 10.8 5.4 2 450 1200 300

FEM #KK 10.8 5.4 2 450 1200 100

FEM #LL 10.8 5.4 2 450 1200 150

FEM #MM 10.8 5.4 2 450 1200 200

FEM #NN 10.8 5.4 2 450 1200 400

As expected, it was found that the strength and stiffness of the diaphragm increases

significantly with the reduction of the plasterboard screw spacing along each batten, as

illustrated in Table 6.23. Placing of plasterboard screws at close spacing not only

provides higher diaphragm strength but also leads to failure at higher displacements, as

illustrated in Figure 6.34. It was also established that the strength of the diaphragm can

be increased approximately 50% with the doubling of the number of plasterboard

screws.

196

Figure 6.34: Load-deflection behaviour for different screw spacing along each ceiling

batten for isolated ceiling diaphragms


for isolated ceiling diaphragms

Model

Designation

Total

ultimate load

(kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m)

FEM #JJ 17.6 1.63 0.34 0.22

FEM #KK 34.0 3.17 0.43 0.31

FEM #LL 26.4 2.44 0.39 0.26

FEM #MM 22.0 2.04 0.36 0.25

FEM #NN 15.2 1.41 0.31 0.20

197

Other patterns of screw fixing were also studied. Seven ceilings were investigated (refer

to Table 6.24) in order to analyse the sensitivity of isolated ceilings to the screw

patterns, as presented in Figure 6.35. The first ceiling (designated as FEM #PP) had the

standard plasterboard screw pattern and was used as a reference.

Table 6.24: Parameters for various screw fixing patterns for isolated ceiling diaphragms

Model

Designation

Length

(m)

Width

(m)

Screw

spacing

(mm)

Batten

spacing

(mm)

Bottom

chord

spacing

(mm)

Additional screws

(from both ends)

along each batten

(refer Fig. 6.34)

FEM #PP 10.8 5.4 300 450 1200 Fig. 6.34(a)

FEM #QQ 10.8 5.4 300 450 1200 Fig. 6.34(b)

FEM #RR 10.8 5.4 300 450 1200 Fig. 6.34(c)

FEM #SS 10.8 5.4 300 450 1200 Fig. 6.34(d)

FEM #TT 10.8 5.4 300 450 1200 Fig. 6.34(e)

FEM #UU 10.8 5.4 300 450 1200 Fig. 6.34(f)

FEM #VV 10.8 5.4 300 450 1200 Fig. 6.34(g)

(a) FEM #PP 300 300

198

(b) FEM #QQ

(c) FEM #RR

(d) FEM #SS

2@150 300 300

300 300 4@150 4@150

6@150 6@150

2@150

199

(e) FEM #TT

(f) FEM #UU

(g) FEM #VV

Figure 6.35: Different screw patterns used for isolated ceiling diaphragms (all

dimensions are in mm)

300

6@100

300 3@100 3@100

300 300

9@100 9@100

6@100

200

The reason for fixing the extra plasterboard screws along the ends of the ceiling is

because the maximum relative displacement between the plasterboard and frame occurs

at these locations. The maximum shear forces due to lateral load occur at the end of the

diaphragm.

Figure 6.36 depicts the load-deflection behaviour for the seven ceilings with different

plasterboard screw patterns. The addition of one extra screw at the end of each batten

(FEM #QQ) increased the ultimate capacity by about 40% (from 17.6 kN to 25.2 kN) in

comparison with a standard ceiling (i.e. FEM #PP) construction system, as illustrated in

Table 6.25. There is no significant distinction between FEM #RR and FEM #SS and

between FEM #UU and FEM #VV, even though ceilings FEM #SS and FEM #VV had

more screws. This is simply because the extra screws which are located at distance of

700 mm or more from the ends transfer little extra load. Most of the load is transferred

from the plasterboard to the frame through the screws along a distance of about 600 mm

from both ends of the diaphragms.

Figure 6.36: Load-deflection curves for different plasterboard screw patterns for

isolated ceiling diaphragms

201

Table 6.25: Load-carrying capacity and stiffness of ceilings with different screw fixing

patterns for isolated ceiling diaphragms

Model Designation

Total ultimate load

(kN)

Ultimate capacity (kN/m)

Tangent stiffness per unit depth

(kN/mm/m)

Secant stiffness per unit depth

(kN/mm/m) FEM #PP 17.6 1.63 0.34 0.22

FEM #QQ 25.2 2.33 0.36 0.27

FEM #RR 26.2 2.43 0.36 0.25

FEM #SS 26.3 2.44 0.36 0.26

FEM #TT 33 3.06 0.40 0.31

FEM #UU 33.8 3.13 0.40 0.29

FEM #VV 34.0 3.15 0.40 0.29

It can be stated that the capacity of isolated ceiling is sensitive to the patterns of the

plasterboard screws. The lateral performance of the diaphragm can be improved through

the addition of a limited number of extra screws. According to this analysis of the

different layouts of screw patterns, ceiling FEM #TT represents an effective case where

the addition of approximately 8% screws along the ends of each batten resulted in

increased capacity by about 85%.

6.6.2.3 Batten Spacing

In this investigation, the length of ceiling was 10.8 m, while the ceiling width was 5.4

m. The spacing of the bottom chord was 1200 mm. Plasterboard screws were placed at

300 mm along the battens. Two models as shown in Table 6.26 were investigated in

order to observe the behaviour of the ceiling due to the change of the ceiling batten

spacing from 450 mm to 600 mm. The resulting load-deflection curves are presented in

Figure 6.37.

Table 6.26: Parameters for varying batten spacing for isolated ceiling diaphragms

Model

Designation

Length

(m)

Width

(m)

Aspect

ratio

Bottom chord

spacing (mm)

Screw

spacing

(mm)

Batten

spacing

(mm) FEM #AA/ 10.8 5.4 2 1200 300 450

FEM #BB/ 10.8 5.4 2 1200 300 600

202

Figure 6.37: Effect of batten spacing on load-deflection behaviour for an isolated ceiling

diaphragm

Table 6.27 shows that the capacity of the ceiling with 450 mm spacing is about 35%

higher than that of the ceiling with 600 mm batten spacing. Since the plasterboard

screws are fixed along the ceiling batten, the number of screws increases with the

increase of the number of ceiling battens. It should be noted that the capacity of the

diaphragm is mainly dependent on the number of plasterboard screws. Therefore, the

capacity of the diaphragm increases with the decrease of the spacing of the ceiling

battens.

Table 6.27: Load-carrying capacity and stiffness of ceilings with different batten

spacing for isolated ceiling diaphragms

Model

Designation

Total

ultimate load

(kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m)

FEM #AA/ 17.6 1.63 0.33 0.22

FEM #BB/ 13.3 1.23 0.29 0.19

203

6.6.2.4 Bottom Chord Spacing

In this investigation, two models (see Table 6.28) were investigated to order to observe

the effect of bottom chord spacing on the strength and stiffness of the diaphragm. These

models included a change of the bottom chord spacing from 600 mm to 1200 mm. The

spacing of the ceiling batten was kept the same (450 mm) for both models. The loading

was mounted parallel to the bottom chords.

Table 6.28: Parameters for varying bottom chord spacing for isolated ceiling

diaphragms

Model

Designation

Length

(m)

Width

(m)

Aspect

ratio

Batten

spacing

(mm)

Screw

spacing

(mm)

Bottom

chord

spacing

(mm)

FEM #CC/ 7.2 4.95 1.45 450 300 1200

FEM #DD/ 7.2 4.95 1.45 450 300 600

The resulting load-deflection curves are presented in Figure 6.38. As expected, there is

no significant variation of strength and stiffness of the isolated diaphragm due to the

reduction of bottom chord spacing from 1200 mm to 600 mm, as depicted in Table 6.29.

Since the strength and stiffness of the diaphragm are mainly dependent on the number

of plasterboard screws, and the plasterboard screws are fixed along the ceiling batten

not to the bottom chords, increasing the chords does not affect the strength and stiffness

of the diaphragm. However, the strength and stiffness of the diaphragm can be increased

due to the change of the bottom chord spacing when the plasterboard is directly fixed to

the bottom chord rather than the battens.

204

Figure 6.38: Load-deflection behaviour of an isolated ceiling diaphragm with bottom

chord spacing

Table 6.29: Load-carrying capacity and stiffness of ceilings with different bottom chord

spacing for isolated ceiling diaphragms

Model

Designation

Total

ultimate

load (kN)

Ultimate

capacity

(kN/m)

Tangent

stiffness per

unit depth

(kN/mm/m)

Secant

stiffness per

unit depth

(kN/mm/m)

FEM #CC/ 16.0 1.62 0.27 0.27

FEM #DD/ 16.6 1.68 0.31 0.31

6.6.3 Investigation 3: Sensitivity of Isolated Ceiling Diaphragms with Different

Structural Arrangements

This investigation focused on the behaviour of isolated ceiling diaphragms with the

following variations:

direction of loading

205

type of testing assembly

direct fixing to bottom chord members

properties of plasterboard screws

The length of the diaphragm was 5.4 m, while the width was 5.4 m. The spacing of the

ceiling batten was kept at 450 mm, while the bottom chord was attached at 900 mm

spacing. The plasterboard screws were fixed at 270 mm spacing along all ceiling

battens.

6.6.3.1 Loading Directions

In all of the experiments conducted in this research, loading was applied parallel to the

bottom chord members. This was done as it was expected to provide the least strength

and stiffness. Therefore, a model was developed to observe the behaviour of the ceiling

diaphragm with the load applied in the direction of the ceiling battens and compared to

that with the diaphragm loaded parallel to the bottom chords. A uniform distribution

loading system was applied to perform the analysis. The load against deflection curves

for both loading directions are depicted in Figure 6.39.

Figure 6.39: Comparison of load-deflection behaviour between loading directions

parallel to batten and parallel to bottom chords

206

From Figure 6.39, it is clear that the capacity of the ceiling diaphragm in loading

applied parallel to the ceiling battens is more than double that for loading applied along

the bottom chord members. The diaphragm loading along the battens also showed

higher stiffness than the loading applied along the bottom chords. This is attributed in

part to the observed higher strength and stiffness of the frame when loading is applied

parallel to the battens, as presented in Figure 6.40. In addition, as mentioned earlier, the

screws are generally connected along each batten. It should be noted that the equivalent

force is simply the sheathing-to-framing connection force parameter multiplied by the

number of resisting connections. For a diaphragm loaded along ceiling battens, the

direct resisting connections are a comparatively much higher number compared to

loading along bottom chord members.

Figure 6.40: Comparison of load-deflection behaviour of frame only (without

plasterboard) between loading directions parallel to batten and parallel to bottom chords

6.6.3.2 Type of Testing Assembly

Cantilever and beam test methods are typically used to observe the behaviour of the

ceiling diaphragm. Generally, the beam test method is the most realistic method for the

207

estimation of the capacity of the diaphragm. However, due to greater complexity of

beam test methods, several researchers have recommended alternative simple cantilever

methods to observe the performance of the diaphragm. This investigation developed an

FE model with the same construction system in order to identify the variation between

the cantilever (racking) and beam tests. Figure 6.41 shows the load capacity-deflection

curves obtained for both cantilever and beam test assemblies.

Figure 6.41: Capacity-deflection curves for cantilever and beam testing assemblies

From Figure 6.41 it is observed that the ultimate capacity of the ceiling diaphragm is

almost the same for both methods. However, there is considerable variation of stiffness

between these methods. Beam test provide much higher stiffness relative to the

cantilever test.

6.6.3.3 Plasterboard Fixing to Different Structural Members

This investigation observed the behaviour of the ceiling diaphragm with varying

plasterboard fixing systems to different structural members. An FE model was

developed with plasterboard connection to the ceiling battens (0.42mm BMT) which is

208

in turn screwed with the bottom chord members, and plasterboard directly connected

with the bottom chord members (0.75mm BMT) without using ceiling battens in

construction. The resulting load-deflection behaviour is shown in Figure 6.42.

As shown in Figure 6.42, the ceiling diaphragm with the plasterboard directly connected

with the 0.75 mm thick bottom chord members shows considerable higher stiffness

(about 75%) and greater (approximately 45%) capacity compared to the diaphragm

constructed with plasterboard connections to 0.42 mm thick ceiling battens.

Figure 6.42: Load-deflection curves for plasterboard-batten fixed and plasterboard-

bottom chord fixed diaphragms

However, if the thickness of the ceiling batten is increased and the plasterboard is

connected with 0.75 mm BMT ceiling battens, it shows approximately 90% higher

capacity and significantly higher stiffness (about 70%) compared to connection with a

plasterboard-to-0.42 mm BMT top-hat batten section. Moreover, when the plasterboard

screws are connected with the 0.75 mm BMT batten section, the tangent stiffness is

similar but secant stiffness is approximately 25% higher. In addition, the capacity of the

209

diaphragm is considerably higher (approximately 35%) than that constructed with

plasterboard directly connected with the 0.75 mm thick bottom chord members (refer to

Figure 6.42). This occurs due to the observed stronger and stiffer screw connection

properties when connecting plasterboard screws with 0.75 mm sections compared to

plasterboard connection with 0.42 mm batten sections. In addition, as mentioned earlier,

the strength and stiffness of the diaphragm is mainly dependent on the plasterboard-

screw connection system.

6.6.3.4 Properties of Plasterboard Screws

The behaviour of isolated plasterboard-clad ceiling diaphragms is mainly dependent on

the number of screws connecting the plasterboard to the steel frame members.

Therefore, it is essential to develop a relationship among the strength of these

connections and the capacity of the complete ceiling. Five ceilings were investigated in

order to analyse this relationship. The standard screw connection properties obtained

from the experimental observation were used for ceiling FEM #R/, which were then

increased by 10% and 25% for ceiling model FEM #S/ and FEM #T/ respectively, and

decreased by 10% and 25% for ceiling model FEM #U/ and FEM #V/ (refer to Figures

6.43 and 6.44). Figure 6.45 shows the load-deflection curves for these five ceilings.

Figure 6.43: Load-deflection properties of field screws

210

Figure 6.44: Load-deflection properties of edge screws

Figure 6.45: Performance of ceiling diaphragms with different plasterboard-steel frame

connection capacities

211

From Figure 6.45, it can be seen that the capacity of the ceiling is highly dependent on

the capacity of the plasterboard-steel frame connection screws. Certainly, the increase in

the capacity of the plasterboard screws by 10% and 25% resulted in the increase of the

ceiling capacity by approximately 9% and 32%. However, the capacity of the ceiling

diaphragm is decreased by about 11% and 27% if the plasterboard screw capacity is

reduced to 10% and 25% respectively.


In this chapter, the development of FE models to simulate the behaviour of the tested

ceiling diaphragms in the experimental program in both cantilever and beam tests has

been described. Analytical models were developed for various configurations and

verified against the test results presented in Chapters 4 and 5.

The analytical models were used to conduct further analyses for different configurations

to extend the findings of the experiments. The conclusions drawn from this chapter are

summarized as follows:

The developed FE models were verified with the experimental cantilever test

results developed FE model and good agreement was found. The deflected

shapes and failure modes obtained in FE models were similar to those observed

in the experiments, where the battens showed significant bending at the bottom

of the diaphragm. The plasterboard screw connections also failed at same

locations as observed during the experiments.

The FE modelling was verified against tests conducted on beam configurations

with boundary conditions (i.e. the effect of plasterboard bearing on top plates of

end walls) as well as without boundary conditions (i.e. isolated ceiling

diaphragms). The behaviour of the diaphragms in FE modelling showed very

good consistency with the experimental results.

Without end walls, all the racking forces are transferred through the screws

which connect the plasterboard to the ceiling battens. The failure of the

diaphragm is a result of the failure of these screw connections. Not all these

screw connections failed at the same time but they progressively tilted and

failure at different locations occurred while the diaphragm was being loaded.

The diaphragm without boundary conditions failed due to the combination of

tearing of plasterboard at both corner screws as well as pulling out of the

212

plasterboard screws located within 900 mm from both ends of the diaphragm.

Failure of the screw connections occurred at the same locations as those

observed during the test.

The diaphragm with boundary conditions failed due to the combination of

bearing of the plasterboard edge as well as tearing of the plasterboard screws at

the ends and pulling out of the plasterboard screws located within 900 mm from

both corners of the diaphragm. The bearing of the plasterboard edges occurred

at almost the same location to that observed in the experiments from both ends

of the diaphragm

The deflected shape of the diaphragm obtained from the FE model is similar to

that observed in the experiments, where the ceiling battens showed significant

bending at the ends of the diaphragm. The maximum relative movement

between the plasterboard and frame occurred at both ends of the diaphragm,

which was also observed in the experiments.

The boundary conditions play a role in the performance of plasterboard-clad

ceiling diaphragms. The presence of end walls not only increases the ultimate

capacity of the ceiling but also increases the displacement at which the ultimate

load occurs. The reason for enhanced performance is due to not only the

transfer of the load from the plasterboard screws to the steel frame but also the

bearing action along the plasterboard edges.

The strength of the ceiling diaphragm is similar when it is subjected to different

loading configurations, such as one-third point loading, mid-span loading, and

uniformly-distributed loading. However, uniform loading provides moderately

higher stiffness than one-third point loading and mid-span loading.

There is no variation of strength of ceiling diaphragms due to the variation of

testing methods such as cantilever tests and beam tests. However, the beam test

method provides considerably higher stiffness than the cantilever test method.

There is no significant variation of ultimate strength due to changes of length.

However, the stiffness decreases with the increase of the ceiling length (i.e.

aspect ratio). Longer ceilings (those with high aspect ratios) exhibit greater

flexural deformation. Hence, failure occurs at a larger deflection compared to

shorter ceilings which have their deflection dominated by shear action.

213

The effect of boundary conditions (i.e. effects of pasteboard bearing on top

plates of end walls) becomes less significant with the increase of ceiling width.

The boundary condition provides a significant effect on strength of ceiling

diaphragm up to ceiling width of 7 m. However, there is no significant variation

of strength due to the consideration of the top plate's effect when the ceiling

width exceeds 7 m.

There is a strong relationship between the plasterboard screw spacing and

strength and stiffness. Placing plasterboard screws at close spacing not only

provides higher diaphragm strength and stiffness but also leads to failure at

higher displacements. The strength of the diaphragm can be increased by

approximately 80% by reducing one-third spacing of plasterboard screws along

each batten.

The lateral performance of the diaphragm can be improved by the addition of a

limited number of extra screws. The addition of a single screw at the end of

each batten provides approximately 30% higher strength and about 10% higher

initial stiffness. The addition of two screws at the end of each batten provides

about 70% higher strength and approximately 20% higher initial stiffness.

There is a significant impact on the ultimate capacity of the diaphragm due to

changes in the gap size between the plasterboard and end walls. The ultimate

capacity of the ceiling increases with the decrease of the gap size. The ultimate

capacity of a ceiling with no gap is approximately 30% higher than that of a

ceiling with a 10 mm gap.

There is a considerable effect on strength and stiffness of the diaphragm due to

an increase of batten spacing from 450 mm to 600 mm. The capacity of a

ceiling with 450 mm spacing is about 20% higher than that of a ceiling with 600

mm batten spacing.

Since the strength and stiffness of the diaphragm are mainly dependent on the

number of plasterboard screws, and the plasterboard screws are fixed along the

ceiling batten not to the bottom chords, the reduction of bottom chord spacing

does not affect the strength and stiffness of the diaphragm.

The strength and stiffness of the ceiling diaphragm in loading applied parallel to

the ceiling battens is significantly higher than that for loading applied along the

bottom chord members. This is attributed in part to the observed higher strength

214

and stiffness of the frame when loading is applied parallel to the battens. In

addition, the direct resisting connections are comparatively much higher

number when diaphragm loading along ceiling battens compared to loading

along bottom chord members. Therefore, the diaphragm capacity in loading

parallel to the bottom chord is the critical state.

Ceiling diaphragms are sensitive to the plasterboard screw connections with the

thickness of the steel members connected to the plasterboard. When the

plasterboard is connected to 0.75 mm BMT ceiling battens, it provides

significantly higher (approximately 90%) capacity and higher stiffness (about

70%) compared to plasterboard connecting to 0.42 mm BMT top-hat batten

sections.

There is a direct relationship between the shear capacities of plasterboard screw

connections and the ultimate load-carrying capacity of ceiling diaphragms.

Increasing the capacity of the plasterboard screw by 10% and 25% resulted in

the ceiling capacity increasing by approximately 9% and 32%. However, the

capacity of the ceiling diaphragm is decreased by about 11% and 27% if the

plasterboard screw capacity is reduced by 10% and 25% respectively.

215

CHAPTER 7

LATERAL LOAD DISTRIBUTION AND INDUSTRIAL APPLICATIONS

7.1 Introduction

Deflection of the diaphragm and shear wall is important for both seismic and wind

loading. This chapter discusses the development of a simplified mathematical model for

the estimation of the deflection of plasterboard-clad steel-framed ceiling diaphragms

under different loading conditions. The simplified mathematical model has been

verified with the experimental results described in Chapter 5, as well as the finite

element model results described in Chapter 6. In this research it is proposed to utilize

this model as the basis for estimating the deflection of diaphragms in Australian

construction practice. This chapter also provides a design guideline for the distribution

of lateral load to the bracing walls through the ceiling diaphragm. Design charts for

maximum spacing of bracing walls for the most common construction systems

(plasterboard-clad screwed to cold-formed steel battens which are in turn screwed to

bottom chords) in Australian steel-framed houses are also reported in this chapter.

7.2 Simplified Mathematical Model to Predict Diaphragm Deflections

Skaggs and Martin (2004) stated that historically, deflection of diaphragms and shear

walls has not been a critical design consideration. There has been a misunderstanding

that the calculation of the deflection of diaphragms is not essential for the design of

buildings. Many engineers/designers are not aware of the deflection of diaphragms.

However, much more attention has been given to after several devastating earthquakes

(for instance, the 1994 Northridge earthquake) and cyclones. Some researchers assume

the diaphragm to be rigid, while others consider it to be flexible. However, the

International Building Code (IBC, 2006) classifies diaphragms on the basis of the

deflections of shear walls and horizontal diaphragms.

The IBC (2006) developed a model to estimate diaphragm deflection. The deflection of

a diaphragm was calculated as the sum of individual contributions to deflection from

structural components. The expression of IBC formula can be written as Equation 7.1:

Δ = (0.052vL3)/EAb + vL/4Gt + Len/1627 + Σ(ΔcX)/2b (7.1)

where,

216

Δ= deflection of diaphragm (mm)

v= maximum shear due to design loads in direction under consideration (N/mm)

L= diaphragm length (mm)

E= elastic modulus of chords (N/mm2)

A= area of chord cross-section (mm2)

b= diaphragm width (mm)

G= modulus of rigidity of the panel sheathing (N/mm2)

t= thickness of the panel sheathing (mm)

en= nail deformation (mm)

ΣΔcX= sum of individual chord-splice slip values of the diaphragm, each multiplied by

its distance to the nearest support (mm)

In the IBC (2006) formula, the first term refers to the deflection due to bending of the

diaphragm; the second term is deflection due to shear; the third component includes

deflection due to nail slip; and the last term refers to the deflection due to splice slip

along the chords.

Although deflection equations provided by the International Building Code (IBC, 2006)

for estimating diaphragm and shear wall deflection, the design values used in the

equations for the different variables are not extensive. For instance, the values of the

panel shear modulus and thickness (together known as panel rigidity, Gt) are specified

for plywood sheathing only (Tissel and Elliot, 2004). However, it should be noted that

the IBC formula is based on the deformation of standard 1.2 m x 2.4 m (4 ft x 8 ft)

plywood sheets which act independently. In addition, the nail slip parameters used in

the IBC formula remain constant. However, in the case of plasterboard ceiling

diaphragms, all the sheets are joined together and act as one panel. Hence, it is essential

to modify the IBC formula and update it for plasterboard-clad ceiling diaphragms.

A plasterboard-clad ceiling diaphragm can be represented by a deep beam with the

sheathing corresponding to the web, and the top chords of end walls corresponding to

the flanges (Saifullah et al. 2012). Using this analogy, a simplified mathematical model

217

has been developed for the prediction of the deflection of a diaphragm under in-plane

loading. This model has been developed for steel-framed structures and it can be

adapted once all relevant input parameters are available. The parameters for the

calculation of the overall deflection can be estimated using the relative contribution of

structural components and sheathing-to-framing connection data. The contributions to

the deflection include (i) deflection due to flexural (bending), (ii) deflection due to

shear, (iii) deflection due to screw slip (sheathing-to-framing connections), and (iv)

deflection due to chord-splice connections. It is common practice in steel-framed houses

in Australia to have additional track segments to connect the top plates of end walls to

ensure continuity. Hence, the deformation (separation) of top plates at the splice

connections can be ignored. Figure 7.1 shows graphical illustrations of these

deformation components. The expression of the proposed simplified model can be

written mathematically as Equation 7.2:

Δdiaphragm = Δbending + Δshear + Δscrew ……………………………………………. (7.2)

(a) deflection due to bending

(b) deflection due to shear

Ceiling

End wall

End wall

Ceiling

218

(c) deflection due to screw slip between plasterboard and steel member

Figure 7.1: Various components of diaphragm deflection

Flange contribution

The contribution of the flange to diaphragm deflection is provided on the basis of the

girder analogy. Two components of the diaphragm deflection occur due to the

contribution of the flange. The first term is due to flexural deformation in the diaphragm

and the second term is due to slippage at flange splices. It should be noted that the

flanges of the diaphragm are assumed to be the top plate of the end walls. The

deflection due to splice slip of the diaphragm is associated with the stresses induced in

the flanges as well as the tolerance of the diaphragm fabrication.

Web shear contribution

The deflection of the girder due to the contribution of web shear with small span-to-

depth ratios is significant (ATC, 1981). However, in steel framing members with

normal span-to-depth ratios, deflection from the contribution of shear is generally of

little significance in the total deflection of the diaphragm.

The web of the diaphragm is represented by the sheathing of the diaphragm and is

considered to carry the shearing stresses introduced in the member due to the applied

lateral loads. It should be mentioned that the modulus of rigidity of the plasterboard-

sheathed panel varies according to the density of the plasterboard board. Web elements

are spliced over the steel framing members so that there are mechanisms for stress

transfer between the web and the flange. It should be noted that the buckling of the web

is typically resisted due to the stiffening effect of the steel framing members to which

the plasterboard sheathing is connected. The loads generally act uniformly distributed

along the length of the diaphragm. Hence, the critical shear condition for the diaphragm

occurs at the supports (i.e. reactions). In the derivation of the deflection due to shear of

Batten or bottom chord of roof truss

Ceiling sheeting

219

the web, it is assumed that the shear stresses are uniformly distributed across the entire

width of the web.

Screw-slip contribution

The deformation of plasterboard to frame screw connections contributes to the overall

deflection of the diaphragm. The deformation at these connections is characterised by

screw slip deformation. These deformation characteristics can be obtained from the tests

outlined in Chapter 3.

7.2.1 Estimation of Deflection Equation Parameters under One-third Loading

The deflection equation is derived on the basis of a number of assumptions: (i) simply

supported, (ii) uniformly screwed, (iii) one-third point loaded, and (iv) constant in

length and width. A representation of a diaphragm under one-third loading conditions is

presented in Figure 7.2. For diaphragms, the contribution of the deflection due to

bending and shear can be obtained using a standard formula.

Figure 7.2: Diaphragm subjected to one-third loading

Diaphragm deflection due to flexural contribution (bending)

Δbending

Where,

220

P = point load at one-third distance

L = length of the diaphragm

E = modulus of elasticity of steel framing members

I = moment of inertia

Since the top plates only resist the bending, E and I refer to the properties of the top

plates of the end wall.

The moment of inertia (I) can be determined by the application of the parallel-axis

theorem as shown in Figure 7.3.

I = (Ic +Ad2)*2

where, Ic = bh3/12

Since the value of Ic is very small compared to d, the term Ic can be ignored.

Therefore, I = 2*A*(b/2)2 = Ab2/2

Figure 7.3: Application of parallel axis theorem for determination of moment of inertia

Again,

Unit shear, v = P/b

P = vb

b

d = b/2

Chord

Chord

221

Δbending

= [vb*L3/ (28.2 * E * (Ab2/2)]

= 0.071vL3/EAb

This derivation ignores the bending contribution of ceiling battens as they are assumed

to have very low stiffness. However, if bending of the diaphragm is such that the bottom

chords of the trusses are in bending, then this term needs to be changed.

Diaphragm deflection due to shear

Based on cleared structural mechanics theory,

Δshear =

where,

fs = form factor for the cross-sectional area = 1 (for simplicity)

Vx= shear force due to actual load

vx= shear force due to unit load

A = cross-sectional area of the web (sheathing) = bt

b = diaphragm depth

t = sheathing thickness

G = modulus of rigidity of the sheathing

Δshear = (1/GA)[ * 2

= *2

=

222

Diaphragm deflection due to screw-slip

Figure 7.4 presents the deflected shape of a typical sheathed frame under in-plane shear

loading. In the case of the equal connection deformation (en) of the horizontal and

vertical components, the deformation of the corner plasterboard sheathing-to-framing

connections in the panel along a 45° line = en/cos45° = en√2. The value of the

connection deformation (en) can be obtained from the shear connection test described in

Chapter 3.

Figure 7.4: Deformed shape of a plasterboard sheathing panel in shear

The deformation component along a line parallel to the plasterboard sheathing panel

diagonal (as shown in Figure 7.4) is en√2 cosØ,

223

where,

Ø = 45°-θ and θ = tan-1(b/a)

b = panel dimension parallel to the applied load

a= panel dimension perpendicular to the applied load

Figure 7.5 shows the deformed shape of a plasterboard sheathing panel. Since the

frame deforms in both corners, the total frame elongation (eframe) with respect to the

panel diagonal = (en√2 cosØ) * 2

Figure 7.5: Deformed shape of a plasterboard sheathing panel

Elongation of the plasterboard sheathing panel occurs due to the horizontal shear from

the loading. Therefore, the horizontal deformation (δh) of the panel is

δh =

= [(vb) * a]/ [(bt) * G]

= va/Gt

The elongation of the plasterboard sheathing panel due to vertical shear deformation (as

shown in Figure 7.6) is calculated as:

Sinθ = eshear/ δh

224

eshear = δh * sinθ

= (va/Gt) * sinθ

In terms of the panel diagonal length (l)

eshear = v * (l * cosθ) * sinθ/Gt

= vlsin2θ/2Gt

= vl * cos(90°-2θ)/2Gt

= vl * cos(2(45°-θ))/2Gt

= vlcos2Ø/2Gt

l = length of the panel diagonal = √ (a2 + b2)

Figure 7.6: Plasterboard sheathing panel elongation with respect to panel diagonal

It is assumed that the ratio of the component of mid-span diaphragm deflection due to

plasterboard sheathing-to-steel framing connection deformation (Δscrew) and elongation

of the frame (eframe) is equal to the ratio of the mid-span deflection due to shear (Δshear)

and panel elongation due to shear (eshear) (Judd, 2005).

Δscrew/ eframe = Δshear/ eshear

Δscrew = Δshear * eframe / eshear

225

= vL/3Gt * [(en√2 cosØ) * 2/ (vlcos2Ø/2Gt)]

= (4√2 cosØ/ 3lcos2Ø) * Len

= Len/C

Δscrew = Len/C

where,

C = 3lcos2Ø/4√2cosØ

Ø = angle formed by the diagonal of a panel with respect to the long edge of panel =

45°-θ

θ = tan-1(b/a)

a = L/3

Δdiaphragm = Δbending + Δshear + Δscrew

+ +

7.2.2 Simplified Mathematical Model Validation against Test Results

The approximate deflection of the plasterboard-sheathed steel-framed ceiling diaphragm

can be obtained using the developed simplified mathematical model which is derived

under one-third point loading conditions. The simplified mathematical model for the

estimation of diaphragm deflection has been verified against the measured deflection

from experimental test results (described in Chapter 5) and found to be in good

agreement, as shown in Figure 7.7. It is worthwhile to mention that all test results

presented in Chapter 5 were based on one-third loading configurations.

226

0

5

10

15

20

25

30

35

1 2 3 4 5

Def

lect

ion

at u

ltim

ate

load

(mm

)

Beam Test Specimen*

Mathematical ModelTest


model and beam test results

*Beam test specimen #1: L= 5.4 m, W = 2.4 m, batten spacing = 600 mm, bottom chord spacing = 900 mm, screw spacing = 270 mm. No plasterboard edge bearing on top plates.

* Beam test specimen #2: L = 5.4 m, W = 2.4 m, batten spacing = 600 mm, bottom chord spacing = 900 mm, screw spacing = 270 mm. Plasterboard edge bearing on top plates.


* Beam test specimen #4: L = 8.1 m, W = 2.4 m, batten spacing = 400 mm, bottom chord spacing = 900 mm, screw spacing = 270 mm. No plasterboard edge bearing on top plates.


7.2.3 Simplified Mathematical Model Modification to Replicate Wind Load

In reality, the wind load acts upon the ceiling diaphragm as uniformly distributed load.

Therefore, it is necessary to modify the simplified mathematical model presented in

Section 7.2.2 and update it for uniformly distributed load, which replicates wind loading

conditions.

Δdiaphragm (midspan) = Δbending + Δshear + Δscrew

227

+ +

where,

v = wL/2b

w = uniformly distribution load

L = length of the diaphragm

b = width of the diaphragm

E = modulus of elasticity of steel framing members

I = moment of inertia

A = cross-sectional area of chord

t = plasterboard thickness

G = modulus of rigidity of the plasterboard

en = deformation of plasterboard to steel framing connection

C = lcos2Ø/√2cosØ

l = panel diagonal length = √ (a2 + b2)

Ø = angle formed by the diagonal of a panel with respect to the long edge of panel =

45°-θ

θ = tan-1(b/a)

a = L/2

In this research, it is proposed to utilize this model as the basis for determining the

deflection and hence, the stiffness of typical steel-framed ceiling diaphragms

constructed in Australia.

228

7.2.4 Sample Calculation of Diaphragm Deflection using Simplified Mathematical

Model

A sample calculation for the estimation of diaphragm deflection using the simplified

mathematical model can be accomplished using the example presented in Figure 7.8.

Deflection of a diaphragm under wind load can be estimated by:

Figure 7.8: Diaphragm configuration showing lateral load along chord direction

Here,

L = 10000 mm

b = 10000 mm

w = 3.5 kN/m

v = wL/2b = 3.5 x 10000/ (2 x 10000) = 1.75 N/mm

E = 200000 N/mm2

A = 120 mm2

en = 6.7 mm (shown in Figure 7.9)

229

Figure 7.9: Average screw load-slip response (source: Chapter 3)

t = 10 mm

G = 180 MPa

a = L/2 = 10000/2 = 5000 mm

= = = 11180 mm

= = 18.40

= 0.4 + 2.4 + 10.0 = 12.8 mm

230

7.2.5 Simplified Mathematical Model Validation against Finite Element Model

Results

The developed simplified mathematical model (shown in Section 7.2.3) subjected to

uniformly distributed loading for plasterboard-sheathed ceiling diaphragms has been

validated against finite element model results (described in Chapter 6), as illustrated in

Figure 7.10. There is good agreement observed between the simplified mathematical

model and the finite element model results for aspect ratios up to 3. However, by

comparing with the FEM results (shown in Figure 7.10), the simplified mathematical

model gives underestimated deflection value for the AR-0.5 specimen and

overestimated deflection value for the specimen with AR greater than 3. When the AR

increases the simplified mathematical model provides monotonically increasing value.

0

5

10

15

20

25

30

FEM #II (AR-0.5)

FEM #HH(AR-0.75)

FEM #FF(AR-1.0)

FEM #AA(AR-1.33)

FEM #BB(AR-2.0)

FEM #CC(AR-3.33)

FEM #DD(AR-4.0)

Defle

ction

at u

ltim

ate l

oad

(mm

)

Mathematical Model FEM


model and FEM results

From the simplified mathematical model it has been observed that deformation of

plasterboard to steel-framing connection is the main parameter for the contribution of

diaphragm deflection. In this research (described in Chapter 3), five samples were tested

to determine the load-slip response of screw. Therefore, the more number of shear

connection tests will provide the more precise value of deformation of plasterboard to

steel-framing connection and as a consequence, the simplified mathematical model will

give diaphragm deflection value closer to FEM results. It should be mentioned that the

parameters considered for these diaphragms in finite element models included spacing

of ceiling battens and bottom chords of 450 mm and 900 mm respectively, 10 mm thick

231

plasterboard, and plasterboard screws fixed along the batten at 270 mm spacing. All of

the diaphragms were loaded parallel to the bottom chords under uniformly distributed

loading conditions.

7.3 Approximate FE model for diaphragm deflection

7.3.1 Deep Beam Model

In this model, deep beam elements are used to model the diaphragm for distributing

wind load to the bracing wall. The diaphragm is modelled using beam elements of

equivalent shear stiffness (GAs) and high value of bending stiffness (EI) to eliminate

the contribution of bending deformation. Bracing walls are modelled as linear springs of

equivalent stiffness (secant stiffness). Figure 7.11 shows the equivalent diaphragm

stiffness for the deep beam model. The equivalent diaphragm stiffness (GAs) for the

deep beam model can be obtained under various loading conditions, as presented in

Equation 7.3.

Figure 7.11: Diaphragm model using deep beam analogy

232

(7.3)

Where, Shear span = (a) L/2 for point load at mid-span

(b) L/3 for one-third loading

(c) approximately L/4 for UDL

Table 7.1 shows the validation of equivalent diaphragm stiffness using the deep beam

model against the experimental results for a diaphragm 5.4 m x 2.4 m with 400 mm

batten spacing. Figure 7.12 shows the deformed shape of the diaphragm using the deep

beam analogy. The maximum deflection of the diaphragm under mid-span point

loading, one-third loading and UDL is similar because of the using different equivalent

diaphragm stiffness (GAs) in the deep beam model.

Table 7.1: Validation of equivalent diaphragm stiffness (5.4 m x 2.4 m- 400 mm batten

spacing) using deep beam model

Observation Shear strength, wL/2 (kN) Δ (mm) KD

(kN/mm)

Equivalent diaphragm stiffness for deep beam model (kN)

Test 6.3 24.0* 0.29 --

Deep beam method (Point load at mid-span)

6.3 21.7 0.29 GAS = KD*L/2 = 783

Deep beam method (One-third loading) 6.3 21.7 0.29 GAS = KD*L/3 = 522

Deep beam method (UDL) 6.3 21.7 0.29 GAS = KD*L/4 = 392

NB: * Test results of beam test specimen as described in Section 5.6.4 in Chapter 5.

(a) Point load at mid-span

233

(b) One-third loading

(c) UDL

Figure 7.12: Diaphragm deformed shape using deep beam model

Therefore, equivalent shear stiffness of the diaphragm (for wind load) for the deep beam

model can be estimated using the following equation:

7.3.2 Plate Element Model

In this method, plate elements are used to model the diaphragm for distributing wind

load to the bracing walls. In the plate model, the plate represents the diaphragm, and the

spring represents the shear walls. The model is analysed subjected to static loads. The

diaphragm is modelled using plate elements of equivalent shear stiffness (Gts) and high

values of bending stiffness (EI) to minimise the contribution of bending deformation.

Bracing walls are modelled as linear springs of equivalent stiffness (secant stiffness).

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The equivalent shear stiffness of diaphragms (for wind load) for the plate element

model can be estimated using Equation 7.4.

(7.4)

where, AR = Aspect ratio of diaphragm = L/b

7.4 Case study

There are several methods for the distribution of lateral loads to the bracing walls

through ceiling diaphragms. A case study was performed for the design of lateral load-

resisting elements using different lateral load distribution methods. The house is

considered for N3/C1 wind classification in Australia. Figure 7.13 shows the

configuration of the house with lateral load-resisting elements along the long direction.

The load is distributed to the walls based on a number of assumptions: (i) diaphragms

are rigid or flexible, (ii) stiffness of the shear wall is almost similar, (iii) the behaviour

of shear walls is linear, and (iv) there is no rotation of the structure due to lateral

loading.

Figure 7.13: Building configuration showing lateral load resisting elements in long

direction

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The properties of the ceiling diaphragm were obtained from the beam test specimen

testing performed by the author, and the properties of the bracing walls (in this case,

fibre cement sheathing) were obtained from the tests performed by my colleague Rojit

Shahi, second companion in the entire research project.

Properties of diaphragm

Plasterboard sheathing, G = 180 MPa

t = 10 mm

Bottom chord, E = 200,000 MPa

A = 120 mm2

Screw-slip en = 6.7 mm (from tests described in Chapter 3)

Batten spacing = 450 mm

Bottom chord spacing = 900 mm

Screw spacing = 270 mm

Strength of diaphragm v = 1.75 kN/m (from tests described in Chapter 5)

Properties of bracing wall

Fibre cement sheathing t = 5 mm

Fastener spacing = 100 mm at perimeter and 150 mm at interior

Design strength of wall = 4.9 kN/m (from test) (Shahi, 2015)

Displacement capacity of wall = 33 mm (from test) (Shahi, 2015)

Stiffness of wall = 0.15 kN/mm/m (from test) (Shahi, 2015)

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7.4.1 Maximum bracing wall spacing

Maximum spacing between bracing walls is estimated based on the wind load and the

design strength of the diaphragm.

If v (1.75 kN/m) is the shear strength per unit width of the diaphragm and w (3.5 kN/m)

is the design wind load (as illustrated in Figure 7.14), then maximum spacing between

bracing wall can be obtained by:

(7.5)

Figure 7.14: Maximum spacing (L) between bracing wall for design wind load (w)

It should be noted that design wind load (w) is estimated based on the location of the

building and the direction of the wind.

Maximum spacing between bracing walls is evaluated using Equation 7.5:

7.4.2 Method 1: Total shear

In this case, estimated horizontal load, w = 3.5 kN/m and maximum spacing between

bracing walls = 10.0 m. After finding the maximum spacing between bracing wall

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panels, the total length of the bracing wall required to resist the wind load is evaluated

based on the strength of the wall. Then, various lengths of bracing walls (summed to

total length; total shear method) are allocated at different locations of the building based

on judgement.

Total length of bracing wall panel required = Wind load/design strength of bracing wall

Wind load = w * length of building = 3.5 * 22 = 77 kN

Total length of bracing wall panel required = 77/4.9 = 15.7 m ≈ 16 m

W1 = 3 m → 3 * 4.9 kN/m = 14.7 kN

W2 = 4 m → 4 * 4.9 kN/m = 19.6 kN

W3 = 5 m → 5 * 4.9 kN/m = 24.5 kN

W4 = 4 m → 4 * 4.9 kN/m = 19.6 kN

Total = 78.4 kN (OK)

7.4.3 Method 2: Deep beam method

Figure 7.15 shows the modelling of a diaphragm using the deep beam model. The

equivalent stiffness of the diaphragm and bracing walls are provided in Tables 7.2 and

7.3 respectively.

Figure 7.15: Diaphragm model using deep beam element

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Table 7.2: Equivalent diaphragm stiffness (GAs) for deep beam method

Diaphragm Diaphragm dimension

Capacity, V (kN)

Deflection, Δ (mm)*

Stiffness, KD (kN/mm)

GAs (kN) Length,

L (m) Width, b (m) AR

D1 7 10 0.7 17.5 10.9 1.63 2860

D2 5 10 0.5 17.5 9.7 1.84 2299

D3 10 10 1.0 17.5 12.8 1.39 3468

* Note: Deflection was calculated based on the simplified mathematical model under

uniformly distributed loading. A sample calculation of this diaphragm deflection is

presented in Section 7.2.4.

Table 7.3: Bracing wall stiffness

Bracing wall

Length (m)

Capacity, V (kN)

Deflection, Δ (mm)

Stiffness, KW (kN/mm)

W1 3.0 14.7 33.0 0.45

W2 4.0 19.6 33.0 0.60

W3 5.0 24.5 33.0 0.75

W4 4.0 19.6 33.0 0.60

Figure 7.16 represents the displacement of both the ceiling diaphragm and shear walls.

The estimation of diaphragm deflection is subjected to uniformly distributed load

representing wind load. The sample calculation of diaphragm deflection is presented in

Section 7.2.4. The strength and deflection of bracing walls obtained from the deep beam

method are compared with the capacities of walls obtained from the experimental

results and presented in Table 7.4. Table 7.4 shows that bracing walls W2 and W3

designed using the total shear method are inadequate in both strength and deflection

capacity, which is revealed using the deep beam method. This is an advantage of the

deep beam method, where bracing walls and diaphragm are designed for both strength

and deflection. Table 7.5 shows the comparison of diaphragm deflection between the

deep beam method, the simplified mathematical model and finite element modelling for

this building configuration. Good agreement was achieved using the deep beam method.

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Figure 7.16: Diaphragm and bracing wall displacement using deep beam model

Table 7.4: Bracing wall strength and deflection check

Bracing wall

Deep beam method Capacity from wall test (Shahi, 2015) Check

Reaction (kN)

Deflection (mm) Strength

(kN) Deflection (mm) Strength Deflection

W1 13.5 30.0 14.7 33.0 OK OK

W2 19.9 33.2 19.6 33.0 Fail Fail

W3 25.1 33.5 24.5 33.0 Fail Fail

W4 18.5 30.8 19.6 33.0 OK OK

Total 77.0 77.0

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Table 7.5: Diaphragm deflection check

Diaphragm

Diaphragm deflection (mm)

Comments Deep beam method

Simplified mathematical

model*

Finite Element model**

D1 7.5 10.9 12.4

OK as deep beam model provides less deflection value. It occurs because to D1 is loaded in deep beam method with load less than ultimate load.

D2 4.8 9.7 11.2

OK as deep beam model provides less deflection value. It occurs because D2 is loaded in deep beam method with load less than ultimate load.

D3 12.6 12.8 14.4

OK as deep beam model provides similar deflection value. It happened as D3 is loaded in deep beam method with ultimate load.

* Note: The simplified mathematical model is based on the diaphragm deflection

formula under uniformly distributed loading. A sample calculation of this diaphragm

deflection is presented in Section 7.2.4.

** Diaphragm deflection from finite element model was shown in Section 6.6 of

Chapter 6.

7.4.4 Method 3: Plate method

The plate element model was developed using commercial software Strand7. In this

method, the diaphragm is modelled using plate elements of equivalent shear stiffness

(Gts) and high values of bending stiffness (EI). Bracing walls are modelled as linear

springs of equivalent stiffness (secant stiffness), as shown in Figure 7.17.

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Figure 7.17: Diaphragm model using plate element method

The equivalent stiffness of the diaphragm and bracing walls are provided in Tables 7.6

and 7.7 respectively. A detailed estimation of equivalent stiffness is provided in Section

7.3.2. The deformed shape of the diaphragm from the plate element model is illustrated

in Figure 7.18. Figure 7.19 presents the displacement of the diaphragm and bracing wall

for the considered building configuration, which is similar to the results from the deep

beam model presented in Figure 7.16.

Table 7.6: Equivalent diaphragm stiffness (Gts) for plate method

Diaphragm Diaphragm dimension

Capacity, V (kN)

Deflection, Δ (mm)

Stiffness KD (kN/mm)

Gts (kN/mm) Length,

L (m) Width, b (m) AR

D1 7 10 0.7 17.5 10.9 1.63 0.29

D2 5 10 0.5 17.5 9.7 1.84 0.23

D3 10 10 1.0 17.5 12.8 1.39 0.35

Table 7.7: Bracing wall stiffness

Bracing wall

Length (m)

Capacity, V (kN)

Deflection, Δ (mm)

Stiffness KW (kN/mm)

W1 3.0 14.7 33.0 0.45

W2 4.0 19.6 33.0 0.60

W3 5.0 24.5 33.0 0.75

W4 4.0 19.6 33.0 0.60

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Figure 7.18: Diaphragm deformed shape from plate element model

Figure 7.19: Diaphragm and bracing wall displacement

Table 7.8 illustrates a comparison of the strength and deflection of bracing walls based

on the experimental test results and the plate element model. Table 7.8 shows that

bracing walls W2 and W3 designed using the total shear method are inadequate in both

strength and stiffness capacity, which is revealed by the plate element method. Table 7.9

shows the comparison of estimated diaphragm deflection between the plate element

method, the simplified mathematical model and finite element modelling for this

configuration of the house. Good agreement was obtained using the plate element

model.

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Table 7.8: Bracing wall strength and deflection check

Bracing wall

Plate method Capacity from wall test (Shahi, 2015) Check

Reaction (kN)

Deflection (mm) Capacity

(kN) Deflection (mm) Strength Deflection

W1 13.7 30.8 14.7 33.0 OK OK

W2 19.7 33.1 19.6 33.0 Fail Fail

W3 24.9 33.4 24.5 33.0 Fail Fail

W4 18.7 31.4 19.6 33.0 OK OK

Total 77.0 77.0

Table 7.9: Diaphragm deflection check

Diaphragm

Diaphragm deflection (mm)

Deflection check Plate method

Simplified mathematical

model*

Finite Element model**

D1 7.3 10.9 12.4

OK as plate method provides less deflection value. It occurs because D1 is loaded in plate method with load less than ultimate load.

D2 4.6 9.7 11.2

OK as plate method provides less deflection value. It occurs because D2 is loaded in plate method with load less than ultimate load.

D3 12.3 12.8 14.4

OK as plate method provides almost equal deflection value. It occurs because D3 is loaded in plate method with ultimate load.

*Note: The simplified mathematical model is based on the diaphragm deflection formula under uniformly distributed loading. A sample calculation of this diaphragm deflection is presented in Section 7.2.4.

** Diaphragm deflection from the finite element model was shown in Section 6.6 of Chapter 6.

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7.4.5 Diaphragm load distribution

In this section, five load distribution methods were used for distributing lateral loads

from the diaphragm to the bracing walls: the deep beam method, the plate element

method, the tributary area method, the relative stiffness method, and the relative

stiffness with torsion method. Figure 7.20 shows the comparison of the distribution of

lateral load to the four bracing walls (as specified in Figure 7.13 in Section 7.4) through

ceiling diaphragms.

Figure 7.20: Diaphragm load distribution to bracing walls

From Figure 7.20 it can be seen that there is little variation in the results from all the

methods mentioned above. This is because the selected case study does not represent

some extreme conditions. However, this variation is reasonable, as the methods studied

here cover a variety of complexities and are based on different principal assumptions

about the load distribution on the structures. There is significant variation in the

calculated wall forces for the most common methods (i.e. tributary area method) in

comparison to the other methods. It should be noted that all of the lateral load

distribution approaches, with the exception of the tributary area and total shear methods,

necessitate the estimation of the characteristics of the wall stiffness. As the load

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distribution methods are highly sensitive to the wall stiffness, it is essential to the

accurate estimation of the stiffness of walls.

The estimation of the stiffness of the wall and ceiling diaphragms was accomplished

based on the experimental testing and finite element modelling. The FE models

generated load-deflection curves under monotonic loading, based exclusively on the

properties of the materials and the individual properties of the sheathing-to-framing

connections. Based on this specific case study, it can be stated that the plate method

provides a good distribution of shear wall reactions compared with the deep beam

model. The next most precise approaches seem to be the relative stiffness method

followed by the other load distribution methods. From Figure 7.20, it can be observed

that the tributary area method is the least satisfactory approach, although this method is

presently recognized as one of the most common methods used by design engineers

because of its simplicity. It can also be concluded that the methods based on the

assumption of rigid horizontal diaphragm action provide the best results. Of the load

distribution methods described above, the deep beam method and the relative stiffness

method are the most practical, as these methods provide satisfactory precision without

using sophisticated computer modelling. However, the relative stiffness method may

not be a suitable approach when the contribution of the transverse wall to the lateral

load distribution is considerable, or when the ceiling and roof diaphragm are more

flexible than the shear walls.

7.5 Design Charts for Industrial Applications

Tests and finite element modelling were performed to obtain information about the

design strength on a wide range of ceiling systems presently used in Australia. Tests and

FE modelling were also performed to investigate the process by which diaphragm

construction systems can be improved with a view to the establishment of a more

rational method of steel-framed house construction.

In the Australian Standard AS 4055:2010, winds are classified as non-cyclonic (regions

A and B) and cyclonic (regions C and D). For each location, the wind speed is provided

for both ultimate and serviceability limit states design.

Design charts can be prepared to provide the maximum spacing of bracing walls for

different categories of wind for non-cyclonic regions (N1 to N6) and for cyclonic

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regions (C1 to C4), classified in accordance with AS 4055:2010. Wind pressures also

depend on the roof geometry and the direction of the wind relative to the orientation of

certain roof shapes. The wind forces also depend on the tributary area. Roof geometrics

include gable ends (shown in Figure 7.21(a), hip ends (shown in Figure 7.21(b) and at

right angles to building length in hip- or gable-end buildings, as shown in Figure

7.21(c)).

(a) Wind force to be resisted by gable ends

(b) Wind force to be resisted by hip ends

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(c) Wind force to be resisted at right angles to building length (hip or gable end

buildings)

Figure 7.21: Configurations of wind load to be resisted by various types of buildings

Figure 7.22 shows a graphical representation of the maximum spacing of bracing walls

with respect to the ceiling depth for wind class N3/C1 based on both strength and

serviceability limit states for roof pitches 5° to 35°. It should be noted that most houses

in Australia have roof pitches between 15° to 25°. This design chart was prepared on the

basis of the results of the ceiling diaphragm tests (described in Chapter 5) and

parametric studies from finite element model results (described in Chapter 6). A sample

calculation for estimating the maximum bracing wall spacing for the wind along the

long direction of a building located in the N3/C1 region is presented is Section 7.4.1.

From Figure 7.22, it is clear that the maximum spacing of the bracing wall decreases

with the increase of the roof pitch. From a practical point of view, there is a 10 mm gap

between the ceiling diaphragm and the end walls. The gap between the plasterboard and

end walls closes when relative movement occurs and the flanges of the top plates of the

end walls bear against the plasterboard edges. This finally leads to the bearing of the

plasterboard edges at the both corners of the diaphragm. As described in Chapter 6

based on parametric studies, the strength and stiffness of the ceiling diaphragm

increased due to the plasterboard bearing on the top plates of the end walls. These

effects are significant up to a ceiling depth of 7 m. Moreover, there is no significant

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variation of the strength and stiffness of the diaphragm due to these considerations for

ceiling depths greater than 7 m. Therefore, these issues were considered in the

preparation of the design chart and a kink in the curves is observed at 7 m. Therefore,

the design chart was prepared based on the capacity of the ceiling diaphragm of 2 kN/m

for ceiling depths up to 7 m; however, 1.8 kN/m capacities is considered for ceiling

depth between 7 m and 16 m. The serviceability limit state was considered on the

maximum deflection limit of L/250 in the preparation of this design chart.

In a house/structure, wind can occur from any direction, and this chart was therefore

prepared based on the critical wind-loading conditions. As an example, for single-storey

houses or the upper storey of two-storey buildings, the maximum spacing between

designated bracing walls for each wind loading direction (i.e. at right angles to the

building length and width) can be obtained from Figure 7.22 for the wind category

N3/C1.

Figure 7.22: Maximum bracing wall spacing for wind class N3/C1

These recommendations are provided for diaphragms loaded parallel to the bottom

chord members. However, loading perpendicular to the bottom chords provides greater

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shear strength, as observed in the parametric studies in the finite element models

presented in Chapter 6. Therefore, the wind loading parallel to the bottom chords is

critical for the design to be considered safe.


This chapter has provided a wide-ranging summary of the procedures for the estimation

of the deflection of plasterboard-sheathed steel-framed ceiling diaphragms. The capacity

of ceiling diaphragms to transfer lateral loads to the bracing walls by diaphragm action

is also illustrated in this chapter. This chapter has also highlighted some limitations in

the design of residential structures in relation to the distribution of lateral loads from the

ceiling and roof to the bracing walls. While the current practice in Australia is simple

and only requires the total sum of wall racking capacities to equal or exceed the total

lateral load, this is only applicable if the spacing between bracing walls is within certain

limits (e.g. AS 1684). In contemporary and architecturally designed houses, the spacing

between bracing walls may exceed the nominal limits with no further guidance given to

the design engineer. The findings from this chapter are summarised as follows:

A simplified mathematical model was developed for determining the deflection

and hence, the stiffness of typical plasterboard-sheathed steel-framed ceiling

diaphragm used in Australia. The model was verified against the experimental

results as well as the finite element model results and found to be in good

agreement. Hence, the deflection of plasterboard-sheathed steel-framed ceiling

diaphragms can be estimated using the new developed model.

A case study was presented for a house to show the distribution of lateral loads

from the plasterboard-clad steel- framed ceiling diaphragms to fibre cement-clad

shear walls. It was shown that the ceiling diaphragm can be accurately

represented by a deep beam or a plate. The equivalent properties of the deep

beam or plate can be determined using a procedure presented in this chapter.

Based on strength and serviceability limit states, the maximum spacing of

bracing walls with respect to the ceiling depth for wind class N3/C1 was

developed. However, similar design charts can be prepared to provide the

maximum spacing of bracing walls under different wind categories in non-

cyclonic regions (N1 to N6) and cyclonic regions (C1 to C4).

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CHAPTER 8

CONCLUSIONS AND RECOMMENDATIONS

8.1 Conclusions

This research reported here involved a detailed literature review, a comprehensive

experimental program and extensive analytical modelling. The experimental program

was based on a typical ceiling framing system. The overall aim of this research is to

quantify the strength and stiffness of typical cold-formed steel-framed plasterboard-

lined ceiling diaphragms subjected to monotonic loading to simulate wind-loading

conditions.

The key factors which affect the strength and stiffness of ceiling and roof diaphragms in

Australian steel-framed domestic structures are discussed in the literature review. From

the literature review, the following findings have been obtained:

Many experimental and analytical modelling studies have been conducted on the

determination of the strength and stiffness of shear walls. However, very few

studies have been undertaken on the determination of the strength and stiffness

of ceiling and roof diaphragms in cold-formed steel houses. Determination of

diaphragm stiffness is essential in the design of light-framed structures, in order

to distribute the lateral loads from the ceiling and roof to the walls.

A key factor which affects the strength and stiffness of lined or clad light frames

is the fixity between the lining material and framing. The behaviour of these

connections in shear tends to dictate the behaviour of the entire lined system.

This is true for walls and ceilings.

Since the behaviour of the connections between the plasterboard and the steel framing

members is a major factor in assessing the strength and stiffness of ceiling diaphragms,

it was essential to conduct shear connection tests. Based on the experimental

observations and subsequent analysis of the shear connection tests, the following

conclusions can be drawn:

For all the edge screw shear connection tests, the failure mode for edge

connections was tearing out of the plasterboard from its edge.

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Field screw shear connections showed plasterboard bearing as well as screw

tilting and head piercing through the plasterboard.

Edge shear connections with 20 mm edge distance achieved approximately 85%

of the ultimate loads of the field screws with the same plasterboard and steel

members.

The ultimate capacity of the plasterboard-to-channel section connection is

approximately 35% higher than that of the plasterboard-to-top hat section for

both field screw and edge screw tests. The initial stiffness of the connection to

the channel section is almost four times that of the connection with the top hat

section. This is due to the greater thickness of the channel sections.

In this thesis, raking/cantilever tests were conducted on three specimens of ceiling

diaphragms. From the results and analyses of the full-scale isolated ceiling diaphragms

in cantilever configuration, the following conclusions can be drawn:

The plasterboard connections failed at the locations where maximum relative

movement between the plasterboard and battens occurred. The failure of screw

connections was in the form of tearing of plasterboard around the screw heads

and pull-through of the plasterboard.

No relative movement was observed between the individual plasterboard sheets.

The entire plasterboard lining rotated as a single unit rather than two

plasterboard sheets rotating individually. No relative displacement was observed

between the ceiling battens and the bottom chords.

There was limited variation (approximately 5.5%) between the results from the

three test specimens, indicating excellent agreement between these test results.

Five full-scale tests were conducted in beam configuration. This set-up is closer to the

real action of a ceiling; however, it is more demanding in terms of testing due to the

larger space and more complex loading and measurement system required. Based on the

results and analyses of the full-scale ceiling diaphragm beam tests, the following

conclusions can be drawn:

The plasterboard connections failed at the locations where maximum relative

movement between the plasterboard and battens occurred. Failure occurred as a

result of tear-out of plasterboard edges at the corners of the specimen. Tear-out

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of plasterboard edges also occurred at the first three bottom corner screws from

the left and right end of the diaphragm.

The top plates of the end walls supporting the roof trusses provided further

bending resistance to the ceiling diaphragm and also provided bearing area for

the plasterboard ceiling as it translates in the direction of an end wall.

The strength of a diaphragm with boundary conditions (i.e. considering the

effects of plasterboard bearing on top plates) is approximately 20% higher than

the strength of a diaphragm without boundary conditions. However, the stiffness

of the diaphragm with boundary conditions is almost the same as the stiffness of

the diaphragm without boundary conditions.

The stiffness of the diaphragm decreases with the increase of aspect ratio

(length/width ratio). The stiffness of a diaphragm with an aspect ratio of 3.4 is

approximately 35% lower than that of a diaphragm with an aspect ratio of 2.3.

However, the strength does not change significantly due to variation of the

aspect ratio.

No relative displacement was observed between the ceiling battens and the

bottom chords. However, considerable bending of the ceiling battens was

observed.

No relative movement was observed to occur between the individual

plasterboard sheets. The whole cladding system translated as a single unit.

In this thesis, analytical modelling has been conducted using a commercially available

finite element analysis package (ANSYS) in order to amalgamate the experimental test

results and to utilise them to develop analytical models of plasterboard-clad steel-

framed ceiling diaphragms. The following conclusions from the analytical modelling

can be drawn:

The developed FE model was found to be in good agreement with the

experimental cantilever test results. The deflected shape and failure mode

obtained in FE modelling were similar to those observed in the experiment,

where the battens showed significant bending at the bottom of the diaphragm.

The FE model results of ceiling diaphragms in beam configuration were found

to be in very good agreement with the experimental test results.

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Without end walls, all the racking forces are transferred via shear action through

the screws which connect the plasterboard to the ceiling battens. The failure of

the diaphragm is a result of the failure of these screw connections. All these

screw connections did not fail at the same time but progressively tilted, and

failure at different locations occurred while the diaphragm was being loaded.

The diaphragm without boundary conditions failed due to the combination of

tearing of plasterboard at corner screws at both ends as well as pulling out of

the plasterboard screws located within 900 mm from both ends of the

diaphragm. Failure of the screw connections occurred at the same locations as

those observed during the tests.

The boundary conditions play a role in the performance of plasterboard- clad

ceiling diaphragms. The presence of end walls not only increases the ultimate

capacity of the ceiling, but also increases the displacement at which the ultimate

load occurs. The reason for the enhanced performance is not only the transfer of

the load from the plasterboard screws to the steel frame but also the bearing

action along the plasterboard edges.

The diaphragm with boundary conditions failed due to the combination of

bearing of the plasterboard edge as well as tearing of the plasterboard screws at

both corners and pulling out of the plasterboard screws located within 900 mm

from both ends of the diaphragm. The bearing of the plasterboard edges

occurred at almost the same location as that observed in the experiments.

The deflected shape of the diaphragm obtained from the FE model is similar to

that observed in the experiment, where the ceiling battens showed significant

bending at the ends of the diaphragm. The maximum relative movement

between the plasterboard and frame occurred at both ends of the diaphragm,

which was also observed in the experiments.

There is no variation of strength of ceiling diaphragm due to different testing

methods such as cantilever tests and beam tests. However, the beam test method

provides considerably higher stiffness than the cantilever test method.

The strength of the ceiling diaphragm is similar when it is subjected to different

loading configurations, such as one-third point loading, mid-span loading, and

uniformly-distributed loading. However, uniform loading provides moderately

higher stiffness than one-third point loading and mid-span loading.

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There is no significant variation of ultimate strength due to changes of length.

However, the stiffness decreases with the increase of the ceiling length (i.e.

aspect ratio). Longer ceilings (those with high aspect ratios) exhibit greater

flexural deformation. Failure occurs at a larger deflection compared to shorter

ceilings which have their deflection dominated by shear action.

The effect of boundary conditions (i.e. effects of plasterboard bearing on end

walls) becomes less significant with the increase of ceiling width. The boundary

condition provides a significant effect on strength of ceiling diaphragm up to

ceiling width of 7 m. However, there is no significant variation of strength due

to the consideration of the top plate's effect when the ceiling width exceeds 7 m.

Placing the plasterboard screws at close spacing not only provides higher

diaphragm strength and stiffness but also leads to failure at higher

displacements. The strength of the diaphragm can be increased by

approximately 80% by reducing one-third screw spacing along each batten.

The lateral performance of the diaphragm can be improved by the addition of a

limited number of extra screws. The addition of a single screw at the end of

each batten provides approximately 30% higher strength and about 10% higher

initial stiffness. The addition of two screws at the end of each batten provides

about 70% higher strength and approximately 20% higher initial stiffness.

There is a significant impact on the ultimate capacity of the diaphragm due to

changes in the gap size between the plasterboard and end walls. The ultimate

capacity of a ceiling increases with the decrease of the gap size. The ultimate

capacity of a ceiling with no gap is approximately 30% higher than that of a

ceiling with a 10 mm gap.

There is a considerable effect on strength and stiffness of the diaphragm due to

increased batten spacing from 450 mm to 600 mm. The capacity of a ceiling

with 450 mm spacing is about 20% higher than that of a ceiling with 600 mm

batten spacing.

Since the strength and stiffness of the diaphragm are mainly dependent on the

number of plasterboard screws, and the plasterboard screws are fixed along the

ceiling batten not to the bottom chords, the reduction of bottom chord spacing

does not affect significantly to the strength and stiffness of the diaphragm.

255

The strength and stiffness of the ceiling diaphragm in loading applied parallel to

the ceiling battens is significantly higher than that for loading applied along the

bottom chord members. This is attributed in part to the observed higher strength

and stiffness of the frame when loading is applied parallel to the battens. In

addition, the direct resisting connections are comparatively much higher

number when diaphragm loading along ceiling battens compared to loading

along bottom chord members. Therefore, the diaphragm capacity in loading

parallel to the bottom chord is the critical state.

Ceiling diaphragms are sensitive to the plasterboard screw connections with the

thickness of the steel members connected to the plasterboard. When the

plasterboard is connected to 0.75 mm BMT ceiling battens, it provides

significantly higher (approximately 90%) capacity and higher stiffness (about

70%) compared to plasterboard connecting to 0.42 mm BMT top-hat batten

sections.

The IBC formula for predicting a diaphragm deflection is based on deformation of

standard 1.2 m x 2.4 m (4 ft x 8 ft) plywood sheets which act independently. However,

in the case of plasterboard-clad ceiling diaphragms, all the sheets are joined together

and they act as one panel. Therefore, it is essential to modify the IBC formula and

update it for plasterboard-clad ceiling diaphragms. The findings from this work are as

follows:

A simplified mathematical model was developed for determining the deflection

and hence, the stiffness of typical plasterboard-sheathed steel-framed ceiling

diaphragm used in Australia. The model was verified against the experimental

results as well as the finite element model results and found to be in good

agreement. Hence, the deflection of plasterboard-sheathed steel-framed ceiling

diaphragms can be estimated using the new developed model.

A case study was presented for a house to show the distribution of lateral loads

from the plasterboard-clad steel- framed ceiling diaphragms to fibre cement-clad

shear walls. It was shown that the ceiling diaphragm can be accurately

represented by a deep beam or a plate. The equivalent properties of the deep

beam or plate can be determined using a procedure presented in Chapter 7.

256

Based on both strength and serviceability limit states, a typical design chart was

prepared for the maximum spacing of bracing walls for single storey or the

upper storey of two-storey buildings in Australia. The limits of the spacing of

the bracing walls in cold-formed steel-framed structures are subject to the use of

plasterboard or other cladding materials of equivalent strength and stiffness

strongly fixed to battens which are in turn firmly fixed to the ceiling or roof

structure.

8.2 Recommendations for Future Research

This research has examined the performance of plasterboard-clad steel-framed ceiling

diaphragms subjected to lateral loading. However, some areas remain where further

work is required. The recommendations from this research are as follows:

All test specimens in this thesis were subjected to monotonic load only. Hence,

diaphragm tests should be conducted under cyclic loadings, which would also

cover seismic actions.

This research was subjected to monotonic load only. There was no inclusion of

the effects of uplift pressure considered in this study. Hence, it is recommended

to perform diaphragms tests that are subjected to both lateral loads and uplift

loads; and compare it with the performance of diaphragms by considering lateral

loads only.

In this research, tests were conducted on single-span ceiling diaphragms only.

Therefore, it is recommended to perform tests on continuous diaphragms to

further validate the developed FE and mathematical models.

There were no openings in the tested diaphragms. Therefore, evaluation of

diaphragm performance with the consideration of openings using tests as well as

analytical models is recommended.

In this thesis, all diaphragms tests were performed on screw-fixed plasterboard.

Therefore, it is important for future research to observe the effects of the use of a

combination of both adhesives and screws on diaphragm strength and stiffness

and failure mechanisms.

257

References

Anderson, G.A. (1990). ‘What affects the strength and stiffness of diaphragms?’ ASAE Paper No. 90-4028, ASABE, St. Joseph, Mich.

Anderson, G.A. (1987), ‘Evaluation of a light-gage metal diaphragm behavior and the diaphragm interaction with post frames’, PhD thesis, Iowa State University, Ames, Iowa.

Adham, S.A., Avanessian, V., Hart, G.C., Anderson, R.W., Elmlinger, J. and Gregory (1990). ‘Shear wall resistance of light gauge steel stud wall system’, Earthquake, Vol. 6, No. l, pp. l-14.

Applied Technology Council (ATC) (1981). ‘Design of horizontal wood diaphragms’, Workshop Proceedings, 10-12 December, Berkeley, California.

ASTM D1761-12 (2012). ‘Standard test methods for mechanical fasteners in wood’, Annual Book of Standards, Vol. 4. No. 10, West Conshohocken, PA.

ASTM E455-04 (2004). ‘Standard test method for static load testing of framed floor or roof diaphragm constructions for buildings’, Annual Book of Standards, West Conshohocken, PA.

Atherton, G.H. (1981). ‘Strength and stiffness of structural particleboard diaphragms’, Project Report 818-151A, Forest Research Laboratory, Oregon State University, Corvallis, Oreg.

Australian Bureau of Statistics (ABS) (2008a). ‘1350.0-Australian Economic Indicators’, ACT, Australia

Australian Bureau of Statistics (ABS) (2008b). ‘8752.0- Building Activity’ ACT, Australia

Australian Institute of Steel Construction (AISC) (1991). ‘Structural performance requirements for Domestic Steel Framing’, National Association of Steel-Framed Housing (NASH).

Barton, A.D. (1997). ‘Performance of steel framed domestic structures subjected to earthquake loads’, PhD thesis, Department of Civil and Environmental Engineer, University of Melbourne, Australia.

Bott, J.W. (2005). ‘Horizontal stiffness of wood diaphragms’, MSc thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

Boughton, G.N. (1988). ‘Full scale structural testing of houses under cyclonic wind loads’, Proceeding of International Conference on Timber Engineering, Forest Products Research Society, Madison, pp. 82-88.

258

Boughton, G.N. and Reardon, G.F. (1982). ‘Simulated wind tests on a house: part-I description’, Technical report No. 12, Cyclone Testing Station, James Cook University, Townsville, Australia.

Boughton, G.N. and Reardon, G.F. (1984), ‘Simulated wind test on the Tongan hurricane house’, Technical Report No. 23, Cyclone Testing Station, James Cook University, Townsville, Australia.

Boughton, G.N. (1984). ‘Simulated high winds tests on a timber framed house’, The Engineering Conference, Brisbane, 2-6 April.

Boughton, G.N. and Reardon, G.F. (1984), ‘Structural damage caused by Cyclone Kathy at Borroloola, N.T.’, Technical Report No. 21, Cyclone Testing Station, James Cook University, Townsville, Australia.

Boughton, G. and Falck, D. (2007). ‘Tropical Cyclone George damage to buildings in the port Hedland area’, Technical Report No. 52, Cyclone Testing Station, James Cook University, Townsville, Australia.

Boughton, G.N., Henderson, D.J., Ginger, J.D., Holmes, J.D., Walker, G.R., Leitch, C.J., Somerville, L.R., Frye U., Jayasinghe, N.C. and Kim, P.Y. (2011). ‘Tropical Cyclone Yasi: structural damage to buildings’, Technical Report No. 57, Cyclone Testing Station, James Cook University, Tonsville.

Breyer, D.E., Kenneth, J.F., Kelly, E.C. and David G.P. (2007). ‘Design of wood structures-ASD/LRFD’, Sixth edition, McGraw-Hill.

Breyer, D.A. (1988). ‘Design of wood structures’, 2nd Ed., Mcgraw-Hill, New York.

Carradine, D.M., Woeste, F.E., Dolan, J.D. and Loferski, J.R. (2002). ‘Utilizing diaphragm action for wind load design of timber frame and structural insulated panel buildings’, Forest Products Journal, Vol.54. No 5.

Cobeen, K. (1997). ‘Seismic design of low-rise light-frame wood buildings-State-of-the-practice and future directions’, Earthquake performance and safety of timber structures, G. C. Foliente, ed., Forest Products Society, Madison, pp. 24–35.

Collins, M., Kasal, B., Paevere, P. and Foliente, G.C. (2005). ‘Three-dimensional model of light frame wood buildings. II: Experimental investigation and validation of analytical model’, Journal of Structural Engineering, Vol. 131, No. 4.

Davies, J.M. and Bryan, E.R. (1982). ‘Manual of stressed skin diaphragm design’, Granada Publishing, New York.

Easley, J.T. (1977). ‘Strength and stiffness of corrugated metal shear diaphragms’, Journal of Structural Division, ASCE Proceedings, Vol. 103.

259

Falk, R.H. and Itani, R.Y. (1989). ‘Finite element modeling of wood diaphragms’, Journal of Structural Engineering, Vol. 115, No. 3, pp. 543-559.

Falk, R.H. and Itani R.Y. (1987). ‘Dynamic characteristics of wood and gypsum diaphragms’, Journal of Structural Engineering, Vol. 113, No. 6.

Federal Emergency Management Agency (1997), ‘NEHRP guidelines for the seismic rehabilitation of buildings’, FEMA-273, Washington, October.

Filiatrault, A., Christovasilis, L.P., Wanitkorkul, A. and Lindt, J.W.V. (2010). ‘Experimental seismic response of a full-scale light-frame wood building’, Journal of Structural Engineering, Vol. 136, No. 3.

Filiatrault, A., Fischer, D., Folz, B. and Uang, C. (2004). ‘Shake table testing of a full-scale two-storey wood frame house’, Journal of Structural Engineering, Vol. 50, No. 5

Fischer, D., Filiatrault, A., Folz, B., Uang, C.M. and Seible, F. (2001). ‘Shake table tests of a two-storey wood frame house’, CUREE Publication No. 6, CUREE, Richmond, California.

Foliente, G.C. (1998). ‘Design of timber structures subject to extreme loads’, Progressive Structural Engineering Materials, Vol. 1, No. 3, pp. 236–44

Foliente, G.C. (1995a). ‘Hysteresis modelling off wood joints and structural systems’, Journal of Structural Engineering, ASCE, Vol. 121, No. 6, 1013-1022.

Foliente, GC (1995b). ‘Earthquake performance of light-frame wood and wood-based buildings: state-of-the-art and research needs’, Proceedings, Pacific Conference on Earthquake Engineering, Melbourne, Australia, 20-22 November, pp. 333-342.

Florida Building code commentary (2007). ‘Structural design’.

Foschi, R.O. (1977), ‘Analysis of wood diaphragms and trusses: Part I, diaphragms’, Canadian Journal of Civil Engineering, Vol. 4, No.3, pp. 345-352.

Gad, E.F. (1997). ‘The response of brick veneer, steel-framed domestic structures under dynamic loading’, PhD thesis, Department of Civil and Environmental Engineering, The University of Melbourne, Australia.

Gad, E.F., Duffield, C.F., Hutchinson, G.L., Mansell, D.S. and Stark, G. (1999). ‘Lateral performance of cold-formed steel-framed domestic structures’, Engineering Structures, Vol. 21, pp. 83–95

Gebremedhin, K.G. (2007). ‘Design and construction practices that affect diaphragm strength and stiffness of post-frame buildings’, Practice Periodical on Structural Design and Construction, Vol. 12, No. 3.

Ge, Y.Z. (1991). ‘Response of wood-frame houses to lateral loads’, MSc thesis, University of Missouri, Columbia, Mo.

260

Golledge, B., Clayton, T. and Reardon, G. (1990). ‘Raking performance of plasterboard clad steel stud walls’, BHP & Lysaght Building Industries Technical Report.

Gyprock (2010). ‘Residential Installation Guide Including Wet Area Systems’, (http://www.gyprock.com.au/Documents/GYPROCK-547-Residential_Installation_Guide-201111.pdf)

Gyprock (2008), ‘Ceiling Systems Installation Guide’, (http://www.gyprock.com.au/Documents/GYPROCK-570-Ceilings_Systems-200806.pdf)

Hancock, G.J. (1994). ‘Cold-formed steel structures’, Australian Institute of Steel Construction, North Sydney, NSW, Australia.

Hausmann, C.T. and Esmay, M.L. (1975). ‘Pole barn wind resistance design using diaphragm action’, ASAE Paper No. 75-4035, ASABE, St. Joseph, Mich.

Henderson, D. and Leitch, C. (2005). ‘Damage investigation of buildings at Minjilang, Cape Don and Smith Point in NT following Cyclone Ingrid’, Technical Report No. 50, Cyclone Testing Station, James Cook University, Townsville.

Henderson, D., Ginger, J., Leitch, C., Boughton, G. and Falck, D. (2006). ‘Tropical cyclone Larry: damage to buildings in the Innisfail area’, Technical Report No. 51, Cyclone Testing Station, James Cook University, Townsville.

International Building Code (IBC) (2006). Final draft, International Code Council, Birmingham.

Itani, R.Y. and Cheung, C.K. (1984). ‘Nonlinear analysis of sheathed wood diaphragms’, Journal of Structural Engineering, Vol. 110, No. 9, pp. 2137-2147.

James, G.W. and Bryant, A.H. (1984). ‘Plywood diaphragms and shear walls’, Proceedings of Pacific Timber Engineering Conference, Auckland, New Zealand, May.

Judd, J.P. (2005). ‘Analytical modeling of wood-frame shear walls and diaphragms’, MSc thesis, Department of Civil and Environmental Engineering, Brigham Young University

Kasal B., Collins M.S., Paevere, P. and Foliente, G.C. (2004). ‘Design models of light frame wood buildings under lateral loads’, Journal of Structural Engineering, Vol. 130, No. 8.

Kasal, B., Leichti, R.J. and Itani, R.Y. (1994). ‘Nonlinear finite-element model of complete light-frame wood structure’, Journal of Structural Engineering, Vol. 120, No. 1, pp. 100–119.

Kasal, B. and Leichti, R.J. (1992). ‘Incorporating load sharing in shear wall design of light-frame structures’, Journal of Structural Engineering, Vol. 118, No. 12, pp. 3350– 3361.

http://www.gyprock.com.au/Documents/GYPROCK-547-Residential_Installation_Guide-201111.pdf

http://www.gyprock.com.au/Documents/GYPROCK-547-Residential_Installation_Guide-201111.pdf

http://www.gyprock.com.au/Documents/GYPROCK-570-Ceilings_Systems-200806.pdf

261

Kataoka, Y. (1989). ‘Application of supercomputers to nonlinear analysis of wooden frame structures stiffened by shear diaphragms’, Proceeding of2nd Pacific Timber Engineering Conference, Vol. 2, University of Auckland, Auckland, New Zealand, pp. 107-112.

Klingner, R.E. (2010). ‘Masonry Structural Design”, McGraw Hill Publication.

Kunnath, S.K., Mehrain, M. and Gates, W.E. (1994). ‘Seismic damage-control design of gypsum-roof diaphragms’, Journal of Structural Engineering, Vol. 120, No. 1.

Liew, Y.L. (2003). ‘Plasterboard as a bracing material: From quality control to wall performance’, PhD thesis, Department of Civil and Environmental Engineering, The University of Melbourne.

Luttrell, L.D. (1991). ‘Diaphragm Design Manual’, 2nd ed., Steel Deck Institute, Inc., Canton, Ohio

Luttrell, L.D. (1988). ‘Shear diaphragm strength’, Proceedings of the National Steel Construction Conference, American Institute of Steel Construction, June.

Mastrogiuseppea, Rogersa C.A., Tremblayb, R. and Nedisanb, C.D. (2008). ‘Influence of non-structural components on roof diaphragm stiffness and fundamental periods of single-storey steel buildings’, Journal of Constructional Steel Research, Vol. 64, pp. 214–227

Miller, T.H. and Pekoz, T. (1994). ‘Behavior of gypsum-sheathed cold-formed steel wall studs’, Journal of Structural Engineering, Vol. 120, No. 5, pp. 1644–50.

NAHBRC (2000). ‘Residential Structural Design Guide: A State-of-the-Art Review and Application of Engineering Information for Light-Frame Homes, Apartments, and Townhouses’.

National Association of Steel-Framed Housing (NASH) (2014). ‘Residential and Low-rise Steel Framing, Part 2: Design solutions’, Handbook.

National Association of Steel-Framed Housing (NASH) (2011). ‘Residential and Low-rise Steel Framing, Part 1: Design Criteria, Amendment C’, Handbook.

National Association of Steel-Framed Housing (NASH) (2009). ‘Design of residential and low-rise steel framing’, Handbook.

National Association of Steel-Framed Housing (NASH) (2005). ‘Residential and Low-rise Steel Framing, Part 1: Design Criteria’, Handbook.

Niu, K.T. (1996). ‘A semi-empirical three-dimensional stiffness model for metal-clad post-frame buildings’, PhD dissertation, Department of Biological and Environmental Engineering, Cornell University, Ithaca, New York.

262

Ohashi, Y. and Sakamoto, I. (1988). ‘Effect of horizontal diaphragm on behaviour of wooden dwellings subjected to lateral load-experimental study on a real size frame model’, Proceeding of International Conference on Timber Engineering, Forest Products Research Society, Madison, pp. 112-120.

Paevere, P.J., Foliente, G. and Kasal, B. (2003). ‘Load-sharing and redistribution in a one-storey wood frame building’, Journal of Structural Engineering, Vol. 129, No. 9, pp. 1275–1284.

Paevere, P.J. (2001). ‘Full-scale testing, modelling and analysis of light-frame structures under lateral loading’, PhD thesis, Dept. of Civil and Environmental Engineering, The University of Melbourne, Parkville, Victoria, Australia.

Paultre, P., Proulx, J., Ventura, C.E., Tremblay R., Rogers C.A., Lamarche, C.P. and Turek M. (2004). ‘Experimental investigation and dynamic simulations of low-rise steel buildings for efficient seismic design’, 13th World Conference on Earthquake Engineering, August 1-6, Vancouver, Canada.

Phillips, T.L., Itani, R.Y. and McLean, D.I. (1993). ‘Lateral load sharing by diaphragms in wood-framed buildings’, Journal of Structural Engineering, Vol. 119, No. 5, pp. 1556–1571.

Phillips, T.L. (1990). ‘Load sharing characteristics of three-dimensional wood diaphragms’, MS thesis, Washington State University, Pullman, Washington.

Reardon, G.F. and Henderson, D. (1996). ‘An investigation into truss holds down details’, Technical Report No. 44, Cyclone Testing Station, James Cook University, Townsville.

Reardon, G.F. (1990). ‘Simulated cyclone wind loading of a Nu–steel house’, Technical Report No. 36, Cyclone Testing Station, James Cook University, Townsville.

Reardon, G.F. (1989). ‘Effect of cladding on the response of houses to wind forces’, Proceeding of 2nd Pacific Timber Engineering Conference, University of Auckland, Auckland, New Zealand.

Reardon, G.F. (1986). ‘Simulated cyclone wind loading of a brick veneer house’, Technical Report No. 2, Cyclone Testing Station, James Cook University, Townsville.

Reardon, G.F. and Mahenderan, M. (1988). ‘Simulated cyclone wind loading of a Melbourne style brick veneer house’, Technical Report No. 34, Cyclone Testing Station, James Cook University, Townsville.

Reardon, G.F. (1987). ‘The structural response of a brick veneer house to simulated cyclone winds’, First National Structural Engineering Conference, Melbourne, 26-28 August.

263

Reardon, G.F. and Oliver, J. (1982). ‘Report on damage caused by Cyclone Isaac in Tonga’, Technical Report No. 13, Cyclone Testing Station, James Cook University, Townsville.

Reardon, G.F. (1980). ‘Damage in the Pilbara caused by cyclones Amy and Dean’, Technical Report No. 4, Cyclone Testing Station, James Cook University, Townsville.

Saifullah, I., Gad, E., Shahi, R., Wilson, J., Lam N.T.K. and Watson K. (2014), ‘Ceiling diaphragm actions in cold formed steel-framed domestic structures’, ASEC-Structural Engineering in Australasia-World Standard, July 9-11, Auckland, New Zealand.

Saifullah I., Gad E., Wilson J., Lam N.T.K. and Watson K. (2012), ‘Review of diaphragm actions in domestic structures’, Australasian Conference on the Mechanics of Structures and Materials, December 11-14, Sydney, Australia

SASI (Swanson Analysis System Inc.) (2014). ‘ANSYS-Engineering analysis system manuals, Version 12.1’, Houston, Pennsylvania, USA.

Shahi, R. (2015). ‘Performance evaluation of cold-formed steel stud shear walls in seismic conditions’, PhD thesis, Department of Infrastructure Engineering, The University of Melbourne.

Skaggs, T. D. and Martin, Z. A. (2004). ‘Estimating wood structural panel diaphragm and shear wall deflection’, Practice Periodical on Structural Design and Construction, Vol. 9, No. 3, pp. 136–141.

Standards Association of Australia (1996). ‘AS 1538: Cold-formed steel structures Code’.

Standards Association of Australia (1993). ‘AS3623: Domestic framing standard’.

Standards Association of Australia (1992). ‘AS1684: National timber framing code’.

Standards Association of New Zealand (1992). Code of practice for general design and design loading for buildings: NZS 4203, Wellington, New Zealand.

Standards Association of Australia/New Zealand (1998). ‘AS/NZS 2588: Gypsum plasterboard,’

Standards Association of Australia (2010). ‘AS1170: Minimum design load on structures’.

Standards Association of Australia (2010). ‘AS1170.2: Wind Forces’.

Standards Association of Australia (2010). ‘AS1170.4: Minimum design load on structures: Earthquake loads’.

Standards Association of Australia (2010). ‘AS 1720.1: Timber Structures- Design Methods’.

http://acmsm.org/

http://acmsm.org/

264

Standards Association of Australia/New Zealand (2005). ‘AS/NZS 4600: Cold-formed steel structures,’

Standards Association of Australia (2010). ‘AS 4055: Wind Loads for Housing’.

Standards Association of Australia (2010). ‘AS 1684.2: Residential timber-framed construction - Non-cyclonic areas’.

Standards Association of Australia (2010). ‘AS 1684.3: Residential timber-framed construction - cyclonic areas’,

Stewart, A., Goodman, J., Kliewer, A. and Salsbury, E. (1988). ‘Full-scale tests of manufactured houses under simulated wind loads’, Proceeding of International Conference on Timber Engineering, Forest Products Research Scoiety, Madison, pp. 97-111.

Schmidt, R.J. and Moody, R.C. (1989). ‘Modeling laterally loaded light-frame buildings’, Journal of Structural Engineering, Vol. 115, No. 1, pp. 201–217.

Sugiyama, H., Naoto, A., Takayuki., U., Hirano., S. and Nakamura, N. (1988). ‘Full scale test on a Japanese type of two-storey wooden frame house subjected to lateral load’. Proceeding of International Conference on Timber Engineering, Forest Products Research Society, Madison, pp. 55-61.

Telue, Y.K. (2001). ‘Behaviour and design of plasterboard lined cold-formed steel stud wall systems’, PhD thesis, Queensland University of Technology, Brisbane.

Tissel, J.R. and Elliot, J.R. (2004). ‘Plywood diaphragm’, Research report 138, APA- The Engineered Wood association.

Tremblay, R., Tarek, B. and André, F. (2000). ‘Experimental behaviour of low-rise steel buildings with flexible roof diaphragms’, 12 Wceee, paper no. 2567

Tremblay, R., Martin, E. and Yang, W. (2004). ‘Analysis, testing and design of steel roof deck diaphragms for ductile earthquake resistance’, Journal of Earthquake Engineering, Vol. 8, No. 5, pp. 775-816

Tuomi, R.L. and McCutcheon, W.J. (1978). ‘Racking strength of light-frame nailed walls’, Structural Division, Vol. 104, No. 7, pp. 1131-1140.

Tuomi, R.L. and McCutcheon, W.J. (1974). ‘Testing of a full-scale house under simulated snow loads and wind loads’, Research Report, FLP 234, USDA Forest Service, Madison, 32pp.

Turnbull, J.E., Mcmartin, K.C. and Quaile, A.T. (1982). ‘Structural performance of plywood and steel ceiling diaphragms’, Canadian Agricultural Engineering, Vol. 24, No. 2.

http://www.saiglobal.com/online/Script/Details.asp?DocN=AS0733794339AT




265

Walker, G.R. and Gonano, D. (1983). ‘Investigation of diaphragm action of ceilings’, Progress Report III, Technical Report No. 20, Department of Civil and Systems Engineering, James Cook University, Townsville, Australia.

Walker, G.R., Boughton G.N. and Gonano, D. (1982). ‘Investigation of diaphragm action of ceilings’, Progress Report II, Technical Report No. 15, Department of Civil and Systems Engineering, James Cook University, Townsville, Australia

Walker, G.R. and Gonano, D. (1981). ‘Investigation of diaphragm action of ceilings’, Progress Report I, Technical Report No. 10, Department of Civil and Systems Engineering, James Cook University, Townsville, Australia.

Walker, G.R. (1978). ‘The design of walls in domestic housing to resist wind’. Design for tropical cyclones, Vol 2. James Cook University, Townsville, Australia.

Wang, C.H. and Foliente, G.C. (2006). ‘Seismic reliability of low-rise non-symmetric wood-frame buildings’, Journal of Structural Engineering, ASCE, Vol. 132, No. 5, 733-744.

White, R.N., Hartand, J. and Warshaw, C. (1977). ‘Shear strength and stiffness of aluminum diaphragms in timber-framed buildings’, Research Report No. 370. Department of Structural Engineering, Cornell University, Ithaca, New York.

Williams, R. (1986). ‘Seismic design of timber structures’, Study Group Review Bulletin of the New Zealand National Society of Earthquake Engineering, Vol. 19, No 1, pp. 40-47

Wolfe, R.W. (1982). ‘Contribution of gypsum wallboard to racking resistance of light walls’, Research Report FPL 439, Forest Products Laboratory, United States Department of Agriculture.

Yoon, T.Y. and Gupta, A.K. (1991). ‘Behavior and failure modes of low-rise wood-framed buildings subjected to seismic and wind forces’, PhD thesis, Department of Civil Engineering, North Carolina State University, Raleigh.

Yu, W.W. (2000). ‘Cold-formed steel design’, Third Edition, John Wiley & Sons, Inc. New York.

Yu, W.W. (1991). ‘Cold-formed steel design’, JohnWiley & Sons, New York.