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i STRUCTURAL BEHAVIOUR OF PRECAST LIGHTWEIGHT FOAMED CONCRETE SANDWICH PANEL (PLFP) WITH SHEAR TRUSS CONNECTORS GOH WAN INN A thesis submitted in fulfilment of the requirement for the award of the Doctor of Philosophy. Faculty of Civil and Environmental Engineering Universiti Tun Hussein Onn Malaysia Jan 2015

i STRUCTURAL BEHAVIOUR OF PRECAST LIGHTWEIGHT … · i structural behaviour of precast lightweight foamed concrete sandwich panel (plfp) with shear truss connectors goh wan inn a

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i

STRUCTURAL BEHAVIOUR OF PRECAST LIGHTWEIGHT FOAMED

CONCRETE SANDWICH PANEL (PLFP) WITH SHEAR TRUSS

CONNECTORS

GOH WAN INN

A thesis submitted in

fulfilment of the requirement for the award of the

Doctor of Philosophy.

Faculty of Civil and Environmental Engineering

Universiti Tun Hussein Onn Malaysia

Jan 2015

v

ABSTRACT

Precast system is playing a very important role in industrialize building system to

construct more affordable and quality houses to meet the high demands. Many

researches have been carried out to develop precast sandwich wall panel with more

benefits such as lighter in weight, environmental friendly and easy to construct

compared to normal reinforced concrete panel. Therefore, a study was carried out to

develop Precast Lightweight Foamed Concrete Sandwich Panel (PLFP) with shear

truss connectors. The objectives of this study are to numerically investigate the PLFP

panel with single and double shear truss connectors to determine its structural

behaviour with validation from experimental work and to develop the empirical

equation to predict its ultimate strength under axial load. PLFP panel is made of

foamed concrete as the outer wythes which enclose a core layer of polystyrene. The

wythes were reinforced with steel bars and tied to each other through the polystyrene

layer by using steel shear connectors (bent at an angle of 45°). Experimental testing

had been conducted to determine the material properties of foamed concrete and steel

bar and used for PLFP model in finite element analysis. Eight half scaled PLFP

panels were tested experimentally under axial load until it failed. Ultimate load

carrying capacity, load lateral deflection profile, strain distributions and failure mode

were recorded. Finite element analysis was carried out on PLFP panels which were

validated with experimental results. Full scaled PLFP panels with single and double

shear truss connectors had been studied numerically to investigate the effects of

geometrical imperfection, slenderness ratio, thickness, and shear connectors toward

its structural behaviour. From the results, it was found that when the rate of

geometrical imperfection and slenderness ratio of PLFP panel increased, the ultimate

load of PLFP panel decreased. The use of double shear truss connectors indicated

improvement in the PFLP’s strength and stability under axial load and longitudinal

shear force compared to single shear truss connectors. An empirical equation which

was modified from previous research is proposed to predict the ultimate load

carrying capacity of PLFP under axial load.

vi

ABSTRAK

Sistem pratuang memainkan peranan yang penting dalam sistem bangunan pra

fabrikasi di kilang untuk membina lebih banyak rumah mampu milik dan berkualiti

untuk memenuhi permintaan yang tinggi. Banyak kajian telah dijalankan untuk

membangunkan panel pratuang sandwich dengan lebih banyak faedah seperti lebih

ringan, mesra alam dan mudah untuk dibina berbanding panel konkrit bertetulang

yang biasa. Oleh itu, satu kajian telah dijalankan untuk membangunkan Panel

Pratuang Sandwich dari konkrit ringan berbusa (PLFP) dengan penyambung ricih

kekuda. Objektif kajian ini adalah untuk menyiasat panel PLFP dengan penyambung

ricih kekuda tunggal dan berganda bagi menentukan kelakuan struktur panel

berdasarkan unsur terhingga dengan pengesahan dari eksperimen dan untuk

menerbitkan persamaan empirikal bagi meramalkan kekuatan muktamad yang boleh

ditanggung di bawah beban paksi. Panel PLFP diperbuat daripada konkrit berbusa

sebagai lapisan dinding luar dan polisterin sebagai lapisan dalam. Lapisan dinding

luar telah diperkukuhkan dengan bar keluli dan terikat kepada satu sama lain melalui

lapisan polisterin dengan menggunakan penyambung ricih kekuda keluli

(dibengkokkan pada sudut 45°). Eksperimen telah dijalankan untuk menentukan ciri-

ciri bahan konkrit berbusa dan keluli bar bagi digunakan untuk memodelkan PLFP

dalam analisis unsur terhingga. Lapan panel PLFP yang berskala separuh telah diuji

dibawah beban paksi sehingga ia gagal. Panel PLFP telah dikaji dengan

menggunakan analisis unsur terhingga untuk menyiasat kesan ketidaksempurnaan

geometri, nisbah kelangsingan, ketebalan, dan penyambung ricih ke atas tingkah

laku strukturnya. Daripada hasil kajian, apabila kadar ketidaksempurnaan geometri

dan nisbah kelangsingan panel PLFP meningkat, beban muktamad panel PLFP

menurun. Penggunaan penyambung ricih kekuda berganda menunjukkan

peningkatan dalam kekuatan dan kestabilan panel PFLP di bawah beban paksi dan

daya ricih membujur berbanding kekuda penyambung ricih tunggal. Persamaan

empirikal yang telah diubahsuai daripada persamaan empirikal yang diterbitkan

dalam kajian terdahuhu telah dicadangkan untuk meramal beban muktamad PLFP

bawah pengaruh beban paksi.

vii

CONTENTS

TITLE i

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

CONTENT vii

LIST OF TABLES xiii

LIST OF FIGURES xvi

LIST OF SYMBOLS AND ABBREVIATIONS xxiii

LIST OF APPENDICES xxvii

CHAPTER 1 INTRODUCTION 1

1.1 Introduction 1

1.2 Problem statement 3

1.3 Research objectives 4

1.4 Significant of study 4

1.5 Scopes of study and limitation of study 4

1.6 Thesis layout 5

CHAPTER 2 LITERATURE REVIEW 7

2.1 Introduction 7

2.2 Material properties 7

2.2.1 Foamed concrete 7

2.2.2 Polystyrene foam 10

2.2.2.1 Physical properties of expanded polystyrene 11

2.2.3 Shear connectors and reinforcement 12

viii

2.2.4 Normal concrete capping 15

2.3 Accuracy of structural models 15

2.3.1 Scale model technique 16

2.4 Finite element analysis 19

2.4.1 Comparison of conventional FEA software 20

2.4.2 Abaqus/Explicit versus Abaqus/Standard 22

2.4.2.1 Choosing between implicit and explicit analysis 24

2.4.3 Element types 24

2.4.3.1 Continuum elements 25

2.4.3.2 Eight node brick element with reduced integration

(C3D8R) 26

2.4.3.3 Shell elements 27

2.4.3.4 Beam elements 27

2.4.3.5 Truss elements 27

2.4.3.6 Rigid body 28

2.4.3.7 Selecting continuum elements 29

2.4.4 Materials modelling by using concrete damaged

plasticity 30

2.4.4.1 Capabilities of concrete damaged plasticity model 33

2.4.4.2 Parameters of concrete damage plasticity 33

2.4.4.3 Previous research by using concrete damage

plasticity 37

2.4.5 Geometrical imperfection 38

2.4.5.1 Minimum initial curvature in column or wall system 40

2.4.5.2 Maximum initial curvature in column or wall system 40

2.4.5.3 Modelling of geometrical imperfections in FEA 42

2.4.6 Previous structural research by using FEA 44

2.5 Previous research on precast sandwich panel 48

2.5.1 Advantages of sandwich panel 49

2.5.2 Previous experimental research on sandwich panel

with single shear truss connectors 49

2.5.3 Previous experimental research on sandwich panel

with double shear truss connectors 56

ix

2.5.4 Previous experimental research on other types

of sandwich panel 58

2.5.5 Summary of previous research on precast sandwich

panel 61

2.6 Previous developed empirical equations for wall

elements 62

2.6.1 Empirical equation from ACI318-89 63

2.6.2 Empirical equation from BS8110 64

2.6.3 Empirical equation from Eurocode 2 64

2.6.4 Empirical equation from previous researchers 65

2.6.5 Comparison of previous developed empirical

equations for wall elements 70

2.7 Conclusion 72

CHAPTER 3 RESEARCH METHODOLOGY 74

3.1 Introduction 74

3.2 Material testing 76

3.2.1 Laboratory testing for mechanical properties of

foamed concrete 76

3.2.1.1 Compressive strength of foamed concrete cube 77

3.2.1.2 Splitting test of foamed concrete cylinder 77

3.2.1.3 Compression test of foamed concrete cylinder 78

3.2.2 Mechanical properties of foamed concrete 78

3.2.2.1 Compressive strength of foamed concrete 79

3.2.2.2 Tensile strength of foamed concrete 80

3.2.2.3 Young’s Modulus and Poisson ratio of foamed

concrete 80

3.2.3 Tensile test on steel bar reinforcement 81

3.3 Experimental investigation on PLFP panel 82

3.3.1 Material properties of PLFP panels 83

3.3.2 Designation and dimension of PLFP panels 84

3.3.3 Fabrication and casting 86

3.3.4 Axial load testing on the PLFP panel 87

3.3.5 Support conditions of axial load testing 89

3.4 Finite element analysis of PLFP panel 90

x

3.5 Summary 90

CHAPTER 4 EXPERIMENTAL STUDY OF PLFP PANEL 91

4.1 Introduction 91

4.2 Ultimate load carrying capacity of PLFP panel 91

4.3 Crack pattern and mode of failure 93

4.4 Load versus horizontal deflection 95

4.5 Load –strain relationship on the wythe surface 96

4.6 Conclusion 99

CHAPTER 5 NUMERICAL SIMULATION OF PLFP PANEL 100

5.1 Introduction 100

5.2 Objectives 101

5.3 Description of the finite element model 101

5.3.1 Element types of each materials 101

5.3.2 Boundary condition and load application 103

5.3.3 Parameters of PLFP panel 106

5.4 Modelling of material properties 107

5.4.1 Material properties of foamed concrete 107

5.4.2 Material properties of normal concrete capping 110

5.4.3 Material properties of main reinforcement and

shear connectors 111

5.4.4 Material properties of polystyrene 111

5.5 Quasi-static analysis of PLFP panel 112

5.6 Convergence study of PLFP panel 114

5.7 FEA verification 115

5.7.1 Validation of ultimate load carrying capacity 116

5.7.2 Failure mode of PLFP panel with single shear truss

connectors 116

5.7.3 Validation of load versus vertical displacement

profile 117

5.7.4 Validation of load versus horizontal displacement

profile 118

5.7.5 Imperfection FEA model versus experiment 119

5.7.6 Validation of FEA with half scaled PLFP panel

from experimental study 122

xi

5.8 Parametric study of PLFP panel with double shear

truss connectors under axial loading 124

5.8.1 Ultimate load carrying capacity for PLFP panel

with double shear truss connectors 124

5.8.2 Failure mode of PLFP panel from FEA 126

5.8.3 Load versus vertical displacement 133

5.8.4 Load versus horizontal displacement 135

5.8.5 Strain distribution across PLFP panel’s thickness 137

5.8.6 Stress distribution 139

5.8.7 Post failure 140

5.8.8 Effects of various thicknesses of polystyrene 145

5.8.9 Effects of various thicknesses of foamed concrete

wythe 146

5.9 Effects of double shear truss connectors on PLFP

panel 148

5.9.1 FEA of PLFP panel under push off loading 149

5.10 Summary of structural behaviour for PLFP panel with

shear truss connectors 153

5.10.1 PLFP panel under axial loading 153

5.10.2 PLFP panel under various slenderness ration and

thickness 154

5.10.3 Failure mode of PLFP panel 154

5.10.4 Effects of PLFP panel with double and single shear

truss connectors 155

5.10.5 Sustainability of PLFP panel as load bearing wall

in low to medium rise building 155

5.11 Conclusion 155

CHAPTER 6 DEVELOPMENT OF EMPIRICAL EQUATION 157

6.1 Introduction 157

6.2 Comparison of results from FEA and empirical

equations 157

6.3 Previous developed empirical equations 159

6.4 Proposed empirical equation 164

6.5 Conclusion 172

xii

CHAPTER 7 CONCLUSION AND RECOMMENDATIONS 173

7.1 Introduction 173

7.2 Conclusion for each objective 173

7.2.1 Objective 1 173

7.2.2 Objective 2 174

7.2.3 Objective 3 175

7.2.4 Objective 4 176

7.3 Recommendations 177

REFERENCES 178

APPENDICES A-H 184

LIST OF PUBLICATIONS 216

LIST OF COMPETITION PARTICIPATED AND

AWARDS 219

VITA 220

xiii

LIST OF TABLES

2.1 Typical mixture details for foamed concrete (BCA, 1994) 8

2.2 Typical properties of foamed concrete (BCA, 1994) 8

2.3 Comparison of strength to density ratio (in MPa per kg/m3

x 1000) (Kunhanandan and Ramamurthy, 2006) 9

2.4 Typical properties of expanded polystyrene

(Texas Foam Inc, 2011) 11

2.5 Scaling laws (Knappet et al., 1996) 16

2.6 Comparison of concrete response (Johnson, 2006) 21

2.7 Comparison of reinforcement response (Johnson, 2006) 22

2.8 Key differences between Abaqus/Standard and

Abaqus/Explicit (Abaqus, 2009) 23

2.9 Concrete damaged plasticity model parameters

(Mokhatar and Abdullah, 2012) 37

2.10 Material parameters of concrete damaged plasticity model

(Newberry et al., 2010) 38

2.11 Test specimens with dimension, aspect ratio and slenderness

ratio of precast reinforced (Benayoune et al., 2007) 50

2.12 Dimension of foamed concrete sandwich panel (Liew, 2011) 52

2.13 Dimension of specimens (Mohamad, Omar and Abdullah 2011) 55

2.14 Dimension of PLFP specimens (Mohamad and Mahdi, 2011) 57

2.15 Axial load capacities for walls taking into account steel

buckling and profiled concrete effects (Wright, 1998) 61

2.16 Summary of previous studies on precast sandwich panel 62

2.17 List of previous researchers and formulas 71

2.18 Summary of tested wall panels and variables used by

previous researchers (Jeung, 2002) 72

3.1 Mixture ratio for foamed concrete casting (Mohamad, 2010) 76

3.2 Compressive strength of foamed concrete at 7th

, 14th

and

28th

day 79

xiv

3.3 Tensile strength of foamed concrete at 28th

Day 80

3.4 Young’s Modulus and Poisson Ratio of foamed concrete at

28th

Day 81

3.5 Mechanical properties of reinforcement 82

3.6 List of half scaled PLFP panels with 50 mm thickness 84

3.7 List of half scaled PLFP panels with other thickness 84

4.1 Ultimate load carrying capacity of PLFP panel 92

4.2 Crack pattern and failure modes of PLFP panel 94

5.1 Element used for each part of PLFP panel 102

5.2 List of full scaled PLFP panel that were analysed by FEA 106

5.3 Properties of foamed concrete in PLFP panel 107

5.4 Concrete damaged plasticity of foamed concrete 108

5.5 Properties of normal concrete capping in PLFP Model 111

5.6 Mechanic properties of steel assigned for reinforcement

and shear connectors in the FEA 111

5.7 Properties of expanded polystyrene 112

5.8 Result of mesh refinement study of PS1 114

5.9 Designation of foamed concrete of PLFP panel with single

shear truss connector 116

5.10 Ultimate load carrying capacity of PLFP panel with single

shear truss connectors 116

5.11 Imperfection study of PLFP panel by FEA 122

5.12 Ultimate load carrying capacity of PLFP panel’s scale

model with double shear truss connectors 123

5.13 Ultimate load of PLFP for perfect and imperfect geometry

model in FEA 125

5.14 Mode of failure of PLFP panels with 100 mm thickness

from FEA 127

5.15 Failure mode of PLFP panels under axial load from FEA 128

5.16 Mode of failure of PLFP panels with 100 mm thickness

from FEA 129

5.17 Vertical and horizontal displacement of PLFP-1 to

PLFP-11 133

xv

5.18 Ultimate load carrying capacity, vertical displacement for

PLFP panels with various thicknesses of polystyrene 145

5.19 Ultimate load carrying capacity, vertical displacement for

PLFP panels with various thicknesses of foamed concrete 147

5.20 Comparison of ultimate axial load carrying capacity load

achieved for PLFP panels with single and double shear

truss connectors 149

5.21 Comparison of vertical displacement and horizontal

displacement for PLFP panels with single and double

shear truss connectors 149

5.22 Comparison of ultimate shear forces achieved for PLFP

panel with single and double shear truss connectors 151

6.1 Comparisons of FEA result versus developed equation

values for PLFP panels 167

xvi

LIST OF FIGURES

2.1 Strength density variation for mixes with sand of different

fineness (Kunhanandan and Ramamurthy, 2006) 9

2.2 Typical stress/strain curves for expanded polystyrene

(Texas Foam Inc, 2011) 12

2.3 One way shear connectors, stiff in only one direction

(PCI committee, 1997) 13

2.4 Two way shear connectors, stiff in at least two

perpendicular directions. (PCI committee, 1997) 14

2.5 Non-composite connectors (PCI committee, 1997) 14

2.6 Normal concrete capping (Mohamad, Omar and

Abdullah, 2011) 15

2.7 Steel reinforcement for model wall sections

(Gran et al., 1996) 17

2.8 Completed four storey reinforced concrete

scale

Building (Vaughan et al., 2011) 18

2.9 Comparison of high speed camera images with equivalent

snapshots from pretest simulation. (Vaughan et al., 2011) 18

2.10 Post failure photos of test article showing collapsed region

compared with snapshot from pretest simulation showing

collapsing section of model (Vaughan et al., 2011) 19

2.11 Common element families in ABAQUS (Abaqus, 2009) 25

2.12 Linear brick, quadratic brick, and modified tetrahedral

elements (Abaqus, 2009) 26

2.13 1x1x1 integration point scheme in hexahedral elements

(Abaqus, 2009) 26

2.14 Elements forming a rigid body. (Abaqus, 2009) 28

xvii

2.15 Response of concrete to uniaxial loading in tension

(Abaqus, 2009), (Jankowial and Lodygowski, 2005;

Jason et al., 2004; Lee and Fenves, 1998 and Mokhatar

and Abdullah, 2012) 31

2.16 Response of concrete to uniaxial loading in compression

(Abaqus, 2009), (Jankowial and Lodygowski, 2005;

Jason et al., 2004; Lee and Fenves, 1998 and Mokhatar

and Abdullah, 2012) 31

2.17 Yield surfaces in the deviatoric plane, corresponding to

different values of . (Abaqus, 2009) 35

2.18 Yield surface in plane stress. (Abaqus, 2009) 35

2.19 Global imperfections (magnified)

(Boissonnade and Somja, 2012) 39

2.20 Local imperfections (magnified)

(Boissonnade and Somja, 2012) 40

2.21 Resultant deflection and curvature profiles to EC2

(Robinson et al., 2011) 41

2.22 Tension zone in a solid eccentrically loaded wall.

(Kuddus, 2010) 41

2.23 Effect of increasing eccentricity on the size of cracked

section (Kuddus, 2010) 42

2.24 Single storey multi-column system: model with initial

Curvature (Artizabal-ochoa, 2012) 43

2.25 Model of an imperfect column with sideway partially

inhibited and rotational end restraints: (a) structural model

with eccentric axial loads applied at the column extremes:

(b) end moments, forces, rotations and deflections: and

(c) column segment including bending moments, shear

and axial forces (Artizabal-ochoa, 2012) 43

2.26 An axially loaded column with initial geometric imperfection

(Xu and Wang, 2008) 44

2.27 Energy level of the whole model for analysis with step time

equal to (i) 1x natural period (ii) 8x natural period

(Abdullah et al., 2007) 45

xviii

2.28 Small scale test set up (left side), Finite element model of

one quarter of the four points bending test (right side)

(Joshani et al., 2012) 46

2.29 Total internal energy and kinetic energy of whole slab versus

time (Joshani et al., 2012) 47

2.30 Damage status at concrete when the mid span deflection

reached 2.3 mm (Joshani et al., 2012) 47

2.31 Strain distribution in precast concrete sandwich panel under

flexural bending (PCI committee, 1997) 49

2.32 Details of a typical precast concrete sandwich panel test

specimen (Benayoune et al., 2007) 51

2.33 Typical strain variation across the mid height of the PCSP

at different load stages. (Benayoune et al., 2007) 51

2.34 The detailing of foamed concrete sandwich panel for

thickness 100 mm (Liew, 2010) 53

2.35 The failure of Panel A (Liew, 2010) 54

2.36 Details of specimen (Mohamad, Omar and Abdullah, 2011) 56

2.37 Section of PE-1 (Mohamad and Mahdi, 2011) 57

2.38 Section of PE-2 (Mohamad and Mahdi, 2011) 58

2.39 Failure mode of control wall elements in compression

(Sumadi and Ramli, 2011) 58

2.40 Failure mode of sandwich wall elements without wire

mesh in compression (Sumadi and Ramli, 2011) 59

2.41 Failure mode of sandwich elements with reinforcement

(wire mesh and others) in compression

(Sumadi and Ramli, 2011) 59

2.42 Schematic diagram of composite walling (Wright, 1998) 60

2.43 Notation for wall (British Standard Institution, 2004) 65

3.1 Methodology of study 75

3.2 Compression test of concrete cube 77

3.3 Split cylindrical test 78

3.4 Tension testing result for 9 mm diameter reinforcement 82

3.5 Details of PLFP panel 85

3.6 Normal concrete Grade 25 was poured at both ends 86

xix

3.7 Polystyrene was placed on top of foamed concrete of the

first wythe layer 87

3.8 Foamed concrete was poured above the polystyrene to form

the second wythe layer and trowelled to obtain a smooth

surface 87

3.9 Axial load test frame 88

3.10 Strain gauges (SG) and linear voltage displacement

transducers (LVDT) locations 88

3.11 Support condition at bottom end condition of the panel 89

3.12 Top end condition for panel and arrangement for applying

pure axial load 89

4.1 Ultimate load carrying capacity versus slenderness ratio

for PLFP-HA1 to PLFP-HA8 92

4.2 Ultimate load carrying capacity versus compressive

strength for PLFP-HA1 to PLFP-HA8 93

4.3 Crack pattern PLFP-HA3, occurred at upper and lower

ends of the panel 94

4.4 Load horizontal deflection curves at mid-height of

PLFP-HA6 96

4.5 Load versus strain graphs for HA-2 97

4.6 Load versus strain graphs for HA-5 98

5.1 Structural model of single shear connectors and double

shear connectors with main reinforcement 102

5.2 Structural model of PLFP panel 103

5.3 Embedded technique for elements constrains 104

5.4 Rigid body as load cell and spreader beam 105

5.5 Supports and loading condition of PLFP panel in FEA 105

5.6 Compression hardening-softening of foamed concrete 109

5.7 Nonlinear compression strain softening of foamed concrete 109

5.8 Tension stiffening of foamed concrete 110

5.9 Tension damage of foamed concrete 110

5.10 Kinetic energy level of the whole model from analysis

with several natural periods. 113

xx

5.11 Internal and kinetic energy level of the whole model with

1 natural period 113

5.12 Meshes density study of FEA 115

5.13 Failure mode of PS2 from experiment and FEA 117

5.14 Load versus vertical load displacement for PS1 118

5.15 Comparison of FEA and experimental result of load

versus horizontal load displacement for PS1 119

5.16 Perfect and imperfect geometry model of PLFP panel 120

5.17 Load versus horizontal displacement at mid height from

experiment and FEA of PS1 panel 121

5.18 Failure mode of PLFP panel from experiment (half scale)

and FEA (full scale) 123

5.19 Comparison of ultimate load carrying capacity of PLFP

panels based on perfect and imperfect geometry model

from FEA 126

5.20 FEA results of load versus vertical displacement for

PLFP-1 to PLFP-11 134

5.21 Vertical displacement of PLFP-1 to PLFP-11 134

5.22 Horizontal displacement versus ultimate load of PLFP-1

to PLFP-11at mid height 135

5.23 FEA results of load versus horizontal displacement 136

5.24 General trend of horizontal displacement for PLFP panel 137

5.25 Vertical strains across the thickness along X axis of

PLFP-11 in perfect geometry mode 138

5.26 Vertical strains across the thickness along X axis of

PLFP-11 in imperfect geometry model 138

5.27 Comparison of stress distribution with damage and crack

pattern of PLFP-11 in imperfect geometry model 140

5.28 Damage status of PLFP-11 vertical displacement

increments from 0 mm to 50 mm 142

5.29 Stress distribution of PLFP-11 under vertical displacement

increments from 0 mm to 50 mm 143

5.30 Horizontal deflection recorded of PLFP-11 under vertical

displacement increments from 0 mm to 50 mm 144

xxi

5.31 Ultimate load versus thicknesses of polystyrene for panel

with various heights (3,200 mm, 3,500 mm, 3,600 mm

and 4,000 mm) 146

5.32 Ultimate load versus thicknesses of foamed concrete for

panel with various heights (3,200 mm, 3,500 mm, 3,600 mm

and 4,000 mm) 148

5.33 Support and loading condition of push off loading FEA 150

5.34 Comparison of shear force capacity for PLFP panel with

single and double shear truss connectors 151

5.35 Stress distribution of PLFP panel with single shear truss

connectors under the shear force FEA 152

5.36 Stress distribution of PLFP panel with double shear truss

connectors under the shear force FEA 153

6.1 Comparisons of FEA and empirical values from empirical

equation (safety factor included) for ultimate load of PLFP

panels 158

6.2 Comparisons of FEA and empirical values from empirical

equations (safety factor excluded) for ultimate load of PLFP

panels 159

6.3 Comparisons of FEA and three closest empirical predictions

for ultimate load carrying capacity of PLFP panels 160

6.4 Percentage difference between ultimate load carrying

capacity from FEA and Equation 6.1 from Eurocode 2 161

6.5 Percentage difference between ultimate load carrying

capacity from FEA and Equation 6.3 from Benayoune

(2007) 163

6.6 Percentage difference between ultimate load carrying

capacity from FEA and Equation 6.4 from Mohamad

(2010) 164

6.7 Comparisons of FEA result and developed Equation 6.5

versus slenderness ratio 167

6.8 Percentage difference between ultimate load carrying

capacity from FEA and Equation 6.5 168

xxii

6.9 Relationship between ultimate load carrying capacity and

slenderness ratio from FEA, equations by previous

researchers and the proposed Equation 6.5 169

6.10 Ultimate load carrying capacity versus slenderness ratio

from FEA and Equation 6.5 for PLFP panels with 125 mm

and 100 mm thicknesses 170

6.11 Percentage difference between ultimate load carrying

capacity from FEA and empirical values proposed from

Equation 6.5 for PLFP panels with 125 mm thickness 171

6.12 Percentage difference between ultimate load carrying

capacity from FEA and empirical values proposed from

Equation 6.5 for PLFP panels with 140 mm thickness 171

xxiii

LIST OF SYMBOLS AND ABBREVIATIONS

b - Overall width of the cross section

B - Length

c/c - centre to centre

C - Concrete cover

D - Damage parameter

e - Eccentricity

E - Young’s Modulus

h - Overall depth of the cross section

H - Height of panel

- Aspect ratio

- Aspect Ratio

- Slenderness ratio

k - 0.8 for wall brace top and bottom against lateral translation and

restrained against rotation at one or both ends.

K - The ratio of the second stress invariant on the tensile meridian

pcf - per cubic foot

t - Overall Thickness

Ѱ - Dilatation angle

σ - Stress

- The ratio of initial equibiaxial compressive yield stress to initial

uniaxial compressive yield stress

- Initial yield

- Ultimate stress

- Maximum principal effective stress

- Uniaxial tensile stress at failure

ε - Strain

- Tensile equivalent plastic strains

xxiv

- Compressive equivalent plastic strains

ϵ - Flow potential eccentricity

- Effective length factor, 1.0 for compressive strength of concrete at 28

days ≤ 50MPa

ρ - Density

υ - Poisson Ratio

μ - Viscosity parameter

- Temperature

Ф - Diameter of shear connector (mm)

- The strength of reduction factor (0.7 for reinforced member)

- Factor taking into account curvature, including second order effects

ASTM - American Standard Test Method

BCA - British Cement Association

BS - British Standard

CFRP - Carbon Reinforced Polymer

CIDB - Construction Industry Development Board of Malaysia

CREAM - Construction Research Institute of Malaysia

C3D8R - Continuum three dimensional 8 node linear brick element

EC2 - Eurocode 2

EPS - Expanded Polystyrene foam

EXP - Experimental Result

FE - Finite element

FEA - Finite Element Analysis

HA - Half scale panel

IBS - Industrialized Building System

LVDT - Linear Voltage Displacement Transducers

PCI - Precast Concrete Institution

PLFP - Precast Lightweight Foamed Concrete Sandwich Panel

PRIMA - 1 Malaysia People’s Housing Programme

PSI - Pounds per square inch

PS - PLFP with single shear truss connectors

R&D - Research and Development

R3D4 - Three dimensional 4 nodes rigid element

xxv

R3 - 3 mm mild steel

R6 - 6 mm mild steel

SG - Strain Gauges

T3D2 - Three dimensional 2 nodes truss element

UTHM - Universiti Tun Hussein Onn Malaysia

XPS - Extruded Polystyrene foam

- The gross area of section

Asc - The total area of steel used

- Total area of longitudinal reinforcement

- uniaxial damage variable due to compression

- uniaxial damage due to tension

E - Modulus Young

Eo - Initial (undamaged) elastic stiffness/ initial modulus of the material

ea - An additional eccentricity due to deflections in the wall

ei - Additional eccentricity covering the effects of geometrical

imperfection

eo - First order of eccentricity

etot - eo + ei

fbo/fco - The ratio of initial equibiaxial compressive yield stress to initial

uniaxial compressive yield stress

- The compressive strength of concrete

- field variable

fy - The tensile strength of the steel

G - Flow potential

J - Energy

- The ratio of the second stress invariant on the tensile meridian

lo - Effective length of the wall

Nu - Design axial strength per unit length of wall (N/mm)

- Axial resistance of wall

- Hydrostatic pressure stress

Pu - The ultimate strength of panel

q - Mises equivalent effective stress

σy - Initial yield

xxvi

t1 - Thickness of concrete wythe

t2 - Thickness of insulation layer

xxvii

LIST OF APPENDICES

APPENDIX TITLE PAGE

A Estimation of loading for 6 storey residential

building 184

B Foamed concrete properties 188

C Results of tension testing on reinforcement 192

D Experimental failure mode and cracking pattern of

PLFP 194

E Data of horizontal deflection and strain for PLFP

panels 197

F Load-horizontal deflection for PLFP panels 205

G Load-strain graphs for PLFP panels 206

H Mode of failure of PLFP from FEA 212

CHAPTER 1

INTRODUCTION

1.1 Introduction

As a developing country, housing demand in Malaysia is increasing day by day

especially in urban areas such as Kuala Lumpur, Penang, Selangor and Johor Bahru.

According to Sultan Sidi (2011) and MacDonald (2011), the high housing prices has

become a problem to the majority of local population. It is stated that, the high price

of the medium cost apartment, condominiums, terraced houses, the semi-detached

and the bungalow units became unaffordable to many. As such, people tend to

migrate away from city centres.

Due to the increase in population and living costs, Malaysia government is

focusing more on low and medium cost housing projects since the Seventh Malaysia

Plan (1996-2000). This is to ensure that the middle low income group with salary

ranging from RM 1,501 to RM 2,500 per month is able to own a house. However,

provision of low medium cost housing from RM 42,001 to RM 60,000 per unit

projected under Seventh Malaysia Plan was very disappointing with only 20.7% or

72,582 completed units from 350,000 units as initially targeted (CIDB, 2007).

Special attention must be given to low and medium cost housing since the majority

of the population in Malaysia falls in this category (Shuid, 2004). Hence,

construction industries must strive to achieve a healthy, efficient, and advance in

technology in order to meet the upcoming market demand.

The Construction Industry Master Plan produced by Construction Industry

Development Board of Malaysia, (CIDB) presented a strategic roadmap for

Malaysia’s construction industry to develop into a sector not only to meet the

challenges of international competition, seize the opportunities in the global market,

but also to make a significant contribution to the nation’s aspirations and the welfare

of its people (CIDB, 2007).

2

Under this plan, there are seven strategies to improve the living standard of

Malaysians and harvest the development of a caring society. The fifth strategic thrust

was to innovate through research and development (R&D) and adopt new

construction method. Innovation in construction techniques and technologies is vital

for developing competitive advantage as it allows improvements in products,

services, more efficient processes and business procedures. Adoption of new

construction techniques and technologies in Industrialized Building System (IBS) is

encouraged. Various efforts have been taken to continue to encourage the

development of IBS components and its usage in the industry.

IBS promotes sustainability from controlled production environment,

minimization of waste generation, extensive usage of energy efficient building

material, effective logistics and long term economic stability which contribute to

better investment in environmental friendly related technologies. The construction

research Institute of Malaysia (CREAM) and other research institutes in Malaysia

has established collaboration in R&D initiative on green construction and

sustainability trough IBS implementation (Kamar et al., 2010).

Besides these efforts, government has also come up with a solution through

schemes such as the 1 Malaysia People’s Housing Programme PR1MA. It was

established in 2011 to plan, develop, construct and maintain affordable housing for

middle-income household in key urban centres (Haziq, 2013). It can be seen that,

Malaysia government is aware of the housing issue and keep looking for initiatives in

order to overcome the problem.

In this study, an effort was taken to develop a precast lightweight foamed

concrete sandwich panel (PLFP) with double shear truss connectors to use as load

bearing wall component. PLFP is a three layer panel element comprising of two

layers of lightweight foam concrete as wythes and polystyrene core as insulation

layer. Its structural behaviour was studied based on experimental testing and finite

element analysis. An empirical equation was proposed based on the results obtained

from finite element analysis (FEA). PLFP is a potential product in IBS industry to

provide benefits to users such as its insulation properties and cost saving nature.

3

1.2 Problem statement

Mass migration of workforce population into the city and industrial centres has

accelerated the demand of affordable and quality houses. High housing price has

become a problem for low to medium income group especially in the cities. The

increasing demand of affordable housing resulted in aggressive research on precast

panel system which includes solid and sandwich panels. Current research had also

widen the scope of study on these panels using various materials such as normal and

lightweight concrete as well as recycled waste material.

The conventional construction and industrialize building system (IBS) mostly

use normal reinforced concrete. This panel system is generally strong but has larger

self-weight, not environmental friendly and longer construction period. As such,

precast sandwich panel system with more benefits compared to the normal reinforced

concrete panel has been studied such as profiled steel sheet dry board wall panel by

Wan Badaruzzaman et al. (2004), precast reinforced concrete panel by Benayoune

(2003) and ferrocement sandwich panel by Sumadi and Ramli (2008). More research

is in need to study on sandwich panel in order to invent lighter, environmental

friendly and easy to construct wall panel.

Previous research on sandwiched precast wall panel using foamed concrete

with single shear truss connectors showed that it could sustain the applied load for

low to medium rise residential building and behaved in a partially composite

behaviour. However, the study was limited to panel with maximum height of 2.8

meter and slenderness ratio of 28 (Benayoune, 2003 and Mohamad, 2010). Further

studies need to be conducted to determine the capacity of this panel system with

various heights and slenderness ratios. In addition, more research has to be carried

out to investigate and improve the effectiveness of the shear truss connectors.

Therefore this research will focus on the study of structural behaviour of precast

lightweight foamed concrete sandwich panel with double shear truss connectors in

term of its load bearing capacity, load deflection profiles and strain distribution. Due

to the limitation of laboratory facilities to test tall panel, computational study using

FEA software ABAQUS was conducted and validated by experimental results.

4

1.3 Research objectives

i. To numerically investigate the PLFP panel with shear truss connectors using

FEA.

ii. To determine the structural behaviour of PLFP in term of ultimate load ( non-

linear), failure mode, vertical and horizontal displacement and strain

distributions from finite element simulations.

iii. To validate the results obtained from FEA by means of experimental work.

iv. To propose an empirical equation of the ultimate load carrying capacity for

PLFP panel with shear truss connectors subjected to axial load.

1.4 Significant of study

This study is aimed to provide information about the structural behaviour of PLFP

with shear connectors. It is able to get a clear and deeper insight on the structural

behaviour and failure mechanisms of the PLFP with single and double shear truss

connectors under axial and push off loading. The results from this study are very

important to assist the design of the PLFP to be used as a precast wall system

especially the ultimate load carrying capacity and failure mechanism. An empirical

equation is proposed in this study which is able to predict the ultimate load carrying

capacity of PLFP under axial loading. The equation can be used to predict the

maximum load of sandwich in non-linear behaviour after the service load.

1.5 Scope and limitation of study

In order to study the structural behaviour of PLFP with shear connectors, scopes of

study is defined in detail to achieve the objectives of this research. PLFP panels up to

four meter height with single and double shear truss connectors was used in the study

by using FEA with validation from experimental data.

Eight half scaled PLFP were tested under axial loading to obtain the

experimental results. Material properties of foamed concrete and steel reinforcement

were determined from laboratory testing and used in FEA for material model. A

parametric study was carried out to investigate the ultimate load carrying capacity,

5

failure mode, vertical and horizontal deflection profiles, strain distribution and the

comparison of effectiveness for single and double shear truss connectors. The results

from the proposed FEA and experiment were analysed and compared. Ultimate load

carrying capacity values of PLFP determined from FEA were used to develop an

empirical equation. A suitable empirical equation is proposed to predict the ultimate

load carrying capacity of PLFP under axial load.

The key finding of this study is the structural behaviour of PLFP and its

developed empirical equation modified from previous equations.

1.6 Thesis layout

This thesis consists of seven (7) chapters. The content of each chapter is described as

below:

Chapter 1

This chapter presents an introduction and the need of the PLFP panel with

shear truss connectors as an alternate building system to provide more affordable

quality housing in order to meet the demand of affordable and quality housing.

Chapter 2

This chapter briefs on the relevant literature review on previous research on

the structural performance on sandwich system with various type of shear connector

and related topics. It also covers the discussion on empirical equations which were

developed from previous researchers and standards to predict the ultimate load

carrying capacity of panels.

Chapter 3

This chapter describes the methodology of the study which includes

experimental studies and FEA. Material testing on foamed concrete and steel were

accomplished to identify the material properties of PLFP for input in the FE model.

6

Upon the completion of FEA and experimental studies, results were used as a basis

for proposing an empirical equation.

Chapter 4

This chapter contains presentation of results from axial loading test on half

scaled panel. Observed structural behaviours during the axial loading test were

ultimate load carrying capacity, horizontal deflection, failure modes and load strain

curves. Results were used to verify the PLFP model in FEA.

Chapter 5

This chapter represents the FEA of PLFP under perfect and imperfect

geometry condition. FEA was validated with data of PLFP with single shear truss

connectors from previous research and experimental study. After the validation, FEA

was conducted on PLFP with double shear truss connectors to study its structural

behaviours.

Chapter 6

This chapter presents the proposed empirical equation to predict the ultimate

load carrying capacity of PLFP. The empirical equation is an improvement from

previous empirical equation in Eurocode2.

Chapter 7

A summary of the major findings of the study together with some

recommendations for further research is summarized in this chapter.

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

Based on present journals many researchers have shown interest in the development

of precast composite sandwich panel. Precast sandwich panel presents a series of

possibilities for the solution of housing problems especially in low and medium cost

housing sector (PCI committee, 1997; Benayoune et al., 2007; Mohamad et al., 2011

and Sumadi and Ramli, 2008).

2.2 Material properties

Sandwich panel is made from various materials for its wythe and core layer. These

include foamed concrete, steel, timber, aluminium and waste material (PCI

committee, 1997; Benayoune et al., 2007; Mohamad et al., 2011 and Sumadi and

Ramli, 2008). Material used in sandwich panel plays a very important role in its

structural behaviour.

2.2.1 Foamed concrete

Foamed concrete is a lightweight material consisting of Portland cement paste or

cement filler matrix (mortar) with a homogeneous void or pore structure created by

introducing air in the form of small bubbles. Introduction of pore is achieved through

preformed foaming agent (foaming agent mixed with a part of mixing water and

aerated to form foam before being added to the mix) and mix foaming (foaming

agent mixed with the matrix) ( Kunhanandan and Ramamurthy, 2006).

By proper control in the foam dosage, a wide range of densities (400 kg/m3 to

1,600 kg/m3) of foamed concrete can be obtained for application in structural,

8

partition, insulation and filling grades (Ramamurthy, Kunhanandan and Indu, 2009).

According to BCA (1994), compressive strength of foamed concrete depends on the

density, initial water to cement ratio and cement content. Density of foamed concrete

can have an influence on the ultimate strength, particularly for the lower density

foamed concrete. Uniformly sized small bubbles appear to produce higher ultimate

strengths at all densities. Table 2.1 and 2.2 show the typical mixture details for

foamed concrete and properties of foamed concrete.

Table 2.1: Typical mixture details for foamed concrete (BCA, 1994)

Type Typical foamed concrete

Wet Density (kg/m3) 500 900 1,300 1,700

Dry Density (kg/m3) 360 760 1,180 1550

Cement (kg/m3) 300 320 360 400

Sand (kg/m3) - 420 780 1,130

Base Mix W/C Ratio Between 0.5 and 0.6

Air Content (%) 78 62 45 28

Table 2.2: Typical properties of foamed concrete (BCA, 1994)

Dry Density

(kg/m3)

Compressive

Strength (MPa)

Thermal

Conductivity

(W/mk)

Modulus of

Elasticity

(Gpa)

Drying Shrinkage

(%)

400 0.5-1.0 0.10 0.8-1.0 0.3-0.35

600 1.0-1.5 0.11 1.0-1.5 0.22-0.25

800 1.5-2.0 0.17-0.23 2.0-2.5 0.20-0.22

1,000 2.5-3.0 0.23-0.30 2.5-3.0 0.18-0.15

1,200 4.5-5.5 0.38-0.42 3.5-4.0 0.11-0.09

1,400 6.0-8.0 0.50-0.55 5.0-6.0 0.09-0.07

1,600 7.5-10.0 0.62-0.66 10.0-12.0 0.07-0.06

Kunhanandan and Ramamurthy (2006) studied properties of foamed concrete

with different types of filler (sand and fly ash). Filler type influenced the foamed

9

concrete properties. Figure 2.1 shown the effects of coarse sand and fine sand on its

compressive strength. For foamed concrete with dry density from 800kg/m3 to

1400kg/m3, the strength varies from 1 MPa to 10 MPa. The strength over density

ratio had also been studied (Table 2.3 depicts the result). Their findings had good

agreement with the foamed concrete strength listed by BCA (1994), and therefore the

properties listed by BCA (1994) was still relevant to be used as a reference and

design guide of the compressive strength and density of foamed concrete.

Figure 2.1: Strength density variation for mixes with sand of different fineness

(Kunhanandan and Ramamurthy, 2006)

Table 2.3: Comparison of strength to density ratio (in MPa per kg/m3 x 1000)

(Kunhanandan and Ramamurthy, 2006)

Design

density, kg/m3

Strength to density ratios for foamed concrete mixes with

Coarse sand Fine sand Fine sand-fly ash Fly ash

1,000 0.77 1.73 1.68 2.79

1,250 3.87 3.63 5.32 7.11

1,500 5.04 6.94 8.64 12.66

Dry density, kg/m3

28-D

ay c

om

pre

ssiv

e st

reng

th, M

Pa

10

2.2.2 Polystyrene foam

Polystyrene foam was used as a building insulation material because of its good

thermal insulation and hyper elastic properties. Polystyrene foam is often used in

insulating concrete forms, structural insulated panel building systems and non-weight

bearing architectural structures. Polystyrene foam commonly used as building

materials are expanded polystyrene foam (EPS) and extruded polystyrene foam

(XPS) types.

According to Scheirs and Priddy (2003) EPS is used in many building

projects for thermal insulation, sound proofing in new buildings or renovation work.

EPS foam slabs are used for the insulation of walls, roofs, floors and ceilings. The

polystyrene particles sizes range between 0.9 and 1.6 mm are preferably used for this

application.

For the thermal insulation of walls, there is a difference between outside and

inside wall and core insulation. For the outside wall insulation the EPS foam is put

directly on the stone bearing structure. A fabric reinforced plastering or a ventilated

facade protects it from the weather exposure. Using sandwich panels of EPS

plasterboards, modern heat insulation standards can be achieved on the walls of older

building. For core insulation, the insulation layer is in- between the bearing wall and

the external weather resistant wall. Another system of insulation is the use of EPS

moulded foam parts (insulated concrete forms) for a combination of outer and inner

wall insulation. A wall is built with these moulded foam parts and filled with

concrete.

Frankl et al. (2011) investigated the behaviour of precast, pre-stressed

concrete sandwich wall panels reinforced with carbon-fibre-reinforced polymer

(CFRP) shear grid. Six panels were designed and tested to evaluate their flexural

reaction under combined vertical and lateral loads. The study included panels

fabricated with two different insulation types: EPS insulation and XPS insulation.

Based on those findings, all panels sustained loads in excess of their factored

design loads and exhibited large deformations before failure. CFRP grid can provide

the required composite action between wythes using either EPS or XPS. For a given

shear transfer mechanism, a higher percentage composite action can be achieved

using EPS insulation rather than XPS insulation, Use of XPS insulation requires an

increase of the shear reinforcement ratio compared to EPS insulation.

11

2.2.2.1 Physical properties of expanded polystyrene

According to Texas Foam Inc (2011), the mechanical properties of expanded

polystyrene depend largely upon density; in general, strength characteristics increase

with density as tabulated in Table 2.4. The data only represents the typical value and

testing data can be different from it with ± 10-15% from listed values.

It is noted that compressive strengths listed in Table 2.4 are not ultimate

values at either a yield or failure point because polystyrene is a hyper elastic material

which yields under compressive loads (as illustrated in the typical stress/strain curves

of Figure 2.2).Compressive strength values that are listed in Table 2.4 are at 10%

deformation, a level often considered to be a minimum value for energy absorption

under impact loadings.

Table 2.4: Typical properties of expanded polystyrene

(Texas Foam Inc, 2011)

Density

Kg/m3

Stress at 10%

Compression

(MPa)

Flexural Strength

(MPa)

Tensile Strength

(MPa)

Shear Strength

(MPa)

16 0.0896 0.1999 0.2137 0.2137

24 0.1654 0.2965 0.3516 0.3654

32 0.2068 0.3999 0.4275 0.4826

40 0.2896 0.5171 0.5102 0.6343

48 0.4413 0.6067 0.6067 0.8136

56 0.4619 0.7239 0.6757 0.9653

64 0.5516 0.8618 0.7446 1.2066

12

Figure 2.2: Typical stress/strain curves for expanded polystyrene

(Texas Foam Inc, 2011)

2.2.3 Shear connectors and reinforcement

PCI committee (1997) had clearly explained the shear connector’s properties and its

function in precast sandwich wall panels. Shear connectors were used to transfer

forces between the two wythes. In some cases, shear connector can be used to

transfer the weight of a non-structural wythe to the structural wythe.

Some shear connector is called one way shear connector; those connectors are

stiff in one direction but flexible in the other. Other shear connectors are stiff in at

least two perpendicular directions and will consequently transfer both longitudinal

and transverse horizontal shears as shown in Figures 2.3, 2.4 and 2.5.

Capacities of shear connectors may be obtained from the connector

manufacturer or in some cases, calculated using allowable steel stresses for bending,

shear and axial forces. In semi composite panels, the assumption is made that the

insulation provides sufficient shear transfer to create composite action during

stripping, handling and erection process, but the shear transfer is not there to provide

composite action for resisting service loads.

13

Figure 2.3: One way shear connectors, stiff in only one direction

(PCI committee, 1997)

14

Figure 2.4: Two way shear connectors, stiff in at least two perpendicular directions.

(PCI committee, 1997)

Figure 2.5: Non-composite connectors

(PCI committee, 1997)

15

2.2.4 Normal concrete capping

Mohamad (2010) applied normal concrete capping at both ends on the PLFP panel

with single shear connectors to distribute the load evenly. The normal concrete

capping applied at both ends is to prevent the panel from premature cracking near

loading and support areas. The design of capping is shown in Figure 2.6 and

strengthened with horizontal and vertical steel bars of 9 mm diameter.

Figure 2.6: Normal concrete capping

(Mohamad, Omar and Abdullah, 2011)

2.3 Accuracy of structural models

According to Sabnis et al. (1983) and Harris et al. (1999), adequate definitions of

reliability and accuracy are difficult to formulate. One obvious measure is the degree

to which a model can duplicate the response of prototypes. Difference in-between

two identical reinforced concrete structures show as high as 20% or more. Multiple

prototypes and multiple models are needed in order to treat the results statically, but

the expense of even a single test structure is usually high. Factors affecting the model

accuracy included model material properties, fabrication accuracy, loading

techniques, measurements methods and interpretation of results, and therefore elastic

models can be built to five extremely high correlations with detailed computer based

results. Elastic model of reinforced concrete structure can predict elastic response

with high accuracy level (error between than 5 to 10%). Carefully designed and

tested strength models of reinforced structures such as beams, frames, shells and

16

other structures normally have maximum errors on the order of less than 15% for the

prediction of post cracking displacement and ultimate load carrying capacity of the

structure.

2.3.1 Scaled model technique

Due to high costs and difficulty to do full scale experimental study for huge and

complex structural problems, previous researchers studied many structures in smaller

scale model. Sabnis et al. (1983) wrote a book as guidance for scaled model

experimental study. Many researchers followed the scaling laws listed in their book

and it was proven to work for full scale model (Knappett et al., 2011).

Knappett et al. (2011) studied small scale modelling of reinforced concrete

structural elements under bending loads at very high scale factors with application of

scaling laws as shown in Table 2.5. Scaling laws was adopted from Harris and

Sabnis (1999). Results proved that scaling technique allows for stiffness, strength

and ductility of structural elements under bending loads to be simultaneously scaled

and failure modes to be accurately reproduced.

Table 2.5: Scaling laws

(Knappet et al., 2011)

Property

Ratio* ( N = scale factor)

Stress, σ

1:1

Strain, ɛ

1:1

Young’s modulus

1:1

Length

1:N

Force

1:N2

17

Gran et al. (1996) studied small scale experimental study with

scale and ¼

scale sample. They studied the compression bending on the scaled reinforced

concrete walls as shown in Figure 2.7. Axial compression combined with bending

was used in the study. The repeatability of the results was excellent and the

comparison between scales achieved good agreement. It was found that scale model

is useful for checking analytical models for failure and post failure response.

Figure 2.7: Steel reinforcement for model wall sections

(Gran et al., 1996)

Vaughan et al. (2011) investigated the use of small scale building models to

study progressive collapse of damaged buildings. A reinforced concrete building

(3 bay x 4 bay, 4 storey) was designed and constructed at

scale as shown in Figure

2.8. FEA was conducted to map out a sequence of tests which provided a

representative range of structural response to several different levels of damage. Pre-

test and post failure predictions were in good agreement with all major aspects of

18

collapse behaviour as seen in Figures 2.9 and 2.10. Tests results provided important

validation to FEA. Small scale testing was therefore found to be practical and useful

for studying the collapse phenomena by stages. Even though there are differences

between full scale and small scale structures due to scaling effects and the practical

challenges of manufacturing a small scale structure, simulation tools can effectively

account for these scaling effects within the computational model.

Figure 2.8: Completed four storey reinforced concrete

scale building

(Vaughan et al., 2011)

Figure 2.9: Comparison of high speed camera images with equivalent snapshots from

pretest simulation.

(Vaughan et al., 2011)

19

Figure 2.10: Post failure photos of test article showing collapsed region compared

with snapshot from pretest simulation showing collapsing section of model

(Vaughan et al., 2011)

2.4 Finite element analysis

Referring to Wahyu (2005), FEA is an analytical tool for predicting responses of

certain engineering systems. The FEA in principle is a numerical approach for

obtaining solutions. Its appeal lies in its use for predicting the field quantities of

complicated structural shapes under general loading. It can also be easily used for

structures with a large number of components. Its accuracy is bounded by all

assumptions it takes and the inherent numerical error it carries.

At present, many conventional FEA software packages are available in the

market such as: DIANA, ABAQUS, ADINA, OpenSees and ATENA. Their

capabilities range from low to sophisticate with excellent graphic capabilities. In the

application of finite element software, three terms are often used: pre-processor,

solution process, and post processor.

Pre-processor: Process of geometric preparation, selection of elements, discretization

of the domain, selection of materials, application of loadings, and the specification of

the boundary conditions.

Solution process: Based on the pre-processing, the software will internally set up the

equilibrium equations which are to be solved through the solution process to produce

the nodal field values (displacements, temperatures, etc.).

20

Post Processor: Process of representing the required analytical parameters. The user

can evaluate the stress distribution, structural displacements, pressure distribution, or

heat flux distribution. Some software programs can even produce a magnificent

graphic representation in stunning colour.

2.4.1 Comparison of conventional FEA software

There are many conventional FEA software packages available in the market for

various purpose of analysis. These software are designed for various types of

analysis such loading study, dynamic study, thermodynamic, aerodynamic, impact

loading study and also others analysis, and therefore a suitable software with

adequate ability to analyse PLFP panel structural behaviour should be identified.

Johnson (2006) summarized the concrete and reinforcement response of

various FEA software in Tables 2.6 and 2.7. It can be seen that all software have the

similarity in term of the response applied but some software did not have the

capability to study the respond. As seen from various FEA research studied by

previous journals, ABAQUS software was one of the popular choice. ABAQUS is

able to predict the respond of reinforced concrete; results from FEA have good

agreement with experimental results. ABAQUS has an extensive library of elements

that can be used to model concrete and steel, including both continuum and structural

elements.

21

Table 2.6: Comparison of concrete response

(Johnson, 2006)

22

Table 2.7: Comparison of reinforcement response

(Johnson, 2006)

2.4.2 Abaqus/Explicit versus Abaqus/Standard

ABAQUS software consists of two analysis products which are Abaqus/Standard and

Abaqus/Explicit. Both products are capable of solving a wide variety of problems.

(Abaqus, 2009).

Abaqus/Standard is a general-purpose analysis product that can solve

traditional implicit finite element analysis for a wide range of linear and nonlinear

problems involving the static, dynamic, thermal, and electrical response of

components.

In contrast, Abaqus/Explicit marches a solution forward through time in small

time increments without solving a coupled system of equations at each increment (or

23

even forming a global stiffness matrix). Abaqus/Explicit is a special-purpose analysis

product that uses an explicit dynamic finite element formulation. It is suitable for

modelling brief, transient dynamic events, such as impact and blast problems, and is

also very efficient for highly nonlinear problems involving changing contact

conditions, such as forming simulations.

The characteristics of implicit and explicit procedures determine which

method is appropriate for a given problem. For those problems that can be solved

with either method, the efficiency determined which product to use. The key

differences for those two products is listed in Table 2.8 and used as guidance in

choosing the suitable method for analysis.

Table 2.8: Key differences between Abaqus/Standard and Abaqus/Explicit.

(Abaqus, 2009)

Quantity Abaqus/Standard Abaqus/Explicit

Element

library

Offers an extensive element library. Offers an extensive library of elements well

suited for explicit analyses. The elements

available are a subset of those available in

Abaqus/Standard.

Analysis

procedures

General and linear perturbation

procedures are available.

General procedures are available.

Material

models

Offers a wide range of material

models.

Similar to those available in

Abaqus/Standard; a notable difference is

that failure material models are allowed.

Contact

formulation

Has a robust capability for solving

contact problems.

Has a robust contact functionality that

readily solves even the most complex

contact simulations.

Solution

technique

Uses a stiffness-based solution

technique that is unconditionally

stable.

Uses an explicit integration solution

technique that is conditionally stable.

Disk space

and memory

Due to the large numbers of iterations

possible in an increment, disk space

and memory usage can be large.

Disk space and memory usage is typically

much smaller than that for

Abaqus/Standard.

24

2.4.2.1 Choosing between implicit and explicit analysis

In order to run analysis for finite element model efficiently, a suitable analysis

method has to be chosen based on suitability and efficiency level. As briefed in the

section before, Abaqus/Standard is more efficient for solving smooth nonlinear

problems; on the other hand, Abaqus/Explicit is the clear choice for a wave

propagation analysis. However, there are certain static or quasi-static problems that

can be simulated well with either program.

Typically, these are problems which usually solved with Abaqus/Standard but

may have difficulty converging due to contact or material complexities, resulting in a

large number of iterations. Such analyses are expensive in Abaqus/Standard because

every single iteration requires a large set of linear equations to be solved.

On the other hand, Abaqus/Explicit determines the solution without iterating

by explicitly advancing the kinematic state from the previous increment. Even

though a given analysis may require a large number of time increments using the

explicit method, the analysis can be more efficient in Abaqus/Explicit if the same

analysis in Abaqus/Standard requires much iteration. Another advantage of

Abaqus/Explicit is that it requires much less disk space and memory than

Abaqus/Standard for the same simulation. For problems in which the computational

cost of the two programs may be comparable, the substantial disk space and memory

savings of Abaqus/Explicit make it attractive (Abaqus, 2009).

2.4.3 Element types

Abaqus software provides wide range of elements for solving different problems.

The element families available include continuum element, shell elements, beam

element, truss elements and rigid elements. Each element is characterized by the

family, degrees of freedom, number of nodes, formulation and integration. Each

element in Abaqus has a unique name, such as T3D2, S4R, or C3D8R. The element

name identifies each of the five aspects of an element. Common element families

used in a stress analysis are shown in Figure 2.11. One of the major distinctions

between different element families is the geometry type that each family assumes.

(Abaqus, 2009).

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