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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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