STATIC AND DYNAMIC PERFORMANCE OF LIGHTWEIGHT HYBRID ... · PDF fileii Static and dynamic performance of lightweight hybrid composite floor plate system Abstract In the modern built

STATIC AND DYNAMIC PERFORMANCE

OF LIGHTWEIGHT HYBRID COMPOSITE

FLOOR PLATE SYSTEM

A.M. Chanaka Madushan Abeysinghe

B.Sc. (Civil Engineering, Honours)

A thesis submitted in partial fulfilment of the requirements for the degree of

Doctor of Philosophy

School of Civil Engineering & Built Environment

Science and Engineering Faculty

Queensland University of Technology

September - 2012

Static and dynamic performance of lightweight hybrid composite floor plate system i

Keywords

Hybrid composite floor plate system, Glass-fiber Reinforced Cement, Polyurethane,

Steel, Experimental testing, Finite Element modelling, Static performance, Dynamic

performance, Human-induced loads, Vibration, Design guidelines

ii Static and dynamic performance of lightweight hybrid composite floor plate system

Abstract

In the modern built environment, building construction and demolition consume a

large amount of energy and emits greenhouse gasses due to widely used conventional

construction materials such as reinforced and composite concrete. These materials

consume high amount of natural resources and possess high embodied energy. More

energy is required to recycle or reuse such materials at the cessation of use.

Therefore, it is very important to use recyclable or reusable new materials in building

construction in order to conserve natural resources and reduce the energy and

emissions associated with conventional materials. Advancements in materials

technology have resulted in the introduction of new composite and hybrid materials

in infrastructure construction as alternatives to the conventional materials. This

research project has developed a lightweight and prefabricatable Hybrid Composite

Floor Plate System (HCFPS) as an alternative to conventional floor system, with

desirable properties, easy to construct, economical, demountable, recyclable and

reusable. Component materials of HCFPS include a central Polyurethane (PU) core,

outer layers of Glass-fiber Reinforced Cement (GRC) and steel laminates at tensile

regions. This research work explored the structural adequacy and performance

characteristics of hybridised GRC, PU and steel laminate for the development of

HCFPS.

Performance characteristics of HCFPS were investigated using Finite Element (FE)

method simulations supported by experimental testing. Parametric studies were

conducted to develop the HCFPS to satisfy static performance using sectional

configurations, spans, loading and material properties as the parameters. Dynamic

response of HCFPS floors was investigated by conducting parametric studies using

material properties, walking frequency and damping as the parameters. Research

findings show that HCFPS can be used in office and residential buildings to provide

acceptable static and dynamic performance. Design guidelines were developed for

this new floor system. HCFPS is easy to construct and economical compared to

conventional floor systems as it is lightweight and prefabricatable floor system. This

floor system can also be demounted and reused or recycled at the cessation of use

due to its component materials.

Static and dynamic performance of lightweight hybrid composite floor plate system iii

Publications

Abeysingh, C.M., D.P. Thambiratnam and N.J. Perera, Development of an

Innovative Hybrid Composite Floor System, In Thirteenth International Conference

on Civil, Structural and Environmental Engineering Computing, B.H.V. Topping and

Y. Tsompanakis, Editors. 2011, Civil-Comp Press, Stirlingshire, Scotland: Chania,

Crete, Greece.

Abeysingh, C.M., D.P. Thambiratnam and N.J. Perera, Investigation of hybridized

polyurethane, glass fibre reinforced cement and steel laminate in structural floor

plate systems, In The First International Postgraduate Conference on Engineering,

Designing and Developing the Built Environment for Sustainable Wellbeing. 2011,

Queensland University of Technology. p. 249-253.

Abeysingh, C.M., D.P. Thambiratnam and N.J. Perera, Innovative Hybrid Composite

Floor Plate System In AES-ATEMA’2012 Tenth International Conference, Y.M.

Haddad, Editor. 2012: McGill University, Montreal, Canada.

Abeysingh, C.M., D.P. Thambiratnam and N.J. Perera, Flexural performance of an

innovative Hybrid Composite Floor Plate System comprising Glass–fibre Reinforced

Cement, Polyurethane and steel laminate. Composite Structures 2013, 95: 179-190.

Thambiratnam D.P. , Perera N.J. , Abeysinghe C.M. , Huang M-H ,De Silva S.S.,

Human Activity-Induced Vibration in Slender Structural Systems. Structural

Engineering International 2012, 22(2): 238-245.

Abeysingh, C.M., D.P. Thambiratnam and N.J. Perera, Dynamic performance

characteristics of an innovative Hybrid Composite Floor Plate System under human-

induced loads. Composite Structures (2012),

http://dx.doi.org/10.1016/j.compstruct.2012.09.015.

http://dx.doi.org/10.1016/j.compstruct.2012.09.015

iv Static and dynamic performance of lightweight hybrid composite floor plate system

Table of Contents

Keywords ................................................................................................................................................. i

Abstract ................................................................................................................................................... ii

Publications ........................................................................................................................................... iii

Table of Contents ................................................................................................................................... iv

List of Figures ..................................................................................................................................... viii

List of Tables ........................................................................................................................................ xii

List of Abbreviations ........................................................................................................................... xiv

List of Symbols .................................................................................................................................... xiv

Statement of Original Authorship ....................................................................................................... xvii

Acknowledgements ........................................................................................................................... xviii

CHAPTER 1: INTRODUCTION ....................................................................................................... 1

1.1 INTRODUCTION ....................................................................................................................... 1

1.2 HCFPS ......................................................................................................................................... 3

1.3 RESEARCH AIMS AND OBJECTIVES.................................................................................... 5

1.4 SIGNIFICANCE AND SCOPE ................................................................................................... 5 1.4.1 Significance ...................................................................................................................... 5 1.4.2 Scope ................................................................................................................................ 6

1.5 THESIS OUTLINE...................................................................................................................... 7

CHAPTER 2: LITERATURE REVIEW ........................................................................................... 9

2.1 CURRENT COMPOSITE CONSTRUCTION APPLICATIONS AND THEIR LIMITATIONS9 2.1.1 Fiber Reinforced Composites (FRC) ................................................................................ 9 2.1.2 Sandwich Composites..................................................................................................... 10 2.1.3 Hybrid composites .......................................................................................................... 14

2.2 IMPORTANCE OF DEVELOPING A HYBRID COMPOSITE FLOOR PLATE SYSTEM .. 15

2.3 PROPERTIES AND ADVANTAGES OF SELECTED MATERIALS FOR HCFPS .............. 18 2.3.1 Steel 18 2.3.2 Polyurethane (PU) .......................................................................................................... 20 2.3.3 Glass fiber Reinforced Cement/Concrete (GRC) ........................................................... 22

2.4 SUMMARY AND IMPLICATIONS ........................................................................................ 24

CHAPTER 3: METHODOLOGY .................................................................................................... 27

3.1 HCFPS DEVELOPMENT ......................................................................................................... 27

3.2 HCFPS CONFIGURATION AND SYMMETRY .................................................................... 27

3.3 EXPERIMENTAL TESTING ................................................................................................... 29 3.3.1 Test Panel ....................................................................................................................... 29 3.3.2 Heel impact test .............................................................................................................. 30 3.3.3 Static load test................................................................................................................. 31 3.3.4 Cyclic loading test .......................................................................................................... 32 3.3.5 Material testing ............................................................................................................... 34

3.4 FINITE ELEMENT (FE) METHOD OF ANALYSIS .............................................................. 35 3.4.1 Pre-processing ................................................................................................................ 35 3.4.2 Analysis and solutions .................................................................................................... 35 3.4.3 Post-processing ............................................................................................................... 36

Static and dynamic performance of lightweight hybrid composite floor plate system v

3.5 FE MODEL VALIDATION ...................................................................................................... 36

3.6 STATIC PERFORMANCE AND PARAMETRIC STUDIES .................................................. 37

3.7 DYNAMIC ANALYSIS OF HCFPS......................................................................................... 38 3.7.1 Human induced walking loads ........................................................................................ 38 3.7.2 Dynamic analysis and floor classification ...................................................................... 40 3.7.3 Acceptance criteria ......................................................................................................... 41 3.7.4 Damping ......................................................................................................................... 44

3.8 DYNAMIC PERFORMANCE AND PARAMETRIC STUDIES OF hcfps ............................. 45

3.9 DESIGN GUIDELINES ............................................................................................................ 45

3.10 SUMMARY ............................................................................................................................... 46

CHAPTER 4: EXPERIMENTAL TESTING .................................................................................. 47

4.1 MATERIAL PROPERTY INVESTIGATION .......................................................................... 47 4.1.1 Formulation of GRC ....................................................................................................... 47 4.1.2 Tensile testing for GRC .................................................................................................. 48 4.1.3 Four-point bending tests for GRC .................................................................................. 48 4.1.4 Cylinder compression test for GRC ................................................................................ 49 4.1.5 Composition of PU ......................................................................................................... 50 4.1.6 Compression test for PU ................................................................................................. 50 4.1.7 Tensile test for PU .......................................................................................................... 51 4.1.8 Three- point bending tests for PU core ........................................................................... 52 4.1.9 Tensile test for steel laminate ......................................................................................... 53

4.2 FABRICATION OF HCFPS TEST SPECIMEN ...................................................................... 53

4.3 SUPPORTING ARRANGEMENT FOR THE TEST PANEL .................................................. 55

4.4 DATA ACQUISITION SYSTEM ............................................................................................. 56

4.5 DYNAMIC TESTING ............................................................................................................... 57 4.5.1 Heel impact test .............................................................................................................. 57 4.5.2 Walking test .................................................................................................................... 61

4.6 STATIC LOAD TESTING ........................................................................................................ 62 4.6.1 Test set up, instrumentation and static load test.............................................................. 62 4.6.2 Static load test results and discussion ............................................................................. 63 4.6.3 Deflection ductility ......................................................................................................... 65

4.7 CYCLIC LOAD TESTING ....................................................................................................... 65 4.7.1 Test set up, instrumentation and cyclic load test ............................................................ 66 4.7.2 Test results and discussion for cyclic loading test .......................................................... 67 4.7.3 Comparison of cyclic loading test results with static load test results ............................ 67

4.8 TESTING OF GRC-PU-GRC COMPOSITE PANEL .............................................................. 68 4.8.1 Test sample size and fabrication ..................................................................................... 68 4.8.2 Test set up and instrumentation ...................................................................................... 69 4.8.3 Static load test results and discussion ............................................................................. 70

4.9 SUMMARY ............................................................................................................................... 72

CHAPTER 5: DEVELOPMENT AND VALIDATION OF FE MODELS ................................... 75

5.1 FE MODEL DEVELOPMENT AND VALIDATION USING DYNAMIC TEST RESULTS

OF HCFPS TEST PANELS .................................................................................................................. 75 5.1.1 Material properties for dynamic analysis ........................................................................ 75 5.1.2 Model description ........................................................................................................... 76 5.1.3 Free vibration analysis and validation with first natural frequency ................................ 76 5.1.4 Linear transient dynamic analysis ................................................................................... 77 5.1.5 Heel impact load function ............................................................................................... 77 5.1.6 Application of the damping to FE models ...................................................................... 78 5.1.7 Dynamic analysis validation with acceleration response of heal impact test .................. 79 5.1.8 Dynamic analysis and validation with walking loads ..................................................... 80

vi Static and dynamic performance of lightweight hybrid composite floor plate system

5.2 FE MODEL DEVELOPMENT AND VALIDATION USING STATIC TEST RESULTS of

HCFPS TEST PANEL .......................................................................................................................... 82 5.2.1 Material properties for static analysis ............................................................................. 82 5.2.2 GRC Material models ..................................................................................................... 82 5.2.3 4 PU material model ....................................................................................................... 83 5.2.4 Steel material model ....................................................................................................... 83 5.2.5 Model description ........................................................................................................... 83 5.2.6 Static analysis, validation and discussion ....................................................................... 84

5.3 FE MODEL DEVELOPMENT AND VALIDATION FOR GRC-PU-GRC COMPOSITE

PANEL .................................................................................................................................................. 87 5.3.1 FE model ........................................................................................................................ 87 5.3.2 Material properties .......................................................................................................... 88 5.3.3 FE model validation ....................................................................................................... 89

5.4 SUMMARY ............................................................................................................................... 90

CHAPTER 6: STATIC PERFORMANCE OF HCFPS ................................................................. 91

6.1 DEVELOPMENT OF HCFPS ................................................................................................... 91 6.1.1 Section configuration for static performance studies ...................................................... 92

6.2 VARIABLES IN PARAMETRIC STUDIES ............................................................................ 93 6.2.1 Section configurations .................................................................................................... 93 6.2.2 FE model for HCFPS ...................................................................................................... 93 6.2.3 Material Properties ......................................................................................................... 94 6.2.4 Loading conditions ......................................................................................................... 95

6.3 RECTANGULAR BEAM AND TAPERED BEAM ................................................................ 96 6.3.1 FE modelling .................................................................................................................. 96 6.3.2 FE analysis results and discussion .................................................................................. 97

6.4 FLEXURAL PERFORMANCE ................................................................................................ 99 6.4.1 FE modelling .................................................................................................................. 99 6.4.2 Properties of GRC .......................................................................................................... 99 6.4.3 Properties of Steel ......................................................................................................... 100 6.4.4 Properties of PU ........................................................................................................... 101 6.4.5 FE abalysis, results and discussion ............................................................................... 101

6.5 COMPARISON OF HCFPS WITH STEEL-DECK COMPOSITE FLOOR SYSTEM USING

STIFFNESS AND SELF-WEIGHT.................................................................................................... 108

6.6 DETERMINATION OF HCFPS SECTION PROPERTIES USING ANALYTICAL

METHODS ......................................................................................................................................... 109 6.6.1 Linear elastic deflection of HCFPS .............................................................................. 111 6.6.2 Stresses in individual component materials .................................................................. 112 6.6.3 Properties of cracked section ........................................................................................ 113

6.7 SHEAR PERFORMANCE ...................................................................................................... 116

6.8 PERFORMANCE OF GRC-PU-GRC PANEL AND SLAB JOINT ...................................... 117 6.8.1 FE modelling of GRC-PU-GRC panel ......................................................................... 117 6.8.2 FE model for slab joint of the adjacent HCFPS panels ................................................ 119 6.8.3 Properties of materials .................................................................................................. 119 6.8.4 FE analysis results and discussion ................................................................................ 119

6.9 SUMMARY ............................................................................................................................. 123

CHAPTER 7: DYNAMIC PERFORMANCE OF HCFPS ........................................................... 125

7.1 STRUCTURAL CONFIGURATION...................................................................................... 125

7.2 DYNAMIC PERFORMANCE OF HCFPS (SINGLE PANEL APPROACH) ....................... 126 7.2.1 FE modelling ................................................................................................................ 127 7.2.2 Material properties ........................................................................................................ 127 7.2.3 Mass of the HCFPS ...................................................................................................... 128 7.2.4 Free vibration analysis .................................................................................................. 129 7.2.5 Parameters that influence the first mode natural frequency of the HCFPS .................. 131

Static and dynamic performance of lightweight hybrid composite floor plate system vii

7.2.6 Damping ....................................................................................................................... 132 7.2.7 Mathematical load model for human induced loads ..................................................... 132 7.2.8 FE transient dynamic analysis ...................................................................................... 133 7.2.9 Results from parametric study and discussion .............................................................. 133 7.2.10 Vibration assessment of HCFPS ................................................................................... 137

7.3 DYNAMIC PERFORMANCE OF HCFPS FLOORS WITH THE STRUCTURAL FRAME141 7.3.1 FE modelling ................................................................................................................ 142 7.3.2 Material properties ........................................................................................................ 142 7.3.3 Mass of the HCFPS floor model ................................................................................... 143 7.3.4 Free vibration analysis of HCFPS floor model ............................................................. 143 7.3.5 Damping ....................................................................................................................... 145 7.3.6 Mathematical load model for human induced loads ..................................................... 145 7.3.7 FE transient dynamic analysis ...................................................................................... 146 7.3.8 Results from parametric study and discussion .............................................................. 146

7.4 CONCLUSIONS...................................................................................................................... 148

CHAPTER 8: CONCLUSIONS AND RECOMMENDATIONS ................................................. 151

8.1 CONTRIBUTION FROM THIS RESEARCH ........................................................................ 151

8.2 DISCUSSION AND SUMMARY ........................................................................................... 152 8.2.1 Experimental Testing and FE model validation ............................................................ 152 8.2.2 Static design of HCFPS ................................................................................................ 154 8.2.3 Dynamic performance of HCFPS ................................................................................. 156 8.2.4 Design guidelines.......................................................................................................... 157 8.2.5 Supporting and connection methods ............................................................................. 160 8.2.6 Limitation of design guidelines .................................................................................... 161 8.2.7 Manufacturing and casting guide .................................................................................. 161 8.2.8 Implications .................................................................................................................. 162 8.2.9 Future work................................................................................................................... 163

BIBLIOGRAPHY ............................................................................................................................. 165

viii Static and dynamic performance of lightweight hybrid composite floor plate system

List of Figures

Figure 1-1: Development of HCFPS using component materials ........................................................... 3

Figure 1-2: Formulation of HCFPS ......................................................................................................... 4

Figure 2-1: Sandwich construction configurations [17] ........................................................................ 10

Figure 2-2: De-lamination failure of a sandwich panel [6] ................................................................... 16

Figure 2-3: Wrinkling failure of sandwich panels [9] ........................................................................... 16

Figure 2-1: Hybrid material configuration in HCFPS ........................................................................... 17

Figure 2-2: How to optimize the performance HCFPS using component material characteristics ....... 18

Figure 2-3: Stress strain behaviour of high tensile steel of three similar specimens [22] ..................... 19

Figure 3-1: Proposed HCFPS panel configuration and symmetry ........................................................ 28

Figure 3-2: Graphical representation of building floor using HCFPS panels ....................................... 28

Figure 3-3: 3200 mm span HCFPS test panel configuration ................................................................. 29

Figure 3-4: A typical acceleration response [35] ................................................................................. 30

Figure 3-5: Static load test arrangement ............................................................................................... 31

Figure 3-6 Load cycles and steps of loading for cyclic loading test [39] .............................................. 32

Figure 3-7: A typical load-deflection curve for six load cycles [39] ..................................................... 33

Figure 3-8: Parameters to calculate the Repeatability [39] .................................................................. 34

Figure 3-9: Dynamic vertical force due to walking step by a person [57]. ......................................... 38

Figure 3-10: Frequency weighted RMS acceleration base curve [55] .................................................. 42

Figure 3-11 Development stages of HCFPS ......................................................................................... 46

Figure 4-1: (a) Tensile testing for GRC specimen, (b) Stress-strain relationships for GRC in

tension .................................................................................................................................. 48

Figure 4-2: (a) Four-point bending test for GRC, (b) Load-deflection plots for GRC in four-

point bending tests ............................................................................................................... 49

Figure 4-3: (a) Compression test for GRC, (b) Stress-strain relationships for GRC in

compression ......................................................................................................................... 50

Figure 4-4: (a) Stress-strain relationships f or PU in compression, (b) Compression testing for

PU core ................................................................................................................................. 51

Figure 4-5: (a) Tensile test for PU core, (b) Stress-strain behaviours of PU in tension ........................ 52

Figure 4-6: (a) Three-point bending test for PU core, (b) Load-deflection plots from bending

test of PU core ...................................................................................................................... 52

Figure 4-7: (a) Dimensions of tensile test specimen, (b) Tensile testing for steel laminate, (c)

Stress-strain relationships for steel laminate in tension ....................................................... 53

Figure 4-8: Section dimensions of HCFPS test panel .......................................................................... 54

Figure 4-9: Casting steps of HCFPS test panel ..................................................................................... 55

Figure 4-10: Test panel supporting arrangement .................................................................................. 56

Figure 4-11: Data acquisition system .................................................................................................... 56

Figure 4-12: Test setup and data acquisition system for heel impact test ............................................. 57

Figure 4-13: (a) Heel impact at the mid-span, (b) 5g Accelerometer and 25 mm LVDT at the

bottom HCFPS panel............................................................................................................ 58

Static and dynamic performance of lightweight hybrid composite floor plate system ix

Figure 4-14: Typical heel impact displacement response at mid-span for panel 1 ................................ 58

Figure 4-15: Typical heel impact acceleration response at mid-span for panel 1 ................................. 59



Figure 4-18: Typical FFT analysis of an acceleration response ........................................................... 61

Figure 4-19: Typical acceleration response at the mid-span for walking test ....................................... 62

Figure 4-20: Loading arrangement for the static load test of HCFPS panel .......................................... 63

Figure 4-21: Load-deflection behaviour of HCFPS panels ................................................................... 64

Figure 4-22: Cracking and failure due to the flexure ............................................................................ 65

Figure 4-23: Cyclic loading test for HCFPS panel ................................................................................ 66

Figure 4-24: Cyclic behaviour of HCFPS panel for first 6 loading cycles ............................................ 67

Figure 4-25: Cyclic behaviour of HCFPS panel .................................................................................... 68

Figure 4-26: GRC-PU-GRC composite panel slab in HCFPS assembly.............................................. 68

Figure 4-27: Determined sectional configuration of composite panel .................................................. 69

Figure 4-28: Loading test setup ............................................................................................................. 70

Figure 4-29: Supporting conditions for loading test .............................................................................. 70

Figure 4-30: Load-deflection curves for A type panels ......................................................................... 71

Figure 4-31: Load-deflection curves for B type panels ......................................................................... 71

Figure 4-32: Failure of one test panel ................................................................................................... 71

Figure 5-1: FE model for dynamic analysis .......................................................................................... 76

Figure 5-2: Mode shape for the first natural frequency ......................................................................... 77

Figure 5-3: Heel impact load function .................................................................................................. 78

Figure 5-4: Computed and measured acceleration responses due to heal impact.................................. 80

Figure 5-5: Computed and measured acceleration responses due to walking ....................................... 81

Figure 5-6: GRC material model ........................................................................................................... 83

Figure 5-7: FE model of HCFPS panel for static loading test ............................................................... 84

Figure 5-8: FE mesh of HCFPS panel ................................................................................................... 84

Figure 5-9: FE model validation with experimental results .................................................................. 85

Figure 5-10: Flexural cracks in the beam of HCFPS at the failure ....................................................... 86

Figure 5-11: Stress and strain distribution at the mid-span of the HCFPS ............................................ 86

Figure 5-12: FE model for GRC-PU-GRC panel .................................................................................. 88

Figure 5-13: Validation for FE model for static test (Type A panel) .................................................... 89

Figure 5-14: Validation for FE model for static test (Type B panel) .................................................... 89

Figure 6-1: Graphical representation of building floor using HCFPS panels ........................................ 91

Figure 6-2: Proposed supporting methods for HCFPS floor to structural frame ................................... 91


Figure 6-4: HCFPS section for parametric study .................................................................................. 92

Figure 6-5: GRC fill replacing PU core in the vicinity of supports ....................................................... 92

Figure 6-6: Section parameters for parametric study ............................................................................ 93

Figure 6-7: FE model of HCFPS ........................................................................................................... 94

x Static and dynamic performance of lightweight hybrid composite floor plate system


Figure 6-10: Variation in stress in the GRC layer (with GRC 10) with change in "a" .......................... 98

Figure 6-11: Continuous glass fiber mesh ............................................................................................. 99

Figure 6-12: GRC material model ....................................................................................................... 100

Figure 6-13: Stress-strain relationship for High strength and mild steel ............................................. 100

Figure 6-14: Load -deflection behaviour of A, B and C type sections ................................................ 102

Figure 6-15: A typical flexural crack development in the beam of the HCFPS .................................. 105

Figure 6-16: Stress and strain distribution at the mid-span of the HCFPS along X-X ........................ 106

Figure 6-17: A typical flexural stress distribution (in GRC and PU) at the mid-span (Type A) ......... 107

Figure 6-18: Load-deflection plots of steel deck floor system and HCFPS ........................................ 109

Figure 6-19: Parameters used to define the properties of HCFPS section .......................................... 110

Figure 6-20: Load-deflection comparison between FE and analytical methods ................................. 111

Figure 6-21: Stresses in component materials at mid span section of HCFPS along X-X .................. 112

Figure 6-22: Tensile crack development in the beam of the HCFPS (Type B) ................................... 114

Figure 6-23: Parameters used to define the properties of cracked HCFPS section ............................. 114

Figure 6-24: Stress distribution of cracked HCFPS section along X-X .............................................. 115

Figure 6-25: Shear stress in GRC outer shell at the vicinity of support .............................................. 116

Figure 6-26: Shear zone of in the HCFPS cross-section ..................................................................... 116

Figure 6-27: GRC-PU-GRC slab of HCFPS ....................................................................................... 118

Figure 6-28: Layer thickness of GRC-PU-GRC panel ........................................................................ 118

Figure 6-29: FE models of GRC-PU-GRC panel ................................................................................ 118

Figure 6-30: Typical detail of the adjacent slab connection ................................................................ 119

Figure 6-31: FE models of contact joint.............................................................................................. 119

Figure 6-32: Performance GRC-PU-GRC panel with GRC 5 and PU 20 ........................................... 121

Figure 6-33: Performance of slab joint with GRC 5 and PU 20.......................................................... 122

Figure 7-1: HCFPS floor plate with steel frame.................................................................................. 125

Figure 7-2: Prefabricated HCFPS panel .............................................................................................. 126

Figure 7-3: Sectional configuration parameters .................................................................................. 126

Figure 7-4: FE model of HCFPS panel .............................................................................................. 127

Figure 7-5: Typical mode shape for the first mode natural frequency ............................................... 130

Figure 7-6: RMS acceleration for section type A, and 3 m span ........................................................ 135

Figure 7-7: RMS acceleration for section type B, and 5 m span ......................................................... 136

Figure 7-8: RMS acceleration for section type C, and 7.5 m span ...................................................... 137

Figure 7-9: Structural configuration of four bay floor model using HCFPS ....................................... 141

Figure 7-10: FE model of four bay HCFPS floor ................................................................................ 142

Figure 7-11: First four modes shape of HCFPS floor model using GRC 10 and PU 75 ..................... 144

Figure 7-12: RMS acceleration of HCFPS floor model with section type C (non-activity panel) ...... 146

Figure 7-13: RMS acceleration of HCFPS floor model with section type C (activity panel) ............. 147

Figure 8-1: Optimum configuration of HCFPS ................................................................................... 154

Figure 8-2: Parameters used to define the properties of HCFPS section ............................................ 158

Static and dynamic performance of lightweight hybrid composite floor plate system xi

Figure 8-3: Parameters used to define the properties of cracked HCFPS section ............................... 159

Figure 8-4: Proposed supporting methods for HCFPS floor to structural frame ................................. 161

Figure 8-5: Cross-section of the HCFPS panel .................................................................................. 161

xii Static and dynamic performance of lightweight hybrid composite floor plate system

List of Tables

Table 2-1: Typical values of steel properties [22] ................................................................................. 19

Table 2-2: Typical values of PU properties [14, 25] ............................................................................. 21

Table 2-3: Typical values of GRC properties [29, 32, 33] .................................................................... 23

Table 3-1: standard test methods for material property investigation ................................................... 35

Table 3-2: Loading cases [48] ............................................................................................................... 37

Table 3-3: Super imposed permanent dead loads for an office floor .................................................... 37

Table 3-4: Design parameters for walking and running loads [49, 55] ................................................. 39

Table 3-5: Recommended response factors [56] ................................................................................... 42

Table 3-6: VDV values (m/s1.75

) for vertical direction vibrations [60] ............................................... 43

Table 4-1: Formulation of GRC ............................................................................................................ 47

Table 4-2: Damping ratios for the HCFPS test panel ............................................................................ 60

Table 4-3: Experimental First natural frequency of HCFPS panels ...................................................... 61

Table 4-4: Summary of material properties obtained from the material testing .................................... 72

Table 5-1: Component material properties for the dynamic analysis .................................................... 75

Table 5-2: Validation of first natural frequency .................................................................................... 77

Table 5-3: Mass proportional stiffness proportional damping for FE model ....................................... 79

Table 5-4: Component material properties for the GRC-PU -GRC , FE model. ................................... 88

Table 6-1: HCFPS section and span parameters ................................................................................... 93

Table 6-2: Properties of Steel ................................................................................................................ 94

Table 6-3: Properties of GRC [12] ........................................................................................................ 95

Table 6-4: Properties of PU [25] ........................................................................................................... 95

Table 6-5: Self-weight of the HCFPS floors ......................................................................................... 96

Table 6-6: Loading cases [48] ............................................................................................................... 96

Table 6-7: HCFPS section and span parameters ................................................................................... 97

Table 6-8: Properties of Steel ................................................................................................................ 97

Figure 6-9: Shear stress in GRC outer shell for type B section ............................................................. 98

Table 6-9: Properties of of GRC ......................................................................................................... 100

Table 6-10: Serviceability deflection of the HCFPS floor with PU 20 ............................................... 102

Table 6-11: Factor of Safety (FOS) for flexural performance of HCFPS with PU 20 and MSteel ........ 103

Table 6-12: Factored deflection to account for creep and shrinkage deformation .............................. 108

Table 6-13: Comparison of stresses in component materials under 5 kPa load .................................. 113

Table 6-14: Properties of of GRC ....................................................................................................... 115

Table 6-15: Shear Capacity of HCFPS sections .................................................................................. 117

Table 6-16: Sectional configuration of GRC-PU-GRC panels ........................................................... 118

Table 6-17: Properties of GRC and PU ............................................................................................... 119

Table 6-18: Performance of 1000 mm one-way span ......................................................................... 121

Table 6-19: Performance of 500 mm cantilever span ......................................................................... 121

Static and dynamic performance of lightweight hybrid composite floor plate system xiii

Table 6-20: Performance of 1000 mm one-way span with slab joint at the centre ............................. 122

Table 7-1: Spans and section dimensions ............................................................................................ 126

Table 7-2: Properties of GRC [12] ...................................................................................................... 128

Table 7-3: Properties of PU [25] ......................................................................................................... 128

Table 7-4: Properties of Steel .............................................................................................................. 128

Table 7-5: Super imposed permanent dead loads for an office floor .................................................. 129

Table 7-6: Mass of the HCFPS floors ................................................................................................. 129

Table 7-7: Modal frequencies of HCFPS panels ................................................................................. 130

Table 7-8: Comparison of first mode natural frequency ..................................................................... 131

Table 7-9: Parameters for the load model[55] ..................................................................................... 133

Table 7-10: VDV assessment of HCFPS using na ............................................................................... 140

Table 7-11: Properties of GRC [12] .................................................................................................... 143

Table 7-12: Properties of PU [25] ....................................................................................................... 143

Table 7-13: Properties of Steel ............................................................................................................ 143

Table 7-14: Modal frequencies of HCFPS model ............................................................................... 145

Table 7-15: Mass proportional damping (α) and stiffness proportional damping (β) for ζ= 5% ........ 145

Table 7-16: Minimum number of activities required generates lower probability adverse

comment of Floor model ................................................................................................... 147

xiv Static and dynamic performance of lightweight hybrid composite floor plate system

List of Abbreviations

HCFPS Hybrid Composite Floor Plate System

GRC Glass-fiber Reinforced Cement

PU Polyurethane

FE Finite Element

FRC Fiber Reinforced Composites

GFRP Glass Fiber Reinforced Polymer

SPS Sandwich Plate System

HCB Hybrid Composite Beam

ASTM American Society for Testing and Materials

AS Australian Standards

ISO International Organization for Standardization

AISC American Institute of Steel Construction

EI Flexural rigidity

LVDT Linear-Variable-Displacement-Transducers

DAS Data Acquisition System

RMS Root-Mean-Square

FFT Fast Fourier Transformation

MSteel Mild Steel

TSteel High Strength Steel

GRC 5, 10, 15, 20 Types of GRC (5, 10, 15, 20 represents modulus of elasticity in GPa)

PU 20, 75, 150, 360 Types of PU (20, 75, 150, 360 represents modulus of elasticity in MPa)

List of Symbols

E, Es Elastic modulus

G, Gs Shear modulus

ρ, ρs Density

τ, τs Shear strength

Lus Ultimate load of HCFPS (load at the yielding point)

Gk Dead Load (kPa)

Qk Imposed Load (kPa)

Static and dynamic performance of lightweight hybrid composite floor plate system xv

F(t) Dynamic load due to human activities

Q Static weight of walking people (kN, kPa)

αn Fourier coefficient

n nth harmonic

f, fp Step frequency or load frequency or activity frequency (Hz)

υn Phase angle

I Second moment of area

m Effective mass

L Span of HCFPS

υn Phase angle

arms Root-Mean-Square acceleration

aw,rms Frequency weighted Root-Mean-Square acceleration

VDV Vibration Dose Value

Ta Exposure period (16 hour day or 8 hour night)

na Number of time a activity will take place in exposure period

apeak Peak acceleration

Ao, A1, … An Acceleration (g)

ζ Structural damping

σcy Compressive yield stress

εcy Compressive yield strain

εcu Ultimate compressive strain

σcr Structural damping

εcr First cracking tensile strain

σtu Tensile stress at the end of tensile model

εtu Ultimate tensile strain

ν Poisons ratio

bb Width of the beam

db Depth of the beam

h Depth HCFPS section

L Width of the slab

yi Distance to centroid (from the bottom) of HCFPS

bi Width of individual components

di Depth of individual components

A Net area of component material

Ai Net area of ith

component material

xvi Static and dynamic performance of lightweight hybrid composite floor plate system

A Area of the transformed section

tPU Thickness of PU in the slab

tGRC, top Thickness of GRC layer at the top

tGRC Thickness of GRC layer

tGRC ESS Thickness GRC layer Either Sides of Steel laminate

tSteel Thickness of Steel laminate

EPU Elastic modulus of PU

EGRC Elastic modulus of GRC

ESteel Elastic modulus of Steel

n1 ESteel / EPU

n2 EGRC / EPU

VCapacity Shear capacity

f1, f2 Modal frequency (Hz)

.

Static and dynamic performance of lightweight hybrid composite floor plate system xvii

Statement of Original Authorship

The work contained in this thesis has not been previously submitted to meet

requirements for an award at this or any other higher education institution. To the

best of my knowledge and belief, the thesis contains no material previously

published or written by another person except where due reference is made.

Signature:

Date: _________________________

QUT Verified Signature

xviii Static and dynamic performance of lightweight hybrid composite floor plate system

Acknowledgements

I was able to complete this research project due to the great support of many sources.

Any contribution to the engineering profession as result of this research project have

been a joint effort of myself, my supervisory team and others who support this

project in various ways. My greatest thanks and appreciation goes to following

people.

First, I would like to express my sincere gratitude to my principal supervisor, Prof.

David Thambiratnam for giving me this opportunity together with his motivation,

great support and excellent guidance to carry out my research work successfully. I

thank him for steering me towards the goals of this research project and for helping

me to overcome the difficulties encountered during the candidature. I would never

have completed without his support and encouragement. I would also like extend

sincere thank to my associate supervisor Adjunct Prof. Nimal Perera for his

professional guidance, rigorous discussions, valuable advices and useful suggestions

given during entire period of time. I wish to thank Dr. Ashar Nasir, for his advices

and useful suggestions for this research. I would also like to thank Prof. Andy Tan

for being panel member for both my confirmation of candidature and final seminar.

Second, I gratefully acknowledge the financial support given by BEE for providing

the Post Graduate Research scholarship to carry out the research work. I would like

to express my special thanks to DomeShells Australia Pte Ltd and Mr. Chris Brown,

who contributed graciously all necessary test materials to carry out experimental

testing. That was an invaluable support for this research to reinforce the findings.

I would also wish to acknowledge the members of the technical staff at QUT for their

generous support given me during my experimental testings. In particular, I wish to

thank to Mr. Greg Tevelen, Mr. Gregory Paterson, Mr. Noel Hartnett, Mr Matthew

Mackay, Mr. Jonathan James and Mr. Anthony Morris for their patience and endless

support in carrying out the experimental testing. In addition, I am also thankful to all

academic and non-academic staff of faculty for the support given in many ways.

Static and dynamic performance of lightweight hybrid composite floor plate system xix

I would also like to gratefully acknowledge Dr Bernadette Bellette for her time and

support given me improving my writing skills. My acknowledgement is further

extended to my fellow researchers and friends for their valuable support in my

research.

Finally, I would like to thank my family and my loving wife Rajima Dilmani for

their love and support during the difficult times, and greatly appreciate all the help

provided. The completion of this thesis would have not been possible without their

encouragement and patience.

xx Static and dynamic performance of lightweight hybrid composite floor plate system

Chapter 1: Introduction 1

Chapter 1: Introduction

1.1 INTRODUCTION

In the modern built environment, building construction and demolition consume a

large amount of energy and emits greenhouse gasses due to the widely used

conventional construction materials such as reinforced concrete, composite concrete

and steel. These materials possess higher embodied energy and more energy is

required to recycle or reuse them at the cessation of use [1]. Moreover, commercially

useful life of buildings in the modern era is becoming shorter due to the higher

demand of available building sites with ever changing land use and lack of suitability

of buildings for developing demands. On average, commercially useful life of

building is less than 50 years although actual useful design life may extend to 100

years or more [2]. However, many buildings are structurally modified or retrofitted

for change of within 20 years. Therefore, it is very important to use recyclable or

reusable new materials in building construction in order to reduce the energy and

emissions associated with conventional materials. In addition, growing limitation in

natural resources, which are used to manufacture conventional building materials,

can also be reduced by developing recyclable or reusable building materials. In this

context, this research project develops an innovative hybrid floor system with

desirable properties, such as lightweight, easy to construct, economical,

demountable, recyclable and reusable.

Advancements in material technology have created a trend for using hybrid

composite materials in infrastructure construction. Hybrid composite and sandwich

materials offer desirable properties, such as being lightweight, easy to construct,

economical, demountable, recyclable and reusable. They are efficient systems,

offering high stiffness-to-weight ratios and high strength-to-weight ratios. Hybrid

composite and sandwich materials have been used effectively instead of conventional

materials in many engineering applications. Typically, sandwich panels comprise of

mainly two materials, which are high strength thin skins and a middle soft core.

Hybrid composite systems comprise of several hybridised materials to form

composites. Hybrid composite components have been used effectively in automotive

2 Chapter 1: Introduction

and aerospace applications [3, 4], while sandwich panels have been used in

aerospace, marine and civil constructions, such as cladding wall panels [5], floor

panels[6-8] and roof panels [9], bridge decks [8], transportation applications [10]

and dome-type shell structures [11]. However, sandwich panels can only be used as

short span floor structures as they are slender and deflect excessively when used as

long span panels. Moreover, sandwich panels exhibit de-lamination and wrinkling

failure under flexural loading. As a consequence, use of sandwich panels in floor

plate construction is limited. Despite the potential to use hybrid composites in floor

construction to overcome the limitation of sandwich panels, hybrid composite

components in floor plate construction has not been adequately investigated and

developed.

Admittedly, Glass-fiber Reinforced Cement (GRC), Polyurethane (PU) and thin steel

laminate have the potential to be used as component materials in hybrid structural

floor plates because they have been successfully used in sandwich construction

applications. GRC is a fiber-reinforced composite material comprising of alkali-

resistant glass fiber, cement and sand as the major constituents [12]. It is lighter than

conventional concrete and can be used to produce thin outer layers of sandwich

panels [11, 12]. PU is a common lightweight foam core material, which has been

extensively utilized in sandwich construction. A wide range of properties can be

achieved with different densities of PU [13]. There is thus a potential for the

development of an innovative hybrid composite floor System using GRC, PU and

steel laminates.

Despite this, applicability of hybridized GRC, PU and steel in structural floor

systems has not yet been studied. For the first time, this research has developed a

new light weight structural floor plate system, called Hybrid Composite Floor Plate

System (HCFPS) as illustrated in Figure 1-1 to investigate the potential application

of GRC, PU and steel hybrids. Configuration of the HCFPS is designed to combine

the inherent strength characteristics of the constituent materials and to eliminate their

weaker characteristics. This research investigates the strength, serviceability and

performance characteristics of HCFPS that can be used in high performance light

weight floor plates for buildings.


Figure 1-1: Development of HCFPS using component materials

1.2 HCFPS

HCFPS exploits the inherent beneficial properties of component materials in such a

manner to optimise the overall performance of the floor plate system. Proposed

HCFPS is assembled using component materials as shown in the Figure 1-2. Width

of HCFPS is limited to 2 m to suit prefabrication and transportation requirements but

adjacent panels are connected using the slab joint shown Figure 1-2. Length of

HCFPS can be varied by changing the material properties and sectional

configuration. A cold-formed thin perforated steel laminate is placed at the bottom of

the beam to improve tensile strength. Perforated steel laminate is used to enhance the

bonding between GRC and steel laminate. The PU core is replaced with a GRC fill in

the vicinity of the supports as shown in Figure 1-2, to enhance the support bearing

capacity of the panel.

When HCFPS panel is subjected to bending, compressive stresses occur mainly in

the slab and tensile stresses occur in the bottom steel laminate. Shear stresses occur

across the web of the beam due to the loading. GRC and PU exhibit better

performance under compressive and shear stresses [12, 14]. Hence, GRC and PU are

profiled and located to attract compressive and shear stresses in the slab and beams

of HCFPS (as shown in the Figure 1-2). Stability of HCFPS section is provided by

the PU core, because it provides connection between and lateral support for thin

GRC layers to prevent the lateral buckling. The steel laminate and GRC attract


higher stresses sue to their elastic modulus, which is significantly higher than that of

PU. In this way, beneficial inherent properties of individual component materials are

combined to achieve optimum performance in the HCFPS.

Figure 1-2: Formulation of HCFPS

HCFPS has high potential for use as a structurally efficient and high perfromance

flooring system. In order to verify these attributes, the static performance of HCFPS,

such as flexural capacity, shear capacity, deflection limits and ductility need to be

investigated when subjected to dead and imposed loading. In addition, HCFPS is

lightweight structure and therefore, needs to be evaluated and designed to comply

with the dynamic performance for comfort and serviceability in relation to human

perception in compliance with acceptable standards.

This research investigates the performance characteristics of steel, PU and GRC in

HCFPS using Finite Element (FE) method simulations supported by experimental

testing. ABAQUS code is used to develop FE models in order to simulate HCFPS

floor configurations and spans. The FE modelling techniques are validated using

experimental testing. Parametric studies are carried out to develop new HCFPS with

design guidelines.


1.3 RESEARCH AIMS AND OBJECTIVES

The main aim of this research is to develop a HCFPS comprising GRC, PU and steel

laminates and determine the performance characteristics.

Additional objectives are to:

o Determine properties of constituent materials

o Experimentally test HCFPS panels to investigate static, dynamic,

cyclic loading and post yield behaviours, mode of failure and ductility.

o Develop FE models and validate by experimental testing

o Perform parametric studies on HCFPS panels in relation to material

properties of GRC, PU, steel and their hybrids to quantify static

performance requirement of HCFPS. FE techniques will be used to

study the influence of parameters such as sectional configuration,

spans, loading limits and support condition

o Determine the vibration characteristic of HCFPS under human-

induced loads

o Investigate and determine the required enhancement of material

properties of hybrid materials for an optimum design that will satisfy

static and dynamic design criteria

o Development of design guidelines

1.4 SIGNIFICANCE AND SCOPE

1.4.1 Significance

This project is significant as the research findings will lead to the development of an

innovative hybrid structural floor plate system with several desirable properties such

as being lightweight, easy to construct, economical, demountable, recyclable and

reusable. Component materials used have been well developed and tested in

standalone applications. However, hybridized use of these materials for the proposed

application is unprecedented. For the first time, GRC, PU and steel hybrids are used

to develop a lightweight and efficient floor plate system with good vibration

performance.

HCFPS can be developed as a prefabricated floor system that can be manufactured in

an offsite factory under controlled conditions to achieve a product of superior quality


with low embodied energy. This floor system is approximately 50% lighter in weight

compared to conventional concrete floors. Therefore, this product is easy to

transport, handle and erect. HCFPS has the potential to revolutionize the construction

of structural floor systems by replacing slow, labour intensive and low quality

construction materials with factory based manufacturing process. Manufactured floor

plates can be assembled with simple connections on site eliminating the heavy,

cumbersome and time consuming material handling, transporting and erecting

processes while minimising safety hazards. HCFPS can be demounted and reused in

other applications or can be recycled as a whole component at the end of

commercially useful life of the buildings.

Additionally, lightweight property of HCFPS floor plates results in reduced load on

the supporting beams and columns. Thereby, sizes of such load-bearing members can

be reduced, yielding economical advantages.

Moreover, lightweight HCFPS floor and reduced size of load bearing members

results in lower mass for building structures. As a consequence, such buildings offer

better performance during earthquakes. In an earthquake, ground shaking generates

internal forces within the buildings called inertial forces, causing damage to building

structures. Magnitude of inertial forces are proptional to the mass of a structure [15].

Hence, the lower the mass of the building lower the strength demand for seismic

loads.

Findings from this research, therefore, provide an efficient, lightweight, economical,

and sustainable structural flooring system that can be recycled and reused as a whole

system compared to conventional floor systems. HCFPS offers multifunctional

structural properties, making it a viable alternative for conventional reinforced

concrete and composite deck floors. It is therefore a product that addresses social and

environmental needs of the global community using material and manufacturing process

with low energy content.

1.4.2 Scope

In this research project, the suitability of HCFPS for structural flooring is

determined. FE simulation was used with limited experimental testing. Material

properties are obtained from limited mechanical testing and available resources and


published manufacturers’ data. Static and dynamic performance characteristics of

HCFPS are investigated. Non-linear behaviour of the HCFPS is investigated under

static performance requirements. Post yield behaviour, mode of failure and ductility

measurements of HCFPS is investigated for the tested specimens. Linear elastic

behaviour of HCFPS is considered for investigating dynamic performance. Fire

resistance and thermal insulation have not been investigated in this research but data

can be obtained from existing information based on studies carried out on such

materials.

1.5 THESIS OUTLINE

This thesis consists of eight chapters and their content is as follows:

Chapter 1: An introduction and background to the research topic, configuration of

HCFPS, aims and objectives, scope and significance of the research have been

described in this chapter.

Chapter 2: This chapter reviews current application of lightweight composites

(sandwich and hybrid) in civil engineering construction. The limitation and

weaknesses of those composites for use in structural floor plate construction are

reviewed. Reasons and importance of developing a HCFPS are also discussed.

Chapter 3: This chapter describes research methodology and the various stages

through which the HCFPS was developed. It also makes references to appropriate

codes or standards and literature used in development.

Chapter 4: This chapter presents the experimental investigations conducted on 3200

mm span HCFPS panels and GRC-PU-GRC composite panels. Material property

investigation, test panels fabrication method, test setup, instrumentation and

experimental results are explained.

Chapter 5: This chapter presents the development of FE models using ABAQUS

and subsequent validation of FE models using experimental test results generated in

Chapter 4.

Chapter 6: This chapter presents the development of HCFPS to satisfy static

performance requirements. Details of parametric studies, which were conducted to


investigate the static performance characteristics and strength capacity of HCFPS,

are explained.

Chapter 7: This chapter investigates dynamic response of HCFPS under human

induced vibration. Findings shows that lightweight HCFPS can be used in residential

and office buildings by evaluating its vibration performance using acceptable

perceptibility limits provided in current design guidelines and standards.

Chapter 8: This final chapter highlights the main contribution of this research, major

findings and recommendations for future research.

Chapter 2: Literature review 9

Chapter 2: Literature review

This chapter will review current application of lightweight composites (sandwich and

hybrid) in civil engineering construction. Research studies that have been carried out

for the development of such composites and their properties will be discussed. The

limitation and weaknesses of those composites for use in structural floor plate

construction will also be reviewed. Furthermore, the reasons and importance of

developing a Hybrid Composite Floor Plate System (HCFPS) will be discussed.

Material that can be used to develop HCFPS and their properties and advantages will

finally be reviewed.

2.1 CURRENT COMPOSITE CONSTRUCTION APPLICATIONS AND

THEIR LIMITATIONS

Advancements in material technology have created a trend for using composite

materials in infrastructure construction. Composite materials are comprised of two or

more materials of different properties, in order to obtain more efficient final

products. The main types of composites are fiber reinforced composites, sandwich

composites and hybrid composites. Composite materials offer desirable properties

such as being lightweight, easy to construct, economical, demountable, recyclable

and reusable. They are efficient systems, offering high stiffness-to-weight ratios and

high strength-to-weight ratios [10]. Composite materials have been used effectively

instead of conventional materials in infrastructure construction. Composite

constriction applications and studies that are related to civil structures will be

reviewed in this section.

2.1.1 Fiber Reinforced Composites (FRC)

FRC are formed by imbedding fibers into a binder material. Continuous or

discontinuous fibers, which are glass, metal and ceramics, have been used in FRC.

Composite fibers act as main load attracting members, whilst binder material holds

the fibers in the intended orientation [16]. FRC have been used in civil construction

for architectural decorating applications, repair and rehabilitation of existing

structures and sandwich construction applications [5]. In this context, FRC

applications related only to the sandwich and hybrid composite construction have

10 Chapter 2: Literature review

been considered. Common FRC materials used in such applications are Glass-Fiber

Reinforced Polymer (GFRP) and Glass-fiber Reinforced Cement (GRC). Their

applications and properties in relation to sandwich and hybrid composite

constructions application will be discussed in section 2.1.2.

2.1.2 Sandwich Composites

Sandwich panels are comprised of two thin, high strength, outer skin laminates and a

central core. The skins attract compressive and tensile stresses that result from

bending, whilst the core not only keeps the two skins apart but also transmits shear

forces to the supports [9]. Skins of sandwich panels are made of aluminium, steel and

FRC such as GRFP and GRC. Cores of the sandwich panels are made as either solid,

honeycomb, truss, Z-shaped, C-shaped, or I-shaped cores using metallic or polymeric

materials such as Polyurethane (PU) as shown in Figure 2-1. The configurations of

the skins are either flat or lightly profiled, but wide variations in the core structure

allow sandwich panels to be used in different applications. Flexural stiffness of

sandwich panels can be increased by increasing the distance between the face plates.

As a consequence, normal flexural stresses in component material can be reduced

[17].

Figure 2-1: Sandwich construction configurations [17]

There are a number of applications of sandwich construction, as a consequence of

combining different facing and core materials. Major sandwich construction

applications in civil constructions are cladding wall panels [5, 9], floor panels [6-8],

roof panels [9], bridge decks [17], transportation applications [10] and dome-type

shell structures [11].


In the last three decades, lightweight sandwich panels, using a thin outer skin with a

low density core, have been developed and used for wall claddings and roof panels.

According to Davies [9] thin steel sheets are the most common material used as skin

for lightweight wall and roof sandwich panels. Aluminium, plywood, chipboard and

gypsum board are also recommended for this. Core materials are basically

categorised into two types, those being bonded and foamed cores. Bonded cores

typically consist of either polystyrene or mineral fibers, which are bonded to the face

plate using a suitable adhesive [9, 18]. Formed cores are typically obtained by

mixing two liquids and no adhesive is necessary as the mixture adheres strongly to

surfaces of skins during chemical process of hardening [9].

According to Davies [9], the load-bearing capacity of lightweight sandwich panels

depends directly on the face and core materials, and secondly, on the adhesion

between the faces and the core. In addition to these, load bearing-capacity is

influenced by the structural dimensions and structural system, including the lengths

of spans, the support widths and the fastening system. Strength with respect to failure

modes has to be determined in order to evaluate the load bearing capacity of

sandwich panels. Failure modes includes tensile failure of the faces, wrinkling failure

of the faces (due to compressive stress), shear failure of the core or the adhesion

between the core and face, crushing failure of the face and core at a support, tensile

or shear failure of fasteners [9].

Davies [9] further explains that the compressive skins of lightweight sandwich panels

can exceed the buckling stresses and result in wrinkling failure. Wrinkling failure is a

significant issue in lightweight panels under bending, because most sandwich panel

consist of thin outer skins. This may determine the ultimate strength of a sandwich

panel. Sandwich panel design, therefore, is governed mostly by the compressive

stress capacity of sandwich skins. Sandwich panels can only be used as short span

floor structures because they become slender and deflect excessively when used as

long span panels. Moreover, sandwich panels exhibit de-lamination and wrinkling

failures under flexural loading. As a consequence there is limited use of sandwich

panels in floor plate construction [9].

Flexural performance of sandwich panels, which are comprised of GFRP skins and

ribs along with a PU core, have been investigated as building claddings and floor


panels by Fam et at. [6]. GFRP ribs were used in between the GFRP skins to enhance

strength and stiffness. Static loading test of full scale 2500 mm span sandwich panel.

31.6 kg/m3 density and 75 mm thick PU foam core along with 1.6 mm GRFP skins

were used for the sandwich panels. One panel without ribs and others with various

internal ribs between two skins were prepared. Panels were tested for one-way

bending with a span of 2300 mm. A uniformly distributed load was applied to the

panel as four equally spaced line loads along the span. This loading system

facilitated curvature of the panel during the deformation, whist maintaining the

uniform loads at each contact point. Fam et al. [6] demonstrated that, flexural

strength and stiffness of the panels can be increased substantially by adding GRFP

ribs. Simplified expressions have been proposed to calculate the deflection, including

terms for shear and flexural deflection. Strength of the 2.5m span panel exhibited

equivalent capacity to those of a similar sized reinforced concrete panel. De-

lamination and buckling failure of compressive faces were observed. This was

because of the 1.6 mm GRFP layer in the compressive faces, which was subjected to

buckling under compressive stress. Even though, this sandwich panel utilised ribs to

enhance the stiffness and strength, there could be excessive deflection problems with

longer spans over 3m. Increasing sandwich thickness or material properties may not

result in an economical structure [6].

Large scale sandwich panels (9145 × 2440 × 78 mm) consisting of GFRP skins that

are connected by GFRP ribs and PU core, were investigated for the building cladding

applications by Sharaf et.al [5]. 8220 mm span sandwich panels with central support

were tested to investigate the flexural performance, by applying uniformly

distributed loads using air pressure and equally spaced line loads. Clear span of 4110

mm achieved a 7.5 kPa, but the respective deflection was about 80 mm. Sharaf et.al

[5] concluded that these panels can be effectively used as cladding panels of

buildings. Further, these panels exhibited wrinkling failure of compression faces and

core shear failure at supports at ultimate loading. Although these panels were capable

of achieving approximately 7.5 kPa ultimate loading, such panels cannot be used in

floor construction because of the excessive deflection [5].

Sandwich panels made of glass fiber reinforced polymer skins and modified phenolic

core were investigated for the building floors by Islam et al. [7]. Core density was

850 kg/m3 and the thickness of fiber composite skin was 1.8 mm of the sandwich


panel. One- and two- way behaviour of 450 mm × 950 mm and 15 mm thick panel

was investigated under point and uniformly distributed loads. Point load was applied

into an area of 100 mm × 100 mm at the centre of panels using a hydraulic jack.

Uniformly distributed load was applied to the panel by using high pressure air bags.

Air bags were placed in between large metal pate and sandwich panel and pressure

was increased to apply the distributed load. These panels can be used instead of

timber decking in floor constructions with timber joist. However, long span floor

structures cannot be constructed with this kind of sandwich panels because overall

thickness these panels are 15 mm and can be vulnerable to excessive deflections

under as long spans.

The Sandwich Plate System (SPS) is a composite system, comprising of metal plates

and a high density PU core. Current and potential SPS applications include ship

repair, ship components, maritime overlays, new bridge construction, bridge deck

repair/rehabilitation, grandstand floors, stadium risers, and building floor systems [8,

17]. Braun et al. [8] has conducted static and dynamic tests on a SPS double L

shaped prototype (12.2m span) riser section for a grandstand. They observed good

static and dynamic performance when compared with stiffened steel or pre-stressed

concrete alternatives. Applicability of SPS in bridge construction has been

investigated by Cousins et al. [17]. They observed that SPS could reach its full

plastic capacity in flexure or compression without local buckling of either faceplate.

However, SPS uses thicker steel plates (about 4 to 5 mm) and shorter spans (less than

4 m). SPS have been proposed to be used with steel beams to obtain longer spans

[17]. If SPS is used for long spans without steel beams, local buckling effects may

result. However, a proper study has not been carried out to evaluate the performance

characteristics of SPS in floor structures, especially for long spans. SPS may not be

economical due to the use of two steel face plates in structural flooring.

Sandwich panels comprised of GRFP and a high density balsa wood core have been

investigated under concentrated loads for civil infrastructure and heavy freight

transportation applications by Dawood et al. [10]. This study investigated different

methods to enhance punching shear capacity of the sandwich panels. This study

demonstrated that indentation resistance of sandwich panels depends on sandwich

configuration and core characteristics. Detail study has not been conducted to

http://en.allexperts.com/e/c/co/composite_material.htm


investigate the flexural performance of such sandwich panels and applicability of

floor structures.

Performance characteristics of a sandwich panel comprised of two GRC faces with a

lightweight PU foam core have been investigated for their application in Dome

Shells Structures [11, 19, 20]. Studies demonstrated that this structure combines the

structural qualities of the compound curved shell and the sandwich panel. A typical

Dome Shells Structure includes a diameter of 6-10 m, with 2.1 m vertical walls

rounding to maximum height of 3.2-4.0 m at its centre. Experimental investigations

of full scale (8 m diameter) dome, which is comprised of 6 mm thick inner/outer

layer of GRC and a 55 mm thick PU core sandwich panel, has been carried out. High

structural qualities of the sandwich section and compound curved shell exhibited

very good performance under static and cyclonic wind loading. Furthermore,

excellent thermal and insulation properties were also observed. DomeShell structures

use low density PU core with outer GRC faces. For dome type structures, entire

sandwich sections are subjected to compression stresses [11].

Flexural performance of GRC-PU-GRC, which consist of 52 mm central PU core

and 6 mm GRC outer faces, have been investigated by Gaston et al. [20]. 1200 mm

span 400 mm wide simply supported sandwich panel was tested one way bending by

applying a central line load. The panel did not demonstrate wrinkling or de

lamination failure in the sandwich panel but overall failure resulted due to the tensile

failure of the bottom GRC layer. Therefore, these sandwich panels may not be used

in long span floor construction because GRC cannot undertake higher tensile stress.

However, short span floor panels (1000 mm span) may be achieved using GRC-PU-

GRC panel.

2.1.3 Hybrid composites

Hybrid composite systems are comprised of several materials hybridised to form

composites. Hybrid composite components have been investigated and used

limitedly in infrastructure constructions that are related to civil engineering.

The possibility of a Hybrid-Composite Beam (HCB) ( 9 m span with 750 mm

depth) as a structural member for USA railway bridges was investigated in 2003

[21]. This beam consisted of a fiber-reinforced polymer outer shell, lightweight core,


arch shaped concrete compression reinforcement and carbon, glass or steel tension

reinforcement. Compression arch reinforcement consists of Portland cement

concrete, which was pumped into profiled arch shaped conduit placed along the

beam. Arch was connected to the bottom tensile reinforcement at the end of the

beams and crest of the arch was at the top surface of the beam at mid-span. Tension

reinforcements was laid at the very bottom of the beam and anchored to the

compression reinforcement at the ends. Beam shell and conduit for the compression

reinforcement were fabricated monolithically using vacuum assisted resin transfer

method [21].

An excel worksheet has been used for the development of the HCB, thereby ultimate

moment and shear capacity were determined. Plastic neutral axis depth was

determined, assuming that plane section remains plane and perpendicular to the

plastic neutral axis. It was also assumed that compression reinforcement reaches to

the ultimate capacity under bending whilst all other materials remain elastic range at

this state [21]. Component material's strains were calculated based on the plastic

neutral axis depth and concrete strain (0.003) and stresses were then calculated using

strains.

Fabrication and design of HCB is complex and was investigated as bridge decks.

This kind of system may not be suitable for building floors as slab components have

to be cast separately and only be used as a beam. Arch type compression

reinforcement may not be able to provide for shallow depth beam that may be

required in floor construction.

2.2 IMPORTANCE OF DEVELOPING A HYBRID COMPOSITE FLOOR

PLATE SYSTEM

As explained in the previous section, sandwich panels have been used in civil

engineering applications, such as cladding wall panels, short span floor panels and

roof panels, bridge decks transportation applications and dome-type shell structures.

A hybrid composite beam system has been investigated as structural member for

railway bridges. Sandwich panels can only be used as short span floor structures

because they become slender and deflect excessively when used as long span panels.

Moreover, sandwich panels exhibit de-lamination and wrinkling failures under

flexural loading as shown in Figures 2-2 and 2-3. Thin skin laminates exhibit


buckling failure as they are quite weak under compressive stress [9]. As a

consequence there is a limited use of sandwich panels in floor plate construction.

Despite the potential to use hybrid composites in floor construction to overcome the

limitations of sandwich panels, their applicability in floor plate construction has not

been adequately investigated and developed.

Figure 2-2: De-lamination failure of a sandwich panel [6]

Figure 2-3: Wrinkling failure of sandwich panels [9]

In most of the above sandwich panel applications, PU is used as a lightweight foam

core material because it bonds with the outer faces during the foaming process. [6, 8,

11]. A wide range of properties can be achieved with different densities of PU [13].

Thin steel laminates offers better performance under tensile stress but is subjected to

buckling under compressive stress [9]. In contrast, GRC offers better compressive

properties but is weaker in tension [20]. GRC is lighter in weight than conventional

concrete [12]. There is a higher potential to develop a hybrid system comprising

GRC, PU, and Steel laminates as a structural floor system. However, applicability of

hybridized GRC, PU and steel in structural floors system has not yet been investigated.

This research investigates the strength, serviceability and performance characteristics of

GRC, PU and steel hybrids that can be used in high performance lightweight floor plates

for buildings. Parametric studies will be carried out to develop a new floor plate system,

Hybrid Composite Floor Plate System (HCFPS), and design guidelines.


Proposed HFPS is assembled using component materials as shown in the Figure 2-1.

A low density PU core at the centre results in a lightweight structure. In the hybrid

assembly, individual component materials are combined to offset any weakness and

achieve the optimum performance. A cold formed thin perforated steel laminate is

placed at the bottom of the beam to improve tensile strength. GRC and PU are

configured to attract compressive and shear stress due to their superior performance

under such stresses [12, 14].

Figure 2-1: Hybrid material configuration in HCFPS

It is well understood that there are a number of weaknesses in available composite

applications with the use of GRC PU thin steel laminates. However, in proposed

HCFPS optimum performance is obtained by mobilising the strength characteristics

of the component materials to offset weakness in composite action and thereby

deliver superior performance as illustrated in Figure 2-2.


Figure 2-2: How to optimize the performance HCFPS using component material characteristics

2.3 PROPERTIES AND ADVANTAGES OF SELECTED MATERIALS

FOR HCFPS

GRC, PU and Steel are the component materials selected to develop HCFPS.

Properties of these materials will be discussed in this section.

2.3.1 Steel

Perforated steel laminate is used as tensile reinforcement to the HCFPS. Cold formed

steel facing have been used extensively as a outer facing of sandwich construction

applications [9, 18]. However, in such sandwich panels load bearing capacity is

usually determined by wrinkling in compression face and shear failure of the core

rather than yielding of the tensile face [9]. Thin steel sheets exhibit poor performance

under compressive stress but better performance under tensile stress in sandwich

constriction applications. Therefore, steel laminate is configured in the tensile zone

Weakness of component materials in available

applications

Tensile failure of GRC sheets

Wrinkling failure of thin steel laminates

Shear failure of PU core

Crushing failure of the core at the

supports

How to eliminate the weakness and combine the

positive inherant properties in HCFPS

Supplement with steel laminate as a reinforcement in tensile zone

Use GRC layes and PU core for

compression zone as GRC-PU-GRC sandwich panel

Combine GRC and PU to

improve shear strength in shear

zones

Supplement with GRC fill at

support regions to replace PU core


of the HCFPS and it is embedded in the GRC layer. Perforated steel laminate can be

used in order to enhance the bonding between GRC and steel laminate.

Mechanical properties

Available properties of mild steel and high strength steel plates are listed in Table

2.1. Typical stress-strain behaviour of high strength steel is shown in Figure 2-3.

Table 2-1: Typical values of steel properties [22]

Name Density

Kg/m3

Young's

Modulus

GPa

Shear

Modulus

GPa

Shear

Strength

MPa

Tensile

strength

MPa

Poisson'

s ratio

MPa

Mild Steel

High Strength Steel

7800

7800

210

210

80

80

105

230

210

550

0.3

0.3

Figure 2-3: Stress strain behaviour of high tensile steel of three similar specimens [22]

Environmental impact

The steel sheet can be protected from corrosion using a layer such as zinc or zinc-

aluminium. The metal layer is then protected with an organic (plastic) layer.

However, corrosion protection is not essential as the steel laminate is embedded in

GRC layer in HCFPS. Steel can be recycled and reused.


2.3.2 Polyurethane (PU)

PU foam has been selected as the core material of HCFPS. It has been used as a core

material in sandwich construction with steel plates to fulfil both insulating and

structural requirements [23]. PU is a substance categorized as a polymer based on

its chemical structure. It is manufactured by combining a polyol, isocyanate, a

blowing agent and an activator through a controlled chemical reaction as a liquid

form [9, 24]. Liquid foam starts to expand rapidly and harden after 3-6 minutes of

mixing. During the process, PU adheres to the face material [9].

Mechanical properties

PU can be formulated and processed into foams of varying densities. The foams are

identified either as flexible or rigid with the density ranging from as little as 16 kg/m3

to as much as 1240 kg/m3 [14, 24]. As a consequence mechanical properties vary

over this density range.

Sharma et al [14] have investigated the relationship between mechanical properties

and density of PU (density range 35 kg/m3 to 1200 kg/m

3). The relationship between

Elastic modulus (E), Shear modulus ), Shear strength (τ) and compressive (Xc)

strength with the density (ρ) is given in following equations [14, 25].

Equation 2-1

Equation 2-2

Equation 2-3

Equation 2-4

In above equations properties of solid PU: Density (ρs) is 1200 kg/m3, Elastic

modulus ( ) = 1.6 GPa, Shear modulus ( ) = 640 MPa, Shear strength = 38

MPa and Compressive strength ( ) = 127 MPa [14].

http://www.wisegeek.com/what-are-polymers.htm

http://www.wisegeek.com/what-is-a-chemical.htm


Compressive and tensile strength of PU foam increase with density [6, 23].

However, tensile strength and compressive strength are marginally similar for lower

densities. Table 2-1 summarise the properties of PU with deferent densities.

Table 2-2: Typical values of PU properties [14, 25]

Density

Young's

Modulus

MPa

Shear

Modulus

MPa

Compressive

Strength

MPa

Shear

Strength

MPa

Tensile

strength

MPa

Poisson's

ratio

MPa

44

64

100

200

300

500

1.2

10.9

23.4

76.1

151.6

361.2

1.5

2.5

5.7

21.2

45.9

121.3

0.125

0.412

0.743

2.415

4.800

11.50

0.172

0.426

0.556

1.807

3.600

8.580

0.150

0.340

1.000

-

-

-

0.3

0.3

0.3

0.3

0.3

0.3

Vibration and sound damping

PU can be used as a sound and vibration damping material because of the glass

transition property. Damping property is enhanced as PU can be deformed repeatedly

and still maintain its original shape [24]. Experimental investigation conducted on a

12 m long SPS grandstand double riser unit with a 32mm PU core and 3.8 mm face

plates, showed good dynamic performance with 2.1% damping ratio [8]. The

damping ratio would be 1% for steel or pre stressed concrete structures of similar

span[8]. This improvement was obtained using a very thin PU layer. Transmission

loss of PU is significant when it is used as core material and can be used in noise

reduction [26]. Yoon et al. [26] has observed marginal transmission loss for

sandwich panel, which is comprised of steel outer sheet and PU core. Hence PU can

be used as a core material in HCFPS not only to improve the damping properties but

also to reduce noise due to human walking.


PU has low environmental impact because it is inert and non toxic and can be

recycled [27]. PU can be successfully recycled to usable formats. There are various

methods that are currently used, such as mechanical recycling, chemical processing,

thermo chemical processing, and energy recovery [28]. PU is derived from oil and


has a recoverable energy value that, in some cases, can be comparable to coal and

slightly less than fuel oil [28].

2.3.3 Glass fiber Reinforced Cement/Concrete (GRC)

GRC have been selected as the outer shell material of the HCFPS. GRC is a

composite material consisting of ordinary Portland cement, Silica sand and water that

is mixed with alkali-resistant glass fibers [29]. The percentage, arrangement and

method of application of Glass fiber can be engineered to suit a wide range of

applications. The advantage of glass fiber is for carrying the tensile force, thus

overcoming the main disadvantage of cement, which has low tensile strength. Spray

and premix are the two methods that have so far been developed for the fabrication

of GRC components.

The method of premix

Constituents (mortar and pre-cut glass fiber) are mixed together into a paste in this

processes and cast by pressing, concreting and vibration [12, 30]. Fiber content of

3.5-4% in total weight is used for this process to facilitate workability and

compaction [12, 31].

Method of spray

Mortar paste and chopped glass fiber are simultaneously deposited from dual spray-

heads into suitable moulds in this process. This method currently account for a large

percentage of GRC production. Three ways of spraying GRC can be seen; manual

spray, mechanized spray and spray-dewater process [30]. Pre-cut glass fiber is

between 25 mm and 40 mm in length and contain about 5% of the total weight of the

mix [12].

Mechanical and Material properties of GRC

Mechanical properties of the GRC varies according to the production method and the

percentage of fiber present in the mix [29, 30]. Table 2-2 presents mechanical

properties for GRC that are cast using two mixing methods. Optimum of glass fiber

content is 5% for spray up method and 3.5% for premix method in total weight [29,

32, 33]


It has been shown that the addition of a polymer to GRC improves the performance

and mechanical properties [34]. Improvement in bending strength and ultimate

tensile strength is marginal for polymer modified GRC compared to normal GRC.

Furthermore, polymer addition substantially increases the durability under natural

weather conditions [34].

Table 2-3: Typical values of GRC properties [29, 32, 33]

Mechanical Property GRC

spray up

GRC

premix

Dry density (kN/m3) 19-21 18-20

Compressive strength (MPa) 50-80 40-60

Young modulus (GPa) 10-20 13-18

Poisson ratio 0.24 0.24

Tension

Ultimate tensile strength (MPa)

Shear

8-11

4-7

Inter lamina shear strength (MPa)

In plane shear strength (MPa)

Bending

Ultimate strength (modulus of rupture) (MPa)

Elastic limit (limit proportionality) (MPa)

3-5

8-11

20-30

7-11

N.A

4-7

10-14

5-8

In the methods explained above, chopped glass fibers are added to the mix and

therefore, fiber arrangement in the matrix is random. Although GRC shows tensile

strength values between 4 to 11 MPa, it provides much better performance under

compression. Ferreira [12] showed that GRC provides greater ductility under

compression when compared with plain mortar.


Environmental impact of GRC is less than that of reinforced concrete [32]. The main

constituents of GRC are based on naturally occurring earth oxides such as silica

sand, Portland cement and glass fibers. Course aggregates are not a constituent of

GRC because it is manufactured as thin layers (6 mm -15 mm). GRC has reduced

cement and aggregate usage than reinforced concrete [32]. As a consequence GRC is

lightweight and has lower embedded energy. GRC can be recycled using lower

energy at the cessation of use.


2.4 SUMMARY AND IMPLICATIONS

This chapter has discussed the currently available lightweight sandwich and hybrid

composite applications in civil engineering construction using current literature.

Their properties were reviewed to find limitations to their use in structural floor plate

construction. Reasons and the importance of developing a Hybrid Composite Floor

Plate System (HCFPS) were discussed considering those limitations of current

composite applications. Properties of materials that are selected to develop HCFPS

were also discussed. The followings conclusions and arguments are made following

the literature review.

Sandwich panels, which are comprised of thin outer shell and central core, have been

studied and used in wall panels, short span floor panels and roof panels, bridge decks

and dome-type shell structures. A hybrid composite beam has been investigated as

structural member for railway bridges. Sandwich panels can only be used as short

span floor structures, because they become slender and deflect excessively when

used as long span panels. They exhibit de-lamination and wrinkling failures under

flexural loading as thin skin laminates are weaker under compressive stress.

Although hybrid composites may be used in floor construction to overcome the

limitation of sandwich panels, it has not yet been investigated.

GRC, PU and steel have been extensively investigated in sandwich construction

applications. However, applicability of hybridized GRC, PU and steel in structural

floors system has not yet been investigated. This research investigates the strength,

serviceability and performance characteristics HCFPS using GRC, PU and steel, to

develop a lightweight floor plates for buildings.

GRC, PU and steel laminates exhibit a number of weaknesses in available composite

applications. However, in proposed HCFPS optimum performance is obtained by

mobilising the strength characteristics of the component materials to offset

weaknesses in proper hybrid configuration and thereby obtain optimum performance.

Properties of steel, PU and GRC have been well investigated separately and that data

can be used to investigate performance characteristics of hybridized GRC, PU and

steel laminate.


Steel, GRC and PU can be recycled to usable formats. Therefore, HCFPS can be

developed as an environmentally friendly structure, which can also be recycled at the

cessation of use.


Chapter 3: Methodology 27

Chapter 3: Methodology

This chapter describes research methodology and the various stages through which

the HCFPS was developed. It also makes references to appropriate codes or

standards and literature used in development.

3.1 HCFPS DEVELOPMENT

This research developed a Hybrid Composite Floor Plate System (HCFPS) using

steel, Polyurethane (PU) and Glass-fiber Reinforced Cement (GRC) according to the

following stages. In first stage, configuration of the HCFPS using component

materials was determined as explained in Sections 1.2 and 2.2. In second stage,

experimental testing of HCFPS panels was conducted to investigate static, dynamic,

cyclic loading and post yield behaviours, mode of failure and ductility. Component

material testing was also conducted to obtain their properties. FE models were

developed and validated using test results generated from experimental testing. In

third stage, parametric studies were performed and HCFPS were developed to satisfy

static performance requirements. FE techniques were used to study the influence of

parameters such as sectional configuration, spans, loading limits and support

condition. The vibration characteristics of HCFPS under human-induced loads were

investigated in the next stage and the required improvements for an optimum design

that satisfy both static and dynamic design criteria were determined. Finally,

guidelines were developed for the design of HCFPS panels.

3.2 HCFPS CONFIGURATION AND SYMMETRY

The proposed HCFPS was assembled using component materials as shown in Figure

3-1. The width of the HCFPS was limited to 2 m to suit prefabrication and

transportation requirements, however it can be varied if necessary. Length of the

HCFPS can be varied by changing the material properties and sectional

configuration. HCFPS, which uses a steel beam column frame system to support it,

can be graphically represented in a building floor as depicted in Figure 3-2. Joint

details between adjacent HCFPS panels and connection methods for supporting

beams will be described Chapter 6, Section 6.8.2.

28 Chapter 3: Methodology

Figure 3-1: Proposed HCFPS panel configuration and symmetry

Figure 3-2: Graphical representation of building floor using HCFPS panels

A half of the HCFPS section can be investigated for the research studies as shown in

Figure 3-1 as the panel is symmetrical and hence results for section with a single

beam are applicable to capture the behaviour of proposed HCFPS panel

configuration with double beams. Therefore, a HCFPS panel with a single beam was

used for the purpose of static and dynamic experimental investigations and computer

model validation. Moreover, experimental testing on HCFPS panel with single beam

was more economical and efficient. Validated FE model was used for the parametric

studies to investigate static and dynamic performance characteristics. Single beam

HCFPS section used for all static performance investigations is adequate as static

behaviour of HCFPS floor panel with multiple beams will be similar. However,

dynamic behaviour of single beam HCFPS could vary from the HCFPS floor panel

with multiple beams due to the change in model mass. Nevertheless, validated FE

model for the single beam HCFPS panel was extended to investigate overall dynamic

Symmetry axis

HCFPS Floor

Steel beams and

columns


behaviour of proposed HCFPS configuration with two beams (refer to Figure 3-1)

and building floors using HCFPS panels (refer to Figure 3-2).

3.3 EXPERIMENTAL TESTING

3.3.1 Test Panel

Experimental investigations were conducted on three 3200 mm span HCFPS panel

with single beam as shown in Figure 3-3a. Span and section configuration were

determined by a preliminary FE analysis. Manual casting procedure was used to cast

the test panel and the beam was tapered (Figure 3-3(a)) to facilitate the casting

process. The PU core was replaced with a 100 mm GRC in the vicinity of the

supports, as shown in Figure 3-3(b). Perforated steel laminate was used to enhance

the bonding between GRC and steel laminate.

(a) Section dimensions

(b) GRC fill replacing PU core near supports

Figure 3-3: 3200 mm span HCFPS test panel configuration


3.3.2 Heel impact test

The heel impact test is a widely used test to investigate the dynamic behaviour of

floors. A person of average weight stands at the centre span of the structure, and to

raise their feet onto their toes approximately 50 mm off the surface and makes a

sudden impact with their heels [22]. This creates a sudden impact force on the floor.

The floor acceleration response is recorded in order to calculate the natural

frequencies and the damping coefficient.

Heel impact tests were performed on all three test panels and an average person (70

kg) was asked to create the heel impact [22] in this study. A 5g accelerometer was

used at mid-span to acquire the vibration response (as time acceleration plots).

Equation 3-1 presented by Ellis [35] was used to calculate the damping coefficient

(ς) from the time- acceleration plots. In this equation, A0 and An are the amplitudes

of ―n‖ successive peaks of the acceleration-time response plot (refer to Figure 3-4).

Damping obtained from this equation is termed ―log decrement damping‖. Murray

[36] stated that model damping, or true damping, is one-half to two-thirds of the

value of the log decrement damping. The first natural frequency of the test floor

panels was calculated by performing a Fast Fourier Transformation (FFT) analysis

for acceleration plots [22, 37, 38].

n

oe

A

A

nlog

2

1

Equation 3-1

Figure 3-4: A typical acceleration response [35]


3.3.3 Static load test

Static loading tests were carried out in order to obtain the load deflection curve to

calibrate the finite element model. Failure modes and ductility of the specimen were

investigated under static loading. Static loading test of the HCFPS panel was

performed according to the loading arrangement shown in Figure 3-5 (a and b). Two

test panels were tested under static loads. Steel plates 10 mm thick and 100 mm

wide, were placed under the slab and beam at the supports, and the plates were

supported by solid circular steel bars, as shown in Figure 3-5(b). Adjustable jacks

were used to support the steel bar under the slab as seen in Figure 3-5(c).

(b) Longitudinal view of loading arrangement supporting method

(c) Side view of the supporting arrangement

Figure 3-5: Static load test arrangement

(a)Loading arrangement


Loads were applied as four line loads along the span using steel spreader beams

through an arrangement shown in Figure 3-5(a). This arrangement was adequate to

simulate a uniformly distributed load (within the means of our testing facilities).

Furthermore, it enabled curvature of the panel during loading, whilst maintaining

uniform loads at the contact locations, similar to the test set up in [15]. Linear-

variation-displacement-transducers (LVDTs), with 0.01 mm sensitivity, were placed

at centre of span to measure deflections. Details of test procedure and

instrumentation will be discussed in Chapter 4.

3.3.4 Cyclic loading test

Cyclic loading test for one HCFPS test panel was conducted according to the

method given in [39]. This method can be adopted to evaluate the performance of

slabs comprised of new materials. The same loading and supporting arrangement that

was used for the static loading test was used for the cyclic loading test. Tests were

conducted using a hydraulic loading system, consisting of a displacement controlled

Moog actuator to control the cyclic loading. Six loading cycles were conducted as

shown in Figure 3-6. Applied load at 50% of the ultimate load (Lus) for the first two

cycles, 75 % (Lus) for next two cycles and 100% (Lus) for the final two cycles was

applied. Ultimate load (Lus) of HCFPS test panel was determined by the static load

testing. Duration of loading steps was maintained throughout the cyclic loading test,

as shown in Figure 3-6. A minimum of 10% of Lus was maintained during the

unloading. Deviation from linearity and Repeatability [39] for the HCFPS test panels

were calculated as explained below and results will be presented in Chapter 4.

Figure 3-6 Load cycles and steps of loading for cyclic loading test [39]


Deviation from linearity

Typical load-deflection results for cyclic load test are shown in Figure 3-7. Deviation

from linearity is a measure of non-linear behaviour of the tested member. Acceptable

value should be less than 25%. and this is calculated using Figure 3-7 and Equation

3-2 [39].

Figure 3-7: A typical load-deflection curve for six load cycles [39]

Equation 3-2

Equation 3-3

Repeatability

Repeatability of deflection is the ratio of deference between maximum and residual

deflections for a set of two identical cycles. Repeatability of the member deflection

can be calculated using Equation 3-4 and Figure 3-8 [39]. Repeatability is calculated

for the three sets of similar cycles. If the repeatability is greater than 95% it is

considered acceptable [39].


Figure 3-8: Parameters to calculate the Repeatability [39]

Equation 3-4

where: is the maximum deflection in Cycle B under a load of Pmax,

is the

residual deflection after Cycle B under a load of Pmin,

is the maximum

deflection in Cycle A under a load of Pmax, and is the residual deflection after

Cycle A under a load of Pmin.

3.3.5 Material testing

Mechanical properties of the materials used in the test panels were determined

separately by conducting a comprehensive material testing program. Standard testing

methods given in ASTM, ISO and Australian Standards (AS) were used as shown in

the Table 3-1. Only a tensile test was conducted for the steel laminate, as steel

laminate in the test panel acts as reinforcement and therefore is subjected to tensile

stress. Test samples and testing instruments were selected according to standard test

methods. Detailed testing procedure and instrumentation will be discussed in Chapter

4.


Table 3-1: standard test methods for material property investigation

GRC PU Steel

Tensile Strength

Tensile modulus

Flexural Strength

Flexural Modulus

Compressive strength

Compressive modulus

ASTM D 3039 [40]

ASTM D 3039 [40]

ASTM C 947 [41]

ASTM C 947 [41]

AS 1012.9 [42]

AS 1012.9 [42]

ISO 1926 [43]

ISO 1926 [43]

ASTM D 790 [44]

ASTM D 790 [44]

ASTM C 365 [45]

ASTM C 365 [45]

AS 1391 [46]

AS 1391 [46]

-

-

-

-

3.4 FINITE ELEMENT (FE) METHOD OF ANALYSIS

FE analysis was used extensively in this research to simulate HCFPS behaviour and

thus investigate its performance characteristics. It is a cost- and time-efficient

method compared with physical experiments. FE simulations have been extensively

used for studies with the support of limited experimental testing.

The commercially available finite element program ABAQUS 6.9-1, (Dassault

Systèmes Simulia Corp. [47]) was used in this research project with ABAQUS CAE

as the pre- and post-processor for the FE simulations [47]. ABAQUS involves the

following three major phases.

3.4.1 Pre-processing

Using ABAQUS CAE pre-processing of the FE models was conducted. At this stage,

FE models were simulated by defining an appropriate finite element mesh, assigning

suitable material properties and applying boundary conditions (restraint or

constraints) and loads. An input file (.inp) was then prepared to submit for analysis.

3.4.2 Analysis and solutions

Analyses of the input files were conducted using ABAQUS 6.9-1, which is installed

in the High Performance Computing (HPC) facility in QUT. HPC consists of a 400

processor SGI Altix XE Cluster with 960 GB memory.

Post-processing

Analysis &

Solutions

Pre-processing


In this phase, the submitted input data is assembled into matrix format and the

numerical analysis is executed. The matrix assembly process of a multi-degree of

freedom system is governed by Equation 3-5.

tFxKxCxM Equation 3-5

In above equation, )(tF is the applied load vector, [M] is the mass matrix, [C] is the

structural damping matrix, [K] is the stiffness matrix, }{x is the displacement vector,

}{x is the velocity vector ))(( dttdxx and }{x

is the acceleration vector

))(( 22 dttxdx .

The element type and material properties are used to define the mass matrix [M],

structural damping matrix [C] and stiffness matrix [K]. Damping matrix was derived

using Reyleigh proportional damping method as a combination of the mass and

stiffness matrices [22]. Acceleration vector }{x , velocity vector }{x and

displacement vector }{x are developed based on the boundary conditions. Applied

external loads on the system are used to define the applied load vector )(tF .

In the analysis and solution phase, the above equation is analysed using displacement

method or stiffness method and solved for displacement and stresses of the system.

In ABAQUS analysis, the output was obtained as a result file (.odb).

3.4.3 Post-processing

Post-processing analysis of output files (.odb) was conducted using ABAQUS CAE

graphically and numerically to interpret the results.

3.5 FE MODEL VALIDATION

A Finite element model of the experimentally tested HCFPS was developed for the

experimentally tested panel. This model was validated with static and dynamic

experimental results. Load-deflection behaviour, first natural frequency and

acceleration response were used for validation and detailed procedure will be

presented in Chapter 5.


3.6 STATIC PERFORMANCE AND PARAMETRIC STUDIES

The validated model was further developed using FE techniques in order to

investigate static performance characteristics of HCFPS by conducting parametric

studies. Sectional configuration, material properties and span lengths were used as

variable parameters in this study. First, sectional configurations were determined for

different spans (3m to 7.5m) for two loading conditions as given in Table 3-2.

Superimposed dead load, which gives a total of 1.0 kPa, is summarised in Table 3-5

[48]. This value may be increased up to 2.0 kPa in residential buildings due to a

higher density of partition walls and heavier floor finishes. In the present study, a

uniform superimposed dead load of 1.0 kPa was for parametric studies, which is

likely to be present on this floor system according to Table 3-3. However, analysis

results will demonstrate that higher super imposed load can also be incorporated

easily for this floor system as required.

Table 3-2: Loading cases [48]

Floor Type Gk Dead Load (kPa)

(Fixed partition and finishes) Qk Live Load (kPa)

Residential Self-weight +1.0 1.5

Offices or work areas Self-weight +1.0 3

Table 3-3: Super imposed permanent dead loads for an office floor

Type of loading Load, kPa

Floor finishes acoucstic insulation + cladding

Suspended ceiling

Suspended services

Lightweight partition, furniture and equipments

Fire protection

0.25

0.10

0.15

0.35

0.15

Flexural and shear stresses and deflection limits were investigated as the

performance characteristics to obtain the optimum configuration. Ductility and creep

and shrinkage deformation of the HCFPS were also evaluated for HCFPS.

Calculation procedure for the design of HCFPS was determined. This process will

be presented in Chapter 6.


3.7 DYNAMIC ANALYSIS OF HCFPS

Developed HCFPS configurations, which satisfy static performance, were analysed

under human induced loads. Serviceability and comfort criteria given in current

design standards and research outcomes were used to evaluate the dynamic

performance of HCFPS. Lightweight HCFPS can be excited under human induced

loads and should be designed to comply with the comfort and serviceability

requirements for human perception. International codes, which define vibration

response limits and the method used to evaluate the dynamic performance are

discussed in this section.

3.7.1 Human induced walking loads

During any human activity, force is repeatedly applied to the floor causing a dynamic

excitation in the floor. A typical pattern of a human induced force - time history is

shown in Figure 3-9.

A number of research studies have been conducted by Bachmann et al.[49], Allen et

al. [50], Maguire et al. [51], Ginty et al. [52], Simith [53], and Ellis et al. [54] to

obtain numerical formulae to express human induced dynamic forces. ISO 10137

(2007) [55], Ellis et al.[54] and Smith et al. [56] provides the latest numerical

expressions (Refer to Equation 3-6) to find vertical dynamic loads resulting from

various human induced actions, such as walking , running and jumping. Idealised

load model given by Equation 3-6 closely matches with the dynamic load resulted

from the actual human loads, which demonstrates in Figure 3-9. Hence, this load

model was selected to use in this research for define walking loads on the HCFPS

panel in FE analyses.

Figure 3-9: Dynamic vertical force due to walking step by a person [57].


Equation 3-6

In above equuation, F(t) is the dynamic force, Q is the static weight of the

participating person, n is the Fourier coefficient corresponding to nth

harmonic, fp

is the pacing frequency, t is the time and υn is the phase angle of the nth

harmonic, n

is the integer designating harmonic of the fundamental and k is the number of

harmonics that characterise the forcing function in the frequency range of interest.

Q should be to be taken as 746 N according to [56]. Bachmann et al. [49] suggested

different values of fp for various pacing of walking. Numerical coefficients for those

paces can be found in ISO 10137 [55] as shown in Table 3-4. It is suggested in [55]

to use phase shift of 900 for the harmonics in order to obtain conservative results.

The above explained parameters are for evaluating dynamic load due to a single

person. However, dynamic response of a floor structure due to a walking crowd is

normally is similar to the individual effect as Ellis [58] observed similar acceleration

levels due to a single person walking and group of people walking. This is mainly

because of the un-coordinated nature of walking human activities [55, 58] and weight

of passive people increasing the effective model mass. ISO 10137 (2007) [55]

suggests a coordination factor to incorporate the dynamic crowd effect. In this

method, dynamic load due to the walking group can be represented by applying a

coordination factor C(N) to the forcing function (refer to equation 3-7).

Table 3-4: Design parameters for walking and running loads [49, 55]

Mode of walking fp (Hz) Numerical coefficient for 1st four harmonics

1 2 3 4

Slow Walk

Normal Walk

Fast Walk

Running

1.7

2.0

2.4

3.0

0.26

0.37

0.52

1.40

0.1

0.1

0.1

0.4

0.06

0.06

0.06

0.10

0.06

0.06

0.06

-

)().()( NCtFtF N Equation 3-7

For example, if the movements of a group of people are un-coordinated, the

coordination factor becomes:


NNNC /)( Equation 3-8

Where N is the number of participants

3.7.2 Dynamic analysis and floor classification

Modal frequency

Modal frequency of HCFPS can be determined by free vibration analysis using FE

techniques. Additionally, simplified analytical methods suggested in the literature

(refer to Equation 3-9) can also be used. However, such methods are applicable only

for beams. Therefore, an adjusted equivalent beam section for HCFPS panel can be

used, but this method will be approximate compared to FE techniques.

32 mL

EIKf n

n

Equation 3-9

In Equation 3-9, EI is dynamic flexural rigidity of the member, m is the effective

mass, L is the span of the member and nK is a constant representing support.

High frequency and low frequency floors

HCFPS is a floor system associated with a lower mass and as a consequence, the first

natural frequency of the system is higher and thus categorised as a high frequency

floor. High frequency floors are defined as floors having a first natural frequency of

10 Hz which is greater than the fourth harmonic of the walking frequency (maximum

of 2.5 Hz) [56]. Preliminary FE studies shows that HCFPS gave a first natural

frequency greater than 10 Hz. As a consequence, HCFPS does not exhibit resonance

vibration due to human activities. Load due to walking in high frequency floors, acts

as an impulsive force, which diminishes before the next step [56].

Steady state and transient state

Response of a floor structure can be categorised as either a transient or steady state

response. Steady state response occurs once the waveform settles down in the

structure. Transient response is when the response of the floor occurs before the

steady state. Resonance can occur with a higher vibration response in low frequency

floors. In contrast, in high frequency floors the transient response is more significant

than the steady state response as resonance cannot occur and applied forces behave


like a series of impulses [56]. Therefore, transient response of the HCFPS is used to

assess the required human perception limits.

Vibration response

Response of a floor structure is measured in terms of acceleration and [55, 56, 59,

60] provides acceleration limits to satisfy human perception. The two values to

represent present the acceleration of a system are peak acceleration and Root-Mean-

Square (RMS) acceleration. Peak acceleration is the highest value of acceleration

resulting from an excitation. Peak acceleration cannot give an indication as to the

duration of time that the floor is subjected to the peak acceleration value. In contrast,

RMS acceleration is an average measurement of the acceleration time -history as

shown in the Equation 3-10. Smith et al. [56] stated that sharp peaks of acceleration

are less significant with lower RMS acceleration. Acceleration time-history can be

obtained from the dynamic FE analysis of the HCFPS and is used to calculate RMS

acceleration.

Equation 3-10

In Equation 3-10: T is the period under consideration, a(t) is the acceleration function

and t is the time.

3.7.3 Acceptance criteria

RMS acceleration limits

ISO 10137 [55] and BS 6472 [60] provide base values of RMS accelerations in

relation to a base curve, which is frequency weighted, to assess human response to

vibration. Moreover, a series of multiplying factors is also presented to adjust the

base curve to suit various environments in which the floors are used. Frequency

weighting factor is used as human perception to vibration varies with frequency [56].

The frequency weighted RMS acceleration base curve for the vertical direction

vibration is presented in Figure 3-10. RMS acceleration values above the curve are

perceptible for humans and values below the curve are imperceptible and do not

cause vibration problems. The base value of RMS acceleration is 5 × 10-3

m/s2 and

because of the frequency weighting, acceptable base value increases for the lower

and higher frequencies as shown in the figure.


Figure 3-10: Frequency weighted RMS acceleration base curve [55]

Response Factor (R)

This base curve is not used directly in practical applications and rather the evaluation

method suggested is the Response factor (R) method. The R of a floor is the ratio

between calculated or measured frequency weighted RMS acceleration ( and

base acceleration value [56].

Equation 3-11

Acceptable R values are suggested for floors depending on their use in [56]. HCFPS

is expected to be used in residential and commercial floors. Hence, response factors

suggested in Table 3-5 were used for dynamic evaluation of HCFPS.

Table 3-5: Recommended response factors [56]

Place Response factor

Residential

Offices

Workshops

Shopping malls

Day

Night

Day

Night

Day

Night

Day

Night

2-4

1.4

4-8

4-8

8

8

4

4


Vibration Dose Value (VDV)

Primarily, R values are determined by considering the continuous vibration of a

floor. In this context, human induced excitation has to be applied as a continuous

load to the floor by using the load model suggested in Equation 3-6. This will give

the worst possible loading scenario and response. If the RMS acceleration calculated

from this method gives a R value less than the values in Table 3-5, the floor vibration

is acceptable. However, continuous loading and vibration are uncommon and human

induced walking loads are intermittent [56]. Therefore, it is suggested to consider the

intermittent nature of the vibrations if the calculated R value is higher than

acceptable values.

In the process of vibration assessment cumulative measure of vibration response for

intermittent activities is more reliable and needs to be used for determining

perceptible levels. ISO 10137 [55] and BS 6472 [60] provide perceptive tolerance

levels for the intermittent vibrations using Vibration Dose Value (VDV ) and can be

calculated using Equation 3-12. Where, is the frequency weighted acceleration

and T is the to total period of the day during which vibration may occur [60] .

Acceptable VDV values suggested in BS 6472 [60] are shown in Table 3-6 for the

probable adverse effect.

Equation 3-12

Table 3-6: VDV values (m/s1.75

) for vertical direction vibrations [60]

Place Low probability of

adverse comment Adverse comment possible

Buildings 16h day

Buildings 8h night

0.2 - 0.4

0.13

0.4-0.8

0.26

Ellis [61] suggests a method (refer to Equation 3-14) to calculate VDV values of a

walking activity by using the in the design stage of floors and this method

was used in this study. Where, na is the number of time the activity will take place in

the exposure period and Ta is the duration of an activity (time taken to walk along the

floor)

Equation 3-13


Suggested VDV values can be substituted in Equation 3-14 by rearranging Equation

3-13 and thus calculate the number of occurrences (na) for evaluation purposes. The

number of occurrences (na) for that activity can then be evaluated depending on the

floor use. If na is unlikely to occur in service, floor will not exceed to threshold VDV

value. In this way the dynamic performance of HCFPS floor was evaluated for use in

office and residential floors. Dynamic evaluation of HCFPS panels will be presented

Chapter 7.

Equation 3-14

3.7.4 Damping

All physical systems have some inherent damping. Damping can be either external or

internal. The material or contact areas within structures such as bearings and joints,

are classified as internal damping materials. External contacts, such as non-structural

elements, are classified as external damping materials. In a floor structure, not only

the components of the structural system but also the non-structural components such

as finishes, partitions and standing objects play a major role in providing damping.

The amount of damping in a structure is determined by a damping ratio. Damping of

floors can greatly decrease the response of a structure driven at a resonant

frequency[62]. However, HCFPS may not give resonant response at a high frequency

due to human induced loads, and impulsive response might be reduced with the

damping.

There are a number of damping levels reported in the literature for different

structural types. In general, damping for bare composite floors is reported to be

between 1.5% - 1.8% [63, 64]. However, use of partitions on the finished floor

system may provide higher damping for the floor. Murray [36] identified a mild

damping level of 3% for an office without permanent partitions. Higher damping

could also arise in a floor with permanent, drywall partitions and this may be as

much as 5% - 6% [36]. Elnimeiri et al.[65] also recommended a damping coefficient

of 4.5% - 6% for finished floors with partitions. Moreover, Brownjohn [66] showed

that damping could increase to 10% depending on the position of items such as

cabinets, bookcases and desks. On the other hand, Sachse [67] proved that the

presence of stationary humans will increase the damping of the structure up to 12%.


Different damping arrangements have been considered within the literature to

prevent large vibration responses. Ljunggren [68] used resilient ceiling connected to

a lightweight floor by a visco elastic material and found a more substantial effect on

damping than the floor itself. Further, Visco-Elastic (VE) dampers can be used

effectively to prevent higher serviceability displacement and acceleration in steel

deck composite floors [22].

Damping characteristics of a sandwich structure can be enhanced by the

polyurethane core. Experimental investigation conducted on a 12 m long SPS

grandstand double riser unit with of 32 mm PU core and 3.8 mm face plates, showed

good dynamic performance with 2.1% damping ratio as given in reference [8]. The

damping ratio would be 1% for steel or pre stressed concrete structures of similar

span[8]. This improvement was obtained using a thin PU core. Thicker PU core of

the HCFPS enhances damping properties.

Damping in the floor structure is difficult to determine and only approximate values

can be provided depending on the floor type and external damping. However, by

using partition and ceiling, external damping can be increased by about 2%

according to the above literature. The inherent damping properties of HFPS were

investigated using experimental studies and external damping due to partition was

considered as 2% for parametric studies.

3.8 DYNAMIC PERFORMANCE AND PARAMETRIC STUDIES OF

HCFPS

Dynamic performance characteristics were investigated for the HCFPS sections,

which had met static performance requirements, using FE techniques as explained in

Section 3.7. RMS acceleration, Response factor (R) and VDV were used as dynamic

performance assessment measurements. Parametric studies were conducted to

investigate the influence parameters on acceleration response and VDV values.

Dynamic evaluation of HCFPS panels will be presented Chapter 7.

3.9 DESIGN GUIDELINES

Guidelines were developed to design the HCFPS system. Thickness of hybrid

components, density of PU, sectional configurations and loading were considered as

the variables to obtained optimum section for particular span. Design calculation


procedure was developed as a design tool. Design guidelines and manufacturing and

installation guidance of prefabricated HCFPS panels will be presented Chapter 8.

3.10 SUMMARY

HCFPS was developed in stages as described in this section. The entire process is

illustrated in the flow chart in Figure 3-11.

Figure 3-11 Development stages of HCFPS

Dtermination of proper configuration for HCFPS using componenet materials

Experimental testing and FE model development and validation for static and dynamic performance

Development of HCFPS to satisfy static performance by condcting paramertric studies using validated FE techniques

Dynamic performance evaluation of HCFPS using validated FE techniques

Development of design gudelines

Chapter 4: Experimental Testing 47

Chapter 4: Experimental Testing

This chapter presents the experimental investigations conducted on 3200 mm span

HCFPS panels and GRC-PU-GRC composite panels, which is top slab of HCFPS.

Material property investigation, fabrication of test panels, test setup, instrumentation

and experimental results are presented.

4.1 MATERIAL PROPERTY INVESTIGATION

A comprehensive test program was carried out to determine the material properties

of the component materials (GRC, PU and steel) used to manufacture HCFPS test

specimens. Both PU and GRC were tested in tension, compression and bending,

whilst the steel sheet was tested in tension. This section presents the details of the

experimental test program and results.

4.1.1 Formulation of GRC

GRC is a cementitious matrix, comprising of cement, sand, water, admixtures and

short-length alkali-resistant glass fibers [31]. All GRC samples were cast using a pre-

mix production method and the formulation of the constituent materials is given in

Table 4-1.

Table 4-1: Formulation of GRC

Constituent materials Percentage of total weight

(%)

Cement (general purpose grey)

Sand (fine washed)

Metakaolin (Power Pozz)

Polymer (Vinnapas 512T)

Super plasticizer

Water

Pre- cut alkali resistant glass fiber

33.8

33.8

8.5

4.1

1.0

14.8

4.0

GRC consists of a random fibre arrangement because glass fibers are mixed with the

cement sand mortar. Therefore, GRC can be treated as an isotropic material and

techniques required by the analysis of GRC stresses, strains and deflections are

identical to those used with isotropic materials [69]. All the GRC samples were

48 Chapter 4: Experimental Testing

selected randomly irrespective to the casting direction. Random specimens exhibitted

similar results in each tensile, compression and bending supporting this argument.

4.1.2 Tensile testing for GRC

The maximum thickness of the GRC layers used for the HCFPS test specimens and

tensile test specimen was 10 mm. Sample size was selected as 250×25 mm

according to ASTM 3039 [40]. Five tensile test specimens were used to represent all

GRC batches. Five GRC batches were prepared using the formulation given in Table

4-1 to cast HCFPS test panels (refer to section 4.2) and five tensile coupons were

cast from the each batch. Uniaxial tension tests were carried out using an Instron

5569 series Mechanical Tester, at a loading rate of 0.5 mm/min as shown in Figure 4-

1a. Longitudinal strains were measured using the built-in extensometer of the test

machine and the stress-strain relationships are illustrated in Figure 4-1b. Average

cracking tensile strength and tensile modulus were obtained as 3.1 MPa and 5.0 GPa,

respectively. Figure 4-1a shows a typical failure mode of a test coupon.

(a) (b)

Figure 4-1: (a) Tensile testing for GRC specimen, (b) Stress-strain relationships for GRC in

tension

4.1.3 Four-point bending tests for GRC

Four-point bending tests were carried out to investigate the flexural behaviour of

GRC. Test specimens for the four-point bending tests were 10×25×200 mm with 152

mm clear span according to ASTM C947 [41]. Testing was conducted using the

same test machine, as per section 4.1.2, with the loading set up shown in Figure 4-2a,

at a 1 mm/min displacement rate. Five test samples representing all GRC batches

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 0.002 0.004 0.006 0.008 0.01 0.012

Str

ess (

MP

a)

Strain (mm/mm)


were used and resultant load deflection plots are given in Figure 4-2b. All the test

samples exhibited a similar initial linear behaviour, but beyond the yielding point

two samples exhibited slightly different behaviour. This could be due to the random

fiber arrangements in the test specimens. Flexural modulus was calculated using the

initial linear behaviour of the plots according ASTM C947 [41] and gave an average

value as 4.8 GPa. The average force at which the force-deflection curve deviates

from linearity was 160N. This value was used to calculate the flexural strength of

GRC as 9.7 MPa, according to the method given in [41].

(a) (b)

Figure 4-2: (a) Four-point bending test for GRC, (b) Load-deflection plots for GRC in four-

point bending tests

4.1.4 Cylinder compression test for GRC

Compression tests were performed to obtain the stress-strain behaviour of GRC in

compression. Three cylindrical specimens of 100 mm diameter and 200 mm height,

representing all GRC batches, were used for this test. Specimens were tested using

Universal Tinius Olsen test machine as shown in Figure 4-3a. Cross-head

displacement was used to calculate the strains. The stress-strain relationships for

GRC in compression are illustrated in Figure 4-3b. Compressive modulus and

compressive strength were calculated as 5.9 GPa and 19.6 MPa respectively.


(a) (b)

Figure 4-3: (a) Compression test for GRC, (b) Stress-strain relationships for GRC in

compression

4.1.5 Composition of PU

AUSTHANE AUE 757 rigid medium-density PU foam (density = 99.8 kg/m3) was

used as the central core of the HCFPS test panel. This foam is generally obtained by

mixing AUE 757 Polyol and ECOISO-GP Isocyanate liquids under controlled

conditions.

Although the PU production was conducted in layer wise pouring process, test

samples were selected randomly from the from the foam core irrespective to the

casting procedure. Random specimens exhibitted similar results in each tensile,

compression and bending demonstrating isotropic nature of PU and this was further

observed by other researchers in [6]

4.1.6 Compression test for PU

Compression tests were conducted to obtain the compressive behaviour of the PU

core. Five prism-shape PU foam coupons, which were 70×70 mm in cross-section

and 50 mm thick, representing all PU batches, were manufactured and tested

according to the ASTM C365-03 [45]. The tests were carried out using an Instron

5569 series Mechanical Tester, by attaching flat loading platens (refer to Figure 4-4a)

with a displacement rate of 0.5 mm/min. The built-in extensometer of the test

machine was used to measure the strains. Stress-strain relationships are presented in

Figure 4-4b, which shows an initial linear response, then a plastic response, followed

0

5

10

15

20

25

0 0.005 0.01 0.015 0.02 0.025 0.03 S

tress (

MP

a)

Strain (mm/mm)


by a strain-hardening behaviour with the increase in strain. The measured plastic

compressive strength and compressive modulus were 0.5 MPa and 26.0 MPa

respectively..

(a) (b)

Figure 4-4: (a) Stress-strain relationships f or PU in compression, (b) Compression testing for

PU core

4.1.7 Tensile test for PU

To determine tensile properties of the PU core, tensile tests were conducted

according to ISO 1926 [43]. Five prism-shaped test specimens, with 10 × 20 mm

cross section and 150 mm length, were tested in the same test machine, as outlined in

section 4.16, and as shown in Figure 4-5a. The built-in extensometer was used to

measure the strain at a loading rate of 0.5 mm/min. It was possible to adopt this test

method for the 99.8 kg/m3 density PU, since it had sufficient stiffness to facilitate

gripping in the test machine. Tensile failure of all test samples occurred around the

centre of the test sample, as depicted in Figure 4-5a. Tensile stress- strain curves are

presented in Figure 4-5b, and average tensile modulus and tensile strength were

obtained as 19.5 MPa and 0.9 MPa respectively.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 S

tress (

MP

a)

Strain (mm/mm)


(a) (b)

Figure 4-5: (a) Tensile test for PU core, (b) Stress-strain behaviours of PU in tension

4.1.8 Three- point bending tests for PU core

To investigate the flexural behaviour of PU, three-point bending tests were

conducted as per ASTM D 790 [44], using five 20×10× 160 mm test specimens. An

Instron 5544A mechanical testing machine was used to measure the load-deflection

behaviour of test specimens by applying a central load at a rate of 2 mm/min as

shown in Figure 4-6a. Load-deflection plots from these tests are illustrated in Figure

4-6b. Maximum average load sustained by test specimens during the bending was

19.1 N. The Elastic modulus and flexural strength were calculated as 22.4 MPa and

2.0 MPa respectively, using the method provided in [44].

(a) (b)

Figure 4-6: (a) Three-point bending test for PU core, (b) Load-deflection plots from

bending test of PU core

0

5

10

15

20

25

0 5 10 15 20 25

Load

(N

)

Deflection (mm)


4.1.9 Tensile test for steel laminate

Tensile tests were conducted on three specimens of the steel laminate. Each

specimen had a thickness of 1 mm with dimensions as shown Figure 4-7a. They were

prepared and tested according to AS 1391 [46], using an Instron 5569 series

Mechanical Tester as shown in Figure 4-7b. Stress-strain relationships obtained from

the tests are shown in Figure 4-7c, from which modulus of elasticity and yield

strength of steel laminate were determined as 209.9 GPa and 201.0 MPa respectively.

(a)

(b) (c)

Figure 4-7: (a) Dimensions of tensile test specimen, (b) Tensile testing for steel laminate, (c)

Stress-strain relationships for steel laminate in tension

4.2 FABRICATION OF HCFPS TEST SPECIMEN

A manual casting method was used to cast the HCFPS test specimens with a step by

step process. Details of section configuration for the 3200 mm span HCFPS test

panel are explained in section 3.3.1. The beam of the test panel was tapered (Figure

4-8) to facilitate the casting process. To enhance the support bearing capacity of the

test panel, the PU core was replaced with a 100 mm GRC in the vicinity of the

supports, as shown in section 3.3.1, Figure 3-2b. Perforated steel laminate was used

to enhance the bonding between GRC and steel laminate. Cover for the steel

laminate was approximately 6 mm in the test specimens, but this was only for the

0

50

100

150

200

250

300

350

400

450

0 0.05 0.1 0.15 0.2 0.25

Str

ess (

MP

a)

Strain (mm/mm)


experimental testing. The cover can be increased in practical applications, if

necessary, depending on the environmental conditions.

Figure 4-8: Section dimensions of HCFPS test panel

Three test specimens were cast using a plywood mould (Figure: 4-9 a). At first, a

6mm thick GRC layer was applied at the bottom of the beam and a 3mm thick

perforated steel plate was placed on top (Figure 4-9b). A second, 6mm thick GRC

layer was applied on top of the steel plate, extending to 10mm thick GRC layers

along the sides of the beam and bottom of the slab (Figure 4-9c). After allowing 2

days of curing time, a central PU core was poured on top of the GRC layers (Figure

4-9d) and allowed to harden for 24 hours. Then the top of PU core was grinded and

levelled off (Figure 4-9e) to obtain the required thickness. Finally, a 10 mm thick

top GRC layer was placed on the hardened PU core (Figure 4-9f). Artificial bonding

agents were not used between GRC and PU, as these two materials achieved a good

bonding during PU hardening and the GRC curing processes (as also evidenced

during the tests). Specimen was left for four week before the testing. Curing time for

the GRC is same as the concrete [69] and PU does not need specific curing time as

cementitious materials. Therefore, curing time of the HCFPS panels will be similar

to the conventional concrete panels. However, this floor system is proposed as a

prefabricated floor system and hence curing time is not significant as in-situ

concrete.


(a) Ply wood Mould (b) Perforated steel laminate

(c) Placing bottom GRC layer (d) Pouring PU core

(e) Grinding and leveling top of PU core (f) Placing top GRC layer

Figure 4-9: Casting steps of HCFPS test panel

4.3 SUPPORTING ARRANGEMENT FOR THE TEST PANEL

For all static and dynamic tests the same supporting arrangement was used. A

specially designed arrangement was used to support the "T" shaped ends of test

panels. The HCFPS panel was supported as shown in Figure 4-10. Steel plates,

which were 10 mm thick and 100 mm wide, were placed under the slab and beam at

the supports to distribute the loads uniformly. The steel plates were supported by

solid circular steel bars, as shown in this Figure. Adjustable jacks were used to

support the steel bar under the slab, also seen in Figure 4-10.


Figure 4-10: Test panel supporting arrangement

4.4 DATA ACQUISITION SYSTEM

Static and dynamic test were conducted for the HCFPS test panels. Displacements,

acceleration and applied load data were acquired using the Data Acquisition System

(DAS) shown in Figure 4-11.

Figure 4-11: Data acquisition system


The DAS consisted of a data recording computer running on Microsoft Windows XP

with a data logger and LabVIEW software was used for data acquisition. The

maximum capacity of the DAS was 50000 samples per second but the maximum

sampling rate required in the experimental tests was 2049. DAS setup provided the

faster and more accurate data for the experimental testing. Method of data acquisition

is discussed under dynamic and static experimental testing separately.

4.5 DYNAMIC TESTING

Two types of dynamic testing were conducted: heel impact and walking tests. Heel

impact tests were the primary type of human induced loads that were used to excite

the HCFPS test panel. Walking tests were also conducted to investigate the vibration

response.

4.5.1 Heel impact test

Heel impact tests can be used to obtain vibration characteristics of the floor panels

[22, 70]. Heel impact tests were performed on all three HCFPS test panels to obtain

the acceleration response. Test set up and data acquisition system are shown in

Figure 4-12 and supporting arrangement was used as explained section 4.3. To apply

the heel impact, an average person (70 kg) was asked to stand at the mid-span of test

panel and to raise their heels approximately 50 mm and produce a sudden impact

(Refer to Figure 4-13a ) [22]. A 5g accelerometer and 25 mm LVDT were used to

acquire acceleration and deflection data at mid-span as shown in Figure 4-13b. Data

was acquired for 3 second period at a rate of 2049 samples per second.

Figure 4-12: Test setup and data acquisition system for heel impact test


(a) ( b)

Figure 4-13: (a) Heel impact at the mid-span, (b) 5g Accelerometer and 25 mm LVDT at the

bottom HCFPS panel

Three heel impacts were performed for each panel and similar acceleration and

displacement responses were obtained. Displacement time histories at the mid-span

were also similar for each panel and a typical displacement-time history plot is

shown in Figure 4-14. Typical acceleration responses of the 5g accelerometer at mid-

span for each HCFPS test panel are presented in Figure 4-15, 4-16 and 4-17.

Figure 4-14: Typical heel impact displacement response at mid-span for panel 1


Figure 4-15: Typical heel impact acceleration response at mid-span for panel 1




Equation 4-1 presented by Ellis [35] was used to calculate the damping coefficient

(ς) from the time- acceleration plots. Damping obtained from this equation is ―log

decrement damping‖. Murray [36] stated that modal damping or true damping is one-

half to two-thirds of the value of the log decrement damping. In this context the first

four successive peaks were used to estimate the damping. Table 4-2 shows the

average damping ratios for each panel according to test results. True damping ratio

of HCFPS test panel can be taken as 5%.

n

oe

A

A

nlog

2

1

Equation 4-1

In above equation, A0 and An are the amplitudes at n successive peaks apart where

A0 is the first peak and n=4 of the acceleration-time response plot.

Table 4-2: Damping ratios for the HCFPS test panel

Panel Log decrement

damping Average True damping

Panel 1

Panel 2

Panel 3

Test 1

Test 2

Test 3

Test 1

Test 2

Test 3

Test 1

Test 2

Test 3

10.48 %

10.10 %

10.05 %

10.04 %

10.10 %

9.80 %

10.25 %

10.35 %

10.60 %

10.20 %

9.98 %

10.40 %

5.10 %

4.99 %

5.20 %

The first natural frequency of the test floor panels was be calculated by performing a

Fast Fourier Transformation (FFT) analysis for acceleration plots [22, 37, 38]. Power

Spectrum was obtained from the FFT analysis. The first peak that can be found in the

Power Spectrum is the first natural frequency of the test panel. Typical FFT analysis

for an acceleration response (acceleration response shown in Figure 4-15) is shown

in Figure 4-18. FFT analysis was conducted for the other acceleration responses and

average first natural frequency was obtained as 22.8 Hz as shown in the Table 4-3.


Figure 4-18: Typical FFT analysis of an acceleration response

Table 4-3: Experimental First natural frequency of HCFPS panels

Panel First natural frequency (Hz) Average

Panel 1

Panel 2

Panel 3

22.83

22.91

22.66

22.8 Hz

4.5.2 Walking test

Walking tests were conducted for the HCFPS test panels to obtain the acceleration

response at the mid-span. Test set up and supporting arrangement were as described

for the heel impact test (explained in section 4.5.1). An average weight person

walked along the test panel at an average speed. In general, average frequency of

walking is 2 Hz, and therefore, average walking speed is calculated as 1.5 m/s

(stride length is 750 mm) [56]. The time spent to walk along the 3200 mm span test

panel was approximately 2.2 seconds. Hence the walking speed on the test panel was

also approximately 1.5 m/s. A typical acceleration response at the mid-span is shown

in Figure 4-19 and exhibits behaviour of a high frequency floor. In high frequency

floors, applied forces due to walking steps behave like a series of impulses and decay

with time prior to the next step [56].


Figure 4-19: Typical acceleration response at the mid-span for walking test

4.6 STATIC LOAD TESTING

Two test panels were used to carry out the static loading test. Tests were carried out

in order to obtain the load-deflection curve to calibrate the finite element model.

Failure modes and ductility of the specimen were investigated during the testing.

4.6.1 Test set up, instrumentation and static load test

Loads were applied as four line loads along the span using 1000 mm steel spreader

beams through an arrangement shown in Figure 4-20 (dimensions and spacing are

given in section 3.3.3). A supporting arrangement was used as explained in section

4.3. Two HCFPS panels were tested in bending with a clear span of 3100 mm. Load

was applied to the panel using a hydraulic pump, which was attached to the loading

frame, as shown in Figure 4-20. A 30 kN load cell was used to measure the load.

This arrangement was adequate to simulate a uniformly distributed load (within the

means of our testing facilities) It enabled the curvature of the panel during loading,

whilst maintaining the uniform loads at the contact locations, similar to the test set up

in [15]. It was hence possible to adequately capture the flexural behaviour of the

HCFPS using this loading arrangement. In order to distribute the loads uniformly, 10

mm rubber pads were placed between the steel spreader beams and the surface of the


HCFPS panel. Three Linear-variable-displacement-transducers (LVDTs), with 0.01

mm sensitivity, were placed at centre of span to measure the deflections.

Figure 4-20: Loading arrangement for the static load test of HCFPS panel

4.6.2 Static load test results and discussion

Loading was continued till it was observed that the HCFPS panel was close to failure

because deflection started increase excessively with crack development. Load versus

mid-span deflection curves for the two test specimens obtained from the static

loading tests are presented in Figure 4-21. Cracking of the bottom GRC layer of the

beam started to occur at a load of 12.5 kN. This was considered as the yielding point

of the HCFPS panel.

Load-deflection results from the static load tests, presented in Figure 4-21, show a

smooth transition from elastic to plastic behaviour, but they do not show clearly a

yielding point. However, flexural cracks were observed during the testing, at 12.5 kN

applied loading in both panels. Vertical cracks then developed on either side of the

beam, as shown in Figure 4-22 (a). Loading was continued until mid-span deflection

reached approximately 50 mm, which was the maximum measurable limit of the

LVDT. At this deflection, cracks in the GRC layer, in the beam of HCFPS test panel,

started to widen (Figure 4-22 (b)) because of the plastic deformation of the steel

laminate. However, complete collapse did not occur, even at the 50 mm central

deflection, as the steel laminate continued to deform plastically with the loading.

Hydraulic Jack

30 kN Load Cell


Furthermore, there was no failure in the slab and the failure occurred only in the

beam. If, the loading had continued beyond the 50 mm deflection at mid-span, there

could be a complete collapse of the HCFPS panel, due to the ultimate failure of the

steel laminate. However, acceptable ductility for the HCFPS panel can be determined

(as explained in Section 4.6.3), with the load-deflection results up to 50 mm mid-

span deflection. Hybrid integrity remained during the entire test and there was no de-

lamination between layers. There was no shear or support bearing failure in HCFPS

specimens even at 50 mm deflection.

Figure 4-21: Load-deflection behaviour of HCFPS panels

In order to establish the linear range of the HCFPS, its load deflection behaviour was

determined from the analysis of a simply supported beam, using an equivalent

flexural stiffness. This equivalent flexural stiffness (EI) of the HCFPS was calculated

as 5.76×10^11

Nmm2, using the values of the Elastic modulus of the component

materials. Four equal loads (with similar spacing as in the test setup shown in Figures

3-4a and 4-9) were used to obtain the load-deflection plot shown in Figure 4-21. This

behaviour can be considered as the linear load-deflection of HCFPS. Load-deflection

results of static loading test, presented in Figure 4-21, demonstrated that the

deflection increased approximately linearly up to a load of 12.5 kN. After this point

the deflection increased non-linearly. The force at the point on the load-deflection

curve where it noticeably deviated from linearity, was considered as the yielding load

as shown in Figure 4-21. This is further supported by the experimental observation,

where flexural cracks started to form at 12.5 kN applied loading.

0

5

10

15

20

25

0 10 20 30 40 50

Load,

kN

Deflection, mm

Test 2

Test 1

Deflection of a beam with equal EI to HCFPS


(a) Vertical cracks in the beam of test panel

(b) Failure only in the beam of HCFPS test panel

Figure 4-22: Cracking and failure due to the flexure

4.6.3 Deflection ductility

Ductility of a structural member can be considered as a measure of its ability to

undergo deformation without a substantial reduction in the flexural capacity [71].

One method of quantifying the ductility is the displacement ductility index, which is

the ratio of ultimate deflection to the deflection at yielding [71] . Ultimate deflection

was considered as 45 mm and deflection at the yielding point 9.6 mm from Figure 4-

21. Deflection ductility index was hence calculated as 4.7 for the HCFPS test panels,

which is acceptable for a structural member.

4.7 CYCLIC LOAD TESTING

Cyclic loading test was conducted for the final test panel. Testing was conducted

according to the method given in Section 3.1.4. Deviation from linearity and

repeatability were calculated to evaluate the cyclic loading performance of the test

panel.


4.7.1 Test set up, instrumentation and cyclic load test

Test was conducted using a hydraulic loading system, consisting of a Moog actuator

as shown in Figure 4-23. Supporting arrangement as explained in section 4.3 was

used. Displacement controlled moog actuator was used to control the cyclic loading

but load was applied using the arrangement explained in Section 4.6.1. LVDTs, with

0.01 mm sensitivity, were placed at centre of span to measure the deflections.

Cyclic loading test was conducted according to the method explained in Section

3.3.4. Ultimate load (Lu) for the cyclic loading was considered as the maximum load

carrying capacity of the HCFPS panel before any failure, which as determined by the

static load testing was 12.5 kN (refer to Section 4.6.2). First, six load cycles were

conducted according to load step method and rate of loading shown in Figure 3-5. 50

% of the ultimate load was applied for the first two load cycles. Then, 75% of

ultimate load was applied for the second two cycles and finally 100% of the ultimate

load was then applied for the last two load cycles. Minimum loading of 1.25 kN,

which is 10% of 12.5 kN, was maintained during the unloading cycles. Load-

deflection behaviour for those six cyclic loading steps is presented in Figure 4-24.

Figure 4-23: Cyclic loading test for HCFPS panel


Figure 4-24: Cyclic behaviour of HCFPS panel for first 6 loading cycles

4.7.2 Test results and discussion for cyclic loading test

The load-deflection plots for the cyclic load test are shown in Figure 4-24. From

these plots the repeatability and deviation from linearity of the member deflection

(before yielding) were evaluated according to [39], which is explained in Section

3.3.4. Repeatability was 99 %, which was more than the recommended minimum

limit of 95%. Deviation from linearity was 10%, which was less than maximum

recommended limit of 25%. Therefore, HCFPS test panel exhibited acceptable cyclic

loading behaviour.

4.7.3 Comparison of cyclic loading test results with static load test results

Additional loading cycles were carried out with 1 kN increments to investigate cyclic

behaviour of the HCFPS panel beyond the yield point. Two loading and unloading

cycles were conducted for each increment up to 20.5 kN. As before, a minimum of

1.25 kN loading was maintained during the unloading. At the end of the cyclic

loading tests, the applied load was increased to obtain a span deflection of 45 mm in

order to compare the load-deflection behaviour (of the panel) under cyclic loading

with that under static loading as shown in Figure 4-25. The panel subjected to the

cyclic load test exhibited similar load-deflection behaviour as the (other) two panels

subjected to static loading (refer to Figure 4-25). Hence, the cyclic load test results

are considered as reliable.

0

2

4

6

8

10

12

14

0 2 4 6 8 10

Load,

(kN

)

Displacement, (mm)


Figure 4-25: Cyclic behaviour of HCFPS panel

4.8 TESTING OF GRC-PU-GRC COMPOSITE PANEL

GRC-PU-GRC composite panel, as shown in Figure 4-25, acts as top slab of the

HCFPS hybrid assembly. Performance of the GRC-PU-GRC composite panel must

to be investigated to determine the structural capacity of the HCFPS slab. Bending

tests of the GRC-PU-GRC composite panel were conducted to investigate structural

behaviour and failure modes.

Figure 4-26: GRC-PU-GRC composite panel slab in HCFPS assembly

4.8.1 Test sample size and fabrication

800 mm × 400 mm panels were selected to test for one-way bending within the

means our testing facilities. Test results were used to validate the FE model and

investigate structural capacity of GRC-PU-GRC panel with 1000 mm one-way and

0

5

10

15

20

25

0 10 20 30 40 50

Load (

kN

)

Deflection (mm)

Cyclic loading

Static test 1

Static test 2


500 mm cantilever span used in HCFPS configuration (refer to Figure 4-26). Two

composite panels with different layer thicknesses were used for the testing. The

sectional configurations of these two types of sections are shown in Figure 4-27 and

two numbers of panels were cast for each type. The GRC-PU-GRC composite panel

specimens were cast layer wise. First, the bottom layer of the panel was cast and

allowed one day for curing and the PU layer was poured on top. Then the top layer

was cast on the hardened PU core. Composition of the GRC layer was the same as

explained in section 4.1.1 and the density of the polyurethane was 62 kg/m3.

a) Type A b ) Type B

Figure 4-27: Determined sectional configuration of composite panel

4.8.2 Test set up and instrumentation

The loading tests of the panels were carried out using a Tenious Olsen Hydraulic

testing machine (300kN Capacity). The loading arrangement of the test consisted of a

spreader circular steel roller to achieve an evenly distributed central line load across

the whole panel (refer to Figure 4-28). Two supports, allowing translations along the

span and rotations about the span, were used. Solid, high strength steel circular rods

(20 mm) arrangement were used as supports (refer to Figure 4-29). Supports were

positioned to obtain a span of 700 mm.

To measure the mid-span vertical deflection of each test panel, a 20 mm linear-

LVDT was attached at the centre of the panel. The deflection reading was directly

obtained from a data acquisition computer.


Figure 4-28: Loading test setup

Figure 4-29: Supporting conditions for loading test

4.8.3 Static load test results and discussion

Mid-span deflections at 50 N load increments were acquired using a data acquisition

system. This static test was done on each of the 4 panels and load-deflection data

were recorded. Four static tests were performed on each panel and the load-

deflection graphs are shown in Figure 4-30 and Figure 4-31. Failure modes of

composite panel were flexural failure at the mid-span as shown in Figure 4-32.

Linear load-deflection behaviour until the failure was observed for both types of

composite panels. Approximately linear load-deflection was observed for all the

panels. Although GRC-PU-GRC panel exhibited a linear behaviour until the failure,

this panel is only a component of HCFPS. Hybrid behaviour of HCFPS exhibited a

ductile behaviour as seen in the experimental testing and there was no failure in the

GRC-PU-GRC slab until the overall failure of the HCFPS panel (refer to Section

4.6.2). There was no delimitation during the loading test, until the flexural failure as


shown in Figure 4-32. Load-deflection data was used to validate FE model of the

GRC-PU-GRC composite panel.

Figure 4-30: Load-deflection curves for A type panels

Figure 4-31: Load-deflection curves for B type panels

Figure 4-32: Failure of one test panel

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0 2 4 6 8

Load,

N

Deflection, mm

0

500

1000

1500

2000

2500

3000

0.0 1.0 2.0 3.0 4.0 5.0

Deflection, mm

Load,

N


4.9 SUMMARY

A comprehensive testing program was undertaken to investigate the behaviour of

HCFPS panel and GRC-PU-GRC composite panel. Dynamic tests, static loading

tests and cyclic loading test of 3200 mm span HCFPS panels were conducted.

Experimental studies also included comprehensive material tests for the constituent

materials.

Material properties for the three component materials (GRC, PU and steel) that were

obtained from the material testing program are summarised in Table 4-4.

Table 4-4: Summary of material properties obtained from the material testing

GRC

(MPa)

PU

(MPa)

Steel

(MPa)

Tensile Strength

Tensile modulus

Flexural Strength

Flexural Modulus

Compressive strength

Compressive modulus

3.1

5.0× 103

9.7

4.8 ×103

19.6

5.9 ×103

0.9

19.5

2.0

22.4

0.5

26.0

201.0

209.9×103

-

-

-

-

Heel impact test was conducted for the HCFPS panel and the damping ratio and first

natural frequency were dtermined as 5% and 22.8 Hz respectively. Walking tests

were also conducted on the HCFPS panel and acceleration responses were obtained.

Acceleration response exhibited a series of impulses and the response decays with

time before the next step, indicating the behaviour of a high frequency floor [56].

Therefore, in HCFPS floors, transient response is more significant than the steady

state.

Maximum load carrying capacity of the HCFPS panel before failure was determined

by the static load testing as 12.5kN. The HCFPS exhibited ductile behaviour and

flexural failure in the beam at mid-span. There was tensile failure of the outer GRC

layer and plastic yielding of the steel laminate. HCFPS displayed a deflection

ductility of 4, which is acceptable for floor plates. There were no support bearing or

shear failures during the testing of HCFPS panels. De-lamination between layers did

not occur until failure. Hence, HCFPS shows flexural failure under distributed loads.


Cyclic loading tests yielded repeatability of 99% and deviation from the linearity of

10%. These values are within the limits given in [39] , showing acceptable cyclic

loading performance of this floor plate

GRC-PU-GRC composite panel, which is top slab of the HCFPS, exhibited linear

load-deflection behaviour and flexural failure due to the loading.

Results obtained from the experimental testing were used to validate FE models

explained in chapter 5.


Chapter 5: Development and Validation of FE models 75

Chapter 5: Development and Validation of FE models

This chapter presents the development of FE models and their subsequent validation

using experimental test results generated in Chapter 4. The commercially available

finite element program ABAQUS 6.9-1 [47] was used with ABAQUS CAE as the

pre- and post-processor for the FE simulations, as described in section 3.4.

5.1 FE MODEL DEVELOPMENT AND VALIDATION USING DYNAMIC

TEST RESULTS OF HCFPS TEST PANELS

FE model for the HCFPS test was developed to conduct free vibration analysis and to

simulate heel impact test. First natural frequency was obtained using free vibration

analysis and validated the FE model with experimentally obtained value. "Modal

Dynamic" analysis procedure available in ABAQUS [47] was used to conduct

transient modal dynamic analysis for heel impact and walking excitation.

Acceleration response of the FE model was obtained from this analysis and

compared with experimental response.

5.1.1 Material properties for dynamic analysis

Dynamic analysis of HCFPS was conducted using linear elastic properties of the

component materials. Materials responds within elastic limits for free vibration and

human induced vibration analysis [56] and hence, properties listed in Table 5-1 were

used in the analysis. These properties were obtained from material test results

presented in Section 4.9.

Table 5-1: Component material properties for the dynamic analysis

Properties PU GRC Steel

Density (kg/m3) 99.8 1983 7800

Elastic Modulus (Mpa) 22.4 5000 210,000

Poisons ratio (ν) 0.3 0.24 0.3

Poisons ratio (ν) for the PU was taken from [72] for the density of 99.8 kg/m3 and ν

of GRC was taken as 0.24 from [73].

http://chanaka-pc:2080/v6.9/books/key/key-link.htm#usb-kws-hmodaldyn


76 Chapter 5: Development and Validation of FE models

5.1.2 Model description

HCFPS test panel was modelled as shown in Figure 5-1 using ABAQUS [47]. 10

mm thick and 100 mm wide steel plates were modelled under the HCFPS panel

(refer to Figure 5-1(a)), in order to simulate the experimental conditions at the

supports. Translations in X, Y and Z directions and rotations in Y and Z directions

were restrained at one end whilst translations in X and Y direction and rotations in Z

and Y directions were restrained at the other end (refer to Figure 5-1 (b)) in order to

simulate the restraint from the steel bars. 3 mm thick perforated steel laminate was

used in the test panel with 30% openings. Effective thickness for steel laminate in the

FE model was taken as 2.1 mm in order to account for the plate openings. C3D8R

eight node liner brick elements were used in the FE model for all parts along with

reduced integration and hourglass control [74]. Convergence study was conducted to

select the optimum mesh size for the FE model. Maximum element size was 25 mm,

and the FE mesh is shown in Figure 5-2 (b).

(a) Support

(b) Mesh

Figure 5-1: FE model for dynamic analysis

5.1.3 Free vibration analysis and validation with first natural frequency

Free vibration analysis of the above described model was conducted and natural

frequencies were obtained. First and second mode natural frequencies were obtained

as 23.64 Hz and 27.66 Hz respectively. Mode shape for the first natural frequency is


shown in Figure 5-2 (which is the bending mode of HCFPS panel). Table 5-2 shows

that the difference in first mode natural frequency obtained from the FE analysis and

experimentally obtained value is only 0.84 Hz (3%). Therefore, FE model is

adequately validated by the experimental results.

Figure 5-2: Mode shape for the first natural frequency

Table 5-2: Validation of first natural frequency

First natural frequency (Hz)

Experimental - Avegrage 22.80

FE results 23.64

5.1.4 Linear transient dynamic analysis

Response of floor structure can be categorised as transient and steady state responses

as described in section 3.7.2. Transient response is the response of the floor before

the steady state. In high frequency floors (>10 Hz) such as HCFPS, transient

response is more significant than the steady state response because resonance cannot

occur and applied forces behave like a series of impulses [56]. Applied heel impact

load of the HCFPS test panel was simulated in the FE model using transient dynamic

analysis to obtain the acceleration response and this was compared with the

experimental response.

5.1.5 Heel impact load function

Applied heel impact load of the HCFPS test panel was simulated in the FE model.

Murray [75] suggested a triangular load function to simulate the load due to a heel

impact test by an average weight person. Load function is a 2670 N initial load that

linearly decreases to zero over a period of 0.05 seconds, which represents an impulse

of 67 Ns [75]. This method was used successfully by Jetann [70] to validate a FE

model for the acceleration response of heel drop test performed on a post-tensioned

concrete slab. Suggested load function was applied to the FE model of HCFPS test


specimen as shown in Figure 5-3. This represents the typical heel impact test of the

panel and corresponding acceleration is shown in Figure 4-16.

Figure 5-3: Heel impact load function

5.1.6 Application of the damping to FE models

Generally, the damping of a structural system is defined as the model damping ratio ζ

(as described in Section 3.7.4). In transient dynamic analysis problems, the damping

matrix cannot be defined as damping ratio, but rather an explicit damping matrix was

defined by Clough et al. [76]. Damping matrix is assumed to be proportional to the

combination of the mass and stiffness matrix and this method is also known as

Reyleigh proportional damping method (combination is shown Equation 5-1). This

method has also been used to incorporate the damping to floor models [22].

KMC Equation 5-1

In above equation, [C] is the system damping matrix, [M] is the mass matrix, [K] is

the stiffness matrix, is the mass proportional damping and is the stiffness

proportional damping.

According to the Reyleigh proportional damping method, relationship between

damping ratio ζ and frequency fn of nth

mode can be obtained in terms of and

as described in equation 5-2 [76].

22

n

n

n

f

f

Equation 5-2

0

500

1000

1500

2000

2500

3000

0 0.5 1 1.5 2 2.5 3

Fo

rce (

N)

Time (Seconds)


If the damping ratios and frequencies for two consecutive modes (mth

and nth

) are

known, and can be obtained by solving two simultaneous equation as shown

in equation 5-3.

nn

mm

n

m

ff

ff

1

1

2

1 Equation 5-3

It can be assumed that the variation of damping ratios for first two natural

frequencies is minor such that (ζ1= ζ2= ζ) [22]. Hence, Equation 5-3 can be

rearranged as Equation 5-4 and and can be calculated by substituting ζ and two

natural frequencies f1 and f2.

1

2 21

21

ff

ff

Equation 5-4

Average damping ratio obtained from the experimental results in Section 4.5.1 (5%)

and first two natural frequencies obtained in section 5.1.3 (f1 = 23.64 Hz and f2 =

27.66 Hz) were used to calculate the mass proportional damping ( ) and stiffness

proportional damping ( ) using the equation 5-4. The calculated and are

shown in Table 5-3.

Table 5-3: Mass proportional stiffness proportional damping for FE model

Damping ratio of 5%

1.245

0.002

5.1.7 Dynamic analysis validation with acceleration response of heal impact test

Heel impact load function described above was applied with Relaigh damping to

obtain acceleration response of the FE model. "Modal Dynamic" analysis procedure

available in ABAQUS [47] was used to conduct linear transient modal dynamic

analysis. Acceleration obtained from the FE analysis was compared with

experimental response shown in Figure 5-4. This demonstrated excellent validation,

as peak acceleration values and time duration of the response decay of the FE

acceleration time-history agreed with the experimental response generated in Section



4.5.1. Hence, FE models can be used to predict the dynamic response of the HCFPS

panels.

(a) FE acceleration time history

(b) Heel impact acceleration response at mid-span for panel 2

Figure 5-4: Computed and measured acceleration responses due to heal impact

5.1.8 Dynamic analysis and validation with walking loads

Walking of a single person along the HCFPS test panel was simulated using FE

techniques. Pan et al. [77] suggested a method to model the steps of a single person

walking by using point loads. Distance between successive strides was calculated

using the pacing frequency. Hence, footfall interval is 0.5 s for a pacing frequency of

2 Hz and thus gives a stride length of 750 mm [57, 78]. Average point load applied

on a floor due to a single step at an average walking speed (2 Hz) is 616 N [57, 78].


This load model was applied to the FE model of HCFPS test panel with damping

data as described in section 5.1.6. The acceleration response was obtained as shown

in Figure 5-5 (a), by conducting transient dynamic analysis. Acceleration response

obtained from FE analysis is similar to the experimental walking response shown in

Figure 5-5 (b) Therefore, FE models can be used simulate the walking activities and

determine vibration response.

(a) Computed acceleration response at mid-span for single person walking

(b) Experimentally measured acceleration response at mid-span for single person walking

Figure 5-5: Computed and measured acceleration responses due to walking


5.2 FE MODEL DEVELOPMENT AND VALIDATION USING STATIC

TEST RESULTS OF HCFPS TEST PANEL

FE model for the HCFPS test panel were developed and non-linear analysis were

used to simulate static load tests. Linear and non-linear properties of the materials

were used in the FE analysis using the "Static" analysis procedure available in

ABAQUS [47]. Load-deflection response of the FE model was obtained from the

analysis and compared with experimental results.

5.2.1 Material properties for static analysis

Material properties for the static analysis were based on the material tests that were

conducted on each component material. Following linear and non-linear properties

were used for GRC, PU and steel for the static analysis of FE models.

5.2.2 GRC Material models

GRC layer of the HCFPS test panel is subjected to compressive, flexural and tensile

stresses under bending. Soranakom et. al [79] suggested a material model to define

all such states of GRC (Figure 5-6) and this model was used in this study. Material

model behaviour of GRC was modelled in ABAQUS by modifying the concrete

damage plasticity model, which is defined for similar behaviour of the concrete.

Linear and non-linear tensile behaviour of GRC was modelled similar to the tensile

test results, as they (refer to 0) agree with the material model behaviour. Although

there is a gradual decrease of compressive stress after reaching a maximum stress

according to compression testing of GRC (section 4.1.4, Figure 4-3), it is assumed as

constant after the peak, as per the suggested material model. This did not affect the

overall results of the analysis as the GRC did not exhibit a compressive failure in the

experimental testing (up to mid-span deflection of 50 mm) or in the FE results

explained in section 5.2.6. Therefore, this approximation was considered reasonable

for FE modelling and analysis.

Values for the material model obtained from the GRC material tests are as follows:

compressive yield stress (σcy) = 19.6 MPa, compressive yield strain (εcy) = 0.0040,

ultimate compressive strain (εcu) = 0.03, cracking tensile strength (σcr) = 3.1 MPa,

first cracking tensile strain (εcr) =0.00062, tensile stress at the end of tensile model

(σtu) = 1 MPa, ultimate tensile strain (εtu) = 0.01 and modulus of elasticity (E=) 4.99

GPa). Poisons ratio of GRC is taken as 0.24 from [73].


Figure 5-6: GRC material model

5.2.3 4 PU material model

PU core was modelled using linear elastic properties of PU (E=22.4, ν =0.3). Poisons

ratio (ν) for the PU was taken from [72] for the density of 99.8 kg/m3. Non-linear

properties of PU were not necessary, since it attracts low stresses due to the lower

elastic modulus compared to the GRC and steel. This is explained further in Section

5.2.6.

5.2.4 Steel material model

Steel laminate in the HCFPS is subjected to tensile stress as it acts as reinforcement.

Elastic properties (E=209.9 GPa, ν =0.3) and plastic stress and strain values were

used in ABAQUS, as obtained from the tensile tests (refer to section 4.1.9). 3mm

thick perforated steel laminate was used in the test panel with 30% openings.

Effective thickness for steel laminate in the FE model was taken as 2.1 mm in order

to account for the plate openings.

5.2.5 Model description

Considering the symmetry of the test panel along the span, a half model of HCFPS

panel was developed with appropriate boundary conditions as illustrated in Figure 5-

7. At the centre of the beam, translations along the Z and X directions and rotations

about the X, Z and Y axes were restrained. 10 mm thick and 100 mm wide steel

plates were modelled under the HCFPS panel at the supports. Translations were

restrained in the Y direction at the supports as shown in Figure 5-7. This model

simulates the test setup, as steel plates were placed under the HCFPS panel as shown

in Figure 4-20 in section 4.6.1. Load spreader beams were also modelled and the load

was applied as illustrated in Figure 5-7.


Figure 5-7: FE model of HCFPS panel for static loading test

C3D8R eight node liner brick elements were used in the FE model for all parts along

with reduced integration and hourglass control [74]. The FE model was meshed as

shown in Figure 5-8. Fine mesh was used in the beam, which exhibited flexural

failure during the testing. Density of the mesh was determined by conducting a

convergence study.

Figure 5-8: FE mesh of HCFPS panel

5.2.6 Static analysis, validation and discussion

Static analysis of the FE model was conducted with the above material models.

Perfect bonding was assumed between each of the materials. This assumption was

supported by the experimental investigation in which no de-lamination was observed

until failure (refer to Sections 4.6.2 and 4.8.3).

Load-deflection behaviour was compared with experimental results to validate the

FE model. FE model exhibited a very good agreement in not only the linear

behaviour but also in the non-linear behaviour captured during the tests, as shown in


Figure 5-9. The FE model exhibits a linear behaviour up to an applied load of 14 kN.

From this point onwards, it exhibits a non-linear behaviour. This value of the load

matched reasonably well with the experimental yielding point (refer to Section

4.6.2), with the small difference due to non uniformities of the material layers in the

experimental panel.

Figure 5-9: FE model validation with experimental results

Furthermore, FE results also exhibited a flexural failure in the central span of the

HCFPS panel beam. Damage due to the tensile failure of the GRC in the FE model is

illustrated in Figure 5-10. The damage parameter of GRC has been defined as the

ratio of cracking strain to the total strain in ABAQUS. GRC and steel laminate

follow the non-linear tensile behaviour after yielding as observed in both the FE

analysis and experimental testing. Further, stresses in individual materials in other

parts of the HCFPS panels did not exceed their capacities. This was also observed in

experimental testing as there was no resulting shear or support bearing failure. The

analysis was conducted only until the mid-span deflection reached 45 mm for the

process of validation, as the computation time increased significantly beyond this

point. Since non-linear behaviour could be predicted up to a deflection ductility

index of 4, which is the ratio of 45 mm to 11 mm, FE prediction was considered as

adequate for further analysis. Thus, FE models can be used for predicting the

behaviour of HCFPS.

0

5

10

15

20

25

0 10 20 30 40 50

Load (

kN

)

Deflection (mm)

Test 2

Test 1

FE model behaviour


Figure 5-10: Flexural cracks in the beam of HCFPS at the failure

Flexural stress and strain distributions along the cross-section at mid-span of HCFPS

at the yielding point (at the applied load of 14 kN and 11 mm deflection, refer to

Figure 5-9) were obtained from FE model as shown in Figure 5-11. Steel laminate

starts to yield at this point as it reaches to tensile yielding stress of 200 MPa (refer to

Figure 4-7). The yielding point obtained in experimental testing of HCFPS panel (at

the applied load of 12.5 kN and 9.9 mm deflection, refer to Figure 4-21) therefore

matches the FE results reasonably well.

PU core attracts insignificant tensile and compressive stresses due to its lower elastic

modulus according Figure 5-11. As PU has a lower tensile capacity, this hybrid

configuration facilitates the avoidance of tensile stress in the PU core. Similarly,

compressive stress in the compression zone of the slab is mostly attracted to the GRC

layer, (though in Figure 5-11 this is not distinct due to the scale).

Figure 5-11: Stress and strain distribution at the mid-span of the HCFPS


At the applied load of 14 kN, compressive stress of the PU core in the slab of

HCFPS, is (Figure 5-11) 0.01 MPa, which is less than the plastic compressive

strength of 0.505 MPa presented in Figure 4-3 (Section 4.1.4). However, PU cannot

be neglected from the FE analysis as PU acts as a core and maintains the integrity of

the sectional configuration of the HCFPS.

Steel laminate acts as reinforcement for the HCFPS by attracting high tensile stress

of 200 MPa (Figure 5-11). The lower most GRC layer at mid-span cracks at the

applied load of 14 kN and hence tensile stress in that layer is zero. The top most

GRC layers in the slab of HCFPS panel attract compressive stress. The compressive

stress then distributes over the area of top slab resulting in lower stress

concentrations in the top most GRC layer of the HCFPS. This can be seen in Figure

5-10 where flexural cracks appear only in the beam of the HCFPS without any

compression failure in the slab. Compressive stress at the top GRC layer is 5.8 MPa

at 14 kN (Figure 5-11) load and the compressive strength of GRC obtained from the

experimental testing is 19.6 MPa. The FE results also showed that the compressive

stress in the top GRC layer did not reach the compressive strength even at 45 mm

mid-span deflection. This behaviour was further supported during the experimental

testing in which compression failure was not evident in the slab of the HCFPS panel.

5.3 FE MODEL DEVELOPMENT AND VALIDATION FOR GRC-PU-GRC

COMPOSITE PANEL

FE models for the GRC-PU-GRC composite test panels were developed and

conducted linear static analysis to simulate static load test explained in Section 4.8.

Linear properties of the materials were used to conduct the FE analysis in ABAQUS

[47]. Load-deflection response FE model was obtained from that analysis and

compared with experimental results

5.3.1 FE model

Layered three-dimensional FE models were developed for the GRC-PU-GRC

composite panel as shown Figure 5-12 (test panel dimensions are given in Section

4.8.1). Translations in X, Y and Z directions and rotations in Y and Z directions

were restrained at one end whilst translations in X and Y direction and rotations in Z

and Y directions were restrained at the other end (refer to Section 4.8.2) in order to

simulate the restrain from the steel bars.


C3D8R eight node liner brick elements were used in the FE model for all parts along

with reduced integration and hourglass control [74]. The FE model was meshed as

shown in Figure 5-12. Density of the mesh was determined by conducting a

convergence study. Mesh was of 10 x 10 x 20 mm size providing 3200 elements.

Perfect bond was assumed to occur between GRC and PU layers in FE model as

there was no de-lamination during the loading test until the flexural failure, as

explained in Section 4.8.3.

Figure 5-12: FE model for GRC-PU-GRC panel

5.3.2 Material properties

The material properties of GRC were obtained from the material testing and

properties of 62 kg/m3

density PU were determined using Equation 5-5 [14]. Material

properties are listed in Table 5-4.

Equation 5-5

(Where modulus of solid PU ( ) and density of solid PU are considered to be

1.6 GPa and 1200 kg/m3 respectively).

Table 5-4: Component material properties for the GRC-PU -GRC , FE model.

Properties PU GRC

Density (kg/m3) 62 1983

Elastic Modulus (Mpa) 10.5 5000

Poisons ratio (ν) 0.3 0.24

Poisons ratio (ν) for the PU was taken from [72] for the density of 62 kg/m3 and ν of

GRC was taken as 0.24 from [73].


5.3.3 FE model validation

Validation was conducted by comparing the load-deflection curve of the FE model

with experimental load-deflection curves. Mean experimental mid-span deflection

values at various loads were obtained from the panels separately for type A and Type

B. The load-deflection data was then plotted in the graph, as seen in Figure 5-13 and

Figure 5-14. FE models generated results that were in agreement with the mean

load–deflection curves. Thus, the validation produced a satisfactory agreement up to

the yielding point of the panels. The validated layer model was used for further

investigations. Parametric study will be conducted to determine structural capacity of

GRC-PU-GRC composite panel as one-way and cantilever spans, which are

component parts of HCFPS (Presented in Chapter 6).

Figure 5-13: Validation for FE model for static test (Type A panel)

Figure 5-14: Validation for FE model for static test (Type B panel)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

0 1 2 3 4 5 6 7

Panel 2

Panel 1

FE Behaviour

Load,

N

Deflection, mm

0

500

1000

1500

2000

2500

3000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Panel 1

Panel 2

FE Behaviour

Deflection, mm

Load,

N


5.4 SUMMARY

FE models were developed for the experimentally tested HCFPS panel (3200 mm

span) and GRC-PU-PU composite panel, which is top slab of HCFPS. These models

were validated with previously generated static and dynamic experimental results.

FE models for the HCFPS test panels were developed and validated using first mode

natural frequency and acceleration response. First mode natural frequency obtained

from the FE analysis agreed with the experimentally obtained value with only 0.84

Hz (3%) difference. Acceleration response of FE model obtained from heel impact

excitation and walking load agreed well the experimentally obtained responses.

Hence, FE models can be used to simulate the walking activities and determine the

vibration response of HCFPS panels.

FE models of HCFPS exhibited a very good agreement with experimental load-

deflection in not only the linear behaviour but also in the non-linear behaviour. FE

results also exhibited a flexural failure in the central span of the HCFPS panel beam

as observed in experimental testing. Failure resulted due to the tensile failure of GRC

and yielding of steel laminate in the flexural zone. Stresses in individual materials in

other parts of the HCFPS panels excluding flexural zone, did not exceed their

capacities. This was also observed in experimental testing as there was no resulting

shear or support bearing failure. Nonlinear, FE analysis was conducted to obtain a

deflection ductility index of 4. Thus, FE models can be used to predict the linear and

non-linear behaviour of HCFPS.

Steel laminate acts as reinforcement for the hybrid by attracting high tensile stress

and yielding of HCFPS panel occurs by yielding of steel laminate. PU core attracted

negligible tensile or compressive stress due to lower elastic modulus but the integrity

of HCFPS section provides by acting as infill material.

FE model was developed for GRC-PU-GRC composite test panel and load-

deflection response of FE model was validated with experimental results. This can be

used to investigate the performance of the top slab of the HCFPS.

Validated FE models will be used for further parametric studies to develop HCFPS

floor system in Chapter 6 and 7.

Chapter 6: Static performance of HCFPS 91

Chapter 6: Static performance of HCFPS

This chapter presents the development of HCFPS to satisfy static performance

requirements by combining the beneficial inherent properties of individual

component materials to achieve optimum performance. Details of parametric studies,

which were conducted to investigate the static performance characteristics and

strength capacity of HCFPS, are explained.

6.1 DEVELOPMENT OF HCFPS

HCFPS can be graphically represented in a building floor as shown in Figure 6-1.

The structural supporting system can be either steel or Reinforced Concrete (R/C).

HCFPS can be fixed to the structural frame as shown in Figure 6-2. Static

performance characteristics of HCFPS were investigated considering these

supporting conditions.

Figure 6-1: Graphical representation of building floor using HCFPS panels

Figure 6-2: Proposed supporting methods for HCFPS floor to structural frame

92 Chapter 6: Static performance of HCFPS

6.1.1 Section configuration for static performance studies

The proposed HCFPS panel can be prefabricated as shown in Figure 6-3. Width of

the HCFPS was limited to 2 m to suit prefabrication and transportation requirements.

Span length of the HCFPS was varied by changing the material properties and

sectional configuration. A HCFPS panel with single beam (refer to Figure 6-4) was

used to investigate static performance as the proposed HCFPS panel is symmetrical

(refer to Figure 6-3). PU core was replaced with GRC in the vicinity of the supports

to enhance the support bearing capacity, as shown in Figure 6-3. Performance

characteristics of the GRC-PU-GRC panel (slab section of the HCFPS) and slab joint

were also investigated separately.


Figure 6-4: HCFPS section for parametric study

Figure 6-5: GRC fill replacing PU core in the vicinity of supports

Axis of symmetry


6.2 VARIABLES IN PARAMETRIC STUDIES

Stiffness and deflection limits, and flexural, shear and support bearing capacity were

investigated as static performance criteria to develop HCFPS. Parametric studies

were conducted on HCFPS using validated FE techniques. Sectional configuration,

properties of component materials, span lengths, loading limits and support

conditions were used as variable parameters in this study.

6.2.1 Section configurations

Three types of HCFPS section configurations were used for the parametric study as

shown in Figure 6-6 and Table 6-1.

Figure 6-6: Section parameters for parametric study

Table 6-1: HCFPS section and span parameters

Type of

Section

Span

(m)

b

(mm)

a

(mm)

t

(mm)

h

(mm)

A

B

C

3.0

5.0

7.5

100

150

200

100

150

200

60

80

80

200

350

450

6.2.2 FE model for HCFPS

Validated FE techniques were used to evaluate the static performance characteristics

of HCFPS. Half models of HCFPS panels were developed, considering the symmetry

of the HCFPS panels along the span (refer to Figure 6-4 and 6-5), with appropriate

boundary conditions as shown in Figure 6-7. Translations along the Z and X

directions and rotations about the X, Z and Y axes were restrained at the centre of the

beam. Translations were restrained in the X, Z and Y directions at the supports, as

shown in Figure 6-7, to obtain the supporting conditions demonstrated in Figure 6-2.


Figure 6-7: FE model of HCFPS

C3D8R eight node liner brick elements were used in the FE model for all

components of the HCFPS, along with reduced integration and hourglass control

[74]. The FE model was meshed as shown in Figure 6-7. Density of the mesh was

determined by conducting a convergence study.

6.2.3 Material Properties

Properties of steel, GRC and PU, listed in Tables 6-2, 6-3 and 6-4, were used for

parametric studies. Properties of high strength steel were obtained as explained in

Section 2.3.1. Properties of Mild steel were obtained from experimental testing in

Section 4.1.9. Material properties can be enhanced by changing the constituents of

GRC [29] and by increasing the density of PU [25]. Properties of GRC were obtained

as explained in Section 2.3.3 [12] and properties of PU were obtained as per Section

2.3.2 [25]. HCFPS can be developed as a economical floor system by using currently

available and widely used material properties of both GRC and PU. The accepted

Young's modulus of GRC is 10 GPa or higher [12]. Properties of GRC 10 can be

obtained economically either by method of spay or premix [12] (refer to Section

2.3.3). Low density PU core is economical and the lowest density for the HCFPS was

selected as 100 kg/m3 (PU 20). Therefore, higher attention was paid to use GRC 10

and PU 20 to develop HCFPS as economical floor system.

Table 6-2: Properties of Steel

Name Density

Kg/m3

Young's

Modulus

GPa

Shear

Modulus

GPa

Shear

Strength

MPa

Tensile

strength

MPa

Poisson's

ratio

M Steel (Mild Steel)

T Steel (High Strength Steel)

7800

7800

210

210

80

80

105

230

210

550

0.3

0.3


Table 6-3: Properties of GRC [12]

Name Density

Kg/m3

Young's

Modulus

GPa

Compressive

Strength

MPa

Shear

Strength

MPa

Tensile

strength

MPa

Poisson's

ratio

GRC 5

GRC 10

GRC 15

GRC 20

1900

1900

1900

1900

5

10

15

20

20

30

40

50

3

4

5

6

3

4

5

6

0.24

0.24

0.24

0.24

Table 6-4: Properties of PU [25]

Name Density

Kg/m3

Young's

Modulus

MPa

Shear

Modulus

MPa

Compressive

Strength

MPa

Shear

Strength

MPa

Tensile

strength

MPa

Poisson's

ratio

PU 20

PU 75

PU 150

PU 360

100

200

300

500

23.4

76.1

151.6

361.2

5.7

21.2

45.9

121.3

0.743

2.415

4.800

11.50

0.556

1.807

3.600

8.580

1.000

-

-

-

0.3

0.3

0.3

0.3

6.2.4 Loading conditions

HCFPS floors were developed for use in residential and office floors. Self-weight of

the HCFPS, using the material properties described in Section 6.2.3, were calculated

as shown in Table 6-5. Average self-weight of the HCFPS can be used as 1 kPa. Two

loading conditions as given in Table 6-6 were used according to AS 1170.1 [48].

Dead and imposed loads were used as combination of (1.25 × Dead load) and (1.5 ×

Imposed Load) according to AS 1170.0 [80]. Performances of HCFPS panels were

investigated under service and ultimate loads.

Performance characteristics of the GRC-PU-GRC composite, which is the top slab

section of HCFPS, will be separately investigated in Sections 6.8. under distributed

and concentrated loads. Concentrated loads were used for residential and office

floors as 1.8 kN and 3.5 kN respectively [48] to investigate the behaviour of GRC

layer and PU core at the location of applied load.


Table 6-5: Self-weight of the HCFPS floors

Type of

Section

Type of

GRC

Mass (kPa)

PU 20 PU 75 PU 150 PU 360

A

B

C

GRC 5

GRC 10

GRC 20

GRC 5

GRC 10

GRC 20

GRC 5

GRC10

GRC 20

0.59

0.69

0.78

0.63

0.78

0.89

0.67

0.87

1.01

0.76

1.04

1.25

Table 6-6: Loading cases [48]

Floor Type

Dead Load (kPa)

(self weight + fixed

partition and finishes)

Imposed

Load

(kPa)

Service load

(kPa)

Ultimate

load

(kPa)

Residential 1.0 + 1.0 1.5 3.5 4.75

Offices or work areas 1.0 + 1.0 3 5.0 7.00

6.3 RECTANGULAR BEAM AND TAPERED BEAM

6.3.1 FE modelling

The proposed HCFPS configuration consists of a rectangular beam. This section

discusses why a rectangular beam section was selected by comparing the

performance of HCFPS sections consisting of tapered and rectangular beams. Three

types of sectional configurations were selected to investigate the performance of

rectangular and tapered beam sections. Spans and section parameters (a, b, d and h)

were determined as shown in Figure 6-8 and Table 6-7. ―a‖ was changed in stages

from a rectangular section to tapered section in increments of 25 mm for each type of

section. Material properties were used as given in Table 6-8 (obtained from Tables 6-

2, 6-3 and 6-4). FE models were developed as described in section 6.2.2.



Table 6-7: HCFPS section and span parameters

Type of

Section

Span

(m)

b

(mm)

a

(mm)

t

(mm)

h

(mm)

A

B

C

3.0

5.0

7.5

100

150

200

100-200

150-250

200-300

60

80

80

200

350

450


Properties PU GRC Steel

Name

Density (kg/m3)

E (Mpa)

Poisons ratio

PU 20

100

0.24

0.3

GRC 5

1900

5, 000

0.24

GRC 10

1900

10,000

0.24

M Steel

7800

210,000

0.3

6.3.2 FE analysis results and discussion

Linear static analyses were conducted to investigate the performance characteristics

of HCFPS. Uniformly distributed loads were applied incrementally (0.5 kPa) from 0

to 10.0 kPa in the analysis. Deflection and flexural, shear and support bearing

capacities of each type of section were studied for each section configuration.

Deflection and flexural capacity did not change significantly with dimension ―a‖ the

for the three types of sections.

A minor variation in shear stress distribution across the beam (refer to Figure 6-8)

was observed with changes in ―a‖. GRC and PU transfer shear stresses across the

beam section of HCFPS. PU core attracts lower shear stress due to the lower elastic

modulus and GRC outer shell transfers higher shear stress across the section. A


typical shear stress distribution (under applied uniformly distributed loads of 7.0

kPa) in the GRC outer layer (across the beam) is shown in Figure 6-8 (for type B

HCFPS section). Ultimate load under 2 kPa dead load and 3 kPa imposed load is 7.0

kPa (refer to Table 6-1). Shear stresses in the GRC outer shell were obtained for all

HCFPS panels by changing ―a‖ under 7.0 kPa load as shown in Figure 6-9. The

stress concentration in the web of the beam decreased with increase of dimension "a"

(refer to Figures 6-9 and 6-10). Only a component of shear force transfers through

the outer GRC layer in the tapered beam, as the GRC layer makes a small angle with

the vertical direction. In contrast, high shear for transfers to the outer GRC layer of

rectangular beam as the GRC layer is vertical. However, the variation of the stress

concentration due to this scenario is minor and all HCFPS panels with rectangular

beams did not exceed the shear capacity of GRC at the expected design ultimate load

of 7.0 kPa (for office floor). Shear capacity of "GRC 10" is 4 MPa, according to

Table 6-2. GRC 10, GRC, 15 or GRC 20 can be used to obtain shear stress capacity

greater than 4 MPa (refer to Table 6-3) in GRC layer of HCFPS. Therefore, with

those materials, rectangular beam section can be used for HCFPS.

Figure 6-9: Shear stress in GRC outer shell for type B section

Figure 6-10: Variation in stress in the GRC layer (with GRC 10) with change in "a"

Continuous glass fiber mesh (refer to Figure 6-11) can be embedded in the GRC

layers instead of chopped glass fibers to improve shear and flexural capacity.

Continuous glass fiber mesh has been used for Domeshells structure construction

[81] to improve the performance of GRC layers at high stress concentrated zones.

Stress carrying capacity of GRC can be improved up to 10-15 MPa [82] by

embedding a continuous glass fiber mesh. Hence, continuous glass fiber mesh can be

0

0.5

1

1.5

2

2.5

3

3.5

Shear

Str

ess (

MP

a)

100 125 150 175 200 225 250 275 300

3 5 7.5 Span (m)

a (mm)


used in high shear stress concentrated zones of the HCFPS beam (refer to Figure 6-9)

to improve the shear bearing capacity and to control possible crack.

Figure 6-11: Continuous glass fiber mesh

The use of rectangular beam sections for HCFPS is economically advantageous as

less material is required. HCFPS sections with tapered beams did not offer

significant improvement in flexural, deflection or shear performance compared to

rectangular beams. Hence a rectangular beam section ("T" shaped) has been selected

for the development of HCFPS. Depth ―h‖, slab thickness ―t‖, width of the beam "b"

and properties of materials will be used for further parametric studies to develop

HCFPS.

6.4 FLEXURAL PERFORMANCE

Flexural performance was the governing design criteria of HCFPS panels as a

flexural failure was observed during experimental testing (refer to sections 4.6.2 and

5.2.6). Flexural performance of A, B and C type HCFPS panels with rectangular

beams (refer to Table 6-1) were studied.

6.4.1 FE modelling

Material properties and applied load were used as variable parameters in the study.

Applied load was increased to obtain linear and non-linear deflection in all HCFPS

panels by using linear and non-linear properties of component materials. FE models

were developed as described in Section 6.2.2.

6.4.2 Properties of GRC

Linear and non-linear material properties of GRC were used in FE analysis using

appropriate material models (refer to Figure 6-12) explained in Section 5.2.2.

Properties for the material model were obtained, as listed in Table 6-9. Parameters

include: compressive yield stress (σcy), compressive yield strain (εcy), ultimate

compressive strain (εcu), cracking tensile strength (σcr), first cracking tensile strain


(εcr), tensile stress at the end of tensile model (σtu) and ultimate tensile strain (εtu) and

modulus of elasticity (E). Density and Poisson's ratio were obtained from Table 6-3.

Figure 6-12: GRC material model

Table 6-9: Properties of of GRC

Name E,Ec

GPa

σcy

MPa

σcr

MPa

σtu

MPa εcy εcu εcr εtu

GRC 5

GRC 10

GRC 15

GRC 20

5

10

15

20

20

30

40

50

3

4

5

6

1

1

1

1

0.0040

0.0030

0.0027

0.0025

0.03

0.04

0.04

0.04

0.00060

0.00040

0.00033

0.00030

0.01

0.01

0.01

0.01

6.4.3 Properties of Steel

Two types of steel were used as given in Table 6-2. Steel laminate in the HCFPS is

subjected to tensile stress. Stress-strain relationships for both types of steel are shown

in Figure 6-13. Elastic properties and plastic stress and strain values were used in

ABAQUS.

(a) High strength steel (T steel) [22] (b) Mild steel (M Steel)

Figure 6-13: Stress-strain relationship for High strength and mild steel

0

50

100

150

200

250

300

350

400

450

0 0.05 0.1 0.15 0.2 0.25

Str

ess (

MP

a)

Strain (‰)


6.4.4 Properties of PU

The PU core was modelled using linear elastic properties as given in Table 6-4. Non-

linear properties of PU were not modelled as it attracts insignificant stresses due to

the very low elastic modulus compared to GRC and steel. This will be explained

further in Section 6.4.5.

6.4.5 FE abalysis, results and discussion

Uniformly distributed loads were applied increment of 0.5 kPa from 0 to 10.0 kPa.

Non-linear static analyses were conducted to investigate the flexural response.

Load-deflection behaviour

Load-deflection behaviour of A, B and C type sections were obtained as shown in

Figure 6-14. Load-deflection plots with modulus of elasticity of 10 GPa and 15 GPa

lay between the two load-deflection plots (GRC 5 and GRC 20) for each section

shown in Figure 6-14.

Stiffness and deflection of the HCFPS can be controlled by adjusting material

properties and section configuration. Stiffness of the HCFPS sections improved with

an increase in elastic modulus of GRC from 5 GPa to 20 GPa for all types, as seen in

Figure 6-14. Yielding limits of the HCFPS sections improved with high strength steel

laminate in comparison to Mild steel laminate. The stiffness or yielding limit of the

HCFPS sections did not significantly change due to the increase in density and

modulus of elasticity of PU. Hence, density of the PU core was maintained as 100

kg/m3

for all sections.

The deflection performance was evaluated at service load using usual criteria of

Span/250 (under both instantaneous and long term total loads) and Span/360 (under

superimposed post construction loads) given in current design standards. The

deflection assessment was carried out at service load without the ultimate load

factors as shown in Table 6-10. This shows that deflections of HCFPS sections

sunder service loads are well below deflection control limit of span /360 and

Span/250. Hence HCFPS can be used to satisfy deflection performance in floor

plates. Deflections of HCFPS panels can be controlled by changing section

configuration and material properties.


Applied ultimate load on office floor (qult, Office= 7 kPa) and residential floor (qult, Resi= 4.75 kPa)

Figure 6-14: Load -deflection behaviour of A, B and C type sections

Table 6-10: Serviceability deflection of the HCFPS floor with PU 20

Type of

Section

Type of

GRC

Residential Office Deflection

control limits

Service

load

(kPa)

Deflection

mm

Service

load

(kPa)

Deflection

mm Span

360

Span

250

A

B

C

GRC 5

GRC 20

GRC 5

GRC 20

GRC 5

GRC 20

3.1

3.1

3.2

3.2

3.3

3.3

2.8

1.3

4.9

2.2

12.6

5.5

4.6

4.6

4.7

4.7

4.8

4.8

4.1

2.0

7.2

3.3

18.3

8.0

8.3

8.3

13.9

13.9

20.8

20.8

12.0

12.0

20.0

20.0

30.0

30.0

0

5

10

15

20

25

0 10 20 30 40

Load (

kP

a)

Deflection (mm)

GRC 5, PU 20, M Steel

GRC 20, PU 20, M steel

Type A Section

Yeilding point

qult,Resi

qult,Office

0

5

10

15

20

25

0 10 20 30 40 50

Load (

kP

a)

Deflection (mm)

GRC 5, PU 20, T Steel

GRC 20, PU 20, T steel

Type A Section

Yeilding point

qult,Office

qult,Resi

0

5

10

15

20

25

30

35

0 10 20 30 40

Load (

kP

a)

Deflection (mm)

GRC 5, PU 20, M Steel GRC 20, PU 20, M steel

Type B Section

Yeilding point

qult,Resi

qult,Office

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Load (

kP

a)

Deflection (mm)

GRC 20, PU 20, T Steel GRC 5, PU 20, T steel

Type B Section

qult,Office

Yeilding point

qult,Resi

0

5

10

15

0 10 20 30 40 50

Load (

kP

a)

Deflection (mm)

GRC 5, PU 20, M Steel

GRC 20, PU 20, M steel

Type C Section

Yeilding point

qult,Resi

qult,Office

0

5

10

15

0 10 20 30 40 50 60

Load (

kP

a)

Deflection (mm)

GRC 5, PU 20, T Steel

GRC 20, PU 20, T steel

Type C Section Yeilding point

qult,Office

qult,Resi


Load carrying capacity of HCFPS

The ultimate load limits in an office floor (7.0 kPa) and residential floor (4.75 kPa)

(refer to Table 6-2) are shown in Figure 6-14. Results show that HCFPS floors

remain within linear elastic region up to the ultimate load. At the ultimate conditions,

individual materials did not exceed their capacities (including shear zone). Ultimate

load carrying capacity of HCFPS sections are shown in Figure 6-14 (yielding point).

Therefore, a Factor of Safety (FOS) for the flexural performance of HCFPS can be

defined as ratio of ultimate load carrying capacity/applied ultimate load. Factor of

safety of each section configuration is shown in Table 6-11. FOS was estimated only

for the material combination of MSteel, PU 20, GRC 20 and GRC 5. FOS higher than

these values when TSteel is used because ultimate load bearing capacity is high as

shown in the Figure 6-14. This factor can be used as per the design requirements by

adjusting section configuration and material properties. Therefore, HCFPS can be

used to satisfy flexural performance requirements in floor plates.

Furthermore, superimposed dead load included in the applied ultimate load is 1.0 kPa

but this can be increased, if required and such increases (up to a point) will also

provide a satisfactory behaviour as evident from Figure 6.14. The ultimate load

carrying capacity of the HCFPS can be improved using "T" steel, section

configuration and material properties according to Figure 6-14.

Table 6-11: Factor of Safety (FOS) for flexural performance of HCFPS with PU 20 and MSteel

Type of

Section

Type of

GRC

Residential (qult,Resi= 4.75 kPa) Office (qult,Office= 7 kPa)

Ultimate load

carrying capacity

(kPa)

FOS

Ultimate load

carrying capacity

(kPa)

FOS

A

B

C

GRC 5

GRC 20

GRC 5

GRC 20

GRC 5

GRC 20

8

10

8

10

7.5

7.8

1.7

2.1

1.7

2.1

1.6

1.6

8

10

8

10

7.5

7.8

1.2

1.4

1.2

1.4

1.1

1.1

Moreover, capacity reduction factor , which is the ratio between envisaged failure

load and theoretical failure load, or partial factor of safety ( m ), as defined in design

codes [83] can be incorporated into the designs of HCFPS . However, this is separate


area of research and has to be investigated considering the individual material

characteristics of GRC, PU and steel and hybrid behaviour of these in relation to the

environmental degradation.

Ductility

Ductility of a structural member can be considered as a measure of its ability to

undergo deformation without a substantial reduction in flexural capacity [71]. One

method of quantifying the ductility is the displacement ductility index, which is the

ratio of ultimate deflection (at the final failure ) to the deflection at yielding [71].

Another way of defining the ductility of a structural member is in terms of strain

energy as the ratio of energy at ultimate strain to the energy at the maximum elastic

displacement [84]. Deflection ductility index method was used in this research as it

was straightforward and directly applicable for the HCFPS panels.

Yielding point deflections of A, B and C types of HCFPS panels are shown in Figure

6-14. FE analyses were conducted to obtain a reasonable deflection beyond the

yielding point as shown in Figure 6-14. Analyses were terminated with deflections

shown in Figure 6-14, as computational time was increased significantly of FE

models. However, it can be expected that deflection may further extend with the steel

laminate yielding. Analysis termination point deflection can be considered as

ultimate deflection (at the final failure) for HCFPS panels. Using the data deflection

ductility index of 4 or higher value for all HCFPS panels can then be estimated

conservatively. Deflection ductility index of HCFPS is hence acceptable for a

structural floor plate.

Failure modes of HCFPS

FE analysis exhibited a flexural failure in the central span of the beam of the all types

of HCFPS (refer to Figure 6-15). GRC and steel laminate show non-linear tensile

behaviour after yielding. Stresses in individual materials in other parts of the HCFPS

panels excluding flexural zone, did not exceed their capacities. Similar behaviour

was observed in experimental testing (refer to Section 4.6.2) and FE validation of test

results (refer to Section 5.2.6). Non-linear behaviour was obtained for all panels up

to a deflection ductility index of 4 as can be seen in Figure 6-15. Stresses in

individual materials in other components (excluding flexural zone) of the HCFPS

panels did not exceed their capacities even after passing yielding point.


Figure 6-15: A typical flexural crack development in the beam of the HCFPS

Stress-strain distribution across mid-span section

Stress and stress-distribution across the HCFPS section at the mid span were used to

evaluate the performance of a hybrid assembly. Stress and strain distribution at mid-

span were obtained as that was the identified critical zone under the bending.

Flexural stress and strain distributions along the cross-section at the mid-span of

HCFPS, at the applied load of 5 kPa were obtained for all HCFPS sections from FE

model as shown in Figure 6-16. A typical stress distribution in FE model is shown in

Figure 6-17. Material types of (GRC 5, PU 20 and M steel) were used for all HCFPS

panels to obtain stress and strain diagrams.

According to flexural stress and strain distributions at the centre of the HCFPS panel,

PU core attracted insignificant tensile or compressive stress due to the comparatively

low elastic modulus as shown in Figure 6-17. PU has low tensile capacity and this

hybrid configuration facilitates the avoidance of tensile stress in the PU core.

Therefore, only linear elastic properties of PU can be used in the FE analysis as its

stresses do not exceed the yielding limits. However, PU acts as a core and maintains

the integrity of the sectional configuration of the HCFPS. Steel laminate acts as

reinforcement for the hybrid by attracting high tensile stress. GRC layers in the slab

of HCFPS panel attract compressive stress (refer to Figure 6-17). FE results

demonstrated that the compressive stress in the top GRC layer did not reach

compressive strength even at 40 mm mid-span deflection for all types of HCFPS

sections. This deflection can be used to obtain deflection ductility of 4. Similar

behaviour was observed during experimental testing in which compression failure

was not evident in the slab of the HCFPS panel (refer to Section 4.6.2).


(a) Stress and strain distribution at the mid-span of the A, B and C type HCFPS under 5

kPa

(b) Typical stress and strain distribution at the mid-span of the HCFPS

Figure 6-16: Stress and strain distribution at the mid-span of the HCFPS along X-X

0

50

100

150

200

-10 10 30 50 70 90 110

Section D

epth

(m

m)

Stress (MPa)

Type A Section

0

50

100

150

200

-0.00075 -0.00025 0.00025 0.00075

Section d

epth

(m

m)

Strain

N/A

Type A Section

0

50

100

150

200

250

300

-10 10 30 50 70 90 110

Section D

epth

(m

m)

Stress (MPa)

Type B Section

0

50

100

150

200

250

300

-0.00075 -0.00025 0.00025 0.00075

Section d

epth

(m

m)

Strain

N/A

Type B Section

0

50

100

150

200

250

300

350

400

450

-10 10 30 50 70 90 110 130

Section D

epth

(m

m)

Stress (MPa)

Type C Section

0

50

100

150

200

250

300

350

400

450

-0.001 -0.0005 0 0.0005 0.001

Section d

epth

(m

m)

Strain

N/A

Type C Section


Figure 6-17: A typical flexural stress distribution (in GRC and PU) at the mid-span (Type A)

When the HCFPS panel is subjected to bending, compressive stresses occur mainly

in the slab, while tensile stresses occur in the bottom steel laminate. Shear stresses

occur across the web of the beam. As GRC and PU exhibit better performance under

compressive and shear stresses [12, 14], they are profiled and located to attract

compressive and shear stresses in the slab and beam of the HCFPS as shown in

Figure 6-3. The continuous GRC layer along the edges provides an encasement to the

HCFPS. Overall, the integrity of the HCFPS section is maintained by the PU core

as it provides a connection between the GRC layers and buckling support for the thin

GRC layers. However, higher tensile, compressive and shear stresses are attracted to

the steel laminate and GRC as their elastic modulus are significantly higher than that

of the PU. Therefore, beneficial inherent properties of individual component

materials based on their performance capability were combined to achieve optimum

performance of the HCFPS.

Creep and shrinkage of HCFPS

Creep deformation of a structural member is defined as the low deformation

followed by the initial elastic deformation under sustained loads [29]. Experimental

test was not conducted to investigate creep and shrinkage behaviour of the HCFPS.

However, GRC is considered as a material which capable of sustaining loads over

prolong periods [29]. Creep deformation in PU core is minimal as it attracts low

stresses in the HCFPS due to the low elastic modulus. HCFPS section contains steel

laminate reinforcement hence GRC and PU are not directly subjected to creep

deformation. Therefore, creep deformation can be considered as conservatively low.

However, for the design purposes elastic deformation obtained from the analysis was

multiplied by a conservative factor of 1.5 to consider any possible creep deformation

with sustained loading as shown in Table 6-12. This shows that creep and shrinkage


deflection factor of 1.5 can be allowed for HCFPS floors and factored deflection can

be still maintained below the deflection control limits. In this context, suitable

material combination needs to be determined so that factored deflection does not

exceed the yielding point of HCFPS (refer to Figure 6-14). Acceptable creep and

shrinkage performance can be achieved for all types of HCFPS with GRC 10, which

is the commonly used type of GRC with modulus of elasticity of 10 GPa. Hence,

GRC 10 is recommended to use in HCFPS construction.

Table 6-12: Factored deflection to account for creep and shrinkage deformation

Type

of

Section

Type of

GRC

Residential Office Deflection

control limits

Service

load deflection

(mm)

Factored

deflection

mm

Service

load deflection

(mm)

Factored

deflection

mm

Span

360

Span

250

A

B

C

GRC 5

GRC 20

GRC 5

GRC 20

GRC 5

GRC 10

GRC 20

2.8

1.3

4.9

2.2

12.6

8.3

5.5

4.2

2.0

7.4

3.3

20

12.5

8.3

4.1

2.0

7.2

3.3

18.3

12.2

8.0

6.2

3.0

10.8

5.0

27.5

18.5

12.0

8.3

8.3

13.9

13.9

20.8

20.8

20.8

12.0

12.0

20.0

20.0

30.0

30.0

30.0

6.5 COMPARISON OF HCFPS WITH STEEL-DECK COMPOSITE

FLOOR SYSTEM USING STIFFNESS AND SELF-WEIGHT

Stiffness and self-weight of HCFPS were compared with an existing conventional

floor system, steel-deck composite floor system with a 3000 mm one way span [85].

Details of testing and material properties of the steel-deck composite floor system are

presented in [22, 85].

Type A (3 m span) HCFPS panel, described in Table 6-1, was used in this study.

Elastic properties of GRC, along with non-elastic properties, were obtained from

Table 6-3 and 6-9. Elastic properties of PU (as described in Section 5.2.3) were

obtained from Table 6-3. Elastic and plastic properties of steel were selected from

Section 6.4.3 and Table 6-2. FE modelling was conducted as explained in Section

6.2.2 and static analyses were conducted by changing material properties.


Steel-deck composite floor system panel was tested by applying central line load

with a clear span of 3000 mm between supports. HCFPS panel was also loaded with

a central line load to obtain the load-deflection response. Stiffness of HCFPS can be

increased to achieve a stiffness close to that of steel deck composite floor system by

improving material properties. Stiffness of HCFPS is similar to steel deck composite

floor system by using material types of GRC 20, PU 20 and M steel (refer to Tables

6-2, 6-3 and 6-4) as shown in Figure 6-18.

Figure 6-18: Load-deflection plots of steel deck floor system and HCFPS

Self-weight of HCFPS test panels were compared with that of a steel-deck composite

system. Self-weight of a 3200 mm span, 1000 mm wide HCFPS panel was

approximately 190 kg using material types of GRC 20, PU 20 and M steel (refer to

Tables 6-2, 6-3 and 6-4). For the same size, self-weight of a steel deck composite

slab with 100 mm thick concrete deck was estimated at 793 kg. Therefore, HCFPS

panels are approximately 70% lighter than conventional steel deck composite slabs.

6.6 DETERMINATION OF HCFPS SECTION PROPERTIES USING

ANALYTICAL METHODS

Section properties of HCFPS were determined by using analytical methods and these

properties can be used to predict the flexural behaviour of HCFPS. Analytical

methods were validated using FE results as explained in this section.

Parameters of the HCFPS section are shown in Figure 6-19 and were used to

determine the properties of the section. Transformed section, which has modulus of

elasticity of PU, was determined using modular ratios (ESteel / EPU) and (EGRC / EPU).

Neutral axis depth ( ) and Second moment of area ( ) of HCFPS section can be

0

5

10

15

20

25

0 10 20 30 40 50 60

Load (

kN

)

Deflection (mm)

HCFPS with GRC 20, PU 20 and M steel

Steel Deck Composite Floor


determined by using the Equation 6-1 and 6-3. Equivalent flexural stiffness of

HCFPS is defined by Equation 6-4.

Figure 6-19: Parameters used to define the properties of HCFPS section

bb – Width of the beam

db – Depth of the beam

h –Depth HCFPS section

L –Width of the slab

yi -Distance to the centroid (from the bottom) of individual components

bi -Width of individual components

di -Depth of individual components

A - Net area of component material

Ai - Net area of ith component material

-Area of the transformed section

tPU – Thickness of PU in the slab

tGRC, top –Thickness of GRC layer at the top

tGRC –Thickness of GRC layer

tGRC ESS –Thickness GRC layer Either Sides of Steel laminate

tSteel – Thickness of Steel laminate

EPU – Elastic modulus of PU

EGRC – Elastic modulus of GRC

ESteel – Elastic modulus of Steel

n1 – ESteel / EPU

n2 – EGRC / EPU

Note- All the areas (A and Ai) of these equations are calculated as net areas of the

component materials

Equation 6-1


Equation 6-2

Equation 6-3

Equation 6-4

6.6.1 Linear elastic deflection of HCFPS

Equivalent flexural stiffness of HCFPS section, , can be used to determine

deflection under loading. Equivalent beam section was assumed using values

of HCFPS to determine the deflection. For example, mid-span deflection due to a

uniformly distributed load can be determined using Equation 6-5. Calculated

deflections using this equation for A, B and C type of sections were compared with

the FE results as shown in Figure 6-20.

Equation 6-5

Figure 6-20: Load-deflection comparison between FE and analytical methods

0

5

10

15

20

25

0 10 20 30 40

Load (

kP

a)

Deflection (mm)

FE GRC 5, PU 20, M Steel

FE GRC 20, PU 20, M steel

Analytical GRC 5, PU 20, M Steel

(a) Type A Section

0

5

10

15

20

25

30

35

0 10 20 30 40

Load (

kP

a)

Deflection (mm)

GRC 5, PU 20, M Steel FE

GRC 20, PU 20, M steel FE

GRC 5, PU 20, M Steel Analytical

GRC 20, PU 20, M Steel Analytical

(b) Type B Section

0

5

10

15

20

25

0 10 20 30 40 50

Load (

kP

a)

Deflection (mm)

GRC 5, PU 20, M Steel FE

GRC 20, PU 20, M steel FE

GRC 5, PU 20, M steel Analytical

GRC 20, PU 20, M steel, Analytical

(c) Type C Section


Comparison demonstrates that this analytical method can be used to predict the linear

elastic deflection of HCFPS. Equation 6-5 calculates only the flexural deflection of

HCFPS and it can be used to calculate the deflection of HCFPS similar to FE results.

This implies that shear deflection of the HCFPS is very small due to uniformly

distributed loads and can be excluded from design requirements.

6.6.2 Stresses in individual component materials

Normal bending stress in each component material at the mid-span of the HCFPS

(shown in Figure 6-21) can be determined by using Equations 6-6, 6-7 and 6-8.

Stresses were derived, assuming that plane section at the mid-span of the HCFPS

remains plane. Stresses in component materials of A, B and C type of HCFPS

sections obtained from FE analysis under 5 kPa loading, were compared with stresses

obtained from analytical methods as shown in Table 6-13. Relevant stress

distributions obtained from FE analysis for A, B and C type of HCFPS sections are

shown in Figure 6-16. Comparison shows that analytical equations can used to

predict stresses in component materials with close agreement to FE results. The small

deference between the analytical and FE results may be due to simplifications in the

analytical methods. FE models were supported as face retrains at the supports (refer

to Figure 6-7) but analytical results were obtained by assuming those supports as a

line supports. However, analytical methods can be used to calculate the approximate

stresses in component materials for design purposes.

Figure 6-21: Stresses in component materials at mid span section of HCFPS along X-X

Equation 6-6

Equation 6-7


Equation 6-8

Table 6-13: Comparison of stresses in component materials under 5 kPa load

Type

of

Section

Type of materials used σSteel

MPa

σGRC,Bottom

MPa

σGRC,Top

MPa

A

B

C

GRC 5, PU 20 M Steel






FE

101.1

60.1

101.2

59.1

120

75

Analytical

109.3

64.9

107.6

66.3

127.7

79.9

FE

2.7

5.1

2.4

6.1

3

5.9

Analytical

2.8

6.5

2.7

6.4

3.2

6.5

FE

1.8

2

3.6

4.1

4.7

5.5

Analytical

1.95

2.5

4.0

4.6

4.8

5.7

6.6.3 Properties of cracked section

Moment capacity of HCFPS sections can be determined as the applied moment at the

yielding point. GRC outer shell in the beam can be cracked (by exceeding stress

tensile capacity of 6.5 MPa for GRC 20 and 4.0 MPa for GRC 5, refer to Table 6-3)

and) as the applied moment is increased. Figure 6-22 shows the damaged zone

(tensile cracks) of the GRC outer layer in the beam of the HCFPS (Type B) at the

centre span. The damage parameter of GRC has been defined as the ratio of cracking

strain to total strain. However, yielding of the HCFPS sections starts with the

yielding of steel laminate. This was observed in experimental testing (refer to Section

4.6.2) and FE validation of test results (refer to Section 5.2.6). Therefore, moment

capacity of HCFPS sections can be calculated by using a cracked section as shown in

Figure 6-23. Tensile capacity is provided only by the steel laminate and compression

capacity is provided by the slab section as shown in Figure 6-22. This can be

confirmed as outer GRC layer cracks with the increase of moment, as shown in

Figure 6-17. Tensile capacity of the PU is insignificant compared to steel and GRC

and can also be excluded from the analysis. Plastic neutral axis depth ( ) and

Second moment of area ( ) of HCFPS section can be determined by using the

Equation 6-9 and 6-11. Equivalent flexural stiffness of HCFPS is

defined from Equation 6-12.


Figure 6-22: Tensile crack development in the beam of the HCFPS (Type B)

Figure 6-23: Parameters used to define the properties of cracked HCFPS section

Equation 6-9

Equation 6-10

Equation 6-11

Equation 6-12

Yielding stress of the steel can be used to calculate the moment capacity of HCFPS

section as shown in Equation 6-13. Stress of GRC layer at the top surface (

(refer to Equation 6-15) can be determined from the strain obtained from Equation 6-

14. It was assumed that stress variation at point of yielding is linear across the

section.

Equation 6-13

Equation 6-14


Equation 6-15

Figure 6-24: Stress distribution of cracked HCFPS section along X-X

Moment capacity ( ) and were obtained from FE analysis and

compared with results obtained from analytical method as shown in Table 6-10.

Comparison shows that analytical results closely agree with the FE results. The small

difference in the analytical and FE results may be due to simplification of the

analytical methods. FE models were supported as face retrains at the supports (refer

to Figure 6-7) but analytical results obtained by assuming as line supports. GRC and

PU below the slab section of the HCFPS was excluded from the analytical

calculation and that may also have affected this difference. However, this

comparison shows that moment capacity of HCFPS sections can be estimated

approximately using analytical methods.

Table 6-14: Properties of of GRC

Type of

Section Type of materials

kNm

σGRC,Top

MPa

A

B

C







FE

10

10.5

28.5

30

49

49.5

Analytical

8.5

9.6

25

26

44.5

45.5

FE

3.11

5.1

6.4

7.9

6.5

7.8

Analytical

3.01

5.2

6.7

8.1

6.8

8.1


6.7 SHEAR PERFORMANCE

Shear capacity of HCFPS section can be estimated by observing the shear stress

distribution in its beam at shear zones. Typical shear stress distribution in the outer

GRC layer is shown in Figure 6-24. Shear resistance across the beam is provided by

GRC layer and PU core. Hence, shear capacity of HCFPS sections can be estimated

as the shear capacity of the PU core and GRC layer in shear flow zone as shown in

Figure 6-25. Although there is a high shear stress concentred zone at the vicinity of

support in the outer GRC layer (refer to Figure 6-25), continuous glass fiber mesh

can be embedded instead of chopped glass fibers to improve shear capacity of GRC

layer as explained in Section 0.

Figure 6-25: Shear stress in GRC outer shell at the vicinity of support

Figure 6-26: Shear zone of in the HCFPS cross-section

Shear capacity of the HCFPS can be estimated using Equation 6-17. In that equation,

τGRC and τPU are shear capacity of GRC and PU and can be obtained from Tables 6-3

and 6-4. AGRC3 and APU2 are the areas of GRC and PU in the shear zone (refer to

Figure 6-26). Table 6-11 shows the shear capacity of each section and shows that

applied shear load is lower than the shear capacity of HCFPS sections.

Equation 6-17


Table 6-15: Shear Capacity of HCFPS sections

Type of

Section Type of materials

kN

Applied shear force

with 5.75 kPa load

(refer to table 6-1)

A

B

C







PU

4.75

4.75

15.32

15.32

29.32

29.32

GRC

8.4

14

16.2

27

22.2

37

Total

13.15

18.75

31.52

42.32

51.52

66.32

8.625

8.625

14.375

14.375

21.5

21.5

HCFPS has higher shear capacity and its inherent shear capacity is adequate for

office and residential floor loading. Although, there is high shear concentration in the

GRC layer at the vicinity of support due to its higher elastic and shear modulus

compare to the PU core, shear bearing capacity of GRC can be improved by

embedding continuous glass fiber mesh in high shear stress concentrated zones of

GRC in the HCFPS (refer to Figure 6-25). High shear stress concentrated zone can

be taken as 0.15 × Span length from the support. Hence it is recommended to supply

a continuous glass fiber mesh in high shear stress concentrated zones of the HCFPS

(refer to Figure 6-9) to improve the shear bearing capacity of GRC. Therefore,

HCFPS provides high shear capacity and high safety factor against a shear failure.

This is further supported by experimental observations as there was no shear failure

in HCFPS test specimens (refer to Section 4.6.2)

6.8 PERFORMANCE OF GRC-PU-GRC PANEL AND SLAB JOINT

6.8.1 FE modelling of GRC-PU-GRC panel

1000 mm one-way span and 500 mm cantilever span of GRC-PU-GRC composite

panel is configured in HCFPS hybrid assembly as shown in Figure 6-21.

Performance characteristics of GRC-PU-GRC panel were investigated using

validated FE techniques. Two types of panels were used in the study, as shown in

Figure 6-28 and Table 6-16. These panels were used in types A, B and C HCFPS

panels as discussed in Section 6.2.1. FE models were developed for 1000 mm one-


way and 500 mm cantilever spans as shown in Figure 6-29. Fully fixed boundary

conditions were used to represent the continuity of GRC-PU-GRC panel in the

HCFPS configuration. FE modelling was conducted as explained in Section 5.3.1.

Figure 6-27: GRC-PU-GRC slab of HCFPS

Figure 6-28: Layer thickness of GRC-PU-GRC panel

Table 6-16: Sectional configuration of GRC-PU-GRC panels

Panel Name t1 GRC (mm) t2 GRC (mm) t PU (mm) t Overall (mm)

60 mm Panel 15 10 35 60

80 mm Panel 15 10 55 80

Figure 6-29: FE models of GRC-PU-GRC panel


6.8.2 FE model for slab joint of the adjacent HCFPS panels

Adjacent HCFPS panels can be connected in a building floor as shown in Figure 6-

30. FE model was developed to investigate the performance of the contact joint as

shown in Figure 6-31. Contact between two panels and fully fixed boundary

conditions at the ends were defined in ABAQUS (refer to Figure 6-31). FE

modelling was conducted as explained in Section 5.3.1.

Figure 6-30: Typical detail of the adjacent slab connection

Figure 6-31: FE models of contact joint

6.8.3 Properties of materials

Linear elastic properties of component materials were used as listed in Table 6-17.

Table 6-17: Properties of GRC and PU

Properties PU GRC

Name

Density (kg/m3)

E (Mpa)

Poisons ratio

PU 20

100

0.24

0.3

GRC 20

1900

20,000

0.24

GRC 5

1900

5,000

0.24

6.8.4 FE analysis results and discussion

Performance characteristics of each model were evaluated under uniformly

distributed and point loads. 0 to 10 kPa distributed loads were applied in 0.5 kPa


increments. 0 to 10 kN point loads were applied in 0.5 kN increments at the centre of

the one-way span and on the contact location with the adjacent slab (refer to Figure

6-30).

Concentrated loads were also used for residential and office floors as 1.8 kN and 3.5

kN respectively [48]. Performance characteristics of GRC-PU-GRC composite slab

section was separately investigated. Concentrated loads were used to investigate the

behaviour of GRC layer and PU core at the location of applied load.

GRC-PU-GRC panel

Maximum distributed design ultimate load on office floors and residential floors are

7.0 kPa and 4.75 kPa respectively (refer to Section 6.2.4). Linear- load deflection

behaviour and failure due to flexural cracking of the GRC was observed in

experimental testing for the GRC-PU-GRC panel. Performance of the composite

panel was obtained for loads up to 10 kPa, which is greater than ultimate design load.

Material capacity and serviceability deflection limit of span/360 (refer to Figure 32)

was not exceeded up to a distributed load of 10 kPa applied to 60 mm and 80 mm

panels spanning one way over the 1000 mm fixed support and 500 mm cantilever.

Maximum principle stresses in the GRC and PU core remain in their individual

capacities under uniformly distributed load or point load (refer to Figure 32).

Maximum stresses were obtained to an applied load of 8.5 kPa at 0.85 (7.0/8) factor

of safety for design purposes. Point load of 3.5 kN was applied at the centre of

spanning panel to obtain deflections and stresses. Stresses in individual material and

deflection remained within the capacity under the concentrated load as shown in

Figure 6-32 (b).

Table 6-18 and 6-19 summarise the results of the parametric studies. Parametric

studies demonstrate that the GRC-PU-GRC composite panel can be used as the slab

of the HCFPS with a high factor of safety. All GRC types (GRC 5, GRC 10, GRC,

15 and GRC 20) can be used with PU 20 for GRC-PU-GRC panel construction based

on parametric study results.


(a) Deflection and stresses under 10 kPa load for 60 mm panel spanning one-way over 1000 mm

(b) Deflection and stresses with 3.5 kN point load for 60 mm panel spanning one-way over 1000 mm

(c) Deflection and flexural stress with 10 kPa distributed load for for 60 mm panel spanning one-way

over 1000 mm

Figure 6-32: Performance GRC-PU-GRC panel with GRC 5 and PU 20

Table 6-18: Performance of 1000 mm one-way span

Name

Service load deflection

mm

Maximum stress in GRC

a MPa

at 5 kPa at 3.5 kN Span/360 at 8.5 kPa at 3.5 kN

60 mm

GRC 5 and PU 20

GRC 20 and PU 20

80 mm

GRC 5 and PU 20

GRC 20 and PU 20

1.0

0.6

0.4

0.3

3.5

2.6

3.3

2.4

2.7

2.7

2.7

2.7

0.50

0.40

0.45

0.38

1.6

1.3

1.7

1.2

Table 6-19: Performance of 500 mm cantilever span

Name

Deflection

mm


MPa

at 5 kPa Span/250 at 8 kPa

60 mm

GRC 5 and PU 20

GRC 20 and PU 20

80 mm

GRC 5 and PU 20

GRC 20 and PU 20

1.5

1.4

1.2

1.1

2.0

2.0

2.0

2.0

1.4

1.1

1.3

1.0


Slab joint of the adjacent HCFPS panels

The slab joint exhibited acceptable performance under distributed point loading.

Performance of the composite panel was obtained up to a 10 kPa applied load, which

is greater than ultimate design load. Individual materials remain within their capacity

under 10 kPa load (refer to Figure 27). ). Maximum stresses were obtained to applied

load of 8.5 kPa at 0.85 (7.0/8) factor of safety for design purposes. Table 6-15

summarises the results of the parametric study for slab joint. All GRC types (GRC 5,

GRC 10, GRC, 15 and GRC 20) can be used with PU 20 for GRC-PU-GRC panel

and slab joint of HCFPS panel based on parametric study results with a high safety

factor. Point load of 3.5 kN was applied on the slab joint to obtain deflections and

stresses. Stresses in individual material and deflection remained within the capacity

under the concentrated load as shown in Figure 6-32 (b).

(a) Deflection and stress under 10 kPa load for slab joint (60 mm) panel

(b) Deflection and stress under 2.0 kN point load on slab joint (60 mm) panel

Figure 6-33: Performance of slab joint with GRC 5 and PU 20

Table 6-20: Performance of 1000 mm one-way span with slab joint at the centre

Name

Deflection

mm


MPa

at 5 kPa at 3.5 kN Span/360 at 8.5 kPa at 3.5 kN

60 mm

GRC 5 and PU 20

GRC 20 and PU 20

80 mm

GRC 5 and PU 20

GRC 20 and PU 20

1.4

1.3

1.1

1.0

4.5

2.8

2.7

2.5

2.7

2.7

2.7

2.7

1.50

1.30

1.20

1.00

3.01

2.85

2.75

2.51


6.9 SUMMARY

Parametric studies were conducted to develop the HCFPS. Sectional configurations,

spans, loading and material properties were used as the parameters in the study.

A rectangular beam was selected for the development of HCFPS. Rectangular beam

sections offered acceptable shear performance. Use of rectangular beam is also

economically advantageous, as less material is required. HCFPS has high shear

capacity and its inherent shear capacity is adequate for office and residential floor

loading.

The static performance of HCFPS is governed by overall stiffness of the HCFPS,

flexural behaviour of GRC and yielding of steel laminate. Stiffness and flexural

performance of the HCFPS can be improved by enhancing the material properties.

Load-deflection behaviour HCFPS floors remain within linear elastic region up to the

ultimate applied load in residential and office floors. At the ultimate applied

conditions, individual materials did not exceed their capacities (including shear

zone). FOS for the flexural performance of HCFPS can be defined as ratio of

ultimate load carrying capacity (at the yielding point)/applied ultimate load. A FOS

of 1.5 or greater value can be obtained for the HCFPS by using appropriate material

combinations. Therefore, HCFPS can be used to satisfy flexural performance

requirements in floor plates.

HCFPS exhibited a flexural failure in the central span of the beam of the HCFPS as

observed in experimental testing. GRC and steel laminate shows non-linear tensile

behaviour after yielding. Non-linear behaviour was obtained for all panels up to a

deflection ductility index of 4 (approximately). Hence ductility index of HCFPS is

acceptable for a structural floor plate.

Elastic deformation obtained from the analysis was multiplied by a conservative

factor of 1.5 to consider any possible creep deformation with sustained loading for

design purposes. Creep and shrinkage deflection factor of 1.5 was allowed for

HCFPS floors and factored deflection can be still maintained below the deflection

control limits.


PU core attracted negligible tensile and compressive stress due to lower elastic

modulus as seen from stress distribution results. Steel laminate acts as reinforcement

for the hybrid by attracting high tensile stress. GRC layers in the slab of HCFPS

panel attract compressive stress. The inherent properties of individual component

materials in this floor system have been combined to achieve optimum performance

based on their beneficial strength characteristics.

GRC-PU-GRC composite panel slab joint in the slab of the HCFPS exhibited

excellent structural capacity and stiffness under uniformly distributed and point

loads.

Flexural and shear capacity, linear elastic deflection and component material stresses

can be derived using suggested analytical methods in this chapter.

Accepted properties of GRC (GRC 10, GRC 15 and GRC 20) are recommended to

construct HCFPS along with PU 20 based on the static performance investigation.

Applicability GRC 5 is limited for HCFPS, as it has low elastic modulus and tensile

and shear capacity. Properties of GRC 10 can be obtained economically either by

method of spay or premix [12]. Low density PU 20 (100 kg/m3) core is economical

to use in HCFPS. Therefore, GRC 10 and PU 20 can be used to develop an

economical HCFPS to satisfy static performance.

HCFPS is lightweight floor system approximately 50-70% lighter than the equivalent

conventional composite slabs. This floor system can be used as a viable alternative to

conventional floor system since it meets structural performance requirements and has

many desirable properties. Longer spans can be obtained, if necessary, by changing

the material properties of component materials and the sectional configuration.

Chapter 7: Dynamic performance of HCFPS 125

Chapter 7: Dynamic performance of HCFPS

Chapter 6 demonstrated that HCFPS panels can be used in floor construction to

satisfy the static performance requirements, such as deflection limits, and shear and

flexural strength capacities. This chapter investigates dynamic response of HCFPS

and identifies characteristics that influence acceleration response under human

induced vibration by conducting parametric studies using experimentally validated

FE models. This chapter also shows that lightweight HCFPS can be used in

residential and office buildings by evaluating its vibration performance using

acceptable perceptibility limits provided in current design guidelines and standards.

7.1 STRUCTURAL CONFIGURATION

HCFPS floor can be represented schematically as shown in Figure 7-1. Dynamic

performance of HCFPS floors was evaluated using two approaches. First, dynamic

performance of typical prefabricated HCFPS (refer to Figure 7-2) was evaluated

using the appropriate boundary conditions, which result as a consequence of the

adjacent HCFPS panels and supporting structural frame. Second, HCFPS floor plate

with supporting structural frame, as shown in Figure 7-1, was used for the dynamic

performance assessment. FE modelling and dynamic analysis was conducted for both

approaches using validated FE techniques described in Chapter 5.

Figure 7-1: HCFPS floor plate with steel frame

126 Chapter 7: Dynamic performance of HCFPS

Figure 7-2: Prefabricated HCFPS panel

7.2 DYNAMIC PERFORMANCE OF HCFPS (SINGLE PANEL

APPROACH)

Three section configurations (Type A, B and C sections), which previously satisfied

static performance requirements (in Chapter 6), were selected to investigate the

dynamic performance. Spans and section configuration parameters are shown in

Figure 7-3 and Table 7-1. Dynamic analysis was conducted for 2 m wide

prefabricated HCFPS panels with their total spans.

Figure 7-3: Sectional configuration parameters

Table 7-1: Spans and section dimensions

Section Type Span

(m)

b

(mm)

t

(mm)

h

(mm)

A

B

C

3.0

5.0

7.5

100

150

200

60

80

80

200

350

450


7.2.1 FE modelling

A typical FE model of single HCFPS panel used in the dynamic analysis is shown in

Figure 7-4. Boundary conditions of the FE model were selected to simulate

connections to the steel beams and adjacent slabs (refer to Figure 7-1). Translations

along the Z and X directions and rotations about the Z axis were restrained at slab

joint connections to simulate the restrain from the adjacent slabs. Translations along

the X, Y and Z were restrained at end supports to simulate connection with the steel

beams.

Figure 7-4: FE model of HCFPS panel

C3D8R eight node liner brick elements were used in the FE models for all


[74]. The FE models were meshed as shown in Figure 7-4. Density of the mesh was

determined by conducting a convergence study.


Properties of GRC, PU and steel used in Chapter 6 for the static performance

investigations (for the A, B and C type of HCFPS sections) were used in the dynamic

performance investigations. Materials respond within elastic limits for free vibration

and human induced vibration analyses according to [56]. Hence, dynamic analysis of

FE models of the HCFPS was conducted using linear elastic properties of the

component materials as listed in Tables 7-2, 7-3 and 7-4.

Properties of PU had minimal effect on the structural capacity of HCFPS section

(refer to Section 6.4.5). However, elastic modulus of PU changes with density [14]

and properties of PU, as listed in Table 7-3, were used to investigate their influence

on the dynamic performance of HCFPS.



Name Density

Kg/m3

Young's Modulus

GPa

Poisson's ratio

GRC 5

GRC 10

GRC 20

1900

1900

1900

5

10

20

0.24

0.24

0.24


Name Density

Kg/m3

Young's Modulus

MPa

Poisson's ratio

PU 20

PU 75

PU 150

PU 360

100

200

300

500

23.4

76.1

151.6

361.2

0.3

0.3

0.3

0.3


Name of material Density

Kg/m3

Young's Modulus

GPa

Poisson's ratio

Steel 7800 210 0.3

7.2.3 Mass of the HCFPS

The dynamic performance of office and residential floors should be investigated

using a floor mass that represents actual service loads [56]. The floor mass should be

equivalent to the summation of the self-weight of the floor plate and superimposed

dead loads due to finishes, ceiling, services and partitions. 10% of the nominal

imposed loads (1.5 kPa for residential and 3.0 kPa for office floors) can also be

added as permanent loads [56]. Superimposed dead loads, which gives a total of 1.0

kPa, are summarised in Table 7-5 [48]. This value may be increased up to 2.0 kPa in

residential buildings due to a higher density of partition walls and heavier floor

finishes. In the present study, a uniform superimposed dead load of 1.0 kPa was used

in the dynamic analysis of HCFPS floors. Table 7-6 shows the self weight of HCFPS

floors and mass of the floor including 1 kPa uniform superimposed dead load.


If the superimposed load is higher than 1.0 kPa, the natural frequencies will be

lowere and the damping properties of the HCFPS would be better due to the high

equivalent floor mass (refer to Section 3.7.4). Therefore, dynamic characteristics

were investigated with 1.0 kPa superimposed as this is the average minimum load

expected on HCFPS floors and as dynamic performance will be better with high floor

mass.

Table 7-5: Super imposed permanent dead loads for an office floor

Type of loading Load, kPa

Floor finishes acoucstic insulation + cladding

Suspended ceiling

Suspended services

Lightweight partition, furniture and equipments

Fire protection

0.25

0.10

0.15

0.35

0.15

Table 7-6: Mass of the HCFPS floors

Type of

Section

Type of

GRC

Mass (kg/m2)

PU 20 PU 75 PU 150 PU 360

A

B

C

GRC 5

GRC 10

GRC 20

GRC 5

GRC 10

GRC 20

GRC 10

GRC 20

w1

60.0

71.0

79.5

w2

162.0

172.9

181.4

w1

64.5

79.8

91.5

w2

166.5

181.8

193.4

w1

69.1

88.7

103.5

w2

171.0

190.7

205.5

w1

78.2

106.5

127.5

w2

180.1

208.5

229.4

w1- Self weight w2- Mass with 1kPa load

7.2.4 Free vibration analysis

Parameters as described above were varied in the FE model of A, B and C type

HCFPS sections. Free vibration analysis was conducted to obtain the modal


frequencies as shown in Table 7-7. Typical mode shape for the first mode natural

frequency is shown in Figure 7-5, which is the bending mode of HCFPS.

First natural frequency (f1) of HCFPS floors increases with the increase of elastic

modulus GRC (refer to Table 7-7). However, f1 decreases with the increase of PU

density, despite the increase of modulus of elasticity of PU with the density. f1 of

types A, B and C HCFPS floors are greater than 10 Hz (refer to Table 7-7). The

maximum possible fourth harmonic of the walking frequency (2.4 Hz) is lower than

the first mode natural frequency [56] of HCFPS floors. Hence resonant vibration is

unlikely to occur and HCFPS can be categorised as high frequency floors.

Figure 7-5: Typical mode shape for the first mode natural frequency

Table 7-7: Modal frequencies of HCFPS panels

Type of

Section

Type of

GRC

Type of PU

PU 20 PU 75 PU 150 PU 360

A

B

C

GRC 5

GRC 10

GRC 20

GRC 5

GRC 10

GRC 20

GRC 10

GRC 20

f1 (Hz)

30.1

34.6

36.8

18.5

22.4

27.5

13.5

16.9

f2 (Hz)

35.5

40.8

43.4

21.8

26.4

32.4

19.3

24.2

f1 (Hz)

25.0

29.7

36.1

18.0

21.7

26.6

13.0

16.1

f2 (Hz)

32.7

38.3

47.3

23.6

28.4

34.8

21.6

26.6

f1 (Hz)

24.6

29.2

35.5

17.5

21.1

25.8

12.5

15.5

f2 (Hz)

32.0

38.0

46.3

27.7

27.4

33.5

21.8

26.8

f1 (Hz)

24.0

28.3

39.3

16.9

20.1

24.5

11.7

14.3

f2 (Hz)

32.6

38.5

46.6

23.0

27.3

33.3

21.5

26.2

High frequency floors are defined as floors having a first natural frequency of 10 Hz

or more, which is greater than the fourth harmonic of the walking frequency

(maximum of 2.4 Hz) [56]. Dynamic loads due to walking on high frequency floors,


act as impulsive forces, which diminish before the next step [56]. This behaviour of

HCFPS was demonstrated in the experimental testing (refer to Section 4.5.2) and FE

modal validation (refer to Section 5.1.8).

7.2.5 Parameters that influence the first mode natural frequency of the HCFPS

The first mode natural frequency of a beam may be determined by a simplified

analytical method (refer to Equation 7-1) suggested in [56] and is used to identify the

parameters that influence the first mode natural frequency of the HCFPS. In this

equation, EI is flexural rigidity of the member, m is the effective mass (for a simply

supported beam 50% of the total mass) and L is the span. First mode natural

frequency of type A HCFPS (3 m span) and HCFPS test panel (3 m span) (refer to

Sections 4.2 and 4.6.2) was calculated using Equation 7-1. Equivalent beam sections

of HCFPS were determined using the flexural rigidity (EI), for the test panel: EI

=6.76×10^11 Nmm2 and for type A HCFPS: EI =1.67×10^12 Nmm

2 (with PU 20

and GRC 10). HCFPS test panels were weighed and average weight was recorded as

202 kg and self-weight of the type A HCFPS section was calculated as 180 kg. These

parameters were substituted in to Equation 7-1 to obtain the first mode natural

frequency as shown in Table 7-8.

312 mL

EIf

Equation 7-1

Table 7-8: Comparison of first mode natural frequency

First natural frequency (Hz)

HCFPS test Panel Type A HCFPS

Only self weight With 1 kPa load

Experimental - Avegrage

FE method

Analytical method

22.80

23.64

24.74

-

40.10

41.15

-

30.1

30.5

The parameters that influence the first mode natural frequency of the HCFPS can be

identified as the flexural rigidity and self-weight. Flexural rigidity of the HCFPS

panel is similar to that of conventional floor systems (refer to Section 0), but the self-

weight of HCFPS panel is lower. The self-weight of a 3.2m span, 1m wide

conventional steel-deck composite floor system is 793kg and first mode natural


frequency 13 Hz [22, 85]. In contrast, the self-weight of the same sized HCFPS panel

is approximately 200 kg (approximately 70 % decrement compared to convetional

systems). Thus, the lightweight HCFPS floors with high first natural frequency

categorised as high frequency floors.

7.2.6 Damping

Damping ratio of concrete and steel-deck composite bare floor systems are in the

range of 1.5 to 2 % [22, 63, 64, 85]. Damping ratio of conventional floors with

finishes and partitions is in the range of 4.5% - 6% [36, 65]. There is an approximate

increase of 2 to 4% in damping ratio due to the finishes and partition in floor

structures. True damping level of 5% of HCFPS is considered conservative based on

experimental tests on the bare test panels. HCFPS floors will have superimposed

dead loads higher than 1.0 kPa in practical applications due to partitions, suspended

services and floor finishes. Hence, a damping ratio of 5 % is feasible for HCFPS

floors in service. Vibration responses of HCFPS floors were comparatively studied

using damping ratios of 3% and 5% in the parametric studies.

True damping ratios of (ζ) 5% and 3% were incorporated into the FE models as

explicit damping matrix for the dynamic analysis. Clough et al. [76] defined the

damping in transient dynamic analysis problems using an explicit damping matrix,

by incorporating the damping ratio. Damping matrix is assumed to be a combination

of mass proportional damping (α) and the stiffness proportional damping (β), known

as Reyleigh proportional damping method [76]. This method is explained in detail in

Section 5.1.6 and Equation 7-2 was used to calculate α and β using the first two

natural frequencies f1 and f2 (in Table 7-7) The calculated α and β values for damping

ratio of 3% and 5% for each type of HCFPS floor were incorporated in FE models.

1

2 21

21

ff

ff

Equation 7-2

7.2.7 Mathematical load model for human induced loads

Continuous walking is the worst possible loading scenario that can be used in design

studies [56]. A mathematical load model to simulate continuous human induced load

F(t) [55] is given in Equation 7-3 (refer to Section 3.7.1) and used to excite the FE

models. Two loading cases were considered; one person walking (Q=745 N [56]) and


a group of people walking (Q= 0.75 KPa). Three types of walking were studied as

listed in Table 7-9.

kn npn tnfQtF 1 )2sin(1)( Equation 7-3

In the above Eq., F(t) is the dynamic force, Q is the static weight of the participating

person, n is the Fourier coefficient corresponding to nth

harmonic, fp is the pacing

frequency, t is the time and n is the phase angle of the nth

harmonic, n is the integer

designating harmonic of the fundamental and k is the number of harmonics that

characterise the forcing function in the frequency range of interest. Phase shift of 900

for each harmonic was used [55]. The numerical values of the first four Fourier

coefficients used to model the human walking load are listed in Table 7-9.

Table 7-9: Parameters for the load model[55]

Mode of

walking fp (Hz)

Numerical coefficient for 1st four

harmonics

1 2 3 4

Slow Walk

Normal Walk

Fast Walk

1.7

2.0

2.4

0.26

0.37

0.52

0.1

0.1

0.1

0.06

0.06

0.06

0.06

0.06

0.06

7.2.8 FE transient dynamic analysis


HCFPS sections. Transient dynamic analysis was performed using continuous

walking loads to obtain the acceleration response. Transient response is more

appropriate than the steady state response in high frequency floors because resonance

cannot occur and applied forces behave like a series of impulses [56].

7.2.9 Results from parametric study and discussion

Acceleration responses due to a single person walking and due to a dynamic

distributed load, which represents a group of people, were observed to be similar.

This kind of behaviour is supported by published findings from previous studies [58].

Walking path was changed to different positions on the slab, however no significant


change in the acceleration response was evident. Although the walking path was

changed perpendicular to the span direction of the (beam of the) HCFPS,

acceleration response did not exhibit a significant variation. The highest acceleration

response for continuous walking (induced at different positions) was observed at the

mid span of HCFPS panels, and this was used for subsequent vibration assessments.

RMS acceleration

As described in Section 3.7.3, response of a floor structure is evaluated in terms of

peak acceleration and Root-Mean Square (RMS) acceleration (arms). Peak

acceleration is the highest value of acceleration resulting from an excitation.

However, it does not provide a measure of the duration of the response. In contrast,

RMS acceleration is an average measurement of the acceleration time-history, as

shown in Equation 7-4. Smith et al. [56] stated that sharp peaks of acceleration are

less significant with lower (arms). T is the period under consideration in Equation 7-4

and (T= 1 second) was used as suggested by Smith et al [56]. This covers at least one

complete cycle of acceleration due to walking activities [56]. Acceleration response

was obtained from the FE analysis and arms values were calculated using Equation 7-

4. All three HCFPS panels were high frequency floors and thus arms acceleration

must be frequency-weighted using a factor of 8/f1 (refer to Section 3.7.3) to obtain

the frequency-weighted RMS acceleration (aw,rms) [55, 56]. Variation of aw,rms values

(due to continuous walking) of A, B and C sections with change in parameters are

shown in Figures 7-6, 7-7 and 7-8.

T

rms dttaT

a0

2)(1

Equation 7-4

aw,rms values vary in parallel with change in forcing frequency in type A, B and C

floors. The lowest aw,rms can be seen for slower walking and the highest aw,rms is seen

for fast walking for all types of HCFPS panels (refer to Figures 7-6, 7-7 and 7-8).

aw,rms changed marginally with an increase in properties of PU core at each forcing

frequency and damping level. Decrement of 15 to 20 % in aw,rms resulted from

increasing PU density from 100 kg/m3 to 500 kg/m3. (refer to Figures 7-6, 7-7 and

7-8). aw,rms decreased by approximately 50 % when the damping ratio was changed

from 3% to 5%, as can be seen in Figures 7-6, 7-7 and 7-8. Similarly, aw,rms


decreased by approximately 40 % with an increase in modulus of elasticity of GRC

from 10 GPa to 20 GPa.

Figure 7-6: RMS acceleration for section type A, and 3 m span

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

1.7 1.7 2 2 2.4 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

500

300

200

100

5% 3% 5% 3% 5% 3% ζ

fp = Forcing frequency , ζ - Damping ratio

PU Density kg/m3

R = 8

R = 4

5% 3% 5% 3% 5% 3% ζ


PU Density kg/m3

R = 8

R = 4

(a) GRC 5, (E=5GPa)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

1.7 1.7 2 2 2.4 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

500

300

200

100

5% 3% 5% 3% 5% 3% ζ


PU Density kg/m3

R = 8

R = 4

(b) GRC 10, (E=10GPa)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

1.7 1.7 2 2 2.4 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

500

300

200

100

5% 3% 5% 3% 5% 3% ζ


PU Density kg/m3

R = 8

R = 4

(c) GRC 20, (E=20GPa)


Figure 7-7: RMS acceleration for section type B, and 5 m span

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1.7 1.7 2 2 2.4 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

500

300

200

100

5% 3% 5% 3% 5% 3% ζ


PU Density kg/m3

R = 8

R = 4

(a) GRC 5, (E=5GPa)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1.7 1.7 2 2 2.4 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

500

300

200

100

5% 3% 5% 3% 5% 3% ζ


PU Density kg/m3

R = 8

R = 4

(b) GRC 10, (E=10GPa)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1.7 1.7 2 2 2.4 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

500

300

200

100

5% 3% 5% 3% 5% 3% ζ


PU Density kg/m3

R = 8

R = 4

(c) GRC 20, (E=20GPa)


Figure 7-8: RMS acceleration for section type C, and 7.5 m span

7.2.10 Vibration assessment of HCFPS

Response factor method (R)

As explained in Section 3.7.3, ISO 10137 [55] and BS 6472 [60] provides base

values of RMS acceleration in relation to a base curve, which is frequency-weighted,

to assess human response to vibration at different frequencies. The base value of

RMS acceleration of 5 × 10-3

m/s2 is suggested for floors with their first natural

frequency between 4 to 8 Hz. Calculated RMS acceleration must be frequency

weighted using a factor of 8/f1 for high frequency floors in order to assess vibration

using the base acceleration level.

However, the base curve is not used directly in practical applications. Instead, the

Response factor (R) method is suggested for vibration assessments. R of a floor is the

0

0.02

0.04

0.06

0.08

0.1

0.12

1.7 1.7 2 2 2.4 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

500

300

200

100

5% 3% 5% 3% 5% 3% ζ


PU Density kg/m3

R = 8

R = 4

(a) GRC 10, (E=10GPa)

0

0.02

0.04

0.06

0.08

0.1

0.12

1.7 1.7 2 2 2.4 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

500

300

200

100

5% 3% 5% 3% 5% 3% ζ


PU Density kg/m3

R = 8

R = 4

(a) GRC 20, (E=20GPa)


ratio between calculated or measured frequency weighted RMS acceleration (aw,rms)

and the base acceleration value [56]. Acceptable R values are given for residential

floors and office floors as 4 (acceptable aw,rms = 0.02 ms -2

) and 8 (acceptable aw,rms

= 0.04 ms-2

) respectively [56]. These levels of aw,rms are shown in Figures 7-6, 7-7

and 7-8.

Type A (3 m span) HCFPS floor exhibits an aw,rms value less than 0.04 ms-2

with 5%

damping level when comprised with GRC having elastic modulus of 10 GPa (GRC

10) and 20 GPa (GRC 20) at all walking frequencies. Change in PU density does not

offer significant advantage in reducing aw,rms and density of 100 kg/m3 (PU 20) can

be used to obtain an aw,rms value less than 0.04 ms-2

. Both type B (5 m span) and

Type C (7.5 m span) resulted in an aw,rms value less than 0.04 ms-2

with 5% damping

level and GRC with 20 GPa (GRC 20) elastic modulus at all walking frequencies.

Vibration Dose Value (VDV) method

aw,rms values were calculated using the continuous loading model described in

Section 5.3. However, continuous loading and vibration are uncommon and human

induced walking loads are intermittent in residential and office buildings [56]. A

cumulative measure of the vibration response for intermittent activities is more

reliable in residential and office floors and needs to be used for assessing the

vibration performance [56] as explained in Section 3.7.3. ISO 10137 [55] and BS

6472 [60] provide perceptible tolerance levels for intermittent vibrations using the

Vibration Dose Value (VDV) which can be calculated using Equation 7-5, in which

aw is the frequency weighted acceleration and T is the total duration of the vibration

[60].

41

0

4)(T

w dttaVDV Equation 7-5

Ellis [61] suggested an alternate procedure, as given in Equation 7-6 to calculate

VDV values of a walking activity by using the aw,rms ( refer to Section 3.7.3) during

design stage of floor plates and this was used in the present study. In Equation 7-6, na

is the number of times the activity will take place in the exposure period (number of

occurrences) and Ta is the duration of an activity (time taken to walk along the floor).

This method is a reverse calculation procedure to obtain number of concurrences (na)

of human activities required reach to perceptible threshold VDV value. aw,rms can be


obtained from the dynamic analysis of the floor plate under human activity. Ta can be

estimated using the floor configuration and walking speed. VDV values are defined

for floor plates for two exposure periods as day and night (refer to Section 3.7.3).

Hence, estimated na can be used as assessing parameter by considering the floor plate

use during the exposure period.

Equation 7-6

Maximum aw,rms acceleration for 5 % damping, under forcing frequencies of 2.4 Hz,

2.0 Hz and 1.7 Hz are shown in Tables 7-10. Those maximum aw,rms values were

obtained for each type of HCFPS panel from Figures 7-6, 7-7 and 7-8 with properties

of materials (PU 20 and GRC 10), required for the static performance (refer to

Section 6.9). aw,rms values were estimated using sinusoidal continuous loading with

one second duration [56] and can be considered as a more accurate representation of

vibration induced by human action (of one intermittent event) to calculate VDV.

Ta values for each span were estimated using a walking speed of 1.1 m/s for fp= 1.7

Hz, 1.5 m/s for fp= 2 Hz, and 2.5 m/s for fp= 2.4 Hz) [56]. Acceptable thresholds of

VDV values are provided in BS 6472 [60] for the "low probability of adverse

comment" as 0.4 m/s1.75

for a 16 hour day and 0.13 m/s1.75

for an 8 hour night for

buildings in service. The number of activities (na) that need to be performed to reach

the acceptable thresholds of VDV were estimated as shown in Table 7-10. A single

walking activity every minute in an office or residential floor during the day is an

unlikely occurrence. Walking activities in residential floors are minimal during the

night. The calculated na values in Table 7-10 are therefore unlikely to occur in

residential and office floors and hence HCFPS floors will not exceed threshold VDV

values. VDV analysis considers the probability of a number of occurrences of

vibration induced activities and provides a reliable estimate of the response based on

the parameter na.


Table 7-10: VDV assessment of HCFPS using na

Section type fp (Hz) Ta (s)

a w,rms (ms-2

)

(PU 20

GRC 10

ζ=5%)

VDV (ms-1.75

) na

A (Span 3.0m)

B (Span 5.0m)

C (Span 7.5m)

2.4

2.0

1.7

2.4

2.0

1.7

2.4

2.0

1.7

1.2

2.0

2.7

2.0

3.3

4.5

3.0

5.0

6.8

0.038

0.028

0.022

0.05

0.045

0.033

0.055

0.048

0.042

0.4 (16 h day)

0.13 (8 h night)

0.4 (16 h day)

0.13 (8 h night)

0.4 (16 h day)

0.13 (8 h night)

0.4 (16 h day)

0.13 (8 h night)

0.4 (16 h day)

0.13 (8 h night)

0.4 (16 h day)

0.13 (8 h night)

0.4 (16 h day)

0.13 (8 h night)

0.4 (16 h day)

0.13 (8 h night)

0.4 (16 h day)

0.13 (8 h night)

47,850 (50 per min)

533

97,396 (100 per min)

1086 (1 per min)

189,299(197 per min)

2111 (2 per min)

9,578 (10 per min)

107

8,795 (9 per min)

97

22,435 (23 per min)

250

7, 518 (8 per min)

83

4,510 (5 per min)

50

5,658 (6 per min)

63

Optimum sectional configurations for static performance requirements and material

properties; PU 20 and GRC 10 (refer to Tables 7-2, 7-3 and 7-4) with 5 % damping

were adequate to provide acceptable vibration performance of all types of HCFPS

panels. Hence density of PU core can be maintained at 100 kg/m3 (PU 20) for all

HCFPS panels to obtain acceptable vibration performance. Vibration response of

HCFPS under walking activities does not exceed the perceptible threshold of VDV

that was estimated in accordance with BS 6472 [60]. Satisfying this criterion

provides further confirmation that HCFPS can achieve acceptable vibration response

under human induced loads. Lightweight HCFPS floor systems can therefore be

effectively designed for use in office and residential buildings to provide acceptable

vibration performance.

Dynamic performance assessment of HCFPS panels was conducted using a single

panel with appropriate boundary conditions. Assessment shows that HCFPS


designed to meet static performance requirements are also adequate to provide

acceptable dynamic performance. However, this is further supported by conducting a

dynamic assessment of full scale HCFPS floor with supporting structural frame.

7.3 DYNAMIC PERFORMANCE OF HCFPS FLOORS WITH THE

STRUCTURAL FRAME

Dynamic behaviour of HCFPS floor (Type C, 7.5 m span) with a structural frame

was studied and compared with the results obtained from the single HCFPS panel

behaviour in Section 7.2. Structural configuration of the floor model is shown in

Figure 7-9. There are four 8.0 m × 7.5 m bays and C type HCFPS panels were used

in the 7.5 m span direction, as shown in Figure 7-9 (a). 457 UB 52 steel beam was

used as primary beams (B1) and columns (C1).

(a) Isometric view of HCFPS floor model

(b) Plan view of HCFPS floor model

Figure 7-9: Structural configuration of four bay floor model using HCFPS

B1 - Main Beam 475 UB 52

B2 - Secondary Beam 305 UB 42

C1 - Column 475 UB 52


7.3.1 FE modelling

FE model of four bay HCFPS floor used in the dynamic analysis is shown in Figure

7-10. Type C HCFPS panels were modelled as described in Section 7.2. HCFPS

panels were connected to the steel frame using pin connection at the joint. It is

recommended to use the height of the columns of the FE model up to their inflection

points [22, 56]. Typically inflection points of columns located at the mid-height of

the columns in multi-story construction [56]. Columns were modelled up to a height

of 1.5 m either side of the floor plate and fixed boundary conditions were used at

opposite ends. The connections were restrained at the beam and column joint node

to avoid rigid body movements of the FE model.

C3D8R eight node liner brick elements were used in the HCFPS panels for all


[74]. Primary and secondary beams were modelled using beam element of 3 DOF,

3B2- linear beam elements. Density of the mesh was determined by conducting a

convergence study.

Figure 7-10: FE model of four bay HCFPS floor


Properties of GRC, PU and steel used in the dynamic performance investigations

HCFPS floor model is shown in Tables 7-11, 7-12 and 7-13. Dynamic analysis of

FE models of the HCFPS was conducted using linear elastic properties of the

component materials as described in Section 7.2.2. Changes in properties of PU

resulted in minimal effect on the structural capacity of HCFPS section (refer to

Section 6.4.5). Furthermore, acceleration level did not significantly reduce due to the


increase in PU density. Hence, PU 20 and PU 75 were used in the parametric studies

on the HCFPS floor model.


Name Density

Kg/m3

Young's Modulus

GPa

Poisson's ratio

GRC 10

GRC 20

1900

1900

10

20

0.24

0.24


Name Density

Kg/m3

Young's Modulus

MPa

Poisson's ratio

PU 20

PU 75

100

200

23.4

76.1

0.3

0.3


Name Density

Kg/m3

Young's Modulus

GPa

Poisson's ratio

T Steel 7800 210 0.3

7.3.3 Mass of the HCFPS floor model

Mass of the HCFPS floor model was used as the summation of self-weight and kPa

superimposed dead load (refer to Section 7.2.3) in the dynamic analysis.

7.3.4 Free vibration analysis of HCFPS floor model

Parameters as described above were varied in the HCFPS FE model and free

vibration analysis was conducted to obtain the modal frequencies as shown in Table

7-14. Typical mode shapes for the first four natural frequencies are shown in Figure

7-11.


(a) First mode natural frequency 12.47 Hz

(b) Second mode natural frequency 13.17 Hz

(c) Third mode natural frequency 16.10Hz

(d) Fourth mode natural frequency 16.98 Hz

Figure 7-11: First four modes shape of HCFPS floor model using GRC 10 and PU 75

First natural frequency (f1) of HCFPS floor model (refer to Figure 7-11 a) was

greater than 10 Hz (refer to Table 7-14) for all material combinations. The maximum

possible fourth harmonic of the walking frequency (2.4 Hz) is lower than the first


mode natural frequency [56] of HCFPS floor model. As consequences resonant

vibration is unlikely.

First natural frequency of Type C HCFPS section (7.5. m span) using GRC 10 and

PU 75 was obtained as 13.0 Hz (refer to Table 7-7). Hence, first natural frequency

obtained from single panel approach closely matches that of obtained with structural

frame (12.47 Hz, refer to Figure 7-11 (a)).

Table 7-14: Modal frequencies of HCFPS model

Type of

GRC

Type of PU

PU 20 PU 75

GRC 10

GRC 20

f1 (Hz)

12.97

15.94

f2 (Hz)

13.70

17.23

f1 (Hz)

12.47

15.33

f2 (Hz)

13.17

16.57

7.3.5 Damping

The true damping ratio (ζ) of 5% was incorporated into the FE models as explicit

damping matrix for the dynamic analysis as described in Section 7.2.6 using first two

natural frequencies in Equation 7-2. Mass proportional damping (α) and the stiffness

proportional damping (β) were calculated as shown in Table 7-15.

Table 7-15: Mass proportional damping (α) and stiffness proportional damping (β) for ζ= 5%

Type of

GRC

Type of PU

PU 20 PU 75

GRC 10

GRC 20

α

0.6662

0.8280

β

0.0037

0.0030

α

0.6405

0.7963

β

0.0039

0.0031

7.3.6 Mathematical load model for human induced loads

Continuous walking is the worst possible loading scenario that can be used in design

studies [56]. A mathematical load model to simulate continuous human induced load

F(t) [55] was used as explained in Equation 7-3 (refer to Section 7.2.7), and used to

excite the FE models.


7.3.7 FE transient dynamic analysis


HCFPS sections. Transient dynamic analysis was performed using continuous

walking loads to obtain the acceleration response. Human induced walking loads

were applied on one panel of the four bay HCFPS floor model (refer to Figure 7-9)

7.3.8 Results from parametric study and discussion


distributed load, which represents a group of people, were observed to be similar as

discussed in Section 7.2.9. Walking path was changed to different positions on the

selected activity bay, however no significant change in the acceleration response was

evident. The highest acceleration responses due to walking loads resulted at the

centre of the activity panel. Non-activity panels show comparatively lower

acceleration level as shown in Figure 7-12. Maximum acceleration values shown in

Figure 7-13 recorded in the floor model were used for vibration assessment. aw,rms

acceleration predicted in Type C section (single panel approach in Section 7.2.9)

closely agrees with the HCFPS floor model results. Maximum aw,rms values (with

GRC 10 and PU 20) for 5 % damping, under forcing frequencies of 2.4 Hz, 2.0 Hz

and 1.7 Hz are presented in Tables 7-16. VDV assessment was conducted as

described in Section 7.2.9.

Figure 7-12: RMS acceleration of HCFPS floor model with section type C (non-activity panel)

0

0.02

0.04

0.06

0.08

0.1

0.12

1.7 2 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

200

100

5% 3% 5% 3% 5% 3% ζ


PU Density kg/m3

R = 4

(a) GRC 10, (10GPa) non-activity panel


Figure 7-13: RMS acceleration of HCFPS floor model with section type C (activity panel)

Table 7-16: Minimum number of activities required generates lower probability adverse

comment of Floor model

Section type fp (Hz) Ta (s)

a w,rms (ms-2

)

(PU 20

GRC 10

ζ=5%)

VDV (ms-1.75

) na

C (Span 7.5m)

2.4

2.0

1.7

3.0

5.0

6.8

0.047

0.043

0.035

0.4 (16 h day)

0.13 (8 h night)

0.4 (16 h day)

0.13 (8 h night)

0.4 (16 h day)

0.13 (8 h night)

8,178 (9 per min)

91

7,004 (7 per min)

78

11,733 (12 per min)

130

0

0.02

0.04

0.06

0.08

0.1

0.12

1.7 2 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

200

100

5% m 5% 5% ζ


PU Density kg/m3

R = 8

R = 4

(a) GRC 10, (10GPa) In activity panel

0

0.02

0.04

0.06

0.08

0.1

0.12

1.7 2 2.4

aw

,rm

s (

ms

-2)

fp (Hz)

200

100

5% 5% 5% ζ


PU Density kg/m3

R = 8

R = 4

(a) GRC 20, (20GPa) In activity panel


The calculated na values in Table 7-16 are, therefore, unlikely to occur in residential

and office floors and, hence, HCFPS floors will not exceed the threshold VDV

values. VDV analysis considers the probability of a number of occurrences of

vibration induced activities and provides a reliable estimate of the response based on

the parameter na. Moreover, predictions that were made using single panel HCFPS

panels are adequate to determine the dynamic performance of HCFPS.

Assessment shows that HCFPS that are designed to satisfy static performance

requirements are adequate to provide acceptable dynamic performance under human

induced walking loads.

7.4 CONCLUSIONS

Dynamic response of HCFPS floors was investigated by conducting parametric

studies using experimentally validated FE models. Material properties, walking

frequency and damping were used as parameters in the parametric study.

The first mode natural frequency of HCFPS floors is greater than 10 Hz and hence

HCFPS can be categorised as a high frequency floor system. The maximum possible

fourth harmonic of the walking frequency (2.4 Hz) is lower than the first mode

natural frequency [56]. As a consequence resonant vibration is a unlikely to occur.

Flexural rigidity of the HCFPS panel is similar to that of conventional floor system

but the self-weight of HCFPS panel is lower by approximately 50-70%. The first

mode natural frequency of HCFPS floors is therefore higher due to its lighter weight.


distributed load, which represents a group of people, were observed to be similar.

aw,rms increased with the increase of walking frequency. aw,rms changed marginally

due to the increase in properties of PU core. aw,rms decreased by approximately 50 %

when the damping ratio was changed from 3% to 5%. aw,rms decreased by

approximately 40 % with an increase in modulus of elasticity of GRC from 10 GPa

to 20 GPa.

Its excellent damping ratio of 5% is considered conservative based on experimental

tests on bare HCFPS test panels. HCFPS floors will have superimposed dead loads


higher than 1.0 kPa due to partitions, suspended services and floor finishes. Hence, a

damping ratio of 5 % is feasible for HCFPS floors in service.

Dynamic analysis of HCFPS panels was conducted using a single panel with

appropriate boundary conditions. This is further supported by the dynamic analysis

of full scale HCFPS floor plate with supporting structural frame exhibiting similar

results of first natural frequency and aw,rms to the single panel approach. Therefore,

dynamic analysis with single panel can be used as efficient method to evaluate

dynamic performance of HCFPS.

Optimum sectional configuration and material properties (GRC 10, GRC 20 and PU

20) to satisfy static performance requirements were adequate to provide acceptable

vibration performance. Vibration response of HCFPS under walking activities does

not exceed the perceptible threshold of VDV that was estimated in accordance with

BS 6472 [60]. Satisfying this criterion provides evidence that HCFPS can achieve

acceptable vibration response under human induced loads.

HCFPS panels design to satisfy static performance using GRC 10 and PU 20 will

offer acceptable vibration performance under human induced walking loads.

Properties of GRC 10 can be obtained economically either by method of spay or

premix [12]. Low density PU 20 (100 kg/m3) core is economical to use in HCFPS.

Therefore, GRC 10 and PU 20 can be used to develop an economical HCFPS to

satisfy static and dynamic performance. Design guidelines for the HCFPS are

presented presents in Chapter 8 based on static and dynamic performance

characteristics.


Chapter 8: Conclusions and recommendations 151

Chapter 8: Conclusions and recommendations

8.1 CONTRIBUTION FROM THIS RESEARCH

This research has developed a novel lightweight Hybrid Composite Floor Plate

System (HCFPS) using GRC, PU and steel laminate as component materials. The

research determined the performance characteristics of HCFPS using Finite Element

(FE) simulations supported by experimental testing. Parametric studies were

conducted to develop the HCFPS in order to satisfy static performance requirements

using sectional configurations, spans, loading and material properties as the

parameters. Dynamic response of HCFPS was investigated by conducting parametric

studies using material properties, walking frequency and damping as the parameters.

HCFPS offers acceptable vibration performance under human induced walking loads

for use in office and residential buildings. Lightweight HCFPS floor systems can

therefore be effectively designed for use in office and residential buildings to provide

acceptable performance characteristics.

The main findings of this study are listed below:

Optimum hybrid sectional configuration using component materials was determined.

Design of the HCFPS is governed by overall stiffness, flexural behaviour of the

HCFPS and yielding of steel laminate.

Stiffness and flexural performance of the HCFPS can be improved by enhancing the

material properties and changing sectional configuration.

HCFPS displayed a deflection ductility of 4, which is acceptable for floor plates.


can be derived using suggested analytical calculation procedure. Hence, design of the

HCFPS can be conducted using these methods.

HCFPS is a lightweight floor system approximately 50% lighter than equivalent

conventional concrete composite floor slabs.

152 Chapter 8: Conclusions and recommendations

The first mode natural frequency of HCFPS floor system is greater than 10 Hz and

hence HCFPS can be categorised as a high frequency floor system. Therefore,

resonant vibration due to human induced loads is unlikely to occur.

HCFPS offers excellent damping ratio of 5% (bare floor) due to the central PU core.

As a consequence, acceleration levels due to human induced loads is reduced.

Vibration response of HCFPS under walking activities does not exceed the

perceptible threshold of VDV that was estimated in accordance with BS 6472 [60].

Dynamic assessment of HCFPS can be conducted either by modelling a prefabricated

HCFPS panel with appropriate boundary conditions or by modelling HCFPS floor

plate with the structural frames as both methods give similar VDV assessment

results.

Dynamic assessment shows that HCFPS designed to satisfy static performance

requirements with (GRC 10 and PU 20) are adequate to provide acceptable dynamic

performance. Therefore, design guidelines of the HCFPS were developed using the

static performance requirements.

8.2 DISCUSSION AND SUMMARY

This research developed HCFPS according to the following stages. The first stage

involved investigating static, dynamic, cyclic loading and post yield behaviours,

mode of failure and ductility of the HCFPS panels. Component material testing was

also conducted to obtain their properties. FE models were developed and validated

using results from experimental testing. In the second stage, parametric studies were

performed and HCFPS were developed to satisfy static performance requirements.

The vibration characteristic of HCFPS under human-induced loads was investigated

in the next stage. Finally, guidelines were developed for the design of HCFPS panels.

8.2.1 Experimental Testing and FE model validation

A comprehensive testing program was undertaken to investigate the behaviour of

HCFPS panel and GRC-PU-GRC composite panel. Dynamic tests, static loading

tests and cyclic loading tests of 3200 mm span HCFPS panels were conducted.

Experimental studies also included a comprehensive material testing program to

obtain the properties of constituent materials.


Heel impact test was conducted for the HCFPS panel and the damping ratio and first

natural frequency were estimated as 5% and 22.8 Hz respectively. Walking tests

were also conducted on the HCFPS panel and acceleration responses were obtained.

Acceleration response exhibited a series of impulses and the response decays with

time before the next step, indicating the behaviour of a high frequency floor [56].

HCFPS exhibited ductile behaviour and flexural failure in the beam at mid-span after

the initial yielding. There was tensile failure of the outer GRC layer and plastic

yielding of the steel laminate. HCFPS displayed a deflection ductility of 4, which is

acceptable for floor plates. There were no support bearing or shear failures during

testing of the HCFPS panels. Furthermore, de-lamination between layers did not

occur until failure. Experimental testing exhibited flexural failure due to the loading.

Cyclic loading test for one HCFPS test panel was conducted according to the

method given in ACI [39]. This method can be used to evaluate the cyclic loading

performance of slabs comprised of new materials. Cyclic loading tests yielded

repeatability of 99% and deviation from linearity by 10%. These values are within

the limits given in [39] , showing acceptable cyclic loading performance of this floor

plate.

GRC-PU-GRC composite panel acts as the top slab of the HCFPS hybrid assembly.

Performance of the GRC-PU-GRC composite panel was experimentally tested to

investigate the behaviour under applied loads. GRC-PU-GRC composite panel

exhibited linear load-deflection behaviour and flexural failure due to the loading.

FE models for the HCFPS test panels were developed and validated using first mode

natural frequency and acceleration response. First mode natural frequency obtained

from the FE analysis agreed with the previously obtained experimental value with

only 0.84 Hz (3%) difference. Acceleration response of FE model obtained from heel

impact excitation walking load agreed with the experimentally obtained response.

Hence, FE models can be used to simulate walking activities and thus determine the

vibration response.

FE model of HCFPS exhibited a very good agreement with experimental load-

deflection in not only the linear behaviour, but also in non-linear behaviour. FE

results also exhibited a flexural failure in the central span of the HCFPS panel beam


as observed in experimental testing. FE model was developed for GRC-PU-GRC test

panel and load-deflection response of FE model was validated with experimental

results. FE model can therefore be used to investigate static performance of HCFPS.

8.2.2 Static design of HCFPS

Parametric studies were conducted to develop the HCFPS using validated FE

techniques. Sectional configurations, spans, loading and material properties were

used as parameters in the study.

Optimum configuration was determined for the HCFPS as shown in Figure 8-1.

Beneficial inherent properties of individual component materials were combined to

achieve optimum performance in the HCFPS.

Figure 8-1: Optimum configuration of HCFPS

Compressive stresses occur mainly in the slab and tensile stresses occur in the

bottom steel laminate under bending according to flexural stress and strain

distributions at the centre of the HCFPS panel. High tensile stresses are attracted to

steel laminate and compressive stresses are attracted to the top GRC, because their

elastic moduli are significantly higher than the PU. Compressive and tensile stresses

of the PU core are negligible due to the low elastic modulus according to flexural

stress and strain distributions at the centre of the HCFPS panel. Hence, a PU core

provides minimal influence on the structural capacity of the HCFPS. However,

overall integrity of HCFPS section is obtained by the PU core, as it provides a


connection between GRC layers. Furthermore PU core offers lateral support for thin

GRC layers to avoid lateral buckling. Core material is therefore important for

practical applications but alternative materials may be used instead of the PU core.

Shear stresses occur across the web of the beam due to loading. PU core was

replaced with GRC fill in the vicinity of the supports as shown in Figure 8-1 to

enhance the support bearing capacity. GRC and PU exhibit better performance under

compressive and shear stresses [12, 14]. Hence, GRC and PU are profiled and

located to attract compressive and shear stresses in the slab and beams of HCFPS (as

shown in the Figure 1-2). "T" beam sections (with rectangular beams) offered

acceptable shear performance. Use of rectangular beam is also economically

advantageous as less material is required. Shear capacity of the HCFPS sections are

higher than the applied shear force and may not significantly influence on the overall

design.

GRC-PU-GRC composite slab of the HCFPS and slab joint, which is used to connect

adjacent HCFPS panels, exhibited excellent structural capacity and stiffness under

uniformly distributed and point loads. GRC-PU-GRC panels with overall thickness

of 60 mm and 80 mm are suggested to be used in HCFPS depending on the loading

requirements and overall design of the HCFPS.

Design of this new floor system is governed by overall stiffness, flexural behaviour

of the HCFPS and yielding of steel laminate. Stiffness and flexural performance of

the HCFPS can be improved by enhancing the material properties and, hence, similar

stiffness to conventional floor systems can also be obtained. Deflection ductility

index of 4 can be obtained for HCFPS panels, which is an acceptable level of

ductility as a floor slab. Creep and shrinkage deformation of HCFPS has not been

experimentally tested but it could be minimal due to presence of steel laminate and

composite action of HCFPS. However, it is suggested to multiply the linear elastic

deflection of HCFPS under service loads using a conservative factor of 1.5 to

account any possible creep deformation under the sustained loads or shrinkage

deformation. Deformation of the HCFPS under the service loads are well below the

span/360 and span/250 limits suggested in design codes, and hence the factored

service loads deflection dose not exceed such limits.


Accepted and currently avaiable properties of GRC (GRC 10, GRC 15 and GRC 20)

are recommended to construct HCFPS along with PU 20 based on the static

performance investigation.


can be derived using the analytical methods summarised in Section 8.2.4 and the

accuracy of these methods were determined using the parametric studies.

8.2.3 Dynamic performance of HCFPS

Dynamic response of HCFPS floors was investigated by conducting parametric

studies using experimentally validated FE models. Material properties, walking

frequency and damping were used as parameters in the parametric study.

Self-weight of HCFPS panel is approximately 50% of conventional

composite/concrete floor systems. The first mode natural frequency of HCFPS floors

is therefore higher due to its lighter weight. The first mode natural frequency of

HCFPS floors is greater than 10 Hz and thus HCFPS can be categorised as a high

frequency floor system. The maximum possible fourth harmonic of the walking

frequency (2.4 Hz) is lower than the first mode natural frequency [56]. As a

consequence resonant vibration is unlikely to occur.

Damping ratio of 5% can be considered conservative based on experimental tests on

bare HCFPS test panels. HCFPS floors will have superimposed dead loads higher

than 1.0 kPa due to partitions, suspended services and floor finishes. Hence, a

damping ratio of 5 % is more feasible for HCFPS floors in service.

Dynamic performance assessment of HCFPS panels was conducted using a single

panel with appropriate boundary conditions. Vibration assessment of HCFPS was

conducted for human induced walking loads that are possible in residential and office

floors. VDV [56, 60] method was used to account for the intermittent nature of such

activities and vibration response of HCFPS under walking activities was checked

with the threshold of VDV values given in BS 6472 [60]. Assessment shows that

HCFPS that are designed to satisfy static performance requirements are adequate to

provide acceptable dynamic performance under human induced walking loads.

Single panel approach is further supported by the dynamic assessment of full scale


HCFPS floor plate with supporting structural frame exhibiting similar behaviour to

the single panel approach.

HCFPS can be designed to satisfy static performance requirements for applications in

residential and office floors. Static design of HCFPS (with material types of GRC 10

and PU 20) will offer acceptable vibration performance under human induced

walking loads. Lightweight HCFPS floor systems can therefore be effectively

designed for use in office and residential buildings to provide acceptable

performance characteristics. Design guidelines for the HCFPS will be presented

based on static performance requirements. Acceptable dynamic performance can be

obtained for HCFPS, which design to satisfy static performance with material types

of GRC 10 and PU 20. However, if required, dynamic performance assessment of

HCFPS floor can be conducted using the method discussed in this thesis.

8.2.4 Design guidelines

Design guidelines of HCFPS were developed using the static performance

requirements, such that the design provides acceptable dynamic performance in the

use of residential and office floors. It is recommended to be use elastic modulus of

GRC and PU equal or greater than 10 GPa (GRC 10) and 22.4 MPa (PU 20)

respectively to obtain the acceptable dynamic performance.

Design guidelines and calculation procedure were developed for the HCFPS system

using analytical equations suggested in Chapter 6 to determine static performance.

Thickness of hybrid components, density of PU, sectional configurations and loading

were considered as the variables to obtain the optimum section for a particular span.

Parameters of the HCFPS section are shown in Figure 8-2 and used to determine the

properties of the section. Neutral axis depth ( ) and Second moment of area ( ) of

HCFPS section can be determined by using Equations 8-1 and 8-3. Equivalent

flexural stiffness of HCFPS is defined by Equation 6-4. Elastic deflection of

the HCFPS can be determined using section properties of HCFPS. For example,

deflection at the centre due to a uniformly distributed load can be found using

Equation 8-5.


Furthermore, this suggested simplified design method can be used to develop a excel

sheet and that can be used as a tool to determine the sizes of the HCFPS panels

depending on the span length and applied loads.

Figure 8-2: Parameters used to define the properties of HCFPS section

yi -Distance to the centroid (from the bottom) of individual components

bi -Width of individual components

di -Depth of individual components

-Area of the transformed section

n1 – ESteel / EPU

n2 – EGRC / EPU

Note that all the areas of this equation are net areas of the component materials.

Equation 8-1

Equation 8-2

Equation 8-3

Equation 8-4

Equation 8-5

Linear elastic stresses in each component material at the mid-span of the HCFPS can

be determined by using Equations 8-6, 8-7 and 8-8.


Equation 8-6

Equation 8-7

Equation 8-8

Moment capacity of HCFPS sections can be calculated by using a cracked section as

shown in Figure 8-3. Tensile capacity is provided only by the steel laminate and

compression capacity is provided by the slab, as shown in Figure 8-3. Plastic neutral

axis depth ( ) and Second moment of area ( ) of HCFPS section can be

determined by using the Equations 8-9 and 8-11. Equivalent flexural stiffness

of HCFPS is defined from Equation 8-12.

Figure 8-3: Parameters used to define the properties of cracked HCFPS section

Equation 8-9

Equation 8-10

Equation 8-11

Equation 8-12

Yielding stress of the steel can be used to calculate the moment capacity of HCFPS

section, as shown in Equation 8-13. Stress of in GRC layer at the top surface


( (refer to Equation 8-15) can be determined using strain. Strain of the GRC

layer can be obtained by using Equation 8-14. It was assumed that stress variation at

point of yielding is linear across the section.

Equation 8-13

Equation 8-14

Equation 8-15

Shear capacity of the HCFPS can be estimated using Equation 8-16.

Equation 8-16

HCFPS has higher shear capacity and its inherent shear capacity is adequate for

office and residential floor loading. Although, there is high shear concentration in the

GRC layer at the vicinity of support due to its higher elastic and shear modulus

compare to the PU core (refer to Section 6.3.2), shear bearing capacity of GRC can

be improved by embedding continuous glass fiber mesh in high shear stress

concentrated zones of GRC in the HCFPS (refer to Figure 6-25). High shear stress

concentrated zone can be taken as (0.15 × Span length) from the support in the beam

of HCFPS. Hence it is recommended to supply a continuous glass fiber mesh in high

shear stress concentrated zones of the HCFPS to improve the shear bearing capacity

of GRC.

8.2.5 Supporting and connection methods

The structural supporting system can be either steel or Reinforced Concrete (R/C).

HCFPS can be fixed to the structural frame as shown in Figure 8-4 as simply support

connections. HCFPS panels should be connected to the supporting structure using the

beam (refer to Figure 8-5) because any hogging moment that could arise due to the

connection would transfer through the continuous glass fiber mesh, which is

provided to enhance the shear capacity of the HCFPS at the support.


Figure 8-4: Proposed supporting methods for HCFPS floor to structural frame

Figure 8-5: Cross-section of the HCFPS panel

8.2.6 Limitation of design guidelines

These analytical methods have only been validated for the spans less than 7.5 m.

Material properties of GRC and PU must to be maintained as follows to obtain the

acceptable dynamic performance. Modulus of elasticity of GRC should be greater

than 10 GPa (GRC 10). Density of PU should be greater than 100 kg/m3 and elastic

modulus greater than 22.4 Mpa (PU 20). Simply supported conditions should be

assumed for the design of HCFPS and the analytical methods are applicable only

under such conditions.

8.2.7 Manufacturing and casting guide

HCFPS test panels were cast using a manual casting procedure. However, a

production process may be developed for automated manufacturing to enhance

production efficiency. In this context, GRC layers can be cast in controlled

conditions and placed at the intended positions. Mechanized spray techniques can be

used to apply the GRC[30]. In this process mortar paste and chopped glass fiber are

simultaneously deposited from dual spray-heads into suitable moulds. This method


currently accounts for a large percentage of GRC production. Modulus of elasticity

up to 20 GPa can be achieved using pre-cut glass fiber between 25 mm and 40 mm in

length and containing 5% of the total weight of the mix [12]. Steel laminate can be

embedded in the bottom layer of GRC (refer to Figure 8-1) during the spray process.

Subsequently, PU core can be injected in between the GRC outer shell. PU is

manufactured by combining a polyol and isocyanate, a blowing agent and an

activator, through a controlled chemical reaction in liquid form [9, 24]. Liquid foam

starts to expand rapidly and becomes hard after 3-6 minutes of mixing. During the

process, PU adheres to the GRC outer shell [9].

Alternative materials can be used for the PU core as it provides the minimal impact

on the structural capacity. However, the bonding between GRC and the core material

must be achieved to avoid the de-lamination. Damping of the HCFPS floors must

also be assessed with alternative materials.

8.2.8 Implications

HCFPS can be used as a viable alternative to conventional floor system since it

meets structural performance requirements and has many desirable properties such as

lightweight, easy to construct, economical, demountable, recyclable and reusable.

HCFPS offers such properties as a consequence of component materials (GRC, PU

and steel laminate)

HCFPS can be developed as an economical floor system by using widely used

properties of GRC and PU in current composite industry. Properties of GRC 10 can

be obtained economically either by method of spay or premix [12]. Low density PU

20 (100 kg/m3) core is used in current sandwich construction applications [11] and

HCFPS can be developed using PU 20 as an economical structure. HCFPS panels

design to satisfy static performance using GRC 10 and PU 20 will offer acceptable

vibration performance under human induced walking loads. Therefore, GRC 10 and

PU 20 can be used to develop an economical HCFPS.

HCFPS can be developed as a prefabricated floor system that can be manufactured in

an offsite factory under controlled conditions to achieve a product of superior quality

with low embodied energy. This floor system is approximately 50% lighter in weight

compared to conventional concrete floors. Therefore, this product is easy to


transport, handle and erect. HCFPS has the potential to revolutionize the construction

of structural floor systems by replacing slow, labour intensive and low quality

construction materials, with factory based manufacturing process. Manufactured

floor plates can be assembled with simple connections on site eliminating the heavy,

cumbersome and time consuming material handling, transporting and erecting

processes, while minimising safety hazard. HCFPS can be demounted and reused in

other applications or can be recycled as a whole component at the end of its

commercially useful life.

Additionally, lightweight property of HCFPS floor plates result in reduced load on

the supporting beams and columns. Thereby, sizes of such load-bearing members can

be reduced, yielding economical advantages.

Moreover, lightweight HCFPS floor and reduced size of load bearing members

results in lower mass for building structures. As a consequence, such buildings offer

better performance during earthquakes. In an earthquake, ground shaking generates

internal forces within the buildings called inertial forces, which in turn, cause the

most damage to building structures. Magnitude of inertial forces are proptional to

the mass of a structure [15]. Hence, the lower the mass of the building lower the

demand of seismic loads.

In conclusion this research, provided an efficient, lightweight, economical, and

sustainable structural flooring system that can be recycled and reused as a whole

system, compared to conventional floor systems. HCFPS offers multifunctional

structural properties, making it a viable alternative for conventional reinforced

concrete and composite deck floors. It is therefore a product that addresses social and

environmental needs of the global community using material and manufacturing process

with low energy content.

8.2.9 Future work

This research shows that HCFPS can be used in residential and office floor

construction using FE modelling with the support of limited experimental testing.

Following future research items are suggested:


Full scale HCFPS floor plate can be experimentally tested to further

investigate performance characteristics and reinforce the findings from this

research.

HCFPS has been designed for simply supported conditions, but further

improvements can be investigated for restrained and continuous supports.

Shear behaviour was identified as insignificant design criteria of the design of

HCFPS according to the current research findings (as a result of HCFPS

configuration). However, shear behaviour of the HCFPS can be

experimentally investigated to further support for this.

Dynamic performance of HCFPS can be further evaluated under human

induced rhythmic activities.

Fire performance of HCFPS can be evaluated experimentally by conducting

fire tests.

Further research investigation can be conducted to determine some sizing

rules for HCFPS using the suggested simplified design guidelines.

Design of HCFPS can be improved by incorporating the capacity reduction

factors in relation partial safety factors of materials.

Static and dynamic behaviour of the slab joint (refer to Figure 8-1) can be

further investigated experimentally using actual HCFPS floor plate.

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STATIC AND DYNAMIC PERFORMANCE OF LIGHTWEIGHT HYBRID ... · PDF fileii Static and dynamic performance of lightweight hybrid composite floor plate system Abstract In the modern built