Strengthening flat slabs at corner columns against

Strengthening flat slabs at corner columns

against punching shear using fibre

reinforcing polymer (FRP)

A thesis submitted to The University of Manchester for the degree of

Doctor of Philosophy in the Faculty of Sciences and Engineering

2018

Bassam Qasim Abdulrahman

School of Mechanical, Aerospace and Civil Engineering

2

Paper produced from this thesis

Abdulrahman, B.Q., Wu, Z. and Cunningham, L.S. (2017). Experimental and numerical

investigation into strengthening flat slabs at corner columns with externally bonded

CFRP. Construction and Building Materials, 139, pp.132-147.

3

Contents

List of figures ................................................................................................................... 9

List of tables ................................................................................................................... 15

Notations ........................................................................................................................ 16

Abstract .......................................................................................................................... 21

Declaration ..................................................................................................................... 23

Copyright Statement ..................................................................................................... 24

Acknowledgements ........................................................................................................ 25

Dedication ...................................................................................................................... 26

1. Chapter 1 Introduction .......................................................................................... 27

1.1 Introduction............................................................................................................ 27

1.2 Problem definition ................................................................................................. 29

1.3 Objective of the research and the methodologies .................................................. 29

1.4 Thesis layout .......................................................................................................... 29

2. Chapter 2 Literature review ................................................................................. 32

2.1 Punching shear in reinforced concrete slabs .......................................................... 32

2.2 Punching shear failure mechanism ........................................................................ 38

2.3 Corner slab-column connections ........................................................................... 42

2.4 Factors influencing punching shear strength of a slab-column connection ........... 43

2.4.1 Concrete compressive strength..................................................................... 43

2.4.2 Strength and ratio of the flexural reinforcement .......................................... 44

2.4.3 Pattern of flexural reinforcement ................................................................. 46

2.4.4 Reinforcement arrangement ......................................................................... 46

2.4.5 Compressive reinforcement ratio ................................................................. 47

2.4.6 Concrete cover.............................................................................................. 48

2.4.7 Concrete tensile strength .............................................................................. 49

2.4.8 Thickness of the slab .................................................................................... 49

2.4.9 Span-depth effect or the size effect .............................................................. 50

2.4.10 Surrounding restraint .................................................................................... 50

2.4.11 Shear reinforcement ..................................................................................... 51

2.4.11.1 Shear reinforcements for new construction ............................................... 52

2.4.11.2 Shear reinforcement for strengthening existing construction .................... 52

2.4.12 Size and shape of loaded area ...................................................................... 53

2.5 Fibre reinforcing polymer (FRP) ........................................................................... 54

4

2.5.1 Fibres ............................................................................................................ 55

2.5.1.1 Carbon Fibre Reinforced Polymer (CFRP) .................................................. 56

2.5.1.2 Glass Fibre Reinforced Polymer (GRP) ....................................................... 56

2.5.1.3 Aramid Fibre Reinforced Polymer (AFRP) ................................................. 56

2.5.1.4 Steel Fibre Reinforced polymer (SFRP) ...................................................... 57

2.5.2 Polymer matrix ............................................................................................. 57

2.6 FRP composite properties ...................................................................................... 58

2.7 Modes of failure of slab-column connections with FRP reinforcement ................ 60

2.7.1 Full composite action failure modes ............................................................ 60

2.7.2 Loss of composite action failure modes ....................................................... 61

2.7.2.1 Debonding of the FRP plate ......................................................................... 61

2.7.2.2 Peeling-off failure mode............................................................................... 62

2.8 Strengthening of slab-column connections against punching shear by using FRP

reinforcement ......................................................................................................... 63

2.8.1 Direct shear strengthening ............................................................................ 63

2.8.2 Indirect (flexural) shear strengthening by externally bonded FRP strips ..... 73

2.8.3 Indirect shear strengthening by prestressed FRP composites ...................... 84

2.9 Opening in slab-column connections .................................................................... 87

2.10 Bond behaviour of FRP-Concrete interface .......................................................... 88

2.10.1 Bond-slip relationship .................................................................................. 89

2.10.2 Bond strength ............................................................................................... 91

2.11 Treatment of punching shear in codes of practice ................................................. 92

2.11.1 American Concrete Institute (ACI): ACI 440.2R-08 [109] ......................... 93

2.11.2 Eurocode 2 [29] and Concrete Society Technical Report 64 [110] ............. 93

2.11.3 Japanese Society of Civil Engineers (JSCE) [112] ...................................... 94

2.11.4 FIB model code Bulletin 66 [113]: .............................................................. 94

2.12 Originality of the research ..................................................................................... 95

2.13 General comments ................................................................................................. 96

3. Chapter 3 Analytical model in finite element formulation ................................ 98

3.1 Finite element method ........................................................................................... 98

3.2 Element choice....................................................................................................... 99

3.2.1 Iso-parametric solid element for concrete .................................................... 99

3.2.2 Embedded truss element for steel............................................................... 102

3.2.3 Shell element for FRP ................................................................................ 103

5

3.2.4 Cohesive element for adhesive ................................................................... 104

3.3 Material modelling............................................................................................... 105

3.3.1 Steel reinforcement modelling ................................................................... 105

3.3.2 FRP reinforcement modelling .................................................................... 106

3.3.3 Concrete modelling .................................................................................... 107

3.4 Failure criteria of concrete ................................................................................... 107

3.4.1 Plasticity parameters .................................................................................. 110

3.4.2 Compressive behaviour of concrete ........................................................... 111

3.4.3 Tensile behaviour of concrete .................................................................... 112

3.4.3.1 Linear tension softening model .................................................................. 113

3.4.3.2 Bilinear tension softening model................................................................ 114

3.4.3.3 Exponential tension softening model ......................................................... 115

3.5 Interaction ............................................................................................................ 115

3.5.1 Steel-concrete interface .............................................................................. 116

3.5.2 FRP-Concrete interface .............................................................................. 116

3.5.2.1 Failure criteria ............................................................................................ 116

3.5.2.2 Damage initiation ....................................................................................... 117

3.5.2.3 Damage evolution ...................................................................................... 118

3.6 General comments ............................................................................................... 119

4. Chapter 4 FE Modelling of Reinforced Concrete Slabs/Beams ....................... 120

4.1 Walker and Regan experimental work ................................................................ 120

4.2 Finite element idealisation ................................................................................... 122

4.3 Investigation of the model parameters ................................................................. 122

4.3.1 Numerical parameters ................................................................................ 122

4.3.1.1 Effect of step time period ........................................................................... 122

4.3.1.2 Mesh size .................................................................................................... 123

4.3.1.3 Number of elements through the slab thickness......................................... 124

4.3.2 Material parameters .................................................................................... 125

4.3.2.1 Tension stiffening ....................................................................................... 125

4.3.2.2 Concrete tensile strength ............................................................................ 126

4.3.2.3 Effect of Young‟s modulus of concrete ..................................................... 126

4.3.2.4 Effect of the dilation angle ......................................................................... 127

4.3.2.5 Effect of Kc ................................................................................................. 128

4.3.3 Load-deflection response ........................................................................... 129

6

4.3.4 Reinforcement stresses ............................................................................... 131

4.4 Validation of Abdullah et al.‟s simply supported slab ........................................ 133

4.4.1 Model description ....................................................................................... 133

4.4.2 Finite element model .................................................................................. 136

4.4.3 Discussion of computational results and comparison with experiments.... 136

4.5 Validation of the retrofitted simply supported reinforced concrete beam ........... 142

4.5.1 Model description ....................................................................................... 142

4.5.2 Finite element model .................................................................................. 143

4.5.3 Discussion of computational results and comparison with experiments.... 144

4.5.4 Interfacial slip profile ................................................................................. 147

4.6 Summary .............................................................................................................. 149

5. Chapter 5 Parametric study on strengthening the Walker and Regan slab-

column connection ............................................................................................... 150

5.1 Effect of bond length in strengthening ................................................................ 151

5.2 Effect of orthogonal configuration in strengthening ........................................... 159

5.3 Effect of diagonal configuration in strengthening ............................................... 160

5.4 Effect of FRP thickness in strengthening ............................................................ 161

5.5 Comparative study with strengthening by steel plates ........................................ 162

5.6 Reinforcement stresses for the strengthened slab-column connection ................ 163

5.7 CFRP stresses and strains .................................................................................... 165

5.8 Behaviour of slab-column connections that fail initially in flexure and which are

strengthened externally by CFRP sheets ............................................................. 171

5.9 Conclusions ......................................................................................................... 172

6. Chapter 6 Experimental Programme Set-up .................................................... 174

6.1 Choice of specimen type ...................................................................................... 174

6.1.1 Details of the specimens ............................................................................. 175

6.1.2 Experimental parameters ............................................................................ 177

6.2 Properties of the materials used in the testing ..................................................... 177

6.2.1 Concrete ..................................................................................................... 177

6.2.2 Steel reinforcement .................................................................................... 179

6.2.3 FRP sheets .................................................................................................. 179

6.3 Preparation of the test specimens ........................................................................ 180

6.3.1 Form work building and the mould ............................................................ 180

6.3.2 Reinforcement ............................................................................................ 181

7

6.3.3 Concrete casting and curing ....................................................................... 181

6.3.4 Concrete surface preparation ...................................................................... 182

6.3.5 Application of the adhesive and applying the CFRP sheets....................... 182

6.4 Instrumentation .................................................................................................... 182

6.4.1 Steel reinforcement strain gauges .............................................................. 184

6.4.2 FRP reinforcement strain gauges ............................................................... 185

6.4.3 Linear variable differential transducers (LVDTs) ...................................... 186

6.5 Test set-up and procedure .................................................................................... 186

6.5.1 Supporting frame ........................................................................................ 186

6.5.2 Binding frame ............................................................................................. 187

6.5.3 Loading frame ............................................................................................ 187

6.5.4 Testing procedure ....................................................................................... 190

7. Chapter 7 Analysis of the results ........................................................................ 192

7.1 Slabs without openings ........................................................................................ 192

7.1.1 Crack pattern .............................................................................................. 192

7.1.2 Modes of failure and load capacity ............................................................ 197


7.1.4 Steel strains ................................................................................................ 200

7.1.5 FRP strains ................................................................................................. 203

7.2 Slabs with openings ............................................................................................. 206

7.2.1 Slab with the opening located next to the column edge ............................. 206

7.2.2 Un-strengthened slab with the opening located 64 mm away from the

column edge ............................................................................................... 210

7.2.3 Un-strengthened slab with the opening located 2d away from the column

edge ............................................................................................................ 212

7.2.4 Crack pattern .............................................................................................. 214

7.2.5 Failure mode and ultimate load .................................................................. 215


7.2.7 Steel strains ................................................................................................ 217

7.2.8 FRP strains ................................................................................................. 220

7.3 Analysis of test results and the observed damage ............................................... 223

7.4 Comparison with design codes ............................................................................ 224

7.5 Conclusions ......................................................................................................... 226

8

8. Chapter 8 Design and Analysis of a Proposed Reinforced Concrete Slab-

Corner Column Connection ................................................................................ 228

8.1 Design of the proposed model ............................................................................. 228

8.2 Strengthening of the proposed slab and parametric study ................................... 229

8.2.1 Configuration 1: Two orthogonal CFRP sheets around the column .......... 230

8.2.2 Configuration 2: Two CFRP sheets parallel to the slab diagonal .............. 230

8.3 Summary of the conducted parametric study ...................................................... 231

8.4 General behaviour of the un-strengthened slab ................................................... 231

8.5 Effect of CFRP configuration on the ultimate load and deflection ..................... 235

8.6 Effect of CFRP thickness on the ultimate load capacity ..................................... 238

8.7 Conclusion ........................................................................................................... 239

9. Chapter 9 Conclusions and Recommendations ................................................. 241

9.1 Conclusions ......................................................................................................... 241

9.2 Recommendations and future work ..................................................................... 244

References .................................................................................................................... 245

Appendix A .................................................................................................................. 259

Word count is 59,793 words.

9

List of figures

Figure 2-1 Critical shear section perimeter for reinforced concrete slab [9] .................. 32

Figure 2-2 Cracks of slabs subjected to concentrated loads [12] .................................... 33

Figure 2-3 Effect of flexural reinforcement ratio on load-deflection response [16] ....... 34

Figure 2-4 Slab deflection during punching test of slab PG-3: (a) deflected shape of the

slab at various loading stages; (b) interpretation of phenomena according to critical

shear crack theory [17] .................................................................................................... 36

Figure 2-5 Radial and tangential strains at surface of slab PG-3 [17] ............................ 37

Figure 2-6 Vertical strains at column face [18] .............................................................. 38

Figure 2-7 Vertical strains at column face (square and circular column) at different load

levels [19] ........................................................................................................................ 38

Figure 2-8 Engineering model for punching shear [11] .................................................. 39

Figure 2-9 Representation of the punching shear capacity of RC slab reinforced with

CFRP [9] ......................................................................................................................... 40

Figure 2-10 Numerically predicted punching strength [7] .............................................. 42

Figure 2-11 Interaction between shearing and flexural strength according to Moe [16] 46

Figure 2-12 Dowel action effect of reinforcement [42] .................................................. 48

Figure 2-13 Effect of concrete cover on punching shear strength [39]........................... 48

Figure 2-14 Influence of effective depth on nominal shear strength [43]....................... 49

Figure 2-15 Effect of span-depth ratio on punching shear strength [48] ........................ 50

Figure 2-16 Compressive membrane action [12] ............................................................ 51

Figure 2-17 Strengthening of slab-column connection (a) FRP as shear reinforcement

[54] (b) added flexural reinforcement [55] ..................................................................... 53

Figure 2-18 Concrete strain on column sides of aspect ratio=3 [44] .............................. 54

Figure 2-19 Fibre orientations in a composites layer [59] .............................................. 55

Figure 2-20 Full composite action failure modes [68] .................................................... 61

Figure 2-21 Debonding failure modes [12] ..................................................................... 62

Figure 2-22 Shear reinforcement arrangements and assumed critical shear section

perimeters of tested slab specimens with three peripheral lines of shear reinforcement

[73] .................................................................................................................................. 64

Figure 2-23 Strengthening patterns and details [75] ....................................................... 65

Figure 2-24 Strengthened specimens with CFRP: (a) 24 CFRP dowels; (b) 32 CFRP

dowels; (c) 40 CFRP dowels; (d) 28 CFRP [78] ............................................................ 67

10

Figure 2-25 FRP rods and screw arrangements on the slab around the column (eight and

24 strengthener positions around the column for type A and B, respectively) [80] ....... 68

Figure 2-26 FRP fan arrangements on the slab around the loading plate (eight, 16 and

24 strengthener positions for types A, B and C, respectively) [54] ................................ 69

Figure 2-27 Dimensions and details of reinforcement of specimens [55] ...................... 74

Figure 2-28 CFRP strengthened specimens [91] ............................................................ 75

Figure 2-29 CFRP repair scheme [92] ............................................................................ 76

Figure 2-30 Layout of openings and FRP reinforcement [97] ........................................ 80

Figure 2-31 Adhesively-bonded anchors (a) sectional, (b) a bottom view: Anchors

connected by steel frame, (c) sectional, (d) bottom view, (e) top view with crossed

CFRP straps above central column, (f) detail view of end-anchor with force washer

between anchor plate and bolt head [102]....................................................................... 85

Figure 2-32 Schematic diagram of a single pull test [70] ............................................... 89

Figure 2-33 Comparison of bond-slip curves available in the literature; quoted from Ko

et al. [107] ....................................................................................................................... 91

Figure 3-1 Equivalent nodal loads produced during contact simulation of constant

pressure on the second-order element face [117] .......................................................... 100

Figure 3-2 Realistic behaviour of an element subjected to pure bending [68] ............. 101

Figure 3-3 Fully integrated linear brick element subjected to pure bending [115] ....... 101

Figure 3-4 Reduced- integration linear brick element subjected to pure bending [115]

....................................................................................................................................... 102

Figure 3-5 Truss element AB embedded in (3-D) continuum element; node A is

constrained to edge 1-4 and node B is constrained to face 2-6-7-3 [68]....................... 103

Figure 3-6 Four-node shell element [115] .................................................................... 104

Figure 3-7 Eight-node cohesive element [115] ............................................................. 105

Figure 3-8 Schematic of FRP composites [121] ........................................................... 106

Figure 3-9 Uniaxial stress-strain curve for concrete [37] ............................................. 112

Figure 3-10 Post-failure tensile behaviour: (a) stress-strain approach; (b) fracture energy

approach [104] .............................................................................................................. 113

Figure 3-11 Linear tension stiffening curve [135] ........................................................ 114

Figure 3-12 Bilinear tension stiffening curve [111] ...................................................... 114

Figure 3-13 Exponential tension stiffening curve [136] ............................................... 115

Figure 3-14 Exponential damage evolution [115] ........................................................ 117

Figure 4-1 Test arrangement from Walker and Regan [29] .......................................... 121

11

Figure 4-2 Steel reinforcement of Walker and Regan‟s slab-column connection [29]. 121

Figure 4-3 Load-deflection curves showing the effects of the different step time periods

on the slab-column connections .................................................................................... 123

Figure 4-4 Load-deflection curves showing the effects of the different mesh sizes on the

slab ................................................................................................................................ 124

Figure 4-5 Load-deflection curves showing the effects on thickness when using

different numbers of elements ....................................................................................... 124

Figure 4-6 Load-deflection curves showing the effect of using different tension

stiffening on the slab ..................................................................................................... 125

Figure 4-7 Load-deflection curves showing the effect of using different concrete tensile

strength on the slab........................................................................................................ 126

Figure 4-8 Load-deflection curves showing the effect of using different concrete

Young's modulus on the slab ........................................................................................ 127

Figure 4-9 Load-deflection curves showing the effect of using different dilation angles

on the slab ..................................................................................................................... 128

Figure 4-10 Load-deflection curves showing the effect of using different Kc on the slab

....................................................................................................................................... 128

Figure 4-11 Load-deflection curves for the experimental and numerical results ......... 130

Figure 4-12 Locations of strain measurements ............................................................. 131

Figure 4-13 Steel stress of the un-strengthened slab at failure load in N/m2 ................ 132

Figure 4-14 Stress state in concrete (N/m2) at load level 86 kN ................................... 133

Figure 4-15 Load configuration and steel reinforcement details for the slab [101] ...... 134

Figure 4-16 Instrumentation of the test slabs [101] ...................................................... 135

Figure 4-17 Load-deflection for the slab-column connections ..................................... 137

Figure 4-18 Steel reinforcement strains ........................................................................ 140

Figure 4-19 FRP reinforcement strains ......................................................................... 142

Figure 4-20 Beam under consideration [147] ............................................................... 143

Figure 4-21 Load versus midspan deflection ................................................................ 145

Figure 4-22 Cracking in the tested beams experimentally and numerically ................. 147

Figure 4-23 Comparison of slip profile at different load levels .................................... 148

Figure 4-24 Cohesive layer at damage initiation (top view) ......................................... 148

Figure 5-1 CFRP configurations on a quarter of the strengthened slab ........................ 157

Figure 5-2 Orthogonal configuration of FRP ................................................................ 159

12

Figure 5-3 Load-deflection curve of the strengthened slabs in orthogonal configuration

....................................................................................................................................... 159

Figure 5-4 Diagonal configuration of CFRP ................................................................. 160

Figure 5-5 Load-deflection curves of the strengthened slabs in a diagonal configuration

....................................................................................................................................... 161

Figure 5-6 Load-deflection curves with different thicknesses and layers..................... 162

Figure 5-7 Comparison between slabs strengthened by steel plates and CFRP sheets . 163

Figure 5-8 Steel stress of the strengthened slab at failure load in N/m2 ....................... 164

Figure 5-9 Maximum principal stress in CFRP (N/m2) ................................................ 166

Figure 5-10 Geometric illustration of punching and section force equilibrium [7] ...... 169

Figure 5-11 Damage in the cohesive elements and the debonding in the CFRP at the

ultimate load .................................................................................................................. 171

Figure 5-12 Effect of reducing the steel reinforcement ratio ........................................ 172

Figure 6-1 Specimen geometry and strengthening configuration ................................ 176

Figure 6-2 Column-slab reinforcement placed in the mould ........................................ 180

Figure 6-3 Complete reinforcement of one slab-column connection............................ 181

Figure 6-4 Surface preparation and delineation ............................................................ 182

Figure 6-5 Test set-up for the RC slab .......................................................................... 183

Figure 6-6 Array of the loading patches ....................................................................... 184

Figure 6-7 Arrangement of steel strain gauges ............................................................. 185

Figure 6-8 CFRP strain gauges in the slabs .................................................................. 185

Figure 6-9 LVDT on the slab centre ............................................................................. 186

Figure 6-10 Supporting frame for the rig test ............................................................... 187

Figure 6-11 Binding frame for the rig test .................................................................... 187

Figure 6-12 Deflected shape of the steel frame under a load of 150 kN ...................... 189

Figure 6-13 Load deflection comparison between using the whole frame or the loading

patches only ................................................................................................................... 190

Figure 6-14 Loading frame ........................................................................................... 190

Figure 6-15 Data Logger used in the test ...................................................................... 191

Figure 7-1 Punching shear failure in (a) slab 1 (b) slab 2 ............................................. 193

Figure 7-2 Numerical model principal maximum plastic strain at peak load indicating

punching shear failure in slab 1 .................................................................................... 194

Figure 7-3 Punching shear failure in slab 2 .................................................................. 195

Figure 7-4 Stiffness degradation in slab 2..................................................................... 195

13

Figure 7-5 Maximum principal stresses of concrete before failure load in slab 2 ........ 196

Figure 7-6 3D state of stress in the slab-column connection at failure ......................... 197

Figure 7-7 Comparison between experimental and model predictions for slabs 1and 2

....................................................................................................................................... 199

Figure 7-8 Steel reinforcement strain for the unstrengthened and strengthened slabs in

experimental and numerical model ............................................................................... 202

Figure 7-9 Stress state in concrete (N/m2) at load level 107 kN ................................... 203

Figure 7-10 CFRP reinforcement strain reading for slab 2 ........................................... 204

Figure 7-11 Maximum principal stress in CFRP (N/m2) .............................................. 205

Figure 7-12 Part of the slab-column connection showing the elbow-shaped strut [23] 206

Figure 7-13 Quarter of the slab showing the opening in different locations ................ 208

Figure 7-14 Load-deflection curves with the opening located at 0d away from the

column edge .................................................................................................................. 208



column edge .................................................................................................................. 212


Figure 7-18 Load deflection curve with the opening located at 2d away from the column

edge ............................................................................................................................... 214

Figure 7-19 Punching shear failure in slab 3 ................................................................ 215

Figure 7-20 Maximum principal stresses of concrete before failure load in the un-

strengthened slab ........................................................................................................... 216

Figure 7-21 Load vs. mid-span deflection .................................................................... 217

Figure 7-22 Steel reinforcement strain reading for strengthened slabs in the

experimental and numerical models.............................................................................. 220

Figure 7-23 CFRP reinforcement strains for slabs 3 and 4 ........................................... 221

Figure 7-24 Maximum principal stress in CFRP (N/m2) .............................................. 222

Figure 7-25 Stiffness degradation in the cohesive layer of the strengthened slabs ...... 223

Figure 7-26 Ultimate punching shear capacity comparison of tested slabs .................. 223

Figure 8-1 Reinforcement details of the proposed designed slab ................................. 229

Figure 8-2 Configuration for the two orthogonal CFRP sheets .................................... 230

Figure 8-3 Two CFRP sheets parallel to the slab diagonal ........................................... 231

Figure 8-4 Cracking of the concrete slab ...................................................................... 233

Figure 8-5 Propagation of concrete cracking to the slab free edge ............................... 234

14

Figure 8-6 Slab failure at ultimate load......................................................................... 234

Figure 8-7 Effect of strengthening the slab by configurations 1 and 2 on the ultimate

load capacity with respect to the un-strengthened slab ................................................. 235

Figure 8-8 Comparison of load-deflection curves for configurations 1 and 2 with the

load-deflection curve of the un-strengthened slab-column connection ........................ 236

Figure 8-9 CFRP debonding from the concrete substrate in configuration 2 ............... 237

Figure 8-10 Effect of orthogonal configuration on ultimate deflection of strengthened

slabs ............................................................................................................................... 238

Figure 8-11 Effect of CFRP thickness on the ultimate load capacity ........................... 239

15

List of tables

Table 2-1 Mechanical properties of some fibres [8] ....................................................... 56

Table 2-2 Typical mechanical properties of common resins [8]..................................... 57

Table 2-3 Summary of existing experimental work on the direct strengthening method

......................................................................................................................................... 72

Table 2-4 Summary of existing experimental work on indirect strengthening method .. 82

Table 2-5 Summary of the existing experimental work on strengthening by prestressed

FRP .................................................................................................................................. 86

Table 4-1 Material properties of Walker and Regan‟s slab-column connection .......... 122

Table 4-2 Material properties of Abdullah et al.‟s slab-column connection ................. 136

Table 4-3 Material properties of Bencardino et al.‟s beams ......................................... 144

Table 5-1 CFRP material properties [148] .................................................................... 150

Table 5-2 Summary of the numerical sensitivity study of applied bond length for slab-

column connection with FRP thickness=1mm .............................................................. 156

Table 5-3 Summary of studying different effective lengths ......................................... 158

Table 5-4 Study of Young's modulus and thickness of CFRP on the bond strength and

punching shear .............................................................................................................. 167

Table 6-1 Details of the slab test series ......................................................................... 177

Table 6-2 Compressive strength of the concrete cylinders used in this study .............. 178

Table 6-3 Concrete mix proportions ............................................................................. 178

Table 6-4 Concrete properties ....................................................................................... 179

Table 6-5 Mechanical properties of the steel rebars ..................................................... 179

Table 6-6 Properties of fibre reinforced polymer composite materials ........................ 180

Table 7-1 Summary of experimental results ................................................................. 197

Table 7-2 Summary of experimental results ................................................................. 215

Table 7-3 Comparison of test results with code predictions ......................................... 224

Table 8-1 Summary of strengthening configuration ..................................................... 231

16

Notations

Latin Letters

depth of neutral axis

cross sectional area of a composite

failure surface area above neutral axis

cross-sectional areas of the fibres in a composite

cross-sectional areas of the matrix in a composite

cross-sectional area of steel reinforcement in a section

constant

width of a section

perimeter length of the critical section

width in mm of the concrete substrate

width in mm of the FRP

C1 and C2 constants for normal weight concrete

constant with a value between 0 and 1

D independent elastic stiffness parameters

D scalar damage variable

effective thickness of a slab

equivalent effective slab depth of a slab

height of the steel reinforcement within a concrete section

longitudinal Young‟s modulus of a composite

perpendicular Young‟s modulus of a composite

concrete Young‟s modulus

Young‟s modulus of the dry fibres

Young‟s modulus of the matrix

concrete compressive strength at 28 days

fck characteristic concrete strength

fcm mean compressive strength of concrete

fctk characteristic tensile strength of concrete

fctsp split tensile strength

total stress of the steel reinforcement

ultimate tensile strength of a concrete section

17

yielding stress of a steel reinforcement in a concrete section

in-plane shear modulus of a composite

minor shear modulus of a composite

shear modulus of the matrix in a composite

interfacial fracture energy in a bond-slip model

shear modulus of the fibres in a composite

base value of the fracture energy

total height of a section

k triaxial compressive stress

Kc ratio of the second stress invariant on the tensile meridian, q(TM), to that on the

compressive meridian, q(CM)

effective bond length of FRP reinforcement to a concrete section

total applied moment in a slab-column connection

number of CFRP plates or sheets used in strengthening a concrete section

total force in the composite

total applied force in the fibres of a composite

total applied force in the matrix of a composite

total punching shear strength of a concrete section

total force required to develop debonding in a bond-slip model

Mises equivalent stress

a relative displacement in a bond-slip model

initial displacement at which damage takes place

finial displacement at which debonding takes place

thickness of the FRP plate

total force due to the effect of the FRP reinforcement area of a slab-column

connection

total force due to the effect of the steel reinforcement area of a slab-column

connection

U critical shear perimeter

fictitious reference value of shear

total punching shear strength in a concrete section

18

vertical punching shear force at the calculated ultimate flexural capacity of the slab

volume fraction of the fibres in a composite

volume fraction of the matrix in a composite

nominal punching shear strength

shear stresses transferred in the X direction in a concrete section in the case of

torsional moments

shear stresses transferred in the Y direction in a concrete section in the case of

torsional moments crack opening

crack opening (mm) for

crack opening (mm) for

Greek Letters

coefficient depends on maximum aggregate size

column location factor in ACI punching shear equation

ratio of long side to short side of the column in ACI punching shear equation

width factor in a bond-slip model

bond length factor in a bond-slip model

a combined factor multiplied by the total punching shear strength of a concrete

section

true strain of steel reinforcement

total strain in the longitudinal direction of a composites

total strain in the perpendicular direction of a composites

concrete strain

inelastic compressive strain of concrete

elastic compressive strain of concrete

elastic tensile strain of concrete

inelastic tensile strain of concrete

nominal ultimate compressive strain in concrete at the peak stress fcm

total strain in the FRP reinforcement in a section

true plastic strain

plastic compressive strain of concrete

nominal strain

ɛr rupture Strain of FRP composite

elastic steel strain

19

tension strain of concrete

Ø diameter of the corresponding bars

( ) eccentricity parameter

base value of the mean compressive cylinder strength

μ viscosity parameter

strengthening efficiency factor

correlation parameter multiplied by the equation of punching shear strength

major Poisson‟s ratio of a composite

minor Poisson‟s ratio of a composite

Poisson‟s ratio of the longitudinal fibres in a composite

Poisson‟s ratio of the matrix in a composite

equivalent reinforcement area of a section

steel reinforcement area ratio in a concrete section

FRP reinforcement area ratio in a concrete section

effective hydrostatic stress

total applied stress in the longitudinal direction of a composite

total applied stress in the perpendicular direction of a composite

⁄ ratio of the initial equibiaxial compressive yield stress to initial uniaxial

compressive yield stress

( ) effective compressive cohesion stress

stress in the fibres of the composites

stress in the matrix of the composites

maximum principal stress

nominal stress of steel reinforcement

true stress of steel reinforcement

( ) effective tensile cohesion stress

concrete stress in x direction

concrete stress in z direction

maximum shear stress of a section

,

and nominal stress components of the adhesive

numerical factor in a bond-slip model

20

reinforcement index of a section

flexural stiffness of FRP reinforcement in a section

flexural stiffness of steel reinforcement in a section

dilation angle

ultimate crack opening displacement of concrete

21

Abstract

Strengthening flat slabs at corner columns against punching shear

using fibre reinforcing polymer (FRP)

Bassam Qasim Abdulrahman, 2018

For the degree of PhD/ Faculty of Engineering and Physical Sciences

The University of Manchester

Using Fibre Reinforcing Polymer (FRP) composites for strengthening and rehabilitation

of reinforced concrete structures has been a viable technique for more than two decades.

Strengthening by FRP composites is often preferred to other strengthening techniques

like steel plates due to the former‟s special features, for example, it is lightweight, non-

corrosive, easy to install, has high tensile strength, and its use results in only minimal

changes to the external appearance of the structure. Additionally, the labour costs are

lower when using this material. The main objectives of this study are: (1) to investigate

the punching shear behaviour of slabs at corner column connections strengthened by

externally bonded FRP sheets using both modelling and experimental methods. The

study concentrates mainly on slabs without shear reinforcement that fail initially due to

punching shear; this is in order to enhance their serviceability and ultimate loading

capacity; (2) to investigate slabs at corner column connections with openings; and (3) to

increase understanding of the behaviour of such slabs and provide recommendations for

strengthening.

None of the current standards‟ specifications - like the ACI-440, Concrete Society

Technical Report TR55 and the Japanese Society of Civil Engineers JSCE - give the

required information for the design of concrete slab-column connections to withstand

punching shear. Furthermore, all the previous studies about the strengthening of slab-

column connections have dealt with interior columns; none have investigated the

strengthening of slabs at the corner column. Thus, this study is the first to investigate,

both experimentally and numerically, the effectiveness of strengthening slabs at the

corner column connection by using carbon fibre reinforcing polymer (CFRP) sheets.

22

The experimental programme comprises casting and testing four full-scale slabs that

have been designed and fabricated in order to simulate exterior slab-column

connections. One of them is the control specimen, which has been designed without any

opening or strengthening. One is similar to the control specimen but strengthened by

CFRP sheets around the corners. The last two slabs are designed similar to the control

specimen but they have openings close to the column. In addition to the openings, they

are strengthened by CFRP sheets.

In addition to the experimental programme, three-dimensional nonlinear finite element

models have been developed and validated against the experimental results. The

comparison between the experimental and the numerical results is based on deflections,

ultimate punching shear capacity, total strains of steel and CFRP reinforcements, crack

pattern and the failure mode. Results are also compared to the Eurocode 2, ACI and the

JSCE to predict the punching shear strength. It is concluded that bonding CFRP sheets

to strengthen a slab at the corner column can increase both the serviceability and the

ultimate strength by (11-21) % depending on the slab size. This limited increase is

associated with the small thickness of the CFRP sheets used in the study, which means

that there is only a small CFRP area resisting the tensile stresses; CFRP with a small

width is used due to the practical constraints.

23

Declaration

No portion of the work referred to in the thesis has been submitted in support of an

application for another degree or qualification of this or any other university or another

institute of learning.

24

Copyright Statement

The author of this thesis (including any appendices and/or schedules to this thesis) owns

any copyright in it (the “Copyright”) and he has given The University of Manchester the

right to use such Copyright for any administrative, promotional, educational and/or

teaching purposes.

Copies of this thesis, either in full or in extracts and whether in hard or electronic copy,

may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as

amended) and regulations issued under it or, where appropriate, in accordance with

licensing agreements which the University has from time to time. This page must form

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The ownership of any patents, designs, trademarks and any and all other intellectual

property rights except for the Copyright (the “Intellectual Property Rights”) and any

reproductions of copyright works, for example graphs and tables (“Reproductions”),

which may be described in this thesis, may not be owned by the author and may be

owned by third parties. Such Intellectual Property Rights and Reproductions cannot and

must not be made available for use without the prior written permission of the owner(s)

of the relevant Intellectual Property Rights and/or Reproductions.

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pdf), in any relevant Thesis restriction declarations deposited in the University Library,

The University Library‟s regulations (see

http://www.manchester.ac.uk/library/aboutus/regulations) and in The University‟s

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http://www.campus.manchester.ac.uk/medialibrary/policies/intellectualproperty

25

Acknowledgements

First and foremost, I would express my deepest gratitude to Almighty Allah for his

continuous blessing of me with the health, wisdom, patience, persistence, understanding and

motivation needed to successfully complete this work.

It is a pleasure to express my sincere appreciation and deepest gratitude to my supervisors,

Dr Jack Wu and Dr Lee S. Cunningham, for their valuable guidance and advice and

continuous support from the beginning to the final level, which enabled me to develop and

understand the whole subject. Without forgetting to express the deepest appreciation and

sincerest thanks to Prof Dr Omar Qarani Aziz for his supervision during the experimental

work at the University of Salahaddin, Kurdistan Regional Government, Iraq.

I also wish to express my sincere thanks to the Kurdistan Regional Government, Iraq, for

their financial support in funding my scholarship.

Many thanks also go to the technical staff at the Civil Engineering departments, College

of Engineering, the University of Salahaddin, for their assistance during the experimental

work for this project.

I also want to express my gratitude to all the staff of the School of Mechanical, Aerospace

and Civil Engineering (MACE) at the University of Manchester. Special thanks go to

Dr Adrian Bell, who gave me very helpful advice and useful comments on my thesis.

Many thanks also go to the IT services team and the postgraduate admission staff of the

School of MACE and the library staff at the University of Manchester for giving me all

the help I needed during my PhD research.

I offer my regards and blessings to my friends and colleagues in the research group who

supported me in all respects during my PhD research. Furthermore, I would not forget to

thank Dr Zeyad Wahab Ahmad and his family for supporting me during the whole study

period especially with the illness of my wife.

Finally, I would like to extend my deepest gratitude to my parents, my brothers, my wife

and my children, who sacrificed a lot, and I could not have made it without their dedication

and encouragement.

26

Dedication

To the spirit of my mother who waited a long time for me to complete my study, but she

died before seeing me today. I say to her, may Allah forgive you and make paradise as

your fate as a requital for your patience and prayers for me and my brothers. To my

father for encouraging me in all my academic endeavours in the pursuit of my study;

this support substantially contributed to its completion. To my brothers for their

encouragement and their support. Special thanks are expressed to my wife for her

personal support, encouragement and great patience during the research period. Finally,

to my beloved children, Harith, Saffanah and Jumana, who are the light of my life, I

dedicate this work.

27

1. Chapter 1 Introduction

1.1 Introduction

Reinforced concrete flat slabs are slabs supported directly on columns without the

addition of beams. They are a popular flooring solution in multi-storey construction due

to their economy and functional advantages and are widely used in both commercial and

residential buildings, cars parks, etc. [1]. The key advantages of the flat slab are as

follows: reduced floor depths in comparison to other systems, thus making space for

services and reducing building heights, and enabling economies in construction through

a reduction in the material cost and construction time via use of simple and efficient

formwork.

However, the clear advantages, flat slabs have inherent weaknesses; in particular, the

connection between the flat slab and the supporting column is the most critical part due

to the concentration of large bending moments and shear forces [2]. In flat slabs, a

complex state of stress may develop in the slab-column connection due to the

transferred bending moments and shear forces in this region. For edge and corner

columns particularly, the free edge may add further complications at the flat slab-

column connection due to the load eccentricities and torsional moments.

The analysis and design of reinforced concrete flat slabs require a vast knowledge of the

possible failure modes [3, 4]. The main failure modes are as follows: overall slab

flexural failure due to bending moments, overall slab shear failure (beam action failure),

local punching shear failure around the slab-column connection and local flexural

failure around the slab-column connection. A combination of all these failure modes

may be the cause of overall failure at loads smaller than the designated failure loads of

each individual failure mode [4].

Punching shear failure in slab-column connections is caused by the principal tension

stress, and it can occur at a load level less than that of flexural failure, especially when

there is enough flexural reinforcement preventing the development of high flexural

stresses [5]. In this case, punching shear failure will take place when the concrete

principal tensile stresses reach the value of the ultimate tensile strength of the concrete.

28

Punching shear failure is one of the most dangerous problems encountered in the

construction of flat slabs [1]. It is affected by the column size, slab depth, existing

flexural reinforcement ratio and the concrete tensile strength. The problem with this

failure is it is brittle and sudden because concrete is unable to accommodate high tensile

stresses that develop close to the slab-column connection.

Through the whole service life of a structure, punching shear may occur as a result of

excessive loads or earthquakes, deterioration due to corrosion of the embedded

reinforcement, freezing, thawing or fire damage, lack of ductility and energy absorption

at the slab-column connection [6]. Punching shear failure can also occur during

construction, especially when casting new floors, as the weight of the new concrete and

shoring systems is transferred to the lower floor, which may exceed the normal in-

service design loads [7].

In some cases, it is necessary to strengthen or retrofit existing slabs due to insufficient

punching shear strength. This strengthening may be required through a change of

building use, the introduction of new openings, loss of strength through deterioration, or

incorrect analysis and design [8].

Reinforced concrete slabs have been strengthened by bonding steel plates with adhesive

or via bolts to the tension surface of the slabs [9]. This method has been used for many

years but has the disadvantage of requiring a great deal of labour and may result in

intrusive changes to the architectural appearance of the structure. Furthermore, the use

of steel plates has all the corrosion risk issues associated with rebar and requires an

appropriate protection/maintenance strategy. Over the last couple of decades, fibre

reinforcing polymer (FRP) composites have been increasingly used in construction

applications. FRP has many appealing features such as a high strength to weight ratio

(usually superior to steel) and high resistance to corrosion. As a result, FRP retrofit

approaches as an alternative to steel have received much attention from the research and

practice community.

29

1.2 Problem definition

Punching shear failure takes place due to the concentration of high shear stresses around

the slab-column connection. In the case of corner columns, these stresses are enhanced

by the combined effect of shear forces and bending moments transferred unequally

around the column. Despite the abundance of studies on FRP strengthening of the

internal column to slab zones, as of yet, no study has focused on the particular case of

the corner column. In view of this, the present investigation was carried out in order to

study the capability of carbon fibre reinforcing polymer (CFRP) in strengthening

reinforced concrete slab at corner columns with and without openings.

1.3 Objective of the research and the methodologies

Based on the location of the slab-column connection, three types of connection form

exist: interior, edge and corner connections. Slabs at edge or corner column connections

are more critical to punching than the interior slab-column connections because of the

relatively high transferred moments between the slab and the column.

The objective of this study is to investigate the punching shear behaviour of the slab at

corner column connections strengthened by externally bonded CFRP sheets using both

modelling and experimental methods. The study concentrates mainly on flat slabs that

have initially failed due to punching shear in order to enhance their serviceability and

ultimate loading capacity. The study also investigates the effect of openings near the

slab-column connections on punching shear and how to strengthen these slabs

accordingly.

1.4 Thesis layout

This thesis contains nine chapters. In Chapter one, an introduction to the problem of

punching shear, the objectives of this study and the methodologies followed to achieve

these objectives are presented.

In Chapter two, a general background to the problem of punching shear and the factors

affecting slab strength are presented. Furthermore, various mechanisms of punching

shear resistance and clear descriptions of theoretical models of the behaviour in addition

to the explanation of the mechanisms in which the proposed CFRP strengthening

scheme increases punching shear capacity. A general overview of the effect of openings

30

in slab-column connections is given in order to enable greater understanding about the

opening‟s location and effect on punching shear. Experimental studies and the methods

used in strengthening slab-column connections with FRP reinforcement are discussed

briefly, in order to increase the knowledge about the punching shear and to demonstrate

the gap in the knowledge that needs to be filled. The bond between the concrete and the

CFRP is described and formulated in order to provide a general view of the behaviour

of such an important factor in strengthening. Finally, some standard specification codes

dealing with FRP are presented to offer an overview of how these codes deal with FRP

strengthening.

In Chapter three, a detailed discussion of the numerical model is presented regarding the

behaviour of each individual material and the choice of the elements required in the

analysis. As the Concrete Damage Plasticity model is intended to be used in this study,

all the parameters regarding this model are described as well as how this model deals

with concrete material numerically. The most important factor that should be taken into

consideration is the interaction between CFRP sheets and the concrete substrate.

Detailed information is presented on how to model that factor and how failure took

place within the interaction area.

In Chapter four, an experimental case study by Walker and Regan is analysed as a

means of validating the numerical model that will be used in the subsequent work. An

additional model of an interior slab-column connection is also modelled. Furthermore,

in order to check the validity of the model in capturing the debonding of CFRP sheets

from the concrete substrate fail in shear, an additional model of a strengthened beam

with shear failure is also tested. This model confirmed the ability of the numerical

model to capture the debonding failure that may take place in the following

experimental work.

Chapter five includes a parametric study conducted based on the effects of the material

parameters, FRP configuration and others to form the baseline for the following work.

A more detailed explanation of the calculation of the effective bond length based on

three main equations with more critical reviews is added. More discussion on choosing

the best effective bond length that will be used in a future experimental work and a

numerical study was also conducted to give more explanation. The effect of the FRP-

31

Concrete bond strength was discussed to give more understanding of how bond strength

can be involved in increasing the total ultimate punching shear capacity. Finally, the

behaviour of slab-column connections was extended to study strengthening of slabs that

fail initially in flexure.

In Chapter six, the experimental work conducted in this study is presented. The choice

of the samples, details, experimental parameters and the material properties are

presented. In addition, the conducting of the experimental work is described.

In Chapter seven, the experimental and the numerical study results are discussed in

detail by presenting the corresponding crack pattern, mode of failure, load-deflection

curves, load-strains in the steel and the CFRP reinforcement. In order to find the

location that has the most severe effect of the opening on the ultimate punching shear

capacity of the slab-column connection, a parametric study is conducted based on that

target. The location with the strongest effect is chosen and then the slab with an opening

in this location is strengthened. Finally, a comparison between the experimental work

and the existing codes and standards is conducted to show the validity of the

experimental work within these codes.

In Chapter eight, a proposed case study is chosen. It is designed and analysed

numerically to give more understanding of the efficiency of strengthening slabs at

corner columns and to validate the structural behaviour in the experimental test. A

parametric study based on the steel flexural reinforcement ratio, the configuration of the

CFRP sheets and the CFRP thickness is conducted. A general conclusion based on this

study is provided to summarise what has been extracted.

Finally, Chapter nine presents the general conclusions and recommendations extracted

from this study.

32

2. Chapter 2 Literature review

In a conventional flat slab-column structure, bending moments as well as vertical loads are

transferred from the slab to the columns especially from uneven distribution of columns or

unequal adjacent span lengths. In interior slab-column connections, moments are generally

small, while on the edge or especially in the corner columns they are large. In all cases, the

applied punching shear stresses have to be less than the ultimate capacity of the connection;

otherwise, shear reinforcement should be added to increase the connection punching shear

strength.

This chapter firstly describes the punching shear failure and mechanism in reinforced

concrete slabs. The specific cases of corner columns and the effect of openings in slabs

based on existing studies are reviewed. Then, the general factors influencing the punching

shear strength and modes of failure are presented. Methods of strengthening slab-column

connections based on the experimental observations are presented briefly. Finally, the

relationships of the bond between the concrete and FRP are also introduced.

2.1 Punching shear in reinforced concrete slabs

Two-way reinforced concrete slabs may fail because of punching shear, which occurs

normally around a column [10]. Punching shear failure is a three-dimensional state of stress

failure that comes from the concentration of the high shear stresses in concrete around the

slab-column connection. It is described by the slab fracturing along critical planes extending

from the slab-column connection from compression to tension surfaces through the slab

depth in an oblique direction away from the column [9]. The punching shear failure for

square columns takes the form of a frustum of a pyramid, as seen in Figure 2-1.

Figure 2-1 Critical shear section perimeter for reinforced concrete slab [9]

33

Punching shear resistance of a concrete slab is provided by a combination of resistances

arising from: un-cracked concrete in compression, aggregate interlock from concrete in

tension, dowel action of the rebar and residual tensile stresses across the inclined cracks

[11]. As cracking takes place in the slabs, the effect of aggregate interlock decreases

until it vanishes when the cracks are large.

When reinforced concrete flat slabs are subjected to loading, circular cracks develop

initially near the slab-column connection with different inclinations based on the

reinforcement ratio; here, flexural cracking is most severe due to the high negative

bending moments at the top [12,13]. From these circular cracks, radial cracks start to

develop because of the negative bending moments in the circumferential direction.

Finally, tangential cracks initiated by the coalescence of the cracks on the tension region

extend through the slab thickness before the slab fails. These cracks occur at a distance

from the column face and failure takes place when the crack reaches the corner of the

slab-column connection, as shown in Figure 2-2.

Figure 2-2 Cracks of slabs subjected to concentrated loads [12]

After these cracks, punching shear occurs via a conical or pyramid shape around the

column by a mean angle of (20-45)o,

depending on the nature and amount of

reinforcement in the slab. The critical section for shear is taken perpendicular to the

plane of the slab from the periphery of the column in a distance with a value that varies

from one specification to another. The shear force to be resisted can be calculated as the

34

total factored load on the area bounded by the panel centrelines around the column less

the load applied within the area defined by the critical shear perimeter unless significant

moments must be transferred from the slab to the column [14].

As stated previously, slab-column connections are not only subjected to vertical loads

but in some cases to unbalanced moments. A combination of such loading cases results

in the critical section perimeter being at or close to the perimeter of the loaded area

where the moment-shear interaction exists. Therefore, more complexity will be added to

the classification of the failure mode at the connections.

One of the design parameters known for influencing the punching shear capacity of

concrete slabs is the steel reinforcement ratio [15]. Increasing the steel reinforcement

ratio leads to cracks that are narrower and shallower because stresses are transferred

across them. Thus, increasing the steel reinforcement ratio increases the overall

punching capacity. It is expected that adding FRP reinforcement to the tension face of a

concrete slab will increase the punching capacity as if the steel reinforcement ratio was

being increased. The flat slab-column connection failure mode and the applied load-

midspan deflection curve are highly dependent on the slab reinforcement ratio and the

steel distribution over the connection [16].

Figure 2-3 Effect of flexural reinforcement ratio on load-deflection response [16]

Figure 2-3 shows that increasing the slab reinforcement ratio increases the ultimate

punching shear strength and decreases the ductility which leads to a brittle failure or a

pure punching shear failure as clearly shown in curves 1-3. Slab failure occurs when the

35

concrete is crushed but the steel reinforcement does not yield. As the reinforcement

ratio decreases, failure of the slab-column connection alters from a pure punching to a

flexural punching. In this failure, the steel reinforcement yields and this yielding

extends to a specific area in the slab around the column before the final punching shear

failure, as shown in curves 4-6. In these types of slabs, it is found that the steel

reinforcement yields but the failure is still by punching due to the lack of ductility. With

a further decrease in the reinforcement ratio, failure alters to pure flexure with large

deflections, as shown in curves 7 and 8. These types of slabs reach their plastic plateau

by large plastic deformations at the onset of the yield line mechanism.

One of the most important features of the punching shear behaviour is the slab-column

connection deflected shape [17]. When a slab-column connection is loaded, after a short

linear elastic part, cracking occurs, which reduces the connection stiffness. Figure 2-4

shows that the rotations in the compression zone of the slab are proposed to be within a

hinge located close to the column. The deflected profile in the slab compression region

can be considered as straight lines, while that in the tension region shows a slight

discontinuity, especially when the shear crack intersects the reinforcement. This

discontinuity can be attributed to the rotation of the outer part of the slab about its

centre of rotation (CR), while the crossing of the flexural reinforcement through the

shear crack alleviates this discontinuity [17].

36

Figure 2-4 Slab deflection during punching test of slab PG-3: (a) deflected shape of the

slab at various loading stages; (b) interpretation of phenomena according to critical

shear crack theory [17]

The concrete compression strains reach their ultimate values adjacent to the column,

while the radial direction strains decrease very rapidly with increasing distance from the

column face, as shown in Figure 2-5.

37

Figure 2-5 Radial and tangential strains at surface of slab PG-3 [17]

The concrete tangential strains are usually higher than the radial strains due to the

concrete decompression near the column face which comes from the local bending of

the compression zone [17]. The concrete compression strain distribution on the faces of

the square or rectangular column shows a concentration of stresses near the column

corners. This concentration increases when increasing the column cross-sectional area,

but it is alleviated by using circular columns [18, 19].

38

Figure 2-6 Vertical strains at column face [18]

Figure 2-7 Vertical strains at column face (square and circular column) at different load

levels [19]

2.2 Punching shear failure mechanism

Applying load to a slab-column connection implies the sequence of many events as (1)

formation of roughly circular cracks around the column periphery on the tension side

and propagation to the compression side, (2) formation of new lateral and diagonal

cracks, and (3) the formation of the shear crack. [11]

With increasing loading, the inclined crack develops towards the compression zone

which prevents the crack propagation. Furthermore, the crack propagation is prevented

by the dowel action of the tension reinforcement [11].

39

The punching shear failure in the compression zone occurs by splitting along the line

AA‟ and/or BB‟ shown in Figure 2-8.

Figure 2-8 Engineering model for punching shear [11]

Where X represents the depth of the compression zone or the neutral axis depth from

the compression zone, d the slab effective depth, h the slab thickness, r is the column

side, D is the column diameter, is the vertical component of the compression zone

resistance, θ is the angle of failure surface, ABCD plane is at the end of the compression

side, A‟B‟C‟D‟ is at the end of tension side, A1B1C1D1 is a plane at mid-depth of the

neutral axis.

When the inclined shear crack develops, the applied load is totally resisted by the

vertical components of compression zone above the neutral axis , the aggregate

interlocking and the dowel action of the flexural reinforcement and the attached

FRP composites [11, 20 and 10]. Thus, the total shear resistance of a slab

connection without shear reinforcement is given by:

( )

The punching failure is a sudden failure characterized by a rapid decrease of the load

carrying capacity. However, the punching crack causing the punching failure is not

formed suddenly but is preceded by the formation of internal microcracks. Because the

micro-crack formation is progressive, steel and composite resistance are gradually

40

activated and the force in the reinforcement can be added to the concrete tensile force as

proposed by the general model of punching shear [9].

Figure 2-9 Representation of the punching shear capacity of RC slab reinforced with

CFRP [9]

During load application, these forces components do not remain isolated but work

together. So, their maximum values do not reach at the same time [11]. The aggregate

interlock effect activates after the appearance of the inclined cracking depends on the

concrete properties, crack width and the relative displacement between the crack faces.

At failure, it is neglected because of the large separation between the crack faces. The

resistance offered by the dowel action is typically small because the maximum shear

stress carried by the dowel action is limited by the tensile strength of the concrete cover

surrounding the reinforcement bars [21]. Cope [22] in 1985 stated that dowel action in

slabs is less significant than in beams as the shear crack is not open over the entire

width of the slab and because of the continuity provided by the reinforcement in two

directions. Thus, dowel action will not be activated as much as in beams fail in shear.

Based on the Critical Shear Crack Theory (CSCT), punching shear failure takes place

when the shear demand equals the available shear strength in a given deformation level

[23]. Furthermore, the punching shear strength depends on the opening width and

roughness of the critical shear crack that develops through the inclined compression

strut carrying shear. Thus, the shear strength can be calculated by assuming free body

41

forces with kinematics at failure characterised by the rotation of the slab. Assuming

such kinematics, not only tensile stresses but also stresses due to aggregate interlocking

develop along the critical shear crack. Increasing the opening of the flexural cracks

causes a decrease in the shear strength as wider cracks have a lower capacity to transfer

shear stresses. For slabs strengthened with FRP composites, lower crack openings will

develop for the same load level due to the confinement of the FRP what causes a stiffer

flexural behaviour and thus an increase in the total punching shear strength. [24]

Farghaly et al. [7] found that the slope of the failure surface above and under the neutral

axis is similar to a linear truncated cone. So, the crack surface is divided into two parts:

above and under the neutral axis. Thus, each part of the crack surface has its own

concrete contribution to the ultimate strength. The punching shear strength is calculated

by integrating the shear stresses around the punching crack surface.

Kinnunen and Nylander [25], Zararis [26] and Zararis and Papadakis [27] stated that the

shear strength is attributed to the compression zone of the intact concrete which

prevents shear slip of the crack surface. It also acts as a buffer preventing any

meaningful contribution of shear slip along the crack interface. Consequently, the

aggregate interlock and the dowel forces are marginal. Farghaly et al [7] stated that the

shear strength in the compression zone is the main contributor to the punching shear

strength and shear strength in the tension zone can be neglected. And thus the dowel

action as the main contributor to the tension zone shear strength can be neglected.

For slabs strengthened by attaching FRP on the tension face, the punching shear

strength can be indirectly increased by increasing the tensile force and the

corresponding compression force (by equilibrium) in the concrete which increases the

shear stresses that integrated around the crack surface in the compression zone. [7]

Figure 2-10 shows that for all slabs simulated by Farghaly et al [7], increasing the FRP

reinforcement area will significantly increase the shear stress capacity in the

compression zone. Meanwhile, the shear strength in the tension zone is almost kept

constant [7].

42

Figure 2-10 Numerically predicted punching strength [7]

Where is vertical component of the compression zone resistance above the neutral

axis and is vertical component of the tension zone resistance below the neutral axis.

From all previous studies, it can be stated that the main purpose of strengthening slab-

column connections by FRP composites is to increases the tension force and the

corresponding compression force in the concrete in order to increases the shear strength

in the compression zone.

2.3 Corner slab-column connections

The importance of flat slab-column connections has resulted in them being used widely

in many constructions. However, in spite of this importance, there are many different

problems associated with them. One of the most dangerous problems encountered in the

construction of flat plates is punching shear failure, which is a catastrophic failure.

Therefore, designing or retrofitting slab-column connections against punching shear

failure is of great importance in structural buildings.

43

The vast majority of the previous studies available in the literature are on interior slab-

column connections where moment transfer is usually relatively small or negligible

[28]. In most of the quoted experimental studies mentioned in the literature, a single

column stub was positioned in the middle of the slab and the boundaries represented the

line of contraflexure, which can be an oversimplification because at the simply

supported no transferred moment is present in both the supports and the line of

contraflexure.

Although it is convenient to test flat slab-column junctions under this boundary

condition, the in-service boundaries are often not properly represented.

Currently, there is limited data on the un-strengthened slab at corner column

connections. In this type of slab, there is often a significant interaction between the

eccentric axial loads transferred to the corner columns and transferred moment. The

existing studies on corner slabs can be classified into three categories: (1) isolated

models consisting of one corner column and a part of a slab representing the negative

moment area; (2) a whole slab supported by four corner columns which provide a

realistic representation of the corner region of a flat slab; and (3) multi-panel slabs [29].

2.4 Factors influencing punching shear strength of a slab-column connection

The punching shear strength of a slab-column connection under static loads is affected

by several factors. These factors have been studied by researchers in order to put

forward a general theoretical model of punching shear. However, previous researchers

have focused on each factor independently, without incorporating the effects of other

factors which have not to be neglected. Concrete compressive strength, flexural and

compressive reinforcement ratio, the pattern of the flexural reinforcement,

reinforcement arrangement, concrete cover, concrete tensile strength, the thickness of

the slab, the span-depth effect, surrounding restraint, shear reinforcement, and the

column shape and the size all affect the punching shear strength of a slab-column

connection. A brief discussion of each factor is presented as follows:

2.4.1 Concrete compressive strength

The effects of concrete strength have been studied experimentally by many researchers.

Elstner and Hognestad [30] were the pioneers in studying the effects of this factor. They

44

found that the punching shear strength is proportional to the cubic root of the concrete

compressive strength. Moe [18] was convinced that the shear failure in a slab-column

connection occurs when the concrete splits without being crushed. Therefore, the

punching shear strength is controlled by the tensile splitting. Moe assumed that the

shear strength is dependent on √ as the concrete tensile strength is proportional

to √ . However, the ratio of the nominal ultimate shear stress to √ shows a

significant scatter in practice due to the scatter in the tensile strength of the concrete.

Later, and based on the numerical study of Ozbolt et al. [31] and Menetrey [10], it was

found that the concrete fracture energy has a large effect on the punching shear strength

of a slab-column connection. Inácio et al. [32] studied the effect of high-strength

concrete on the punching shear strength of slabs. They found that the punching shear

capacity increases by 43% but rupture is also more brittle when compared to normal

strength capacity.

2.4.2 Strength and ratio of the flexural reinforcement

The design of slab-column connections was primarily based on the work conducted by

Moe [18] and the ACI-ASCE Committee 326 and there have not been any considerable

changes to the punching considerations since that time [33]. Punching shear strength

could be affected by the strength and the ratio of the flexural reinforcement. There have

been very few studies considering the flexural reinforcement strength as the main factor.

The earliest study was conducted by Moe [18] in 1961. Later, Dilger et al. [34] in 2005

explained that, for such a case, the yield strength of the flexural reinforcement is

reached before punching. They also concluded that, if the flexural reinforcement

strength is varied without approaching the yield point, the crack width will be affected.

Therefore, the punching shear capacity is not influenced by the yield strength of the

flexural reinforcement [34].

The effect of the flexural reinforcement ratio was studied by Yitzhaki [35] in 1966, and

he proved that the punching shear strength depends proportionally on the flexural

reinforcement ratio. Yitzhaki depended on the work of Moe [18] from 1961 in which he

proposed a relation between

and

as follows:

45

( )

Where is the nominal punching shear strength, is a constant with a value between

0 and 1, is the fictitious reference value of shear √ , is a constant,

is the perimeter length of the critical section, is the effective thickness of a slab, and

is the vertical punching shear force at the calculated ultimate flexural capacity of

the slab. The magnitude of does not have a physical relation directly to the

mechanism of failure, but it reflects several other important affects, such as the

distribution of cracking, the amount of elongation of the tensile reinforcement,

magnitude of compressive stresses in the critical section and the depth of the neutral

axis at failure. Figure 2-11 shows the interaction between shearing strength and flexural

strength. It is clear that if

,

approaches a constant value, this means that if a

slab is designed to fail in pure flexure, which is the most preferred mode of failure in

design, the nominal punching shear strength can be calculated based on √ ,

which is independent of the flexural reinforcement ratio. Most of the design codes that

take into consideration the effect of the flexural reinforcement ratio use this factor with

a power function. Previous studies concluded that the punching shear strength is a

function of the reinforcement ratio raised to the power of one-quarter. But later studies

by Dilger [36] proved that the punching shear strength is a function raised to the power

of one-third, as is suggested by the Eurocode 2 [37] and the British codes [38].

Percentage of the flexural reinforcement is considered as a factor that affects the

punching shear strength of any slab-column connection, as increasing the ratio leads to

an increase in the punching shear strength. Ebead and Marzouk [15] found that two-way

slabs reinforced with less than 0.5% reinforcement ratio tend to fail in flexure rather

than in punching. Two-way slabs reinforced with (0.5-1)% tend to fail in flexural

punching, while those reinforced with more than 1% reinforcement ratio tend to fail in

pure punching shear. Thus, increasing the flexural reinforcement ratio increases the

overall punching capacity and it also increases the post-cracking stiffness and decreases

the ductility, which may alter the failure mode from a ductile to a brittle one.

46

Figure 2-11 Interaction between shearing and flexural strength according to Moe [16]

2.4.3 Pattern of flexural reinforcement

Kinnunen and Nylander [25] in 1960 studied the effect of reinforcement distribution on

the punching shear strength of a slab-column connection. They found that the ultimate

punching shear capacity can be increased by (20-50)% for circular slabs reinforced with

orthogonal reinforcement mesh rather than ring mesh. They also found that slabs

reinforced with orthogonal steel bars nearly behave axis-symmetrically in terms of

deflections and shear forces distribution, even though their reinforcement is not axis-

symmetric.

On the basis of their test, they developed a rational theory to estimate punching shear

strength which depended on assuming that the punching strength is achieved for a given

critical rotation. This theory is still one of the best models for describing the punching

shear phenomenon, even though is never included in any codes of practice nowadays

[23].

2.4.4 Reinforcement arrangement

Elstner and Hognestad [30] in 1956 and Moe [18] in 1961 studied the effect of

concentrating flexural reinforcement over the column region on the overall punching

shear of a slab-column connection. They compared the results to slabs reinforced with

uniformly distributed reinforcement. In Elstner and Hognestad‟s slabs, half of the

flexural reinforcement was distributed within a distance equal to the slab‟s effective

47

depth, d, while in Moe‟s slabs, the flexural reinforcement was arranged between

uniform spacing and 82% placed within the slab‟s effective depth. From both tests, they

found that the reinforcement concentration could not increase the punching shear

strength but it may decrease it. This can be attributed to the large radial sectors that are

left almost unreinforced due to the concentration of the flexural reinforcement.

Therefore, a slight decrease in strength and a reduction of ductility could be a result of

reinforcement concentration. Later studies of Alexander and Simmonds [39] in 1992

and McHarg et al. [40] in 2000 investigated the effect of adding extra reinforcement

over the column strip which reduces the initial reinforcement spacing. They found that

all the slabs failed due to punching, but with an increase in the ultimate punching shear

capacity of 14% and a decrease in the ductility. Although the failure was due to

punching, the bar force profile showed that anchorage failure occurred in the central

bar. Based on this observation, they concluded that the slabs tested by Elstner and

Hognestad [30] and Moe [18] failed actually due to anchorage failure. They also

concluded that the above observation may explain why concentrating the reinforcement

through the column region does not increase punching shear capacity.

2.4.5 Compressive reinforcement ratio

Elstner and Hognestad [30] in 1956 were the earliest researchers to study the effects of

compression reinforcement on the overall punching shear capacity of a slab-column

connection. They reported that

or, if the flexural reinforcement value is small,

the change in the compression reinforcement has a negligible effect on the ultimate

punching shear strength.

Manterola [41] in 1966 tried to study that effect by testing 12 slab-column connections

with different compression to tension reinforcement ratios, 0, 0.5, and 1. He found that

the ultimate punching shear strength is not affected by the compression reinforcement

when the tension reinforcement is small. However, increasing the compression

reinforcement from zero to an amount that equals the tension reinforcement could

increase the punching shear capacity by about 30%. Nevertheless, there is no clear

evidence about how the compression reinforcement affects the punching shear strength

of a slab-column connection. Pan and Moehle [42] in 1992 observed that, if the

compression reinforcement extends through the column, it can provide some residual

48

ability to span to the adjacent supports if one support is damaged. They can act as a

suspension net holding the slab and support some loading after punching shear failure

and prevent a catastrophic failure by increasing the dowel effect after punching, which

is necessary to prevent the progressive collapse of the structure, as shown in Figure 2-

12.

Figure 2-12 Dowel action effect of reinforcement [42]

2.4.6 Concrete cover

The cover of the reinforcement is an important parameter affecting the punching shear

capacity similar to the slab‟s effective depth. Increasing the concrete cover causes a

reduction in the slab‟s effective depth and vice versa. Alexander and Simmonds [39]

tried to explain the effect of the concrete cover by testing a series of interior slab-

column connections based on changing the concrete cover‟s depth. They found that a

slab with a larger concrete cover can withstand a larger load before failure, compared to

a slab with a smaller cover, albeit the difference is about 3%, but the former‟s behaviour

is less stiff than the latter, as slabs with smaller concrete covers suffer from larger bond

deformation, as shown in Figure 2-13.

Figure 2-13 Effect of concrete cover on punching shear strength [39]

49

2.4.7 Concrete tensile strength

The influence of the tensile strength is related to the concrete compressive strength as

there is a correlation between compression and tension. Increasing the concrete tensile

strength will increase the load at which the first flexural crack appears, and thus the

response of the structure will be stiffer as compared to a structure with low concrete

tensile strength [7]. The concrete tensile strength has a major effect on the slab

punching shear strength. The punching shear failure occurs when the shear stress

exceeds the tensile splitting strength of the concrete. In studying the effect of this factor,

it is concluded that increasing the concrete tensile strength increases both the ultimate

load capacity and deflection [7].

2.4.8 Thickness of the slab

Regan [43] in 1986 studied the effect of slab thickness in punching shear by

investigating six specimens with different slab thicknesses. In his test, the effective slab

depths were limited to (80, 160 and 250) mm. The results proved that the nominal shear

strength increases when decreasing the slab‟s effective depth (d), which agrees

reasonably well with the size factor (√ ⁄

) used in BS8110 [30], as shown in Figure 2-

14.

Figure 2-14 Influence of effective depth on nominal shear strength [43]

Regan stated that the slab depth range in his test is limited, but the tests carried out by

Kinnunen et al. [44] in 1978 with an effective depth of up to 619 mm further confirmed

50

the fourth root relationship. Bazant and Cao [45] in 1987 found the same conclusion and

they stated that increasing the slab thickness results in a steep decline in the post-peak

behaviour of the load-deflection curve, showing a brittle behaviour. Recent

experimental studies conducted by Guandalini et al. [17], Li [46] and Birkle and Dilger

[33] confirmed that the punching shear capacity decreases significantly with the slab

effective depth increment.

2.4.9 Span-depth effect or the size effect

The size effect is one of the outstanding aspects of fracture mechanics. Lovrovich and

McLean [47] in 1990 concluded that the punching shear strength was significantly

increased for a span-depth ratio below six, as shown in Figure 2-15. They also

concluded that the strength enhancement may be attributed to the formation of an

idealised compression strut which leads to an arch mechanism in the slabs, and in-plane

compressive forces resulting from friction at the support. Falamaki and Loo [48] in

1992 stated that using large-scale model structures would help to eliminate the size

effect problem.

Figure 2-15 Effect of span-depth ratio on punching shear strength [48]

2.4.10 Surrounding restraint

Based on the results of Taylor and Hayes [49] in 1965, a useful effect of edge restraint

is that it can increase the ultimate punching shear strength of a low reinforcement ratio

up to 60%. Slabs with a low reinforcement ratio exhibited high ductility and were more

51

likely to fail in a flexure. The ductile behaviour allows compressive membrane forces to

fully develop, as shown in Figure 2-16.

Figure 2-16 Compressive membrane action [12]

Slabs with high reinforcement ratio were not affected by the edge restraint or in some

cases there was a negligible effect. Therefore, these slabs failed by punching shear as

sudden rupture took place. It is possible that the slab fails before the membrane action

develops. Rankine and Long [50] in 1987 and Kuang and Morley [51] in 1992 noticed

that the edge restraint enhances the punching shear strength of a slab-column connection

in all cases, and may also change the failure mode, because the developed membrane

forces enhance the shear and flexural capacity of the slab and at the same time reduce

the ductility.

It can be seen from previous studies that the restraint can enhance the ultimate load

strength of a slab-column connection, but reduce the ductility of the slab. Nevertheless,

it is difficult to quantify the degree of the enhancement because it depends on the in-

plane restraint provided by the surrounding structure.

2.4.11 Shear reinforcement

Building structures should be designed to fail in a ductile mode with large deformations

when subjected to a catastrophic loading, in order to give a clear warning of impending

failure. Shear reinforcements are used to enhance both the ultimate strength and the

ductility of a slab-column connection. Their role is mainly to control the opening of the

critical shear crack and increase the area of the compression zone and aggregate

interlock, which results in increasing the shear strength [47]. Shear reinforcements are

bars (or other shapes) crossing the inclined cracks to prevent punching shear failure.

These bars should have an adequate tension strength, ductility and good anchorage to

52

develop their strength to resist punching shear. The placement of the shear

reinforcement is very important as it should be positioned in a way that it intersects with

the inclined shear cracks. There are many types of shear reinforcements used to

strengthen new or existing reinforced concrete slabs.

2.4.11.1 Shear reinforcements for new construction

In this case, shear reinforcements are embedded with the flexural reinforcements before

the concrete casting. They can be divided into two groups [52]:

1) Bent bars, stirrups and Shearband.

2) Headed reinforcements including shear studs and headed bars.

Only limited types of these reinforcements, such as shear bolts, can be used in the post-

strengthening application of existing reinforced concrete slabs, while others, such as

steel Shearbands, need to be applied at the time of construction.

2.4.11.2 Shear reinforcement for strengthening existing construction

Existing concrete slabs may need to be strengthened due to insufficient punching shear

capacity as mentioned previously in 1-1. Many methods have been proposed to

strengthen these structures. A steel support can be installed around the column on the

bottom of the slab. Steel plates and vertical steel bolts are used as shear reinforcement

[53]. This technique can effectively increase both the ultimate load and the ductility of

the strengthened connection. Also, reinforced concrete capital or a drop panel can be

added to the bottom of a slab. However, the most effective strengthening method

nowadays is using FRP sheets or plates around the column. In this method, FRP is used

either as shear studs embedded vertically around the column or added as prestressed or

non-prestressed FRP sheets or plates to the exposed surface of the slab. The first

method‟s disadvantage is that it requires drilling through the thickness of the slab to

allow post-fixing of the FRP, and is hence an intrusive procedure with associated risks

such as rebar strikes, etc., as clearly shown in 2.7.1 later. In contrast, in the second

method, the slab-column is strengthened in flexure and causes an increase in the shear

strength indirectly to varying degrees, as clearly shown in 2.7.2, 2.7.3 later. Figure 2-17

shows the strengthening by FRP as shear reinforcement and as added flexural

reinforcement.

53

2.4.12 Size and shape of loaded area

Moe [18] in 1961 proposed a linear variation in shear strength with side dimensions of

the column based on experimental results when the side length of a loaded area was

between 0.75d and 3d, where d is the slab thickness. Regan [43] in 1986 tried to explain

the effect of column size on punching shear by testing five slabs where the loaded area

is the only significant variable. He used circular columns with diameters of 54, 110, 150

and 170 mm in addition to a square column with dimensions of 102 × l02 mm square.

The results proved the linear relationship for the loaded dimension provided that it

exceeds 0.75d. When the loading area is small (side dimension less than about 0.75d),

the slab failed in local crushing and therefore the strength of the slab is less than that

predicted by the linear relationship.

Otherwise, if the loading side dimension is greater than 0.75d, the length of the critical

section will increase as the loading area increases, resulting in an increase in the shear

strength of the slab. Therefore, it is recommended to use slab drop panels or column

capitals instead of increasing the column size to increase the punching shear resistance.

Most of the available test data in the literature indicate that slabs over circular columns

are stronger than those over square or rectangular columns with the same perimeter

(a) (b)

Figure 2-17 Strengthening of slab-column connection (a) FRP as shear reinforcement

[54] (b) added flexural reinforcement [55]

54

[19]. This improvement in shear strength is related to the absence of stress

concentrations at the corners of the square or rectangular columns.

Hawkins et al. [56] in 1971 tested nine slabs in which the perimeter length was held

constant but the aspect ratio was varied. They found that increasing the aspect ratio

decreases the shear strength of a slab-column connection because the behaviour of the

slab transforms from two-way bending to one-way bending. Therefore, the beam action

shear tends to develop at the long faces of the column. This also reflects the tendency

for the shear force to be concentrated at the end of a wide column, as observed in the

experiment as shown in Figure 2-18. They also concluded that, when the aspect ratio for

a rectangular column is greater than two, the strength can be lower than that for a square

column.

Figure 2-18 Concrete strain on column sides of aspect ratio=3 [44]

2.5 Fibre reinforcing polymer (FRP)

The concept of FRP can be traced back to 5000 BC, where Mesopotamians used straw

to reinforce mud bricks [57]. The first use of actual FRP was in the early 1950s in

aerospace engineering. Later, the use of FRP composites increased, especially in

strengthening existing reinforced concrete structures. This increase in uptake was due to

the attractive properties of the FRP composites, like their high strength-to-weight ratio,

low thermal conductivity and corrosion resistance, and the ability of the materials and

the geometry to be tailored to satisfy both the strength and the stiffness for the intended

application. Composite materials consist of two or more materials that are used to

generate the required properties of the composite which cannot be obtained with any of

the constituents alone [58]. The reinforcement is stiffer and stronger than the matrix and

55

it usually takes up to 70% of the compound volume. Thus, the strength and the stiffness

of a composite come from the strength and stiffness of the fibres. FRP composites are

made by embedding a special type of fibres in a specific resin matrix, which is used to

bind fibres together. FRP composites differ from any other construction materials due to

their anisotropy. Therefore, FRP composite properties change with the direction of the

fibres; primarily, strength and stiffness vary with the fibre direction. Figure 2-19 shows

the fibre orientations in a composites layer.

Figure 2-19 Fibre orientations in a composites layer [59]

External strengthening by FRP composites can be classified based on the type of the

composites used: strengthening by plates and strengthening by sheets. Strengthening by

plates is more desirable than sheets, albeit sheets may be used in some specific cases.

The reasons behind this desirability are that the number of fibres in plates is greater than

in sheets of the same cross-section, which can give the former more strength than the

latter. On the other hand, the sheets‟ flexibility makes handling and installation more

difficult than when using plates.

2.5.1 Fibres

The major role of the fibres is to carry the load along their longitudinal direction. So,

the strength and stiffness of the composite are dependent on fibres ability to carry the

load. The most common types of fibres used in composite constructions are Carbon,

Glass, Aramid and Steel fibres. Unlike steel reinforcing fibres, polymer fibre types

exhibit linear elastic stress-strain behaviour up to failure. They fail in a brittle rupture

under tension loads [58]. Depending on the fibres used, FRP composites can be

classified as shown in Table 2-1:

56

Table 2-1 Mechanical properties of some fibres [8]

Fibre type Elastic modulus

[GPa]

Tensile strength

[MPa]

Failure strain

[%]

Carbon (HS/S) 160-250 1400-4930 0.8-1.9

Carbon (IM) 276-317 2300-7100 0.8-2.2

E glass 69-72 2400-3800 4.5-4.9

S-2 glass 86-90 4600-4800 5.4-5.8

Aramid (Kevlar 29) 83 2500 -

Aramid (Kevlar 49) 131 3600-4100 2.8

2.5.1.1 Carbon Fibre Reinforced Polymer (CFRP)

Carbon fibres are made from polyacrylonitrile (PAN), pitch, or rayon fibre precursors

[60]. In general, there are two main types of carbon fibres: high modulus and high

strength [60]. The difference between these types is a result of the differences in fibre

microstructure. High-modulus fibres have a high modulus of about 970 GPa with lower

strength of about 690 MPa, while high-strength fibres have a modulus of about140 GPa

and strength of about 2070 MPa. Carbon fibres are highly resistant to alkali or acid

attack [58], although galvanic corrosion may occur if the fibres are in contact with

metals. Carbon fibres are about five to 10 times more expensive than other types of

fibres.

2.5.1.2 Glass Fibre Reinforced Polymer (GRP)

Glass fibres have been used in many civil engineering applications because of their low

cost and high specific strength [60]. The modulus of elasticity of glass fibres is 70-85

GPa, while the ultimate tensile strength is 1850-4200 MPa. Glass fibres are good at

resisting impact loads, and they exhibit very good electrical and thermal insulation

properties.

2.5.1.3 Aramid Fibre Reinforced Polymer (AFRP)

Aramid fibres have good mechanical properties and a low density with a high resistance

to impact loads [60]. Aramid fibres have been classified as having high tensile strength,

a medium modulus, and a very low density as compared with glass and carbon fibres.

They have a tensile strength higher than that of glass fibres, and the modulus is about

57

50% higher than that of glass. They also have the ability to insulate both electricity and

heat [60].

2.5.1.4 Steel Fibre Reinforced polymer (SFRP)

In addition to the previous types of fibre composite materials, an additional type has

emerged that uses high-strength steel fibres and is commonly known as steel-FRP

(SFRP). The steel fibres have a tensile strength of about 2400 to 3100 MPa and an

elastic modulus of about 200 GPa. Nowadays, SFRP is used to strengthen concrete

structures in a similar manner to other externally bonded FRP materials because it

demonstrates a linear elastic stress-strain relationship that is similar to carbon and glass

fibres [60].

2.5.2 Polymer matrix

The main role of the matrix in a composite material is to transfer stresses between

fibres, protect the fibres from environmental factors, maintain their alignment and

protect their surfaces from mechanical abrasion [61]. In general, there are two types of

matrix: organic and inorganic. Organic matrices, also known as resins or polymers, are

the most commonly used nowadays. Polymers can be divided into two types according

to the effect of heat on their properties: thermoplastic and thermosetting. Thermoplastics

are softened and melted with heating and finally hardened again with cooling.

Thermosets are formed from a chemical reaction between resin and hardener when they

are mixed together and then undergo a non-reversible chemical reaction to form a hard,

infusible product [8]. In general, the three most common organic resins currently used

are polyester, vinyl ester and epoxy. In spite of the higher cost of epoxy compared to the

other types, it is usually the favoured one. Table 2-2 gives the material properties of the

three types of matrix.

Table 2-2 Typical mechanical properties of common resins [8]

Matrix/resin

Elastic

Elastic modulus

(GPa)

Tensile strength

(MPa)

Failure Strain

(%)

Polyester 3.1-4.6 50-75 1.0-6.5

Vinylester 3.1-3.3 70-81 3.0-8.0

Epoxy 2.6-3.8 60-85 1.5-8.0

58

2.6 FRP composite properties

FRP composites can be considered as anisotropic materials in which material properties

are different in each material direction. However, FRP materials with fibres totally

directed in one direction are considered one directional or unidirectional material.

When tensile stresses are applied parallel to the fibre direction, the strain in the

matrix will be the same as that in the fibres [62], and then the corresponding stresses

can be given as in equation (2-3):

( )

In which the subscripts f and m represent the fibres and matrix respectively and

refers to the strain in the direction of fibres. When , which is usually the

normal case, the fibres bear the major part of the applied load P.

For a composite material with a total cross-sectional area of A, the average force in the

section can be given by equation (2-4):

( )

However, the total force in the section comes from the forces from both the fibres and

the matrix, so equation (2-4) can be rewritten as in equation (2-5):

( )

But the forces in the fibre and matrix are:

( )

Thus, equation (2-4) can be rewritten as in equation (2-7):

( )

59

Where , are the cross-sectional areas of the fibres and the matrix respectively.

Substituting equation (2-4) and the relation, the final equation of the longitudinal

Young‟s modulus of the composite can be concluded as in equation (2-8):

( )

However,

represent the volume fractions of the fibres and matrix

respectively.

By using the same way, the perpendicular Young‟s modulus of the composites can be

found . In this case, the transverse applied load is the same in both the fibres and the

matrix, so the assumptions start with . The corresponding strains are:

and

( )

Thus the strain can be given as in equation (2-10):

( )

And by substituting (2-9) it can be concluded:

( )

By substituting the final equation of the perpendicular Young‟s modulus can

be concluded as in equation (2-12):

( )

( )

The major Poisson‟s ratio can be determined based on equation (2-13):

( )

60

In which are the Poisson‟s ratio for both the fibres and the matrix respectively.

And thus the in-plane shear modulus can be described as in equation (2-14):

( )

Where are the shear moduli of the fibres and epoxy respectively.

2.7 Modes of failure of slab-column connections with FRP reinforcement

When externally bonded FRP reinforcement is added to a slab-column connection,

different failure modes from ductile to brittle can be developed, as explained earlier in

2.1. These failure types have been investigated by many researchers in relation to

interior slab-column connections and it has been found that they can be affected by the

slab reinforcement ratio [63, 64 and 65]. The research has classified these failure modes

into two main modes, which are full composite action failure modes and loss of

composite action failure modes [12].

2.7.1 Full composite action failure modes

In this failure mode, there are another three sub-categories:

Mode 1: Steel yielding followed by concrete crushing (flexural punching failure). This

failure mode may occur with a yield of the steel reinforcement locally around the

column in the tension zone followed by crushing of the concrete in the compression

zone without any damage in the FRP reinforcement [66].

Mode 2: Steel yielding followed by FRP rupture (pure flexural failure). This failure

mode may occur in slabs with low reinforcement ratios of both steel and FRP and it is

better that it occurs before compressive concrete failures [67]. Typically, this mode of

failure is the most desirable failure mode because it causes large deflection prior to

failure as it gives an indication of the status of the structure before failure, which may

prevent or reduce the loss of human life.

Mode 3: Concrete compressive crushing (pure punching shear failure). This failure

mode may occur in slabs reinforced with a high reinforcement ratio [53]. It occurs by

concrete crushing in the compression zone, while both the reinforcement steel and the

61

FRP are intact. This is attributed to the large biaxial compression resulting from

bending effects plus the vertically applied load. This failure mode is a brittle one and

takes place with a small deflection. Finally, the slab fails in a local area around the

column.

Figure 2-20 Full composite action failure modes [68]

2.7.2 Loss of composite action failure modes

The bond between the FRP and the concrete substrate is the main parameter affecting

failure modes [69]. These failure modes are more related to beams than to slabs. Thus,

their names are related to beams. The possible failure modes are as follows:

2.7.2.1 Debonding of the FRP plate

The most recognised failure mode is the FRP plate debonding locally or completely

from the concrete substrate [69]. In such a case, the external FRP plates will not

continue to contribute to the slab strength, which may result in a brittle failure,

especially when no stress distribution from the FRP to the interior steel reinforcement

occurs. Localised debonding means a local failure in the bond between the FRP and the

concrete substrate. Thus, the strength of the overall structure will not be greatly

affected.

The failure in the bond between the FRP and the concrete substrate may take place at

different interfaces. Figure 2-21 shows the different bond failures as named:

62

1 Debonding in the concrete near the surface or along a weakened layer, e.g. along

the line of embedded steel reinforcement.

2 Debonding at the interface between concrete and adhesive or adhesive and FRP

(adhesion failure).

3 Debonding in the adhesive (cohesion failure).

4 Debonding inside the FRP (interlaminar shear failure).

Figure 2-21 Debonding failure modes [12]

The most common debonding failure is the debonding in the concrete near the surface

or along a weakened layer since the shear and tensile strength of the adhesive is usually

higher than the tensile strength of the concrete [70]. Furthermore, the new development

in the strengthening system tries to reduce the probability of other debonding failures,

by depending on making structural adhesives that can work even in a harsh environment

and make them more compatible with the resin used in FRP manufacturing. Thus,

failure is more likely to occur in a few millimetres through the concrete thickness [70].

2.7.2.2 Peeling-off failure mode

The last failure mode is when the FRP is peeled off from the concrete substrate in which

the full composite action is lost [71]. This failure type starts at the end of the FRP plate

63

and ends up with debonding propagation inwards. It happens due to stress concentration

at the plate end, which is usually shear stress, with a few normal stresses arising due to

the non-zero bending stiffness of the laminate. When the crack occurs in the concrete

near the plate end, it may propagate to the steel reinforcement and extend horizontally,

which may cause separation of the concrete cover along the plane of the tensile

reinforcement [71]. Many sub-categories of this failure type are presented as follows

based on the starting point of the debonding process:

Peeling-off in un-cracked anchorage zone. The FRP may peel-off in the

anchorage zone as a result of bond shear fracture through the concrete substrate.

Peeling-off caused by unevenness of the concrete surface. Due to the

imperfections during the surface preparation process, a localised debonding of

the FRP may take place.

Flexural crack peeling-off, sometimes known as intermediate crack (IC) induced

interfacial debonding. The FRP peeling-off may also occur at the tip of a

flexural crack due to the horizontal propagation of such a crack.

Shear crack peeling-off, sometimes known as critical diagonal crack (CDC)

induced interfacial debonding.

2.8 Strengthening of slab-column connections against punching shear by using

FRP reinforcement

FRP has been used to enhance the mechanical properties of concrete slab-column

connections by providing post-cracking tensile resistance of concrete and controlling the

width of the inclined cracks.

In some cases, it is necessary to strengthen the slab-column connections because of

insufficient punching shear strength resulting from different reasons. Many

investigations have been conducted on strengthening the slab-column connections. All

have examined methods to delay or prevent punching shear failure. In this section, a

review of the common FRP strengthening techniques is presented.

2.8.1 Direct shear strengthening

FRP elements in various forms have been used as shear reinforcement by embedding

them vertically as shear studs through the thickness of the slab or as loops from top to

64

bottom surfaces through the slab thickness [72]. Holes are drilled vertically through the

slab thickness (by using PVC pipes put vertically before concrete casting in the specific

places), then FRP fabrics are woven through these holes to form shear reinforcement

around the column.

Sissakis and Sheikh [72, 73] in 2000 and 2007 were the first to apply this strengthening

method. They adopted an innovative approach for strengthening slab-column

connections with CFRP as shear reinforcement. The test was carried out by testing 32

specimens of dimensions 1500 ×1500 ×150 mm interior connections. These specimens

were divided into four series with different concrete compression strength. Each series

had several slab specimens cast with one of four hole configurations, as shown in Figure

2-22. An increase in the shear strength, ductility and energy dissipation capacity of the

slab-column connections was shown for the strengthened slabs. The shear strength

increase was over 80% and an enhancement in the ductility of over 700% was observed.

Figure 2-22 Shear reinforcement arrangements and assumed critical shear section

perimeters of tested slab specimens with three peripheral lines of shear reinforcement

[73]

Binici and Bayrak [74, 75 and 76] in 2003 and 2005 were also pioneers in applying this

novel technique to increase the punching shear capacity, the displacement ductility and

the post-punching resistance of slab-column connections. They applied a strengthening

technique based on using CFRP strips vertically around the column to strengthen

interior slab-column connections. Fifteen specimens were tested under concentric and

65

eccentric monotonic loading, but by using the same tensile reinforcement ratio of

1.76%. The strengthened specimens were strengthened using CFRP strips embedded

vertically by two patterns (A and B patterns: the A specimens had shear reinforcement

legs arranged in double cross patterns around the loading area, whilst the B specimens

had shear reinforcement placed in a snowflake arrangement extending from the centre

and corner of the column side) in previous holes in the slabs and loaded up to failure, as

shown in Figure 2-23.

Figure 2-23 Strengthening patterns and details [75]

66

Additional CFRP plates were bonded to the bottom face of the slab and put in a

direction perpendicular to the flexural reinforcement so as not to provide any strength to

the slabs in flexure and to work as holes sealer. The diagonal strips in the strengthened

slabs were used to prevent failure to occur inside the strengthened area.

It was concluded that the failure mode was pure punching, which could possibly be

shifted to combined flexure and punching. This is due to the use of CFRP as closed

stirrups which increased the strength and ductility of the specimen. CFRP loops were

anchored by overlapping them at the compressive zone of the slab, which did not cause

damage in the shear reinforcement region. It was also found that using CFRP as shear

reinforcement in two patterns (A and B) can increase the punching shear resistance

under monotonic transfer of shear and unbalanced moments by 60%, based on the

pattern and number of layers.

Erdogan et al. [77, 78] in 2007 and 2010 conducted an experimental investigation for

strengthening and enhancing interior slab-column connections against punching shear.

The specimens were strengthened with CFRP strips driven vertically into the slabs

around the column in different amounts and configurations. The strips were configured

orthogonally and circularly around the column, as shown in Figure 2-24. The final ends

of the CFRP dowels in some strengthened specimens were fanned and bonded to

additional CFRP strips patched onto the top and bottom slab surfaces. In the other

strengthened specimens, additional CFRP patches were bonded onto the compression

and tension faces of the strengthened specimens. The effect of the CFRP patches was

ignored because of their insufficient length.

It was concluded that the strengthening technique led to an enhancement in the vertical

load-carrying capacity of (33.4-133)% and the post-punching shear capacity of (135.5-

240)%.

67

Figure 2-24 Strengthened specimens with CFRP: (a) 24 CFRP dowels; (b) 32 CFRP

dowels; (c) 40 CFRP dowels; (d) 28 CFRP [78]

Similar to their previous work, Erdogan et al. [79] in 2013 adopted an experimental

programme to study the effect of CFRP strips in rehabilitating pre-damaged slab-

column connections. They studied five (2/3) scale slab-column connections of

dimensions 2130 × 2130 × 150 mm with a central column stub of 300 × 300 mm. These

slabs were divided into two series depending on the concrete compression strength (low

and normal) with flexural reinforcement ratio of 1.86% to achieve punching shear

failure only. Two control specimens were kept un-strengthened and loaded for failure.

After failure, these specimens with two additional specimens were rehabilitated and

strengthened with CFRP strips by the same configuration proposed by Binici and

Bayrak (2003). These CFRP strips were driven through drilled holes in the slabs made

after concrete casting to simulate rehabilitation and strengthening of slab-column

connections in the field. The last specimen was loaded up to 75% of the control

specimen ultimate load then rehabilitated using CFRP strips.

It was concluded that using CFRP externally to rehabilitate pre-damaged slabs could

restore punching shear capacity of fully damaged slabs to levels above their undamaged

68

conditions with either low or normal concrete strength. It was also noticed that using

CFRP strips enhanced the punching shear capacity of the strengthened connections by

about 74% over the control specimen and decreased the displacement by up to 2.5 times

that at an ultimate load of the control specimen. It was also concluded that using CFRP

strips increased the post-punching capacity up to 90%.

Meisami et al. [80] in 2013 conducted an experimental programme to examine the

applicability of FRP rods in strengthening against punching shear. The programme

consisted of testing six reinforced concrete slabs identical in length and width but with

different depths up to failure under a central monotonic load. The slabs were 1200 ×

1200 mm with 85,105 mm thicknesses and flexural reinforcement ratios of 1.1% and

2.2%. Two of these specimens were control specimens while three of the others were

strengthened by FRP rods embedded vertically in holes through the slabs by two

configurations (eight and 24 rods), as shown in Figure 2-25.

Figure 2-25 FRP rods and screw arrangements on the slab around the column (eight and

24 strengthener positions around the column for type A and B, respectively) [80]

During the initial stage of loading, cracks propagated in orthogonal directions close to

the applied load. After the load was increased, cracks propagated from slab centre to the

corners and shear failure started to become evident.

69

It was concluded that, for the FRP strengthened slabs, punching shear capacity was

increased by 17% for the eight rods and 67% for the 24 rods, and the failure mode was

altered from punching to a flexure mode.

Meisami et al. [54] again in 2015 conducted an experimental study building on their

previous study but using FRP fans. The arrangement and number of FRP fans were

similar to their previous work in addition to a new strengthening type, as shown in

Figure 2-26.

Figure 2-26 FRP fan arrangements on the slab around the loading plate (eight, 16 and

24 strengthener positions for types A, B and C, respectively) [54]

In their study, they found that the punching shear capacity increased with the increase in

the number of fans used to strengthen the slab-column connection. They also found that

increasing the fan numbers can shift the failure mode from shear to flexural shear or

even pure flexure depending on the number of fans used.

Gouda and El-Salakawy [81] in 2016 tested six full-scale square interior slab-column

connections with 2800 mm side length and 200 mm thickness in addition to a 300 mm

70

square column stub extended for 1000 mm above and below the slab. These slabs were

tested up to failure by vertical shear forces and unbalanced moments. The main flexural

reinforcement of the whole slabs was No. 16 GRP bars on the tension side and there

was no reinforcement provided on the compression side. Many different parameters

were studied in the test, like the moment-to-shear ratio, GRP double-headed shear studs

ratio and the type of GRP bar surface texture. It was noticed that increasing the

moment-to-shear ratio reduced the ultimate punching shear capacity and increased the

deflections. In addition, using GRP shear studs increased the punching shear capacity

but without changing the failure mode.

El-Gendy and El-Salakawy [82] again tested six full-scale GRP reinforced concrete

slab-column edge connections. These slabs were divided into two groups in order to

show the effect of a new type of GRP shear reinforcement in the first group and the

effect of the moment-to-shear ratio in the second group. The slab-column connections

consisted of 2800 × 1550 × 200 mm with a 300 mm square column extending above and

below the slab. All the slabs were reinforced by GRP reinforcement in the flexure. GRP

bars with headed ends were used to strengthen the slab-column connection against

punching shear. It was noticed that all the slabs without shear reinforcement failed by

punching shear failure with no signs of flexural failure. However, for the strengthened

slabs, even though the failure mode was not changed, the total ultimate punching shear

capacity increased by about 46% with an increase in the deflection of about 142%,

giving considerable ample warning before failure. It was also noticed that increasing the

moment-to-shear ratio decreased both the punching shear capacity and deflection.

Based on the previous studies conducted by Hawkins [83] and Broms [84], it can be

seen that the direct method is more effective in strengthening the existing slab-column

connections than the other strengthening methods like increasing the column size,

increasing the slab thickness and adding column capitals or drop panels. It was found

that this method can increase the slab strength by 17% to 133% depending on the

number of vertical CFRP rods or fans used in strengthening. It was also noticed that

using vertical rods can affect the post-punching capacity by increasing it by between

90% and 240% by adding more loads to the failed structure. In addition, this method is

effective in strengthening slab-column connections not only under gravity shear but also

under un-strengthened moments. This method is able to increase the punching shear

71

strength and the ductility. Furthermore, it can change the failure mode from punching to

flexural punching or pure flexure, which is the most desired type of failure in structures.

However, in spite of the previous important characteristics of this method, there are

some drawbacks related to the drilling of large numbers of closely spaced holes through

the slab thickness, as the drill may strike the internal steel reinforcement, especially if

there is not enough information regarding their distribution in the slab. Table 2-3 shows

the summary of all the existing work on this method.

72

Table 2-3 Summary of existing experimental work on the direct strengthening method

Researcher Type of sample test Specimen dimensions

(mm)

Number of

samples Strengthening with FRP

% enhancement in

ultimate strength Failure mode

Sissakis and Sheikh

2000,2007 [72,73]

Interior slab-column

connections 1500×1500×150 32

CFRP laminates as shear

reinforcement 80 Punching shear failure

Binici and Bayrak

2003, 2005

[74,75,76]


connections 2133×2133×152 15

CFRP strips vertically around the

column 60

Punching (control) to flexural

punching (strengthened)

Erdogan 2007,

2010,2013 [77,78

and 79]


connections 2130×2130×150 5

Strips driven vertically through the

slab thickness, some fanned 33.4-133 Punching shear

Meisami et al. 2013

[80]


connections 1200×1200×(85,105) 6 FRP rods through the slab thickness

17 for 8 rods

67 for 24 rods

Punching (control) to flexure

(strengthened)

Meisami et al.

2015[54]


connections 1200×1200×(85,105) 6 Fanned FRP through the thickness 29.7 -72.5

Punching (control) to flexural

punching or flexural (strengthened)

Gouda and El-

Salakawy 2016 [81]


connections 2800×2800×200 6 GRP double-headed shear studs 18-23 Punching shear

El-Gendy and El-

Salakawy 2016 [82]

Slab-column edge

connection 2800 × 1550 × 200 6 GRP bars with headed ends 46 Punching shear

73

2.8.2 Indirect (flexural) shear strengthening by externally bonded FRP strips

Strengthening of slab-column connections with FRP sheets or plates has more

advantages than strengthening by steel plates. It does not need excessive labour and has

a minimal effect on section geometry. This has made researchers concentrate their

investigations on the benefits of FRP as an externally strengthening material. However,

most of the previous studies were conducted on an internal slab-column connection with

very few studies on the edge slab-column connection. Up to now, there has been no

study on the strengthening of slabs at corner columns.

The early studies on strengthening slab-column connections by using FRP were

conducted by Erki and Heffernan [85] in 1995 and Tan [86] in 1996. In their studies,

they strengthened slab-column connections by applying FRP reinforcement to the whole

tension surface of the slab. The difference between the slabs in the two studies was the

flexural reinforcement ratio and the type of the FRP used. In the first study, the control

slab was designed to fail in flexure, while in the latter it was punching shear.

Nevertheless, the increase in the ultimate punching shear capacity was 19% for slabs

reinforced by GRP and 84% for those with CFRP. In spite of that, Tan concluded that

this increase is due to bonding bidirectional FRP reinforcement rather than

unidirectional. Unidirectional CFRP and GRP reinforcement did not exhibit a

significant increase in punching shear resistance. This is because of their weak strength

in the direction perpendicular to the fibre direction. Later studies by Wang and Tan [87]

in 2001, and Chen and Li [88, 89] in 2000 and 2005 proved that the presence of GRP

layers increased the punching shear capacity, especially for slabs of low concrete

compression strength and flexural reinforcement ratio. In all studies, the concrete

cracking cannot be fully observed due to the existence of the FRP reinforcement on the

whole surface of the slab. Furthermore, there is no debonding failure between the FRP

and the concrete substrate, except at the area around the column stub.

Rather than strengthening the slab-column connection by using FRP on the full tension

surface of the slab, further studies by Harajli and Soudki [55] in 2003, Van Zowl and

Soudki [90] in 2003, Sharaf et al. [91] in 2006 and Esfahani et al. [64] in 2009 were

conducted by using CFRP plates distributed around the column in interior slab-column

connections. In order to investigate the effectiveness of such strengthening, the slab

thickness, steel reinforcement ratio and the CFRP amount, configuration and size were

74

considered the main parameters in the studies. Figure 2-27 shows the summary for the

tested slabs in [55].

Figure 2-27 Dimensions and details of reinforcement of specimens [55]

Harajli and Soudki and Van Zowl and Soudki found that using CFRP changed the

failure mode and increased the punching shear capacity by between 17% and 45%.

However, Sharaf et al. found that this increase was between (6-16)% because the

control slab failed by punching shear and the strengthening had no effect on the failure

mode. In addition, the configuration of CFRP laminates orthogonally or skewed, as

shown in Figure 2-28, made no difference to the strength added to the control specimen.

However, Esfahani et al. found that strengthening by CFRP sheets was more effective

for slabs with higher-strength concrete compared to those with lower strength. In

addition, increasing the size of the CFRP sheets can increase the punching shear

capacity of the slabs. They also noticed that the punching shear capacity was enhanced

especially for high compression strength slabs and low flexural reinforcement ratios.

75

Figure 2-28 CFRP strengthened specimens [91]

76

In contrast to previous studies, Soudki et al. [92] in 2012 extended their previous work

to provide a greater understanding of the number of CFRP strips and their location to

the column. In this study, they noticed that the location of the CFRP had an effect on the

results. They also found that the slabs reinforced with strips placed offset to the column

produced a relatively higher increase in punching capacity. It was also concluded that

the strengthened specimens experienced higher punching loads than the control

specimen, especially with skewed and offset CFRP strips, which had punching shear

capacity of 29.1% greater than that of the control specimen. It was also noticed that

increasing the number of CFRP strips does not increase the punching capacity of the

slabs.

Figure 2-29 CFRP repair scheme [92]

From all previous studies, it can be concluded that using FRP sheets in the critical

section of the slab-column connection can delay the formation and growth of the tensile

flexural and shear cracks. This can be achieved by increasing the flexural strength of the

slab in the vicinity of the column, which consequently improves the two-way shear

resistance of the connection. Furthermore, it can produce cracks with a smaller width

than those in un-strengthened slabs. This is attributed to the ability of the CFRP strips to

77

arrest crack propagation. The crack control is optimal when the fibres are oriented

perpendicular to the crack.

El-Salakawy et al. [6] in 2004 tested seven full-scale reinforced concrete edge slab-

column connections strengthened by FRP sheets against punching shear. Three of these

slabs had an opening in the column vicinity, while the others did not. They used either

glass or carbon FRP sheets in addition to shear bolts to strengthen the slabs. They found

that using FRP did not change the distance at which the shear cracks propagated away

from the face of the column as in the control slab. They also concluded that the presence

of FRP delayed the opening of flexural cracks, added flexural stiffness to the slabs and

increased the two-way shear resistance between (2-25)%. In addition, the presence of

FRP sheets and steel bolts increased the slab punching shear capacity.

Further studies were conducted by Ebead and Marzouk [15] in 2004, Harajli et al. [93]

in 2006 and Urban and Tarka [94] in 2010 to study the effect of combining shear bolts

with CFRP strips in strengthening interior slab-column connections. In [15] the

reinforcement ratio of all slabs was 1.0% to ensure pure punching failure mode, while in

[93] the reinforcement ratio was one of other studied parameters, like the slab thickness

and bolt configuration. The increase in the ultimate punching shear capacity in [15] was

9% because they tested the control specimen until failure and then half of that failure

load was applied to the strengthened specimens before strengthening as an initial load.

On the contrary, Harajli et al. and Urban and Tarka found that using shear bolts with

FRP sheets increased the punching shear capacity by (10-77)% by altering the failure

mode from punching to a flexure, which led to an increase in the ductility.

Using steel bolts alone or a combination of FRP sheets and steel bolts pushed the

punching shear plane further outward in comparison with the control specimens. In

contrast to the strengthening slabs, using FRP reinforcement has no effect on the

position of the shear failure plane, as stated previously by El-Salakawy et al. [6].

78

Michel et al. [95] in 2007 conducted an experimental study to evaluate the punching

load capacity of concrete slabs strengthened by CFRP. The study started by testing four

concrete slabs of dimensions of 1200 × 1200 × 100 mm with steel reinforcement of a

ratio of 0.636% and externally strengthened by CFRP sheets. One of these slabs was

kept un-strengthened, while the others were strengthened. The third slab was pre-

cracked before being strengthened by CFRP sheets in order to evaluate the effect of

externally bonded CFRP reinforcement on the slab behaviour, while the second and the

fourth were strengthened directly with cross-ply CFRP layers. They concluded that the

mid-span deflections of the second and fourth slabs were reduced by 35% and 45%

respectively. They also noticed that the cracking load was increased by 40% for the

second slab and 48% for the fourth slab, while for the third slab there was no significant

increase.

Farghaly and Ueda [96, 7] in 2009 and 2011 evaluated experimentally and analytically

the strengthening of interior slab-column connections strengthened by CFRP. In their

work, they found that the angle at which the shear cracks propagate away from the

column was not influenced by the area of the CFRP sheets.

Based on their numerical study, they derived an analytical model dependent on the

similarity in the slopes of the failure surface above and under the neutral axis. They

stated that the punching shear strength is calculated by integrating the shear stresses

around the punching crack surface. They calculated numerically the values of the

punching shear strength for the two parts above and under the neutral axis. They

concluded that the shear strength in the compression zone is the main contributor to the

punching shear strength and the shear strength in the tension side can be neglected.

Based on the previous conclusions, they derived their analytical model and validated it

in their experimental work as follows:

√ [ ( ) ] ( )

Where k is the triaxial compressive stress that exists near the loading plate= , is

the tensile strength of concrete, is the compressive strength of concrete, is the

79

failure surface area above the neutral axis, and are the modulus of elasticity of

steel and FRP respectively, and is a combined factor defined as:

[ ( ) ]√ ( )

For their experimental work, it was noticed that the punching shear capacity was

increased between 20% and 40% more than the control slab. It was also observed that

increasing sheet width led to a lower slip value at the CFRP-Concrete interface due to

the uniform stresses transferred between the CFRP and the concrete.

Tan [97] in 2012 and Durucan and Anil [98] in 2015 adopted an experimental

programme to investigate the use of an FRP system in restoring the ultimate strength of

reinforced concrete flat slabs having openings of different sizes and locations. In [97],

the openings were set to 500 × 500 mm while in [98] they were set to square openings

of 300 or 500 mm. In both studies, two locations along the diagonal and the mid-width

of the slab were studied, as shown in Figure 2-30. It was concluded that the ultimate

strength of the slabs having opening was restored to that of the solid slab when the

opening was placed along the diagonal at twice the effective depth from the column

stub. This increase was due to the high elastic modulus of the CFRP strips, which

contributed to the slab‟s initial stiffness. It was also noticed that the strength was about

85% of the solid slab when the opening was diagonally adjacent to the column stub or

when it was located along the mid-width at twice the effective depth from the column

stub. However, the strength restoration was about 60% only for a slab with an opening

located adjacent to the column stub at mid-width.

80

Figure 2-30 Layout of openings and FRP reinforcement [97]

Bonding FRP reinforcement to the tension zone of a concrete slab-column connection

may enhance its flexural strength, and by return, its shear strength will be enhanced up

to a certain limit that the flexural shear strength of the slab is less than its ultimate shear

strength. After that limit, increasing the area of FRP reinforcement will not greatly

increase the shear strength of the slab or the stiffness, but a brittle punching is expected

unless shear reinforcement is used. This has also been confirmed by Chen and Li [89]. It

is also concluded that using FRP composites to strengthening slab-column connections

increased the punching shear strength by between 6% and 84%, depending on the

81

amount of FRP and configuration in addition to their offset from the column face. The

effect of compressive strength showed that punching shear strength increased,

especially in low compressive strength slabs. It is also noticed that using more layers of

FRP can lead to a premature debonding failure due to the increased horizontal shear

between the concrete and the FRP composites.

Finally, increasing the FRP width may cause a lower slip between the FRP and the

concrete face because of the uniform stress distribution between the FRP and the

concrete surface. Table 2-4 provides a summary of all the mentioned studies that use

this method.

82

Table 2-4 Summary of existing experimental work on indirect strengthening method


(mm)

Number of


% enhancement in


Erki and Heffernan

1995 [85]


connections 1000×1000×50 6 Externally bonded GRP and FRP

19 for GRP

84 for CFRP

Flexure (control) to punching

(strengthened)

Tan 1996 [86] Interior slab-column


Carbon plates, Carbon sheets, Glass

fabrics 40-190 Punching shear

Chen 2000, 2005

[88,89]


connections 1000×1000×100 18 Externally bonded GRP 17-95


(strengthened)

Wang and Tan 2001

[87]


connections 1750×1750×120 4 Externally bonded CFRP sheets 0-1 Punching shear

Harajli and Soudki

2003,2006 [55,93]


connections 670×670×(75 or 55) 18

Externally bonded CFRP sheets, shear

bolts and FRP sheets

17-45 for only sheets

32-77 for bolts and

sheets


(strengthened by sheets)

Punching (control) to a flexure

(strengthened by bolts and sheets)

Van Zowl and

Soudki 2003 [90]


connections 1220×1220×100 6 Externally bonded CFRP sheets 29 Punching shear

El-Salakawy et al

2004 [6]

Edge slab-column


Externally bonded GRP or CFRP

sheets

2-6 for one FRP layer

23 for two FRP layers Punching shear

Ebead and Marzouk

2004 [15]



CFRP, GRP strips of L shape in

addition to steel bolts 9 Punching shear

Sharaf et al. 2006

[91]

Interior slab column

connections 2000×2000×150 5 Various CFRP configurations 6-16 Punching shear

Michel et al. 2007

[95]


connections 1200 × 1200 × 100 4 Externally bonded CFRP sheets 15-30 Punching shear

Esfahani et al. 2009

[64]


connections 1000 × 1000 × 100 15 Externally bonded CFRP sheets 3-30


(strengthened)

Urban and Tarka

2010 [94]



CFRP strips with additional shear

bolts

10 for CFRP

36 for additional bolts Punching shear

83

Farghaly and Ueda

2009,2011 [96,7]


connections 1600 × 1600 × 120 3 Externally bonded CFRP sheets 40 Punching shear

Soudki et al. 2012

[92]


connections 1220 × 1220 × 100 6 Externally bonded CFRP strips 29


(strengthened)

Tan 2012 [97]


connections with

openings

2200 × 2200 × 100 5 Externally bonded CFRP strips (60-100) of the control

slab Punching shear

Durucan and Anil

2015 [98]


connections 2000×2000×120 8 Four orthogonal CFRP sheets 55 Punching shear

84

2.8.3 Indirect shear strengthening by prestressed FRP composites

Wight et al. [99] in 2003 were the pioneers in studying the effect of prestressed CFRP

plates in strengthening slab-column connections against punching shear. Later studies

by Kim et al. [100] in 2009 and Abdullah et al. [101] in 2013 conducted experimental

work to investigate the effectiveness of prestressed CFRP plates on the overall

behaviour of flat slabs. In all studies, one slab was kept un-strengthened as a control

slab, while others were strengthened by non-prestressed or prestressed CFRP plates.

Different prestressing forces are applied in each study. Wight et al. applied 16% of the

ultimate tensile strength of the CFRP plate, while Kim et al. applied 16% and Abdullah

et al. applied (7,15 and 30)% of the ultimate tensile strength of the CFRP plate.

Wight et al. and Kim et al. concluded that the punching shear capacity and the severity

of the punching damage depend on the presence and configuration of the external FRP

reinforcement. They also noticed that the punching shear resistance was increased by

between (25-35)% when the specimen had prestressed CFRP plates. This was because

the bonded CFRP sheets delayed crack formation and progression by preventing

concrete movement on either side of the cracks. Furthermore, they noticed that the

effect of the prestressing improves not only the strength but also the rigidity of the

structure, decreasing the internal steel strains and changing the cracking pattern.

However, Abdullah et al. concluded that using prestressed CFRP strips improved the

deflection and cracking but did not enhance the ultimate behaviour as much as non-

prestressed CFRP.

Koppitz et al. [102] in 2014 adopted a new mechanical anchoring system to study the

effect of prestressing CFRP strips against punching shear. The new anchoring system

consisted of a steel frame located on the compression side of the slab to anchor the

CFRP strips extended from the tension side, as shown in Figure 2-31.

Three full-scale slab-column connections were tested using the new anchoring system.

The straps were added after casting and drilling the concrete slabs at an angle of 34˚.

They concluded that using prestressed CFRP strips eliminated the residual slab rotations

and closed the residual cracks, and thus increased the punching shear resistance.

85

Figure 2-31 Adhesively-bonded anchors (a) sectional, (b) a bottom view: Anchors

connected by steel frame, (c) sectional, (d) bottom view, (e) top view with crossed

CFRP straps above central column, (f) detail view of end-anchor with force washer

between anchor plate and bolt head [102]

Using prestressed FRP composites can enhance the cracking capability of the section by

approximately 25% and thus increase the punching shear strength by about 35%. This

increase is accompanied by an increase in the structural rigidity and decrease in the

internal steel reinforcement strains by eliminating the residual slab rotations.

86

Table 2-5 Summary of the existing experimental work on strengthening by prestressed FRP


(mm)

Number of


% enhancement in


Wight et al. 2003

[99]


connections 3000 × 3000 × 90 4

Prestressed or non-prestressed CFRP

plates 35 Punching shear

Kim et al. 2009

[100]


connections 2360 × 2360 × 150 4

Prestressed or non-prestressed CFRP

plates 20 Punching shear

Abdullah et al. 2013

[101]



Non-prestressed and prestressed

CFRP plates

42 for non-prestressed

8 for prestressed

flexure (control) to punching

(strengthened)

Koppitz et al.

2014[102]


connections

3200×3200×(260,180,

320) 3 prestressed CFRP plates 67-114 Punching shear

87

2.9 Opening in slab-column connections

One of the most common reasons for strengthening a slab is due to the introduction of

openings post-construction. During the service life of reinforced concrete buildings,

openings are often added in the vicinity of the columns [103]. These openings are

necessary for the installation of stairs, elevators, ducts, pipes and the like.

The effects of openings on the flat slab to the column system have been studied by

several researchers [98]. They found that openings not only reduce the slab-to-column

zone strength but may also alter the failure mode from a ductile to a brittle one. In such

a situation the structural performance of the slab-column connections depends on the

shape, size and location of the opening with respect to the applied load. In general it is

not easy to accurately evaluate these influences, but empirical methods have been used

and it has been concluded that in slabs with small openings the design is usually based

on moments from the same analysis as solid slabs, and the reinforcement cut by the

opening should be rearranged along the opening edges and properly anchored [104].

These approaches should be applied if the opening is square and has a side length no

more than 0.2 times the shorter span of the slab. For larger openings, there are still no

detailed guidelines for the design of the required reinforcement [104].

Punching shear failure remains a key issue in reinforced concrete slabs with openings.

Presently, all the work regarding the behaviour of slab-column connections with

openings is concentrated on the punching shear failure in flat plates where the opening

is located either adjacent to or near the interior or edge column [105].

To date, there are no readily available investigations on the effect of the opening near

the corner column, and especially adjacent to the slab free edge. As stated by El-

Salakawy et al. [106], many factors affect the existence of the opening near the slab-

column conjunction. These factors are opening size, location and distance from a

supporting column. They concluded that an opening as large as the column size should

not be constructed in flat slabs. This study examines the effect of the opening adjacent

to the column with one side coincident with the column side and the other parallel to the

slab free edge, both in the strengthened and un-strengthened cases. In line with current

88

general recommendations, the investigated square opening size is set not to exceed 80%

of the column size [106].

2.10 Bond behaviour of FRP-Concrete interface

The bond between the FRP and the concrete is the main factor that affects the efficiency

of the external FRP reinforcement and the mechanical behaviour of the strengthened

reinforced concrete structures [107]. In various debonding tests, it has been found that

the stress state of the interface is similar to that in a pull test, as shown in Figure 2-32

[70]. This type of testing is not only used to find the ultimate shear stress (bond stress)

but also to find the local bond-slip behaviour of the interface.

It has been found by the existing pull tests that failure of the FRP-Concrete interface is

by cracking in the concrete layer adjacent to the adhesive layer instead of the FRP

debonding [70]. This can be attributed to the fact that the adhesive shear strength is

normally greater than the concrete tensile strength. In Figure 2-32, the dotted lines

identify a typical fracture plane in the debonding of FRP.

The following parameters govern the local bond-slip behaviour: (a) the concrete

strength fc', (b) the bond length L, (c) the FRP plate axial stiffness E, (d) the FRP-to-

Concrete width ratio, (e) the adhesive stiffness, and (f) the adhesive strength [70]. A

very important aspect of the behaviour of these bonded joints is the existence of the

effective length beyond which any increase in the bond length will not affect the bond

ultimate load [70]. There are many formulas used to find the value of the effective bond

length, all of which are based on the previous parameters.

89

Figure 2-32 Schematic diagram of a single pull test [70]

2.10.1 Bond-slip relationship

To understand the bond behaviour, it is necessary to characterise the local bond-slip

behaviour, which is the most important factor in describing the efficiency and the

performance of the interface between FRP and concrete [107]. A number of bond stress-

slip models have been proposed, as shown in Figure 2-33, but the model of Lu et al. is

so far the best-proposed model because it offers some useful advantages [107]. The

model was compared to 253 pull test results conducted previously and achieved the best

fit among the other models available in the literature. This model is divided into elastic

ascending and plastic descending parts. The maximum bond stress in the elastic part is

defined with the relative displacement (slip) corresponding to it. The end of the plastic

part, which corresponds to zero bond stress, has a relative displacement. A linear

ascending branch was adopted for the simplicity of data entry into the FE model. The

model is given as follows:

( )

(

) ( )

90

The maximum shear stress (MPa) is governed as stated previously by the concrete

tensile strength, (MPa), and the FRP width ratio, , and taken as follows:

( )

Where is taken as follows:

√ ⁄

⁄ ( )

Where , are the widths in mm of the FRP and concrete substrate respectively. The

slip depends on (MPa) and as well and can be taken as follows:

( )

The factor in equation (2-18) is related to the interfacial fracture energy (the energy

required to introduce a unit area of interfacial-bond crack), as follows:

( )

√ ( )

91

Figure 2-33 Comparison of bond-slip curves available in the literature; quoted from Ko

et al. [107]

2.10.2 Bond strength

From 1996 onwards, many theoretical models have been developed in order to predict

the strength of FRP-Concrete interface in strengthened concrete structures [70]. All

these models are based on the pull test results. Research in the literature has proved that

the bond strength is directly proportional to the square root of the interfacial fracture

energy √ regardless of the bond-slip curve shape [108]. Most of the models do not

provide an explicit formula for the bond strength. Thus, the bond strength has to be

determined numerically. It is found that Lu et al [70] model gives results in close

agreement with test results. So, it is recommended to be used in calculation of the bond

strength in the next chapters of this study.

The bond strength is the ultimate load carrying capacity of the FRP-Concrete interface.

The bond strength of the FRP-Concrete bonded joint in terms of interfacial fracture

energy is given by:

√ ( )

Where is the bond length factor and given by:

92

{ (

)

} ( )

The analytical solution for the effective bond length is given by:

( )

( ) ( )

Where:

√

√

( )

[ √

]

The factor of 0.99 implies that the effective bond length is the one at which 99% of the

bond strength of an infinitely long bonded joint is achieved. Furthermore, units of

megapascals and millimetres shall be used in calculating the bond strength.

2.11 Treatment of punching shear in codes of practice

Although the strengthening and repairing of reinforced concrete slab-column

connections with FRP have been used for more than two decades, it is still a

researchable area and hence there is no pure punching shear equation for such slabs. All

the previous studies were individual efforts aimed at studying specific cases. There

should be a tendency in collecting all these studies in order to find a unique punching

shear equation that can be used in the analysis and design of slabs. Nevertheless, some

codes only give a general overview of how FRP is applied to concrete, while others try

to expand their punching shear equation to accommodate the effect of FRP. These codes

depend on changing the flexural reinforcement ratio and the corresponding slab

effective depth to take into account the effect of CFRP.

( )

In which or the slab height

93

( )

Following is the summary of these codes:

2.11.1 American Concrete Institute (ACI): ACI 440.2R-08 [109]

The ACI code does not take into account the effect of the flexural reinforcement in the

punching shear equation, but it gives a general overview of strengthening and repairing

slab-column connections. Therefore, the effect of strengthening by CFRP will not be

directly considered. The ACI code considers the slab effective depth based on equation

(2-27). The general equations of punching shear are presented as follows:

{

√

√ (

)

√ (

)}

( )

is a resistance factor for concrete and has a value of 0.75, is the concrete

compressive strength, is the ratio of long side to short side of the column, b0 is the

critical shear perimeter of the slab, is column location factor: 4 for interior columns,

3 for edge columns and 2 for corner columns, and d is the slab effective depth.

2.11.2 Eurocode 2 [29] and Concrete Society Technical Report 64 [110]

Eurocode 2 [37] and the Concrete Society Technical Report 64 [110] rules are based on

the CEB/FIP Model Code 1990 [111] in dealing with punching shear. This equation can

be extended to cover the slab-column connections strengthened by FRP as follows:

( ) ⁄ ( )

√( ⁄ ) ( )

√( ) ( )

94

2.11.3 Japanese Society of Civil Engineers (JSCE) [112]

The Japanese Society of Civil Engineers (JSCE) [112] considers the effect of the

flexural reinforcement area by the same way of using the equivalent reinforcement ratio

and the slab effective depth:

⁄ ( )

Where:

√ (

) ( )

√ ⁄

( )

√

( ⁄ ) ( )

: design compressive strength of concrete (N/mm2)

= peripheral length of loaded area

: Peripheral length of the design cross section located at a distance d/2 from the

loaded area.

is a partial safety factor generally equal to 1.3

( )

2.11.4 FIB model code Bulletin 66 [113]:

FIB model code depends on the critical shear crack theory in calculating the punching

shear strength. This code does not take the effect of the flexural reinforcement in

consideration. So, only the effective slab depth will be considered when using FRP

strengthening.

√

( )

95

The parameter depends on the deformations (rotations) of the slab and follows from:

( )

Where is the mean value [in mm] of the (flexural) effective depth for the x and y

directions. Provided that the size of the maximum aggregate particles, , is not less

than 16 mm, in equation (2-38) can be taken as 1.0.

If concrete with a maximum aggregate size smaller than 16 mm is used, the value of

in equation (2-38) is assessed as:

( )

Where is in mm.

The rotation around the supported area is calculated as follows:

( )

The value of the rotation can be approximated as 0.22 Lx or 0.22 Ly for the x and y

directions, respectively, for regular flat slabs where the ratio of the spans (Lx/Ly) is

between 0.5 and 2.0.

2.12 Originality of the research

Based on the previous studies regarding the strengthening of slab-column connections

that have been presented in this chapter, there is clear knowledge to the author about the

strengthening of slab-column connections. Thus, it can assert that there is no study

about the strengthening of slabs at the corner column. In addition, the existence of an

opening near the corner columns has not yet been studied. Therefore, the research

originality comes from studying the entire behaviour of the connection due to the effect

96

of strengthening by CFRP and how to deal with the opening and the best way to

strengthen it.

2.13 General comments

Strengthening slab-column connections against punching shear by using FRP

composites is still a researchable area because the available research comprises

individual efforts focusing on certain cases. Furthermore, none of the specification

standards provide specific information on how to design and apply FRP composites

especially for such connections. However, developing comprehensive design guidelines

requires more and more research on each specific point related to slab-column

connection, material properties, geometry, nature of loading and column location with

respect to the slab. Therefore, further research is required to provide a full

understanding of the punching behaviour of the slab-column connections strengthened

with FRP.

Punching shear is the most dangerous failure that can occur to slabs because it happens

in a brittle manner without preceding notice. Many researchers have studied this

problem in order to overcome it and have found their own results, which later have been

incorporated into the codes and design guideline standards. All of these guidelines give

general information about using FRP sheets or plates for strengthening slab-column

connections and do not provide a determinate outline of how to design concrete slab-

column connections to withstand punching shear. Furthermore, all codes, standards and

guidelines have taken their specifications from studying interior slab-column

connections only. Studying the interior slab-column connections is not perfectly correct

as the boundary conditions are simply supported. Simply supported conditions have

rotational deformations, while there are no rotational deformations along the line of

contraflexure.

Studies on the effect of the opening have proved that it does not only reduce the

connection strength but may also alter the failure mode to a brittle failure. Thus, the

effect of the opening near the slab-column connection is studied here.

The present study provides a fresh investigation of strengthening flat slab to corner

column connections against punching shear, by using externally bonded CFRP with a

97

view to developing optimum strengthening layouts for the specific geometry and stress

states associated with this scenario. In addition, it is the first study to investigate the

effect of openings near the corner column.

98

3. Chapter 3 Analytical model in finite element

formulation

Numerical techniques have been used widely in engineering fields. One of the most

powerful techniques is the finite element (FE) method. After the mathematical concept

of the method was recognised, its popularity started to increase, along with the

development of new finite elements. The invention of the digital computer has given a

fast means of performing the complex calculations involved in finite element analysis,

and thus many problems have become simpler. With the development of high-speed

digital computers, the finite element method progressed at an impressive rate.

Understanding the material properties is the first step in modelling a structure

numerically. The analysis and design of any reinforced or strengthened concrete

structure require prior understanding of its mechanical properties [114].

Punching shear failure is a three-dimensional (3D) state of stress problem due to the

large shear stresses that exist around the connection [43]. Therefore, it is necessary that

three-dimensional material modelling and constitutive relationships be adopted to

effectively predict the transverse shear failure.

This chapter summarises some typical important mechanical properties of each

individual material used and how they are dealt with in analysis. These data are

essential for generalised mathematical modelling. They are of interest in relation to the

complex 3D stress states in slabs near columns.

3.1 Finite element method

The finite element method is the most powerful technique used in the numerical

solution of engineering problems. However, in structural engineering, modelling the

behaviour of reinforced concrete is a difficult challenge in finite element analysis. The

difficulty comes from the inherent complexity and brittle fracture behaviour of the

concrete, which causes difficulty in developing an accurate constitutive model to obtain

a reliable or converged solution numerically [114]. One of the most encountered

problems in numerical solutions is divergence. Divergence may come from the

99

difficulty of representing the nonlinearity of the reinforced concrete due to the cracking

of the concrete, aggregate interlocking of the cracked concrete, bond-slip between the

steel and the concrete and the dowel action of the steel reinforcement [114].

This chapter introduces and discusses the elements chosen in the analysis, and the

modelling of the material properties of the concrete, steel, FRP and the adhesive.

3.2 Element choice

The materials used in the analyses consist of concrete, reinforcing steel, FRP composite

and the adhesive. The selection of the element type is attributed to the problem that will

be analysed. In many structural problems, the structure cannot be represented as an

assemblage of only one type of element. In such cases, it is necessary to use two or

more types of elements for discretisation. Reliable constitutive models for concrete,

reinforcing steel, the FRP composite and the bonding adhesives are available in the

ABAQUS material library.

3.2.1 Iso-parametric solid element for concrete

Many types of three-dimensional (3D) elements are available in the ABAQUS elements

library, such as continuum and beam elements. The most common model for concrete-

based studies is the three-dimensional continuum or brick element [115]. The most

important feature of this element is its ability to represent both linear and nonlinear

behaviour of the concrete. In the linear stage, the concrete is considered as an isotropic

material up to cracking, while in the nonlinear stage; the concrete may undergo

plasticity and/or creep [116].

The ABAQUS solid elements library has many three-dimensional elements in first-

order and second-order interpolation. They can be used to model any shape problems of

linear or nonlinear stress-displacement. The main elements that can be used for concrete

modelling are C3D8, C3D20 and C3D10M.

The first-order C3D8 element is generally used in most 3D finite element models

because of its quick solution and good accuracy. The second-order C3D20 element has

more integration points in each element compared with the C3D8. This could provide

more details if the differences in each element are very big, but it may increase the

100

analysis time. The C3D10M element is suitable for some irregular shapes, but its

accuracy is not as good as the cube elements [115].

Second-order elements can cause problems with contact when they are used as a slave

surface because of the method used to calculate the equivalent nodal loads when a

pressure load is applied on the face of the element, as shown in Figure 3-1 [117]. Figure

3-2 shows a constant pressure applied to the face of the second-order element without a

mid-face node, which may cause opposite forces at the corners of the applied pressure.

To solve this issue, ABAQUS automatically inserts a mid-face node to any face of a

second-order brick element that defines a slave surface to consistently distribute the

contact pressure over the slave surface, and thus it increases the analysis time.

Figure 3-1 Equivalent nodal loads produced during contact simulation of constant

pressure on the second-order element face [117]

By considering both the running time and the accuracy of the numerical analysis,

ABAQUS first-order solid element type C3D8 was chosen in this numerical study.

In the first-order solid elements, there are two types of elements based on the

mathematical theory used in defining the element behaviour, which are fully and

reduced integrated elements.

101

Shear locking is a problem encountered in all the fully integrated, first-order, solid

elements when they are subjected to bending. It can be defined as the formation of shear

strains that do not really exist in pure bending. To explain the shear locking problem, if

an element is under pure bending, it will distort similar to Figure 3-2.

Figure 3-2 Realistic behaviour of an element subjected to pure bending [68]

The horizontal dashed lines along direction 1 in Figure 3-3 distort with a constant curve

similar to the curve of the element and the vertical dashed lines are still perpendicular to

them. The behaviour of any finite element totally depends on the number of integrated

points in the element. In the first-order (linear) brick elements, the fully integrated linear

brick element (C3D8) consists of two integration points in each direction, thus it uses a

2×2×2 array, and when it is subjected to pure bending, the upper and lower sides of the

element change their length but the element cannot bend, as shown in Figure 3-3.

Figure 3-3 Fully integrated linear brick element subjected to pure bending [115]

It can be noticed that the upper dashed lines increased in length, causing tension stresses

along them, while the lower lines decreased in length and this resulted in compression

stresses. The length of the vertical dashed lines does not change if the displacement is

assumed to be very small, so the normal stress along direction 2 is zero. This is

consistent with a right angle between the horizontal and vertical dashed lines. However,

the angle has changed, which causes shear stresses. This is absolutely incorrect as the

shear stresses are zero in a pure bending state. Therefore, inaccurate results can result

due to pseudo shear stress introduced in this type of element subjected to pure bending.

This means that the bending state created shear deformations rather than the intended

bending deformations.

Reduced integration is used in the linear solid elements to reduce the problem with

shear locking. These elements have only one integration point in the middle of the

102

element, as shown in Figure 3-4. In these elements, the vertical and the horizontal

dashed lines passing the integration point are always perpendicular to each other.

Therefore, shear stress will not be introduced. Thus, and with relatively fine mesh, good

agreement with the real structure can be achieved. In spite of the number of elements

through the height of the structure, the curvature must be large enough to calculate the

bending of the structure [115].

Figure 3-4 Reduced- integration linear brick element subjected to pure bending [115]

Another point to note when using the first-order element is that ABAQUS requires first-

order elements to be used for those parts of a model that form a slave surface like the

slab in this study.

For all these reasons, the C3D8R element is used to simulate the concrete elements.

3.2.2 Embedded truss element for steel

Two methods are found in ABAQUS to represent steel reinforcement. The first method

is to smear the reinforcement as layers between the concrete, while the second method

is to model the reinforcements as discrete truss elements. Modelling the reinforcement

by truss elements is the most favoured method as it is the closest method to the real

distribution of the reinforcements [118].

A three-dimensional two nodes truss element (T3D2) is used to represent the internal

steel reinforcement. These elements are embedded into the concrete (host) elements as

shown in Figure 3-5:

103

Figure 3-5 Truss element AB embedded in (3-D) continuum element; node A is

constrained to edge 1-4 and node B is constrained to face 2-6-7-3 [68]

Embedding means that in any direction the translational degree of freedom at the node

in the reinforcement element is eliminated by constraining it to the interpolated value of

the corresponding degree of freedom in the host solid element. When an embedded node

is positioned near the edge or face of the host element, this node makes a small

adjustment to its position in order to precisely lie on the edge or face of the host

element. In this way, an embedded element may share some nodes with the host

element and a perfect bond can be assumed between host and embedded elements.

3.2.3 Shell element for FRP

Shell elements are used to model structures in which the thickness is smaller than the

other dimensions and thus the out-of-plane normal stress in the thickness is neglected

[119]. Two types of shell elements are found in ABAQUS: continuum and conventional

shell elements. They have similar kinematic and constitutive behaviours but the

continuum shell element looks like a three-dimensional solid. In the analysis of the

continuum shell element, the thickness is determined by the element nodal geometry. In

contrast, the thickness of the conventional shell element is defined through the

definition of the section property. The more economic approach in terms of

computational efficiency is to use a conventional shell element. A conventional shell

element (S4R) with four nodes and reduced integration point can be used to model the

FRP composite, as shown in Figure 3-6. In this element, Kirchhoff constraint is

enforced; that is, plane sections normal to the mid-section of the shell remain normal to

the mid-surface [119].

104

Figure 3-6 Four-node shell element [115]

3.2.4 Cohesive element for adhesive

Cohesive elements can be used in modelling the behaviour of adhesive joints, interfaces

in composites, and other situations in which the integrity and strength of interfaces are

important [120]. To represent these elements, the intended application should be taken

into consideration. Some assumptions related to the deformation and stress state are

considered to be the basis of these elements‟ representation. Thus, the response of the

cohesive elements is classified based on:

Continuum description of the material.

A traction-separation description of the interface.

The modelling of adhesive joints includes situations in which two bodies are connected

together by a glue-like material. The modelling of cohesive elements based on a

continuum description is suitable when the glue has a finite thickness. In this case, the

modelling depends directly on using material properties measured experimentally, like

the stiffness and the strength. On the other hand and when the adhesive material is thin

and for all practical purposes may be considered to be of zero thickness, a traction-

separation modelling is suitable to model the behaviour of the specific joints. The

adhesive layer has to be modelled by using a single layer of cohesive elements so that

the element will not distort when debonding takes place [115]. In this study as the

adhesive layer is thin, traction-separation modelling was chosen.

As mentioned in 2-10 and based on the model of Lu et al. [70], the adhesive shear

strength, the initial slip in which damage in the cohesive layer occurs, the damage

evolution, and the final slip in which debonding occurs can be stated and inputted in

ABAQUS. The elements used to model this region were three-dimensional eight-node

cohesive elements (COH3D8), as shown in Figure 3-7.

105

Figure 3-7 Eight-node cohesive element [115]

3.3 Material modelling

Reinforced concrete is a material that is used in the construction of many concrete

structures. Understanding its behaviour should begin with an understanding of its

components.

3.3.1 Steel reinforcement modelling

The steel reinforcement in a reinforced concrete structure is defined based on the stress-

strain results of the uniaxial tensile tests conducted on the steel sample. In ABAQUS,

the elastic behaviour of the steel is characterised by the elastic modulus and Poisson‟s

ratio, while the plastic part of the steel‟s behaviour is defined by true stress ( ) and true

plastic strain (

) data pairs, as follows:

( ) ( )

( ) ( )

Where is the nominal steel strain.

106

3.3.2 FRP reinforcement modelling

Most composite materials consist of two materials: reinforcement or fibres and matrix.

The reinforcement is stiffer and stronger than the matrix. FRP composites are an

anisotropic material and their properties are not the same in all directions, as shown in

Figure 3-8:

Figure 3-8 Schematic of FRP composites [121]

The CFRP composite strip is considered to be an orthotropic elastic material which has

nine independent elastic stiffness parameters. However, this orthotropic material has

approximately similar properties in any direction perpendicular to the fibres direction.

Therefore, it can be considered to be transversely isotropic. Thus, the stiffness

parameters can be reduced to five.

The material properties of the composite material were studied experimentally and the

results are used in the numerical simulation. The material properties required for the

modelling are:

The overall thickness of the composite strip.

Fibre direction orientation in the composite strip.

Young‟s modulus of the composite strip in the longitudinal and one of the

transverse directions.

Major Poisson‟s ratio in the direction of the fibres.

The shear modulus of the composite strip in the three planes of stresses.

The composite strip failure criterion is defined based on a stress-based failure criterion

called Hill-Tsai failure theory [121]. In this failure criterion, the input data required for

107

the failure envelope are the maximum tensile and compressive strength of the composite

in longitudinal and transverse directions to the fibres. In addition, the maximum shear

stress in the plane of the composite (longitudinal-transverse plane) is required in the

definition. If the stresses in the direction parallel to the fibres are denoted by ( ) and

those transverse to the fibres by ( ), the failure criterion governing equation is:

(

)

(

)

(

)

( )

If , then is the maximum tensile stress; otherwise, is the

maximum compressive stress. If , then is the maximum tensile stress;

otherwise, is the maximum compressive stress. is the maximum

shear stress in the plane of the composite (longitudinal-transverse plane).

3.3.3 Concrete modelling

The general failure modes of the concrete section are cracking in tension and crushing

in compression. The concrete failure process is represented by irreversible deformations

and the stiffness degradation of the material, which leads to a decrease in the stress with

a corresponding increase in the strain, which is called strain softening [122]. The most

important constitutive model that describes the concrete failure depends on combining

plasticity with damage. Plasticity models alone are unable to capture the material

stiffness degradation, while damage models are not suitable for representing the

irreversible deformations [122]. Concrete behaviour in ABAQUS is modelled by the

damage-plasticity model, which is able to give suitable and reasonable results for the

numerical simulation of the 3D state of stress corresponding to the punching shear

failure [123]. The concrete damage plasticity model used in this study is presented as

below.

3.4 Failure criteria of concrete

Failure of a concrete section occurs when the section‟s ultimate strength is reached.

According to the concrete‟s properties and based on its ultimate compressive and tensile

strength, concrete failure can be divided into a compressive failure defined by many

small cracks that develop in the direction of the loading, resulting in a crushing, or a

108

tensile failure defined by the formation of major cracks perpendicular to the loading

direction. Thus, the cracking and post-cracking of the section are the most important

aspects and they should be modelled precisely. The ABAQUS concrete damage-

plasticity model uses the yield function proposed by Lubliner et al. (1989) and

incorporates the modifications proposed by Lee and Fenves (1998) to account for the

different evolution of strength under tension and compression [123]. The concrete

damage-plasticity model in ABAQUS assumes that cracking in a concrete section

occurs when the triaxial state of stress reaches a failure surface determined in terms of

effective stresses by the following equation [124]:

( )

( ( )⟨ ⟩ ⟨ ⟩) (

) ( )

Where:

(

⁄ )

(

⁄ )

( )

(

)

( )

( ) ( ) ( )

( )

( )

The factor appears only in the triaxial compression state.

is the effective hydrostatic stress

√

( ) is the Mises equivalent stress

is the maximum principal stress

( ) is the compressive stress

( ) is the tensile stress

Kc is the ratio of the second stress invariant on the tensile meridian, q(TM), to that on the

compressive meridian, q (CM).

109

Cracking is assumed to occur when the stress reaches a failure surface that is called the

Crack Detection Surface [125]. This failure surface is a linear relationship between the

equivalent pressure stress, p, and the Mises equivalent deviatoric stress, q. When the

concrete damage-plasticity model in ABAQUS detects a crack, by default it stores the

crack orientation for subsequent calculations. Subsequent cracking at the same point is

restricted to being orthogonal to this direction since stress components associated with

an open crack are not included in the definition of the failure surface used for detecting

the additional cracks.

One of the most important aspects of the failure analysis of concrete structures is the

modelling of the crack initiation and propagation. The crack process in the concrete

structures is not a sudden onset of the new free surface but a continuous forming and

connection of microcracks [126]. Cracks are assumed to occur when a principal stress or

strain exceeds its limiting value or when the concrete tensile stresses reach one of the

failure surfaces either in the biaxial tension region or in a combined tension-

compression region [127]. These cracks occur in a plane perpendicular to the direction

of the offending principal stress or strain and this crack direction is fixed for all

subsequent loading. The cracks imply an infinite number of parallel fissures across the

element-integration point. The formation of the microcracks is represented as a

softening behaviour of the material which causes the localisation and redistribution of

strain in the concrete structure. The microcracking process in the concrete causes a

stiffness degradation which is modelled by defining a relationship between the stresses

and effective stresses to give a Cauchy stress to relate the effective stress through

stiffness degradation [126]. In ABAQUS, the uniaxial tensile stresses responses are

characterised to represent the damage in the concrete. The response is linear until the

value of the failure stress is reached in which the onset of microcracking. Beyond that

stress, the formation of microcracking is represented by a softening response which

induces strain localisation in the concrete structure.

The concrete model is a smeared crack model which does not track any individual

cracks. Constitutive calculations are performed independently at each integration point

for each element in the mesh of the structure. The concrete cracking response enters into

these calculations by the way in which the cracks affect the stresses and the material

110

stiffness associated with the integration point [127]. By contrast, the discrete crack

model reflects the concrete cracking closely. It models the cracks directly by a

displacement-discontinuity in an interface element that separates two solid elements.

But, this model does not fit the nature of the finite element method by implying a

continuous change in the nodal connectivity which needs an automatic remeshing, the

crack has to follow a predefined path along the element edges and it is computationally

difficult [128]. Smeared crack model is attractive not only due to preserving the finite

element nature but also in not imposing restrictions in the crack orientation. It is for

these two main reasons the smeared crack model quickly replaced the discrete crack

model and came into widespread of use as in this study.

The unquestionable advantage of the Concrete Damage Plasticity model is the fact that

it is based on parameters that have an explicit physical interpretation [129]. The exact

role of the above parameters and the mathematical methods used to describe the

development of the boundary surface in the three-dimensional space of stresses are

explained in the ABAQUS user‟s manual. The other parameters describing the

performance of the concrete are determined for uniaxial stress.

For this reason, it is necessary to input the concrete‟s behaviour in uniaxial tension and

compression. To consider the effect of the triaxial state, it is necessary to refer to the

dilation angle and the failure surface by using the yield function presented above [125].

The concrete behaviour in ABAQUS is represented based on the plasticity parameters,

the compressive behaviour of concrete and the tensile behaviour of concrete as follows:

3.4.1 Plasticity parameters

The constitutive model of the concrete material is represented in ABAQUS programme

based on the work by Lubliner et al. (1989) and incorporates the modifications proposed

by Lee and Fenves (1998). The evolution of the yield surface is controlled by two

hardening variables, one in tension and one in compression. Non-associated flow is

assumed where the flow potential is the Drucker-Prager hyperbolic function [8]. For

these functions, a couple of parameters must be defined.

111

Dilation angle (Ψ) represents the angle of inclination of the failure surface

towards the hydrostatic axis. Using low values of the dilation angle produces

brittle behaviour while using higher values gives more ductile behaviour [130].

Eccentricity ( ) defines the rate at which the flow potential tends to a straight

line as the eccentricity tends to zero (0.1 is the default value to be used in

ABAQUS).

For the yield function, the ratio of the initial equibiaxial compressive yield stress to the

initial uniaxial compressive yield stress is set to 1.16. Furthermore, the ratio of the

second stress invariant on the tensile meridian, q(TM), to that on the compressive

meridian, q (CM) Kc is set to 2/3. Finally, the viscosity parameter that usually helps to

improve the rate of convergence of the slab model in the softening region is set to zero

[8].

3.4.2 Compressive behaviour of concrete

Depending on the uniaxial compression test that can be conducted on a concrete section,

the stress-strain relation can be accurately described. The response of the concrete is

linear until initial yield value and it is non-recoverable, then it is characterised by stress

hardening until the maximum compressive strength, followed by strain softening until

failure.

ABAQUS needs to define both stress hardening and strain softening in terms of

compressive stress (σc) and inelastic strain ( ):

( )

( )

Where E0 is the initial modulus of elasticity

There are many equations that can be used in modelling concrete sections, one of which

is the model of BS EN 1992-1-1:2004 Euro code 2 [37] which is used in this study.

112

Figure 3-9 Uniaxial stress-strain curve for concrete [37]

3.4.3 Tensile behaviour of concrete

When tensile stresses are applied to a reinforced concrete member, concrete cracks

occur at discrete locations in which the concrete tensile strength is violated. In spite of

cracking of concrete, the concrete between cracks still can carry tensile stresses. Thus,

the partially cracked concrete member stiffness is higher than that of a fully cracked

section. This effect is known as "Tension Stiffening or Stress Softening" [131]. There

are three approaches to describe stress softening which are stress-strain, stress-crack

opening displacement and stress-fracture energy. Stress-crack opening and stress-

fracture energy can be used alternatively because they are connected to each other.

Stress-strain softening may lead to mesh sensitivity, meaning that the analysis does not

converge to a unique solution as the mesh is refined, because mesh refinement results in

narrower crack bands rather than formation of additional cracks [12]. The softening data

are characterised in the same way to the compressive behaviour that means in terms of

tensile stress (σt) and inelastic strain ( ) or the crack opening displacements shown in

Figure 3-10-a.

( )

( )

The cracks are treated in the way of smeared crack approach; that is, individual “macro”

cracks are not tracked, and constitutive calculations are performed independently at

each integration point of the element. The presence of cracks is accounted by the stress

and stiffness degrading associated with the material at the integration point.

113

The description of cracking and failure within finite element analysis of quasi-brittle

materials such as concrete has led to two fundamentally different approaches: the

discrete and the smeared one. The smeared crack approach is based on the development

of appropriate continuum material models; cracks are smeared over a certain finite

element area corresponding to a Gauss point of the finite element [132]. Traditional

smeared-crack models are known to be susceptible to stress locking and possible

instability at late stages of the loading process [133]. The main issue in this approach is

the modification of the stiffness properties and equilibrium conditions at integration

points of cracked areas. The smeared crack models are usually formulated in stress-

strain space.

Figure 3-10 Post-failure tensile behaviour: (a) stress-strain approach; (b) fracture energy

approach [104]

In return, stress-crack opening or stress-fracture energy developed by Hillerborg (1976)

[134] is able to control the deficiency of stress-strain approach as shown in Figure 3-10-

b. Depending on the stress-crack opening approach, three models of tension stiffening

were chosen in this study as follows:

3.4.3.1 Linear tension softening model

This approach requires that after cracking the stress goes linearly to zero at the ultimate

displacement, as shown in Figure 3-11:

114

Figure 3-11 Linear tension stiffening curve [135]

In this approach, the ultimate displacement ( ) that can be estimated from the fracture

energy ( ) when no stress can be transferred is

, where is the maximum

tensile stress that the concrete can carry.

3.4.3.2 Bilinear tension softening model

In a cracked concrete section subjected to a tensile stress, a bilinear stress-crack opening

can be used to represent stress softening according to the CEB-FIP model [111], as


Figure 3-12 Bilinear tension stiffening curve [111]

( )

( )

115

Where:

= the crack opening (mm)

= the crack opening (mm) for

= the crack opening (mm) for

= coefficient depends on maximum aggregate size

3.4.3.3 Exponential tension softening model

Cornelissen et al. [136] in 1986 conducted a regression analysis for the inelastic

deformations in the post-peak region of reinforced light and normal weight concrete

members and found the best fit curve to represent stress-crack opening displacement, as


Figure 3-13 Exponential tension stiffening curve [136]

(

) ( ) ( )

( ) * (

)

+ (

) ( )

Where C1 and C2 are 3 and 6.93 respectively for normal weight concrete.

3.5 Interaction

In this study, there are two types of interactions. The first one is between the concrete

and the steel reinforcement, while the second is between the concrete and the CFRP

sheets. Below is a brief description of each interaction.

116

3.5.1 Steel-concrete interface

One of the most difficult and controversial aspects of the finite element analysis of

reinforced concrete structures is the modelling of the interaction between the

reinforcement and the concrete [119]. Most of the controversy comes from the fact that

many finite element models are able to simulate the experimental behaviour without

considering the effect of the bond-slip. In spite of the bond-slip arising partially from

concrete fracture, other factors like the crushing, chemical adhesion and friction

between concrete and reinforcement bar play a huge role. Therefore, the detailed

modelling of bond-slip is extremely complex, even though it is associated with one bar.

As mentioned, the reinforcement is represented by truss elements embedded through the

host elements of the concrete continuum, which can assume a full bond between the

concrete and the steel reinforcement. The structural effects that are associated with the

bond between concrete and steel, like the tension stiffening, bond-slip and dowel action,

are indirectly considered in ABAQUS by modifying some aspects of the plain concrete

to imitate them [115]. This can be achieved by introducing some tension stiffening into

the concrete modelling to simulate load transfer across cracks through the rebar. Tensile

behaviour of concrete in softening should be modified in order to account for these

effects, based on the reinforcement ratio, aggregate size, mesh size and the bond

characteristics, by introducing the tension stiffening as well to allow the post-failure

behaviour to be defined. This modelling results in a significant reduction in the number

of nodes and elements needed to account for the effect of bond-slip, especially in the 3D

simulation.

3.5.2 FRP-Concrete interface

When considering externally bonded FRP to strengthen or repair a concrete section, the

most important part that should be taken into consideration is the bond between the

concrete substrate and the FRP. Three parameters have to be taken into consideration in

modelling the FRP-Concrete interface, which are as follows:

3.5.2.1 Failure criteria

The traction-separation model available in ABAQUS assumes initially linear elastic

behaviour followed by the initiation and evolution of damage, as shown in Figure 3-14.

The elastic behaviour is written in terms of an elastic constitutive matrix that relates the

117

nominal stresses to the nominal strains across the interface [115]. The nominal stresses

are the force components divided by the original area at each integration point, while

the nominal strains are the separations divided by the original thickness at each

integration point. The default value of the original constitutive thickness is 1.0 if the

traction-separation response is specified, which ensures that the nominal strain is equal

to the separation (i.e., relative displacements of the top and bottom faces). The

constitutive thickness used for the traction-separation response is typically different

from the geometric thickness chosen based on the adhesive thickness.

Figure 3-14 Exponential damage evolution [115]

The FRP debonding occurs when the slip value U0 corresponding to the maximum shear

stress defined in the bond-slip model is reached at any point. In the cases of a sufficient

bond length, the failure occurs initially around the load application point and then

moves towards the FRP plate ends. While when there is insufficient bond length, the

debonding starts at the FRP plate end and spreads to the whole FRP plate [137].

3.5.2.2 Damage initiation

Damage initiation is the beginning of degradation of the response of a material point

when the failure criterion is satisfied. In order to simulate the damage initiation in the

cohesive elements, there are four damage initiation criteria: maximum stress, quadratic

stress, maximum strain and quadratic strain criterion [138]. Under mixed-mode loading,

an interaction between modes must be taken into consideration. The quadratic stress

damage criterion considers the interaction of the traction components in predicting the

damage initiation. Furthermore, the high sensitivity of the damage initiation to the strain

118

and displacement makes stress-based criterion give a more accurate damage prediction

when compared to other models [138].

In this study, the damage is assumed to initiate when a quadratic interaction function

reaches a value of one. This criterion can be represented as:

,⟨ ⟩

-

{

}

{

}

( )

Where

represents the nominal tensile strength that causes failure (usually the tensile

strength of the concrete, as the failure occurs in the concrete not in the adhesive). Where

if (tension) and otherwise. By using the Macaulay bracket, it is

assumed that compression does not cause damage. and

represent the peak

values of the nominal shear stress when the deformation is in the first or the second

shear direction, respectively. They are calculated based on Lu et al.‟s [70] model.

3.5.2.3 Damage evolution

The damage in the cohesive elements refers to the debonding in the FRP strips [115]. It

is important to assume the damage initiation and the damage evolution law. The damage

evolution law describes the rate at which the material stiffness is degraded once the

corresponding initiation criterion is reached, and it was assumed as an exponential

damage evolution law based on Lu et al.‟s model [70]. The damage response is defined

as a tabular function of the differences between the relative motions at ultimate failure

and the relative motions at damage initiation,( ), while the damage variables are

determined based on equation 3-15, as follows:

( )

A scalar damage variable, D, represents the stiffness degradation or the overall damage

in the material and captures the combined effects of all the active mechanisms. It

initially has a value of 0. If damage evolution is modelled, D monotonically evolves

from 0 to 1 upon further loading after the initiation of damage.

119

In the analysis of concrete structures especially strengthened by FRP composites, two

approaches exist to simulate the FRP-Concrete interface [139]. The first one is called

mesoscale approach. In this approach, the simulation of concrete cracking adjacent to

the adhesive layer requires a very fine element mesh. And thus, the debonding is

simulated directly by modelling the cracking of concrete elements and hence the

interface elements are avoided. Recent works [140] on the debonding modelling has

proved the difficulty of simulating FRP debonding using the concrete constitutive

model. It is also difficult to use this approach, especially in 3D modelling as it requires

extensive computational resources. In the second approach, the FRP-Concrete interface

is simulated by using a predefined bond-slip relationship to link the FRP and concrete

elements. The FRP debonding in this approach is simulated as the failure of the

interface elements. So, choosing an accurate bond-slip model could give very accurate

results. In spite of this approach is not a truly predictive model, but it can give an

accurate result with a little time consumption. So, it will be used in this study.

In general, the debonding of FRP composites occurs within a thin layer of concrete

instead of the adhesive layer because the tensile strength of the adhesive is usually

higher than that of the concrete unless a weak adhesive is used [141]. This layer has a

small thickness in comparison with the dimensions of the whole concrete elements. So,

the interface debonding can be simulated as the interfacial cracking using the cohesive

elements between the FRP and the concrete.

3.6 General comments

The modelling needs to incorporate the best understanding of the behaviour of each

material in the structure. The first step to understanding the behaviour of the structure is

to choose the correct element type for each component and then choose the suitable

behaviour that represents the behaviour of that corresponding component (elastic,

plastic, linear or nonlinear, etc.). It is also clear that the way of applying the loads

(point, pressure load, etc.) has a big effect on the best simulation.

120

4. Chapter 4 FE Modelling of Reinforced Concrete

Slabs/Beams

In this chapter, a numerical study was conducted in order to simulate the structural

behaviour of reinforced concrete slabs and beams and to give more understanding of the

failure mechanisms that can occur in real situations. An experimental work conducted

by Walker and Regan [29] in 1987 is intended to be simulated by FE to considering it as

a baseline structural form to study numerically the strengthening of slabs at corner

columns. Furthermore, two additional models were also tested to check the ability of the

model to capture the CFRP strains and to identify the debonding issues that may occur

during simulation.

4.1 Walker and Regan experimental work

The slab at the corner column connection had dimensions of 2000 × 2000 mm with a

thickness of 80 mm, as shown in Figure 4-1. Four corner columns of a cross section 160

× 160 mm with a height of 720 mm were used to support this slab. The slab was

reinforced with Ø6 mm reinforcement in the bottom side with a distance of 90 mm

between bars, while in the top overhead columns only four bars of the same diameter

were extended to 650 mm with a distance of 200 mm between them in each direction.

These bars were put through the slab thickness to give an effective slab depth of 64 mm.

The columns were reinforced by the same type of reinforcement but with a different

diameter of 12 mm. Column stirrups were also used to fix the column longitudinal

reinforcement in its locations and to prevent the columns from buckling. These stirrups

were Ø6 mm distributed every 150 mm along the column length, as shown in Figure 4-

2. The columns were monolithically cast from the top with the slab and were designed

to be pin-supported at the base. The material properties of the concrete and the steel

reinforcement are presented in Table 4-1.

The load was applied monotonically by a hydraulic jack to give a load applied to 16

steel loading patches of dimensions 50 × 50 mm distributed equally over the slab

surface in order to transfer loading to the whole slab.

121

Figure 4-1 Test arrangement from Walker and Regan [29]

Figure 4-2 Steel reinforcement of Walker and Regan‟s slab-column connection [29]

(a) Top steel reinforcement (a) Bottom steel reinforcement

(c) Column steel reinforcement

122

Table 4-1 Material properties of Walker and Regan‟s slab-column connection

Material Description Value

Concrete

*Elastic modulus, GPa 32.6

Characteristic cylinder compressive strength (fc), MPa 37.4

Characteristic tensile strength (ftsp), MPa 2.52

Reinforcement

Ø 6 mm

*Elastic modulus, GPa 200

Yield strength (fy), MPa 595

*Ultimate stress, (MPa) 684

Ø 12 mm




* Material properties are assumed based on Eurocode 2 [37].

4.2 Finite element idealisation

The first step in this analysis is to study the un-strengthened slab and to validate it to the

experimental results obtained from Walker and Regan [29]. The elements used in the

analysis were C3D8R for the concrete sections and T3D2 for the steel section. The

influence of the parameters is then studied separately.

4.3 Investigation of the model parameters

4.3.1 Numerical parameters

Three parameters having a significant effect on the computational cost and finite

elements prediction are studied. These parameters are:

1. Step time period and load increment.

2. Mesh size.

3. A number of elements through the slab thickness.

For this study, material parameters are kept constant as they are taken from Table 4-1.

4.3.1.1 Effect of step time period

Step time is the total duration of applying the effect within a specific step [115]. It is an

important factor that must be chosen accurately in ABAQUS/EXPLICIT, as it should be

long enough to avoid the dynamic effect and at the same time short enough to minimise

the computing cost. Figure 4-3 shows a comparative study between the solutions of

three step times (0.1, 0.5 and 1 second) and Walker and Regan‟s experimental results.

Reducing the step time causes the slab-column connection to be affected dynamically.

Thus, reducing the step time to 0.1 seconds reduces the solution time to 16 minutes,

while, increasing the step time to 1 second makes the response more smooth but with a

123

very long solution time of five hours. In addition, increasing the step time will not

change the total behaviour of the slab-column connection. Thus, the best step time is 0.5

seconds as used in this study which gives a total solution time of one hour.

Figure 4-3 Load-deflection curves showing the effects of the different step time periods

on the slab-column connections

4.3.1.2 Mesh size

In order to study the effect of the element size on the numerical study, the load-

deflection response was the reference parameter selected in determining the appropriate

mesh size. Thus, all other parameters should be kept un-changed. The slab thickness

was divided into six elements with an element height of 13.33 mm. Four element sizes

(10, 20, 40 and 80) mm were studied. The mesh was said to be converged when an

increase in the mesh density (or decreasing the element size) had a negligible effect on

the obtained results.

Based on the results shown in Figure 4-4, the convergence study implies that the 20 mm

mesh size converges to the 10 mm mesh size. Therefore, it was decided to adopt the 20

mm mesh size for the rest of the analysis to reduce the amount of mesh used and the

computer time. Another point is that the 10 mm mesh size gives a fluctuation in the

results due to the dynamic effect adopted in the quasi-static analysis in

ABAQUS/Explicit. On the other hand, the 40 mm and 80 mm mesh sizes result in

stiffer behaviour of the slab-column connection.

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

Lo

ad

(k

N)

Slab underside central point deflection (mm)

Walker and Regan

0.1 seconds

0.5 seconds

1 second

124

Figure 4-4 Load-deflection curves showing the effects of the different mesh sizes on the

slab

4.3.1.3 Number of elements through the slab thickness

Increasing the number of elements through the slab thickness means increasing the

Gauss points in which stresses are calculated. This increase is to accommodate the

nonlinearity of concrete when cracks propagate through the slab thickness. Increasing

the number of elements through the thickness will increase the element aspect ratio

which may result in irregular predicted responses, as shown in Figure 4-5.

Figure 4-5 Load-deflection curves showing the effects on thickness when using

different numbers of elements

It is noticed that increasing elements through the slab thickness does not improve the

prediction of the response, but it increases the computational time and in some cases

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35 40 45

Lo

ad

(K

N)


Walker and Regan

mesh size 10 mm

mesh size 20 mm

mesh size 40 mm

mesh size 80 mm

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

Lo

ad

KN


Walker and Regan

three elements

six elements

nine elements

125

may cause solution divergence as it is not allowed in the analysis. Thus, the option

using six elements within the slab thickness is chosen for the whole analysis.

4.3.2 Material parameters

To study the effect of the material parameters, all other numerical parameters are kept

constant. Five parameters are studied, as follows:

4.3.2.1 Tension stiffening

Three types of tension stiffening curves (linear, bilinear and exponential) are chosen to

study their effects on the entire behaviour of the slab-column connection. The relation

of the tension stiffening is based on stress-crack opening displacement. It can be seen

from Figure 4-6 that the linear tension stiffening gives higher loads than the other types

up to the ultimate punching shear failure, with a fluctuation in the response after the

concrete cracking. Bilinear tension stiffening gives lower loads than the other types,

with a fluctuation after cracking. The exponential tension stiffening gives the most

realistic results compared to the experiment with less fluctuation. Therefore, exponential

tension stiffening is chosen to use in the nonlinear solution. It is worth mentioning that

this fluctuation after cracking comes from the dynamic effects in the nonlinear solution.

Figure 4-6 Load-deflection curves showing the effect of using different tension

stiffening on the slab

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35 40 45

Lo

ad

(k

N)


Walker and Regan

linear tension stiffening

bilinear tension stiffening

exponential tension stiffening

126

4.3.2.2 Concrete tensile strength

The effect of the concrete tensile strength is illustrated in Figure 4-7. Increasing the

concrete tensile strength would increase the load at first cracking and the total absorbed

energy. It can be seen also that higher tensile strength can provide higher stiffness for

the reinforced concrete slab-column connection. It is also apparent that increasing the

tensile strength would increase the elastic range to give a higher cracking load. The

tensile strength of the concrete has a major effect on the total ultimate punching shear as

the punching shear failure is a combination of shearing and splitting without crushing.

Thus, punching shear strength is controlled by the tensile splitting of the concrete. In

finite element analysis, low tensile strength may cause a divergence in the solution

compared to the experimental results and cause a lower punching shear capacity.

Figure 4-7 Load-deflection curves showing the effect of using different concrete tensile

strength on the slab

4.3.2.3 Effect of Young’s modulus of concrete

The effect of Young‟s modulus of concrete is illustrated in Figure 4-8. In this study, the

assumed value of Young‟s modulus taken from Table 4-1 was reduced to (50, 75)% in

order to understand the effect of Young‟s modulus on the results. Choosing an incorrect

value for Young‟s modulus may cause a divergence problem for the numerical results

with their corresponding experimental results. Increasing Young‟s modulus value

increases the elastic range to give a higher cracking load. However, the increase can

give stiffer response compared to low values of Young‟s modulus, as shown in Figure

4-8.

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

Lo

ad

(k

N)


Walker and Regan

tensile strength=0.5fctm

tensile strength=0.75fctm

tensile strength=fctm

127

Figure 4-8 Load-deflection curves showing the effect of using different concrete

Young's modulus on the slab

4.3.2.4 Effect of the dilation angle

Dilation angle (Ψ), as defined previously, is the angle of the internal friction of the

concrete material. Thus, it ranges between 30 and 37 for normal concrete. However, to

study its effect, its value is ranged between 12 and 37 to give more understanding of

how it affects the total behaviour. Figure 4-9 shows the effect on the slab-column

response of changing the dilation angle. It can be seen that the best response can be

obtained from a dilation angle of 37˚. However, changing the dilation angle value may

cause divergence problems in the nonlinear solution. The numerical model terminates in

certain steps because the dilation angle affects the concrete principal stresses developed

from the externally applied loading.

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

Lo

ad

(K

N)


Walker and Regan

Young's modulus=0.5E

Young's modulus=0.75E

Young's modulus=E

128

Figure 4-9 Load-deflection curves showing the effect of using different dilation angles

on the slab

4.3.2.5 Effect of Kc

Figure 4-10 shows the effect of changing the Kc value on the response of the slab-

column connection. Three different values of Kc are used: 0.5, 0.667 and 1. From Figure

4-10 it can be concluded that changing the Kc value does not affect the entire response

of the slab-column connection. Thus, it was decided to use the default value of 0.667,

which is suggested by ABAQUS (2013).

Figure 4-10 Load-deflection curves showing the effect of using different Kc on the slab

From the previous parametric study, the most appropriate simulation scheme includes

using concrete elements of 20 mm and six elements through the slab thickness. For the

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

Lo

ad

(K

N)


Walker and Regan

dilation angle=12

dilation angle=20

dilation angle=30

dilation angle=37

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40 45

Lo

ad

(K

N)


Walker and Regan

Kc=0.5

Kc=0.667

Kc=1

129

material, a dilation angle of 37˚, Young‟s modulus equals to the calculated concrete

Young‟s modulus, concrete tensile strength equals to that calculated and exponential

tension stiffening are considered to form the most appropriate scheme in the simulation.

4.3.3 Load-deflection response

The applied load versus the vertical midspan deflections presents an idea of the

structural response and the sequence of events in the loading scenario. Based on the

previous parametric study, the most appropriate simulation scheme mentioned above

can be used for the analysis. The same response as reported in the experimental work is

compared to the response from the analysis and it shows a reasonable agreement, with

an over-prediction to the point of initial cracking. The difference in the pre-crack

behaviour may be due to the variation in the tensile strength and Young‟s modulus in

the specimen compared to the properties adopted from the cylinder test, as referred to in

the parametric study in 4.3.2.2 and 4.3.2.3. This difference could be due to the

difference in the elastic range of the concrete tensile strength which is about (7-10)% of

ultimate compressive strength [127] and the range of calculating Young‟s modulus of

about (30-40)% of ultimate compressive strength [142]. Furthermore, Menetrey [10]

studied the effect of concrete tensile strength on the ultimate punching shear capacity

and found that there is a scatter in the punching shear capacity when concrete tensile

was changed. Furthermore, there is another factor that causes the difference between the

experimental and the numerical results. This factor is the modulus of rupture of the

concrete. It is defined as the maximum normal stress in the concrete slab calculated

from the ultimate bending moment under the assumption that the slab behaves

elastically [143]. The model was designed with an ultimate load of 36 kN/m2 that causes

a moment of 12 kN.m in the section, while in experiment the model had different

moment value due to the difference in the ultimate load and the concrete material

properties, especially the concrete tensile strength, furthermore to the microcracks that

may exist in the concrete before loading which causes less loading. The accuracy in

achieving the cracking load in the finite element was a controversial study for many

researchers. Winkler et al [123] found that the general agreement between the

experimental and the numerical is not satisfying especially with the high strength up to

the onset of first cracking and the corresponding deflections which gives a higher

stiffness compared to the experimental work. This can be due to the finite element

programme itself and how it deals with cracking. Furthermore, Enochsson et al [144]

130

concluded that the main difference between the experimental and the numerical

simulation is found in the elastic region and the initiation of the nonlinearity. This is

believed to be a consequence of the boundary conditions and the inability of the model

in modelling the crack propagation in a proper way. Furthermore, isotropic damage

models give a more brittle behaviour compared to other softening constitutive models,

due to the stiffness degradation in all directions [145]. Similarly, the full bond

assumption in the numerical model may lead to a stiffer response in the pre-crack region

[133,146]. The full bond cannot account for the rotation of the slab about the critical

crack, which may result in additional deflections. For this reason, it underestimates the

deflections, which are less realistic than in the real situation. Another factor that is

assumed to affect the results is the amount of tension stiffening assumed in the analysis.

The load-deflection curves for the experimental and the numerical results are presented

in Figure 4-11.

Figure 4-11 Load-deflection curves for the experimental and numerical results

In both the experimental and numerical studies, cracking was observed first on the top

surface of the slab-column connection close to the inner corner of the column which

then propagated to the free edges of the slab; cracking was then observed on the lower

surface of the slab at slightly higher loads. No cracking developed parallel to the

diagonals of the slab. With increasing load, cracks propagated across the free edges

following an inclined path away from the column edges to give torsional cracks and

punching shear failure. Torsional moments developed simultaneously with bending

moments and shear forces when the external loads acted transversely at a distance from

the supporting columns [14].

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4.3.4 Reinforcement stresses

At loads close to failure, the first yielding took place in the bottom steel reinforcement

at the middle of the free edge between the columns and then spread along the slab centre

when the structure failed in punching, as also stated in the experimental work.

Three locations in each direction of the slab were chosen to draw the strains on the top

and bottom reinforcement. The first one is at the mid-distance between the columns in

the bottom reinforcement, the second one is at the slab centre in the bottom

reinforcement and the last one is over the column, as shown in Figure 4-12.

(a) Bottom Steel Reinforcement (b) Top Steel Reinforcement

Figure 4-12 Locations of strain measurements

Figure 4-12-a shows that the maximum tension stress in the bottom steel reinforcement

occurs at the mid-distance between columns, while Figure 4-12-b shows that the

maximum steel stresses in the top steel reinforcement occur over columns. However,

the bottom steel reinforcement has more stresses than the top reinforcement. The stress

profiles at the locations of maximum tension stress in the X and Z directions are shown

in Figure 4-13 with respect to loading steps.

132

(a) Load-stress of the reinforcement in the X direction

(b) Load-stress of the reinforcement in the Z direction

Figure 4-13 Steel stress of the un-strengthened slab at failure load in N/m2

Rebar in the top reinforcement over the columns does not reach yield stress (595 MPa)

before the punching shear failure occurs. This is common in punching shear scenarios

where no prior yielding or only a local yielding of the rebar occurs around the column

[17]. There is a reduction in the strain values before failure at a load level of 86 kN, as

shown in Figure 4-13. A possible explanation is that concrete crushing in the

compression zone has initiated and this causes a redistribution of strains in this area.

This is confirmed in Figure 4-14, which indicates the concrete compressive strength has

been reached at this load level where the column was removed to show the stress

distribution through the slab thickness. It is worth mentioning that steel between the

columns recorded yield at nearly the ultimate load, while at mid-slab no yielding

occurred.

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Figure 4-14 Stress state in concrete (N/m

2) at load level 86 kN

4.4 Validation of Abdullah et al.’s simply supported slab

4.4.1 Model description

Abdullah et al [101] tested a series of slab-column connections under a monotonic

loading to simulate an interior connection. The first slab was un-strengthened to act as

the control slab, while the others were externally strengthened with prestressed or non-

prestressed CFRP plates. The slabs were 1800 × 1800 × 150 mm with 1600 mm clear

distance between supports. In the middle of each slab, there was a column stub of 250 ×

250 × 150 mm on the top surface only. All these slabs were reinforced with 8Ø12 mm

in both directions, while the column stub was reinforced mainly with 4Ø12 mm and

3Ø8 mm as stirrups spaced at 100 mm. In all these slabs, the clear concrete cover was

set at 20 mm to the flexural reinforcement. The strengthened slabs were strengthened by

two CFRP plates with a width of 100 mm and thickness of 1.2 mm in each direction

around the column stub. Figure 4-15 shows the geometry and details of the slabs.

134

Figure 4-15 Load configuration and steel reinforcement details for the slab [101]

Seven strain gauges were mounted on some steel bars and distributed around the

column, as shown in Figure 4-16-a, to give an overview of the steel behaviour in this

area. Many strain gauges were also mounted on the CFRP plates, as shown in Figure 4-

16-b, to show the strain profile on the CFRP. Furthermore, a linear variable differential

transducer (LVDT) was put at the centre of the bottom face of the slab to measure the

deflection. Figure 4-16 shows the arrangement of the strain gauges in the steel and the

CFRP plates.

135

(a) Location of strain gauges on steel bars

(b) Location of strain gauges on CFRP plates

Figure 4-16 Instrumentation of the test slabs [101]

136

4.4.2 Finite element model

To decrease the computing time, only a quarter of the slab is modelled due to the

symmetry in geometry, loading and supports. Two slabs are modelled; the first slab is

the control and the second is the strengthened slab with non-prestressed CFRP plates.

The ABAQUS is also used to model the slabs. The load is applied as a pressure on the

column stub and the same elements are used as previously for the concrete; steel

reinforcements. To model the CFRP sheets and the adhesive layer, a conventional shell

element (S4R) with four nodes and one reduced integration point is used. The cohesive

layer is modelled using COH3D8 elements, as explained previously. The material

properties of the concrete, steel and CFRP are presented in Table 4-2.

Table 4-2 Material properties of Abdullah et al.‟s slab-column connection


Concrete

Elastic modulus, GPa 28.504

Poisson ratio 0.2

Characteristic compressive strength (fc), MPa 35.5

Split cylinder tensile strength (ftsp), MPa 3.6

Reinforcement

Ø 8 mm

Elastic modulus, GPa 163

Poisson ratio 0.3


Ultimate stress, (MPa) 655

Yield strain 0.003

Ø 12 mm


Poisson ratio 0.3


Ultimate stress, (MPa) 655

Yield strain 0.0034

CFRP

Longitudinal modulus (E1), GPa 172

*Transverse in-plane modulus(E2=E3), GPa 14.05

*In-plane shear modulus (G12=G13), GPa 5.127

*Out-of-plane shear modulus (G23), GPa 4.39

*Major in-plane Poisson ratio, ν12= ν13 0.29

*Out-of-plane Poisson ratio, ν23 0.6

Characteristic tensile strength (ft), MPa 2640

* Material properties are taken from Abdullah et al [12]

4.4.3 Discussion of computational results and comparison with experiments

The validation of the FE simulation in terms of ultimate load, mid-span deflection and

the ultimate strain in both the steel and the CFRP plates is compared to those in the

experiment to check the simulation validity. Based on the previously investigated

parameters, an element size of 15 mm is adequate in validating the experimental results.

137

Figure 4-17 shows the comparison between the experimental and the numerical

simulations for both the control and the strengthened slabs. It can be noticed that there

is a good correlation between the experimental and the numerical results up to the

ultimate load, even though the FE model gives stiffer behaviour in both cases. This may

be attributed to using the full bond between the concrete and the steel rebars as it

prevents any slip between them. The control slab failed in flexure punching mode due to

the yielding of the flexural reinforcement at failure, and that yielding spread over a large

area of the slab. In contrast, the strengthened slab failed in punching shear as shown in

Figure 4-17 with a sudden decrease in the loading after ultimate load. Figures 4-18 and

4-19 show the strain in the reinforcement.

Figure 4-17 Load-deflection for the slab-column connections

The strengthened slab failed due to the sudden punching of the column through the slab.

This failure can be recognised by the concrete being crushed on the compression side of

the slab-column connection. This crushing usually occurs either because the principal

compressive strain exceeds 0.0035 or because the principal compressive stress exceeds

the specified concrete compressive strength (fc). In this study, the crushing is

characterised based on the value of the concrete compressive strain.

In all cases, the numerical results have lower strains compared to those in the

experimental work. One of the reasons is related to the full bond, as mentioned earlier,

but another reason is related to the level of tension stiffening added to the concrete in

numerical simulation. Furthermore, the probability of cracking near the location of the

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strain gauges in the experimental study causes some discrepancy in the numerical

results. The numerical simulation considers the cracks as smeared cracks on the surface

of the concrete elements, while in the experiment they are discrete cracks.

(a) Strain gauge 1

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(c) Strain gauge 3

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(d) Strain gauge 4

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(g) Strain gauge 7

Figure 4-18 Steel reinforcement strains

(a) Fibre strain gauge 1

(b) Fibre strain gauge 2

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(c) Fibre strain gauge 5

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(f) Fibre strain gauge 13

Figure 4-19 FRP reinforcement strains

4.5 Validation of the retrofitted simply supported reinforced concrete beam

4.5.1 Model description

In order to check the validity of the model in capturing the debonding that may occur in

the CFRP sheets, a numerical study using a strengthened beam with a shear failure is

modelled. Bencardino et al [147] tested a series of simply supported reinforced concrete

beams under four-point bending. In this study, beam B2.1 the un-strengthened and beam

B2.2 the strengthened were studied in detail. They designed the whole beams to fail in

shear, and thus they were all identical in every aspect except for their loading regime. In

the current study, the focus was on the beams that strengthened in flexure and failed by

shear in order to simulate the debonding of the CFRP plate that took place in the

experiment.

The beams had a rectangular cross section of 140 mm in width and 300 mm in height

with a total length of 5000 mm. The total span between the supports was fixed at 4800

mm. The total load was applied at two points that divide the length between supports to

three parts as shown in Figure 4-20-a.

(a) Supports, loading and reinforcement distribution

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(b) Geometry and reinforcement of beams

(c) Length of CFRP laminate

Figure 4-20 Beam under consideration [147]

The beams were reinforced in flexure with 2Ø16 mm in tension and compression side.

The beams had no internal reinforcement in the shear spans. However, both the tension

and compression reinforcement were tied together by 10Ø6 mm stirrups distributed at

150 mm. Three of these stirrups were provided under each load point, and two over

each support as shown in Figure 4-20-a. The clear concrete cover to the flexural

reinforcement was set to 25 mm in all the beams.

The retrofitted beams were strengthened with CFRP plates with a thickness of 1.2 mm

and a width of 80 mm, with a total length of 4700 mm. The CFRP laminate was put

along the longitudinal centre line of the beam after preparing the concrete surface and

removing the undesired cement past, dust and grease that had occurred due to moulding.

4.5.2 Finite element model

A finite element modelling was also performed by using the commercially available

software ABAQUS to model the nonlinear behaviour of the beams. The load was

144

applied as a uniform pressure over two steel-bearing plates on the top surface of the

beam, as in the experiment. Due to the symmetry, a quarter of the beam was modelled

in order to reduce the computing time. The same elements as used in the previous

analysis were also used for all the concrete, steel, CFRP and cohesive materials. The

material properties of the concrete, steel and FRP are presented in Table 4-3.

Table 4-3 Material properties of Bencardino et al.‟s beams

4.5.3 Discussion of computational results and comparison with experiments

Based on the numerical parameters investigated previously, it was found that mesh with

an element size of 30 mm can give the best fit to the experimental results with little

computing time required. Numerical results were compared to the experimental results


Concrete

Control

beam


Poisson ratio 0.2

Compressive cylinder strength

(fc), MPa 35.1

Tensile split strength (ft), MPa 2.3

Strengthened

beam


Poisson ratio 0.2

Compressive cylinder strength

(fc), MPa 38.2

Tensile split strength (ft), MPa 2.7

Reinforcement

Ø 6 mm


*Poisson ratio 0.3

*Yield strength (fy), MPa 595

*Yield strain 2975µm/m


Ø 16 mm


Poisson ratio 0.3

Yield strength (fy), MPa 541.2

Yield strain 2706µm/m

Ultimate stress, (MPa) 626.1

CFRP

Density, g/cm3 1.6

Longitudinal modulus (E1), GPa 150

**Transverse in-plane modulus(E2=E3), GPa 15

**In-plane shear modulus (G12=G13), GPa 6.5

**Out-of-plane shear modulus (G23), GPa 5.3

**Major in-plane Poisson ratio, ν12= ν13 0.3

**Out-of-plane Poisson ratio, ν23 0.45

Characteristic tensile strength (ft), MPa 2400

* Based on Table (4-1)

** Material properties are manually calculated

145

to validate them. Figure 4-21 shows the comparison between these results for both the

control and the retrofitted beams. It can be seen that there is a very good agreement

between the numerical and the experimental results as in Abdullah et al model in 4.4.3.

This can be attributed to the values of the concrete tensile strength and Young‟s

modulus used in numerical simulation and how are close to that in experimental.

(a) Control beam

(b) Strengthened beam

Figure 4-21 Load versus midspan deflection

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The control beam failed in shear and with a brittle manner with a formation of a

diagonal shear crack near the left support. The ultimate load was 82.5 kN with a total

deflection of 34 mm. The strain in the tension steel reinforcement was 2090 µm/m

which is less than the yielding strain.

The strengthened beam behaved very similarly to the control un-strengthened beam. It

also failed in shear with almost the same ultimate load as the control beam. The total

deflection was 26 mm and the maximum tensile strain in the CFRP reinforcement was

1981µm/m which is only about 14% of its ultimate failure strain.

(a) Quarter of the control beam numerically

(b) Strengthened beam experimentally

147

(a) Quarter of strengthened beam numerically

Figure 4-22 Cracking in the tested beams experimentally and numerically

There is no big difference between the crack propagation and the final crack pattern for

the control and the strengthened beams. But there are a few wide flexural cracks in the

control beam, while in the strengthened beam there are many flexural cracks with a

smaller width. This is due to the confinement of the cracks by the CFRP plates.

The cracks obtained numerically are similar to those in the experiment, which can prove

the ability of the model to capture the fracture mechanism in the beams.

4.5.4 Interfacial slip profile

The adhesive layer between the concrete surface and the CFRP sheets is modelled by

using cohesive elements, as presented previously. The behaviour of the interface is

modelled based on Lu et al.‟s [70] bond-slip model. In this model, damage is initiated

when either interface shear stress ( or ) or the effective displacement at damage

initiation (S0) is violated. In this study, the damage is evaluated based on the difference

in the horizontal displacement between two adjacent nodes of concrete elements and the

CFRP elements and compared to the effective displacement at damage initiation.

Initiation of damage occurs when the slip between the concrete and the CFRP sheet

reaches the value of the effective displacement at damage initiation (S0) of 0.05 mm, but

the final debonding takes place at a slip (Sf) of 0.8 mm as mentioned in 2.10.1 and

2.10.2. Figure 4-23 shows the change in the slip between the concrete and the CFRP

sheet in different load values. Because the beam fails in shear, debonding does not occur

at the plate end before the maximum load. This is due to the less transferred loads

through the interface.

148

After failure, the increase of the shear crack causes an increase in the slip profile due to

the gradual loss of stiffness in the concrete. The slip was observed to vary from the

beam centre towards the plate end.

Figure 4-23 Comparison of slip profile at different load levels

Figure 4-24 shows the quadratic stress state of the cohesive layer at the ultimate load of

82.44 kN to explain the damage initiation as referred in 3.5.2.2. From the figure, it can

be seen that the initial effective displacement was violated below the load due to the

concentration of shear stresses, but the debonding was not initiated at both the plate end

and the flexural cracks region even that the concrete was cracking.

Figure 4-24 Cohesive layer at damage initiation (top view)

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Distance from the beam centre toward the

end support (m)

20.1940.4260.0980.7382.44

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When cracking occurs, the axial force in the concrete section cannot be sustained by the

beam section. Thus, this force is transmitted to the CFRP plate through the cohesive

layer, causing shear stresses in the layer. The increase of this shear stress can cause the

debonding in the CFRP plate.

4.6 Summary

Bonding FRP sheets to the tension face of reinforced concrete slabs with a low

reinforcement ratio can increase the punching capacity and shift the failure from

flexural failure to flexural punching or pure punching shear failure. From the results of

the simulation presented, it can be seen that the finite element model is able to predict

the deflections, strains in steel, FRP and the failure mode reasonably well compared to

the experiment.

Mesh size has a big role in the convergence of the finite element model, as choosing the

element size incorrectly makes the model divergent to the experimental results. Tension

stiffening also has a big effect on the results because more tension stiffening can make

the model stiffer, while less tension stiffening can make the model soft. It is also seen

that the type of model used to represent the concrete tension behaviour after cracking

also has an effect on the results.

150

5. Chapter 5 Parametric study on strengthening the

Walker and Regan slab-column connection

A numerical study is conducted to strengthen the slab-column connection by using

CFRP sheets. The width of the CFRP sheet was kept as 50 mm and different thicknesses

were used. These FRP sheets were put around the corner column in two specific

configurations. In the first configuration, the CFRP sheets were placed orthogonally to

the slab edges and adjacent to the slab-column connection at different distances from

the column face. In the second configuration, the CFRP sheets were placed diagonally

with an angle of 45˚ to the slab edges. They were adjacent to the column at different

distances from the column interior corner, as will be explained later in this chapter. The

CFRP thickness was also studied to understand the effect that changing the CFRP area

has on the strengthening.

Many different parameters such as the CFRP location, configuration and thickness are

studied numerically based on the effective direction of CFRP with the concrete tensile

stresses against the concrete cracking and the stress state in order to find the best fit to

be used in the experimental programme later. In all the numerical studies, except the

thickness effect, the material properties are taken for CFRP sheet with properties as

presented in Table 5-1.

Table 5-1 CFRP material properties [148]

Material Thickness

(mm)

Width

(mm)

Modulus of Elasticity

(GPa)

Tensile Strength

(MPa)

CFRP sheet 1 50 122.5 2082.5

Furthermore, and in order to fully understand the effectiveness of strengthening by

CFRP, the diameter of the steel reinforcement of the un-strengthened slab is reduced to

make the slab fail initially by flexure, and then the slab is strengthened. In this case, an

initial flexural failure of the slab is intended to study how CFRP changes the failure

mode and how to achieve higher load capacity for such slabs. A detailed study of each

case is presented as follows:

151

5.1 Effect of bond length in strengthening

The effective bond length is a length in which the forces induced in the FRP are

transferred to the concrete through the shear stress within this short length [148]. It is

the length beyond which any increase in the bond length will not affect the ultimate load

that the sheets can transfer, or it is the required length that can be provided in order to

prevent debonding of FRP from the strengthened specimen [70]. Therefore, it is

necessary to focus more on understanding the influence of the effective bond length on

strengthening and shear stresses transfer as it is considered an important factor to

determine the maximum bond strength of the interface. Consequently, most of the bond

strength models use this length as the basis to predict the maximum bond strength. If

the slab extends beyond the corner column face, it is not really critical, as the FRP can

be extended on the slab beyond the column face to increase the bonding length; the

most critical case is when the slab edge coincides with the column face. In this case, it is

difficult to extend the FRP beyond the slab sides, especially for FRP plates due to their

rigidity. Therefore, in this case, it is necessary to use sheets because they are easy to

fold, which will be used in this study. The strengthened slab is strengthened by CFRP

sheets with a width of 50 mm and a thickness of 1 mm with different lengths. The

CFRP sheets are applied firstly to the top surface of the slab near the column, and then

they are extended to the slab sides, which are 80 mm in depth. Finally, they are

extended to the bottom surface of the slab.

There are many formulas that can be used to find the theoretical value of the effective

bond length, like the ACI-440-2R [109] and FIB model code Bulletin 14 [149], all of

which are based on some of the previous parameters mentioned in 2.10. However, most

of the existing bond length models consider only the effect of the FRP stiffness and

concrete strength [141]. Furthermore, most of the existing models neglect the adhesive

layer properties [150]. But, generally, there are two FRP-Concrete interface bonding

systems, namely plate bonding and sheet bonding [141]. A higher-quality control is

possible with the FRP plate bonding system compared with the sheet bonding system,

as the latter has a greater potential for construction defects due to the difficulty in

controlling the mixing resin and the curing of FRP composites [141].

ACI equation:

152

√

√ √

√

It is important to mention that the ACI equation was suggested based on the work of

Chen and Teng [151, 152]. They suggested that the relationship of the bond stress-slip

after the ultimate shear stress is represented by a linear decrease in the stress up to the

ultimate slip when the shear stress becomes zero which is not really linear. They also

suggested a relationship for the effective bond length based on the assumption that the

stress distribution is uniform across the whole cross-section of the concrete, as well as

in the bonded plate which is not really true due to the localized bond behaviour.

Furthermore, the ACI equation depends on using the concrete cylinder compressive

strength which is available in most tested experimental works, rather than the concrete

tensile strength, as used by Neubauer and Rostasy [153], because the tensile strength is

not available for all the examined tested experimental data or it may be estimated. In

this case, the ACI equation is weak in the calculation of the effective bond length as it

was derived for a specific geometry used in the tested samples and it seems to be

conservative in regards to this study.

FIB model code Bulletin 14:

√

√

It is worth mentioning here that the FIB model took its effective bond length equation

from the experimental work of Neubauer and Rostasy [153]. They conducted a series of

double shear tests on CFRP-to-Concrete bonded joints. And they concluded that the

relationship of the bond stress-slip after the ultimate shear stress is also represented by a

linear decrease in the stress. This can be considered another weak point in choosing the

FIB model equation of the effective bond length. The bond stress-slip is not necessarily

linear. Furthermore, the equation was derived based on an experimental work with

limited material properties of the concrete and the CFRP. Furthermore, the FIB model

equation depends on a bond length coefficient with a value obtained through

calibration with test results but the code suggests its value is equal to 2. Thus, this can

be considered as a weak point and the equation cannot be made as a general equation

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because changing the material properties does not have to be a major effect and the

equation has to be applied for all material properties.

Lu et al.‟s [70] formula:

Most of the existing bond stress-slip models are based on experimental or numerical

analysis. Thus, the accuracy of predicting the shear stress or displacement is variable.

Therefore, a more reasonable and general approach is to determine the bond length

based on the relationship between the bond stress and the corresponding slip [70,107

and 141]. The shape of the bond stress-slip has a big effect on the results. It is found

that the exponential expression can fit the experimental results very well [70,107

and141]. The development of Lu et al.‟s model was initially based on the theoretical

model of Yuan et al [154]. Then it employed a new approach in which mesoscale finite

element results with appropriate numerical smoothing are exploited together with the

test results of 253 pull specimens collected from existing studies.

This model also has an analytical solution for the effective bond length as explained in

equation (2-26). So, Lu et al.‟s formula will be used here in this study.

By application of equations (2-19) to (2-26), the effective bond length can be calculated

as follows:

√ ⁄

⁄ √

( ⁄ )

( ⁄ )

√

√

√

( ) √

( )

[ √

]

[ √

( )

]

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( )

( )

( )

( )

In all previous formulas, is the number of plates used in the strengthening, is the

FRP Young's modulus, is the thickness of the FRP plate and is the concrete

cylinder compressive strength, is a factor taken from the FIB model code, is the

mean tensile strength of the concrete, is the width of the FRP composite, is the

width of the concrete section, is the maximum shear stress in the FRP-Concrete

bond, is the width effect factor, is the effective displacement at damage initiation

corresponding to the maximum shear stress, and is finial displacement at which

debonding takes place when the shear stress becomes zero.

It is noticeable from previous formulas that there is a big difference between the ACI,

FIB and Lu et al. equations in regards to the effective bond length value. This difference

is due to the weakness of the ACI and FIB model equations in dealing with the

parameters that affect the bond length. These equations are weak because they only use

the properties of the FRP, Young‟s modulus and thickness, without taking into

consideration the whole interfacial components and what happens to the FRP when the

load is transferred to it. Furthermore, they do not take the FRP width into consideration.

Lu et al.‟s equation is simple and has a rigorous analytical derivation in which other

parameters like the peak bond stress, the corresponding slip value and the FRP and the

strengthened concrete width are considered in addition to the final debonding that may

occur. All these bond properties are included numerically in the calculation of the bond

length and cannot be found in the theoretical values calculated by the ACI and FIB

models.

The other important factor that has to be considered in comparing all these equations is

the concrete material properties because the failure will happen within a few millimetres

in the concrete substrate. The ACI equation takes the ultimate concrete compressive

strength into consideration, while the FIB model equation considers the tensile strength.

The failure in the FRP-Concrete bond is not a compressive failure. Therefore, using

155

compressive concrete strength in the ACI equation can add more weakness in this

equation. Using the ultimate tensile strength of the concrete as in the FIB model

equation is also not enough as the failure would occur by shear along the FRP-Concrete

surface. Thus, Lu et al.‟s [70] model considers using the ultimate shear stress of the

bond. Using shear stress is better than using concrete strength properties because the

failure of the bond occurs by shear, not compression or tension, which can give a more

realistic representation in the calculation of the bond length.

It is important to mention that all previous models were derived based on applying the

loads directly to FRP plates attached to a concrete substrate which causes a direct shear

to be placed on the plate. But, in this study, no direct tensile load was applied to the

FRP sheets and the tension stresses are transferred from the applied load on the concrete

surface to the FRP sheets due to the bending stresses in the whole structure. The

principle could be the same but the application is different. Furthermore, all previous

models were derived based on using FRP plates while in this study FRP sheets were

used instead. It is also possible to use these equations but with more caution, especially

with regard to controlling the mixing resin and the curing of the FRP composites.

Furthermore, the total interfacial fracture energy is an important parameter to determine

the stress transfer capability of the FRP-Concrete interface [155]. Using the fracture

energy can ensure accurate predicting of the bond strength capacity and thus the

effective bond length. Due to its clear physical meaning, it is very useful to apply it in

numerical analysis for deriving bond strength and anchorage length models, as well as

for clarifying the debonding failure mechanisms of FRP sheet-concrete interfaces in

more comprehensive ways [156]. Therefore, Lu et al.‟s model is going to be used rather

than the ACI or FIB model.

As the force transfers through the FRP-Concrete bond by the shear stress in the

adhesive, Diab et al. [150] conducted an experimental study to find the effect of the

adhesive layer by considering different thicknesses of this layer. They concluded that

using a less stiff adhesive leads to higher bond strength. A flexible adhesive layer

increases the effective bond length which results in the redistribution of shear stresses

along the bond length. Therefore, the bond length has to be increased to accommodate

the effect of the bonding adhesive.

156

Based on these formulas, a value of larger bond length according to Lu et al.‟s equation

will be used in this study to provide more assurance that debonding failure will be

prevented from occurring.

To develop a greater understanding of the bond length and find its exact value

numerically, many different lengths are used in a numerical sensitivity study, like 300,

350, 400, 450 and 500 mm ranging from a value less than the theoretically calculated

bond length to about twice the calculated bond length, for the FRP orthogonal

configuration as presented in Figure 5-1, as shown in Table 5-2. It is worth mentioning

that the numerical model‟s stiffness degradation mentioned in Table 5-2 has to be less

than 1.0 in order to ensure no debonding (where a value of 1.0 refers to the onset of

debonding).

Table 5-2 Summary of the numerical sensitivity study of applied bond length for slab-

column connection with FRP thickness=1mm

No. Length

(mm)

Load

(kN)

Def.

(mm)

Stiffness

degradation

Failure

mode

1 300 (on slab) 134.97 35.13 1 Debonding

2 350 (on slab) 134.99 35.15 1 Debonding

3 400 (on slab) 143.71 43.43 0.999 Punching

4 450 (on slab) 143.64 43.29 0.999 Punching

5 500 (on slab) 143.63 43.19 0.999 Punching

6 500 (on slab)+80 (slab

thickness)=580 144.73 43.96 0.968 Punching

7 500 (on slab)+ 80 (slab

thickness)+50 (on bottom)=630 144.48 42.51 0.902 Punching

8

500 (on slab)+80 (slab

thickness)+100 (on

bottom)=680

144.42 42.52 0.903 Punching

9

500(on slab)+80 (slab

thickness)+150 (on

bottom)=730

143.13 41.33 0.895 Punching

157

CFRP configuration 3

V= (50,100,150) mm

Figure 5-1 CFRP configurations on a quarter of the strengthened slab

The stresses of the concrete substrate are transferred to the CFRP through the adhesive

layer. With increased loading, the shear stresses along the plate-to-concrete interface

increase and, when the shear strength of the interface is violated, debonding starts to

take place along the plate-to-concrete interface and extends to the free end of the CFRP

sheet to give total sheet debonding. In this case, a local end debonding occurs because

punching shear of the slabs takes place before complete debonding of the CFRP,

especially when the bonding length is small.

Changing the FRP thickness or number of layers can result in different bond lengths

based on the application of equation (2-26). Table 5-3 shows that doubling up of the

FRP layers with the same thickness causes an increase in the bond length by about 40%.

As is well known, increasing the FRP thickness layers can increase the susceptibility to

debonding by increasing the horizontal shear between the FRP and the concrete

substrate. Therefore, the best thing here is to use one thin FRP sheet extend the FRP to a


V= (300,350,400,450,500) mm


158

distance more than the required bond length. Based on this study, the decision was to

use one layer of FRP with a thickness of 1 mm and work on reducing the debonding

susceptibility by increasing the bond length. Thus, the bond length will be as in case 6

in Table 5-2.

Table 5-3 Summary of studying different effective lengths

Number of FRP

layers

FRP thickness

(mm)

Theoretically required bond

length (mm)

1 1 313.87

2 1 443.68

1 1.2 343.78

2 1.2 485.98

1 1.6 396.89

2 1.6 561.08

1 2 443.68

2 2 627.25

Applying the CFRP sheets to the top surface of the slab with lengths of 300 mm and

350 mm causes a debonding in the CFRP sheets before failure, as shown above in Table

5-2. In these strengthening lengths, the failure mode was by end debonding of the CFRP

sheets before the final punching failure of the slab. However, increasing the length up to

400 mm changes the failure mode to punching shear failure. This means that the critical

numerical bond length is 400 mm. It should be noted that this length includes the region

from the slab‟s free edge towards the point of zero moments. This is because the value

of the effective length depends on many parameters related to the fibre sheet itself, like

the stiffness, thickness and the FRP-to-concrete width ratio.

As mentioned in Chapter three (3.5.2.1, 3.5.2.2 and 3.5.2.3) and based on equations (3-

16) and (3-17), the damage in the interface layer happens when the damage variables

(D) reach the maximum value of 1. The ultimate load is taken from the numerical study

where debonding or punching shear occurs without debonding. Table 5-3 gives a

summary of the numerical study conducted on the bond length. It can be seen that

lengths of 400, 450 and 500 mm are susceptible to debonding as the overall stiffness is

close to 1, as stated in 3.5.2.3. Thus, extending the sheets down the slab sides or the

bottom side of the slab increases the punching shear capacity and decreases the

susceptibility to debonding.

159

5.2 Effect of orthogonal configuration in strengthening

The CFRP sheets are placed at distances of 0, 5, 10 and 15 mm away from the column

face, as presented in Figure 5-2. Load-deflection curves for all these cases are presented

in Figure 5-3:

Figure 5-2 Orthogonal configuration of FRP

Figure 5-3 Load-deflection curve of the strengthened slabs in orthogonal configuration

From Figure 5-3 it can be noticed that placing CFRP strips close to or away from the

column edge does not make a big difference. Nevertheless, the maximum punching

shear strength can be obtained by placing CFRP at a distance of 15 mm from the

column face. This is attributed to the improvement in rotational resistance provided by

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50

Lo

ad

(k

N)


Walker and Regan

Numerical strengthened at 0 mm from the column edge




V= (0, 5, 10, 15) mm

160

the CFRP sheets as they bridge across the diagonal shear crack and limit crack opening.

In decreasing the discontinuity at the slab rotation in the critical shear crack region, a

reduction in the deflection is also observed in the early loading steps, causing stiffer

behaviour than seen in the un-strengthened slab.

5.3 Effect of diagonal configuration in strengthening

CFRP sheets are placed diagonally at an angle of 45˚ to the slab edges in three different

locations chosen to place the CFRP parallel to the slab‟s diagonal and with a length of

500 mm, as shown in Figure 5-4. In this configuration, the CFRP sheets are used to

bridge the concrete cracking on the slab‟s top surface in order to transfer tensile stresses

directly. The location of the CFRP sheets is changed with respect to its closeness to the

loading by (50, 90 and 125) mm. Load-deflection curves for all the cases are presented

in Figure 5-5:

Figure 5-4 Diagonal configuration of CFRP

V= (50, 90, 125) mm

161

Figure 5-5 Load-deflection curves of the strengthened slabs in a diagonal configuration

Figure 5-5 shows that there is no big difference between placing the CFRP sheets near

to or away from the load as the most important factor here is how the CFRP sheets

bridge the concrete cracking. Furthermore, strengthening of the slab by using CFRP

parallel to the slab diagonal gives an ultimate load of 137.67 kN because of the low

value of the effective bond length that causes debonding before achieving ultimate

punching shear capacity.

5.4 Effect of FRP thickness in strengthening

As the width of the CFRP strips is limited to 50 mm due to the limited space between

the column face and the loading, the need to increase the punching shear strength entails

changing either the CFRP thickness or the numbers of the layers used in the

strengthening. A comparative study is conducted between two types of CFRP sheets

with different thicknesses and based on using one layer of CFRP sheet under the

orthogonal configuration. Figure 5-6 provides a comparison between different CFRP

thicknesses:

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35 40 45

Lo

ad

(K

N)


Numerical strengthened with V=50 mm



162

Figure 5-6 Load-deflection curves with different thicknesses and layers

Figure 5-16 shows that increasing the CFRP thickness from 0.117 mm to 0.6 mm

increases the punching shear capacity from 132 kN to 140 kN respectively. In addition,

increasing the number of CFRP layers (one to two layers) increases the ultimate

punching shear capacity from 138 kN to 144 kN. Although there is no great difference

between the ultimate punching shear capacities, the increase is still due to the increase

in the area of CFRP that resists the tensile stresses transferred along the critical shear

crack sides. Additionally, although there is no great difference between the ultimate

punching shear capacity in the case of using 0.117 mm or 0.6 mm CFRP sheet, the

maximum punching shear strength happens when using two layers of CFRP sheets of a

thickness of 0.6 mm.Finally, it can be concluded that the best strengthening scheme is

the one using two orthogonal layers of CFRP strips with a thickness of 0.6 mm and at a

distance of 15 mm from the column edge.

5.5 Comparative study with strengthening by steel plates

Far from the disadvantages of strengthening by steel plates, like corrosion, high labour

costs in installation, and intrusive changes to the architectural appearance of the

structure, a further comparative study is conducted to provide more understanding of the

strengthening by CFRP and steel plates. Many steel plate sections have been used in this

study. The width was kept to 50 mm but the thickness was changed based on the

minimum thickness that the manufacturers can provide for steel plates. In addition, an

idealised steel plate with a thickness equal to the CFRP thickness is used. It has been

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35 40 45

Lo

ad

(k

N)


thickness=0.117 mm (one layer)

thickness=0.234 mm (two layers)

thickness=0.6 mm (one layer)

thickness=1.2 mm (two layers)

163

observed that using steel plates with a thickness similar to the CFRP thickness causes a

yielding and rupture failure in the steel plates before the final punching shear failure.

However, increasing the steel plate thickness causes a debonding failure in the Plate-to-

concrete interface in addition to the steel plate yielding before the punching shear

failure, like when using a thickness of 3 mm. For greater plate thickness, the failure

mode transfers to debonding failure with a debonding load that decreases with increases

in the plate thickness. This confirms that the increasing plate thickness causes an

increase in the horizontal shear between the concrete and the plate, which can cause

earlier debonding. Figure 5-7 shows the load and corresponding deflection for different

slabs strengthened by different plate sections in comparison to the slab strengthened by

CFRP sheets.

Figure 5-7 Comparison between slabs strengthened by steel plates and CFRP sheets

5.6 Reinforcement stresses for the strengthened slab-column connection

Similar behaviour to that of the un-strengthened slab is also shown for the strengthened

slab. Yielding of the steel reinforcement begins in the bottom steel reinforcement

adjacent to the slab edge and starts to spread along the slab centre when the structure

fails in punching.

The same locations chosen previously in Figure 4-8 are also used to draw the stress

variations in the top and bottom steel reinforcements, as shown in Figure 5-13.

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35 40 45

Lo

ad

(k

N)


Steel plate 50x0.8 mm

Steel plate 50x3 mm

Steel plate 50x6 mm

Steel plate 50x10 mm

CFRP sheets

164

(a) Load-Stress of Steel Reinforcement in X direction

(b) Load-Stress for of Steel Reinforcement in Z direction

Figure 5-8 Steel stress of the strengthened slab at failure load in N/m2

As the strengthening by CFRP increases the ultimate load capacity, more loads are

transferred to both the top steel reinforcement and the CFRP sheets. The existence of

the CFRP causes a reduction in the steel stresses as compared to the un-strengthened

slab as compared between Figures 5-8 and 4-13. The same behaviour for the un-

strengthened slab is also seen for the strengthened slab, in which no yielding took place

in the top reinforcement rebars over the columns before the punching shear failure. The

reinforcement at the mid-distance between the columns yielded at nearly the ultimate

load, while at mid-slab the rebars did not yield. A smaller reduction in the top steel

reinforcement stresses was also noticed. This may be due to the effect of CFRP in

sharing the tensile stresses with the steel reinforcement.

0

20

40

60

80

100

120

140

160

0 200 400 600

Lo

ad

(k

N)

Steel stress (MPa)

Top steel reinforcement (X)

Mid-distance between columns (X)

Mid-slab (X)

0

20

40

60

80

100

120

140

160

0 200 400 600

Lo

ad

(k

N)

Steel stress (MPa)

Top steel reinforcement (Z)

Mid-distance between columns (Z)

Mid-slab (Z)

165

5.7 CFRP stresses and strains

The behaviour of CFRP strips is linear elastic because CFRP is a brittle material and

does not exhibit a plastic behaviour. When a slab-column connection is strengthened by

CFRP, part of the stresses is transferred by the CFRP and thus additional loads can be

added to the slab-column connection. CFRP strips try to transfer the tensile stresses

across the cracks and delay the crack opening, which increases the crack initiation load.

Figure 5-9 shows the maximum principal stresses in the CFRP sheet at first cracking

and ultimate load. At first cracking, it can be seen that the maximum stresses take place

close to the inner corner of the column where concrete cracking initiates. Stresses

decrease towards the slab centre. At failure, the punching shear crack passes the CFRP

sheet and causes a sudden increase in the maximum principal stresses in the CFRP

sheet.

It is clear that the maximum stress in FRP reaches about 20% of its ultimate strength

and does not reach the failure stress of CFRP, which is 2082.5 MPa, as stated in the

manufacturing scheme. As stated in ACI 440.2R-08 [109], debonding happens when the

strain in CFRP reaches 90% of the ultimate composite strain. Thus, it means that

debonding does not happen in this case. Stress values decrease away from the slab edge

as the CFRP is out of the punching zone.

(a) CFRP maximum principal stress at first cracking

166

(b) CFRP maximum principal stress at ultimate load

Figure 5-9 Maximum principal stress in CFRP (N/m2)

In practical design, it is well known that the designer needs to know the stresses rather

than the loads carried by the FRP. Therefore, Chen and Teng [151] suggested that by

the application of equation (2-24) and

the maximum stress in the bonded plate at

failure is:

√

√

( )

They concluded, based on equation (5-1), that plates with a high Young‟s modulus and

a small thickness have to be used if high stresses are needed on the bonded plate.

The maximum stress reached in the CFRP sheet and the ratio of that stress to the

ultimate stress of the sheets can be calculated as follows:

√ ( ) √

√ √

167

It is noticeable that this value is in agreement with the percent of maximum stresses

reached in the CFRP in the numerical simulation of Figure 5-9.

To validate the conclusion from equation (5-1), a numerical study was conducted by

strengthening the Walker and Regan slab with CFRP sheets with different Young‟s

modulus and thicknesses as in Table 5-4.

Table 5-4 Study of Young's modulus and thickness of CFRP on the bond strength and

punching shear

CFRP

Young‟s

modulus

(GPa)

CFRP

thickness

(mm)

CFRP

stiffness

(EI)

Bond

strength

(kN)

Ultimate

punching

shear

strength

(kN)

CFRP

stress

(MPa)

Failure

type

100 1 0.41 785.97 139.3 366.8 Punching

100 2 3.33 1111.54 141.2 337.6 Punching

100 3 11.25 1361.35 141.1 270.1 Debonding

200 1 0.83 1111.54 141.8 564.6 Punching

300 1 1.25 1361.35 143.7 730.5 Punching

200 2 6.66 1571.95 142.2 528.3 Punching

300 3 33.75 2357.93 134.4 389.2 Debonding

Table 5-4 shows that increasing the FRP stiffness does not give more increase in the

ultimate punching shear capacity. Furthermore, failure type may change from punching

to FRP debonding. It is also clear that increasing Young‟s modulus and the thickness of

the FRP causes an increase in the FRP-Concrete bond strength as calculated based on

equation (2-24). Increasing the bond strength by increasing the FRP thickness causes a

small increase in the ultimate punching shear capacity due to the increase in the FRP

area. But at the same time, increasing the FRP thickness causes an increase in the

horizontal shear between the FRP sheet and the concrete slab which causes debonding

in the FRP before attaining higher punching shear capacity as in using FRP with 3 mm

thickness. Furthermore, increasing the FRP thickness causes a decrease in the total

stresses transferred to it.

Increasing the bond strength by increasing the FRP Young‟s modulus also causes a

small increase in the ultimate punching shear capacity. But it is noticeable that the total

168

stresses transferred to the FRP sheets also increased. This increase in the stresses causes

an increase in the neutral depth as calculated by equation (2-27) and an increase in the

length of the slope of punching shear in the compression side and thus the integrated

shear stresses along the punching crack.

Therefore, to increase the punching shear capacity by increasing the bond strength and

the FRP stresses and the corresponding concrete compression stress, it is necessary to

keep the same FRP thickness but with a higher FRP Young‟s modulus.

Linking to the results of the experimental work in Chapter seven, the ultimate bond

strength is 17.45 kN which gives a ratio of the stress to the tensile strength in the FRP of

0.26 as follows:

√ √

The effectiveness of the FRP strengthening material bonded to the tension surface of a

concrete member is highly dependent on the bond strength between the FRP and the

concrete [157]. Bonded stresses are generated along the interface through the forces

transferred between the FRP and the concrete member. The importance of the bond

strength is in controlling the total force transferred to the CFRP reinforcement prior to

debonding. Low values of bond strength could affect the structural stiffness at early

stages of loading, which would cause a lower ultimate load due to early debonding

cracks [12].

The punching shear failure takes place in the concrete section due to that section‟s

weakness against tensile stresses. Increasing the FRP tensile stresses depends on the

FRP-Concrete bond strength. Increasing the bond strength between the concrete and the

FRP can control the debonding in FRP-strengthened structures, which can allow the

transfer of more forces to the FRP reinforcement. Furthermore, attaching the FRP in a

169

direction parallel to the direction of the tensile stresses in the concrete causes an

increase in the punching shear capacity. The greater the transferred forces in the FRP,

the greater the additional forces in the corresponding intact concrete. In return, this can

cause an increase in the vertical component of the compression zone over the neutral

axis and consequently the punching shear strength capacity. Figure 5-10-a shows the

geometric illustration of the punching shear. As explained by Farghaly et al. [7] in 2.2,

the slope of the failure surface above and under the neutral axis is similar to part 1

above the neutral axis and part 2 under. On the basis of geometric illustration and the

neglecting of part 2 contribution (as explained in 2.2), the punching shear strength will

be as follows:

( ) ( )

In which is the radius of the column, is the radius in the slab at the neutral axis

level, is the length of the slope along the punching shear surface and is the shear

stress in part 1. From Figure 5-10-b, it is clear that transferring more stresses to the FRP

reinforcement with enough bond length causes an increase in the compression force of

the concrete. Furthermore, the neutral axis depth (x) based on the equilibrium between

all resulted forces would be increased. Increasing (x) can increase the length of the

slope along the punching shear crack and cause an increase in the integrated shear stress

along the punching crack.

The bond strength is a function of the properties and geometry of the specimen and it

has tacitly the effect of the bond length. The best attempt to improve the punching shear

(a) (b)

Figure 5-10 Geometric illustration of punching and section force equilibrium [7]

170

capacity is to increase the bond strength of the FRP-Concrete interface by increasing the

FRP Young‟s modulus based on equation (5-1). The FRP to concrete width is taken into

consideration due to the localised bond failure and the ratio has a significant effect on

the overall bond strength [158]. If the FRP width is smaller than the concrete width,

then the transferred force from the FRP to the concrete leads to a non-uniform

distribution of stresses across the concrete width.

Increasing the bond length of the FRP-Concrete interface to the effective bond length

can cause an increase in the bond strength and consequently the punching shear

capacity. Any increase in the bond length over the effective bond length will not

increase the bond strength.

Getting low values of stresses or strains in the FRP reinforcement means low tensile

forces transferred to the CFRP from the total applied load. Low tensile forces in the

CFRP means that the corresponding compression force in the intact concrete has a small

value and hence the total enhancement in the punching shear capacity is also small,

based on what was explained in 2.2.

Figure 5-11 shows that the debonding does not occur to all the FRP strips, but there are

some local areas with higher stresses near the slab edge. It is evident that the CFRP

materials contribute to an increase in the capacity until the bond between the FRP

material and the concrete fails [15]. Debonding cracks appear at loading steps after the

ultimate punching shear capacity, which results in a separation of the CFRP from the

concrete substrate. These cracks are located along the edges of the length of the

strengthening material. They appear simultaneously to the accelerated concrete cracking

after the CFRP debonds from the slabs without rupturing the CFRP material.

171

Figure 5-11 Damage in the cohesive elements and the debonding in the CFRP at the

ultimate load

5.8 Behaviour of slab-column connections that fail initially in flexure and which

are strengthened externally by CFRP sheets

In order to study the effect of using CFRP in strengthening slab-column connections,

the flexural reinforcement ratio of the un-strengthened slab is changed to different

values to vary the failure mode from flexure to punching. Changing the failure mode

can be achieved by reducing the slab flexural reinforcement area. This reduction can be

performed by either reducing the number of bars or using the same number but with

smaller diameter. In this study, and in order to keep the even distribution of the bars in

the slab with respect to the initial slab (Walker and Regan), the flexural reinforcement

area is reduced by using a smaller bar diameter. Figure 5-12 shows the percentages of

the flexural reinforcement ratio with respect to the initial un-strengthened slab

reinforcement ratio. In addition, it shows the ratio of the ultimate punching shear

capacity with respect to the un-strengthened slab ultimate punching shear capacity. The

study is conducted based on strengthening the slabs in the orthogonal configuration

based on the previous studies. As the area of the CFRP sheets cannot be increased by

increasing the CFRP width, the area is increased by increasing the thickness. Thus, the

study is conducted by using (0.6, 1.2 and 1.8) mm CFRP thickness.

172

Figure 5-12 Effect of reducing the steel reinforcement ratio

Slabs with reinforcement ratios of (50 and 62.5)% of the Walker and Regan slab

reinforcement ratio fail by flexure. Strengthening these slabs gives only a small increase

in the ultimate strength because the failure takes place in the slab centre while

strengthening is around the columns, which makes the CFRP reinforcement less

effective. Changing the failure mode to flexural punching by using reinforcement ratios

(75-87.5)% of the Walker and Regan slab reinforcement ratio causes an increase in the

ultimate strength of more than 20%. This can be attributed to the ability of the steel

reinforcement to accommodate more stresses before failure, causing a reduction in the

slab stiffness by the formation of a horizontal plateau associated with the formation of

other radial and tangential flexural cracks over the column. Slabs with a reinforcement

ratio similar to the Walker and Regan slab reinforcement ratio fail by punching shear

causing a moderate increase in the ultimate strength of these strengthened slabs. This is

because the CFRP sheets that resist the punching shear are small in area.

5.9 Conclusions

In this study, many limitations have been applied to the slab-column connection like the

clear distance between the column edge and the loading and CFRP thickness. All these

limitations affected the increase in the ultimate capacity. So that the maximum was

about 21%, as in the case of using an orthogonal configuration in addition to side CFRP

strengthening, even though it reduced the total deflection. This increase is the maximum

value that can be achieved for strengthened slabs based on the previous study related to

CFRP configuration, location and thickness.

0.95

1

1.05

1.1

1.15

1.2

1.25

45 50 55 60 65 70 75 80 85 90 95 100 105

No

rma

lise

d l

oa

d

Reinforcement ratio (% of Walker and Regan slab steel reinforcement ratio)

Maximum load (0.6) Maximum load (1.2) Maximum load (1.8)

173

For slabs with low reinforcement ratios and which initially fail by flexure, a small

increase in the loading capacity is apparent due to the small size of the CFRP sheets

used in the analysis. However, increasing the reinforcement ratio can increase the total

ultimate punching capacity.

The effect that the bond between FRP and concrete has on the results should not be

forgotten; it can be seen that the debonding does not happen according to the required

bonding length chosen based on the sensitivity analysis, even though there is an

increase in the stresses transferred to the CFRP sheets on the downside of the slab.

174

6. Chapter 6 Experimental Programme Set-up

Based on the previous studies mentioned in the literature review, it is well demonstrated

that there are many different strengthening techniques that can be used to strengthen

slab-column connections. All these techniques have a significant effect on the punching

shear behaviour. They are able to increase the ultimate strength of the connection whilst

with decreasing or maintaining the same ductility.

The details of the experimental work conducted in the Structure and Concrete

Laboratory at the University of Salahaddin, Kurdistan Regional Government, Iraq are

presented here. In the experimental work, structural tests were conducted on four slab-

column connections. Some of these slabs are strengthened with FRP whether there is an

opening or not, while one slab is kept un-strengthened to act as the control slab. The

objective of this experimental work is to study the effect of strengthening a slab at its

corner column connections to increase their capacity and investigate how to achieve the

best strengthening scheme in both cases, with and without an opening.

Material properties are also studied by testing some samples in order to obtain the

properties that are later used in the numerical modelling. This chapter presents the

structural tests of these slab-column connections with their details, preparation methods,

instrumentation, experimental set-up and testing procedure.

6.1 Choice of specimen type

The range of the specimens used in the investigations quoted previously was quite large,

and any slab-column connection specimen is a legitimate subject to being studied based

on the targeted results. Many theoretical models have been proposed based on the

differences between different models and comparison with experimental work.

However, a complete theory for the punching shear strength of slab-column connections

strengthened with FRP has not been delivered, and thus actual theoretical approaches

are completely reliant on empirical data. In this situation, it is necessary to take into

account the suitability of experimental models in terms of their ability to simulate real

conditions using prototypes. One extremist of the modelling is to use specimens with

full-scale panels to represent a real-life situation. These models are structurally realistic

175

in order to avoid the problems regarding the boundary conditions, but, as a result, they

are very expensive and need a very large laboratory area in which to test them.

Otherwise, it is necessary to test some additional specimens in order to study different

experimental parameters. At the other extremist, conventional punching specimens can

be used to study the zone around a single column. These models can allow a relatively

large number of specimens with various boundary conditions. In order to make some

judgement on the relative characteristics of the various models between these extremes,

it is necessary to take into account the target of the study in order to reduce some

redundant parameters that may not be really important to a specific test.

The first step is to decide the specimen geometry because it should be large enough to

be realistic and at the same time small enough to be investigated effectively. Then the

choice of loading method is another important issue. The specimen should be loaded

based on the intended results that can be extracted from the test.

6.1.1 Details of the specimens

The purpose of this study is to investigate the punching shear behaviour of the slab at

corner column connections strengthened by CFRP with and without an opening in the

column region. Therefore, the specimens are provided with sufficient flexural and

strengthening reinforcement. The layout of the specimens and their geometry with

reinforcement and strengthening details are presented in Figure 6-1-(a-c). All the slabs

were 2 × 2 m square with a thickness of 80 mm. These slabs are attached to four 160 ×

160 mm square, 720 mm high columns cast monolithically with the slab, as shown in

Figure 6-1-c. The slabs are reinforced with Ø6 mm reinforcing steel with a clear

distance of 90 mm at the bottom in both directions, while the top reinforcement is 4Ø6

mm extended to a distance of 650 mm over the column region in both directions with a

clear distance between them of 200 mm. The clear concrete cover to the flexural

reinforcement is 10 mm to give an effective slab depth of 64 mm at the top and bottom.

The columns are reinforced with 4Ø12 mm diameter standard ribbed bars as the main

reinforcement with ties of Ø6 mm distributed at 150 mm centres, as shown previously

in Figure 4-2. Table 6-1 gives the details for all the slabs.

Slab 1 is the control specimen, which is unaltered, i.e. without openings and without

CFRP strengthening. This is designed to fail in punching shear at a total load of 36

176

kN/m2 (including self-weight) based on Eurocode 2 [37] to ensure pure punching shear

failure. Slab 2 is similar to the control specimen but is strengthened with CFRP sheets

of a width of 50 mm and a thickness of 0.6 mm around the corner columns, as shown in

Figure 6-1-a. The remaining two slabs, 3 & 4, have openings near the slab-column

intersection, as shown in Figure 6-1-b. For the slabs with openings, the investigated

opening size is set not to exceed 80% of the square column size in line with general

recommendations [106]. Consequently, an opening size of 100 × 100 mm is formed

close to each column. All the strengthened slabs have the same CFRP sheets bonded

externally to their top surface (i.e. the loaded surface), around the four columns in an

orthogonal configuration. The CFRP sheets extend along the slab surface by 500 mm

for all strengthened slabs. In all cases, an additional length of CFRP extends 80 mm

down the sides of the concrete at the slab edges. In general, the CFRP sheets are

attached adjacent to the slab-column connection at a distance of 15 mm from the

column face due to practical constraints.

(a) Slab 2 plan view (b) Slabs 3 and 4 plan view

(c) Slabs 1-4 end elevation

Figure 6-1 Specimen geometry and strengthening configuration

All the dimensions are in mm.

The CFRP sheets are extended beyond

the slab edges by 80 mm.

177

Table 6-1 Details of the slab test series

Specimen Bottom steel

reinforcement

Top steel

reinforcement

Column reinforcement

and stirrups CFRP strengthening

Existence

of opening

slab 1

Ø 6 mm @ 90

mm with concrete clear

cover of 10

mm

4 no. Ø 6 mm @ 200 mm

over each

column

extending 650 mm in each

direction with

concrete cover of 10 mm

Longitudinal reinforcement: 4 Ø 12

mm

Stirrups: Ø 6 mm distributed every 150

mm

No strengthening No opening

slab 2 Strengthened by orthogonally

distributed CFRP No opening

slabs 3& 4

Strengthened by orthogonally distributed CFRP and additional

CFRP around the opening

One

opening

near each column

6.1.2 Experimental parameters

The study of punching shear behaviour in slab-column connections implies three main

parameters: the concrete‟s compressive strength, flexural reinforcement ratio and the

column‟s geometry [159]. However, in this study, the focus is to study the effectiveness

of strengthening slabs at corner column connections with and without the existence of

an opening, so the parameters included are more related to the strengthening scheme

rather than to the materials or the geometry. All the previous parameters studied in the

numerical study, like the CFRP thickness, the CFRP configuration with respect to the

column interior edge and their distance from the column, are fixed now.

6.2 Properties of the materials used in the testing

Material properties are determined by conducting isolated tests on each material as

follows:

6.2.1 Concrete

Before starting the experimental study, it is necessary to study the material properties of

the concrete mix and to find the best concrete mix that gives the required compressive

strength at 28 days. A concrete mix that gives the required cylinder compressive

strength of 37.4 MPa is designed based on ASTM-C33 [160], while an additional eight

trial mixes are studied by casting nine 150 × 150 × 150 mm cubes from each mix and

testing them at 28 days, as in Table 6-2.

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Table 6-2 Compressive strength of the concrete cylinders used in this study

No. Mix contents Content ratios Fc' at

28 days

(MPa)

1 Cement : Sand : Gravel : Water 1 : 1.35 : 2.02 : 0.430 36.53








Control Cement : Sand : Gravel : Water 1 : 1.40 : 2.11 : 0.446 34.53

After that, the third mix was chosen to be used in the casting of the slab-column

connections as it is the best one to give the required concrete compressive strength of

37.4 MPa at 28 days. Thus, the required materials for producing one cubic metre of

concrete are presented as shown in Table 6-3.

Table 6-3 Concrete mix proportions

Cement

(Kg)

Fine aggregate

(Kg)

Coarse aggregate

(Kg)

Water

(Kg or Litter)

466 582.5 871.5 185

The flat slab specimens were constructed with a normal-weight ready-mix concrete

using a maximum aggregate size of 10 mm. They were cast on the same day from the

same batch by using a mixing truck provided by Iberia Company in Erbil and cured for

28 days. Six concrete cylinders of 150 × 300 mm were tested according to ASTM C496

[161] and ASTM C496 [162] at 28 days in order to find the average concrete

mechanical properties, as shown in Table 6-4. Further to this, twelve 150 × 150 × 150

mm cubes (in place of cylinders due to practical constraints) were used to determine the

compression strength on the day of testing based on BS1881-P116 [163].

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Table 6-4 Concrete properties

6.2.2 Steel reinforcement

Two types of steel reinforcement are used in the slab-column connections: Ø6 mm

reinforcement is used for reinforcing the slabs and as stirrups for the columns, while

Ø12 mm reinforcement is used to reinforce the columns. The tensile properties of the

steel reinforcement are also investigated by testing samples to find the yield strength,

ultimate strength and the elongation based on ASTM A370 [164]. Table 6-5 shows the

mechanical properties of the steel rebars.

Table 6-5 Mechanical properties of the steel rebars

6.2.3 FRP sheets

One type of unidirectional carbon fibre sheet is used in this study. The material was

provided by Easycomposites, UK [148], with a cross-sectional area of (50 × 0.6) mm. It

is usually used together with Weber.tec EP structural adhesive [165] to form the

composite strengthening system in accordance with Concrete Society Technical Report

55 [166]. This type of carbon fibre sheet is a high-strength fibre with Young's modulus

of 240 GPa and a tensile strength of 4000 MPa, as provided by the manufacturer.

Adding the epoxy to the carbon fibre sheets forms a composite with material properties

that differ from its constitutive material properties. Therefore, five samples are prepared

and tested based on ASTM D30 [167] in order to find the specific material properties of

these composites, as shown in Table 6-6.

Slab

Properties at 28 days

Age at

test

(days)

Cube

compressive

strength at

test days

(MPa)

Cylinder

compressive

strength

(MPa)

Tensile

strength

(MPa)

Modulus of

elasticity

(GPa)

Slabs 1&2 37.8 2.9 28.3 70 49.2

Slabs 3&4 37.8 2.9 28.3 71 49.3

Diameter

(mm)

Young Modulus

(GPa)

Yield stress

(MPa) Yield strain

Ultimate stress

(MPa)

6 198 597 0.003 629

12 167 570 0.0034 655

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Table 6-6 Properties of fibre reinforced polymer composite materials

Material Thickness

(mm)

Modulus of Elasticity

(GPa)

Shear Modulus

(GPa)

Tensile Strength

(MPa)

Dry Fibre 0.6 240 25 4000

Epoxy Resin - 5 1.8 19

Composite sheet 0.8 96.3a, 6.7

b 2.8(xy),2.5(yz) 911

a,40

c

a parallel to the fibre direction based on equations in Appendix A and the experimental test

b perpendicular to the fibre direction based on equations in Appendix A

c perpendicular to fibre direction based on the manufacturer‟s details

6.3 Preparation of the test specimens

6.3.1 Form work building and the mould

Plywood plates are used in forming the mould for all the slab-column connections in

order to allow the columns to be cast monolithically to the slab. The samples are cast in

a reverse way, which means that the slab is down and the columns are up. Before

casting the concrete, a thick layer of nylon foil is used to cover the mould in order to de-

mould the slab-column connection easily without any damage. The slabs are secured by

four steel bars of a diameter 16 mm acting as lifting anchors from down in order to

enable safe lifting and placing. Figure 6-2 shows the mould with the reinforcement

before casting.

Figure 6-2 Column-slab reinforcement placed in the mould

181

6.3.2 Reinforcement

The internal steel reinforcement and the external CFRP sheets are cut to the required

lengths based on the experimental plan for casting and strengthening. CFRP sheets are

easy to cut using hand scissors, while the steel reinforcement is cut by using big steel

scissors. The column reinforcement is cut by using a power disc cutter and then bent to

the required lengths. The slab reinforcement is assembled by using galvanised coated

wires to bind the reinforcement to each other. Plastic hangers were used to lift both the

bottom and top reinforcements to their specific location in the slab-column connection.

The CFRP reinforcement is attached to the concrete surface by using Weber.tec bonding

adhesive. Figure 6-3 shows the complete reinforcement of one slab-column connection

positioned in the mould and ready for concrete casting.

6.3.3 Concrete casting and curing

The concrete mix is provided by a mixing truck based on the previous ratios. One slab-

column connection is cast at a time. When concrete is placed in the mould, a hand

vibrator is used to shake the concrete for preventing of air bubbles formation. After

casting, the top surface is levelled by using a hand trowel to ensure a smooth finish. The

test slabs, control cubes and cylinders are cast at the same time and from the same

concrete batch. One hour later, the slabs and the control cubes and cylinders are covered

with nylon sheets to stop the moisture from escaping during the first day of casting. The

next day, the moulds are opened and the slabs are soaked with water for 28 days, and

later they are kept at room temperature until the testing day. In addition, the control

cubes and cylinders are also continuously cured in water.

Figure 6-3 Complete reinforcement of one slab-column connection

182

6.3.4 Concrete surface preparation

To develop a full bond adhesion between the CFRP and the concrete surface, the

surface is prepared by cleaning and levelling the concrete substrate. A surface grinder

with a vacuum cleaner is passed over the concrete surface until it is uniform and the

exposed aggregate appears. The concrete surface is delineated in order to locate the

CFRP in the exact required location, as shown in Figure 6-4.

Figure 6-4 Surface preparation and delineation

6.3.5 Application of the adhesive and applying the CFRP sheets

After preparing the concrete surface, the CFRP is also prepared by spreading it out and

preventing it from crimping. The bonding adhesive is applied to both the CFRP and the

concrete surfaces, taking care to avoid air bubbles. The adhesive layer is formed by

mixing 2/3 Epoxy resin and 1/3 Epoxy hardener as provided by Weber Building

Solutions, UK [165]. The CFRP is attached to the concrete surface by hand, achieving

adhesion and without causing a loss in the required adhesive thickness of 3 mm, in

accordance with Concrete Society Technical Report 55 [166]. Finally, the excessive

adhesive is removed from the sides of the CFRP sheets to keep the surface as clean as

possible.

6.4 Instrumentation

Each slab-to-column zone is instrumented to provide detailed information regarding the

structural behaviour throughout the entire loading history. The data recorded in the test

comprise loading, deflections, and strains in the steel and CFRP sheets. Loading is

applied gradually at a rate of 3 kN/min from a hydraulic jack with a capacity of 2500

kN. To apply a uniformly distributed load on the slab, a steel frame consisting of one

plate with dimensions 1500 × 1500 × 20 mm thick stiffened by eight 50 × 50 × 2 mm

183

square hollow sections is used (Figure 6-5). Below the hollow sections, 16 arrayed steel

pads each with dimensions 50 × 50 × 10 mm at 500 mm centres are used to deliver the

patch loads to the slab surface, thus approximating a uniformly distributed load, as

shown in Figure 6-6. All the four columns of each slab are designed to be pin-supported

at the base. The deflection profile of the slab is measured via an LVDT at the centre of

its lower face.

(a) Schematic view

(b) Laboratory photograph

Figure 6-5 Test set-up for the RC slab

Hydraulic Jack

Steel plate 1500×1500×20

mm

Hollow section 50×50×2

mm

Loading Patch

50×50×10 mm

Specimen

184

Figure 6-6 Array of the loading patches

6.4.1 Steel reinforcement strain gauges

To measure the strains in the steel, six strain gauges are fixed to the rebar, as shown in

Figure 6-7. These strain gauges are distributed on the locations of the maximum strains

over the column, mid slabs and the mid-distance between the columns. The used strain

gauges are foil-type, two-wire temperature compensating, with a resistance of 120

ohms, a gauge length of 6 mm and base material dimensions of 3.4 × 10 mm. The steel

reinforcement surface is refined by using a file in order to attach strain gauges. Strain

gauges are bonded to the surface of the steel reinforcement by using the proper adhesive

and they are coated with specialised silicon to protect them during casting and prevent

water from affecting them.

185

Figure 6-7 Arrangement of steel strain gauges

6.4.2 FRP reinforcement strain gauges

In the strengthened slabs, three more strain gauges are attached to the CFRP sheets to

measure the average longitudinal strain, as shown in Figure 6-8. The same type of strain

gauge is also used for the CFRP. The strain gauges are attached to the CFRP by using a

specialised adhesive and then connected to the acquisition system.

(a) Slabs without openings (b) Slabs with openings

Figure 6-8 CFRP strain gauges in the slabs

(a) Top steel reinforcement (b) Bottom steel reinforcement (full

rebar layout omitted for clarity)

FSG3 FSG2

FSG1

FSG3

FSG2

FSG1

186

6.4.3 Linear variable differential transducers (LVDTs)

The deflection profile of the slab is measured via an LVDT at the centre of its lower

face, as shown in Figure 6-9. The needle of the LVDT is positioned on the concrete

surface after the surface has been perfectly cleaned and smoothed.

Figure 6-9 LVDT on the slab centre

6.5 Test set-up and procedure

The test set-up is designed in order to bear twice the entire expected applied load from

the loading rig. It consists of three main parts in addition to the testing frame in the lab,

as shown previously in Figure 6-5. The slab-column connections are tested in an upside-

down position like the real situation in real structures. This is conducted according to

the test set-up available in the laboratory by applying the load at 16 steel loading

patches distributed equally over the slab surface. This testing set-up causes tensile

cracks in the bottom soffit of the slab and over the column region.

6.5.1 Supporting frame

All the four columns of the slab-column connections are supported on a steel section

that rests on the testing frame. This section consists of W12 × 19 wide flange steel

beams with a flange width of 100 mm to bear twice the proposed loading and to stop the

frame from bending upward in the frame midspan or downward at the ends.

Furthermore, this frame is fixed from the middle to the testing frame during the whole

test. Steel plates of dimensions 185 × 185 × 10 mm are used in order to allow the

column to rest on it, as shown in Figure 6-10.

187

Figure 6-10 Supporting frame for the rig test

6.5.2 Binding frame

A steel frame is used to prevent the horizontal movement of the columns. Therefore, the

slab-column connection will be simply supported without moment transfer to the

supports. This frame consists of four square spaces connected to each other by a

rectangular tube of dimensions 100 × 50 × 2 mm. These spaces consist of steel plates of

185 × 120 × 20 mm to act as a frame support, as shown in Figure 6-11.

Figure 6-11 Binding frame for the rig test

6.5.3 Loading frame

The applied load is distributed over 16 steel patches to be transferred to the slab-column

connection and to work as a uniformly distributed load on the whole slab surface. At the

beginning, the load is applied to a steel plate of 1500 × 1500 × 20 mm; in return, it

transfers the load to tubes of 50 × 50 × 2 mm and the small steel patches. The choice of

the steel plate and the tubes is to increase the frame stiffness in order to protect the

frame from undesired deflection in the centre, which would causes incorrect readings.

The frame was designed to work in an elastic range without any plasticity, which allows

the frame to be in agreement with the applied load and deflected concrete slab and

return to its original shape after loading removal. Furthermore, choosing less thick

188

plates causes either a large deflection in the frame mid-point, which could cause lifting

to the far ends of the frame, or a cut in the welding of the plate to the steel tubes. This is

what can cause incorrect loading application. In contrast to this, a thicker plate would

not add more stability to the frame but could increase the initial dead loads applied to

the concrete slabs and thus could add more initial cracks before loading.

The loading frame is designed and analysed in ABAQUS as an indeterminate structure

with multi-degrees of freedom and rests directly on the concrete slab. The study was

conducted by applying the load on the steel frame in which it transfers the loads to the

concrete slab and thus the supports below the concrete columns. When the steel frame

deflects, the slab deflects in a agreement with the steel frame. Applying the load to the

frame centre without fixation to the loading patches to the concrete surface can result in

them lifting. But, due to the high stiffness and rigidity of the frame, in comparison with

the concrete slab, especially in the frame centre (due to the additional cross stiffeners at

the middle of the central panel) further to the short distances between the cross tubes,

the frame would work in a agreement with the deflected concrete slab under low values

of applied load and deflection (141.6kN and 46.5 mm respectively). In addition, the

steel frame is working in the middle of the slab due to its short length in comparison to

the slab length. This makes the frame work under a concave bending only under the

loading in contrast to the slab which has a convex bending near the supporting columns.

This principle confirms the continuous contact between the frame and the concrete slab

under the whole loading application.

Figure 6-12-a shows the deflected shape in the vertical direction (Y-direction) of the

whole slab and the steel frame under the ultimate failure load of the concrete slab. It can

be seen that both the steel frame and the concrete slab deflect with the same deflection

value, which confirms the continuous contact between them. Furthermore, Figure 6-12-

b shows one corner of the slab with part of the steel frame. It shows that there is no

uplifting of the far end of the steel frame due to the load application and it deflects

similar to the slab deflection. To provide more understanding of the load application,

Figure 6-13 shows a comparison between using the whole frame in the loading

application and using only the patch loads with an equally distributed load on each

patch. It is clear from Figure 6-13 that using the patch loads only makes no big

difference to the whole response compared to using the whole frame. Using the whole

189

frame causes fewer deflections for the same load in comparison with using patch loads

only because the stiffness of the frame prevents more deflections from developing,

especially after concrete cracking. But the total difference in both cases is not more than

1%. Furthermore, the problem with using the whole frame with the whole slab is that it

is a very time-consuming method. Thus, in future studies, a quarter of the slab with only

the loading patches will be used.

(a) Deflected shape of the whole steel frame and the concrete slabs

(b) One corner of the concrete slab with part of the steel frame

Figure 6-12 Deflected shape of the steel frame under a load of 150 kN

190

Figure 6-13 Load deflection comparison between using the whole frame or the loading

patches only

The length of the loading frame was limited to allow enough distance for the CFRP

sheets around the column, and to prevent loading application over the CFRP sheets.

Figure 6-14 shows the loading frame from the bottom side to explain the arrangement of

both the steel tubes and the loading patches.

Figure 6-14 Loading frame

6.5.4 Testing procedure

The slabs are instrumented to provide detailed information throughout the entire loading

history. All the information is collected by using an electronic data logger system

shown in Figure 6-15 and recorded for each load increment up to and including the final

collapse load. Before testing, all the measuring equipment like the strain gauges and the

LVDT is carefully checked to make sure that it has been properly installed and

connected and the initial readings are recorded at the zero loading.

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40

Load

(K

N)


The whole frame

Patch loads only

191

During the test, the specimens are carefully inspected by applying the load gradually.

The load is monitored during the test by a display connected to the hydraulic jack.

During the loading, the entire load-deflection, load-strain in steel and CFRP is

monitored until slab failure. The test is terminated when a failure occurs by the column

being penetrated via the slab. The concrete crack path is carefully studied for all the

cases.

Figure 6-15 Data Logger used in the test

192

7. Chapter 7 Analysis of the results

A general explanation of the total data acquired experimentally and numerically for the

connections is dealt with in this chapter. Although the test outcomes might provide

profitable knowledge on the punching shear of the slab, a numerical study is also

conducted in order to gain further insight into the structural behaviour of the slabs and

to validate the experimental results. A general interpretation of any discrepancy from

the usual behaviour is provided based on the ultimate punching shear capacity and the

failure mode.

The comparison between the experiments and numerical results is based on the

following aspects of structural behaviour:

1- Crack pattern.

2- The failure mode.

3- The load-deflection response.

4- Strains in the steel and the FRP reinforcements.

5- The ultimate load capacity of the slabs.

In order to explain the results briefly, they should be connected to each other by at least

one link. The load is considered the most common link to make the comparison simpler

and clearer. Therefore, the load-deflection, load-steel reinforcement strain and load-

CFRP strain relationships are prepared and compared. The ultimate slab-column

connection punching shear capacity and the failure mode are also investigated in order

to give the general behaviour of the samples. Using CFRP sheets and their effect in

strengthening is also discussed briefly.

7.1 Slabs without openings

7.1.1 Crack pattern

Both slabs 1 and 2 in the experimental and numerical studies failed by punching shear

with the inherent brittle characteristics but at different load levels based on the presence

of CFRP, as shown in Figures 7-1 and 7-2. Cracking is observed first on the top surface

of the slab-column connections close to the inner corner of the column, which then

propagated to the free edges of the slab; cracking is then observed on the lower surface

193

of the slab at slightly higher loads. No cracking developed parallel to the diagonals of

the slab. With increasing load, cracks propagate across the free edges following an

inclined path away from the column edges to give torsional cracks and punching shear

failure. Torsional moments develop simultaneously with bending moments and shear

forces when the external loads act transversely at a distance from the supporting

columns [14], as shown in Figure 7-1.

(a)

(b)

Figure 7-1 Punching shear failure in (a) slab 1 (b) slab 2

The typical inclination of punching shear cracks is shown in Figure 7-1 for slabs 1 and

2. There is only one sheet that bridges the shear crack in each direction. In addition, the

tensile resistance of the CFRP sheets perpendicular to their longitudinal axis is small;

therefore, they will be less effective in resisting the corresponding tensile stresses and

shear crack formation in that direction. In view of this, shear crack propagation away

194

from the column face is approximately the same in both slabs. Based on these

observations, it can be concluded that using CFRP reinforcement has no major effect on

the position of the punching shear crack, as suggested by other researchers [6, 55 and

96]. The concrete damage plasticity model adopted in the finite element model used in

ABAQUS does not directly show the direction of the cracks, but it assumes that the

direction of the vector normal to the crack plane is parallel to the direction of the

maximum principal plastic strain in concrete [115]. Figure 7-2 shows the maximum

principal plastic strains at the slab-column intersection of slab 1 at the ultimate

punching load. It can be seen from the figure that the critical shear crack is formed at

the intersection point of the slab-to-column zone, causing a reduction in the ability to

carry the compression stresses to the column, as described by Muttoni [23]. In slab 2,

the CFRP sheets debond from the concrete substrate near the shear crack after the peak

load due to the relatively high vertical displacement across the shear crack, as shown in

Figure 7-3. It should be noted that, up to ultimate load in the experiments, CFRP

debonding does not occur in any of the strengthened slabs. Figure 7-4 shows the

numerical model‟s stiffness degradation in the cohesive elements for slab 2, revealing

that the maximum stiffness degradation is globally less than 1.0 (where a value of 1.0

refers to the onset of debonding). Close examination of Figure 7-4 indicates that some

localised areas are approaching debonding, particularly at the very edges of the CFRP

along the sides of the slab, which is consistent with the experimental behaviour shown

in Figure 7-3.

Figure 7-2 Numerical model principal maximum plastic strain at peak load indicating

punching shear failure in slab 1

195

Figure 7-3 Punching shear failure in slab 2

Figure 7-4 Stiffness degradation in slab 2

When the slab reaches the ultimately applied load, failure occurs that appears to be

caused by cracks that propagate towards the slab-column intersection causing a sudden

decrease of the applied load from its peak of 141.2 kN. The stress state in the vicinity of

the column prior to the failure indicates a state of triaxial compression, and thus all the

compressive stresses are transferred to the column by the formation of an idealised

compression strut. Figure 7-5 shows the intersection point of the slab-column in the step

before failure. It also shows the formation of the idealised compression strut.

196

Furthermore, there are some tensile stresses still working in that region perpendicular to

the idealised compression strut.

Figure 7-5 Maximum principal stresses of concrete before failure load in slab 2

Muttoni [23] in 2008 stated that the punching shear strength of a slab decreases due to

the formation of a shear crack propagating through the slab thickness. At the flat slab-

to-column zone, a compressive stress field which may be idealised as an inclined strut is

generated through the depth of the slab and carries the shear forces to the column. In the

lead-up to punching shear failure, tensile stresses are generated transverse to the

inclined strut, leading to cracking. The shear strength of the section decreases

progressively as the shear crack opens, eventually leading to punching shear failure.

Table 7-1 gives a summary of both the load at first cracking and the ultimate load with

the corresponding deflections and failure mode of the slabs in the experimental study. It

can be seen that using CFRP delays the onset of concrete cracking from 34.2 kN to

about 38.6 kN for slab 2. This may in part be attributed to the improvement in rotational

resistance provided by the CFRP sheets as they bridge across the diagonal shear crack

and limit crack opening. Theoretically, decreasing the discontinuity caused by the slab

rotation in the critical shear crack region would lead to a reduction of the overall mid-

span deflection.

197

Table 7-1 Summary of experimental results

7.1.2 Modes of failure and load capacity

When concrete slab-column connections are loaded up to failure, the concrete between

the shear crack tip and the slab-column intersection is in a triaxial state of compressive

stress, but the concrete strain corresponding to the smallest compressive stress will be

changed to a tensile strain and it is oriented approximately normal to the shear crack

[168], as shown in Figure 7-6. The compressive stress in this direction has a confining

effect that prohibits the shear crack progressing through the compression zone.

However, when the confining pressure is reduced due to the horizontal cracking,

punching shear failure will take place suddenly.

Figure 7-6 3D state of stress in the slab-column connection at failure

Slab-column connections are continuously loaded until the punching shear failure takes

place. After that, the slabs are unable to accommodate more loads and hence the loading

and the corresponding deflection are considered to be at their ultimate point.

slab

Load at first

cracking

(kN)

Mid-span

deflection at

first cracking

(mm)

Ultimate load

(kN)

Ultimate mid-

span deflection

(mm)

Failure

Mode

1 34.2 1.2 127.4 33.8 Punching

2 38.6 1.0 141.2 46.5 Punching

198

The response of the structure – like the load-deflection curve, strains in the steel and

CFRP reinforcement, and the crack pattern – can give an indication of the final failure

of the slab-column connection.

For slab 2, no cracks can be observed below the CFRP sheet. Nevertheless, some cracks

can be observed away from the CFRP sheets.

As the ultimate punching shear capacity was reached, a loud noise was heard due to the

slab failure by punching. After failure, the CFRP sheets were investigated and it was

found that they debonded from the concrete substrate, as shown in Figure 7-3.

The general behaviour of the samples indicates a stiff pre-cracking stage followed by a

nonlinearly elastic stage until the punching shear failure suddenly causes a sharp drop in

the load-deflection response. In general, the stiffness of the strengthened slab is

increased by using CFRP sheets. This increase is due to the confinement of the concrete

on the tension side and effect of the CFRP in redistributing the tensile stresses near the

slab-column intersection.


As discussed earlier in 6.5.3, the application of the load to the frame causes a uniform

distribution to the 16 loading patches distributed on the slab surface. In return, these

loading patches will uniformly distribute the load to the whole surface of the slab and

equal reactions can be obtained on each supporting column. In the numerical study, a

quarter of the slab was analysed. Thus, reactions from the numerical study were

multiplied by 4 to obtain the total applied load which was compared with the

experimental load. Figure 7-7 shows the comparison between the experimental and the

numerical results for the slabs without openings. Referring to the previous mesh

sensitivity and tension stiffening analysis mentioned in 4.3.1.2 and 4.3.2.1, a mesh with

an element size of 20 mm and six elements through the slab thickness with exponential

tension stiffening gives the numerical results calibrated to those in the experiment. It is

noticed that the numerical model gives a reasonable agreement with the experimental

results. In both slab cases, the numerical model over-predicts the point of initial

cracking. The difference in the pre-crack behaviour may be due to the variation in the

tensile strength and Young‟s modulus in the specimen compared to the properties

199

adopted from the cylinder test, as was explained in 4.3.2.2 and 4.3.2.3. Similarly, the

full bond assumption in the numerical model may lead to a stiffer response in the pre-

crack regime [132].

The load-deflection measured at the slab centre for both slabs 1 and 2 in the experiment

and numerical simulation is the base of all other results. The ultimate load-carrying

capacity of slab 2 was 141.2 KN, about 11% more than that of slab 1.

It can be noticed that, before concrete cracking, slab deflection is low and the load-

deflection relationship is completely linear with high slab stiffness. Therefore, the

stresses and strains vary linearly across the slab thickness. On the onset of cracking, the

composite material behaves elastically in tension and compression. A flexural crack or

hinge occurs when there is a sudden decrease in the slab load-carrying capacity, as seen

in Figure 7-7.

Figure 7-7 Comparison between experimental and model predictions for slabs 1and 2

In slab 2, the external CFRP reinforcement has delayed the onset of concrete cracking

from 34.2 kN to about 38.6 kN by bridging the discontinuity at the critical crack region

and limiting crack opening, leading to a small reduction in the slab central deflection

compared to slab 1 at the same load level. In decreasing the discontinuity at the slab

rotation in the critical shear crack region, a reduction in the deflection is also observed

in the early steps of loading, causing stiffer behaviour than seen in slab 1. For slab 2, the

presence of the CFRP ultimately led to a modest increase in peak load and deflection. In

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addition, these CFRP sheets try to prevent the slab from shear failure by confining the

concrete materials and transferring tensile stresses perpendicular to the shear crack.

Despite the presence of strengthening, there is no major difference between the

transferred biaxial bending moments in slabs 1 and 2. Therefore, the propagation of the

shear crack is approximately the same in both slabs, as shown in Figure 7-1.

Increasing the applied loading causes other flexural cracks approximately perpendicular

to the first flexural cracks. When the concrete slab cracks, the tensile stresses are

transferred to the steel or CFRP reinforcement crossing the crack, while the uncracked

section still carries a certain amount of stress. As a result of that cracking propagation,

the section‟s neutral axis is shifted towards the compression face. After that, the load-

deflection curve is continuously ascending until the final shear cracking passes the

compression side and causes the punching shear failure.

7.1.4 Steel strains

Figure 7-8 shows a comparison between the experimental and the numerical results for

the strains in the rebar for both slabs 1 and 2. It can be seen that both the numerical and

the experimental results are in good agreement throughout the entire loading range.

(a) Strain gauge 1

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(b) Strain gauge 2

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(e) Strain gauge 5

(f) Strain gauge 6

Figure 7-8 Steel reinforcement strain for the unstrengthened and strengthened slabs in

experimental and numerical model

Parts of the rebar in the top mesh over the columns reach a yield strain of (3000

microstrains) before the punching shear failure takes place. This is common in punching

shear scenarios where prior yielding of the rebar occurs locally around the column [17].

In the experiment, strains at gauges 1 and 2 and the corresponding position in the

numerical model show a reduction before failure at a load level of 107 kN, as shown in

Figure 7-8-(a and b). A possible explanation is that concrete crushing in the

compression zone has initiated and this causes a redistribution of strains in this area.

This is confirmed with the numerical modelling, which indicates the concrete‟s

compressive strength has been reached at a similar load level, as shown in Figure 7-9, in

which the column was removed for clarity to show the stress distribution through the

slab thickness.

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203

Figure 7-9 Stress state in concrete (N/m

2) at load level 107 kN

At loads close to failure, yielding began in the rebar of the bottom adjacent to the slab

edges and spread along the centre lines when the structure failed in punching. Strain

gauges 3 and 4 yielded at nearly the ultimate load, while strain gauges 5 and 6 did not

yield up to ultimate load. This is similar to the information provided by Eurocode 2 [37]

and ACI [169]: that more loads are transferred to the column strip in the mid-distance

between columns on the slab edges than are transferred to the middle strip.

The strain gauges were placed on the steel rebars in the same locations with respect to

the column but in orthogonal directions. In the vertical direction with respect to the slab

thickness, they have different locations as in mesh they must be placed over each other.

This difference in locations caused the differences in total strain readings in orthogonal

directions, as shown in Figure 7-8.

7.1.5 FRP strains

Figure 7-10 shows the strains in the CFRP reinforcement from both the experiment and

the numerical model. Strains are measured adjacent to the interior column corner where

maximum biaxial bending and torsional moments are expected. Therefore, the location

of these strain gauges should be near the zone where the critical shear crack develops. It

can be seen that the strain profile of the CFRP sheet is approximately compatible with

the steel strain profile, even though the locations of their strain gauges are different,

which can prove that the structural system is working in harmony with each of its

components. Before cracking, the increase in the CFRP strain is approximately linear

204

with a few strains, while, after the formation of cracking, the strain increases similar to

the increase in the steel reinforcement strains. This increase is due to the sudden transfer

of stresses to the reinforcement because of shear cracking.

Figure 7-10 CFRP reinforcement strain reading for slab 2

It is also seen that all the strain gauges have an approximately horizontal transfer at a

load level of about 125 kN, which indicates that the shear crack has passed the strain

gauge locations, and part of those stresses are transferred to the adjacent steel

reinforcement. Based on the numerical results, the maximum strain in the CFRP occurs

at the slab edges, as seen in Figure 7-11. The maximum strains in the numerical model

are around 11% of the rupture strain of 0.017 (as in FSG2), which is close to the strains

in the corresponding location in the experiment.


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Figure 7-11 shows the maximum principal stresses in the CFRP sheet at first cracking

and ultimate load. At the onset of cracking, it can be seen that the maximum stresses

occur close to the inner corner of the column where concrete cracking initiates, while

stresses decrease towards the slab centre in line with the distribution of moments. At

failure, the opening of the punching shear crack and the associated increase in rotation

causes an increase in the maximum principal stresses in the CFRP, particularly around

the edge of the slab where a greater degree of mobilisation can be observed. At failure,

the punching shear crack passes the CFRP sheet and causes a sudden increment of the

maximum principal stresses in the CFRP sheet.

When a slab-column connection is strengthened by FRP, a part of the stresses

transferred by steel reinforcement will be transferred by FRP and thus additional loads

can be added to the slab-column connection. Clearly, the presence of the CFRP is

beneficially influencing the stress state in the column zone. However, no major effect

can be added to the slab by increasing the CFRP area. As the un-strengthened slab

failed by punching, the failure occurs with a limited rebar yielding. If the slab is

strengthened by CFRP, this limitation in rebar yielding can cause the FRP strengthening

to have only a limited influence on the connection even with a bigger FRP area [24].

Otherwise, reducing the CFRP area means reducing the area that resists the tensile

206

stresses produced from the horizontal tensile part in the elbow-shaped strut shown in

Figure 7-12 due to the development of the critical shear crack.

Figure 7-12 Part of the slab-column connection showing the elbow-shaped strut [23]

7.2 Slabs with openings

In the design and construction of reinforced concrete slab-column connections, it is

often necessary to add openings in the vicinity of the columns [103]. „Vicinity of the

column‟ refers to the zone where transverse shear stresses are the largest and thus these

openings decrease the shear strength of the slab system.

In order to provide more information about the most severe effect of the openings on the

punching shear capacity, a numerical study was conducted to compare the results for

these slabs with openings near the slab-column connection to those without. In the solid

slab-column connection, the column is located at the corner and the loading is applied

near the column. This makes adding an opening diagonally to the column difficult.

Thus, all the openings are located adjacent to the column face.

The opening size is set to 100 × 100 mm and it is intended to be located adjacent to the

column in three locations (0, 64 and 128) mm away from the column face. In each

location, the opening is moved alongside the column edge to give more understanding

of the opening‟s effect. The openings were located adjacent to the column face and

parallel to the interior column edge, mid-side of the column, and the opening edges

were parallel to the slab‟s free edge, as shown in Figures 7-13, 7-15 and 7-17.

7.2.1 Slab with the opening located next to the column edge

In this location, the openings are put next to the column edge but their location along

the column edge is varied, as shown in Figure 7-13. The first location is where the edge

of the opening is parallel to the interior column edge (Location A), mid-side of the

207

column (Location B) and parallel to the slab‟s free edge (Location C). A comparison

between the results for the three locations based on the load-deflection response is

presented in Figure 7-14 with respect to the un-strengthened control slab.

(a) Opening at location A

(b) Opening at location B

208

(c) Opening at location C

Figure 7-13 Quarter of the slab showing the opening in different locations


column edge

It is clear that the effect of the opening on the ultimate punching shear capacity is the

greatest when the opening is situated away from the slab‟s free edge. This behaviour

can be attributed to the tensile stresses in the concrete being concentrated at the top

surface of the slab near the inner corner of the column, but the existence of the opening

here causes these stresses to pass through it and cause a reduction in the ultimate

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209

punching shear capacity. These cracks pass near the inner corner of the column at about

45˚ to the slab edges and pass through the opening following an inclined path away

from the column edges to give torsional cracks and punching shear failure.

In the case of torsional moments, it is well known that the shear stresses , are

affected by the torsional moments based on the following equations [134]:

( )

( )

In which is the length of the critical section perimeter, and are the shear force

and moment transferred from the slab to the column respectively, and are the

coordinates of any point on the critical section, and are the second moment of area

of the critical section about the x and y-axes, and = 0.4 is the eccentricity fraction,

which depends on the proportion of transmitted moments and shear based on Eurocode

2 [37].

It is well known that each face of a column in a connection is affected by shear stresses.

In a corner column, the column is under the effect of shear stresses from two faces only.

Based on the symmetry, shear stresses in both directions are equal. Thus:

resulting in a total shear resultant equal to √

or √

Then √

Angle of that resultant is

√ which gives diagonal stresses

resulting in diagonal cracks in the corner of the slab-column intersection.

210

7.2.2 Un-strengthened slab with the opening located 64 mm away from the

column edge

In this location, the opening is placed away from the column edge at a distance equal to

the slab‟s effective depth, as shown in Figure 7-15. Three different locations are also

chosen, as in the previous example. A comparison between the results of the three

locations is presented in Figure 7-16 with respect to the un-strengthened control slab. It

is seen that the ultimate capacity of the slab increases when the distance between the

opening and the column increases. This can be attributed to the effect of the opening in

reducing the punching shear capacity and the concentration of the tensile stresses is

pushed away from the column.

(a) Opening at location AA

211

(b) Opening at location BB

(c) Opening at location CC


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column edge

7.2.3 Un-strengthened slab with the opening located 2d away from the column

edge

In this location, the opening is placed away from the column edge with a distance equal

to twice the slab‟s effective depth (d=64mm), as shown in Figure 7-17. The same three

locations are also used. A comparison between the results of the three locations is

presented in Figure 7-18 with respect to the un-strengthened control slab.

(a) Opening at location AAA

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(b) Opening at location BBB

(c) Opening at location CCC


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Figure 7-18 Load deflection curve with the opening located at 2d away from the column

edge

It can be seen from Figures 7-14, 7-16 and 7-18 that the effect of the opening decreases

when it is located away from the column edge. This can be attributed to the fact that, as

the tensile stresses are concentrated near the interior corner of the column, cracking

occurs in that location. As the opening is near the column corner, cracks will pass

through the opening, which results in shearing to the slab at that location and punching

shearing.

In all the cases, it is found that the most critical case is when the opening is located next

to the column edge with its edge parallel to the interior edge of the column. Thus, this

case is studied in more detail in order to strengthen the slab with FRP sheets.

7.2.4 Crack pattern

As mentioned previously, initial cracks are located near the inner corner of the column.

With increasing the applied load, the existence of the opening makes these cracks

passing through the opening to make an inclined path away from the column edges.

Finally, these cracks give a punching shear failure.

By looking at the final failure as shown in Figure 7-19, it can be noticed that large

cracks occurred along the CFRP sides, while relatively small cracks occurred below

them. This is basically because of the ability of CFRP sheets to prevent or at least

reduce cracking below them as compared to the un-strengthened slab-column

connection.

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215

Figure 7-19 Punching shear failure in slab 3

Before the final punching shear failure, shear cracks are observed at the top surface of

the slab, sides of the slab and the interior edges of the openings. These cracks initiated

from the opening corners and developed towards forming the final punching shear

crack. In slabs 3 and 4, it is found that cracks intersect the opening edge, whilst, in slabs

without openings, these cracks develop on the inner corner of the column and then

propagate towards the slab edges. This indicates that failure cracks are transferred to the

weakest locations in the slabs, which are the openings.

7.2.5 Failure mode and ultimate load

This study is concentrating on slabs that totally fail by punching shear. Thus, all the

slabs failed by punching. It is seen that strengthening by CFRP sheets has not changed

the failure mode but has increased the total ultimate load and the corresponding

deflection. Table 7-2 gives a summary of both the load at first cracking and ultimate

load with their corresponding deflections and slab failure modes in the experimental

study.

Table 7-2 Summary of experimental results

slab

Load at

first

cracking

(kN)

Mid-span

deflection at

first cracking

(mm)

Ultimate load

(kN)

Ultimate mid-span

deflection (mm)

Failure

Mode

3 33.2 1.4 109.8 32.9 Punching

4 31.6 1.9 125.9 41.2 Punching

216

As indicated previously, in punching shear, the state of stresses near the column is a

triaxial compression, which means the cracking has reached the slab-column

intersection and formed the compression strut. Figure 7-20 shows the intersection point

of the slab-column in a step before failure. It is clear in the figure that there are some

tensile stresses still working in that region. In addition, the compression strut starts to

form.

Figure 7-20 Maximum principal stresses of concrete before failure load in the un-

strengthened slab

For the slabs that have openings, it is clear that the ultimate punching shear capacity

significantly decreased to 99.8 kN due to the effect of the opening as compared to the

solid slab. Using CFRP sheets has increased the ultimate punching shear capacity of

such slabs to 109.8 kN and 125.9 kN in slabs 3 and 4 respectively. This means they had

a (10-26)% increase when compared to the numerical un-strengthened slabs.


A summary of the experimental tests for slabs 3 and 4 and the corresponding numerical

simulation is shown in Figure 7-21. In addition to these results, the results of the

numerical simulation for the slabs with openings and the un-strengthened slab are

presented.

The observed load-deflection curves for the strengthened slabs are compared to the un-

strengthened slab in order to verify the effectiveness of CFRP in strengthening. In

addition, these results are also compared to the solid slab to show the ability of the

CFRP in restoring the capacity of the slab-column connection.

217

Figure 7-21 Load vs. mid-span deflection

The same general behaviour in slabs 1 and 2 is also seen in slabs 3 and 4. The cracking

load in slabs 3 and 4 is less than that of slab 1 where the existence of an opening affects

the total stiffness and ultimate strength of the slabs. Small differences between the

numerical models in both the strengthened and un-strengthened cases are observed in

the ultimate strength and deflection. For the experimental cases, there are some

differences between the ultimate load and deflection for each slab. The general

behaviour is similar, with both slabs failing in the same manner.

It is noticed that strengthening slabs 3 and 4 gives an increase in the ultimate load of

(10-26)% when compared to the numerical un-strengthened slabs, as shown in Figure 7-

21. Additionally, it is observed that strengthening can restore the original ultimate

capacity of the solid slab as these CFRP sheets try to resist weakness in the section

caused by the existence of the opening.

7.2.7 Steel strains

When an opening is added to a slab-column connection, it usually cuts the slab‟s steel

flexural reinforcement. Thus, one steel bar in each direction equal to that interrupted by

the opening was added on the sides of the opening, as stated by the ACI concrete

standards [169]. This additional reinforcement increases the initial reinforcement ratio,

which may result in the occurrence of the punching shear by reducing the ductility of

the slab, as stated in load-deflection curves previously.

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The existence of the opening reduces the load at first cracking compared to that in slab

1. Due to the CFRP strengthening, cracking can be delayed up to a load approximately

equal to the cracking load of slab 1, as shown in Figure 7-21. It is noticed that the steel

reinforcement over the column incurs fewer strains as compared to the reinforcement in

slab 1 as shown in Figure 7-8 because the existence of the opening has reduced the total

ultimate load. An approximately similar reduction in the steel reinforcement is also

shown in Figure 7-22 due to the initiation of concrete crushing, as discussed previously

for slabs 1 and 2. It is also noticed that the steel reinforcement has not yielded before the

occurrence of the failure.

(a) Strain gauge 1

(b) Strain gauge 2

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(c) Strain gauge 3

(d) Strain gauge 4

(e) Strain gauge 5

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(f) Strain gauge 6

Figure 7-22 Steel reinforcement strain reading for strengthened slabs in the

experimental and numerical models

7.2.8 FRP strains

It can be seen from Figure 7-23 that the maximum strain in the CFRP does not reach the

ultimate tensile strain or the rupture strain of 0.017. At the early stages of loading, FSG

1 and FSG 2 recorded more strains than FSG 3 because cracks initially developed near

the interior corner of the column. With increasing load, more cracks developed in the

concrete around the opening. At this stage, FSG 3 recorded the maximum strain in the

CFRP sheets due to further crack development in that region. At failure, it was seen that

the diagonal cracking passes through the high-stress concentration zone between the

opening and the slab edge below FSG 3, as shown in Figure 7-19 previously, thus

giving the high strain reading in FSG3.

(a) CFRP strain gauge FSG1

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(b) CFRP strain gauge FSG2

(c) CFRP strain gauge FSG3

Figure 7-23 CFRP reinforcement strains for slabs 3 and 4

At failure, all the stresses are distributed along the CFRP in order to reduce the

probability of CFRP rupture, and thus stresses are transferred to the strain gauge 3

location.

Figure 7-24 shows the distribution of the maximum principal stresses in the CFRP sheet

at first cracking and ultimate load. At both stages, it can be seen that the CFRP is

working harder than in slab 2 as a result of the presence of the opening and associated

increased stress concentration in the column-slab zone.

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Close examination of Figure 7-25 indicates some localised areas are approaching

debonding, particularly at the edges of the CFRP along the sides of the slab, which is

consistent with the experimental behaviour shown in Figure 7-3.

223

Figure 7-25 Stiffness degradation in the cohesive layer of the strengthened slabs

7.3 Analysis of test results and the observed damage

This research studies the behaviour of strengthened slab-column connections against

punching shear failure. The response of the samples based on the applied load is

considered as the base for other behavioural aspects like the load-strain in steel or FRP,

and the yielding load. Furthermore, the failure mode of the slab-column connection can

be concluded from the relationship between the applied loading and the corresponding

central deflection.

Figure 7-26 shows the normalised ultimate punching shear capacity in the experiment

compared with slab 1. It is clear from the diagram that strengthening slab 2 increases the

ultimate punching shear capacity. On the other hand, openings in the slabs decreased the

total load capacity.

Figure 7-26 Ultimate punching shear capacity comparison of tested slabs

00.10.20.30.40.50.60.70.80.9

11.11.2

Slab 1

Slab 2

Slab 3

Slab 4

224

7.4 Comparison with design codes

None of the concrete standards have a pure punching shear equation for slabs

strengthened by CFRP composites. Some of these standards, like the ACI, Eurocode,

Japanese Society of Civil Engineers (JSCE) and the FIB model code, try to include a

general punching shear equation by entering the effect of FRP reinforcement on the

initial slab flexural reinforcement ratio and effective depth. By this way, the punching

shear strength of FRP strengthened slab is determined by adding the contribution of the

external FRP reinforcement to the contribution from the internal steel reinforcement in

increasing the tensile force and the corresponding compression force (by equilibrium) in

the concrete which increases the shear strength in the compression zone [7, 109]. Table

7-3 gives a comparison between the experimental results and the code prediction values

based on changing the general punching shear equation as explained in equations (2-27)

and (2-28). It is worth mentioning that ACI concrete standards and the FIB model code

do not take into account the effect of the flexural reinforcement ratio. Thus, the effect of

strengthening by CFRP is only considered based on the slab‟s effective depth. Eurocode

2 and JSCE consider the effect of the flexural reinforcement area, so a change to the

effective slab depth and the reinforcement ratio based on the equations mentioned in

2.11 would be used.

Table 7-3 Comparison of test results with code predictions

Slab Vult

test

Vult predicted Vult test / Vult predicted

ACI Eurocode 2 JSCE FIB ACI Eurocode 2 JSCE FIB

Slab 1 127.4 151 113.6 133.5 146 0.84 1.12 0.95 0.87

Slab 2 141.2 167 137.8 160.3 161.2 0.84 1.02 0.88 0.87

Slab 3 109.8 124 137.8 125.5 116.1

0.88 0.79 0.87 0.94

Slab 4 125.9 1.01 0.91 1.00 1.08

Mean value 0.89 0.96 0.92 0.94

The four codes of practice mentioned above are considered in the comparison with the

test results. ACI standard specifications, JSCE and the FIB model code take the

punching shear perimeter to be at d/2 away from the column face. The shear stress

acting on this perimeter is a function of √ and the ratio of the side dimensions of the

column to the effective slab depth. In ACI standards, there are three equations to

calculate the punching shear strength. One of these equations considers the shear

strength independent of the ratio of the column size to slab depth. It is only based on the

225

concrete compressive strength. In Eurocode, the punching shear perimeter occurs at 2d

away from the column face and the shear stress acting on this perimeter is a function

of √

.

The ACI standard specifications and the FIB model code overestimate the applied

loading especially in slabs without openings. This is because their formulas take into

account the effect of the column geometry and the slab size without considering the

flexural reinforcement area. Another reason is that the ACI formula considers the failure

surface as straight lines causing a square punching shear perimeter without considering

the curvatures at the corners, which may increase the failure surface. While other

standards consider the punching shear perimeter always has rounded corners. FIB

model use the critical shear crack theory in the calculation of the punching shear

strength. So based on this theory, aggregate size has a big effect on the calculation of

the punching shear strength which is ignored in other codes as explained in 2.11. FIB

model use also the rotations around the column in consideration when calculating the

punching shear strength. Furthermore, the steel reinforcement material properties are

taken into consideration. So, it can be said that ACI formula does not take the effect of

the flexural reinforcement ratio in consideration, while other codes consider.

On the other hand, the Eurocode equation gives more realistic results than the other

codes formula for slabs without openings. However, for slabs containing openings, it

overestimates the values because the failure surface based on Eurocode is taking place

at a distance of 2d from the column face. Thus, the existence of an opening has no effect

on the punching shear perimeter because the opening does not intersect with the failure

surface as shown for the slabs with openings.

JSCE gives an overestimation as compared with the experimental results and especially

for the strengthened slab without openings. This is related to the method used to

calculate the punching shear perimeter.

Furthermore, ACI standards specification take in consideration a strength reduction

factor for the general punching shear equations. While other codes do not use that factor

but use safety factors for each individual material. In addition, ACI standards and the

226

FIB model code do not take a size factor into consideration; Eurocode and the JSCE

take that into consideration and they have a limit value for that as explained in 2.11.

At the end, the location of the column has an effect on the calculation of the punching

shear strength. ACI code and the FIB model have a specific value for the location factor

for each column. Eurocode and the JSCE do not have a specific value to the location

factor, but that factor enters tacitly in calculating the punching shear perimeter.

7.5 Conclusions

CFRP sheets are used to strengthen slab-column connections. This strengthening leads

to an increase in the initial stiffness and moderately improves the total ultimate

punching shear capacity. Based on the CFRP sheets‟ area, thickness and location with

respect to the column, it can be seen that using CFRP sheets increased the ultimate

capacity by approximately 11%. However, for the slabs with openings, it was found that

using CFRP sheets enables them to reach the ultimate strength of the un-strengthened

solid slab. The strengthened slabs exhibited more loads and deflections than the un-

strengthened slab.

For the comparison with the codes of standards mentioned in 2.11, it can be seen that

the Eurocode equations give the most realistic results in relation to the experimental

programme for the solid slabs. However, for slabs with openings, the ACI standards

give the most realistic results. This depends on how the punching shear perimeter is

calculated, as the punching cracks pass through the opening, while in Eurocode they

pass out of the opening, which can give more applied load.

Based on the current studies, the most important points to be concluded are:

1- Strengthening slabs at corner columns by surface-mounted CFRP strips resulted

in delaying the initiation of flexural cracks in the slabs.

2- The externally bonded CFRP sheets reduced the total strain in the internal steel

bars over the column region as compared to the un-strengthened slab-column

connections.

3- The strengthened slab-column connections have stiffer behaviour than the un-

strengthened slab because the CFRP reduces the rotation around the critical

shear crack.

227

4- The existence of openings reduced the ultimate punching shear capacity.

Strengthening with CFRP allowed these slabs to recover the ultimate punching

shear capacity to a level commensurate with the slab without openings.

5- Eurocode equations give the most realistic results with the experimental

programme for the solid slabs. However, for slabs with openings, ACI standards

and JSCE give the most realistic results.

228

8. Chapter 8 Design and Analysis of a Proposed

Reinforced Concrete Slab-Corner Column Connection

The experimental study presented previously has given an indication of the structural

performance of slabs at corner columns. In this section, a proposed corner-slab column

junction with geometry common in practice is studied to assess performance and to gain

further understanding.

8.1 Design of the proposed model

An isolated slab at corner columns similar to the slab tested in the experimental study is

also designed in accordance with Eurocode 2 [37]. The slab dimensions are 7 m × 7 m ×

275 mm and this is supported by four columns 3 m in height to represent a real case of

slabs at corner columns. The column cross sections are each 500 × 500 mm and they are

monolithically cast with the slab from the top, while the column‟s base boundary

conditions are made to be simply supported. The concrete compressive strength of the

structure is chosen as 30 MPa and all the other constitutive properties are taken based

on Eurocode 2 [37], including the tensile strength and Young‟s modulus. The steel

reinforcement tensile strength is 500 MPa and Young‟s modulus is 200 GPa. The

material properties are considered as average with no partial safety factors. In the design

of the slab, the material properties for neither the steel reinforcement nor the concrete

are modified, in order to achieve a pure structural behaviour without the effect of partial

material factors. The control specimen is designed for an ultimate load of 24.4 kN/m2

which includes self-weight and which is distributed on the whole slab surface to ensure

pure punching shear failure.

The design of the structure is based on the flexural distribution of moments; all the

flexural reinforcement is chosen based on the transferred moment to the column or

middle strips. The top steel reinforcement is placed over the columns only and

distributed over a 1.75 m distance in each direction. The top steel reinforcement consists

of 22Ø12 mm bars distributed 80 mm centres also giving a reinforcement ratio of 0.594

in each direction. Figure 8-1 shows the details of the proposed un-strengthened designed

slab. The column reinforcement is 4Ø25 mm bars with a bar at each corner. The stirrups

229

are made of Ø12 mm bars distributed vertically every 150 mm along the whole length

of the column and overlapped within the slab.

Figure 8-1 Reinforcement details of the proposed designed slab

The behaviour of the concrete and the steel reinforcement in addition to the elements

required to model each individual material in the numerical analysis are taken based on

the previous study. Thus, the presentation of the results is carried out directly by

comparing the un-strengthened and the strengthened models.

8.2 Strengthening of the proposed slab and parametric study

In order to provide a greater understanding of the efficiency of strengthening slabs at

corner columns, a parametric study is conducted based on changing the following:

Both the top and bottom flexural steel rebar reinforcement ratios of the un-

strengthened slab.

The geometric configuration of the CFRP sheets.

Top reinforcement

X direction 22 Ø 12

@ 80 mm c/c

Top reinforcement

Z direction 22 Ø 12

@ 80 mm c/c

Bottom reinforcement

X direction 88 Ø 12

@ 80 mm c/c

Bottom reinforcement

Z direction 88 Ø 12

@ 80 mm c/c

230

The thickness of the CFRP.

The CFRP configurations were selected based on that studied previously in Chapter

five, as the most appropriate strengthening solutions used in real strengthening.

In all the strengthening schemes, the CFRP sheets have a width of 300 mm and

thickness of 0.8 mm as a base value and the material properties are taken from Table 6-

6. Furthermore, the CFRP sheets configurations are shown in Figures 8-2 and 8-3.

8.2.1 Configuration 1: Two orthogonal CFRP sheets around the column

Similar to that studied in the experimental programme in Chapters six and seven, two

orthogonal CFRP sheets were put around the column, as shown in Figure 8-2, to

provide a greater understanding of their strengthening effect on a larger scale.

Figure 8-2 Configuration for the two orthogonal CFRP sheets

8.2.2 Configuration 2: Two CFRP sheets parallel to the slab diagonal

In this configuration, the CFRP sheets are attached directly perpendicular to the

concrete cracking, bridging the cracks on the slab surface, as shown in Figure 8-3.

231

Figure 8-3 Two CFRP sheets parallel to the slab diagonal

8.3 Summary of the conducted parametric study

In all the previous configurations, the proposed designed slab reinforcement ratio was

considered the base for all other slabs. The flexural reinforcement ratio was changed to

(50, 62.5, 75 and 87.5)% of the proposed designed slab. Further studies were conducted

by changing the thickness of the CFRP added to such slabs to 1.2 and 1.8 mm. Table 8-

1 provides a summary of all the previous configurations.

Table 8-1 Summary of strengthening configuration

8.4 General behaviour of the un-strengthened slab

Based on a parametric study analysis regarding the mesh size, tension stiffening

behaviour and the concrete dilation angle, mesh with an element size of 20 mm and an

exponential tension stiffening and 300 dilation angle is able to model the slab-column

connection and provide reasonable accuracy in terms of the ultimate load in the

analytical design calculations with a difference of about 5%.

The intended failure mode of the slab is punching shear; hence, the un-strengthened slab

fails by punching. The bottom steel rebars have a vital role in the behaviour of the slab-

Configuration Description Sub-

configurations Description

1

Two orthogonal

CFRP sheets

around the

column

1-A On slab top surface only

1-B On slab top surface and sides

1-C On slab top surface, sides and

bottom surface

2

Two CFRP

sheets parallel to

the slab diagonal

Attached to the top surface

parallel to the slab diagonal by

a length of 1500 mm

232

column connection. Reducing the bottom steel flexural reinforcement ratio causes a

change in the failure mode from punching to pure flexure because the steel rebars yield

at the slab‟s free edge between the columns and spread to the slab centre before

achieving the ultimate punching shear capacity. Changing the top steel reinforcement

ratio has no great effect on the behaviour of the slab-column connection because the

bottom steel rebars are designed to make the slab fail in punching without yielding or

with yield in a limited area before final punching shear failure. However, reducing the

top steel bars can cause yielding in the steel bars over the column without concrete

crushing at the bottom side of the slab over the columns, especially for slabs of low top

steel reinforcement ratio. Increasing both the top and bottom flexural steel

reinforcement areas increases the probability of punching with the inherent brittle

characteristics but with different levels of load and deflection. Any change in the

reinforcement ratio will be conducted based on reducing the rebar diameter in order to

keep the even distribution of the steel reinforcement with respect to the designed

proposed slab. Thus, the number of all reinforcing bars for both top and bottom meshes

will be maintained without change.

At first, cracking is observed on the top surface of the slab in the column region and

then on the lower surface at the slab‟s free edge (the mid-distance between the columns)

at slightly higher loads, as shown in Figure 8-4. In addition, no cracking developed

parallel to the diagonals of the slab. Cracks propagated across the free edges following

an inclined path away from the column edges at higher loads, as shown in Figure 8-5.

When the slab reaches the ultimate applied load, failure happens due to cracks

propagating towards the slab-column intersection, causing a sudden decrease of the

applied load, as shown in Figure 8-6. The slab behaved elastically with a linear increase

in loading with a high stiffness up to the onset of the first crack, and then less stiffness

is introduced.

233

(a) First cracking on the top surface at load 4.4 kN/m

2

(b) First cracking on the bottom surface at load 9.3 kN/m

2

Figure 8-4 Cracking of the concrete slab

234

Figure 8-5 Propagation of concrete cracking to the slab free edge

Figure 8-6 Slab failure at ultimate load

The same behaviour noticed in the experimental study of Chapter seven for both top and

bottom steel bars is also seen in the case of the full-scale slab-column connection.

Yielding does not occur for the top steel reinforcement within the punching shear region

over the columns. The top steel reinforcement records a reduction in the strain values

before failure. In the bottom steel reinforcement, there is no recorded yield for any of

the steel bars. However, the steel bars on the bottom side at the slab edges between the

235

columns record stresses and strains more than those in the corresponding middle strips

due to the distribution of bending moments along the free edges of the slab.

In all the steel reinforcement, there is a difference between the values of the stresses or

strains for the same orthogonal reinforcement. This is due to the difference in the

vertical location of the steel bars within the slab, as there is a bar diameter difference

between them.

8.5 Effect of CFRP configuration on the ultimate load and deflection

Adding CFRP reinforcement to the concrete slabs in different configurations can

increase the ultimate load applied to the concrete slab. However, in some cases, it does

not increase the load, especially when the CFRP sheets are placed in a direction not

perpendicular to the concrete crack direction or not directly intersecting the concrete

cracking. A summary of the applied load for the proposed strengthened slab with

respect to CFRP sheets of a thickness of 0.8 mm and the change in the steel

reinforcement ratio is presented in Figure 8-7. In all these figures, the slab

reinforcement ratio for both top and bottom bars was reduced to (50, 62.5, 75 and

87.5)% of the reinforcement ratio of the proposed designed slab. For example, slabs

reinforced with 50% of the proposed designed slab have a reinforcement ratio of

(

) Furthermore, the load was normalised by calculating the ratio

between the ultimate load in the case of the strengthened to that in the un-strengthened

slab.

Figure 8-7 Effect of strengthening the slab by configurations 1 and 2 on the ultimate

load capacity with respect to the un-strengthened slab

1

1.02

1.04

1.06

1.08

1.1

1.12

45 50 55 60 65 70 75 80 85 90 95 100 105

No

rmal

ise

d lo

ad

Reinforcement ratio %

Configuration 1-A Configuration 1-B Configuration 1-C Configuration 2

236

Reducing the flexural steel reinforcement ratio to (50, 62.5)% of reinforcement ratio of

the proposed designed slab on both top and bottom meshes changed the failure mode

from punching to a pure flexural failure. This is confirmed by the yielding of the

flexural reinforcement at the slab‟s free edge between the columns, and this yielding

spread to the slab centre and gave a high value of deflection. Increasing the flexural

reinforcement ratio to (75, 87.5)% changes the failure mode to a flexural punching in

which the flexural reinforcement yielded in a specific area before the final failure of

punching shear. Figure 8-8 shows the load-deflection curves for all the configurations.

In this figure, CFRP sheets with a thickness of 0.8 mm were used to strengthen the

slabs, while the flexural steel reinforcement ratio was kept as in the proposed slab

design, without being changed.

Figure 8-8 Comparison of load-deflection curves for configurations 1 and 2 with the

load-deflection curve of the un-strengthened slab-column connection

Investigating Figure 8-7 shows that adding CFRP orthogonally around the columns

could increase the ultimate load capacity by about 10% over that of the un-strengthened

slabs, especially in slabs with a low reinforcement ratio. This is commonly due to the

initial failure mode of the slab and the location of the CFRP. These slabs failed in

flexure at the slab centre, while the strengthening was in the column region, making

these CFRP sheets have a lesser effect on the total slab behaviour.

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80

Load

KN

Midspan Deflection mm

Un-strengthened

Configuration 1-A

Configuration 1-B

Configuration 1-C

Configuration 2

237

From Figure 8-7, it can be seen that the best configuration in strengthening slabs at

corner columns is when using CFRP sheets orthogonally around the column. In this

case, greater loads can be accommodated by the slab-column connection, as explained

earlier in Chapter seven. The same ratio for the ultimate punching shear capacity

observed in the experimental work of Chapter seven is also noticed here in the full-scale

slab-column connection for the orthogonal CFRP sheets, which is 11%. This confirms

that the full-scale slab has no great effect on the load capacity.

Figure 8-7 shows that, when CFRP sheets are added in a direction parallel to the slab

diagonals, no great effect on the ultimate load capacity can be added.

In the case of slabs strengthened by CFRP sheets parallel to the slab diagonals, an

increase in the ultimate load capacity occurs as the slab flexural reinforcement ratio

increases, as these CFRP sheets will work directly against punching shear by bridging

the shear cracks on the horizontal surface of the slab.

What should be referred to here is increasing the CFRP thickness can increase the

horizontal shear between the CFRP and the concrete surface, which can cause more

susceptibility to debonding or even actual debonding, as presented previously in the

case of configuration 2 (Figure 8-8), as shown in Figure 8-9.

Figure 8-9 CFRP debonding from the concrete substrate in configuration 2

238

In some cases, strengthening a slab with a low reinforcement ratio causes an increase in

the ultimate load capacity but with a decrease in the total deflection, and at the same

time does not change the failure mode. Furthermore, adding CFRP sheets parallel to the

slab diagonals causes a reduction in the total deflection as they try to prevent the

concrete section from rotating around the critical shear crack.

For slabs strengthened in an orthogonal configuration, adding the CFRP sheets can

increase the total deflection, as shown in Figure 8-10. For slabs with a low

reinforcement ratio, adding CFRP sheets can increase the total deflection to 30% with

respect to the deflection of the un-strengthened slab. However, increasing the flexural

reinforcement ratio reduces the percentage to 13% with a corresponding increase in the

ultimate load. Therefore, in all previous studies, it is recommended to use an orthogonal

CFRP configuration for strengthening slabs at corner columns.

Figure 8-10 Effect of orthogonal configuration on ultimate deflection of strengthened

slabs

8.6 Effect of CFRP thickness on the ultimate load capacity

Adding CFRP sheets to strengthen concrete slabs at corner column connections can

increase the ultimate load capacity and/or the ultimate deflection to limited values based

on the configuration and thickness of the CFRP. Increasing the thickness of the CFRP

sheets would increase the horizontal shear between the concrete and the CFRP, which

can cause debonding failure before the final punching shear. Thus, the thicker the CFRP

is, the more susceptible it is to debond. Figure 8-11 shows the increase in the load

capacity for different CFRP thicknesses for the best configuration (configuration 1).

1

1.2

1.4

45 50 55 60 65 70 75 80 85 90 95 100 105

No

rmal

ise

d d

efl

ect

ion

Steel reinforcement ratio (% of the reinforcement ratio of the proposed

designed slab)

Configuration 1-A Configuration 1-B Configuration 1-C

239

Figure 8-11 Effect of CFRP thickness on the ultimate load capacity

Further studies on the utilisation of CFRP sheets demonstrated that the maximum stress

ratio of 20% of its ultimate strength is noticed when the slab is strengthened by

configuration 2. In this configuration, the CFRP sheets work directly on the concrete

cracking in a very small area around the column. Due to the susceptibility to debond,

more stresses are transferred to the CFRP sheets and this causes an increase in the

CFRP strength up to 41% of its ultimate strength.

Further studies on comparing the shear stress with the maximum shear stress in concrete

show that maximum load of 31.8 kN/m2 obtained from orthogonal configuration gives a

shear stress of 1.144 MPa which is less than the maximum shear of 1.35 MPa. By

comparison with that achieved in experimental work of Chapters six and seven in which

maximum applied load was 141 kN which gives shear stress of 1.72 MPa less than the

maximum shear stress of 2.1 MPa. This comparison gives an indication that in all these

cases the failure was either by flexure as in slabs with low reinforcement ratios or by

punching shear due to shearing and splitting in the concrete as it is normal in punching

shear.

8.7 Conclusion

Based on the numerical study presented in this chapter and the comparison with load

calculated in the initial design of the slab-column connection, the following conclusions

can be made:

1- The general behaviour of the full-scale slab is similar to that studied

experimentally based on the numerical study.

1

1.05

1.1

1.15

1.2

45 50 55 60 65 70 75 80 85 90 95 100 105

No

rmal

ise

d lo

ad

Steel reinforcement ratio (% of the reinforcement ratio of the proposed

designed slab)

CFRP thickness=0.8 mm CFRP thickness=1.6 mm CFRP thickness=1.8 mm

240

2- The same behaviour of the steel reinforcement is also shown in the full-scale

slab.

3- The best configuration in strengthening is using orthogonal CFRP sheets around

the column.

241

9. Chapter 9 Conclusions and Recommendations

This research has investigated the effectiveness of strengthening reinforced concrete flat

slab-to-column corner connections by using CFRP sheets experimentally and

numerically. In the experimental study, four full-scale un-strengthened and strengthened

flat slab specimens are studied. One of these specimens is the control specimen, which

has no variation introduced to it. One of the other specimens is similar to the control but

strengthened by CFRP. Further variation in the test series is introduced via the addition

of openings near the slab-column intersections. The structural performance of the

strengthened specimens is compared with that of the un-strengthened specimen in terms

of ultimate punching shear resistance, deflection profile and strain profile, etc.

Further to the experimental study, a numerical study is also conducted to analyse all the

slabs by using the finite element method. The Concrete Damage Plasticity model

adopted in ABAQUS is involved in the analysis. Eight-node 3D continuum elements

(C3D8R) are chosen for the concrete. The reinforcement mesh consists of two-node

truss elements (T3D2). The reinforcement mesh is embedded through the concrete

elements with a full bond with these elements. The conventional 2D shell elements

(S4R) are used to model the CFRP material. The bond between the CFRP and the

concrete is modelled using cohesive elements (COH3D8).

This study also compares the predicted punching shear strength to that in the ACI,

Eurocode 2, JSCE and the FIB model codes of practice. Modes of failure and punching

shear strength are also addressed. The following conclusions and recommendations can

be drawn from the present study.

9.1 Conclusions

The purpose of strengthening the column-slab connection is to increase the punching

shear capacity. Using CFRP composites should add more ductility to the slab. But,

depending on the CFRP strengthening configuration, it may be the case that less

ductility incurs regardless of the increased overall achieved load. Based on the current

study, the most important conclusions are:

242

1- Strengthening slabs at corner columns by CFRP composites resulted in delaying the

initial flexural cracks in the slabs. This delay has improved the slab response by a

modest increase in the ultimate punching shear capacity of slab 2 from 127.4 kN to

141.2 kN and the sustained deflection from 33 mm to 46 mm, which may give

considerable warning before failure instead of sudden punching shear failure.

2- Different CFRP strengthening configurations were studied as in 5.2 and 5.3. The

greater ultimate load enhancements were attained from an orthogonal arrangement of

CFRP with the addition of longitudinal CFRP along the slab edges.

3- For slabs 2, 3 and 4 strengthened by CFRP, the CFRP caused an increase in their

effective depth, as presented in equation (2-27). This increase in the effective depth

corresponded to an increase in the concrete compression depth. Based on the Critical

Shear Crack Theory and the punching shear mechanism presented in 2.2, the increased

concrete depth caused an increase in the integrated shear stresses around the punching

crack surface or the concrete compressive force and thus the punching shear capacity, as

also explained in 5-7.

4- For slabs at corner columns, attaching CFRP lamina to the concrete surface around

the column gives an increase in the punching shear capacity of about (7-20)% over the

un-strengthened slab, as presented previously in Figure 5-12. Slabs that fail initially in

punching have a smaller cracking width, which gives more effect of the intact concrete

on the compression force leading to an increase in the total punching shear capacity.

5- The punching shear capacity is increased by increasing the bond strength of the FRP-

Concrete substrate. The bond strength is increased by increasing the FRP Young‟s

modulus or by using FRP with less thickness, based on equation (5-1). This increase in

the bond strength causes an increase in the CFRP stresses and the corresponding

concrete compression stress, which causes an increase in the neutral depth and an

increase in the length of the slope of punching shear in the compression side and thus

the integrated shear stresses along the punching crack as explained in 5-7.

6- Strengthening slabs by CFRP results in delaying the initiation of the concrete

cracking and an increase in the initial slab stiffness of about 20% over the un-

strengthened slab due to an increase in the first cracking load of about 12% and a

reduction in the deflection of about 20% as presented in Table 7-1. This is attributed to

the fact that the CFRP strips bridge the punching shear crack and thus alleviate the

discontinuity in the member rotation at the critical shear crack region; this, in return

reduces the deflection resulting from the slab rotation. The increase also comes from

243

increasing the effect of aggregate interlocking at early stages of loading before the

development of the shear crack and the dowel action of the flexural reinforcement as

stated previously in 2.2.

7- Steel reinforcement over the column region results in a reduction in the strain value

before failure because the concrete in the compression side starts crushing before

failure, causing a redistribution of these strains to the whole slab reinforcement.

8- Using CFRP reinforcement causes a reduction in the stresses of the steel

reinforcement over the column region as part of the whole stresses transferred to the

steel reinforcement will be transferred to the CFRP reinforcement.

9- For strengthened slabs, the steel reinforcement in the bottom of the slab‟s free edge

between columns has more stresses than that in the middle of the slab. This is due to the

difference in the value of the transferred moments to the column and middle strips. This

is similar to what is stated by Eurocode 2 [37] and ACI [169] where about 60% of the

positive moment in the slab will transfer to the column strip and the other 40% will

transfer to the slab middle strip as explained in Table I-1 of Eurocode 2 [37].

10- The existence of the opening reduced the ultimate punching shear capacity.

Strengthening with CFRP allowed the slab to recover the ultimate punching shear

capacity to a level commensurate with the slab without openings, as explained in Table

7-2.

11- Increasing the slab size has no great effect for slabs that fail initially in punching

shear and which are then strengthened by CFRP around the corner columns. Fourteen

percent is the maximum increase in the ultimately applied load even when changing the

slab size, depending on the CFRP thickness used in the study, as presented in Chapter

eight.

12- Using CFRP reinforcement has no major effect on the position of the shear failure

plane. The tensile resistance of the CFRP sheets perpendicular to their longitudinal axis

is small; therefore, they will be less effective in resisting the corresponding tensile

stresses and shear crack formation in that direction. Thus, the corresponding propagated

shear cracks away from the column face are approximately the same in both

strengthened and un-strengthened slabs.

13- Bonding CFRP to the top surface of a slab at the corner column by a specific bond

length is not enough. An additional length has to be added to the slab edges to increase

the bond length and avoid the CFRP debonding from the substrate, as explained in

Table 5-3.

244

14- CFRP area can be increased by increasing the width or the layers. This increase will

be up to a limit of the CFRP premature bond failure due to the increased horizontal

shear between the concrete and the CFRP.

15- Comparing the test results to four other design codes shows that there is a close

agreement in the failure mode and the ultimate capacity of the solid slabs to the

Eurocode equations. However, for slabs with openings, the comparison shows a close

agreement in the failure mode and the ultimate capacity to the ACI and JSCE standards

as explained in 7.4. The very limited experimental observations have to be increased in

order to obtain more understanding of the behaviour of slabs at corner columns and how

they are close to other codes of standards.

9.2 Recommendations and future work

The current investigation is limited to reinforced concrete flat slabs on corner columns

without shear reinforcement. In addition, the reinforcement directions are orthogonal to

the slab‟s free edges. Thus, a number of further research studies are suggested to

improve the knowledge and understanding in this area:

1- Since the current study is on flat slabs on corner columns without shear

reinforcement, further studies should be conducted on slabs having a different type of

shear reinforcement.

2- Since the current study is on reinforcement directed orthogonally to the slab‟s free

edges, further studies should be conducted where the reinforcement is directed

diagonally to the slab‟s free edges, as recommended by the ACI code of standards.

3- Further studies should be conducted to cover more different strengthening

parameters like the FRP material type, FRP stiffness and width of the FRP by reducing

the limitations encountered in this study.

4- Further studies should be conducted by changing the reinforcement type from

traditional steel to FRP reinforcement to accommodate further insights into the

behaviour of slabs on corner columns reinforced by FRP reinforcement, as

recommended by ACI 440.2R-08 [109].

5- Since the FE model in ABAQUS does not show directly the crack direction, further

studies should be conducted by introducing a cohesive element between the concrete

elements to give more accurate discrete cracks in respect of this phenomenon.

245

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Documents

Strengthening flat slabs at corner columns against