Structural Analysis of Strengthened RC Slabs A thesis submitted to The University of Manchester for the degree of Doctor of Philosophy in the Faculty of Science and Engineering 2018 Mohammadtaher Davvari SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL ENGINEERING
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Strengthening Two-way R.C. SlabsRC Slabs
A thesis submitted to The University of Manchester for the degree of Doctor of
Philosophy in the Faculty of Science and Engineering
2018
2
2.3. Two-way RC slab behaviour .............................................................................. 33
2.4. Strengthening of two-way RC slabs ................................................................... 40
2.4.1. Flexural strengthening................................................................................. 40
2.4.2.1. Punching failure mechanism ............................................................................ 44
2.4.2.2. Effective parameters for punching strength ..................................................... 48
2.4.2.3. Punching strengthening methods ..................................................................... 52
2.5. Slabs strengthened with FRP .............................................................................. 58
2.5.1. The behaviour and failure mode of FRP strengthened slabs ...................... 58
3
2.5.1.1. FRP strengthened RC slabs with full of composite action ............................... 58
2.5.1.2. FRP strengthened RC slabs with a partial loss of composite action ................ 60
2.5.2. Bond behaviour between concrete and FRP ............................................... 62
2.5.3. Design codes estimation in composite action ............................................. 67
2.5.3.1 Evaluation of the slabs punching strength ........................................................ 67
2.5.3.2. Evaluation of the slabs flexural capacity ......................................................... 70
2.5.4. Prestressed FRP as an external reinforcement ............................................ 72
2.6. Summary ............................................................................................................. 73
3. Strengthening RC slabs with non-prestressed and prestressed FRP ...... 73
3.1. Introduction ......................................................................................................... 74
3.2.2. Kim et al.’s experimental investigation ...................................................... 79
3.3. Numerical Modelling .......................................................................................... 83
3.3.2.2. Concrete damage modelling ............................................................................. 87
3.3.3. Steel modelling ........................................................................................... 95
3.3.4. FRP modelling ............................................................................................ 96
3.3.6. Finite element type and mesh.................................................................... 100
3.3.7. Mesh convergence..................................................................................... 104
3.3.8. Validation of finite element models .......................................................... 105
3.4. Analysis and discussion of results .................................................................... 108
3.5. The optimum FRP prestress ratio to strengthen RC slabs ................................ 123
3.6. Summary ........................................................................................................... 130
4.1. Introduction ....................................................................................................... 132
4.2. Experimental test .............................................................................................. 133
4.2.1. Rationale behind choosing the dimension of the tested slabs ................... 134
4
4.2.3. Materials.................................................................................................... 139
4.2.5. Measurement instrumentation ................................................................... 146
4.3. Results and discussion ...................................................................................... 150
4.3.1. Experimental and FE model results .......................................................... 150
4.3.2. Slabs with an initial low tensile reinforcement ratio (category L) ............ 152
4.3.2.1. Control specimen with a low tensile reinforcement ratio (L0) ...................... 152
4.3.2.2. Shear strengthened slab with a low tensile reinforcement ratio (LS) ............ 155
4.3.2.3. FRP strengthened slab with an initial low tensile reinforcement ratio (LF) .. 158
4.3.2.4. FRP and shear strengthened slab with low tensile reinforcement ratio (LFS)163
4.3.3. Slabs with an initial high tensile reinforcement ratio (category H) .......... 171
4.3.3.1. Control specimen with a high tensile reinforcement ratio (H0) ..................... 171
4.3.3.2. Shear strengthened slab with a high tensile reinforcement ratio (HS) ........... 174
4.3.3.3. FRP strengthened slab with an initial high tensile reinforcement ratio (HF) . 178
4.3.3.4. FRP and shear strengthened slab with high tensile reinforcement ratio (HFS) ... 184
4.3.4. Assessment of models to predict the capacity of the slabs ....................... 188
4.4. Summary ........................................................................................................... 190
5.2.2. The compressive reinforcement ................................................................ 196
5.2.3. The pattern of FRP sheets to strengthen RC slabs .................................... 200
5
5.2.4. The number of FRP sheets ........................................................................ 201
5.2.5. The thickness of FRP sheets to strengthen RC slabs ................................ 203
5.3. Summary ........................................................................................................... 205
References ................................................................................................. 211
Figure 2-1. Strengthening RC structures with steel members ............................................................... 27
Figure 2-2. Strengthening RC elements with FRP on the Country Hills Boulevard Bridge ................. 29
Figure 2-3. Fibre reinforced polymer matrix. ....................................................................................... 29
Figure 2-4. Unidirectional FRP, woven FRP and FRP laminate. ......................................................... 30
Figure 2-5. Strengthening RC structure using an FRP plate ................................................................. 31
Figure 2-6. Strengthening RC columns with FRP sheets. ..................................................................... 32
Figure 2-7. Stress-strain curve for FRPs and mild steel. ....................................................................... 32
Figure 2-8. One-way and two-way RC slabs. ....................................................................................... 33
Figure 2-9. Load–deflection curves of typical ductile and brittle materials ......................................... 35
Figure 2-10. Effective parameters in RC sections of flexural members. .............................................. 36
Figure 2-11. Two-way RC slab failure mode based on the steel reinforcement ratio ........................... 37
Figure 2-12. Typical load-deflection curves of flat slabs with ductile and brittle failures. .................. 37
Figure 2-13. Load-rotation curves of RC slabs with varying tensile reinforcement ratios ................... 38
Figure 2-14. Load-deflection curves of RC slabs with varying tensile reinforcement ratio ................. 39
Figure 2-15. Experimental layout of the slabs in Ebead et al. .............................................................. 41
Figure 2-16. FRP strengthening patterns in Elsayed et al. .................................................................... 43
Figure 2-17. Load-deflection curves of the specimens in Limam et al.. ............................................... 43
Figure 2-18. Slab failure in Limam et al. .............................................................................................. 44
Figure 2-19. Direct (one-way) shear and punching shear failure positions .......................................... 45
Figure 2-20. Loaded areas in one-way shear and punching failure ...................................................... 46
Figure 2-21. Slab deformation during punching test ............................................................................ 46
Figure 2-22.Radial and tangential concrete strains at different distances from the column side. ......... 47
Figure 2-23. Crack angle in a concrete flat slab ................................................................................... 48
Figure 2-24. Effective dimensions to calculate the capacity of slabs in Rankin and Long model. ....... 49
Figure 2-25. Relation between the punching strength and flexural capacity of slabs ........................... 50
Figure 2-26. Examples of shear reinforcement in RC slabs. ................................................................. 51
Figure 2-27. Details and strengthening patterns of RC slabs in Genikomsou and Polak. .................... 53
Figure 2-28. Load-deflection curves of slabs from Genikomsou and Polak ......................................... 54
Figure 2-29. Strengthening patterns from Sissakis and Sheikh ............................................................ 54
Figure 2-30. Load–deformation curves of slabs from Sissakis and Sheikh .......................................... 55
Figure 2-31. Critical shear section of slabs with and without shear reinforcement .............................. 55
Figure 2-32. Details and strengthening pattern of RC slabs from Chen and Li. ................................... 56
Figure 2-33. Load-deformation curves of the slabs from Chen and Li ................................................. 57
Figure 2-34. Details and dimensions of the specimen in Harajli and Soudki ....................................... 58
Figure 2-35. Failure modes of FRP strengthened slabs with full composite action .............................. 60
Figure 2-36. De-bonding failure modes ................................................................................................ 60
Figure 2-37. Different kinds of FRP de-bonding initiated in the concrete. .......................................... 61
Figure 2-38. CDC de-bonding .............................................................................................................. 62
Figure 2-39. De-bonding due to the unevenness of concrete. ............................................................... 62
Figure 2-40. Single and double shear tests to investigate the bond strength ........................................ 63
Figure 2-41. Shear-slip relation in differently strengthened concretes ................................................. 64
Figure 2-42. Bond-slip models in Lu et al. investigation ...................................................................... 64
7
Figure 2-43. Experimental and theoretical results of bond strength and effective length..................... 66
Figure 2-44.Control perimeters around the loaded areas according to Eurocode 2. ............................. 68
Figure 2-45. Strain and stress distribution over the slab thickness ....................................................... 69
Figure 2-46. Control perimeters around the loaded areas according to ACI 318. ................................ 70
Chapter 3
Figure 3-1. Abdullah’s test layout......................................................................................................... 76
Figure 3-2. Applying prestressed FRP plates to the RC structures surface. ......................................... 77
Figure 3-3. Abdullah’s test setup. ......................................................................................................... 78
Figure 3-4. Load-deflection curves of the RC slabs in Abdullah’s study. ............................................ 79
Figure 3-5. Kim et al.’s test layout........................................................................................................ 80
Figure 3-6. Anchorage system at the FRP`s end plate. ......................................................................... 81
Figure 3-7. Load-deflection curves of the RC slabs in Kim et al. study. .............................................. 82
Figure 3-8. Uniaxial compression stress-strain curve for concrete. ...................................................... 85
Figure 3-9. Tensile behaviour of concrete ............................................................................................ 86
Figure 3-10. Modified tensile behaviour of concrete on Abaqus. ......................................................... 86
Figure 3-11. Potential surfaces for the yield and plastic. ...................................................................... 89
Figure 3-12. The relations among the principal stresses at failure........................................................ 91
Figure 3-13. The failure surfaces in the deviatoric plane for different values of ............................ 92
Figure 3-14. Concrete damage parameters in compression. ................................................................. 93
Figure 3-15. Concrete damage parameters in tension. .......................................................................... 93
Figure 3-16. Parameters of flow potential ............................................................................................ 94
Figure 3-17. Stress–strain curve of steel ............................................................................................... 95
Figure 3-18. Tri-linear stress–strain curve for steel material. ............................................................... 95
Figure 3-19. Unidirectional, transversely isotropic lamina ................................................................... 97
Figure 3-20. Local and global coordinate axes. .................................................................................... 98
Figure 3-21. Boundary condition and loading situation in the FEM modelling of slab R0. ................. 99
Figure 3-22. The elements in the Abaqus library ................................................................................ 100
Figure 3-23. The different shapes of the continuum element ............................................................. 100
Figure 3-24. Finite element model partitioning. ................................................................................. 101
Figure 3-25. First- and second-order 3D elements.............................................................................. 101
Figure 3-26. Reduced and fully integrated methods ........................................................................... 102
Figure 3-27. The natural deformation of an element under a pure bending moment. ........................ 103
Figure 3-28. The deformation of a fully integrated linear element under a pure bending moment. ... 103
Figure 3-29. The deformation of a linear element to reduced integration under a bending moment. . 103
Figure 3-30. Mesh sensitivity analysis of samples R-F0 and RC-F0. ................................................. 105
Figure 3-31. Load–deflection curves of the models in Abdullah’s study. .......................................... 107
Figure 3-32. Load–deflection curves of the models in Kim et al.’s study. ......................................... 108
Figure 3-33. Concrete cracks in R0. ................................................................................................... 109
Figure 3-34. Tensile crack propagation (Tension damage) in R0. ...................................................... 109
Figure 3-35. Concrete cracks in RC0. ................................................................................................. 110
Figure 3-36. Stress distribution and sectional analysis of flexural punching failure mode. ............... 111
Figure 3-37. Concrete cracks in R-F0. ................................................................................................ 112
Figure 3-38. Concrete cracks in RC-F0. ............................................................................................. 112
Figure 3-39. Slab section at the position of the prestressed end plate. ............................................... 115
Figure 3-40. The stress zones across the section of slabs at the prestressed FRP end plate. .............. 116
8
Figure 3-41.Distributions of normal stresses in the concrete section near the end plate. ................... 116
Figure 3-42. Flexural-shear cracks cause de-bonding near the end plate in R-F30. ........................... 117
Figure 3-43. Concrete cracks on the tension surface of R-F15. .......................................................... 117
Figure 3-44.Concrete cracks in R-F30. ............................................................................................... 118
Figure 3-45.Slab section at the position of prestressed end plate in RC-F15. .................................... 120
Figure 3-46. The stress distribution in RC slab strengthened with prestressed FRP. ......................... 122
Figure 3-47. The slabs failure mode by varying the FRP prestress ratio. ........................................... 124
Figure 3-48. The optimum FRP prestress ratio for different sets of effective parameters. ................. 126
Figure 3-49. Graph provided to find the optimum FRP prestress ratio to strengthen RC slabs.......... 129
Chapter 4
Figure 4-2. Bending moments of slabs in different conditions. .......................................................... 135
Figure 4-3. Continuous slabs. ............................................................................................................. 135
Figure 4-4. Category L slab layout. .................................................................................................... 136
Figure 4-5. Category H slab layout. .................................................................................................... 137
Figure 4-6. FRP sheets on the tension surface of the FRP strengthened specimens. .......................... 137
Figure 4-7. Actual and required FRP lengths. .................................................................................... 138
Figure 4-8. Positions of vertical (shear) reinforcement in the shear strengthened samples. ............... 139
Figure 4-9. Slab mould prepared for concrete casting. ....................................................................... 142
Figure 4-10. Support frame. ................................................................................................................ 142
Figure 4-11. Casting concrete in the mould and samples. .................................................................. 143
Figure 4-12. Applying vertical (shear) reinforcement. ....................................................................... 144
Figure 4-13. Slab preparation to apply FRP sheets. ............................................................................ 145
Figure 4-14. FRP sheets applied on the tension surface of the slab. ................................................... 146
Figure 4-15. Strain gauge positions relative to the tensile reinforcement of the slabs. ...................... 146
Figure 4-16. Concrete strain gauge positions around the column zone. ............................................. 147
Figure 4-17. FRP strain gauge positions. ............................................................................................ 148
Figure 4-18. Testing procedure. .......................................................................................................... 149
Figure 4-19. Load–deflection curves of the RC slabs. ........................................................................ 151
Figure 4-20. Load–deflection curves of the experimental and FE models for L0. ............................. 152
Figure 4-21. Cracks in the experimental and FE models for L0. ........................................................ 153
Figure 4-22. Load–strain curves of the internal tensile reinforcement. .............................................. 153
Figure 4-23. Load–strain curve of the concrete in the column vicinity. ............................................. 154
Figure 4-24. Sectional analysis of an RC slab with low tensile reinforcement ratio .......................... 154
Figure 4-25. Load–deflection curves of the experimental and FE models for LS. ............................. 155
Figure 4-26. Cracks in the experimental and FE models for LS. ........................................................ 156
Figure 4-27. Load–strain curves of the internal tensile reinforcement. .............................................. 156
Figure 4-28. Load–strain curve of the concrete in the column vicinity. ............................................. 157
Figure 4-29. Load–deflection curves of the experimental and FE models for LF. ............................. 158
Figure 4-30. Punching failure in the column vicinity of LF. .............................................................. 158
Figure 4-31. Load–strain curve of the concrete in the column vicinity. ............................................. 159
Figure 4-32. Load–strain curves of the internal tensile reinforcement. .............................................. 159
Figure 4-33. Load–strain curves of the CFRP composites. ................................................................ 160
Figure 4-34. Stress and strain distributions in the FRP strengthened slab section. ............................. 161
Figure 4-35. Sectional analysis of RC slabs with high tensile reinforcement ratio ............................ 162
9
Figure 4-36. Concrete cracks in the tension surface of LF. ................................................................ 163
Figure 4-37. Load–deflection curves of the experimental and FE models for LFS. ........................... 164
Figure 4-38. Punching failure initiating from the shear strengthened zone. ....................................... 164
Figure 4-39. Load–strain curve of the concrete in the column vicinity. ............................................. 164
Figure 4-40. Load–strain curves of the internal tensile reinforcement. .............................................. 165
Figure 4-41. Load–strain curves of the CFRP sheets. ......................................................................... 165
Figure 4-42. Punching failure in LF and LFS. .................................................................................... 167
Figure 4-43. Strut and tie model for punching failure of RC slabs ..................................................... 167
Figure 4-44. Effect of applied forces on the critical compressive strut of an RC flat slab. ................ 168
Figure 4-45. Vertical (shear) reinforcement mechanism to increase the slab punching strength. ...... 168
Figure 4-46. Critical compressive strut in an RC slab considering shear strengthening..................... 169
Figure 4-47. Concrete cracks in the tension surface of LFS. .............................................................. 170
Figure 4-48. Load–deflection curves of the experimental and FE models for H0. ............................. 171
Figure 4-49. Punching failure in the column vicinity of H0. .............................................................. 171
Figure 4-50. Load–strain curve of the concrete in the column vicinity. ............................................. 172
Figure 4-51. Load–strain curves of the internal tensile reinforcement. .............................................. 172
Figure 4-52. Concrete cracks in the tension surface of H0. ................................................................ 173
Figure 4-53.Load–deflection curves of the experimental and FE models for HS. .............................. 174
Figure 4-54. Flexural punching failure in HS. .................................................................................... 174
Figure 4-55. Load–strain curves of the steel reinforcement. .............................................................. 175
Figure 4-56. Load–strain curve of the concrete in the column vicinity. ............................................. 175
Figure 4-57. Punching failure in H0 and HS. ..................................................................................... 176
Figure 4-58. Concrete cracks in the tension surface of HS. ................................................................ 177
Figure 4-59. Load–deflection curves of the experimental and FE models for HF. ............................. 178
Figure 4-60. Punching failure in HF. .................................................................................................. 179
Figure 4-61. Load–strain curve of the concrete in the column vicinity. ............................................. 179
Figure 4-62. Load–strain curves of the steel reinforcement. .............................................................. 180
Figure 4-63. Load–strain curves of the CFRP composites. ................................................................ 180
Figure 4-64. RC slabs strut and tie models before and after FRP strengthening. ............................... 182
Figure 4-65. Critical compressive struts in un-strengthened and FRP strengthened slabs. ................ 183
Figure 4-66. Concrete cracks on the tension face of HF. .................................................................... 184
Figure 4-67. Load–deflection curves of the experimental and FE models for HFS. .......................... 185
Figure 4-68. Concrete cracks on the tension face of HFS................................................................... 185
Figure 4-69. Load–strain curve of the concrete strain in the column vicinity. ................................... 186
Figure 4-70. Load–strain curves of the steel reinforcement. .............................................................. 186
Figure 4-71. Load–strain curves of the CFRP composites. ................................................................ 187
Chapter 5
Figure 5-1. Slab with 0.3% tensile reinforcement ratio (S-0.3). ......................................................... 192
Figure 5-2. Slab with 0.5% tensile reinforcement ratio (S-0.5). ......................................................... 192
Figure 5-3. Slab with 0.85% tensile reinforcement ratio (S-0.85). ..................................................... 193
Figure 5-4. Slab with 1.1% tensile reinforcement ratio (S-1.1). ......................................................... 193
Figure 5-5. Slab with 1.6% tensile reinforcement ratio (S-1.6). ......................................................... 193
Figure 5-6. Load–tensile reinforcement ratio curve. ........................................................................... 194
Figure 5-7. Deflection–tensile reinforcement ratio curve. .................................................................. 195
Figure 5-8. Load–deflection curves of RC slabs with different tensile reinforcement ratio. .............. 195
10
Figure 5-9. The arrangement of reinforcements in SC-0.5. ................................................................ 197
Figure 5-10. The arrangement of reinforcements in SC-1.1. .............................................................. 197
Figure 5-11. Load–deflection curves of RC slabs with and without compressive reinforcements. .... 198
Figure 5-12. Orthogonal and skewed pattern of FRP sheets to strengthen RC slabs. ......................... 200
Figure 5-13. Load–deflection curves of strengthened RC slabs by varying strengthening patterns. .. 201
Figure 5-14. FRP strengthening patterns with different FRP layers. .................................................. 202
Figure 5-15. Load–deflection curves of strengthened RC slabs by varying FRP layers. .................... 203
Figure 5-16. Load–deflection curves of strengthened RC slabs by varying FRP thickness. .............. 204
11
Table 3-2. Characteristics of different kinds of FRP composites ......................................................... 30
Table 2-3. Tensile reinforcement requirements for the RC flexural structures..................................... 36
Table 2-4. Effect of FRP strengthening on the flat RC slabs in Ebead et al. model ............................. 42
Table 2-5. Specimen characteristics in Elsayed et al. ........................................................................... 43
Table 2-6. Test results from Genikomsou and Polak. ........................................................................... 53
Table 2-7. Test results from Chen and Li ............................................................................................. 57
Chapter 3
Table 3-2. Properties of the steel bars. .................................................................................................. 76
Table 3-3. Properties of FRP. ............................................................................................................... 77
Table 3-4. Ultimate load capacity of the slabs in Abdullah’s investigation. ........................................ 79
Table 3-5. Properties of the concrete. ................................................................................................... 80
Table 3-6. Properties of the steel bars. .................................................................................................. 81
Table 3-7. Properties of CFRP. ............................................................................................................. 81
Table 3-8. The ultimate load capacity of the slabs in Kim et al. investigation ..................................... 82
Table 3-9. Parameters of the CDP model ............................................................................................. 94
Table 3-10. Comparison between numerical and experimental results. ............................................. 106
Table 3-11. A comparison between R-F30 and R2-F30 in terms of load capacity. ............................ 119
Table 3-12. The effect of varying slab depth with ultimate load capacity in earlier de-bonding. ...... 119
Table 3-13. Comparing the FRP strengthened slabs based on their effective parameters. ................. 121
Table 3-14. Different variable sets of concrete tensile strength and slab depth. ................................. 127
Table 3-15. The relation between the effective parameters to find the optimum FRP prestress ratio.128
Chapter 4
Table 4-1. Slabs labelled according to the strengthening method. ..................................................... 133
Table 4-2. Estimation of the required FRP lengths based on Chen and Teng’s suggestion. .............. 138
Table 4-3. Concrete mix design. ......................................................................................................... 140
Table 4-4. Concrete properties of different slabs. ............................................................................... 140
Table 4-5. Mechanical properties of the steel bar. .............................................................................. 140
Table 4-6. CFRP composite properties ............................................................................................... 141
Table 4-7. Experimental and FE model results. .................................................................................. 150
Table 4-8. Comparison between the control and shear strengthened specimens. ............................... 157
Table 4-9. Comparison between L0 and LF. ...................................................................................... 161
Table 4-10. Comparison between L0 and LFS. .................................................................................. 166
Table 4-11. Comparison between LF and LFS. .................................................................................. 166
Table 4-12. Comparison between H0 and HS. .................................................................................... 176
Table 4-13. Comparison between H0 and HF. .................................................................................... 181
12
Table 4-14. Comparison between H0 and HFS. ................................................................................. 187
Table 4-15. Comparison between HF and HFS. ................................................................................. 188
Table 4-16. Experimental results and model estimations to predict the punching capacity of slabs. . 188
Chapter 5
Table 5-2. Steel reinforcements properties. ........................................................................................ 191
Table 5-3. Model results by varying their tensile reinforcement ratios. ............................................. 194
Table 5-4. The effect of different strengthening methods on RC slabs in different conditions. ......... 196
Table 5-5. Models description. ........................................................................................................... 197
Table 5-8. The effect of compressive reinforcement on the behaviour of RC slabs. .......................... 198
Table 5-9. The effect of strengthening methods on RC slabs with compressive reinforcement. ........ 199
Table 5-10. Models description. ......................................................................................................... 200
Table 5-11. The effect of different strengthening patterns on the behaviour of RC slabs. ................. 200
Table 5-12. Models description. ......................................................................................................... 202
Table 5-13. The effect of varying FRP layers on the behaviour of strengthened RC slabs. ............... 203
Table 5-14. Models description. ......................................................................................................... 203
Table 5-15. The effect of varying FRP thickness on the behaviour of strengthened RC slabs. .......... 204
13
Abstract
In this thesis, the experimental programmes and numerical investigations are described that
have been conducted to partially cover the knowledge gap in the field of strengthening two-
way reinforced concrete (RC) flat slabs. The conducted studies demonstrate that the most
common method to strengthen two-way RC slabs is by applying fibre reinforced polymers
(FRP) on the tension surface of the slabs. Applying prestressed FRP to strengthen two-way flat
slabs combines the advantages of both FRP strengthening and prestressing to enhance the
efficiency of the strengthening methods. Hence, two previous studies on strengthening two-
way flat slabs with non-prestressed and prestressed FRP are analysed to clarify the effect of
different strengthening methods…
A thesis submitted to The University of Manchester for the degree of Doctor of
Philosophy in the Faculty of Science and Engineering
2018
2
2.3. Two-way RC slab behaviour .............................................................................. 33
2.4. Strengthening of two-way RC slabs ................................................................... 40
2.4.1. Flexural strengthening................................................................................. 40
2.4.2.1. Punching failure mechanism ............................................................................ 44
2.4.2.2. Effective parameters for punching strength ..................................................... 48
2.4.2.3. Punching strengthening methods ..................................................................... 52
2.5. Slabs strengthened with FRP .............................................................................. 58
2.5.1. The behaviour and failure mode of FRP strengthened slabs ...................... 58
3
2.5.1.1. FRP strengthened RC slabs with full of composite action ............................... 58
2.5.1.2. FRP strengthened RC slabs with a partial loss of composite action ................ 60
2.5.2. Bond behaviour between concrete and FRP ............................................... 62
2.5.3. Design codes estimation in composite action ............................................. 67
2.5.3.1 Evaluation of the slabs punching strength ........................................................ 67
2.5.3.2. Evaluation of the slabs flexural capacity ......................................................... 70
2.5.4. Prestressed FRP as an external reinforcement ............................................ 72
2.6. Summary ............................................................................................................. 73
3. Strengthening RC slabs with non-prestressed and prestressed FRP ...... 73
3.1. Introduction ......................................................................................................... 74
3.2.2. Kim et al.’s experimental investigation ...................................................... 79
3.3. Numerical Modelling .......................................................................................... 83
3.3.2.2. Concrete damage modelling ............................................................................. 87
3.3.3. Steel modelling ........................................................................................... 95
3.3.4. FRP modelling ............................................................................................ 96
3.3.6. Finite element type and mesh.................................................................... 100
3.3.7. Mesh convergence..................................................................................... 104
3.3.8. Validation of finite element models .......................................................... 105
3.4. Analysis and discussion of results .................................................................... 108
3.5. The optimum FRP prestress ratio to strengthen RC slabs ................................ 123
3.6. Summary ........................................................................................................... 130
4.1. Introduction ....................................................................................................... 132
4.2. Experimental test .............................................................................................. 133
4.2.1. Rationale behind choosing the dimension of the tested slabs ................... 134
4
4.2.3. Materials.................................................................................................... 139
4.2.5. Measurement instrumentation ................................................................... 146
4.3. Results and discussion ...................................................................................... 150
4.3.1. Experimental and FE model results .......................................................... 150
4.3.2. Slabs with an initial low tensile reinforcement ratio (category L) ............ 152
4.3.2.1. Control specimen with a low tensile reinforcement ratio (L0) ...................... 152
4.3.2.2. Shear strengthened slab with a low tensile reinforcement ratio (LS) ............ 155
4.3.2.3. FRP strengthened slab with an initial low tensile reinforcement ratio (LF) .. 158
4.3.2.4. FRP and shear strengthened slab with low tensile reinforcement ratio (LFS)163
4.3.3. Slabs with an initial high tensile reinforcement ratio (category H) .......... 171
4.3.3.1. Control specimen with a high tensile reinforcement ratio (H0) ..................... 171
4.3.3.2. Shear strengthened slab with a high tensile reinforcement ratio (HS) ........... 174
4.3.3.3. FRP strengthened slab with an initial high tensile reinforcement ratio (HF) . 178
4.3.3.4. FRP and shear strengthened slab with high tensile reinforcement ratio (HFS) ... 184
4.3.4. Assessment of models to predict the capacity of the slabs ....................... 188
4.4. Summary ........................................................................................................... 190
5.2.2. The compressive reinforcement ................................................................ 196
5.2.3. The pattern of FRP sheets to strengthen RC slabs .................................... 200
5
5.2.4. The number of FRP sheets ........................................................................ 201
5.2.5. The thickness of FRP sheets to strengthen RC slabs ................................ 203
5.3. Summary ........................................................................................................... 205
References ................................................................................................. 211
Figure 2-1. Strengthening RC structures with steel members ............................................................... 27
Figure 2-2. Strengthening RC elements with FRP on the Country Hills Boulevard Bridge ................. 29
Figure 2-3. Fibre reinforced polymer matrix. ....................................................................................... 29
Figure 2-4. Unidirectional FRP, woven FRP and FRP laminate. ......................................................... 30
Figure 2-5. Strengthening RC structure using an FRP plate ................................................................. 31
Figure 2-6. Strengthening RC columns with FRP sheets. ..................................................................... 32
Figure 2-7. Stress-strain curve for FRPs and mild steel. ....................................................................... 32
Figure 2-8. One-way and two-way RC slabs. ....................................................................................... 33
Figure 2-9. Load–deflection curves of typical ductile and brittle materials ......................................... 35
Figure 2-10. Effective parameters in RC sections of flexural members. .............................................. 36
Figure 2-11. Two-way RC slab failure mode based on the steel reinforcement ratio ........................... 37
Figure 2-12. Typical load-deflection curves of flat slabs with ductile and brittle failures. .................. 37
Figure 2-13. Load-rotation curves of RC slabs with varying tensile reinforcement ratios ................... 38
Figure 2-14. Load-deflection curves of RC slabs with varying tensile reinforcement ratio ................. 39
Figure 2-15. Experimental layout of the slabs in Ebead et al. .............................................................. 41
Figure 2-16. FRP strengthening patterns in Elsayed et al. .................................................................... 43
Figure 2-17. Load-deflection curves of the specimens in Limam et al.. ............................................... 43
Figure 2-18. Slab failure in Limam et al. .............................................................................................. 44
Figure 2-19. Direct (one-way) shear and punching shear failure positions .......................................... 45
Figure 2-20. Loaded areas in one-way shear and punching failure ...................................................... 46
Figure 2-21. Slab deformation during punching test ............................................................................ 46
Figure 2-22.Radial and tangential concrete strains at different distances from the column side. ......... 47
Figure 2-23. Crack angle in a concrete flat slab ................................................................................... 48
Figure 2-24. Effective dimensions to calculate the capacity of slabs in Rankin and Long model. ....... 49
Figure 2-25. Relation between the punching strength and flexural capacity of slabs ........................... 50
Figure 2-26. Examples of shear reinforcement in RC slabs. ................................................................. 51
Figure 2-27. Details and strengthening patterns of RC slabs in Genikomsou and Polak. .................... 53
Figure 2-28. Load-deflection curves of slabs from Genikomsou and Polak ......................................... 54
Figure 2-29. Strengthening patterns from Sissakis and Sheikh ............................................................ 54
Figure 2-30. Load–deformation curves of slabs from Sissakis and Sheikh .......................................... 55
Figure 2-31. Critical shear section of slabs with and without shear reinforcement .............................. 55
Figure 2-32. Details and strengthening pattern of RC slabs from Chen and Li. ................................... 56
Figure 2-33. Load-deformation curves of the slabs from Chen and Li ................................................. 57
Figure 2-34. Details and dimensions of the specimen in Harajli and Soudki ....................................... 58
Figure 2-35. Failure modes of FRP strengthened slabs with full composite action .............................. 60
Figure 2-36. De-bonding failure modes ................................................................................................ 60
Figure 2-37. Different kinds of FRP de-bonding initiated in the concrete. .......................................... 61
Figure 2-38. CDC de-bonding .............................................................................................................. 62
Figure 2-39. De-bonding due to the unevenness of concrete. ............................................................... 62
Figure 2-40. Single and double shear tests to investigate the bond strength ........................................ 63
Figure 2-41. Shear-slip relation in differently strengthened concretes ................................................. 64
Figure 2-42. Bond-slip models in Lu et al. investigation ...................................................................... 64
7
Figure 2-43. Experimental and theoretical results of bond strength and effective length..................... 66
Figure 2-44.Control perimeters around the loaded areas according to Eurocode 2. ............................. 68
Figure 2-45. Strain and stress distribution over the slab thickness ....................................................... 69
Figure 2-46. Control perimeters around the loaded areas according to ACI 318. ................................ 70
Chapter 3
Figure 3-1. Abdullah’s test layout......................................................................................................... 76
Figure 3-2. Applying prestressed FRP plates to the RC structures surface. ......................................... 77
Figure 3-3. Abdullah’s test setup. ......................................................................................................... 78
Figure 3-4. Load-deflection curves of the RC slabs in Abdullah’s study. ............................................ 79
Figure 3-5. Kim et al.’s test layout........................................................................................................ 80
Figure 3-6. Anchorage system at the FRP`s end plate. ......................................................................... 81
Figure 3-7. Load-deflection curves of the RC slabs in Kim et al. study. .............................................. 82
Figure 3-8. Uniaxial compression stress-strain curve for concrete. ...................................................... 85
Figure 3-9. Tensile behaviour of concrete ............................................................................................ 86
Figure 3-10. Modified tensile behaviour of concrete on Abaqus. ......................................................... 86
Figure 3-11. Potential surfaces for the yield and plastic. ...................................................................... 89
Figure 3-12. The relations among the principal stresses at failure........................................................ 91
Figure 3-13. The failure surfaces in the deviatoric plane for different values of ............................ 92
Figure 3-14. Concrete damage parameters in compression. ................................................................. 93
Figure 3-15. Concrete damage parameters in tension. .......................................................................... 93
Figure 3-16. Parameters of flow potential ............................................................................................ 94
Figure 3-17. Stress–strain curve of steel ............................................................................................... 95
Figure 3-18. Tri-linear stress–strain curve for steel material. ............................................................... 95
Figure 3-19. Unidirectional, transversely isotropic lamina ................................................................... 97
Figure 3-20. Local and global coordinate axes. .................................................................................... 98
Figure 3-21. Boundary condition and loading situation in the FEM modelling of slab R0. ................. 99
Figure 3-22. The elements in the Abaqus library ................................................................................ 100
Figure 3-23. The different shapes of the continuum element ............................................................. 100
Figure 3-24. Finite element model partitioning. ................................................................................. 101
Figure 3-25. First- and second-order 3D elements.............................................................................. 101
Figure 3-26. Reduced and fully integrated methods ........................................................................... 102
Figure 3-27. The natural deformation of an element under a pure bending moment. ........................ 103
Figure 3-28. The deformation of a fully integrated linear element under a pure bending moment. ... 103
Figure 3-29. The deformation of a linear element to reduced integration under a bending moment. . 103
Figure 3-30. Mesh sensitivity analysis of samples R-F0 and RC-F0. ................................................. 105
Figure 3-31. Load–deflection curves of the models in Abdullah’s study. .......................................... 107
Figure 3-32. Load–deflection curves of the models in Kim et al.’s study. ......................................... 108
Figure 3-33. Concrete cracks in R0. ................................................................................................... 109
Figure 3-34. Tensile crack propagation (Tension damage) in R0. ...................................................... 109
Figure 3-35. Concrete cracks in RC0. ................................................................................................. 110
Figure 3-36. Stress distribution and sectional analysis of flexural punching failure mode. ............... 111
Figure 3-37. Concrete cracks in R-F0. ................................................................................................ 112
Figure 3-38. Concrete cracks in RC-F0. ............................................................................................. 112
Figure 3-39. Slab section at the position of the prestressed end plate. ............................................... 115
Figure 3-40. The stress zones across the section of slabs at the prestressed FRP end plate. .............. 116
8
Figure 3-41.Distributions of normal stresses in the concrete section near the end plate. ................... 116
Figure 3-42. Flexural-shear cracks cause de-bonding near the end plate in R-F30. ........................... 117
Figure 3-43. Concrete cracks on the tension surface of R-F15. .......................................................... 117
Figure 3-44.Concrete cracks in R-F30. ............................................................................................... 118
Figure 3-45.Slab section at the position of prestressed end plate in RC-F15. .................................... 120
Figure 3-46. The stress distribution in RC slab strengthened with prestressed FRP. ......................... 122
Figure 3-47. The slabs failure mode by varying the FRP prestress ratio. ........................................... 124
Figure 3-48. The optimum FRP prestress ratio for different sets of effective parameters. ................. 126
Figure 3-49. Graph provided to find the optimum FRP prestress ratio to strengthen RC slabs.......... 129
Chapter 4
Figure 4-2. Bending moments of slabs in different conditions. .......................................................... 135
Figure 4-3. Continuous slabs. ............................................................................................................. 135
Figure 4-4. Category L slab layout. .................................................................................................... 136
Figure 4-5. Category H slab layout. .................................................................................................... 137
Figure 4-6. FRP sheets on the tension surface of the FRP strengthened specimens. .......................... 137
Figure 4-7. Actual and required FRP lengths. .................................................................................... 138
Figure 4-8. Positions of vertical (shear) reinforcement in the shear strengthened samples. ............... 139
Figure 4-9. Slab mould prepared for concrete casting. ....................................................................... 142
Figure 4-10. Support frame. ................................................................................................................ 142
Figure 4-11. Casting concrete in the mould and samples. .................................................................. 143
Figure 4-12. Applying vertical (shear) reinforcement. ....................................................................... 144
Figure 4-13. Slab preparation to apply FRP sheets. ............................................................................ 145
Figure 4-14. FRP sheets applied on the tension surface of the slab. ................................................... 146
Figure 4-15. Strain gauge positions relative to the tensile reinforcement of the slabs. ...................... 146
Figure 4-16. Concrete strain gauge positions around the column zone. ............................................. 147
Figure 4-17. FRP strain gauge positions. ............................................................................................ 148
Figure 4-18. Testing procedure. .......................................................................................................... 149
Figure 4-19. Load–deflection curves of the RC slabs. ........................................................................ 151
Figure 4-20. Load–deflection curves of the experimental and FE models for L0. ............................. 152
Figure 4-21. Cracks in the experimental and FE models for L0. ........................................................ 153
Figure 4-22. Load–strain curves of the internal tensile reinforcement. .............................................. 153
Figure 4-23. Load–strain curve of the concrete in the column vicinity. ............................................. 154
Figure 4-24. Sectional analysis of an RC slab with low tensile reinforcement ratio .......................... 154
Figure 4-25. Load–deflection curves of the experimental and FE models for LS. ............................. 155
Figure 4-26. Cracks in the experimental and FE models for LS. ........................................................ 156
Figure 4-27. Load–strain curves of the internal tensile reinforcement. .............................................. 156
Figure 4-28. Load–strain curve of the concrete in the column vicinity. ............................................. 157
Figure 4-29. Load–deflection curves of the experimental and FE models for LF. ............................. 158
Figure 4-30. Punching failure in the column vicinity of LF. .............................................................. 158
Figure 4-31. Load–strain curve of the concrete in the column vicinity. ............................................. 159
Figure 4-32. Load–strain curves of the internal tensile reinforcement. .............................................. 159
Figure 4-33. Load–strain curves of the CFRP composites. ................................................................ 160
Figure 4-34. Stress and strain distributions in the FRP strengthened slab section. ............................. 161
Figure 4-35. Sectional analysis of RC slabs with high tensile reinforcement ratio ............................ 162
9
Figure 4-36. Concrete cracks in the tension surface of LF. ................................................................ 163
Figure 4-37. Load–deflection curves of the experimental and FE models for LFS. ........................... 164
Figure 4-38. Punching failure initiating from the shear strengthened zone. ....................................... 164
Figure 4-39. Load–strain curve of the concrete in the column vicinity. ............................................. 164
Figure 4-40. Load–strain curves of the internal tensile reinforcement. .............................................. 165
Figure 4-41. Load–strain curves of the CFRP sheets. ......................................................................... 165
Figure 4-42. Punching failure in LF and LFS. .................................................................................... 167
Figure 4-43. Strut and tie model for punching failure of RC slabs ..................................................... 167
Figure 4-44. Effect of applied forces on the critical compressive strut of an RC flat slab. ................ 168
Figure 4-45. Vertical (shear) reinforcement mechanism to increase the slab punching strength. ...... 168
Figure 4-46. Critical compressive strut in an RC slab considering shear strengthening..................... 169
Figure 4-47. Concrete cracks in the tension surface of LFS. .............................................................. 170
Figure 4-48. Load–deflection curves of the experimental and FE models for H0. ............................. 171
Figure 4-49. Punching failure in the column vicinity of H0. .............................................................. 171
Figure 4-50. Load–strain curve of the concrete in the column vicinity. ............................................. 172
Figure 4-51. Load–strain curves of the internal tensile reinforcement. .............................................. 172
Figure 4-52. Concrete cracks in the tension surface of H0. ................................................................ 173
Figure 4-53.Load–deflection curves of the experimental and FE models for HS. .............................. 174
Figure 4-54. Flexural punching failure in HS. .................................................................................... 174
Figure 4-55. Load–strain curves of the steel reinforcement. .............................................................. 175
Figure 4-56. Load–strain curve of the concrete in the column vicinity. ............................................. 175
Figure 4-57. Punching failure in H0 and HS. ..................................................................................... 176
Figure 4-58. Concrete cracks in the tension surface of HS. ................................................................ 177
Figure 4-59. Load–deflection curves of the experimental and FE models for HF. ............................. 178
Figure 4-60. Punching failure in HF. .................................................................................................. 179
Figure 4-61. Load–strain curve of the concrete in the column vicinity. ............................................. 179
Figure 4-62. Load–strain curves of the steel reinforcement. .............................................................. 180
Figure 4-63. Load–strain curves of the CFRP composites. ................................................................ 180
Figure 4-64. RC slabs strut and tie models before and after FRP strengthening. ............................... 182
Figure 4-65. Critical compressive struts in un-strengthened and FRP strengthened slabs. ................ 183
Figure 4-66. Concrete cracks on the tension face of HF. .................................................................... 184
Figure 4-67. Load–deflection curves of the experimental and FE models for HFS. .......................... 185
Figure 4-68. Concrete cracks on the tension face of HFS................................................................... 185
Figure 4-69. Load–strain curve of the concrete strain in the column vicinity. ................................... 186
Figure 4-70. Load–strain curves of the steel reinforcement. .............................................................. 186
Figure 4-71. Load–strain curves of the CFRP composites. ................................................................ 187
Chapter 5
Figure 5-1. Slab with 0.3% tensile reinforcement ratio (S-0.3). ......................................................... 192
Figure 5-2. Slab with 0.5% tensile reinforcement ratio (S-0.5). ......................................................... 192
Figure 5-3. Slab with 0.85% tensile reinforcement ratio (S-0.85). ..................................................... 193
Figure 5-4. Slab with 1.1% tensile reinforcement ratio (S-1.1). ......................................................... 193
Figure 5-5. Slab with 1.6% tensile reinforcement ratio (S-1.6). ......................................................... 193
Figure 5-6. Load–tensile reinforcement ratio curve. ........................................................................... 194
Figure 5-7. Deflection–tensile reinforcement ratio curve. .................................................................. 195
Figure 5-8. Load–deflection curves of RC slabs with different tensile reinforcement ratio. .............. 195
10
Figure 5-9. The arrangement of reinforcements in SC-0.5. ................................................................ 197
Figure 5-10. The arrangement of reinforcements in SC-1.1. .............................................................. 197
Figure 5-11. Load–deflection curves of RC slabs with and without compressive reinforcements. .... 198
Figure 5-12. Orthogonal and skewed pattern of FRP sheets to strengthen RC slabs. ......................... 200
Figure 5-13. Load–deflection curves of strengthened RC slabs by varying strengthening patterns. .. 201
Figure 5-14. FRP strengthening patterns with different FRP layers. .................................................. 202
Figure 5-15. Load–deflection curves of strengthened RC slabs by varying FRP layers. .................... 203
Figure 5-16. Load–deflection curves of strengthened RC slabs by varying FRP thickness. .............. 204
11
Table 3-2. Characteristics of different kinds of FRP composites ......................................................... 30
Table 2-3. Tensile reinforcement requirements for the RC flexural structures..................................... 36
Table 2-4. Effect of FRP strengthening on the flat RC slabs in Ebead et al. model ............................. 42
Table 2-5. Specimen characteristics in Elsayed et al. ........................................................................... 43
Table 2-6. Test results from Genikomsou and Polak. ........................................................................... 53
Table 2-7. Test results from Chen and Li ............................................................................................. 57
Chapter 3
Table 3-2. Properties of the steel bars. .................................................................................................. 76
Table 3-3. Properties of FRP. ............................................................................................................... 77
Table 3-4. Ultimate load capacity of the slabs in Abdullah’s investigation. ........................................ 79
Table 3-5. Properties of the concrete. ................................................................................................... 80
Table 3-6. Properties of the steel bars. .................................................................................................. 81
Table 3-7. Properties of CFRP. ............................................................................................................. 81
Table 3-8. The ultimate load capacity of the slabs in Kim et al. investigation ..................................... 82
Table 3-9. Parameters of the CDP model ............................................................................................. 94
Table 3-10. Comparison between numerical and experimental results. ............................................. 106
Table 3-11. A comparison between R-F30 and R2-F30 in terms of load capacity. ............................ 119
Table 3-12. The effect of varying slab depth with ultimate load capacity in earlier de-bonding. ...... 119
Table 3-13. Comparing the FRP strengthened slabs based on their effective parameters. ................. 121
Table 3-14. Different variable sets of concrete tensile strength and slab depth. ................................. 127
Table 3-15. The relation between the effective parameters to find the optimum FRP prestress ratio.128
Chapter 4
Table 4-1. Slabs labelled according to the strengthening method. ..................................................... 133
Table 4-2. Estimation of the required FRP lengths based on Chen and Teng’s suggestion. .............. 138
Table 4-3. Concrete mix design. ......................................................................................................... 140
Table 4-4. Concrete properties of different slabs. ............................................................................... 140
Table 4-5. Mechanical properties of the steel bar. .............................................................................. 140
Table 4-6. CFRP composite properties ............................................................................................... 141
Table 4-7. Experimental and FE model results. .................................................................................. 150
Table 4-8. Comparison between the control and shear strengthened specimens. ............................... 157
Table 4-9. Comparison between L0 and LF. ...................................................................................... 161
Table 4-10. Comparison between L0 and LFS. .................................................................................. 166
Table 4-11. Comparison between LF and LFS. .................................................................................. 166
Table 4-12. Comparison between H0 and HS. .................................................................................... 176
Table 4-13. Comparison between H0 and HF. .................................................................................... 181
12
Table 4-14. Comparison between H0 and HFS. ................................................................................. 187
Table 4-15. Comparison between HF and HFS. ................................................................................. 188
Table 4-16. Experimental results and model estimations to predict the punching capacity of slabs. . 188
Chapter 5
Table 5-2. Steel reinforcements properties. ........................................................................................ 191
Table 5-3. Model results by varying their tensile reinforcement ratios. ............................................. 194
Table 5-4. The effect of different strengthening methods on RC slabs in different conditions. ......... 196
Table 5-5. Models description. ........................................................................................................... 197
Table 5-8. The effect of compressive reinforcement on the behaviour of RC slabs. .......................... 198
Table 5-9. The effect of strengthening methods on RC slabs with compressive reinforcement. ........ 199
Table 5-10. Models description. ......................................................................................................... 200
Table 5-11. The effect of different strengthening patterns on the behaviour of RC slabs. ................. 200
Table 5-12. Models description. ......................................................................................................... 202
Table 5-13. The effect of varying FRP layers on the behaviour of strengthened RC slabs. ............... 203
Table 5-14. Models description. ......................................................................................................... 203
Table 5-15. The effect of varying FRP thickness on the behaviour of strengthened RC slabs. .......... 204
13
Abstract
In this thesis, the experimental programmes and numerical investigations are described that
have been conducted to partially cover the knowledge gap in the field of strengthening two-
way reinforced concrete (RC) flat slabs. The conducted studies demonstrate that the most
common method to strengthen two-way RC slabs is by applying fibre reinforced polymers
(FRP) on the tension surface of the slabs. Applying prestressed FRP to strengthen two-way flat
slabs combines the advantages of both FRP strengthening and prestressing to enhance the
efficiency of the strengthening methods. Hence, two previous studies on strengthening two-
way flat slabs with non-prestressed and prestressed FRP are analysed to clarify the effect of
different strengthening methods…
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