Reinforced Concrete Deep Beams

Cover......Page 1
Reinforced Concrete Deep Beams......Page 3
Preface......Page 5
Contributors......Page 6
Contents......Page 11
Introduction......Page 17
History and development......Page 18
CIRIA Guide 2......Page 20
CIRIA Guide ‘Simple Rules’......Page 21
CIRIA Guide ‘Supplementary Rules’......Page 24
Flexural strength: simply supported deep beams......Page 27
Shear strength and web reinforcement......Page 28
Shear strength......Page 29
Flexural strength......Page 32
Shear strength......Page 33
References......Page 34
Current concepts for beam design......Page 37
Flexural capacity......Page 39
Shear capacity......Page 45
Compressive force path concept......Page 52
Deep beam behaviour at ultimate limit state......Page 54
Causes of failure......Page 56
Arch and tie action......Page 60
Effect of transverse reinforcement......Page 61
Modelling......Page 63
Design method......Page 66
Verification of design method......Page 69
References......Page 73
Notation......Page 76
Introduction......Page 77
Beam with circular web openings......Page 79
Flexural cracks......Page 81
General behaviour in shear failure ( under four- point loading)......Page 82
Effect of web opening......Page 83
Diagonal mode of shear failure load......Page 84
Definitions......Page 85
Criterion of failure and strength theory......Page 88
Ultimate shear strength......Page 90
Evaluation of web opening parameters......Page 93
Ultimate shear strength......Page 95
Simplified design expression......Page 96
Ultimate strength in flexure......Page 98
Extension of theory of ultimate shear strength of beams to fourpoint loading......Page 101
Recommendations for design of beams for shear and flexure......Page 104
Design example......Page 105
References......Page 109
Introduction......Page 111
Previous tests......Page 113
Continuous deep beams vs continuous shallow beams......Page 115
Elastic analysis......Page 118
Finite element analysis......Page 119
Truss models......Page 120
Truss models for continuous deep beams......Page 121
Design of continuous deep beams......Page 125
Design example......Page 126
Summary......Page 128
References......Page 129
Introduction......Page 131
Review of current knowledge......Page 132
Modes of failure......Page 135
Mode of failure 1: flexural- shear failure......Page 136
Mode of failure 4: splitting with compression failure......Page 138
Analysis......Page 139
ACI Building Code......Page 140
CIRIA Guide 2......Page 142
Method of Taner et al.......Page 143
Method of Subedi for flanged beams with web stiffeners......Page 144
Design example 1: Beam- panel P311 ( Taner et al, 1977)......Page 146
Design example 2: ACI Code......Page 149
References......Page 151
Introduction......Page 153
Early tests on deep beams under top and bottom loading......Page 154
Description of test specimens......Page 157
Crack patterns......Page 158
Crack widths......Page 160
American Concrete Institute......Page 162
Schütt’s equations......Page 165
Top- loaded wall- beams......Page 166
Bottom- loaded wall- beams......Page 168
Combined top and bottom loading......Page 169
References......Page 172
Notation......Page 173
Introduction......Page 174
Shear element......Page 176
Effective transverse compression......Page 177
Fundamental assumptions......Page 180
Stress transformation ( equilibrium)......Page 181
Strain transformation ( compatibility)......Page 182
Material laws......Page 183
Solution algorithm......Page 184
Accuracy......Page 186
Shear- span- to- height ratio......Page 189
Longitudinal reinforcement......Page 191
Transverse reinforcement......Page 192
Derivation of equation......Page 193
Calibration......Page 194
References......Page 196
Notation......Page 198
Limit analysis......Page 199
Rigid, perfectly plastic model......Page 200
Concrete modelling......Page 201
Reinforcement modelling......Page 203
Yield lines......Page 204
Shear strength of deep beams......Page 206
Lower bound analysis......Page 207
Upper bound analysis......Page 212
Experimental evidence......Page 216
Shear reinforcement......Page 217
Conclusion......Page 218
References......Page 219
Notation......Page 220
Concept of finite element method......Page 221
Triangular plane stress elements......Page 223
Isoparametric quadrilaterals......Page 227
Stiffness matrix of rectangle with sides 2a×2b......Page 231
Finite element model for cracked reinforced concrete......Page 234
Modelling of reinforcing steel bars......Page 236
Point element or linkage element......Page 237
Discrete cracking model......Page 238
Smeared cracking model......Page 239
Modelling of constitutive relationships of concrete......Page 241
Constitutive relationship of steel bars......Page 242
Stiffness of cracked element......Page 243
Solution procedure......Page 244
Increment procedure......Page 245
Iterative procedure......Page 246
Flow chart of the non-linear analysis procedure......Page 249
References......Page 252
Notation......Page 254
Introduction......Page 255
Ultimate load behaviour......Page 257
Current design methods.CIRIA Guide 2 (1977)......Page 259
CIRIA Guide Supplementary Rules......Page 260
CIRIA Guide Appendix C: Single-Panel Method......Page 262
The equivalent-column method......Page 264
Theoretical background......Page 265
Stability analysis of columns: graphical method......Page 269
Stability analysis of columns: improved graphical methods......Page 276
Stability analysis of columns: analytical method......Page 286
Deep beam buckling: comparison with test results......Page 294
References......Page 297