Reinforced Concrete Beams, Columns and Frames: Mechanics and ULS Design

Reinforced Concrete Beams, Columns and Frames......Page 2
Copyright\r......Page 3
Table of Contents......Page 4
Preface......Page 8
1.1.1. Simplified rectangular behavior ? rectangular cross-section......Page 14
1.1.2. Simplified rectangular behavior ? T-cross-section......Page 29
1.1.3. Comparison of design between serviceability limit state and ultimate limit state......Page 35
1.1.4. Biaxial bending of a rectangular cross-section......Page 41
1.2.1. Bilinear constitutive law for concrete ? rectangular cross-section......Page 50
1.2.2. Parabola?rectangle constitutive law for concrete ? rectangular cross-section......Page 57
1.2.3. T-cross-section ? general resolution for bilinear or parabola? rectangle laws for concrete......Page 66
1.2.4. T-cross-section ? general equations for composed bending with normal forces......Page 79
1.3.1. Theoretical formulation of the interaction diagram......Page 95
1.3.2. Approximation formulations......Page 107
1.3.3. Graphical results for general cross-sections......Page 111
2.2.1. General......Page 116
2.3.1. Elastic critical load and effective buckling length......Page 118
2.3.3. Concrete column instability ? limit load......Page 123
2.4.1. Global and local second-order effects......Page 125
2.4.2. Single members......Page 126
2.4.3. Frame mechanics ? braced and bracing columns......Page 128
2.4.4. Moment equilibrium at joints......Page 132
2.5.1. Maximum first- and second-order moment at the same section......Page 133
2.5.2. Maximum first- and second-order moment at different sections......Page 137
2.5.3. Curvature-based maximum moment expression......Page 149
2.5.4. Unbraced frame application example......Page 154
2.6.1. Local, lower slenderness limits ? general......Page 157
2.6.2. EC2 ? local lower slenderness limits......Page 161
2.6.3. NS-EC2 ? Local lower slenderness limits......Page 163
2.6.4. Comparison of the EC2 and NS-EC2 limits......Page 168
2.6.5. Local upper slenderness limit......Page 169
2.6.6. Global lower slenderness limit\r......Page 172
2.7.1. General......Page 176
2.7.2. Effects on load and deformation capacity......Page 178
2.7.3. Approximate calculation of creep effects......Page 182
2.8.2. Stiffening structural elements......Page 189
2.8.3. Stiffened and isolated structural elements......Page 193
2.9.1. Principles, equilibrium and compatibility......Page 194
2.9.2. Equilibrium and compatibility at multiple sections......Page 196
2.9.3. Optimization......Page 198
2.10.1. Stiffness assumptions......Page 200
2.10.2. EC2 approach......Page 202
2.10.3. ACI 318 approach......Page 203
2.11.1. General......Page 204
2.11.2. Simplified second-order analysis......Page 205
2.11.3. Method based on nominal stiffness......Page 207
2.11.4. Method based on nominal curvature......Page 213
2.12.1. Simplified design methods......Page 217
2.12.2. Alternative design methods......Page 218
2.12.3. Design example ? framed column......Page 220
3.1.1. Definitions and exact member analysis......Page 226
3.1.2. EC2 effective length of isolated members......Page 231
3.1.3. Alternative effective length expressions......Page 232
3.1.4. Columns with beam restraints......Page 235
3.2.2. Method of means ? typical steps......Page 240
3.2.3. Application of the method of means......Page 243
3.3.1. General considerations......Page 249
3.3.2. Flexibility factors......Page 253
3.3.3. System instability and “system? effective lengths......Page 256
3.3.4. Instability of partially braced column ? example......Page 261
3.3.5. Instability of partially braced frame ? example......Page 264
3.3.6. Sway buckling of unbraced multistory frames......Page 269
3.4.1. General......Page 275
3.4.2. Partially braced column ? example......Page 277
3.4.3. Partially braced frame ? example......Page 279
3.4.4. Sway magnifier prediction of frames with single curvature regions......Page 281
3.4.5. Iterative elastic analysis method......Page 284
3.4.6. Global magnifiers for sway and moments......Page 285
A1.1. Introduction......Page 291
A1.2.1. Canonical form......Page 292
A1.2.2. Resolution ? one real and two complex roots......Page 293
A1.2.4. Resolution ? three real roots......Page 295
A1.3.1. Summary of Cardano’s method......Page 297
A1.3.2. Resolution of a cubic equation ? example......Page 298
A1.4. Roots of a quartic function ? principle of resolution......Page 299
Appendix 2 Steel Reinforcement Table......Page 301
Bibliography......Page 302
Index......Page 316