Critical Excitation Methods in Earthquake Engineering

Front Cover......Page 1
Critical Excitation Methods in Earthquake Engineering......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface......Page 11
Permission Details......Page 15
1.1 What is critical excitation?......Page 18
1.2 Origin of critical excitation method (Drenick's approach)......Page 20
1.3 Shinozuka's approach......Page 24
1.4 Historical sketch in early stage......Page 25
1.5 Various measures of criticality......Page 26
1.6 Subcritical excitation......Page 27
1.7 Stochastic excitation......Page 28
1.8 Convex models......Page 29
1.9 Nonlinear or elastic–plastic SDOF system......Page 30
1.10 Elastic–plastic MDOF system......Page 31
1.12 Robust structural design......Page 32
1.13 Critical excitation method in earthquake-resistant design......Page 34
2.1 Introduction......Page 40
2.2 Stationary input to single-degree-of-freedom model......Page 41
2.3 Stationary input to multi-degree-of-freedom model......Page 43
2.4 Conservativeness of bounds......Page 46
2.5 Non-stationary input to SDOF model......Page 48
2.6 Non-stationary input to MDOF model......Page 51
2.7 Numerical examples for SDOF model......Page 53
2.8 Numerical examples for MDOF model......Page 55
2.9 Conclusions......Page 57
3.2 Modeling of input motions......Page 60
3.3 Response of non-proportionally damped model to non-stationary random excitation......Page 61
3.4 Critical excitation problem......Page 66
3.5 Solution procedure......Page 67
3.6 Critical excitation for acceleration (proportional damping)......Page 68
3.7 Numerical examples (proportional damping)......Page 70
3.8 Numerical examples (non-proportional damping)......Page 71
3.9 Numerical examples (various types of damping concentration)......Page 72
3.10 Conclusions......Page 75
4.1 Introduction......Page 80
4.3 Acceleration response of non-proportionally damped model to non-stationary random input......Page 81
4.4 Critical excitation problem......Page 86
4.5 Solution procedure......Page 87
4.6 Numerical examples......Page 89
4.8 Model with non-proportional damping-2......Page 90
4.9 Model with proportional damping......Page 95
4.10 Conclusions......Page 97
5.1 Introduction......Page 98
5.2 Statistical equivalent linearization for SDOF model......Page 99
5.3 Critical excitation problem for SDOF model......Page 101
5.5 Relation of critical response with inelastic response to recorded ground motions......Page 103
5.6 Accuracy of the proposed method......Page 108
5.7 Criticality of the rectangular PSD function and applicability in wider parameter ranges......Page 110
5.9 Statistical equivalent linearization for MDOF model......Page 112
5.10 Critical excitation problem for MDOF model......Page 117
5.11 Solution procedure......Page 118
5.12 Relation of critical response with inelastic response to recorded ground motions......Page 119
5.13 Accuracy of the proposed method......Page 122
5.14 Conclusions......Page 124
6.1 Introduction......Page 129
6.2 Non-stationary random earthquake ground motion model......Page 130
6.3 Mean-square drift......Page 131
6.5 Double maximization procedure......Page 132
6.6 Discretization of envelope function......Page 133
6.7 Upper bound of mean-square drift......Page 134
6.8 Numerical examples......Page 135
6.10 Conclusions......Page 140
7.2 Problem for fixed design......Page 147
7.3 Problem for structure-dependent critical excitation......Page 149
7.4 Solution procedure......Page 150
7.5 Numerical design examples......Page 153
7.6 Response to a broader class of excitations......Page 154
7.7 Response to code-specified design earthquakes......Page 158
7.8 Conclusions......Page 159
8.1 Introduction......Page 163
8.2 Earthquake input energy to SDOF system in frequency domain......Page 165
8.3 Property of energy transfer function and constancy of earthquake input energy......Page 166
8.4 Critical excitation problem for earthquake input energy with acceleration constraint......Page 168
8.5 Critical excitation problem for earthquake input energy with velocity constraint......Page 170
8.6 Actual earthquake input energy and its bound for recorded ground motions......Page 171
8.7 Conclusions......Page 178
9.2 Earthquake input energy to proportionally damped multi-degree-of-freedom system (frequency-domain modal analysis)......Page 182
9.3 Earthquake input energy to non-proportionally damped MDOF system (frequency-domain modal analysis)......Page 185
9.4 Earthquake input energy without modal decomposition......Page 188
9.5 Examples......Page 189
9.7 Conclusions......Page 196
10.1 Introduction......Page 198
10.2 Earthquake input energy to fixed-base SDOF system......Page 200
10.3 Earthquake input energy to SSI systems......Page 201
10.4 Actual earthquake input energy to fixed-base model and SSI system......Page 209
10.5 Critical excitation for earthquake energy input in SSI system......Page 215
10.6 Critical excitation problem......Page 219
10.7 Upper bound of Fourier amplitude spectrum of input......Page 221
10.8 Solution procedure and upper bound of input energy......Page 222
10.9 Critical excitation problem for velocity constraints......Page 223
10.10 Solution procedure for velocity constraint problems......Page 224
10.11 Numerical examples 1 (one-story model)......Page 225
10.12 Numerical examples 2 (three-story model)......Page 228
10.13 Conclusions......Page 231
11.1 Introduction......Page 238
11.2 Transfer function to bedrock acceleration input......Page 239
11.3 Earthquake input energy to structure–pile system......Page 241
11.4 Earthquake input energy to structure......Page 243
11.5 Input energies by damage-limit level earthquake and safety-limit level earthquake......Page 244
11.6 Critical excitation for earthquake energy input in structure–pile–soil system......Page 253
11.7 Conclusions......Page 254
12.2 Non-stationary ground motion model......Page 261
12.3 Probabilistic earthquake energy input rate: a frequency-domain approach......Page 262
12.4 Critical excitation problem for earthquake energy input rate......Page 267
12.5 Solution procedure for double maximization problem......Page 269
12.6 Mean energy input rate for special envelope function......Page 271
12.7 Critical excitation problem for non-uniformly modulated ground motion model......Page 273
12.8 General problem for variable envelope function and variable frequency content......Page 274
12.9 Numerical examples......Page 275
12.10 Conclusions......Page 281
E......Page 284
N......Page 285
S......Page 286
V......Page 287