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 |  موضوع: كتاب Design of Reinforced Concrete Buildings for Seismic Performance السبت 06 مارس 2021, 11:39 pm | |
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أخوانى فى الله
أحضرت لكم كتاب
Design of Reinforced Concrete Buildings for Seismic Performance
Practical Deterministic and Probabilistic Approaches
Mark Aschheim, Enrique Hernández-Montes, and Dimitrios Vamvatsikos
و المحتوى كما يلي :
Contents
Acknowledgments xix
Authors xxi
Section i
introduction 1
1 Introduction 3
1.1 Historical context 3
1.2 Purpose and objectives 3
1.3 Key elements 4
1.4 Illustration of design approach 5
1.5 Organization of book 7
References 7
Section ii
Seismic Demands 9
2 Seismology and site effects 11
2.1 Purpose and objectives 11
2.2 Earthquake sources and wave propagation 11
2.3 Earthquake magnitude and macroseismic intensity 14
2.4 Near-source, topographic, and site effects on ground motion 17
2.5 Geological and geotechnical hazards 18
2.6 Quantitative measures of intensity based on ground motion records 19
References 25
3 Dynamics of linear elastic SDOF oscillators 27
3.1 Purpose and objectives 27
3.2 Equation of motion 27
3.2.1 Newton’s first and second laws of motion 27
3.2.2 Free-body diagram for SDOF systems 28
3.3 Undamped free vibration of linear elastic systems 30
3.4 Damped free vibration of linear elastic systems 31viii Contents
3.5 Forced vibration of linear elastic systems and resonance 32
3.6 Numerical solutions of damped forced vibration 35
3.7 Earthquake-induced ground excitation 39
3.7.1 Equation of motion for linear elastic response 39
3.7.2 Response history 40
3.7.3 Elastic response spectrum 41
3.7.4 Elastic design spectrum 46
3.7.5 Determination of characteristic period of the ground motion 48
References 49
4 Dynamics of nonlinear SDOF oscillators 51
4.1 Purpose and objectives 51
4.2 Introduction 51
4.3 Hysteretic behavior 52
4.4 Influence of hysteretic features on dynamic response 56
4.5 Energy components in nonlinear response 58
4.6 Hysteretic models 61
4.6.1 Takeda model 63
4.6.2 Ibarra–Medina–Krawinkler model 66
4.6.3 Flag-shaped models 66
4.7 Damping in the nonlinear response of SDOF oscillators 68
4.8 Response of individual oscillators 69
4.8.1 Equation of motion 69
4.8.2 Solution approaches 70
4.8.3 Solution by linear acceleration method 71
4.8.4 Nondimensional response parameters 72
4.8.5 Trends in inelastic response 74
4.8.6 Variability in inelastic response as seen
with incremental dynamic analysis 77
4.9 Inelastic response spectra 79
4.9.1 Constant ductility iterations 80
4.9.2 Types of inelastic response spectra 81
4.9.3 Graphical forms of inelastic response spectra 82
4.10 Predictive relationships and design spectra 85
4.10.1 Development of R–μ–T relationships 85
4.10.2 Newmark–Hall 85
4.10.3 FEMA-440 R–μ–T relationship 87
4.10.4 Cuesta et al. R–μ–T/Tg relationship 88
4.10.5 SPO2IDA 88
4.10.6 Flag-shaped models 88
4.11 P-Δ effects for SDOF systems 91
4.11.1 Basic formulation 91
4.11.2 Effective height formulation 92
4.11.3 Energy components 94
4.11.4 Practical observations and limits 94Contents ix
4.12 Equivalent linearization 96
References 97
5 Dynamics of linear and nonlinear MDOF systems 101
5.1 Purpose and objectives 101
5.2 Linear elastic systems 101
5.2.1 Equation of motion of a linear elastic
system subjected to applied forces 101
5.2.2 Equation of motion of a linear elastic
system subjected to base excitation 103
5.2.3 Undamped free vibration and natural modes and frequencies 105
5.2.4 Orthogonality of mode shapes 110
5.2.5 Modal decomposition of displacement history 110
5.2.6 Modal response history analysis 111
5.2.7 Modal decomposition of effective force 111
5.2.8 Damping of linear elastic systems 112
5.2.9 Equivalent (statically applied) lateral forces 114
5.2.10 Effective modal mass 115
5.2.11 Effective modal height 116
5.2.12 Peak response estimates by response spectrum analysis 117
5.3 Nonlinear systems 118
5.3.1 Equation of motion for nonlinear systems 118
5.3.2 Solution by direct integration time history analysis 119
5.3.3 Treatment of damping 120
5.3.4 Inelastic response assessment via nonlinear
response history analysis 122
References 127
6 Characterization of dynamic response using Principal
Components Analysis 129
6.1 Purpose and objectives 129
6.2 Introduction 129
6.3 Theory 130
6.4 Application to displacement response 131
6.5 PCA mode shapes of various response quantities 135
6.6 Modal interactions 137
6.7 Comparison of elastic and PCA mode shapes 139
References 142
7 Equivalent SDOF systems and nonlinear static (pushover) analysis 143
7.1 Purpose and objectives 143
7.2 Introduction 143
7.3 Theoretical derivation of conventional ESDOF system 143
7.4 Nonlinear static (pushover) analysis 145x Contents
7.5 Displacement estimates 149
7.6 Representation of cracking and crack closure
in models; geometric similarity 150
7.7 Energy-based pushover 155
7.8 Challenges faced in estimating other response quantities 161
References 164
Section iii
essential concepts of earthquake-Resistant Design 165
8 Principles of earthquake-resistant design 167
8.1 Purpose and objectives 167
8.2 Specific principles 167
8.2.1 Ductile structural systems can be designed for reduced forces 167
8.2.2 Energy dissipation is not an objective
(but decoupling response from input is) 169
8.2.3 Deformation demands must be accommodated 169
8.2.4 Choice of structural system impacts performance 169
8.2.5 Use complete, straightforward, and redundant load paths 170
8.2.6 Avoid brittle failures using capacity design principles 171
8.2.7 Incorporate higher mode effects 172
8.2.8 Use recognized LFRSs and detailing provisions 173
8.2.9 Recognize limitations of planar thinking and analysis 174
8.2.10 Keep diaphragms elastic and stiff 175
8.2.11 Provide for deformation compatibility 175
8.2.12 Eliminate unnecessary mass 176
8.2.13 Avoid irregularities 176
8.2.14 Anchor nonstructural components to the structure 177
8.2.15 Restrain mechanical equipment and piping 177
8.2.16 Restrain building contents 177
8.2.17 Avoid pounding between adjacent structures 177
8.3 Additional considerations 178
References 178
9 Stability of the yield displacement 181
9.1 Purpose and objectives 181
9.2 Introduction 181
9.3 Kinematics of yield—Members 181
9.4 Kinematics of yield—Lateral force resisting systems 186
9.5 Yield drift estimates for reinforced concrete lateral force-resisting systems 189
9.5.1 Moment–resistant frames 190
9.5.2 Cantilever walls 191
9.5.3 Coupled walls 191
9.6 Post-tensioned walls 191
References 192Contents xi
10 Performance-based seismic design 193
10.1 Purpose and objectives 193
10.2 Introduction 193
10.3 Performance expectations in building codes 194
10.4 Modern performance objectives 195
10.5 Treatment of performance objectives in design 195
10.6 Consideration of performance objectives in preliminary design 196
10.7 Design validation and iteration 199
References 201
11 Plastic mechanism analysis 203
11.1 Purpose and objectives 203
11.2 Ductile weak links 203
11.3 Plastic mechanism analysis 204
11.4 Interaction with gravity load 209
11.5 Reinforced concrete lateral force-resisting systems 211
11.6 Design for designated mechanisms 212
11.7 Consideration of multi-degree-of-freedom effects 216
References 217
12 Proportioning of earthquake-resistant structural systems 219
12.1 Purpose and objectives 219
12.2 Introduction 219
12.3 Generic drift profiles 219
12.4 Estimates of modal parameters for preliminary design 221
12.5 Proportioning for ductile response 221
12.6 The influence of overstrength on system ductility demands 224
12.6.1 Overstrength and implied system ductility
capacities from an American perspective 225
12.6.2 Overstrength and implied system ductility
capacities from a Eurocode perspective 228
12.7 Interstory drift 230
12.7.1 Application of interstory drift limits from an
American perspective 231
12.7.2 Application of interstory drift limits from a Eurocode perspective 234
12.8 Vertical distribution of strength and stiffness 235
12.8.1 Distribution of base shear over height 235
12.8.2 Modification of base shear 238
12.8.3 Design of components based on plastic mechanism analysis 239
References 243
13 Probabilistic considerations 245
13.1 Purpose and objectives 245
13.2 Probability and statistics for safety assessment 245xii Contents
13.2.1 Fundamentals of probabilistic modeling 247
13.2.2 Mathematical basis of probability 247
13.2.3 Conditional probability 249
13.2.4 Random variables and univariate distributions 250
13.2.5 Standard univariate distribution models 251
13.2.6 Multivariate probability distributions and correlation 256
13.2.7 Derived distributions (or how to propagate
probability/uncertainty via Monte Carlo) 258
13.2.8 Modeled versus unmodeled variables and practical treatment 261
13.2.8.1 Examples of modeled versus unmodeled variables 262
13.2.8.2 The first-order assumption for model error 263
13.2.8.3 Smeared versus discrete treatment
of unmodeled uncertainty 264
13.3 Probabilistic seismic hazard analysis 266
13.3.1 Occurrence of random events and the Poisson process 266
13.3.2 The seismic hazard integral 269
13.3.3 Seismic sources 270
13.3.4 Magnitude–distance distribution 270
13.3.5 Ground motion prediction equations 272
13.3.6 Hazard surface, hazard curves, and uniform hazard spectra 272
13.3.7 Risk-targeted spectra 275
13.4 Assessment of performance 276
13.4.1 Performance objectives 277
13.4.2 Practical assessment of performance 278
13.4.2.1 MAF format 279
13.4.2.2 DCFD format 282
13.4.3 Example of application 285
13.4.3.1 MAF format 286
13.4.3.2 DCFD format—Single stripe 290
13.4.3.3 DCFD format—Double stripe 292
13.5 Performance-based design 294
13.5.1 Introduction 294
13.5.2 YFS 294
13.5.3 Example of application 297
References 300
14 System modeling and analysis considerations 303
14.1 Purpose and objectives 303
14.2 Use of analysis for design 303
14.3 Analysis considerations 304
14.3.1 Nonlinearities represented in the analysis 304
14.3.2 Information required for modeling response 305
14.3.3 Use of equivalent single degree-of-freedom systems 305
14.3.4 Simulated collapse modes and force-protected members 305
14.4 Spatial complexity of model 306Contents xiii
14.4.1 Selection of components to represent 306
14.4.2 Choice of two- and three-dimensional models 306
14.4.3 Representation of gravity framing in the model 307
14.4.4 Use of simplified models 308
14.4.5 Discretization in modeling structural system 309
14.5 Floor and roof diaphragm considerations 310
14.6 P-Δ and P-δ effects 312
14.7 Damping 314
14.8 Foundations and soil–structure interaction 316
14.9 Model development and validation 317
References 318
Section iV
Reinforced concrete Systems 319
15 Component proportioning and design based on ACI 318 321
15.1 Purpose and objectives 321
15.2 Introduction 321
15.3 Strength reduction factors 322
15.4 Specified materials 322
15.5 Beams of special moment-resistant frames 323
15.5.1 Beam width and depth 323
15.5.2 Beam longitudinal reinforcement 323
15.5.2.1 Member proportioning 324
15.5.3 Beam probable flexural strength 325
15.5.4 Beam transverse reinforcement configuration 325
15.5.5 Beam transverse reinforcement spacing 326
15.6 Columns of special moment-resistant frames 328
15.6.1 Section dimensions and reinforcement limits 328
15.6.1.1 Column proportioning 328
15.6.2 Column flexural strength 330
15.6.3 Column transverse reinforcement configuration 332
15.6.4 Column transverse reinforcement spacing requirements 332
15.6.4.1 Confinement in potential plastic
hinge zones and at lap splices 332
15.6.4.2 Transverse reinforcement outside of
potential plastic hinge zones 335
15.6.4.3 Transverse reinforcement for shear strength 335
15.7 Beam-column joints in special moment-resistant frames 337
15.7.1 Joint proportioning 338
15.7.1.1 Joint dimensions 338
15.7.1.2 Joint shear strength 339
15.7.2 Transverse reinforcement 339
15.7.3 Development of longitudinal reinforcement 343
15.8 Special structural walls and coupled walls 344xiv Contents
15.8.1 Proportioning of slender walls 346
15.8.2 Proportioning of coupled walls 348
15.8.3 Detailing of boundary zones 349
15.8.4 Shear strength 352
15.8.5 Curtailment of reinforcement over the height 353
15.8.6 Design of wall piers 354
15.8.7 Anchorage and splices of reinforcement 355
15.8.7.1 Anchorage of longitudinal reinforcement 355
15.8.7.2 Splices of longitudinal reinforcement 355
15.8.7.3 Anchorage of horizontal web reinforcement 355
15.8.8 Force transfer and detailing in regions of discontinuity 356
15.8.8.1 Strut and tie models 356
15.8.8.2 Detailing at boundaries of wall piers 356
15.8.8.3 Detailing at the base of coupled shear walls 357
15.8.8.4 Detailing for transfer to collectors 357
15.8.9 Detailing for constructability 358
15.8.9.1 Openings in walls 358
15.8.9.2 Shear strength at construction joints (shear friction) 358
15.9 Coupling beams 358
15.9.1 Proportioning of coupling beams 358
15.10 Post-tensioned cast-in-place walls 359
15.10.1 Guidelines for proportioning post-tensioned walls 363
15.10.2 Modeling the load–displacement response
of post-tensioned walls 363
15.11 Rocking footings 364
15.11.1 Proportioning of rocking footings 365
15.12 Floor diaphragms, chords, and collectors 367
15.13 Gravity framing 368
15.14 Foundations 368
References 368
16 Component proportioning and design requirements according to
Eurocodes 2 and 8 371
16.1 Purpose and objectives 371
16.2 Introduction 371
16.3 The seismic action in Eurocode-8 373
16.3.1 Design spectrum 375
16.3.2 Material safety factors and load combination in analysis 375
16.4 Performance of the structural system 377
16.4.1 Behavior factor (q) and system ductilities 378
16.4.2 Story drift limits 380
16.5 Design of beams and columns in DCM and DCH structures 380
16.6 Design of walls in DCM and DCH structures 385
References 389Contents xv
17 Component modeling and acceptance criteria 391
17.1 Purpose and objectives 391
17.2 Introduction 391
17.3 Background 392
17.3.1 Moment–curvature response 392
17.3.2 Plastic hinge models for load–deformation response of members 395
17.3.3 Model fidelity 397
17.3.4 Robust design in the context of modeling uncertainty 399
17.4 Expected material properties 401
17.5 Properties of confined concrete 402
17.6 Nominal, reliable, and expected strengths 403
17.7 Element discretization and modeling 404
17.7.1 Sources of flexibility 404
17.7.2 Hysteretic behavior 404
17.7.3 Modeling—Element formulations 406
17.7.3.1 Distributed plasticity elements 406
17.7.3.2 Lumped plasticity elements 408
17.7.4 Generalized load–displacement models 408
17.8 Component modeling 409
17.8.1 Beams and Tee beams 409
17.8.1.1 Effective stiffness 409
17.8.1.2 Beam plastic hinge (and anchorage slip) 412
17.8.1.3 Acceptance criteria for beam plastic hinge rotations 414
17.8.2 Columns 414
17.8.2.1 Column stiffness 414
17.8.2.2 Column plastic hinge (and anchorage slip) 418
17.8.2.3 Acceptance criteria for column plastic hinge rotations 419
17.8.3 Beam-column joints 419
17.8.3.1 Joint stiffness 419
17.8.3.2 Acceptance criteria for beam-column
joint deformations 421
17.8.4 Walls and coupled walls 421
17.8.4.1 Stiffness of elastic wall elements 421
17.8.4.2 Wall plastic hinges 423
17.8.4.3 Acceptance criteria for wall plastic hinges 423
17.8.5 Coupling beams 424
17.8.5.1 Proportioning of coupling beams 424
17.8.5.2 Elastic stiffness 425
17.8.5.3 Coupling beam plastic hinge 425
17.8.5.4 Acceptance criteria for coupling beam plastic rotations 425
17.8.6 Post-tensioned reinforced concrete walls 425
17.8.6.1 Modeling of post-tensioned walls 425
17.8.6.2 Acceptance criteria 426
17.8.7 Collectors, floor diaphragms, and chords 426xvi Contents
17.8.8 Rocking footings as plastic hinges 426
17.8.8.1 Modeling and acceptance criteria for rocking footings 426
References 428
Section V
Design methods and examples 431
18 Design methods 433
18.1 Purpose and objectives 433
18.2 Introduction 433
18.3 Design Method A (quasi-code) 435
18.4 Design Method B (simplified dynamic) 437
18.5 Design Method C (dynamic) 441
18.6 Treatment of uncertainty 441
18.7 Confidence levels in design and capacity assessment 444
References 445
19 Design examples 447
19.1 Purpose and objectives 447
19.2 Introduction 447
19.3 Application of yield frequency spectra and
performance assessment methodologies 447
19.4 Site seismic hazard and ground motions 450
19.5 Material properties 454
19.6 Moment frame plan, elevation, and modeling (Examples 1–3) 454
19.6.1 Distributed plasticity model 455
19.6.2 Lumped plasticity model 456
19.6.2.1 Columns 457
19.6.2.2 Beams 457
19.6.2.3 Example of calculating beam modeling
parameters and assessment criteria 458
19.7 Example 1: Moment-resistant frame designed using Method A 461
19.7.1 POs 461
19.7.2 Use of nonlinear response analysis in this example 461
19.7.3 Required base shear strength 461
19.7.4 Design lateral forces and required member strengths 462
19.7.5 Sizing of RC members 465
19.7.6 Preliminary evaluation of the initial design 467
19.7.7 Nonlinear modeling and acceptance criteria 470
19.7.8 Performance evaluation of the initial design
by nonlinear dynamic analysis 472
19.8 Example 2: Moment-resistant frame designed using Method B 481
19.8.1 Performance objectives 481
19.8.2 Use of nonlinear response analysis in this example 482
19.8.3 System ductility limit 482Contents xvii
19.8.4 Assumptions required to generate YFS based on ASCE-7 UHS 482
19.8.5 Required base shear strength 482
19.8.6 Design lateral forces and required member strengths 483
19.8.7 Sizing of RC members 484
19.8.8 Preliminary evaluation of the initial design by
nonlinear static (pushover) analysis 487
19.8.9 Nonlinear modeling and acceptance criteria 489
19.8.10 Performance evaluation of the initial design
by nonlinear dynamic analysis 490
19.9 Example 3: Moment-resistant frame designed using Method C 494
19.9.1 POs 494
19.9.2 Use of nonlinear response analysis in this example 494
19.9.3 System ductility limits 494
19.9.4 Assumptions required to generate YFS 495
19.9.5 Required yield strength coefficient, Cy * 495
19.9.6 Required base shear strength 497
19.9.7 Design lateral forces and required member strengths 497
19.9.8 Sizing of RC members 498
19.9.9 Preliminary evaluation of the initial design by
nonlinear static (pushover) analysis 499
19.9.10 Nonlinear modeling and acceptance criteria 501
19.9.11 Performance evaluation of the initial design
by nonlinear dynamic analysis 504
19.10 Example 4: Coupled wall designed using Method A 509
19.10.1 Coupled wall example plan and elevation 509
19.10.2 POs 509
19.10.3 Use of nonlinear response analysis in this example 509
19.10.4 Required base shear strength 510
19.10.5 Design lateral forces and required member strengths 512
19.10.6 Sizing of RC members 513
19.10.7 Preliminary evaluation of the initial design 514
19.10.8 Nonlinear modeling and acceptance criteria 514
19.10.9 Performance evaluation of the initial design
by nonlinear dynamic analysis 518
19.11 Example 5: Cantilever shear wall designed using Method B 522
19.11.1 Cantilever wall example plan and elevation 522
19.11.2 POs 523
19.11.3 Use of nonlinear response analysis in this example 523
19.11.4 System ductility limit 523
19.11.5 Assumptions required to generate YFS based on EC-8 UHS 524
19.11.6 Required base shear strength 524
19.11.7 Design lateral forces and required member strengths 524
19.11.8 Sizing of RC members 524
19.11.9 Preliminary evaluation of the initial design
by nonlinear static (pushover) analysis 525
19.11.10 Nonlinear modeling and acceptance criteria 526xviii Contents
19.11.11 Performance evaluation of the initial design
by nonlinear dynamic analysis 530
19.12 Example 6: Unbonded post-tensioned wall designed using Method C 532
19.12.1 Floor plan and elevation 532
19.12.2 POs 533
19.12.3 Use of nonlinear response analysis in this example 533
19.12.4 Effect of quantity of seven-wire strands on wall behavior 533
19.12.5 Design approach 534
19.12.6 YFS based on an assumed normalized capacity curve 535
19.12.7 Design strength 536
19.12.8 Nonlinear modeling and acceptance criteria 538
19.12.9 Performance evaluation of the initial design
by nonlinear response history analysis 541
References 544
Appendix 1 547
Appendix 2 561
Appendix 3 569
Index 57
Index
Accelerogram
recorded, 40
response history, 40–41
Admissible design region, 196–198
Analysis
in design, 294–297, 303–304
uncertain initial conditions, 304
Backbone curve, 60, 66, 88, 95, 408–413
Base shear modification, 238–239
Beam–column joints
acceptance criteria, 421, 423
actions, 337–338
anchorage slip (in beam models), 413–414
anchorage slip (in column models), 418
development of longitudinal reinforcement,
344–345
proportioning, 338–339
stiffness, 419–421, 422
transverse reinforcement, 339–343
Beams
acceptance criteria, 414
cross section limits, 323
effective stiffness, 409–412
longitudinal reinforcement, 323–324
plastic hinge model, 412–413
probable flexural strength, 325
proportioning, 324
transverse reinforcement, 325–328
Behavior factor, 73, 228, 229, 234, 372, 375,
378–380
Building contents, 177
Capacity, 55, 63, 73
curve, 149, 150
design principle, 171–172
spectrum, 82,83
Chain analogy, 203, 216, 303
Chords, 367, 426
Collapse mechanism analysis, see plastic
mechanism analysis
Collectors, 367, 426
Columns
acceptance criteria, 419
biaxial loading, 174
confinement, 328–329, 332–335
cross section limits, 328
effective stiffness, 414–418
plastic hinge model, 418–419
proportioning, 328–331
shear strength, 335–337
transverse reinforcement, 332–337
yield curvature, 415–418
Confidence level, 277, 278, 282, 288, 292, 444
in design and assessment, 444–445
Confined concrete, 402–403; see also columns;
confinement
Coupled walls, 421–425
proportioning, 348
stiffness, 421–422
Coupling beams, 424–425
acceptance criteria, 425
effective stiffness, 425
plastic hinge model, 425
proportioning, 424–425
Curvature ductility, 73, 195, 328, 329, 383, 385
Cyclic degradation, 404–405
D’Alembert’s principle, 28
Damping, 314–316
mass–proportional, 68, 113, 121, 315
matrix, 102, 111, 112, 120, 144, 316
Caughey damping, 112
Rayleigh damping, 112, 315
ratio, 31, 33, 40, 111, 113
stiffness–proportional, 68, 315
DCFD, 278, 282, 283, 290–293, 449, 479, 480,
491
Deformation compatibility, 175
Demand, 4, 72–74, 169
curves, 198–199
Design
method A, 434, 435–437
method B, 434, 438–441
method C, 434, 441–442
spectrum, 375
elastic,46–47
inelastic (R–μ–T), 85–90574 Index
Diaphragms, 175, 367
Displacement
relative, 11, 28, 39–43, 57, 58, 69, 94
response spectrum, 41–43
Distributed plasticity models, 406–407
Ductility
capacity, 73, 168, 169, 226–228, 314, 329
class (DCL, DCM, DCH), 228–230, 372–379
demand, 72, 73, 80, 85–90, 143, 193, 219
Dynamic
loading; ground excitation, 29, 39, 58
magnification factor, 33–35
Earthquake
intensity, 14–17
magnitude, 14–17
site effect, 17
source, 11–14
Effective
modal height, 116
modal mass, 114–116
Energy
damping, 58, 59
dissipated, 53, 59, 60
dissipation, 169
expended strain, 59, 157, 360
geometric, 94
input, 48, 58, 94
kinetic, 57, 58, 361
potential, 57, 58
recoverable strain, 59, 360
strain, 11, 43, 53, 57, 59, 157, 360, 361
Energy–based pushover
derivation, 155–158
example, 158–161
Equal displacement rule, 74, 79, 84
Equivalent lateral force method, 227, 232,
235–236
Equivalent SDOF system
accuracy of displacement estimates, 150
and MDOF system, 147, 151–152
derivation, 143–149
estimation of other response quantities,
161–164
Equivalent static force, 43, 45, 109
ESDOF, 143–144
Examples
bridge pier (YFS), 297–300
bridge pier (YPS), 5–7
cantilever shear wall (Method B), 522
coupled shear wall (Method A), 509
moment–frame (Method A), 461
moment–frame (Method B), 481
moment–frame (Method C), 494
post–tensioned wall (Method C), 532
Expected material properties, 401–402
Fiber elements, 406
Floor accelerations, 169–170
Foundation, 368
flexibility, 316–317
Fragility function, 277, 279, 289
Free vibration
eigenvalues, 105, 108
eigenvectors, 105, 108, 110
damped, 31
undamped, 30
Frequency
natural, 30, 32
damped natural frequency, 32
Generalized load–displacement curve, 408–409
Generic drift profiles, 219–220
Gravity
framing, 368
load–resisting system, 175–176
Hazard
curve 197, 262, 272–275
curve slope, 275–277
risk–targeted spectra, 275, 276
surface, 272–275, 290, 296, 434
uniform hazard spectra, 272, 274, 439,
450–453
Higher mode effects, 172–173, 216, 235–236
Hysteretic
behavior, 404–405
curves
backbone, 66, 95, 403, 408, 413
capacity boundary, 55–56
skeleton curve, 404–405
diagram, 52
model, 61–67
modelflag–shape, 66, 88
Incremental dynamic analysis (IDA), 77, 125,
454
In–cycle degradation, 405
Interarrival time, 252, 267
Interstory drift, 230–231
implied ASCE/SEI 7 roof drift limit, 231–234
implied Eurocode 8 roof drift limit, 234–235
Irregularities, 176–177
Lateral force distributions, 235–238
Load paths, 170–171
Lower–bound theorem, 206
LRFD, 278, 284
Lumped plasticity models, 406, 408
Mass
reduction, 176
matrix, 102, 106, 131, 162
Material requirements, 322–323
MDOF, 101–127
MDOF effects, see higher mode effects
Mean annual frequency, 3, 5, 7, 88, 196, 224,
234, 252, 275, 277, 283, 307, 440, 447Index 575
Mechanical systems, 177
Modal combination
CQC, 117, 118
SRSS, 109, 117, 118, 264, 291
Modal parameter estimates, 221
Modal participation factor, 111, 115, 144, 162,
318
Model validation, 317–318
Modeling
diaphragms, 310–312, 426
gravity framing, 307–308
leaning column, 314
P–Δ effects, 312–314
simplified models, 308–309
two– and three–dimensional models,
306–307
Moment–curvature analysis, 391–394
Momentum, 27
Monte Carlo simulation, 258–261
Neutral axis depth, 392
Nonlinear static analysis, 143–163
Nonlinearities, types of, 304–305
Nonstructural components, 177
Numerical time–step solution
dispersion, 39
linear acceleration method, 36, 38, 71, 120
numerical damping, 39
piecewise exact method, 36, 38
Overstrength, 224–225
coefficient, 228, 229, 379
Performance
assessment, 127, 177, 245, 266, 278,
447–450
objectives, 3, 195, 196, 247, 481
basic framework, 195–196
in building codes, 194–195
in preliminary design, 196–199
Performance–based
design, 4, 195, 196, 294
earthquake engineering, 245, 276, 277, 449
framing equation, 276
Period
characteristic or corner, 48–49
natural, 29–30
Plastic hinge model
accuracy, 397–399
description, 395–396, 398
Plastic mechanism analysis
example, 208–209
component design, 239–243
in design, 212–213
limit on gravity load, 209–211
preferred mechanisms, 211–212
Poisson process, 252, 266–269
Post–tensioned walls, 359–365
acceptance criteria, 426
modeling, 363–364
plastic hinge models, 425–426
Pounding, 177–178
Principal components analysis
computation with R, 133–134
eigenvalues, 129–131, 134
eigenvectors, 129–131, 134
modal interactions, 137–139
theory, 130–131
Probabilistic seismic hazard analysis
GMPE, 269, 272, 273
Gutenberg–Richter, 270
integral, 269
Pseudo–acceleration, 27, 43–49, 82, 86
Pushover analysis, see nonlinear static analysis
P–δ effects, 313–314
P–Δ effects, 92–94, 118–121, 305, 307–314
Random variable, 250–251
CCDF, 250
CDF, 250–259
coefficient of variation, 251
conditional distribution, 255
correlation, 256–258
dependence, 247
derived distribution, 256, 258–261
dispersion, 250, 251
distribution, 250–251
expected value, 250
exponential distribution, 247, 251–254
fractile / percentile, 251
joint distribution, 258–260
lognormal distribution, 247, 251, 254–256
mean, 250–256
median, 251–255
multivariate, 256
normal distribution, 247, 251, 253–256
PDF, 250–259
standard deviation, 251
support, 250
uniform distribution, 247, 251, 253, 254
univariate, 250, 251
variability, 251
variance, 254, 260, 261
Ratcheting, 210
R–C–T, see R–μ–T
Reduced forces, 167–169
Resonance, 33–34
Response spectrum
acceleration, 42–43
displacement, 41–43
elastic, 41–46
inelastic, 79–84
pseudo–acceleration, see response spectrum
acceleration
tripartite, 43–47
Return period, 228, 232, 234, 252, 268,
269, 371, 380, 434, 440, 451, 496,
502, 538576 Index
Rocking footings
acceptance criteria, 427
modeling, 426–427
proportioning, 365–366
R–μ–T, 84–90
Cuesta et al., 88
FEMA–440, 87
Flag–shaped models, 88–90
Nassar and Krawinkler, 89
Newmark–Hall, 85–87
SPO2IDA, 88
SDOF, 27–97
Shear friction, 358
Shear wall, see structural wall
Simulated collapse modes, 305
Soil structure interaction, 316–317
Stiffness
degradation, 54, 62–63, 71, 88, 96, 404, 456
matrix, 102, 104, 106, 119
geometric stiffness matrix, 119
tangent stiffness matrix, 121, 132
Strain rate effects, 398–399
Strength
degradation, 54, 55, 66, 75, 77, 94, 346,
405
reduction factors, 322
Structural wall
acceptance criteria, 423–424
anchorage and splicing of longitudinal
reinforcement, 355
anchorage of horizontal reinforcement,
355–356
boundary zones, 349–352
coupled walls, 345–346, 348
coupling beams, 358–359
curtailment of longitudinal reinforcement,
353–354
detailing at openings and discontinuities,
356–357, 358
plastic hinge model, 423
shear strength, 352–353
slender walls, 344–347
stiffness, 421–423
types, 344–345
wall piers, 355–356
System ductility capacity
derived for ASCE/SEI 7,225–227
derived for Eurocode 8, 228–230
Tension stiffening, 395
Total probability theorem, 249, 269
Uncertainty
aleatory, 246, 296
discrete, 264
epistemic, 246, 273, 277–278, 296
modeled, 264, 265
propagation, 258–261
smeared, 264, 265
treatment in design, 441, 443
unmodeled, 264, 265
Uncracked stiffness, 151–152
Uniqueness theorem, 206
Upper–bound theorem, 204
Wall, see shear wall
YFS, see yield frequency spectra
Yield displacement
axially loaded bar, 181–182
cantilever reinforced concrete beam, 183–186
cantilever steel beam, 182–183
definition, 61
reinforced concrete moment–resistant
frames, 186–189
estimates
cantilever shear walls, 191
coupled shear walls, 191
post–tensioned walls, 191–192
reinforced concrete moment–resistant
frames, 190–191
Yield frequency spectra, 88, 149, 224, 294–297
YFS, 88, 149, 224, 294–297
YFS–T,294, 434, 535–537, 540
YFS–TNE, 535–536
Yield point spectra (YPS)
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