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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
![كتاب Design of Reinforced Concrete Buildings for Seismic Performance D_o_r_13](https://i.servimg.com/u/f61/15/36/74/14/d_o_r_13.jpg) 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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