Dynamics of structures /
Clough, Ray W.
Dynamics of structures / Ray W. Clough, Joseph Penzien. - 2nd - New York: McGraw-Hill, 1993 - 738 p.
CONTENIDO
Preface xv
List of Symbols xvii
1. Overview of Structural Dynamics 1
Fundamental Objective of Structural Dynamics Analysis 1
Types of Prescribed Loadings 2
Essential Characteristics of a Dynamic Problem 3
Methods of Discretization 4
Lumped-Mass Procedure 4
Generalized Displacements 5
The Finite-Element Concept 7
Formulation of the Equations of Motion 9
Direct Equilibration using d´Alembert´s Principle 9
Principle of Virtual Displacements 10
Variation al Approach 10
PART I. SINGLE-DEGREE-OF-FREEDOM SYSTEMS 2
2. Analysis of Free Vibrations 15
Components of the Basic Dynamic System 15
Equation of Motion of the Basic Dynamic System 16
Influence of Gravitational Forces 17
Influence of Support Excitation 18
Analysis of Undraped Free Vibrations 20
Damped Free Vibrations 25
Critically-Damped Systems 26
Under critically-Damped Systems 27
Over critically-Damped Systems 32
3. Response to Harmonic Loading 33
Undraped System 33
Complementary Solution 33
Particular Solution 33
General Solution 34
System with Viscous Damping 36
Resonant Response 42
Accelerometers and Displacement Meters 45
Vibration Isolation 46
Evaluation of Viscous-Damping Ratio 52
Free-Vibration Decay Method 52
Resonant Amplification Method 53
Half-Power (Band-Width) Method 54
Resonance Energy Loss per Cycle Method 56
Complex-Stiffness Damping 58
4. Response to Periodic Loading 65
Fourier series Expressions of Periodic Loading 65
Trigonometric Form 65
Exponential Form 66
Response to the Fourier series Loading 67
Preview of Frequency-Domain Analysis 69
5. Response to Impulsive Loading 73
General Nature of Impulsive Loading 73
Sine-Wave Impulse 74
Rectangular Impulse 77
Triangular Impulse 78
Shock or Response Spectra 79
Approximate Analysis of Impulsive-Load Response 82
6. Response to General Dynamic Loading: Superposition Methods 87
Analysis through the Time Domain 87
Formulation of Response Integral 87
Numerical Evaluation of Response Integral 89
Analysis through the Frequency Domain 97
Fourier Response Integral 98
Discrete Fourier Transforms (DVF) 100
Fast Fourier Transforms (FFT) 102
Evaluation of Dynamic Response 106
Relationship between the Time- and Frequency-Domain Transfer Functions 109
7. Response to General Dynamic Loading: Step-by-Step Methods 111
General Concepts 111
Piecewise Exact Method 112
Numerical Approximation Procedures General Comments 116
Second Central Difference Formulation 117
Integration Methods 120
Euler-Gauss Procedure 120
New mark Beta Methods 121
Conversion to Explicit Formulation 123
Incremental Formulation for Nonlinear Analysis 124
Summary of the Linear Acceleration Procedure 127
8. Generalized Single-Degree-of-Freedom Systems 133
General Comments on SDOF Systems 133
Generalized Properties: Assemblages of Rigid Bodies 134
Generalized Properties: Distributed Flexibility 140
Expressions for Generalized System Properties 145
Vibration Analysis by Rayleigh's Method 149
Selection of the Rayleigh Vibration Shape 152
Improved Rayleigh Method 156
PART II. MULTI-DEGREE-OF-FREEDOM SYSTEMS 159
9. Formulation of the MDOF Equations of Motion 169
Selection of the Degrees of Freedom 169
Dynamic-Equilibrium Condition 171
Axial-Force Effects 173
10. Evaluation of Structural-Property Matrices 175
Elastic Properties 175
Flexibility 175
Stiffness 176
Basic Structural Concepts 177
Finite-Element Stiffness 179
Mass Properties 184
Lumped-Mass Matrix 184
Consistent-Mass Matrix 185
Damping Properties 189
External Loading 189
Static Resultants 190
Consistent Nodal Loads 190
Geometric Stiffness 191
Linear Approximation 191
Consistent Geometric Stiffness 194
Choice of Property Formulation 196
Undamped Free Vibrations 201
Analysis of Vibration Frequencies 201
Analysis of Vibration Mode Shapes 204
Flexibility Formulation of Vibration Analysis 208
Influence of Axial Forces 208
Free Vibrations 208
Buckling Load 209
Buckling with Harmonic Excitation 210
Orthogonality Conditions 211
Basic Conditions 211
Additional Relationships 212
Normalizing 214
12. Analysis of Dynamic Response Using Superposition 219
Normal Coordinates 219
Uncoupled Equations of Motion: Undamped 221
Uncoupled Equations of Motion: Viscous Damping 222
Response Analysis by Mode Displacement Superposition 223
Viscous Damping 223
Complex-Stiffness Damping 230
Construction of Proportional Viscous Damping Matrices 234
Rayleigh Damping 234
Extended Rayleigh Damping 237
Alternative Formulation 240
Construction of Nonproportional Damping Matrices 242
Response Analysis using Coupled Equations of Motion 245
Time Domain 245
Frequency Domain 246
Relationship between Time- and Frequency- Domain Transfer Functions 247
Practical Procedure for solving Coupled Equations of Motion 251
Interpolation Procedure for Generation of Transfer Functions 254
13. Vibration Analysis by Matrix Iteration 259
Preliminary Comments 259
Fundamental Mode Analysis 260
Proof of Convergence 265
Analysis of Higher Modes 267
Second-Mode Analysis 267
Analysis of Third and Higher Modes 271
Analysis of Highest Mode 272
Buckling Analysis by Matrix Iteration 275
Inverse Iteration the Preferred Procedure 279
Inverse Iteration with Shifts 281
Special Eigenproblem Topics 285
Eigenproperty Expansion 286
Symmetric Form of Dynamic Matrix 288
Analysis of Unconstrained Structures 290
14. Selection of Dynamic Degrees of Freedom 293
Finite-Element Degrees of Freedom 293
One-Dimensional Elements 294
Two- and Three-Dimensional Elements 294
Kinematic Constraints 295
Static Condensation 296
Rayleigh Method in Discrete Coordinates 298
Rayleigh-Ritz Method 299
Subspace Iteration 304
Reduction of Modal Truncation Errors 306
General Comments on Coordinate Reduction 306
Modal Contributions 307
Static Correction Procedure 311
Mode Acceleration Method 313
Derived Ritz Vectors 314
Preliminary Comments 314
Derivation Details 316
Tridiagonal Equations of Motion 319
Loss of Orthogonality 322
Required Number of Vectors 323
15. Analysis of MDOF Dynamic Response: Step-by-Step Methods 325
Preliminary Comments 325
Incremental Equations of Motion 327
Step-by-Step Integration: Constant Average Acceleration Method 328
Step-by-Step Integration: Linear Acceleration Method 330
Strategies for Analysis of Coupled MDOF Systems 332
Localized Nonlinearity 332
Coupled Effects Treated as Pseudo-Forces 336
16. Variational Formulation of the Equations of Motion 341
Generalized Coordinates 341
Hamilton's Principle 342
Lagrange's Equations of Motion 344
Derivation of the General Equations of Motion for Linear Systems 351
Constraints and Lagrange Multipliers 356
PART III. DISTRIBUTED-PARAMETER SYSTEMS
17. Partial Differential Equations of Motion 365
Beam Flexure: Elementary Case 366
Beam Flexure: Including Axial-Force Effects 368
Beam Flexure: Including Viscous Damping 369
Beam Flexure: Generalized Support Excitations 370
Axial Deformations: Undamped 373
18. Analysis of Undamped Free Vibrations 377
Beam Flexure: Elementary Case 377
Beam Flexure: Including Axial-Force Effects 386
Beam Flexure: With Distributed Elastic Support 388
Beam Flexure: Orthogonality of Vibration Mode Shapes 389
Free Vibrations in Axial Deformation 391
Orthogonality of Axial Vibration Modes 392
19. Analysis of Dynamic Response 397
Normal Coordinates 397
Uncoupled Flexural Equations of Motion: Undamped Case 400
Uncoupled Flexural Equations of Motion: Damped Case 403
Uncoupled Axial Equations of Motion: Undamped Case 407
Wave-Propagation Analysis 411
Basic Axial-Wave-Propagation Equation 411
Consideration of Boundary Conditions 415
Discontinuity in Bar Properties 418
PART IV. RANDOM VIBRATIONS
20. Probability Theory 427
Single Random Variable 427
Important Averages of a Single Random Variable 432
One-Dimensional Random Walk 434
Two Random Variables 442
Important Averages of Two Random Variables 451
Scatter Diagram and Correlation of Two Random Variables 455
Principal Axes of Joint Probability Density Function 458
Rayleigh Probability Density Function 461
Random Variables 463
Linear Transformations of Normally Distributed Random Variables 465
21. Random Processes 471
Definition 471
Stationary and Ergodic Processes 473
Autocorrelation Function for Stationary Processes 478
Power Spectral Density Function for Stationary Processes 484
Relationship Between Power Spectral Density and Autocorrelation Functions 485
Power Spectral Density and Autocorrelation Functions for Derivatives of Processes 488
Superposition of Stationary Processes 490
Stationary Gaussian Processes: One Independent Variable 492
Stationary White Noise 498
Probability Distribution for Maxima 501
Probability Distribution for Extreme Values 506
Nonstationary Gaussian Processes 510
Stationary Gaussian Process: Two or More Independent Variables 511
22. Stochastic Response of Linear SDOF Systems 517
Transfer Functions 517
Relationship between Input and Output Autocorrelation Functions 518
Relationship between Input and Output Power Spectral Density Functions 522
Response Characteristics for Narrowband Systems 524
Nonstationary Mean Square Response Resulting from Zero Initial Conditions 528
Fatigue Predictions for Narrowband Systems 532
23. Stochastic Response of Linear MDOF Systems 539
Time-Domain Response for Linear Systems using Normal Modes 539
Frequency-Domain Response for Linear Systems using Normal Modes 541
Normal Mode Forcing Function due to Discrete Loadings 543
Normal Mode Forcing Function due to Distributed Loadings 547
Frequency-Domain Response for Linear Systems having Frequency-Dependent Parameters and/or Coupled Normal Modes 548
PART V. EARTHQUAKE ENGINEERING
24. Seismological Background 555
Introductory Note 555
Seismicity 556
Earthquake Faults and Waves 558
Structure of the Earth 559
Plate Tectonics 563
Elastic-Rebound Theory of Earthquakes 567
Measures of Earthquake Size 571
25. Free-Field Surface Ground Motions 575
Fourier and Response Spectra 575
Factors influencing Response Spectra 581
Design Response Spectra 586
Dual Strategy of Seismic Design 586
Peak Ground Accelerations 587
Response Spectrum Shapes 590
Uniform-Hazard Site-Specific Response Spectra 595
Two Horizontal Components of Motion 597
Design Accelerograms 597
Response Spectrum Compatible Accelerograms 598
Principal Axes of Motion 603
Spatially Correlated Motions 607
26. Deterministic Earthquake Response: Systems on Rigid Foundations 613
Types of Earthquake Excitation 613
Response to Rigid-Soil Excitations 615
Lumped SDOF Elastic Systems, Translational Excitation 615
Generalized-Coordinate SDOF Elastic Systems, Translational Excitation 617
Lumped MDOF Elastic Systems, Translational Excitation 623
Comparison with ATC-3 Recommended Code Provisions 638
Distributed-Parameter Elastic Systems, Translational Excitation 640
Lumped MDOF Elastic Systems, Rotational Excitation 642
Lumped MDOF Elastic Systems, Multiple Excitations 644
Lumped SDOF Elastic-Plastic Systems, Translational Excitation 647
Combining Maximum Modal Responses 650
Mean Square Response of a Single Mode 650
Covariance of Response Produced by Two Modes 652
SRSS and CQC Combination of Modal Responses 653
Combining Two-Component-Excitation Responses 657
27. Deterministic Earthquake Response: Including Soil-Structure 660
Soil-Structure Interaction by Direct Analysis 669
Kinematic Interaction for Translational Excitation; the Tau Effect 670
Direct Inclusion of a Bounded Soil Layer 673
Substructure Analysis of SSI Response 674
Lumped SDOF Systems on Rigid Mat Foundation 674
General MDOF System with Multiple Support Excitations 679
Generation of Boundary Impedances 689
Response of Underground Structures 704
Free-Field Ground Motions due to Propagating Plane Waves 704
Racking Deformations of Cross Sections 705
Overall Axial and Flexural Deformations 706
Influence of Transverse Joints on Axial Deformations 709
28. Stochastic Structural Response 711
Modeling of Strong Ground Motions 711
Stochastic Response of Linear Systems 711
SDOF Systems 711
MDOF Systems 712
Extreme-Value Response of Nonlinear Systems 713
SDOF Systems 713
MDOF Systems 723
Design Considerations 726
Allowable Ductility Demand versus Ductility Capacity 729
Index 731
0070113947
STRUCTURAL DYNAMICS
FREE VIBRATIONS
HARMONIC LOADING
PERIODIC LOADING
IMPULSIVE LOADING
SUPERPOSITION METHODS
STEP-BY STEP-METHOD
CARGA DINAMICA
DINAMICA-ESTRUCTURAS
DINAMICA ESTRUCTURAL
624.042.8 C625
Dynamics of structures / Ray W. Clough, Joseph Penzien. - 2nd - New York: McGraw-Hill, 1993 - 738 p.
CONTENIDO
Preface xv
List of Symbols xvii
1. Overview of Structural Dynamics 1
Fundamental Objective of Structural Dynamics Analysis 1
Types of Prescribed Loadings 2
Essential Characteristics of a Dynamic Problem 3
Methods of Discretization 4
Lumped-Mass Procedure 4
Generalized Displacements 5
The Finite-Element Concept 7
Formulation of the Equations of Motion 9
Direct Equilibration using d´Alembert´s Principle 9
Principle of Virtual Displacements 10
Variation al Approach 10
PART I. SINGLE-DEGREE-OF-FREEDOM SYSTEMS 2
2. Analysis of Free Vibrations 15
Components of the Basic Dynamic System 15
Equation of Motion of the Basic Dynamic System 16
Influence of Gravitational Forces 17
Influence of Support Excitation 18
Analysis of Undraped Free Vibrations 20
Damped Free Vibrations 25
Critically-Damped Systems 26
Under critically-Damped Systems 27
Over critically-Damped Systems 32
3. Response to Harmonic Loading 33
Undraped System 33
Complementary Solution 33
Particular Solution 33
General Solution 34
System with Viscous Damping 36
Resonant Response 42
Accelerometers and Displacement Meters 45
Vibration Isolation 46
Evaluation of Viscous-Damping Ratio 52
Free-Vibration Decay Method 52
Resonant Amplification Method 53
Half-Power (Band-Width) Method 54
Resonance Energy Loss per Cycle Method 56
Complex-Stiffness Damping 58
4. Response to Periodic Loading 65
Fourier series Expressions of Periodic Loading 65
Trigonometric Form 65
Exponential Form 66
Response to the Fourier series Loading 67
Preview of Frequency-Domain Analysis 69
5. Response to Impulsive Loading 73
General Nature of Impulsive Loading 73
Sine-Wave Impulse 74
Rectangular Impulse 77
Triangular Impulse 78
Shock or Response Spectra 79
Approximate Analysis of Impulsive-Load Response 82
6. Response to General Dynamic Loading: Superposition Methods 87
Analysis through the Time Domain 87
Formulation of Response Integral 87
Numerical Evaluation of Response Integral 89
Analysis through the Frequency Domain 97
Fourier Response Integral 98
Discrete Fourier Transforms (DVF) 100
Fast Fourier Transforms (FFT) 102
Evaluation of Dynamic Response 106
Relationship between the Time- and Frequency-Domain Transfer Functions 109
7. Response to General Dynamic Loading: Step-by-Step Methods 111
General Concepts 111
Piecewise Exact Method 112
Numerical Approximation Procedures General Comments 116
Second Central Difference Formulation 117
Integration Methods 120
Euler-Gauss Procedure 120
New mark Beta Methods 121
Conversion to Explicit Formulation 123
Incremental Formulation for Nonlinear Analysis 124
Summary of the Linear Acceleration Procedure 127
8. Generalized Single-Degree-of-Freedom Systems 133
General Comments on SDOF Systems 133
Generalized Properties: Assemblages of Rigid Bodies 134
Generalized Properties: Distributed Flexibility 140
Expressions for Generalized System Properties 145
Vibration Analysis by Rayleigh's Method 149
Selection of the Rayleigh Vibration Shape 152
Improved Rayleigh Method 156
PART II. MULTI-DEGREE-OF-FREEDOM SYSTEMS 159
9. Formulation of the MDOF Equations of Motion 169
Selection of the Degrees of Freedom 169
Dynamic-Equilibrium Condition 171
Axial-Force Effects 173
10. Evaluation of Structural-Property Matrices 175
Elastic Properties 175
Flexibility 175
Stiffness 176
Basic Structural Concepts 177
Finite-Element Stiffness 179
Mass Properties 184
Lumped-Mass Matrix 184
Consistent-Mass Matrix 185
Damping Properties 189
External Loading 189
Static Resultants 190
Consistent Nodal Loads 190
Geometric Stiffness 191
Linear Approximation 191
Consistent Geometric Stiffness 194
Choice of Property Formulation 196
Undamped Free Vibrations 201
Analysis of Vibration Frequencies 201
Analysis of Vibration Mode Shapes 204
Flexibility Formulation of Vibration Analysis 208
Influence of Axial Forces 208
Free Vibrations 208
Buckling Load 209
Buckling with Harmonic Excitation 210
Orthogonality Conditions 211
Basic Conditions 211
Additional Relationships 212
Normalizing 214
12. Analysis of Dynamic Response Using Superposition 219
Normal Coordinates 219
Uncoupled Equations of Motion: Undamped 221
Uncoupled Equations of Motion: Viscous Damping 222
Response Analysis by Mode Displacement Superposition 223
Viscous Damping 223
Complex-Stiffness Damping 230
Construction of Proportional Viscous Damping Matrices 234
Rayleigh Damping 234
Extended Rayleigh Damping 237
Alternative Formulation 240
Construction of Nonproportional Damping Matrices 242
Response Analysis using Coupled Equations of Motion 245
Time Domain 245
Frequency Domain 246
Relationship between Time- and Frequency- Domain Transfer Functions 247
Practical Procedure for solving Coupled Equations of Motion 251
Interpolation Procedure for Generation of Transfer Functions 254
13. Vibration Analysis by Matrix Iteration 259
Preliminary Comments 259
Fundamental Mode Analysis 260
Proof of Convergence 265
Analysis of Higher Modes 267
Second-Mode Analysis 267
Analysis of Third and Higher Modes 271
Analysis of Highest Mode 272
Buckling Analysis by Matrix Iteration 275
Inverse Iteration the Preferred Procedure 279
Inverse Iteration with Shifts 281
Special Eigenproblem Topics 285
Eigenproperty Expansion 286
Symmetric Form of Dynamic Matrix 288
Analysis of Unconstrained Structures 290
14. Selection of Dynamic Degrees of Freedom 293
Finite-Element Degrees of Freedom 293
One-Dimensional Elements 294
Two- and Three-Dimensional Elements 294
Kinematic Constraints 295
Static Condensation 296
Rayleigh Method in Discrete Coordinates 298
Rayleigh-Ritz Method 299
Subspace Iteration 304
Reduction of Modal Truncation Errors 306
General Comments on Coordinate Reduction 306
Modal Contributions 307
Static Correction Procedure 311
Mode Acceleration Method 313
Derived Ritz Vectors 314
Preliminary Comments 314
Derivation Details 316
Tridiagonal Equations of Motion 319
Loss of Orthogonality 322
Required Number of Vectors 323
15. Analysis of MDOF Dynamic Response: Step-by-Step Methods 325
Preliminary Comments 325
Incremental Equations of Motion 327
Step-by-Step Integration: Constant Average Acceleration Method 328
Step-by-Step Integration: Linear Acceleration Method 330
Strategies for Analysis of Coupled MDOF Systems 332
Localized Nonlinearity 332
Coupled Effects Treated as Pseudo-Forces 336
16. Variational Formulation of the Equations of Motion 341
Generalized Coordinates 341
Hamilton's Principle 342
Lagrange's Equations of Motion 344
Derivation of the General Equations of Motion for Linear Systems 351
Constraints and Lagrange Multipliers 356
PART III. DISTRIBUTED-PARAMETER SYSTEMS
17. Partial Differential Equations of Motion 365
Beam Flexure: Elementary Case 366
Beam Flexure: Including Axial-Force Effects 368
Beam Flexure: Including Viscous Damping 369
Beam Flexure: Generalized Support Excitations 370
Axial Deformations: Undamped 373
18. Analysis of Undamped Free Vibrations 377
Beam Flexure: Elementary Case 377
Beam Flexure: Including Axial-Force Effects 386
Beam Flexure: With Distributed Elastic Support 388
Beam Flexure: Orthogonality of Vibration Mode Shapes 389
Free Vibrations in Axial Deformation 391
Orthogonality of Axial Vibration Modes 392
19. Analysis of Dynamic Response 397
Normal Coordinates 397
Uncoupled Flexural Equations of Motion: Undamped Case 400
Uncoupled Flexural Equations of Motion: Damped Case 403
Uncoupled Axial Equations of Motion: Undamped Case 407
Wave-Propagation Analysis 411
Basic Axial-Wave-Propagation Equation 411
Consideration of Boundary Conditions 415
Discontinuity in Bar Properties 418
PART IV. RANDOM VIBRATIONS
20. Probability Theory 427
Single Random Variable 427
Important Averages of a Single Random Variable 432
One-Dimensional Random Walk 434
Two Random Variables 442
Important Averages of Two Random Variables 451
Scatter Diagram and Correlation of Two Random Variables 455
Principal Axes of Joint Probability Density Function 458
Rayleigh Probability Density Function 461
Random Variables 463
Linear Transformations of Normally Distributed Random Variables 465
21. Random Processes 471
Definition 471
Stationary and Ergodic Processes 473
Autocorrelation Function for Stationary Processes 478
Power Spectral Density Function for Stationary Processes 484
Relationship Between Power Spectral Density and Autocorrelation Functions 485
Power Spectral Density and Autocorrelation Functions for Derivatives of Processes 488
Superposition of Stationary Processes 490
Stationary Gaussian Processes: One Independent Variable 492
Stationary White Noise 498
Probability Distribution for Maxima 501
Probability Distribution for Extreme Values 506
Nonstationary Gaussian Processes 510
Stationary Gaussian Process: Two or More Independent Variables 511
22. Stochastic Response of Linear SDOF Systems 517
Transfer Functions 517
Relationship between Input and Output Autocorrelation Functions 518
Relationship between Input and Output Power Spectral Density Functions 522
Response Characteristics for Narrowband Systems 524
Nonstationary Mean Square Response Resulting from Zero Initial Conditions 528
Fatigue Predictions for Narrowband Systems 532
23. Stochastic Response of Linear MDOF Systems 539
Time-Domain Response for Linear Systems using Normal Modes 539
Frequency-Domain Response for Linear Systems using Normal Modes 541
Normal Mode Forcing Function due to Discrete Loadings 543
Normal Mode Forcing Function due to Distributed Loadings 547
Frequency-Domain Response for Linear Systems having Frequency-Dependent Parameters and/or Coupled Normal Modes 548
PART V. EARTHQUAKE ENGINEERING
24. Seismological Background 555
Introductory Note 555
Seismicity 556
Earthquake Faults and Waves 558
Structure of the Earth 559
Plate Tectonics 563
Elastic-Rebound Theory of Earthquakes 567
Measures of Earthquake Size 571
25. Free-Field Surface Ground Motions 575
Fourier and Response Spectra 575
Factors influencing Response Spectra 581
Design Response Spectra 586
Dual Strategy of Seismic Design 586
Peak Ground Accelerations 587
Response Spectrum Shapes 590
Uniform-Hazard Site-Specific Response Spectra 595
Two Horizontal Components of Motion 597
Design Accelerograms 597
Response Spectrum Compatible Accelerograms 598
Principal Axes of Motion 603
Spatially Correlated Motions 607
26. Deterministic Earthquake Response: Systems on Rigid Foundations 613
Types of Earthquake Excitation 613
Response to Rigid-Soil Excitations 615
Lumped SDOF Elastic Systems, Translational Excitation 615
Generalized-Coordinate SDOF Elastic Systems, Translational Excitation 617
Lumped MDOF Elastic Systems, Translational Excitation 623
Comparison with ATC-3 Recommended Code Provisions 638
Distributed-Parameter Elastic Systems, Translational Excitation 640
Lumped MDOF Elastic Systems, Rotational Excitation 642
Lumped MDOF Elastic Systems, Multiple Excitations 644
Lumped SDOF Elastic-Plastic Systems, Translational Excitation 647
Combining Maximum Modal Responses 650
Mean Square Response of a Single Mode 650
Covariance of Response Produced by Two Modes 652
SRSS and CQC Combination of Modal Responses 653
Combining Two-Component-Excitation Responses 657
27. Deterministic Earthquake Response: Including Soil-Structure 660
Soil-Structure Interaction by Direct Analysis 669
Kinematic Interaction for Translational Excitation; the Tau Effect 670
Direct Inclusion of a Bounded Soil Layer 673
Substructure Analysis of SSI Response 674
Lumped SDOF Systems on Rigid Mat Foundation 674
General MDOF System with Multiple Support Excitations 679
Generation of Boundary Impedances 689
Response of Underground Structures 704
Free-Field Ground Motions due to Propagating Plane Waves 704
Racking Deformations of Cross Sections 705
Overall Axial and Flexural Deformations 706
Influence of Transverse Joints on Axial Deformations 709
28. Stochastic Structural Response 711
Modeling of Strong Ground Motions 711
Stochastic Response of Linear Systems 711
SDOF Systems 711
MDOF Systems 712
Extreme-Value Response of Nonlinear Systems 713
SDOF Systems 713
MDOF Systems 723
Design Considerations 726
Allowable Ductility Demand versus Ductility Capacity 729
Index 731
0070113947
STRUCTURAL DYNAMICS
FREE VIBRATIONS
HARMONIC LOADING
PERIODIC LOADING
IMPULSIVE LOADING
SUPERPOSITION METHODS
STEP-BY STEP-METHOD
CARGA DINAMICA
DINAMICA-ESTRUCTURAS
DINAMICA ESTRUCTURAL
624.042.8 C625