Foreword xxi Preface xxiii Acknowledgments xxxi PART I SINGLE-DEGREE-OF-FREEDOM SYSTEMS 1 1 Equations of Motion, Problem Statement, and Solution Methods 3 1.1 Simple Structures 3 1.2 Single-Degree-of-Freedom System 7 1.3 Force--Displacement Relation 8 1.4 Damping Force 12 1.5 Equation of Motion: External Force 14 1.6 Mass--Spring--Damper System 19 1.7 Equation of Motion: Earthquake Excitation 23 1.

8 Problem Statement and Element Forces 26 1.9 Combining Static and Dynamic Responses 28 1.10 Methods of Solution of the Differential Equation 28 1.11 Study of SDF Systems: Organization 33 Appendix 1 : Stiffness Coefficients for a Flexural Element 33 2 Free Vibration 39 2.1 Undamped Free Vibration 39 2.2 Viscously Damped Free Vibration 48 2.3 Energy in Free Vibration 56 2.4 Coulomb-Damped Free Vibration 57 3 Response to Harmonic and Periodic Excitations 65 Part A: Viscously Damped Systems: Basic Results 66 3.

1 Harmonic Vibration of Undamped Systems 66 3.2 Harmonic Vibration with Viscous Damping 72 Part B: Viscously Damped Systems: Applications 85 3.3 Response to Vibration Generator 85 3.4 Natural Frequency and Damping from Harmonic Tests 87 3.5 Force Transmission and Vibration Isolation 90 3.6 Response to Ground Motion and Vibration Isolation 91 3.7 Vibration-Measuring Instruments 95 3.8 Energy Dissipated in Viscous Damping 99 3.

9 Equivalent Viscous Damping 103 Part C: Systems with Nonviscous Damping 105 3.10 Harmonic Vibration with Rate-Independent Damping 105 3.11 Harmonic Vibration with Coulomb Friction 109 Part D: Response to Periodic Excitation 113 3.12 Fourier Series Representation 114 3.13 Response to Periodic Force 114 Appendix 3 : Four-Way Logarithmic Graph Paper 118 4 Response to Arbitrary, Step, and Pulse Excitations 125 Part A: Response to Arbitrarily Time-Varying Forces 125 4.1 Response to Unit Impulse 126 4.2 Response to Arbitrary Force 127 Part B: Response to Step and Ramp Forces 129 4.3 Step Force 129 4.

4 Ramp or Linearly Increasing Force 131 4.5 Step Force with Finite Rise Time 132 Part C: Response to Pulse Excitations 135 4.6 Solution Methods 135 4.7 Rectangular Pulse Force 137 4.8 Half-Cycle Sine Pulse Force 143 4.9 Symmetrical Triangular Pulse Force 148 4.10 Effects of Pulse Shape and Approximate Analysis for Short Pulses 151 4.11 Effects of Viscous Damping 154 4.

12 Response to Ground Motion 155 5 Numerical Evaluation of Dynamic Response 165 5.1 Time-Stepping Methods 165 5.2 Methods Based on Interpolation of Excitation 167 5.3 Central Difference Method 171 5.4 Newmark''s Method 174 5.5 Stability and Computational Error 180 5.6 Nonlinear Systems: Central Difference Method 183 5.7 Nonlinear Systems: Newmark''s Method 183 6 Earthquake Response of Linear Systems 197 6.

1 Earthquake Excitation 197 6.2 Equation of Motion 203 6.3 Response Quantities 204 6.4 Response History 205 6.5 Response Spectrum Concept 207 6.6 Deformation, Pseudo-velocity, and Pseudo-acceleration Response Spectra 208 6.7 Peak Structural Response from the Response Spectrum 217 6.8 Response Spectrum Characteristics 222 6.

9 Elastic Design Spectrum 230 6.10 Comparison of Design and Response Spectra 239 6.11 Distinction between Design and Response Spectra 241 6.12 Velocity and Acceleration Response Spectra 242 Appendix 6 : El Centro, 1940 Ground Motion 246 7 Earthquake Response of Inelastic Systems 257 7.1 Force--Deformation Relations 258 7.2 Normalized Yield Strength, Yield Strength Reduction Factor, and Ductility Factor 264 7.3 Equation of Motion and Controlling Parameters 265 7.4 Effects of Yielding 266 7.

5 Response Spectrum for Yield Deformation and Yield Strength 273 7.6 Yield Strength and Deformation from the Response Spectrum 277 7.7 Yield Strength--Ductility Relation 277 7.8 Relative Effects of Yielding and Damping 279 7.9 Dissipated Energy 280 7.10 Supplemental Energy Dissipation Devices 283 7.11 Inelastic Design Spectrum 288 7.12 Applications of the Design Spectrum 295 7.

13 Comparison of Design and Response Spectra 301 8 Generalized Single-Degree-of-Freedom Systems 305 8.1 Generalized SDF Systems 305 8.2 Rigid-Body Assemblages 307 8.3 Systems with Distributed Mass and Elasticity 309 8.4 Lumped-Mass System: Shear Building 321 8.5 Natural Vibration Frequency by Rayleigh''s Method 328 8.6 Selection of Shape Function 332 Appendix 8 : Inertia Forces for Rigid Bodies 336 PART II MULTI-DEGREE-OF-FREEDOM SYSTEMS 343 9 Equations of Motion, Problem Statement, and Solution Methods 345 9.1 Simple System: Two-Story Shear Building 345 9.

2 General Approach for Linear Systems 350 9.3 Static Condensation 367 9.4 Planar or Symmetric-Plan Systems: Ground Motion 370 9.5 One-Story Unsymmetric-Plan Buildings 375 9.6 Multistory Unsymmetric-Plan Buildings 381 9.7 Multiple Support Excitation 385 9.8 Inelastic Systems 390 9.9 Problem Statement 390 9.

10 Element Forces 391 9.11 Methods for Solving the Equations of Motion: Overview 391 10 Free Vibration 401 Part A: Natural Vibration Frequencies and Modes 402 10.1 Systems without Damping 402 10.2 Natural Vibration Frequencies and Modes 404 10.3 Modal and Spectral Matrices 406 10.4 Orthogonality of Modes 407 10.5 Interpretation of Modal Orthogonality 408 10.6 Normalization of Modes 408 10.

7 Modal Expansion of Displacements 418 Part B: Free Vibration Response 419 10.8 Solution of Free Vibration Equations: Undamped Systems 419 10.9 Systems with Damping 422 10.10 Solution of Free Vibration Equations: Classically Damped Systems 423 Part C: Computation of Vibration Properties 426 10.11 Solution Methods for the Eigenvalue Problem 426 10.12 Rayleigh''s Quotient 428 10.13 Inverse Vector Iteration Method 428 10.14 Vector Iteration with Shifts: Preferred Procedure 433 10.

15 Transformation of k = 2 m to the Standard Form 438 11 Damping in Structures 445 Part A: Experimental Data and Recommended Modal Damping Ratios 445 11.1 Vibration Properties of Millikan Library Building 445 11.2 Estimating Modal Damping Ratios 450 Part B: Construction of Damping Matrix 452 11.3 Damping Matrix 452 11.4 Classical Damping Matrix 453 11.5 Nonclassical Damping Matrix 462 12 Dynamic Analysis and Response of Linear Systems 465 Part A: Two-Degree-of-Freedom Systems 465 12.1 Analysis of Two-DOF Systems without Damping 465 12.2 Vibration Absorber or Tuned Mass Damper 468 Part B: Modal Analysis 470 12.

3 Modal Equations for Undamped Systems 470 12.4 Modal Equations for Damped Systems 473 12.5 Displacement Response 474 12.6 Element Forces 475 12.7 Modal Analysis: Summary 475 Part C: Modal Response Contributions 480 12.8 Modal Expansion of Excitation Vector p ( t ) = s p ( t ) 480 12.9 Modal Analysis for p ( t ) = s p ( t ) 484 12.10 Modal Contribution Factors 485 12.

11 Modal Responses and Required Number of Modes 487 Part D: Special Analysis Procedures 494 12.12 Static Correction Method 494 12.13 Mode Acceleration Superposition Method 497 12.14 Mode Acceleration Superposition Method: Arbitrary Excitation 498 13 Earthquake Analysis of Linear Systems 511 Part A: Response History Analysis 512 13.1 Modal Analysis 512 13.2 Multistory Buildings with Symmetric Plan 518 13.3 Multistory Buildings with Unsymmetric Plan 537 13.4 Torsional Response of Symmetric-Plan Buildings 548 13.

5 Resp.