| |
| |
| Foreword | |
| |
| |
| Preface | |
| |
| |
| Preface to the Second Edition | |
| |
| |
| Preface to the First Edition | |
| |
| |
| Acknowledgments | |
| |
| |
| |
| Single-Degree-of-Freedom Systems | |
| |
| |
| |
| Equations of Motion, Problem Statement, and Solution Methods | |
| |
| |
| |
| Simple Structures | |
| |
| |
| |
| Single-Degree-of-Freedom System | |
| |
| |
| |
| Force-Displacement Relation | |
| |
| |
| |
| Damping Force | |
| |
| |
| |
| Equation of Motion: External Force | |
| |
| |
| |
| Mass-Spring-Damper System | |
| |
| |
| |
| Equation of Motion: Earthquake Excitation | |
| |
| |
| |
| Problem Statement and Element Forces | |
| |
| |
| |
| Combining Static and Dynamic Responses | |
| |
| |
| |
| Methods of Solution of the Differential Equation | |
| |
| |
| |
| Study of SDF Systems: Organization | |
| |
| |
| |
| Stiffness Coefficients for a Flexural Element | |
| |
| |
| |
| Free Vibration | |
| |
| |
| |
| Undamped Free Vibration | |
| |
| |
| |
| Viscously Damped Free Vibration | |
| |
| |
| |
| Energy in Free Vibration | |
| |
| |
| |
| Coulomb-Damped Free Vibration | |
| |
| |
| |
| Response to Harmonic and Periodic Excitations | |
| |
| |
| |
| Viscously Damped Systems: Basic Results | |
| |
| |
| |
| Harmonic Vibration of Undamped Systems | |
| |
| |
| |
| Harmonic Vibration with Viscous Damping | |
| |
| |
| |
| Viscously Damped Systems: Applications | |
| |
| |
| |
| Response to Vibration Generator | |
| |
| |
| |
| Natural Frequency and Damping from Harmonic Tests | |
| |
| |
| |
| Force Transmission and Vibration Isolation | |
| |
| |
| |
| Response to Ground Motion and Vibration Isolation | |
| |
| |
| |
| Vibration-Measuring Instruments | |
| |
| |
| |
| Energy Dissipated in Viscous Damping | |
| |
| |
| |
| Equivalent Viscous Damping | |
| |
| |
| |
| Systems with Nonviscous Damping | |
| |
| |
| |
| Harmonic Vibration with Rate-Independent Damping | |
| |
| |
| |
| Harmonic Vibration with Coulomb Friction | |
| |
| |
| |
| Response to Periodic Excitation | |
| |
| |
| |
| Fourier Series Representation | |
| |
| |
| |
| Response to Periodic Force | |
| |
| |
| |
| Four-Way Logarithmic Graph Paper | |
| |
| |
| |
| Response to Arbitrary, Step, and Pulse Excitations | |
| |
| |
| |
| Response to Arbitrarily Time-Varying Forces | |
| |
| |
| |
| Response to Unit Impulse | |
| |
| |
| |
| Response to Arbitrary Force | |
| |
| |
| |
| Response to Step and Ramp Forces | |
| |
| |
| |
| Step Force | |
| |
| |
| |
| Ramp or Linearly Increasing Force | |
| |
| |
| |
| Step Force with Finite Rise Time | |
| |
| |
| |
| Response to Pulse Excitations | |
| |
| |
| |
| Solution Methods | |
| |
| |
| |
| Rectangular Pulse Force | |
| |
| |
| |
| Half-Cycle Sine Pulse Force | |
| |
| |
| |
| Symmetrical Triangular Pulse Force | |
| |
| |
| |
| Effects of Pulse Shape and Approximate Analysis for Short Pulses | |
| |
| |
| |
| Effects of Viscous Damping | |
| |
| |
| |
| Response to Ground Motion | |
| |
| |
| |
| Numerical Evaluation of Dynamic Response | |
| |
| |
| |
| Time-Stepping Methods | |
| |
| |
| |
| Methods Based on Interpolation of Excitation | |
| |
| |
| |
| Central Difference Method | |
| |
| |
| |
| Newmark's Method | |
| |
| |
| |
| Stability and Computational Error | |
| |
| |
| |
| Analysis of Nonlinear Response: Central Difference Method | |
| |
| |
| |
| Analysis of Nonlinear Response: Newmark's Method | |
| |
| |
| |
| Earthquake Response of Linear Systems | |
| |
| |
| |
| Earthquake Excitation | |
| |
| |
| |
| Equation of Motion | |
| |
| |
| |
| Response Quantities | |
| |
| |
| |
| Response History | |
| |
| |
| |
| Response Spectrum Concept | |
| |
| |
| |
| Deformation, Pseudo-velocity, and Pseudo-acceleration Response Spectra | |
| |
| |
| |
| Peak Structural Response from the Response Spectrum | |
| |
| |
| |
| Response Spectrum Characteristics | |
| |
| |
| |
| Elastic Design Spectrum | |
| |
| |
| |
| Comparison of Design and Response Spectra | |
| |
| |
| |
| Distinction between Design and Response Spectra | |
| |
| |
| |
| Velocity and Acceleration Response Spectra | |
| |
| |
| |
| El Centro, 1940 Ground Motion | |
| |
| |
| |
| Earthquake Response of Inelastic Systems | |
| |
| |
| |
| Force-Deformation Relations | |
| |
| |
| |
| Normalized Yield Strength, Yield Strength Reduction Factor, and Ductility Factor | |
| |
| |
| |
| Equation of Motion and Controlling Parameters | |
| |
| |
| |
| Effects of Yielding | |
| |
| |
| |
| Response Spectrum for Yield Deformation and Yield Strength | |
| |
| |
| |
| Yield Strength and Deformation from the Response Spectrum | |
| |
| |
| |
| Yield Strength-Ductility Relation | |
| |
| |
| |
| Relative Effects of Yielding and Damping | |
| |
| |
| |
| Dissipated Energy | |
| |
| |
| |
| Energy Dissipation Devices | |
| |
| |
| |
| Inelastic Design Spectrum | |
| |
| |
| |
| Applications of the Design Spectrum | |
| |
| |
| |
| Comparison of Design and Response Spectra | |
| |
| |
| |
| Generalized Single-Degree-of-Freedom Systems | |
| |
| |
| |
| Generalized SDF Systems | |
| |
| |
| |
| Rigid-Body Assemblages | |
| |
| |
| |
| Systems with Distributed Mass and Elasticity | |
| |
| |
| |
| Lumped-Mass System: Shear Building | |
| |
| |
| |
| Natural Vibration Frequency by Rayleigh's Method | |
| |
| |
| |
| Selection of Shape Function | |
| |
| |
| |
| Inertia Forces for Rigid Bodies | |
| |
| |
| |
| Multi-Degree-of-Freedom Systems | |
| |
| |
| |
| Equations of Motion, Problem Statement, and Solution Methods | |
| |
| |
| |
| Simple System: Two-Story Shear Building | |
| |
| |
| |
| General Approach for Linear Systems | |
| |
| |
| |
| Static Condensation | |
| |
| |
| |
| Planar or Symmetric-Plan Systems: Ground Motion | |
| |
| |
| |
| Unsymmetric-Plan Buildings: Ground Motion | |
| |
| |
| |
| Symmetric-Plan Buildings: Torsional Excitation | |
| |
| |
| |
| Multiple Support Excitation | |
| |
| |
| |
| Inelastic Systems | |
| |
| |
| |
| Problem Statement | |
| |
| |
| |
| Element Forces | |
| |
| |
| |
| Methods for Solving the Equations of Motion: Overview | |
| |
| |
| |
| Free Vibration | |
| |
| |
| |
| Natural Vibration Frequencies and Modes | |
| |
| |
| |
| Systems without Damping | |
| |
| |
| |
| Natural Vibration Frequencies and Modes | |
| |
| |
| |
| Modal and Spectral Matrices | |
| |
| |
| |
| Orthogonality of Modes | |
| |
| |
| |
| Interpretation of Modal Orthogonality | |
| |
| |
| |
| Normalization of Modes | |
| |
| |
| |
| Modal Expansion of Displacements | |
| |
| |
| |
| Free Vibration Response | |
| |
| |
| |
| Solution of Free Vibration Equations: Undamped Systems | |
| |
| |
| |
| Free Vibration of Systems with Damping | |
| |
| |
| |
| Solution of Free Vibration Equations: Classically Damped Systems | |
| |
| |
| |
| Computation of Vibration Properties | |
| |
| |
| |
| Solution Methods for the Eigenvalue Problem | |
| |
| |
| |
| Rayleigh's Quotient | |
| |
| |
| |
| Inverse Vector Iteration Method | |
| |
| |
| |
| Vector Iteration with Shifts: Preferred Procedure | |
| |
| |
| |
| Transformation of k[phi] = [omega superscript 2]m[phi] to the Standard Form | |
| |
| |
| |
| Damping in Structures | |
| |
| |
| |
| Experimental Data and Recommended Modal Damping Ratios | |
| |
| |
| |
| Vibration Properties of Millikan Library Building | |
| |
| |
| |
| Estimating Modal Damping Ratios | |
| |
| |
| |
| Construction of Damping Matrix | |
| |
| |
| |
| Damping Matrix | |
| |
| |
| |
| Classical Damping Matrix | |
| |
| |
| |
| Nonclassical Damping Matrix | |
| |
| |
| |
| Dynamic Analysis and Response of Linear Systems | |
| |
| |
| |
| Two-Degree-of-Freedom Systems | |
| |
| |
| |
| Analysis of Two-DOF Systems without Damping | |
| |
| |
| |
| Vibration Absorber or Tuned Mass Damper | |
| |
| |
| |
| Modal Analysis | |
| |
| |
| |
| Modal Equations for Undamped Systems | |
| |
| |
| |
| Modal Equations for Damped Systems | |
| |
| |
| |
| Displacement Response | |
| |
| |
| |
| Element Forces | |
| |
| |
| |
| Modal Analysis: Summary | |
| |
| |
| |
| Modal Response Contributions | |
| |
| |
| |
| Modal Expansion of Excitation Vector p(t) = sp(t) | |
| |
| |
| |
| Modal Analysis for p(t) = sp(t) | |
| |
| |
| |
| Modal Contribution Factors | |
| |
| |
| |
| Modal Responses and Required Number of Modes | |
| |
| |
| |
| Special Analysis Procedures | |
| |
| |
| |
| Static Correction Method | |
| |
| |
| |
| Mode Acceleration Superposition Method | |
| |
| |
| |
| Analysis of Nonclassically Damped Systems | |
| |
| |
| |
| Earthquake Analysis of Linear Systems | |
| |
| |
| |
| Response History Analysis | |
| |
| |
| |
| Modal Analysis | |
| |
| |
| |
| Multistory Buildings with Symmetric Plan | |
| |
| |
| |
| Multistory Buildings with Unsymmetric Plan | |
| |
| |
| |
| Torsional Response of Symmetric-Plan Buildings | |
| |
| |
| |
| Response Analysis for Multiple Support Excitation | |
| |
| |
| |
| Structural Idealization and Earthquake Response | |
| |
| |
| |
| Response Spectrum Analysis | |
| |
| |
| |
| Peak Response from Earthquake Response Spectrum | |
| |
| |
| |
| Multistory Buildings with Symmetric Plan | |
| |
| |
| |
| Multistory Buildings with Unsymmetric Plan | |
| |
| |
| |
| Reduction of Degrees of Freedom | |
| |
| |
| |
| Kinematic Constraints | |
| |
| |
| |
| Mass Lumping in Selected DOFs | |
| |
| |
| |
| Rayleigh-Ritz Method | |
| |
| |
| |
| Selection of Ritz Vectors | |
| |
| |
| |
| Dynamic Analysis Using Ritz Vectors | |
| |
| |
| |
| Numerical Evaluation of Dynamic Response | |
| |
| |
| |
| Time-Stepping Methods | |
| |
| |
| |
| Analysis of Linear Systems with Nonclassical Damping | |
| |
| |
| |
| Analysis of Nonlinear Systems | |
| |
| |
| |
| Systems with Distributed Mass and Elasticity | |
| |
| |
| |
| Equation of Undamped Motion: Applied Forces | |
| |
| |
| |
| Equation of Undamped Motion: Support Excitation | |
| |
| |
| |
| Natural Vibration Frequencies and Modes | |
| |
| |
| |
| Modal Orthogonality | |
| |
| |
| |
| Modal Analysis of Forced Dynamic Response | |
| |
| |
| |
| Earthquake Response History Analysis | |
| |
| |
| |
| Earthquake Response Spectrum Analysis | |
| |
| |
| |
| Difficulty in Analyzing Practical Systems | |
| |
| |
| |
| Introduction to the Finite Element Method | |
| |
| |
| |
| Rayleigh-Ritz Method | |
| |
| |
| |
| Formulation Using Conservation of Energy | |
| |
| |
| |
| Formulation Using Virtual Work | |
| |
| |
| |
| Disadvantages of Rayleigh-Ritz Method | |
| |
| |
| |
| Finite Element Method | |
| |
| |
| |
| Finite Element Approximation | |
| |
| |
| |
| Analysis Procedure | |
| |
| |
| |
| Element Degrees of Freedom and Interpolation Functions | |
| |
| |
| |
| Element Stiffness Matrix | |
| |
| |
| |
| Element Mass Matrix | |
| |
| |
| |
| Element (Applied) Force Vector | |
| |
| |
| |
| Comparison of Finite Element and Exact Solutions | |
| |
| |
| |
| Dynamic Analysis of Structural Continua | |
| |
| |
| |
| Earthquake Response and Design of Multistory Buildings | |
| |
| |
| |
| Earthquake Response of Linearly Elastic Buildings | |
| |
| |
| |
| Systems Analyzed, Design Spectrum, and Response Quantities | |
| |
| |
| |
| Influence of T[subscript 1] and [rho] on Response | |
| |
| |
| |
| Modal Contribution Factors | |
| |
| |
| |
| Influence of T[subscript 1] on Higher-Mode Response | |
| |
| |
| |
| Influence of [rho] on Higher-Mode Response | |
| |
| |
| |
| Heightwise Variation of Higher-Mode Response | |
| |
| |
| |
| How Many Modes to Include | |
| |
| |
| |
| Earthquake Analysis and Response of Inelastic Buildings | |
| |
| |
| |
| Nonlinear Response History Analysis | |
| |
| |
| |
| Equations of Motion: Formulation and Solution | |
| |
| |
| |
| Computing Seismic Demands: Factors To Be Considered | |
| |
| |
| |
| Story Drift Demands | |
| |
| |
| |
| Strength Demands for SDF and MDF Systems | |
| |
| |
| |
| Approximate Analysis Procedures | |
| |
| |
| |
| Motivation and Basic Concept | |
| |
| |
| |
| Uncoupled Modal Response History Analysis | |
| |
| |
| |
| Modal Pushover Analysis | |
| |
| |
| |
| Evaluation of Modal Pushover Analysis | |
| |
| |
| |
| Simplified Modal Pushover Analysis for Practical Application | |
| |
| |
| |
| Earthquake Dynamics of Base-Isolated Buildings | |
| |
| |
| |
| Isolation Systems | |
| |
| |
| |
| Base-Isolated One-Story Buildings | |
| |
| |
| |
| Effectiveness of Base Isolation | |
| |
| |
| |
| Base-Isolated Multistory Buildings | |
| |
| |
| |
| Applications of Base Isolation | |
| |
| |
| |
| Structural Dynamics in Building Codes | |
| |
| |
| |
| Building Codes and Structural Dynamics | |
| |
| |
| |
| International Building Code (United States), 2006 | |
| |
| |
| |
| National Building Code of Canada, 2005 | |
| |
| |
| |
| Mexico Federal District Code, 2004 | |
| |
| |
| |
| Eurocode 8, 2004 | |
| |
| |
| |
| Structural Dynamics in Building Codes | |
| |
| |
| |
| Evaluation of Building Codes | |
| |
| |
| |
| Base Shear | |
| |
| |
| |
| Story Shears and Equivalent Static Forces | |
| |
| |
| |
| Overturning Moments | |
| |
| |
| |
| Concluding Remarks | |
| |
| |
| |
| Structural Dynamics in Building Evaluation Guidelines | |
| |
| |
| |
| Nonlinear Dynamic Procedure: Current Practice | |
| |
| |
| |
| SDF-System Estimate of Roof Displacement | |
| |
| |
| |
| Estimating Deformation of Inelastic SDF Systems | |
| |
| |
| |
| Nonlinear Static Procedure | |
| |
| |
| |
| Concluding Remarks | |
| |
| |
| |
| Frequency-Domain Method of Response Analysis | |
| |
| |
| |
| Notation | |
| |
| |
| |
| Answers to Selected Problems | |
| |
| |
| Index | |