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Edition: 2ND 01

Copyright: 2001

Publisher: Prentice Hall, Inc.

Published: 2001

International: No

Copyright: 2001

Publisher: Prentice Hall, Inc.

Published: 2001

International: No

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This second edition includes many topics encompassing the theory of structural dynamics and the application of this theory regarding earthquake analysis, response, and design of structures. Covers the inelastic design spectrum to structural design; energy dissipation devices; Eurocode; theory of dynamic response of structures; structural dynamics theory; and more. Ideal for readers interested in Dynamics of Structures and Earthquake Engineering.

**I. SINGLE-DEGREE-OF-FREEDOM SYSTEMS.**

**1. 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. Appendix 1: Stiffness Coefficients for a Flexural Element.

**2. Free Vibration. **

Undamped Free Vibration. Viscously Damped Free Vibration. Energy in Free Vibration. Coulomb-Damped Free Vibration.

**3. 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. Appendix 3: Four-Way Logarithmic Graph Paper.

**4. 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.

** 5. 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.

**6. 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 ad Response Spectra. Distinction between Design and Response Spectra. Velocity and Acceleration Response Spectra. Appendix 6: El Centro, 1940 Ground Motion.

**7. 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.

** 8. 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. Appendix 8: Inertia Forces for Rigid Bodies.

**II. MULTI-DEGREE-OF-FREEDOM SYSTEMS.**

**9. 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 Building: Ground Motion. Symmetric-Plan Buildings: Torsional Excitation. Multiple Support Excitation. Inelastic Systems. Problem Statement. Element Forces. Methods for Solving the Equations of Motion: Overview.

**10. 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**ø = ...w2**m**ø to the Standard Form.

**11. 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.

**12. 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)** =

*Special Analysis Procedures.*

Static Correction Method. Mode Acceleration Superposition Method. Analysis of Nonclassically Damped Systems.

**13. 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.

**14. Reduction of Degrees of Freedom. **

Kinematic Constraints. Mass Lumping in Selected DOFs. Rayleigh-Ritz Method. Selection of Ritz Vectors. Dynamic Analysis Using Ritz Vectors.

**15. Numerical Evaluation of Dynamic Response. **

Time-Stepping Methods. Analysis of Linear Systems with Nonclassical Damping. Analysis of Nonlinear Systems.

**16. 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.

**17. 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 Function. Element Stiffness Matrix. Element Mass Matrix. Element (Applied) Force Vector. Comparison of Finite Element and Exact Solutions. Dynamic Analysis of Structural Continua.

**III. EARTHQUAKE RESPONSE AND DESIGN OF MULTISTORY BUILDINGS.**

**18. Earthquake Response of Linearly Elastic Buildings. **

Systems Analyzed, Design Spectrum, and Response Quantities. Influence of *T** 1* and

**19. Earthquake Response of Inelastic Buildings. **

Allowable Ductility and Ductility Demand. Buildings with ''Weak'' or ''Soft'' First Story. Buildings Designed for Code Force Distribution. Limited Scope. Appendix 19: Properties of Multistory Buildings.

**20. 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.

**21. Structural Dynamics in Building Codes. **

*Building Codes and Structural Dynamics.*

International Building Code (United States), 2000. National Building Code of Canada, 1995. Mexico Federal District Code, 1993. Eurocode 8. Structural Dynamics in Building Codes.

*Evaluation of Building Codes.*

Base Shear. Story Shears and Equivalent Static Forces. Overturning Moments. Concluding Remarks.

Appendix A: Frequency Domain Method of Response Analysis.

Appendix B: Notation.

Appendix C: Answers to Selected Problems.

Index.

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Summary

This second edition includes many topics encompassing the theory of structural dynamics and the application of this theory regarding earthquake analysis, response, and design of structures. Covers the inelastic design spectrum to structural design; energy dissipation devices; Eurocode; theory of dynamic response of structures; structural dynamics theory; and more. Ideal for readers interested in Dynamics of Structures and Earthquake Engineering.

Table of Contents
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. Appendix 1: Stiffness Coefficients for a Flexural Element.

Undamped Free Vibration. Viscously Damped Free Vibration. Energy in Free Vibration. Coulomb-Damped Free Vibration.

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.

Fourier Series Representation. Response to Periodic Force. Appendix 3: Four-Way Logarithmic Graph Paper.

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.

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.

Solution of Free Vibration Equations: Undamped Systems. Free Vibration of Systems with Damping. Solution of Free Vibration Equations: Classically Damped Systems.

Modal Equations for Undamped Systems. Modal Equations for Damped Systems. Displacement Response. Element Forces. Modal Analysis: Summary.

Static Correction Method. Mode Acceleration Superposition Method. Analysis of Nonclassically Damped Systems.

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.

Peak Response from Earthquake Response Spectrum. Multistory Buildings with Symmetric Plan. Multistory Buildings with Unsymmetric Plan.

Formulation Using Conservation of Energy. Formulation Using Virtual Work. Disadvantages of Rayleigh-Ritz Method.

Finite Element Approximation. Analysis Procedure. Element Degrees of Freedom and Interpolation Function. Element Stiffness Matrix. Element Mass Matrix. Element (Applied) Force Vector. Comparison of Finite Element and Exact Solutions. Dynamic Analysis of Structural Continua.

International Building Code (United States), 2000. National Building Code of Canada, 1995. Mexico Federal District Code, 1993. Eurocode 8. Structural Dynamics in Building Codes.

**I. SINGLE-DEGREE-OF-FREEDOM SYSTEMS.**

**1. Equations of Motion, Problem Statement, and Solution Methods. **

**2. Free Vibration. **

**3. 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.*

*Systems with Nonviscous Damping.*

Harmonic Vibration with Rate-Independent Damping. Harmonic Vibration with Coulomb Friction.

*Response to Periodic Excitation.*

**4. 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.*

** 5. 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.

**6. 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 ad Response Spectra. Distinction between Design and Response Spectra. Velocity and Acceleration Response Spectra. Appendix 6: El Centro, 1940 Ground Motion.

**7. 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.

** 8. 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. Appendix 8: Inertia Forces for Rigid Bodies.

**II. MULTI-DEGREE-OF-FREEDOM SYSTEMS.**

**9. 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 Building: Ground Motion. Symmetric-Plan Buildings: Torsional Excitation. Multiple Support Excitation. Inelastic Systems. Problem Statement. Element Forces. Methods for Solving the Equations of Motion: Overview.

**10. Free Vibration. **

*Natural Vibration Frequencies and Modes.*

*Free Vibration Response.*

*Computation of Vibration Properties.*

**k**ø = ...w2**m**ø to the Standard Form.

**11. 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.

**12. 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 Response Contributions.*

**p (t)** =

*Special Analysis Procedures.*

**13. Earthquake Analysis of Linear Systems. **

*Response History Analysis.*

*Response Spectrum Analysis.*

**14. Reduction of Degrees of Freedom. **

Kinematic Constraints. Mass Lumping in Selected DOFs. Rayleigh-Ritz Method. Selection of Ritz Vectors. Dynamic Analysis Using Ritz Vectors.

**15. Numerical Evaluation of Dynamic Response. **

Time-Stepping Methods. Analysis of Linear Systems with Nonclassical Damping. Analysis of Nonlinear Systems.

**16. 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.

**17. Introduction to the Finite Element Method. **

*Rayleigh-Ritz Method.*

*Finite Element Method.*

**III. EARTHQUAKE RESPONSE AND DESIGN OF MULTISTORY BUILDINGS.**

**18. Earthquake Response of Linearly Elastic Buildings. **

Systems Analyzed, Design Spectrum, and Response Quantities. Influence of *T** 1* and

**19. Earthquake Response of Inelastic Buildings. **

Allowable Ductility and Ductility Demand. Buildings with ''Weak'' or ''Soft'' First Story. Buildings Designed for Code Force Distribution. Limited Scope. Appendix 19: Properties of Multistory Buildings.

**20. 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.

**21. Structural Dynamics in Building Codes. **

*Building Codes and Structural Dynamics.*

*Evaluation of Building Codes.*

Base Shear. Story Shears and Equivalent Static Forces. Overturning Moments. Concluding Remarks.

Appendix A: Frequency Domain Method of Response Analysis.

Appendix B: Notation.

Appendix C: Answers to Selected Problems.

Index.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 2001

International: No

Published: 2001

International: No

**I. SINGLE-DEGREE-OF-FREEDOM SYSTEMS.**

**1. Equations of Motion, Problem Statement, and Solution Methods. **

**2. Free Vibration. **

**3. 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.*

*Systems with Nonviscous Damping.*

Harmonic Vibration with Rate-Independent Damping. Harmonic Vibration with Coulomb Friction.

*Response to Periodic Excitation.*

**4. 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.*

** 5. 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.

**6. 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 ad Response Spectra. Distinction between Design and Response Spectra. Velocity and Acceleration Response Spectra. Appendix 6: El Centro, 1940 Ground Motion.

**7. 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.

** 8. 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. Appendix 8: Inertia Forces for Rigid Bodies.

**II. MULTI-DEGREE-OF-FREEDOM SYSTEMS.**

**9. 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 Building: Ground Motion. Symmetric-Plan Buildings: Torsional Excitation. Multiple Support Excitation. Inelastic Systems. Problem Statement. Element Forces. Methods for Solving the Equations of Motion: Overview.

**10. Free Vibration. **

*Natural Vibration Frequencies and Modes.*

*Free Vibration Response.*

*Computation of Vibration Properties.*

**k**ø = ...w2**m**ø to the Standard Form.

**11. 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.

**12. 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 Response Contributions.*

**p (t)** =

*Special Analysis Procedures.*

**13. Earthquake Analysis of Linear Systems. **

*Response History Analysis.*

*Response Spectrum Analysis.*

**14. Reduction of Degrees of Freedom. **

Kinematic Constraints. Mass Lumping in Selected DOFs. Rayleigh-Ritz Method. Selection of Ritz Vectors. Dynamic Analysis Using Ritz Vectors.

**15. Numerical Evaluation of Dynamic Response. **

Time-Stepping Methods. Analysis of Linear Systems with Nonclassical Damping. Analysis of Nonlinear Systems.

**16. 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.

**17. Introduction to the Finite Element Method. **

*Rayleigh-Ritz Method.*

*Finite Element Method.*

**III. EARTHQUAKE RESPONSE AND DESIGN OF MULTISTORY BUILDINGS.**

**18. Earthquake Response of Linearly Elastic Buildings. **

Systems Analyzed, Design Spectrum, and Response Quantities. Influence of *T** 1* and

**19. Earthquake Response of Inelastic Buildings. **

Allowable Ductility and Ductility Demand. Buildings with ''Weak'' or ''Soft'' First Story. Buildings Designed for Code Force Distribution. Limited Scope. Appendix 19: Properties of Multistory Buildings.

**20. 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.

**21. Structural Dynamics in Building Codes. **

*Building Codes and Structural Dynamics.*

*Evaluation of Building Codes.*

Base Shear. Story Shears and Equivalent Static Forces. Overturning Moments. Concluding Remarks.

Appendix A: Frequency Domain Method of Response Analysis.

Appendix B: Notation.

Appendix C: Answers to Selected Problems.

Index.