Structural Dynamics: Theory and Computation
by Paz, Mario; Leigh, William E.Edition: 5th
Format: Hardcover
Pub. Date: 2004-01-01
Publisher(s): SPRINGER VERLAG INC
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Summary
The book is interesting as well as scholarly and encourages the reader to continue rather than to put it down. The presentation and the many diagrams are excellent - Structural Engineer.
Author Biography
Mario Paz Speed Scientific School University of Louisville KY William Leigh University of Central Florida Orlando
Table of Contents
| Preface to the Fifth Edition | p. xvii |
| Preface to the First Edition | p. xxi |
| Structures Modeled as a Single-Degree-of-Freedom System | p. 1 |
| Undamped Single-Degree-of-Freedom System | p. 3 |
| Degrees of Freedom | p. 4 |
| Undamped System | p. 5 |
| Springs in Parallel or in Series | p. 7 |
| Newton's Law of Motion | p. 8 |
| Free Body Diagram | p. 9 |
| D' Alembert's Principle | p. 10 |
| Solution of the Differential Equation of Motion | p. 12 |
| Frequency and Period | p. 14 |
| Amplitude of Motion | p. 16 |
| Summary | p. 22 |
| Problems | p. 23 |
| Damped Single-Degree-of-Freedom System | p. 31 |
| Viscous Damping | p. 31 |
| Equation of Motion | p. 32 |
| Critically Damped System | p. 33 |
| Overdamped System | p. 34 |
| Underdamped System | p. 35 |
| Logarithmic Decrement | p. 37 |
| Summary | p. 44 |
| Problems | p. 45 |
| Response of One-Degree-of-Freedom System to Harmonic Loading | p. 49 |
| Harmonic Excitation: Undamped System | p. 49 |
| Harmonic Excitation: Damped System | p. 52 |
| Evaluation of Damping at Resonance | p. 60 |
| Bandwidth Method (Half-Power) to Evaluate Damping | p. 61 |
| Energy Dissipated by Viscous Damping | p. 63 |
| Equivalent Viscous Damping | p. 64 |
| Response to Support Motion | p. 67 |
| Force Transmitted to the Foundation | p. 75 |
| Seismic Instruments | p. 78 |
| Response of One-Degree-of-Freedom System to Harmonic Loading Using SAP2000 | p. 80 |
| Summary | p. 92 |
| Analytical Problem | p. 94 |
| Problems | p. 96 |
| Response to General Dynamic Loading | p. 101 |
| Duhamel's Integral-Undamped System | p. 101 |
| Duhamel's Integral-Damped System | p. 110 |
| Response by Direct Integration | p. 110 |
| Solution of the Equation of Motion | p. 112 |
| Program 2-Response by Direct Integration | p. 117 |
| Program 3-Response to Impulsive Excitation | p. 120 |
| Response to General Dynamic Loading Using SAP2000 | p. 126 |
| Summary | p. 137 |
| Analytical Problems | p. 137 |
| Problems | p. 141 |
| Response Spectra | p. 149 |
| Construction of Response Spectrum | p. 149 |
| Response Spectrum for Support Excitation | p. 153 |
| Tripartite Response Spectra | p. 154 |
| Response Spectra for Elastic Design | p. 157 |
| Influence of Local Soil Conditions | p. 161 |
| Response Spectra for Inelastic Systems | p. 163 |
| Response Spectra for Inelastic Design | p. 166 |
| Program 6-Seismic Response Spectra | p. 171 |
| Summary | p. 174 |
| Problems | p. 174 |
| Nonlinear Structural Response | p. 179 |
| Nonlinear Single Degree-of-Freedom Model | p. 179 |
| Integration of the Nonlinear Equation of Motion | p. 181 |
| Constant Acceleration Method | p. 182 |
| Linear Acceleration Step-by-Step Method | p. 184 |
| The Newmark Beta Method | p. 187 |
| Elastoplastic Behavior | p. 188 |
| Algorithm for the Step-by-Step Solution for Elastoplastic Single-Degree-of-Freedom System | p. 190 |
| Program 5-Response for Elastoplastic Behavior | p. 196 |
| Summary | p. 198 |
| Problems | p. 198 |
| Structures Modeled as Shear Buildings | p. 203 |
| Free Vibration of a Shear Building | p. 205 |
| Stiffness Equations for the Shear Building | p. 205 |
| Natural Frequencies and Normal Modes | p. 209 |
| Orthogonality Property of the Normal Modes | p. 214 |
| Rayleigh's Quotient | p. 218 |
| Program 8-Natural Frequencies and Normal Modes | p. 220 |
| Free Vibration of a Shear Building Using SAP2000 | p. 221 |
| Summary | p. 225 |
| Problems | p. 227 |
| Forced Motion of Shear Building | p. 231 |
| Modal Superposition Method | p. 231 |
| Response of a Shear Building to Base Motion | p. 238 |
| Program 9-Response by Modal Superposition | p. 244 |
| Harmonic Forced Excitation | p. 246 |
| Program 10-Harmonic Response | p. 251 |
| Forced Motion Using SAP2000 | p. 254 |
| Combining Maximum Values of Modal Response | p. 265 |
| Summary | p. 266 |
| Problems | p. 267 |
| Reduction of Dynamic Matrices | p. 271 |
| Static Condensation | p. 271 |
| Static Condensation Applied to Dynamic Problems | p. 275 |
| Dynamic Condensation | p. 285 |
| Modified Dynamic Condensation | p. 293 |
| Program 12-Reduction of the Dynamic Problem | p. 296 |
| Summary | p. 299 |
| Problems | p. 299 |
| Framed Structures Modeled as Discrete Multi-Degree-of-Freedom Systems | p. 303 |
| Dynamic Analysis of Beams | p. 305 |
| Shape Functions for a Beam Segment | p. 305 |
| System Stiffness Matrix | p. 311 |
| Inertial Properties-Lumped Mass | p. 314 |
| Inertial Properties-Consistent Mass | p. 315 |
| Damping Properties | p. 320 |
| External Loads | p. 320 |
| Geometric Stiffness | p. 322 |
| Equations of Motion | p. 326 |
| Element Forces at Nodal Coordinates | p. 333 |
| Program 13-Modeling Structures as Beams | p. 336 |
| Dynamic Analysis of Beams Using SAP2000 | p. 339 |
| Summary | p. 347 |
| Problems | p. 347 |
| Dynamic Analysis of Plane Frames | p. 353 |
| Element Stiffness Matrix for Axial Effects | p. 353 |
| Element Mass Matrix for Axial Effects | p. 355 |
| Coordinate Transformation | p. 359 |
| Program 14-Modeling Structures as Plane Frames | p. 367 |
| Dynamic Analysis of Frames Using SAP2000 | p. 370 |
| Summary | p. 376 |
| Problems | p. 376 |
| Dynamic Analysis of Grid Frames | p. 381 |
| Local and Global Coordinate Systems | p. 381 |
| Torsional Effects | p. 382 |
| Stiffness Matrix for a Grid Element | p. 384 |
| Consistent Mass Matrix for a Grid Element | p. 385 |
| Lumped Mass Matrix for a Grid Element | p. 385 |
| Transformation of Coordinates | p. 386 |
| Program 15-Modeling Structures as Grid Frames | p. 392 |
| Dynamic Analysis of Grid Frames Using SAP2000 | p. 395 |
| Summary | p. 403 |
| Problems | p. 403 |
| Dynamic Analysis of Three-Dimensional Frames | p. 407 |
| Element Stiffness Matrix | p. 407 |
| Element Mass Matrix | p. 409 |
| Element Damping Matrix | p. 410 |
| Transformation of Coordinates | p. 410 |
| Differential Equation of Motion | p. 414 |
| Dynamic Response | p. 415 |
| Program 16-Modeling Structures as Space Frames | p. 415 |
| Dynamic Response of Three-Dimensional Frames Using SAP2000 | p. 418 |
| Summary | p. 426 |
| Problems | p. 427 |
| Dynamic Analysis of Trusses | p. 429 |
| Stiffness and Mass Matrices for the Plane Truss | p. 429 |
| Transformation of Coordinates | p. 432 |
| Program 17-Modeling Structures as Plane Trusses | p. 438 |
| Stiffness and Mass Matrices for Space Trusses | p. 441 |
| Equation of Motion for Space Trusses | p. 443 |
| Program 18-Modeling Structures as Space Trusses | p. 444 |
| Dynamic Analysis of Trusses Using SAP2000 | p. 446 |
| Summary | p. 459 |
| Problems | p. 459 |
| Dynamic Analysis of Structures using the Finite Element Method | p. 463 |
| Plane Elasticity Problems | p. 464 |
| Triangular Plate Element for Plane Elasticity problems | p. 465 |
| SAP2000 for Plane Elasticity Problem | p. 472 |
| Plate Bending | p. 477 |
| Rectangular Element for Plate Bending | p. 478 |
| SAP2000 for Plate Bending and Shell Problems | p. 484 |
| Summary | p. 491 |
| Problems | p. 493 |
| Time History Response of Multidegree-of-Freedom Systems | p. 495 |
| Incremental Equations of Motion | p. 495 |
| The Wilson-[theta] Method | p. 497 |
| Algorithm for Step-by-Step Solution of a Linear System Using the Wilson-[theta] Method | p. 500 |
| Initialization | p. 500 |
| For Each Time Step | p. 500 |
| Program 19-Response by Step Integration | p. 505 |
| The Newmark Beta Method | p. 506 |
| Elastoplastic Behavior of Framed Structures | p. 508 |
| Member Stiffness Matrix | p. 508 |
| Member Mass Matrix | p. 511 |
| Rotation of Plastic Hinges | p. 513 |
| Calculation of Member Ductility Ratio | p. 514 |
| Time-History Response of Multidegree-of-Freedom Systems Using SAP2000 | p. 515 |
| Summary | p. 521 |
| Problems | p. 522 |
| Structures Modeled with Distributed Properties | p. 525 |
| Dynamic Analysis of Systems with Distributed Properties | p. 527 |
| Flexural Vibration of Uniform Beams | p. 527 |
| Solution of the Equation of Motion in Free Vibration | p. 529 |
| Natural Frequencies and Mode Shapes for Uniform Beams | p. 531 |
| Both Ends Simply Supported | p. 531 |
| Both Ends Free (Free Beam) | p. 534 |
| Both Ends Fixed | p. 535 |
| One End Fixed and the other End Free (Cantilever Beam) | p. 537 |
| One End Fixed and the other End Simply Supported | p. 538 |
| Orthogonality Condition Between Normal Modes | p. 540 |
| Forced Vibration of Beams | p. 542 |
| Dynamic Stresses in Beams | p. 547 |
| Summary | p. 549 |
| Problems | p. 550 |
| Discretization of Continuous Systems | p. 553 |
| Dynamic Matrix for Flexural Effects | p. 554 |
| Dynamic Matrix for Axial Effects | p. 556 |
| Dynamic Matrix for Torsional Effects | p. 558 |
| Beam Flexure Including Axial-Force Effect | p. 560 |
| Power Series Expansion of the Dynamic Matrix for Flexural Effects | p. 563 |
| Power Series Expansion of the Dynamic Matrix for Axial and for Torsional Effects | p. 564 |
| Power Series Expansion of the Dynamic Matrix Including the Effects of Axial Forces | p. 565 |
| Summary | p. 566 |
| Special Topics: Fourier Analysis, Evaluation of Absolute Damping, Generalized Coordinates | p. 567 |
| Fourier Analysis and Response in the Frequency Domain | p. 569 |
| Fourier Analysis | p. 569 |
| Response to a Loading Represented by Fourier Series | p. 570 |
| Fourier Coefficients for Piecewise Linear Functions | p. 573 |
| Exponential Form of Fourier Series | p. 574 |
| Discrete Fourier Analysis | p. 575 |
| Fast Fourier Transform | p. 578 |
| Program 4-Response in the Frequency Domain | p. 580 |
| Summary | p. 586 |
| Problems | p. 586 |
| Evaluation of Absolute Damping from Modal Damping Ratios | p. 593 |
| Equations for Damped Shear Building | p. 593 |
| Uncoupled Damped Equations | p. 595 |
| Conditions for Damping Uncoupling | p. 596 |
| Program 11-Absolute Damping From Modal Damping Ratios | p. 602 |
| Summary | p. 604 |
| Problems | p. 604 |
| Generalized Coordinates and Rayleigh's Method | p. 607 |
| Principle of Virtual Work | p. 607 |
| Generalized Single-Degree-of-Freedom System-Rigid Body | p. 609 |
| Generalized Single-Degree-of-Freedom System-Distributed Elasticity | p. 612 |
| Shear Forces and Bending Moments | p. 617 |
| Generalized Equation of Motion for a Multistory Building | p. 621 |
| Shape Function | p. 624 |
| Rayleigh's Method | p. 628 |
| Improved Rayleigh's Method | p. 636 |
| Shear Walls | p. 639 |
| Summary | p. 642 |
| Problems | p. 643 |
| Random Vibration | p. 649 |
| Random Vibration | p. 651 |
| Statistical Description of Random Functions | p. 652 |
| Probability Density Function | p. 654 |
| The Normal Distribution | p. 656 |
| The Rayleigh Distribution | p. 657 |
| Correlation | p. 659 |
| The Fourier Transform | p. 663 |
| Spectral Analysis | p. 665 |
| Spectral Density Function | p. 669 |
| Narrow-Band and Wide-Band Random processes | p. 671 |
| Response to Random Excitation: Single-Degree-of-Freedom System | p. 675 |
| Response to Random Excitation: Multiple-Degree-of-Freedom System | p. 681 |
| Relationship Between Complex Frequency Response and Unit Impulse Response | p. 681 |
| Response to Random Excitation: Two-degree-of-freedom System | p. 683 |
| Response to Random Excitation: N Degree of Freedom System | p. 688 |
| Summary | p. 691 |
| Problems | p. 692 |
| Earthquake Engineering | p. 697 |
| Uniform Building Code 1997: Equivalent Lateral Force Method | p. 699 |
| Earthquake Ground Motion | p. 700 |
| Equivalent Lateral Force Method | p. 703 |
| Earthquake-Resistant Design Methods | p. 703 |
| Seismic Zone Factor | p. 703 |
| Base Shear Force | p. 704 |
| Distribution of Lateral Seismic Forces | p. 711 |
| Story Shear Force | p. 711 |
| Horizontal Torsional Moment | p. 712 |
| Overturning Moment | p. 713 |
| P-Delta Effect (P-[delta]) | p. 713 |
| Redundancy/Reliability Factor p | p. 715 |
| Story Drift Limitation | p. 715 |
| Diaphragm Design Forces | p. 716 |
| Earthquake Load Effect | p. 717 |
| Irregular Structures | p. 717 |
| Summary | p. 726 |
| Problems | p. 726 |
| Uniform Building Code 1997: Dynamic Method | p. 731 |
| Modal Seismic Response of Buildings | p. 731 |
| Modal Equation and Participation Factor | p. 732 |
| Modal Shear Force | p. 733 |
| Effective Modal Weight | p. 734 |
| Modal Lateral Forces | p. 735 |
| Modal Displacements | p. 735 |
| Modal Drift | p. 736 |
| Modal Overturning Moment | p. 736 |
| Modal Torsional Moment | p. 737 |
| Total Design Values | p. 737 |
| Provisions of UBC-97: Dynamic Method | p. 738 |
| Scaling of Results | p. 740 |
| Program 24-UBC 1997 Dynamic Lateral Force Method | p. 750 |
| Summary | p. 754 |
| Problems | p. 755 |
| International Building Code IBC-2000 | p. 757 |
| Response Spectral Acceleration: S[subscript s], S[subscript 1] | p. 757 |
| Soil Modification Response Spectral Acceleration: S[subscript MS], S[subscript M1] | p. 758 |
| Design Response Spectral Acceleration: S[subscript DS], S[subscript D1] | p. 759 |
| Site Class Definition: A, B, ...F | p. 760 |
| Seismic Use Group (SUG) and Occupancy Importance Factor (I[subscript E]) | p. 760 |
| Seismic Design Category (A, B, C, D, E and F) | p. 761 |
| Design Response Spectral Curve: S[subscript a] v.s. T | p. 763 |
| Determination of the Fundamental Period | p. 766 |
| Minimum lateral Force Procedure [IBC-2000: Section 1616.4.1] | p. 767 |
| Simplified Analysis Procedure [IBC-2000: Section 1617.5] | p. 768 |
| Seismic Base Shear | p. 768 |
| Response Modification Factor R | p. 768 |
| Vertical Distribution of Lateral Forces | p. 769 |
| Equivalent Seismic Lateral Force Method: [IBC-2000: Section 1617.4] | p. 769 |
| Distribution of Lateral Forces | p. 771 |
| Overturning Moments | p. 771 |
| Horizontal Torsional Moment | p. 772 |
| P-Delta Effect (P-[delta]) | p. 772 |
| Story Drift | p. 773 |
| Redundancy/Reliability Factor | p. 774 |
| Earthquake Load Effect | p. 775 |
| Building Irregularities | p. 775 |
| Summary | p. 781 |
| Appendices | p. 783 |
| Answers to Problems in Selected Chapters | p. 785 |
| Computer Programs | p. 793 |
| Glossary | p. 795 |
| Selected Bibliography | p. 803 |
| Index | p. 807 |
| Table of Contents provided by Rittenhouse. All Rights Reserved. |
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