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DYNAMICS OF STRUCTURES
PRENTICE-HALL INTERNATIONAL SERIES IN CIVIL ENGINEERING AND ENGINEERING MECHANICS William J. Hall, Editor Au and Christiano, Structural Analysis Bathe, Finite Element Procedures Biggs, Introduction to Structural Engineering Chopra, Dynamics of Structures: Theory and Applications to Earthquake Engineering, 4/e Cooper and Chen, Designing Steel Structures Cording et al., The Art and Science of Geotechnical Engineering Hendrickson and Au, Project Management for Construction, 2/e Higdon et al., Engineering Mechanics, 2nd Vector Edition Hultz and Kovacs, Introduction in Geotechnical Engineering Johnston, Lin, and Galambos, Basic Steel Design, 3/e Kelkar and Sewell, Fundamentals of the Analysis and Design of Shell Structures Kramer, Geotechnical Earthquake Engineering MacGregor, Reinforced Concrete: Mechanics and Design, 3/e Melosh, Structural Engineering Analysis by Finite Elements Nawy, Prestressed Concrete: A Fundamental Approach, 3/e Nawy, Reinforced Concrete: A Fundamental Approach, 4/e Ostwald, Construction Cost Analysis and Estimating Pfeffer, Solid Waste Management Popov, Engineering Mechanics of Solids, 2/e Popov, Mechanics of Materials, 2/e Schneider and Dickey, Reinforced Masonry Design, 3/e Wang and Salmon, Introductory Structural Analysis Weaver and Johnson, Structural Dynamics by Finite Elements Wolf, Dynamic Soil–Structure Interaction Young et al., The Science and Technology of Civil Engineering Materials
DYNAMICS OF STRUCTURES Theory and Applications to Earthquake Engineering Anil K. Chopra University of California at Berkeley Fourth Edition Prentice Hall
Vice President and Editorial Director, ECS: Marcia J. Horton Executive Editor: Holly Stark Vice President, Production: Vince O’Brien Senior Managing Editor: Scott Disanno Art Director: Jayne Conte Art Editor: Greg Dulles Cover Design: Bruce Kenselaar Manufacturing Buyer: Lisa McDowell Executive Marketing Manager: Tim Galligan Cover Photo: Transamerica Building, San Francisco, California. The motions shown are accelerations recorded during the Loma Prieta earthquake of October 17, 1989 at basement, twenty-ninth floor, and forty-ninth floor. Courtesy Transamerica Corporation. Credits and acknowledgments for material from other sources and reproduced, with permission, in this textbook appear on appropriate page within text. Copyright c 2012, 2007, 2001, 1995 Pearson Education, Inc., publishing as Prentice Hall, One Lake Street, Upper Saddle River, NJ 07458. All rights reserved. Manufactured in the United States of America. This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, 501 Boylston Street, Suite 900, Boston, MA 02116, fax your request to 617-671-3447, or e-mail at http://www.pearsoned.com/legal/permission.htm. Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps. The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for the incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs. Library of Congress Cataloging-in-Publication Data on File 10 9 8 7 6 5 4 3 2 1 ISBN 10: 0-13-285803-7 ISBN 13: 978-0-13-285803-8
Dedicated to Hamida and Nasreen with gratitude for suggesting the idea of working on a book and with appreciation for patiently enduring and sharing these years of preparation with me. Their presence and encouragement made this idea a reality.
Overview PART I SINGLE-DEGREE-OF-FREEDOM SYSTEMS 1 2 3 4 5 6 7 8 Equations of Motion, Problem Statement, and Solution Methods Free Vibration Response to Harmonic and Periodic Excitations Response to Arbitrary, Step, and Pulse Excitations Numerical Evaluation of Dynamic Response Earthquake Response of Linear Systems Earthquake Response of Inelastic Systems Generalized Single-Degree-of-Freedom Systems 1 3 39 65 125 165 197 257 307 vii
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