Modal

Response Spectrum Method
In Seismic Analysis and Design of Structures
AJAYA K U M A R GUPTA.
Prokssor o Civil Engineering f North Carolina State University

F O R E W O R D BY

WILLIAM J. H A L L
Professor and Head. Civil Engineering of Universit.~ lllinois at Urbana Champaign

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BLACKWELL SCIENTIFIC PUBLICATIONS
BOSTON OXFORD LONDON EDINBURGH MELBOURNE

Q 1990 by

DISTRIBUTORSBlackwell Scientific Publications, Inc. Editorial offices: 3 Cambridge Center. Suite 208 Cambridge, Mas~gchusetts 02142, USA Osney Mead, Oxford OX2 OEL, England 25 John Street, London WClN 2BL, England 23 Ainslie Place, Edinburgh EH3 6M, Scotland 107 Bany Street. Carlton ' Victoria 3053, Australia
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All rights reserved. No part of this book may be reproduced in any form or by anyelectronic or mechanical means, including information storage and retrieval systems, without permission in writing from the publisher, except by a reviewer who may quote brief passages in a review First published 1990 Set by Tima Graphics, Singapore Printed and bound at the University Press, Cambridge. England 90 91 92 93 4 3 2 1

USA Blackwell Scientific Publications, Inc. Published BusinessServices PO Box 447 Brookline Village Massachusetts 02 147 (Orders: Tel: 61 7 524-7678) Canada Oxford University Press 70 Wynford Drive Don Mills Ontario M3C 159 (Orders: Tel: 416 441-2941) Australia Blackwell Scientific Publications (Australia) Pty Ltd 107 Barry Street Carlton, Victoria 3053 (Orders: Tek 03 347-0300) Outside North America and Australia Marston Book S e ~ c e Ltd s PO Box 87 OxfordOX2 ODT (Orders: Tel: 01 1 44 865 79 1155) Library of Congress Cataloging-in-Publication Data Gupta Ajaya K . Response spectrum method in seismic analysis and design of structures / Ajaya Kumar Gupta; foreword by W.J. Hall. (New directions in cm. Pcivil engineering) ISBN 0-86542-1 15-3 1. Earthquake engineering. 2. Structural engineering. 3. Seismic waves. 1. Title. 11. Series. TA654,6.G87 1990624.1'7626~20

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British Library Cataloguing-in-Publication Data Gupta, Ajaya Kumar Response spectrum method in seismic analysis and design of structures, I. Structure. Analysis I. Title 11. Series 624.1'7 1 ISBN 0-632-02755-X

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New Dirdons
SERIES E D C T Q ~ W.F.

in Civil Engineering
CH E N Purdue University

Dedicated to my parents Dr Chhail Bihari Lal Gupta andMrs Taravali Gupta

Contents

Foreword, ix Preface, xi Acknowledgments, xv
1 Structural dynamics and response spectrum, 1
I. 1 Single-degree-of-freedom system, I

1.2 Response spectrum, 2 1.3 Characteristics of the earthquake response spectrum, 6 1.4 Multi-degree-of-freedom systems. 7 References, 10

2 Design spectrum, 11
2.1 Introduction, I I 2.2 'Average' elastic spectra, 12 2.3Site-dependent spectra. 16 2.4 Design spectrum for inelastic systems, 23 2.5 Comments. 27 References, 28

3 Combination of modal responses, 30
3.1 3.2 3.3 3.4 Introduction, 30 Modes with closely spaced frequencies, 31 High frequency modes-rigid response, 39 High frequency modes-residual rigid response, 45 References. 49

4 Response to multicomponents of earthquake, 51
4.1 4.2 4.3 4.4 4.5 4.6Introduction, 5 1 Simultaneous variation in responses, 52 Equivalent modal responses, 55 Interaction ellipsoid, 59 Approximate method, 60 Application to design problems, 62 References, 64

5 Nonciassically damped systems, 66
5.1 Introduction, 66 5.2 Analytical formulation, 67 5.3 Response spectra. 7 1

viii 1 CONTENTS

5.4 5.5 5.6 5.7 5.8

Key frequencies f L and f H , 74 Modal combination,75 Modal combination for high frequency modes, 77 Modal combination for high frequency modes-residual Application, 8 1 References, 87

rigid response, 78

6 Response of secondary systems, 89
6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.1 1 Introduction, 89 Formulation of the coupled problem, 9 1 Coupled modal properties, 95 Coupled response calculation, 98 Comparison of coupled response with...