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Solutions Manual To Accompany

R.W. Clough and J. Penzien

D·YNAMICS OF STRUCTURES .

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Second Edition

Francisco Medina University of Puerto Rico, Mayaguez

McGraw-Hili, Inc. New York SI. Louis Son Francisco Auckland Bogota eOlacos Lisbon london Madrid Mexico City Mijon Monlreol New Delhi Sydr,·?y Tokyo TOlOnlo Son Juan Singapore

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Solutions Manual to Accompany Clough/Peiwen

DYNAMICS OF STRUCTURES -

Second Edition

Copyright 0 1995 by McGraw-Hili, Inc. All rights reserved. Printed in the United States of Americo. The contents. or parts thereof. may be reproduced for use with DYNAMICS OF STRUCTURES - Second Edition Joseph Penzien Ray W. Clough provided such reproductions beor copyright notice. but may not be reproduced in any form for any other purpose wifhout permission of the publisher. ISBN 0-07-011395·5 1 2 3 4 5 6 7 8 9 0 BKM BKM 9 0 9 8 7 6 5

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PREFACE

This Solutions Manual contains the solution to all the problems proposed in the text Dynamics of Structures. To solve many of these problems, the student should be very familiar with trigonometric and hyperbolic relationships, integral and differential calculus, matrix algebra, and matrix structural analysis. The student also ~as to have some knowledge of differential equations, and probability and theory of residues (these last two topics for Part IV). The problems were solved from the first edition of the book, systematically and for no particular reason, when I was pursuing graduate studies at Berkeley in the late 70s, without haying in mind that these solutions would later be assembled in a Solutions Manual. Therefore, the way the solutions are carried out may not be optimally didactic.or elegant; however, they present the advantage of showing a step-by-step procedure that a regular student would perform in attempting to solve these problems in a homework or test framework, or simply just for fun. All the problems can be solved by hand, but in a small number of cases it was preferred to present a solution carried out with the help of a computer progra·m or a programmable calculator. Some of the problems may be solved differently (especially in Part IV); however, the answers are correct, and almost all have been independently checked. In order to prepare the Solutions Manual, the existing solutions for the first edition of the book were revised to C!mform to the new edition, and then transcribed into the manual's current format. This procedure was checked carefully. Nevertheless, if the reader notic~s any error, I would be pleased to be advised. Finally, I wish to thank the book's authors for allowing me to have an enjoyable time while studying in Berkeley. The transcription of the solutions was patiently done by Mr. Jose Orozco, who deserves to be given all the credit for it. Francisco Medina Mayagiiez, December 1994

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