THEORY OF MATRIX STRUCTURAL ANALYSIS J. S. PRZEMIENIECKI PROFESSOR OF MECHANICS AND ASSISTANT DEAN FOR RESEARCH AIR FORCE INSTITUTE OF TECHNOLOGY

Chapters 1 - 6 McGRAW-HILL BOOK COMPANY NEW YORK ST. LOUIS SAN FRANCISCO TORONTO LONDON SYDNEY

THEORY OF MATRIX STRUCTURAL ANALYSIS Copyright© 1968 by McGraw-Hill. Inc. All Rights Reserved. Printed in the United States of America. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic,' mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Library of Congress Catalog Card Number 67-19151 50904 1234567890MAMM7432106987

PREFACE The matrix methods of structural analysis developed for use on modern digital computers, universally accepted in structural design, provide a meant for rapid and accurate analysis of complex structures under both static and dynamic loading conditions.

The matrix methods are based on the concept of replacing the actual con-tinuous structure by an equivalent model made up from discrete structural elements having known elastic and inertial properties expressible in matrix form. The matrices representing these properties are considered as building blocks which, when fitted together in accordance with a set of rules derived from the theory of elasticity, provide the static and dynamic properties of the actual structure.

In this text the general theory of matrix structural analysis is presented. The following fundamental principles and theorems and their applications to matrix theory are discussed: principles of virtual displacements and virtual forces, Castigliano's theorems, minimum-strain-energy theorem, minimum-complementary-strain-energy theorem, and the unit-displacement and unit-load theorems. The matrix displacement and force methods of analysis are presented together with the elastic, thermal, and inertial properties of the most commonly used structural elements. Matrix formulation of dynamic analysis of structures, calculation of vibration frequencies and modes, and dynamic response of undamped and damped structural systems are included. Furthermore, structural synthesis, nonlinear effects due to large deflections, inelasticity, creep, and buckling are also discussed.

The examples illustrating the various applications of the theory of matrix structural analysis have been chosen so that a slide rule is sufficient to carry out the numerical calculations. For the benefit of the reader who may be unfamiliar with the matrix algebra. Appendix A discusses the matrix operations and their applications to structural analysis. Appendix B gives an extensive bibliography on matrix methods of structural analysis.

This book originated as lecture notes prepared for a graduate course in Matrix Structural Analysis, taught by the author at the Air Force Institute of Technology and at the Ohio State University. The book is intended for both the graduate student and the structural engineer who wish to study modern methods of structural analysis; it should also be valuable as a reference source for the practicing structural engineer.

Dr. Peter J. Torvik, Associate Professor of Mechanics, Air Force Institute of Technology, and Walter J. Mykytow, Assistant for Research and Technology, Vehicle Dynamics Division, Air Force Flight Dynamics Laboratory, carefully read the manuscript and made many valuable suggestions for improving the contents. Their contributions are gratefully acknowledged. Wholehearted thanks are also extended to Sharon Coates for her great patience and cooperation in typing the entire manuscript.

J, S. PRZEMIENIECKI