This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest. Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 26201_00_fm_pi-xii.qxd 12/1/10 4:48 PM Page i MATRIX ANALYSIS OF STRUCTURES Second Edition Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.qxp 9/17/07 4:22 PM Page viii 1 2 3 4 5 6 7 8 9 10 11 This page was intentionally left blank 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 S 50 R 51 1st Pass Pages 26201_00_fm_pi-xii.qxd 12/8/10 11:47 AM Page iii MATRIX ANALYSIS OF STRUCTURES Second Edition ASLAM KASSIMALI Southern Illinois University—Carbondale Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 26201_00_fm_pi-xii.qxd 12/8/10 11:47 AM Page iv Matrix Analysis of Structures, © 2012, 1999 Cengage Learning Second Edition ALL RIGHTS RESERVED. No part of this work covered by the copyright Aslam Kassimali herein may be reproduced, transmitted, stored, or used in any form or Publisher, Global Engineering: by any means graphic, electronic, or mechanical, including but not Christopher M. Shortt limited to photocopying, recording, scanning, digitizing, taping, web distribution, information networks, or information storage and retrieval Acquisitions Editor: Randall Adams systems, except as permitted under Section 107 or 108 of the 1976 Senior Developmental Editor: Hilda Gowans United States Copyright Act, without the prior written permission of Editorial Assistant: Tanya Altieri the publisher. 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Purchase any of our products at your local college store or at our preferred online store www. Printed in the United States of America 1 2 3 4 5 6 7 13 12 11 10 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 26201_00_fm_pi-xii.qxd 12/1/10 4:48 PM Page v IN MEMORY OF MY FATHER, KASSIMALI B. ALLANA Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.qxp 9/17/07 4:22 PM Page viii 1 2 3 4 5 6 7 8 9 10 11 This page was intentionally left blank 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 S 50 R 51 1st Pass Pages 26201_00_fm_pi-xii.qxd 12/1/10 4:48 PM Page vii CONTENTS 1 INTRODUCTION 1 1.2 Classical, Matrix, and Finite-Element Methods of Structural Analysis 3 1.3 Flexibility and Stiffness Methods 4 1.4 Classification of Framed Structures 5 1.6 Fundamental Relationships for Structural Analysis 12 1.7 Linear versus Nonlinear Analysis 20 1.8 Software 21 Summary 21 2 MATRIX ALGEBRA 23 2.1 Definition of a Matrix 24 2.2 Types of Matrices 25 2.4 Gauss–Jordan Elimination Method 38 Summary 45 Problems 46 3 PLANE TRUSSES 48 3.1 Global and Local Coordinate Systems 49 3.2 Degrees of Freedom 52 3.3 Member Stiffness Relations in the Local Coordinate System 58 3.4 Finite-Element Formulation Using Virtual Work 67 3.6 Member Stiffness Relations in the Global Coordinate System 85 3.7 Structure Stiffness Relations 89 3.8 Procedure for Analysis 105 Summary 122 Problems 123 4 COMPUTER PROGRAM FOR ANALYSIS OF PLANE TRUSSES 128 4.2 Assignment of Structure Coordinate Numbers 140 4.3 Generation of the Structure Stiffness Matrix 143 4.4 Formation of the Joint Load Vector 148 4.5 Solution for Joint Displacements 150 vii Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 26201_00_fm_pi-xii.qxd 12/1/10 4:48 PM Page viii viii Contents 4.6 Calculation of Member Forces and Support Reactions 152 Summary 159 Problems 161 5 BEAMS 162 5.2 Member Stiffness Relations 171 5.3 Finite-Element Formulation Using Virtual Work 185 5.4 Member Fixed-End Forces Due to Loads 191 5.5 Structure Stiffness Relations 197 5.6 Structure Fixed-Joint Forces and Equivalent Joint Loads 206 5.7 Procedure for Analysis 214 5.8 Computer Program 224 Summary 245 Problems 245 6 PLANE FRAMES 249 6.2 Member Stiffness Relations in the Local Coordinate System 256 6.4 Member Stiffness Relations in the Global Coordinate System 276 6.5 Structure Stiffness Relations 284 6.6 Procedure for Analysis 299 6.7 Computer Program 317 Summary 334 Problems 335 7 MEMBER RELEASES AND SECONDARY EFFECTS 340 7.1 Member Releases in Plane Frames and Beams 341 7.2 Computer Implementation of Analysis for Member Releases 361 7.4 Computer Implementation of Support Displacement Effects 385 7.5 Temperature Changes and Fabrication Errors 390 Summary 410 Problems 411 8 THREE-DIMENSIONAL FRAMED STRUCTURES 417 8.3 Space Frames 456 Summary 494 Problems 494 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 26201_00_fm_pi-xii.qxd 12/2/10 7:41 PM Page ix Contents ix 9 SPECIAL TOPICS AND MODELING TECHNIQUES 499 9.1 The Structure Stiffness Matrix Including Restrained Coordinates— An Alternative Formulation of the Stiffness Method 500 9.2 Approximate Matrix Analysis of Rectangular Building Frames 506 9.3 Condensation of Degrees of Freedom, and Substructuring 514 9.4 Inclined Roller Supports 530 9.9 Solution of Large Systems of Stiffness Equations 553 Summary 568 Problems 569 10 INTRODUCTION TO NONLINEAR STRUCTURAL ANALYSIS 572 10.1 Basic Concept of Geometrically Nonlinear Analysis 574 10.2 Geometrically Nonlinear Analysis of Plane Trusses 579 Summary 601 Problems 601 APPENDIX A COMPUTER SOFTWARE 603 APPENDIX B FLEXIBILITY METHOD 605 BIBLIOGRAPHY 612 ANSWERS TO SELECTED PROBLEMS 614 INDEX 629 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.qxp 9/17/07 4:22 PM Page viii 1 2 3 4 5 6 7 8 9 10 11 This page was intentionally left blank 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 S 50 R 51 1st Pass Pages 26201_00_fm_pi-xii.qxd 12/1/10 4:48 PM Page xi PREFACE The objective of this book is to develop an understanding of the basic principles of the matrix methods of structural analysis, so that they can be efficiently im- plemented on modern computers. Focusing on the stiffness approach, Matrix Analysis of Structures covers the linear analysis of two- and three-dimensional framed structures in static equilibrium. It also presents an introduction to nonlin- ear structural analysis and contains the fundamentals of the flexibility approach. The book is divided into ten chapters. Chapter 1 presents a general intro- duction to the subject, and Chapter 2 reviews the basic concepts of matrix alge- bra relevant to matrix structural analysis. The next five chapters (Chapters 3 through 7) cover the analysis of plane trusses, beams, and plane rigid frames. The computer implementation of the stiffness method is initiated early in the text (beginning with Chapter 4), to allow students sufficient time to complete devel- opment of computer programs within the duration of a single course. Chapter 8 presents the analysis of space trusses, grids, and space rigid frames, Chapter 9 covers some special topics and modeling techniques, and Chapter 10 provides an introduction to nonlinear structural analysis. All the relationships necessary for matrix stiffness analysis are formulated using the basic principles of the me- chanics of deformable bodies. Thus, a prior knowledge of the classical methods of structural analysis, while helpful, is not essential for understanding the mater- ial presented in the book. The format of the book is flexible enough to enable in- structors to emphasize topics that are consistent with the goals of the course. Each chapter begins with a brief introduction that defines its objectives, and ends with a summary outlining its salient features.
