net http://www.net LIBROS UNIVERISTARIOS Y SOLUCIONARIOS DE MUCHOS DE ESTOS LIBROS LOS SOLUCIONARIOS CONTIENEN TODOS LOS EJERCICIOS DEL LIBRO RESUELTOS Y EXPLICADOS DE FORMA CLARA VISITANOS PARA DESARGALOS GRATIS.net P1: TIX/XYZ P2: ABC JWST071-FM JWST071-Waas July 4, 2011 11:3 Printer Name: Yet to Come ANALYSIS OF STRUCTURES www.net P1: TIX/XYZ P2: ABC JWST071-FM JWST071-Waas July 4, 2011 11:3 Printer Name: Yet to Come ANALYSIS OF STRUCTURES AN INTRODUCTION INCLUDING NUMERICAL METHODS Joe G. Waas College of Engineering University of Michigan, USA A John Wiley & Sons, Ltd.net P1: TIX/XYZ P2: ABC JWST071-FM JWST071-Waas July 4, 2011 11:3 Printer Name: Yet to Come This edition first published 2011 C 2011 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. 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, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloging-in-Publication Data Eisley, Joe G. Analysis of structures : an introduction including numerical methods / Joe G. Includes bibliographical references and index. Structural analysis (Engineering)–Mathematics.1 71–dc22 2011009723 A catalogue record for this book is available from the British Library. Print ISBN: 9780470977620 E-PDF ISBN: 9781119993285 O-book ISBN: 9781119993278 E-Pub ISBN: 9781119993544 Mobi ISBN: 9781119993551 Typeset in 9/11pt Times by Aptara Inc., New Delhi, India www.net P1: TIX/XYZ P2: ABC JWST071-FM JWST071-Waas July 4, 2011 11:3 Printer Name: Yet to Come We would like to dedicate this book to our families. To Marilyn, Paul and Susan —Joe To Dayamal, Dayani, Shehara and Michael —Tony www.net P1: TIX/XYZ P2: ABC JWST071-FM JWST071-Waas July 4, 2011 11:3 Printer Name: Yet to Come Contents About the Authors xiii Preface xv 1 Forces and Moments 1 1.3 Forces in Mechanics of Materials 3 1.5 Moment of a Concentrated Force 9 1.6 Distributed Forces—Force and Moment Resultants 19 1.7 Internal Forces and Stresses—Stress Resultants 27 1.8 Restraint Forces and Restraint Force Resultants 32 1.9 Summary and Conclusions 33 2 Static Equilibrium 35 2.2 Free Body Diagrams 35 2.3 Equilibrium—Concentrated Forces 38 2.1 Two Force Members and Pin Jointed Trusses 38 2.2 Slender Rigid Bars 44 2.3 Pulleys and Cables 49 2.4 Equilibrium—Distributed Forces 55 2.5 Equilibrium in Three Dimensions 59 2.6 Equilibrium—Internal Forces and Stresses 62 2.1 Equilibrium of Internal Forces in Three Dimensions 65 2.2 Equilibrium in Two Dimensions—Plane Stress 69 2.3 Equilibrium in One Dimension—Uniaxial Stress 70 2.7 Summary and Conclusions 70 3 Displacement, Strain, and Material Properties 71 3.2 Displacement and Strain 71 3.net P1: TIX/XYZ P2: ABC JWST071-FM JWST071-Waas July 4, 2011 11:3 Printer Name: Yet to Come viii Contents 3.4 Linear Material Properties 77 3.1 Hooke’s Law in One Dimension—Tension 77 3.3 Hooke’s Law in One Dimension—Shear in Isotropic Materials 82 3.4 Hooke’s Law in Two Dimensions for Isotropic Materials 83 3.5 Generalized Hooke’s Law for Isotropic Materials 84 3.5 Some Simple Solutions for Stress, Strain, and Displacement 85 3.8 Fiber Reinforced Composite Laminates 90 3.1 Hooke’s Law in Two Dimensions for a FRP Lamina 91 3.2 Properties of Unidirectional Lamina 94 3.9 Plan for the Following Chapters 96 3.10 Summary and Conclusions 98 4 Classical Analysis of the Axially Loaded Slender Bar 99 4.2 Solutions from the Theory of Elasticity 99 4.3 Derivation and Solution of the Governing Equations 109 4.4 The Statically Determinate Case 116 4.5 The Statically Indeterminate Case 129 4.6 Variable Cross Sections 136 4.7 Thermal Stress and Strain in an Axially Loaded Bar 142 4.8 Shearing Stress in an Axially Loaded Bar 143 4.9 Design of Axially Loaded Bars 145 4.10 Analysis and Design of Pin Jointed Trusses 149 4.11 Work and Energy—Castigliano’s Second Theorem 153 4.12 Summary and Conclusions 162 5 A General Method for the Axially Loaded Slender Bar 165 5.2 Nodes, Elements, Shape Functions, and the Element Stiffness Matrix 165 5.3 The Assembled Global Equations and Their Solution 169 5.4 A General Method—Distributed Applied Loads 182 5.5 Variable Cross Sections 196 5.6 Analysis and Design of Pin-jointed Trusses 202 5.7 Summary and Conclusions 211 6 Torsion 213 6.2 Torsional Displacement, Strain, and Stress 213 6.3 Derivation and Solution of the Governing Equations 216 6.4 Solutions from the Theory of Elasticity 225 6.5 Torsional Stress in Thin Walled Cross Sections 229 6.6 Work and Energy—Torsional Stiffness in a Thin Walled Tube 231 6.7 Torsional Stress and Stiffness in Multicell Sections 239 6.8 Torsional Stress and Displacement in Thin Walled Open Sections 242 www.net P1: TIX/XYZ P2: ABC JWST071-FM JWST071-Waas July 4, 2011 11:3 Printer Name: Yet to Come Contents ix 6.10 Continuously Variable Cross Sections 254 6.11 Summary and Conclusions 255 7 Classical Analysis of the Bending of Beams 257 7.2 Area Properties—Sign Conventions 257 7.3 Derivation and Solution of the Governing Equations 260 7.4 The Statically Determinate Case 271 7.5 Work and Energy—Castigliano’s Second Theorem 278 7.6 The Statically Indeterminate Case 281 7.7 Solutions from the Theory of Elasticity 290 7.8 Variable Cross Sections 300 7.9 Shear Stress in Non Rectangular Cross Sections—Thin Walled Cross Sections 302 7.10 Design of Beams 309 7.12 Summary and Conclusions 314 8 A General Method (FEM) for the Bending of Beams 315 8.2 Nodes, Elements, Shape Functions, and the Element Stiffness Matrix 315 8.3 The Global Equations and their Solution 320 8.4 Distributed Loads in FEM 327 8.5 Variable Cross Sections 341 8.6 Summary and Conclusions 345 9 More about Stress and Strain, and Material Properties 347 9.2 Transformation of Stress in Two Dimensions 347 9.3 Principal Axes and Principal Stresses in Two Dimensions 350 9.4 Transformation of Strain in Two Dimensions 354 9.6 Stress Transformation and Principal Stresses in Three Dimensions 358 9.7 Allowable and Ultimate Stress, and Factors of Safety 361 9.10 Orthotropic Materials—Composites 365 9.11 Summary and Conclusions 366 10 Combined Loadings on Slender Bars—Thin Walled Cross Sections 367 10.2 Review and Summary of Slender Bar Equations 367 10.3 Bending in One Plane 370 10.3 Axial and Torsional Loads 372 10.4 Axial and Bending Loads—2D Frames 375 www.net P1: TIX/XYZ P2: ABC JWST071-FM JWST071-Waas July 4, 2011 11:3 Printer Name: Yet to Come x Contents 10.5 Bending in Two Planes 384 10.1 When Iyz is Equal to Zero 384 10.2 When Iyz is Not Equal to Zero 386 10.6 Bending and Torsion in Thin Walled Open Sections—Shear Center 393 10.7 Bending and Torsion in Thin Walled Closed Sections—Shear Center 399 10.8 Stiffened Thin Walled Beams 405 10.9 Summary and Conclusions 416 11 Work and Energy Methods—Virtual Work 417 11.2 Introduction to the Principle of Virtual Work 417 11.3 Static Analysis of Slender Bars by Virtual Work 421 11.3 Beams in Bending 427 11.4 Combined Axial, Torsional, and Bending Behavior 430 11.4 Static Analysis of 3D and 2D Solids by Virtual Work 430 11.5 The Element Stiffness Matrix for Plane Stress 433 11.6 The Element Stiffness Matrix for 3D Solids 436 11.7 Summary and Conclusions 437 12 Structural Analysis in Two and Three Dimensions 439 12.2 The Governing Equations in Two Dimensions—Plane Stress 440 12.3 Finite Elements and the Stiffness Matrix for Plane Stress 445 12.4 Thin Flat Plates—Classical Analysis 452 12.5 Thin Flat Plates—FEM Analysis 455 12.7 Stiffened Shell Structures 466 12.8 Three Dimensional Structures—Classical and FEM Analysis 470 12.9 Summary and Conclusions 477 13 Analysis of Thin Laminated Composite Material Structures 479 13.1 Introduction to Classical Lamination Theory 479 13.2 Strain Displacement Equations for Laminates 480 13.3 Stress-Strain Relations for a Single Lamina 482 13.4 Stress Resultants for Laminates 486 13.5 CLT Constitutive Description 489 13.6 Determining Laminae Stress/Strains 492 13.7 Laminated Plates Subject to Transverse Loads 493 13.8 Summary and Conclusion 498 14 Buckling 499 14.2 The Equations for a Beam with Combined Lateral and Axial Loading 499 14.3 Buckling of a Column 504 14.4 The Beam Column 512 14.5 The Finite Element Method for Bending and Buckling 515 14.6 Buckling of Frames 524 www.net P1: TIX/XYZ P2: ABC JWST071-FM JWST071-Waas July 4, 2011 11:3 Printer Name: Yet to Come Contents xi 14.7 Buckling of Thin Plates and Other Structures 524 14.8 Summary and Conclusions 527 15 Structural Dynamics 529 15.2 Dynamics of Mass/Spring Systems 529 15.2 Forced Motion—Resonance 540 15.3 Forced Motion—Response 547 15.3 Axial Vibration of a Slender Bar 548 15.1 Solutions Based on the Differential Equation 548 15.2 Solutions Based on FEM 560 15.1 Torsional Mass/Spring Systems 567 15.2 Distributed Torsional Systems 568 15.5 Vibration of Beams in Bending 569 15.1 Solutions of the Differential Equation 569 15.2 Solutions Based on FEM 574 15.6 The Finite Element Method for all Elastic Structures 577 15.7 Addition of Damping 577 15.8 Summary and Conclusions 582 16 Evolution in the (Intelligent) Design and Analysis of Structural Members 583 16.2 Evolution of a Truss Member 584 16. Slender Bar Analysis 584 16. Rectangular Bar—Plane Stress FEM 585 16. Rectangular Bar with Pin Holes—Plane Stress Analysis 586 16. Rectangular Bar with Pin Holes—Solid Body Analysis 587 16. Add Material Around the Hole—Solid Element Analysis 588 16. Bosses Added—Solid Element Analysis 590 16. Reducing the Weight—Solid Element Analysis 591 16.3 Evolution of a Plate with a Hole—Plane Stress 592 16.4 Materials in Design 594 16.5 Summary and Conclusions 594 A Matrix Definitions and Operations 595 A.5 Differentiating and Integrating a Matrix 598 A.6 Summary of Useful Matrix Relations 599 B Area Properties of Cross Sections 601 B.2 Centroids of Cross Sections 601 B.3 Area Moments and Product of Inertia 603 B.4 Properties of Common Cross Sections 609 www.net P1: TIX/XYZ P2: ABC JWST071-FM JWST071-Waas July 4, 2011 11:3 Printer Name: Yet to Come xii Contents C Solving Sets of Linear Algebraic Equations with Mathematica 611 C.2 Systems of Linear Algebraic Equations 611 C.3 Solving Numerical Equations in Mathematica 611 C.4 Solving Symbolic Equations in Mathematica 612 C.5 Matrix Multiplication 613 D Orthogonality of Normal Modes 615 D.2 Proof of Orthogonality for Discrete Systems 615 D.3 Proof of Orthogonality for Continuous Systems 616 References 617 Index 619 www.net P1: TIX/XYZ P2: ABC JWST071-babout JWST071-Waas July 6, 2011 9:48 Printer Name: Yet to Come About the Authors Joe G. Eisley received degrees from St. Louis University, BS (1951), and the California Institute of Technology, MS (1952), PhD (1956), all in the field of aeronautical engineering. He served on the faculty of the Department of Aerospace Engineering from 1956 to 1998 and retired as Emeritus Professor of Aerospace Engineering in 1998. His primary field of teaching and research has been in structural analysis with an emphasis on the dynamics of structures. He also taught courses in space systems design and computer aided design. After retirement he has continued some part time work in teaching and consulting. Waas is the Felix Pawlowski Collegiate Professor of Aerospace Engineering and Professor of Mechanical Engineering, and Director, Composite Structures Laboratory at the University of Michigan.
