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STRENGTH OF MATERIALS Revised Fourth Edition WILLIAM A NASH Professor of Civil Engineering University of Massachusetts Adapted by NILANJAN MALLIK Assistant Professor Department of Machanical Engineering Institute of Technology, Banaras Hindu University Varanasi Tata McGraw HIii Education Private Limited NEW DELHI McGraw-Hill Offices New Delhl New York St Louis San Francisco Auckland Bogot~ Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal San Juan Santiago Singapore Sydney Tokyo Toronto Copyrighted mate Tata McGraw-Hill Adapted in India by arrangement with The McGraw-Hill Companies, Inc., New York Sales Territories: India, Pakistan, Nepal, Bangladesh, Sri Lanka andl3hutan Schaum's Outline of Strength of Materials, Revised Fourth Edition Fourth reprint 2012 RAXACRZHRAADX Copyright © 2010, 2007, 1998, 1994, 1972, by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission of The McGraw-Hill Companies, Inc. including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning ISBN-13: 978-0-07-070033-8 ISBN-10: 0-07-070033-8 Vice President and Managing Director—McGraw-Hill Education: Asia Pacific Region: Ajay Shukla Head—Higher Education Publishing and Marketing: Vibha Mahajan Manager—Sponsoring SEM & Tech. Ed.: Shalini Jha Associate Sponsoring Editor: Suman Sen Development Editor: Devshree Lohchab Executive—Editorial Services: Sohini Mukherjee Sr Production Manager: P L Pandita Dy Marketing Manager: SEM & Tech. Ed: Btu Ganesan General Manager—Production: Rajender P Ghansela Asst. General Manager— Production: B L Dogra Information contained in this work has been obtained by Tata McGraw-Hill, from sources believed to be reliable. However, neither Tata McGraw-Hill nor its authors guarantee the accuracy or completeness of any information published herein, and neither Tata McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that Tata McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought Published by Tata McGraw Hill Eduiatipn Private Limited, 7 West Patel Nagar, New Delhi 110 008, and printed at Nice Printing Press, Delhill0 051 Cover: A P Offset The McGraw-Hill Companies Tom yp arents, WilliAaN ma sahn Rdo sNea sh, fort heyierao rpfsa tigeunitd taonwcamery cd a ree,� -WillAiN aams h Tom ym other-in-law LatSem tS.u bhRroay choudhuri -NilaMnajlalni k Contents Preface to the Revised Fourth Edition xv Preface xvii 1. CENTROIDS, MOMENTS OF INERTIA, AND PRODUCTS OF INERTIA OF PLANE AREAS 1.1-1.22 1.1 First Moment of an Element of Area 1.1 1.2 First Moment of a Finite Area 1.1 1.3 Centroid of an Area 1.2 1.4 Second Moment or Moment of Inertia of an Element of Area 1.2 1.5 Second Moment or Moment of Inertia of a Finite Area 1.2 1.6 Parallel-Axis Theorem for Moment of Inertia of a Finite Area 1.3 1.7 Radius of Gyration 1.3 1.8 Polar Moment of Inertia 1.4 1.9 Product of Inertia of an Element of Area 1.4 1.10 Product of Inertia of a Finite Area 1.4 1.11 Parallel-Axis Theorem for Product of Inertia of a Finite Area 1.4 1.12 Principal Moments of Inertia 1.5 1.13 Principal Axes 1.5 1.14 Information from Statics 1.5 Solved Problems 1.6 Review Questions 1.18 Supplementary Problems 1.19 Answers to Review Questions 1.22 2. MOMENTS OF INERTIA OF MATERIAL BODIES 2.1-2.6 2.1 Moment of Inertia of a Rigid Body 2.1 2.2 Radius of Gyration 2.1 2.3 Moment of Inertia of a Lamina 2.1 2.4 Moment of Inertia of Three-dimensional Bodies 2.2 2.5 Relation between Radii of Gyration for Parallel Axes 2.2 2.6 Product of Inertia and Principal Axis 2.2 2.7 Change of Direction of Axis of Inertia 2.2 viii Contents Solved Problems 2.2 Review Questions 2.4 Supplementary Problems 2.5 Answers to Review Questions 2.5 3. TENSION AND COMPRESSION 3.1-3.45 3.1 Internal Effects of Forces 3.1 3.2 Mechanical Properties of Materials 3.5 3.3 Dynamic Effects 3.9 3.4 Dynamic and Impact Loads 3.10 3.5 Classification of Materials 3.11 3.6 Elastic Versus Plastic Analysis 3.11 Solved Problems 3.12 Review Questions 3.36 Supplementary Problems 3.38 Answers to Review Questions 3.43 4. STATICALLY INDETERMINATE FORCE SYSTEMS TENSION AND COMPRESSION 4.1-4.28 4.1 Definition of a Determinate Force System 4.1 4.2 Definition of an Indeterminate Force System 4.2 4.3 Force Method of Analysis 4.3 4.4 Method of Elastic Analysis 4.3 4.5 Analysis for Ultimate Strength (Limit Design) 4.3 Solved Problems 4.4 Review Questions 4.22 Supplementary Problems 4.23 Answers to Review Questions 4.28 5. DIRECT SHEAR STRESSES 5.1-5.15 5.1 Definition of Shear Force 5.1 5.2 Definition of Shear Stress 5.1 5.3 Comparison of Shear and Normal Stresses 5.1 5.4 Deformations due to Shear Stresses 5.2 5.5 Shear Strain 5.2 5.6 Modulus of Elasticity in Shear 5.2 5.7 Bolted Joints 5.3 5.8 Welded Joints 5.3 Solved Problems 5.3 Review Questions 5.12 Supplementary Problems 5.13 Answers to Review Questions 5.15 Contents ix 6. TORSION 6.1-6.29 6.1 Definition of Torsion 6.1 6.2 Twisting Moment 6.1 6.3 Polar Moment of Inertia 6.1 6.4 Torsional Shearing Stress 6.2 6.5 Shearing Strain 6.2 6.6 Modulus of Elasticity in Shear 6.2 6.7 Angle of Twist 6.2 6.8 Computer Solution 6.3 6.9 Power Transmission 6.3 6.10 Plastic Torsion of Circular Bars 6.3 6.11 Stress Concentrations in Torsionally Loaded Members 6.3 6.12 Torsion in Non-Circular Sections 6.3 Solved Problems 6.5 Review Questions 6.25 Supplementary Problems 6.26 Answers to Review Questions 6.28 7. BIAXIAL STRESSES, COMBINED STRESSES, AND GENERAL STATE OF STRESSES 7.1-7.46 7.1 Introduction 7.1 7.2 General Case of Two-dimensional Stress 7.1 7.3 Sign Convention 7.1 7.4 Stresses on an Inclined Plane 7.2 7.5 Principal Stresses 7.2 7.6 Directions of Principal Stresses; Principal Planes 7.2 7.7 Computer Implementation 7.2 7.8 Shearing Stresses on Principal Planes 7.3 7.9 Maximum Shearing Stresses 7.3 7.10 Directions of Maximum Shearing Stress 7.3 7.11 Normal Stresses on Planes of Maximum Shearing Stress 7.3 7.12 Mohr's Circle 7.4 Solved Problems 7.5 Review Questions 7.40 Supplementary Problems 7.41 Answers to Review Questions 7.44 8. THIN-WALLED PRESSURE VESSELS 8.1-8.21 8.1 Nature of Stresses 8.1 Solved Problems 8.3 Review Questions 8.19 x Contents Supplementary Problems 8.19 Answers to Review Questions 8.21 9. THICK-WALLED PRESSURE VESSELS 9.1-9.15 9.1 Nature of Stresses 9.1 9.2 Shrink Fitting 9.3 Solved Problems 9.4 Review Questions 9.13 Supplementary Problems 9.14 Answers to Review Questions 9.14 10. SHEARING FORCE AND BENDING MOMENT 10.1-10.33 10.1 Definition of a Beam 10.1 10.2 Types of Loading 10.2 10.3 Effects of Loads 10.3 10.4 Internal Forces and Moments in Beams 10.3 10.5 Shear and Moment Equations 10.5 10.6 Singularity Functions 10.5 10.7 Computer Implementation 10.6 Solved Problems 10.6 Review Questions 10.25 Supplementary Problems 10.25 Answers to Review Questions 10.33 11. ELASTIC DEFLECTION OF BEAMS: DOUBLE-INTEGRATION METHOD 11.1-11.38 11.1 Introduction 11.1 11.2 Definition of Deflection of a Beam 11.1 11.3 Importance of Beam Deflections 11.2 11.4 Methods of Determining Beam Deflections 11.2 Solved Problems 11.4 Review Questions 11.33 Supplementary Problems 11.33 Answers to Review Questions 11.38 12. ELASTIC DEFLECTION OF BEAMS: METHOD OF SINGULARITY FUNCTIONS 12.1-12.28 Solved Problems 12.2 Supplementary Problems 12.26 13. STATICALLY INDETERMINATE ELASTIC BEAMS 13.1-13.21 13.1 Statically Determinate Beams 13.1 13.2 Statically Indeterminate Beams 13.1 Contents xi Solved Problems 13.2 Review Questions 13.17 Supplementary Problems 13.17 Answers to Review Questions 13.21 14. STRESSES IN BEAMS 14.1-14.46 14.1 Types of Loads Acting on Beams 14.1 14.2 Effects of Loads 14.1 14.3 Types of Bending 14.1 14.4 Nature of Beam Action 14.1 14.5 Neutral Surface 14.2 14.6 Neutral Axis 14.2 14.7 Bending Moment 14.2 14.8 Elastic Bending of Beams 14.2 14.9 Plastic Bending of Beams 14.4 Solved Problems 14.5 Review Questions 14.41 Supplementary Problems 14.42 Answers to Review Questions 14.46 15. SPECIAL TOPICS IN ELASTIC BEAM THEORY 15.1-15.32 15.1 Shear Center 15.1 15.2 Shear Flow 15.1 15.3 Unsymmetric Bending 15.1 15.4 Curved Beams 15.2 15.5 Springs 15.2 Solved Problems 15.5 Review Questions 15.30 Supplementary Problems 15.30 Answers to Review Questions 15.32 16. PLASTIC DEFORMATIONS OF BEAMS 16.1-16.18 16.1 Introduction 16.1 16.2 Plastic Hinge 16.1 Solved Problems -16.2 Review Questions 16.15 Supplemetary Problems 16.15 Answers to Review Questions 16.18 17. COLUMNS 17.1-17.38 17.1 Definition of a Column 17.1 17.2 Types of Failure of a Column 17.1