Strength Of Materials This page intentionally left blank Strength Of Materials Fifth Edition William A. Nash, Ph.D. Former Professor of Civil Engineering University of Massachusetts Merle C. Potter, Ph.D. Professor Emeritus of Mechanical Engineering Michigan State University Schaum’s Outline Series New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2011, 1998, 1994, 1972 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. ISBN: 978-0-07-163507-3 MHID: 0-07-163507-6 The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-163508-0, MHID: 0-07-163508-4. All trademarks are trademarks of their respective owners. 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Preface This fifth edition of Schaum’s Strength of Materials book has been substantially modified by the second author to better fit the outline of the introductory Strength of Materials (Solid Mechanics) course, and to better fit the presentation of material in most introductory textbooks on the subject. In addition, the fol- lowing changes have been made: 1. Problem solutions and Supplementary Problems are presented using the metric SI units only. 2. The computer programs have been omitted. The use of MATLAB or other programs are available to students if more complicated problems are of interest. 3. The more advanced materials and problems that are not found in an introductory course have been omitted for simplicity of presentation. This book is intended to be used in an introductory course only. 4. A short chapter on Fatigue, a subject included on the Fundamentals of Engineering Examination, has been added. It is a modified chapter, based on a section on Fatigue written by my friend and previous colleague, Charlie Muvdi, from “Engineering Mechanics of Materials,” by B. B. Muvdi and J. W. McNabb. 5. A section on Combined Loading has been added. 6. The chapter on Centroids and Moments of Inertia has been omitted; it is assumed to have been part of a Statics course that precedes Solid Mechanics. Strength of Materials, also called The Mechanics of Materials or Solid Mechanics, provides the basis for the design of the components that make up machines and load-bearing structures. In Statics, the forces and moments acting at various points in a structural component or at points of contact with other structures were determined. The forces, stresses, and strains existing within a component were not of interest. In Solid Mechanics, we will consider questions like, “What load will cause this structure to fail?”, “What maximum torque can this shaft transmit?”, “What material should be selected for this component?”, “At what load will this column buckle?” Such questions were not of interest in a Statics course. But, before any of these questions can be answered, we must calculate the forces and moments acting on the components that make up a structure or machine. So, Statics always precedes the study of Strength of Materials. Sometimes Statics is combined with Strength of Materials in one course since they are so closely related. I would like to thank the estate of the late William Nash for allowing me to create this fifth edition of a book that obviously required much diligent work by Professor Nash. Many thanks are also given to Dr. Charlie Muvdi who provided good advice on the content of this revision. It was a pleasure working with Kimberly Eaton of McGraw-Hill in making the many decisions required in such a venture. MERLE C. POTTER, E. LANSING, MI Michigan State University, 2010 v This page intentionally left blank Contents CHAPTER 1 Tension and Compression 1 1.1 Internal Effects of Forces 1.2 Mechanical Properties of Materials 1.3 Statically Indeterminate Force Systems 1.4 Classification of Materials 1.5 Units CHAPTER 2 Shear Stresses 27 2.1 Shear Force and Shear Stress 2.2 Deformations Due to Shear Stresses 2.3 Shear Strain CHAPTER 3 Combined Stresses 35 3.1 Introduction 3.2 General Case of Plane Stress 3.3 Principal Stresses and Maximum Shearing Stress 3.4 Mohr’s Circle CHAPTER 4 Thin-Walled Pressure Vessels 49 4.1 Introduction 4.2 Cylindrical Pressure Vessels 4.3 Spherical Pressure Vessels CHAPTER 5 Torsion 59 5.1 Introduction 5.2 Torsional Shearing Stress 5.3 Shearing Strain 5.4 Combined Torsion and Axial Loading CHAPTER 6 Shearing Force and Bending Moment 73 6.1 Basics 6.2 Internal Forces and Moments in Beams 6.3 Shear and Moment Equations with Diagrams 6.4 Singularity Functions CHAPTER 7 Stresses in Beams 97 7.1 Basics 7.2 Normal Stresses in Beams 7.3 Shearing Stresses in Beams 7.4 Combined Loading CHAPTER 8 Deflection of Beams 123 8.1 Basics 8.2 Differential Equation of the Elastic Curve 8.3 Deflection by Integration 8.4 Deflections Using Singularity Functions 8.5 Deflections Using Superposition vii viii Contents CHAPTER 9 Statically Indeterminate Elastic Beams 143 9.1 Basics CHAPTER 10 Columns 159 10.1 Basics 10.2 Critical Load of a Long Slender Column 10.3 Eccentrically Loaded Columns 10.4 Design Formulas for Columns Having Intermediate Slenderness Ratios CHAPTER 11 Fatigue 175 Index 185 CHAPTER 1 Tension and Compression 1.1 Internal Effects of Forces In this book we shall be concerned with what might be called the internal effects of forces acting on a body. The bodies themselves will no longer be considered to be perfectly rigid as was assumed in statics; instead, the calculation of the deformations of various bodies under a variety of loads will be one of our primary concerns in the study of strength of materials. Axially Loaded Bar The simplest case to consider at the start is that of an initially straight metal bar of constant cross section, loaded at its ends by a pair of oppositely directed collinear forces coinciding with the longitudinal axis of the bar and acting through the centroid of each cross section.