Pré-visualização14 páginas

Instructors and Solutions Manual to accompany Mechanics of Materials Seventh Edition Ferdinand P. Beer Late of Lehigh University E. Russell Johnston, Jr. Late of University of Connecticut John T. DeWolf University of Connecticut David F. Mazurek United States Coast Guard Academy Prepared by Amy Mazurek PROPRIETARY AND CONFIDENTIAL This Manual is the proprietary property of McGraw-Hill Education and protected by copyright and other state and federal laws. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. iii TO THE INSTRUCTOR As indicated in its preface, Mechanics of Materials is designed for the first course in mechanics of materials\u2014or strength of materials\u2014offered to engineering students in the sophomore or junior year. However, because of the large number of optional sections that have been included and the maturity of approach that has been achieved, this text can also be used to teach a more advanced course. The text has been divided into units, each corresponding to a well-defined topic and consisting of one or several theory sections followed by sample problems and a large number of problems to be assigned. In order to accommodate courses of varying emphases, considerably more material has been \u2018included than can be covered effectively in a single three-credit-hour course. To assist the instructors in making up a schedule of assignments that best fits their classes, the various topics presented in the text have been listed in Table I and both a minimum and a maximum number of periods to be spent on each topic have been suggested. Topics have been divided into three categories: core topics that will probably be covered in every course; additional topics that can be selected to complement this core to form courses of various emphases; and finally topics that can be used with more advanced students. The problems have been grouped according to the portions of material they illustrate and have been arranged in order of increasing difficulty, with problems requiring special attention indicated by asterisks. The instructor\u2019s attention is called to the fact that problems have been arranged in groups of six or more, all problems of the same group being closely related. This means that the instructor will easily find additional problems to amplify a particular point that has been brought up in the discussion of a problem assigned for homework. Since half of the problems are stated in SI units and half in U.S. customary units, it also means that the instructor has the choice of assigning problems using SI units and problems using U.S. customary units in whatever proportion is found to be most desirable for a given class. To assist in the preparation of homework assignments Table II provides a brief description of all groups of problems and a classification of the problems in each group according to the units used. It should also be noted that answers to all problems with a number set in roman type are given at the end of the text, while problems with a number set in italic are not. In Table III six alternative lists of possible assignments have been suggested. Four of these lists consist of problems whose answers are given at the end of the text, and two of problems whose answers are not. Half of the problems in each list are stated in SI units and half in U.S. customary units. For those instructors who wish to emphasize the use of SI units, four additional lists of problems have been given in Table IV, in which 75% of the problems use SI units. Since the lists in Tables III and IV cover the entire text, instructors will want to select those groups of sections that are best suited to the course they wish to teach. For a typical one-semester course consisting of 42 class meetings and including four quizzes, as many as 38 of the 46 available groups can be selected. Since the approach used in this text differs in a number of respects from the approach used in other books, the instructor is advised to read the preface to Mechanics of Materials, in which the authors have outlined their general philosophy. Attention is particularly called to the fact that iv statically indeterminate problems are first discussed in Chapter 2 and are considered throughout the text for the various loading conditions encountered. Thus, students are presented at an early stage with a method of solution that combines the analysis of deformations with the conventional analysis of forces used in statics, and will have become thoroughly familiar with it by the end of the course. The concept of plastic deformation is also introduced in Chap. 2, where it is applied to the analysis of members under axial loading, while problems involving the plastic deformation of circular shafts and of prismatic beams are considered in optional sections of Chaps. 3 and 4, respectively. On the other hand, while the concept of stress at a point is introduced in Chap. 1, the discussion of the transformation of stresses is delayed until Chap. 7, after students have discovered for themselves the need for special techniques, such as Mohr\u2019s circle. In this edition, shear and bending-moment diagrams are introduced at the beginning of Chap. 5 and applied immediately to the design of beams in that chapter and in the next. A brief description, chapter by chapter, of the topics included in the text will be found in the following pages. It is hoped that this material will help instructors organize their courses to best fit the needs of their students. The authors of Mechanics of Materials, 7/e, wish to thank Professor Dean P. Updike of the Department of Mechanical Engineering and Mechanics at Lehigh University and Amy Mazurek for having written the problem solutions contained in this Manual. John T. DeWolf David F. Mazurek v DESCRIPTION OF THE MATERIAL CONTAINED IN MECHANICS OF MATERIALS, Seventh Edition Chapter 1 Introduction\u2013Concept of Stress The main purpose of this chapter is to introduce the concept of stress. After a short review of Statics in Section 1.1 emphasizing the use of free-body diagrams, Sections 1.2 through 1.2 discuss normal stresses under an axial loading, shearing stresses\u2014with applications to pins and bolts in single and double shear\u2014and bearing stresses. This section also introduces the student to the concepts of analysis and design. Section 1.2A emphasizes the fact that stresses are inherently statically indeterminate and that, at this point, normal stresses under an axial loading can only be assumed to be uniformly distributed. Moreover, such an assumption requires that the axial loading be centric. Section 1.2D is devoted to the application of these concepts to the analysis of a simple structure. Section 1.2E describes how students should approach the solution of a problem in mechanics of materials using the SMART methodology: Strategy, Modeling, Analysis and Reflect & Think. Section 1.2E also discusses the numerical accuracy to be expected in such a solution. Problems included in the first lesson also serve as a review of the methods of analysis of trusses, frames, and mechanisms learned in statics. Section 1.3 discusses the determination of normal and shearing stresses on oblique planes under an axial loading, while Section 1.4 introduces the components of stress under general loading conditions. This section emphasizes the fact that the components of the shearing stresses exerted on perpendicular planes, such as \u3c4xy and \u3c4yx, must be equal. It also introduces