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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 
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. 
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 
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 
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 
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