Ferdinand P. Beer (Deceased),
Lehigh University E. Russell Johnston, Jr.,
University of Connecticut John T. DeWolf,
University of Connecticut
ISBN: 0072980907 Copyright year: 2006
Book Preface
OBJECTIVES
The main objective of a basic mechanics course should be to develop in
the engineering student the ability to analyze a given problem in a simple
and logical manner and to apply to its solution a few fundamental and
well-understood principles. This text is designed for the first course in mechanics
of materials—or strength of materials—offered to engineering students
in the sophomore or junior year. The authors hope that it will help
instructors achieve this goal in that particular course in the same way that
their other texts may have helped them in statics and dynamics.
GENERAL APPROACH
In this text the study of the mechanics of materials is based on the
understanding of a few basic concepts and on the use of simplified
models. This approach makes it possible to develop all the necessary
formulas in a rational and logical manner, and to clearly indicate the
conditions under which they can be safely applied to the analysis and
design of actual engineering structures and machine components.
Free-body Diagrams Are Used Extensively. Throughout the
text free-body diagrams are used to determine external or internal forces.
The use of “picture equations” will also help the students understand the
superposition of loadings and the resulting stresses and deformations.
Design Concepts Are Discussed Throughout the Text Whenever
Appropriate. A discussion of the application of the factor of safety
to design can be found in Chap. 1, where the concepts of both allowable
stress design and load and resistance factor design are presented.
A Careful Balance Between SI and U.S. Customary Units Is
Consistently Maintained. Because it is essential that students be
able to handle effectively both SI metric units and U.S. customary units,
half the examples, sample problems, and problems to be assigned have
been stated in SI units and half in U.S. customary units. Since a large
number of problems are available, instructors can assign problems using
each system of units in whatever proportion they find most desirable for their class.
Optional Sections Offer Advanced or Specialty Topics. Topics
such as residual stresses, torsion of noncircular and thin-walled
members, bending of curved beams, shearing stresses in non-symmetrical
members, and failure criteria, have been included in optional sections for
use in courses of varying emphases. To preserve the integrity of the subject,
these topics are presented in the proper sequence, wherever they logically
belong. Thus, even when not covered in the course, they are highly
visible and can be easily referred to by the students if needed in a later
course or in engineering practice. For convenience all optional sections
have been indicated by asterisks.
CHAPTER ORGANIZATION
It is expected that students using this text will have completed a
course in statics. However, Chap. 1 is designed to provide them with
an opportunity to review the concepts learned in that course, while
shear and bending-moment diagrams are covered in detail in Secs. 5.2
and 5.3. The properties of moments and centroids of areas are
described in Appendix A; this material can be used to reinforce the
discussion of the determination of normal and shearing stresses in
beams (Chaps. 4, 5, and 6).
The first four chapters of the text are devoted to the analysis of
the stresses and of the corresponding deformations in various structural
members, considering successively axial loading, torsion, and
pure bending. Each analysis is based on a few basic concepts,
namely, the conditions of equilibrium of the forces exerted on the
member, the relations existing between stress and strain in the material,
and the conditions imposed by the supports and loading of
the member. The study of each type of loading is complemented by
a large number of examples, sample problems, and problems to be
assigned, all designed to strengthen the students’ understanding of
the subject.
The concept of stress at a point is introduced in Chap. 1, where
it is shown that an axial load can produce shearing stresses as well
as normal stresses, depending upon the section considered. The fact
that stresses depend upon the orientation of the surface on which
they are computed is emphasized again in Chaps. 3 and 4 in the
cases of torsion and pure bending. However, the discussion of computational
techniques—such as Mohr’s circle—used for the transformation
of stress at a point is delayed until Chap. 7, after students
have had the opportunity to solve problems involving a combination
of the basic loadings and have discovered for themselves the need
for such techniques.
The discussion in Chap. 2 of the relation between stress and strain
in various materials includes fiber-reinforced composite materials.
Also, the study of beams under transverse loads is covered in two separate chapters. Chapter 5 is devoted to the determination of the
normal stresses in a beam and to the design of beams based on the
allowable normal stress in the material used (Sec. 5.4). The chapter
begins with a discussion of the shear and bending-moment diagrams
(Secs. 5.2 and 5.3) and includes an optional section on the use of singularity
functions for the determination of the shear and bending moment
in a beam (Sec. 5.5). The chapter ends with an optional section
on nonprismatic beams (Sec. 5.6).
Chapter 6 is devoted to the determination of shearing stresses in
beams and thin-walled members under transverse loadings. The formula
for the shear flow, q = VQ/I, is derived in the traditional way.
More advanced aspects of the design of beams, such as the determination
of the principal stresses at the junction of the flange and web
of a W-beam, have been moved to Chap. 8, an optional chapter that
may be covered after the transformations of stresses have been discussed
in Chap. 7. The design of transmission shafts has been moved
to that chapter for the same reason, as well as the determination of
stresses under combined loadings that can now include the determination
of the principal stresses, principal planes, and maximum shearing
stress at a given point.
Statically indeterminate problems are first discussed in Chap. 2 and
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. In this way, they will have become thoroughly
familiar with this fundamental method by the end of the course.
In addition, this approach helps the students realize that stresses themselves
are statically indeterminate and can be computed only by considering
the corresponding distribution of strains.
The concept of plastic deformation is introduced in Chap. 2, where
it is applied to the analysis of members under axial loading. Problems
involving the plastic deformation of circular shafts and of prismatic
beams are also considered in optional sections of Chaps. 3, 4, and 6.
While some of this material can be omitted at the choice of the instructor,
its inclusion in the body of the text will help students realize
the limitations of the assumption of a linear stress-strain relation and
serve to caution them against the inappropriate use of the elastic torsion
and flexure formulas.
The determination of the deflection of beams is discussed in Chap. 9.
The first part of the chapter is devoted to the integration method and to
the method of superposition, with an optional section (Sec. 9.6) based
on the use of singularity functions. (This section should be used only
if Sec. 5.5 was covered earlier.) The second part of Chap. 9 is optional.
It presents the moment-area method in two lessons instead off three as
in our previous edition.
Chapter 10 is devoted to columns and contains new material on the
design of wood columns. Chapter 11 covers energy methods, including
Castigliano’s theorem.
PEDAGOGICAL FEATURES
Each chapter begins with an introductory section setting the purpose
and goals of the chapter and describing in simple terms the material to
be covered and its application to the solution of engineering problems.
Chapter Lessons. The body of the text has been divided into
units, each consisting of one or several theory sections followed by sample
problems and a large number of problems to be assigned. Each unit
corresponds to a well-defined topic and generally can be covered in one
lesson.
Examples and Sample Problems. The theory sections include
many examples designed to illustrate the material being presented and
facilitate its understanding. The sample problems are intended to show
some of the applications of the theory to the solution of engineering problems.
Since they have been set up in much the same form that students
will use in solving the assigned problems, the sample problems serve the
double purpose of amplifying the text and demonstrating the type of neat
and orderly work that students should cultivate in their own solutions.
Homework Problem Sets. Most of the problems are of a practical
nature and should appeal to engineering students. They are primarily
designed, however, to illustrate the material presented in the
text and help the students understand the basic principles used in
mechanics of materials. The problems have been grouped according to
the portions of material they illustrate and have been arranged in order
of increasing difficulty. Problems requiring special attention have been
indicated by asterisks. Answers to problems are given at the end of the
book, except for those with a number set in italics.
Chapter Review and Summary. Each chapter ends with a review
and summary of the material covered in the chapter. Notes in the margin
have been included to help the students organize their review work,
and cross references provided to help them find the portions of material
requiring their special attention.
Review Problems. A set of review problems is included at the
end of each chapter. These problems provide students further opportunity
to apply the most important concepts introduced in the chapter.
Computer Problems. The availability of personal computers
makes it possible for engineering students to solve a great number of
challenging problems. In this new edition of Mechanics of Materials, a
group of six or more problems designed to be solved with a computer
can be found at the end of each chapter. Developing the algorithm
required to solve a given problem will benefit the students in two different
ways: (1) it will help them gain a better understanding of the
mechanics principles involved; (2) it will provide them with an opportunity
to apply the skills acquired in their computer programming course
to the solution of a meaningful engineering problem.
Fundamentals of Engineering Examination. Engineers who
seek to be licensed as Professional Engineers must take two exams.
The first exam, the Fundamentals of Engineering Examination, includes
subject material from Mechanics of Materials. Appendix E lists
the topics in Mechanics of Materials that are covered in this exam along
with problems that can be solved to review this material.
ACKNOWLEDGMENTS
The authors thank the many companies that provided photographs for
this edition. We also wish to recognize the determined efforts and
patience of our photo researcher Sabina Dowell.
Our special thanks go to Professor Dean Updike, of the Department
of Mechanical Engineering and Mechanics, Lehigh University, for his
patience and cooperation as he checked the solutions and answers of
all the problems in this edition.
We also gratefully acknowledge the help comments and suggestions
offered by the many users of previous editions of Mechanics of
Materials.E. Russell Johnston, Jr.
John T. DeWolf
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