Schaum's Outlines Strength of Materials

201 Pages·2011·4.12 MB·English

Strength Of
Materials
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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
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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
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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. For static equilibrium the magnitudes of the forces
must be equal. If the forces are directed away from the bar, the bar is said to be in tension; if they are directed
toward the bar, a state of compression exists. These two conditions are illustrated in Fig. 1-1.
Under the action of this pair of applied forces, internal resisting forces are set up within the bar and their
characteristics may be studied by imagining a plane to be passed through the bar anywhere along its length
and oriented perpendicular to the longitudinal axis of the bar. Such a plane is designated as a-a in Fig. 1-2(a).
If for purposes of analysis the portion of the bar to the right of this plane is considered to be removed, as in
Fig. 1-2(b), then it must be replaced by whatever effect it exerts upon the left portion. By this technique of
introducing a cutting plane, the originally internal forces now become external with respect to the remaining
portion of the body. For equilibrium of the portion to the left this ‘‘effect’’ must be a horizontal force of mag-
nitude P. However, this force P acting normal to the cross section a-a is actually the resultant of distributed
forces acting over this cross section in a direction normal to it.
At this point it is necessary to make some assumption regarding the manner of variation of these distrib-
uted forces, and since the applied force P acts through the centroid it is commonly assumed that they are
uniform across the cross section.
a
P P
a
(a)
P P
(b)
Fig. 1-1 Axially loaded bars. Fig. 1-2 Internal force.
Normal Stress
Instead of speaking of the internal force acting on some small element of area, it is better for comparative
purposes to treat the normal force acting over a unit area of the cross section. The intensity of normal force
1