Mechanics of Materials

873 Pages·2011·30.741 MB·English

by  Roy R. Craig

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SOME USEFUL PHYSICAL PROPERTIES
(USCS UNITS AND SI UNITS)
Property1 USCS SI
Aluminum
specific weight 169 lb(cid:2)ft3 26.6 kN(cid:2)m3
mass density 5.26 slugs(cid:2)ft3 2710 kg(cid:2)m3
Concrete2
specific weight 150 lb(cid:2)ft3 23.6 kN(cid:2)m3
mass density 4.66 slugs(cid:2)ft3 2400 kg(cid:2)m3
Steel
specific weight 490 lb(cid:2)ft3 77.0 kN(cid:2)m3
mass density 15.2 slugs(cid:2)ft3 7850 kg(cid:2)m3
Water (fresh)
specific weight 62.4 lb(cid:2)ft3 9.81 kN(cid:2)m3
mass density 1.94 slugs(cid:2)ft3 1000 kg(cid:2)m3
Acceleration of gravity (g)
(at earth’s surface)
recommended value 32.2 ft(cid:2)sec2 9.81 m(cid:2)sec2
standard international value 32.1740 ft(cid:2)sec2 9.80665 m(cid:2)sec2
Atmospheric pressure
(at sea level)
recommended value 14.7 psi 101 kPa
standard international value 14.6959 psi 101.325 kPa
1Except as noted,the tabulated values are typical,or average,values.
2The specific weight of concrete made of cement,sand,and stone or gravel ranges from 140 to 150 lb(cid:2)ft3.The values tabulated
here are average values for steel-reinforced concrete.The specific weight of concrete made with lightweight aggregate ranges from
90 to 115 lb(cid:2)ft3.
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CONVERSION FACTORS BETWEEN THE SI
AND U.S CUSTOMARY SYSTEMS
Quantity U.S Customary to SI SI to U.S Customary
Acceleration 1 in.(cid:7)s2(cid:2)0.0254 m(cid:7)s2* 1 m(cid:7)s2(cid:2)39.37 in.(cid:7)s2
1 ft(cid:7)s2(cid:2)0.3048 m(cid:7)s2* 1m(cid:7)s2(cid:2)3.281 ft(cid:7)s2
Area 1 in2(cid:2)645.2 mm2 1 mm2(cid:2)1.550(10(cid:3)3) in2
1 ft2(cid:2)0.092 90 m2 1 m2(cid:2)10.76 ft2
Distributed load 1 lb(cid:7)ft (cid:2)14.59 N(cid:7)m 1 kN(cid:7)m (cid:2)68.52 lb(cid:7)ft
Force 1 lb (cid:2)4.448 N 1 N (cid:2)0.2248 lb
Length 1 in (cid:2)25.4 mm* 1 m (cid:2)39.37 in.
1 ft (cid:2)0.3048 m* 1 m (cid:2)3.281 ft
1 mi (cid:2)1.609 km 1 km (cid:2)0.6214 mi
Mass 1 slug (cid:2)14.59 kg 1 kg (cid:2)0.06852 slug
Moment of force;torque 1 1b (cid:4)ft (cid:2)1.356 N (cid:4)m (cid:4) 1 N m (cid:2)0.7376 1b (cid:4)ft
1 1b (cid:4)in.(cid:2)0.1130 N (cid:4)m (cid:4) 1 N m (cid:2)8.851 1b (cid:4)in.
Power 1 lb (cid:4)ft(cid:7)s (cid:2)1.356 W 1 W (cid:2)0.7376 lb (cid:4)ft(cid:7)s
1 hp (cid:2)745.7 W 1 kW (cid:2)1.341 hp
Pressure;stress 1 psi (cid:2)6.895 kPa 1 kPa (cid:2)0.1450 psi
1 ksi (cid:2)6.895 MPa 1 MPa (cid:2)145.0 psi
1 psf (cid:2)47.88 Pa 1 Pa (cid:2)0.02089 psf
Second moment of area 1 in4(cid:2)0.4162(106) mm4 1 m4(cid:2)2.402(10(cid:3)6) in4
Velocity 1 in.(cid:7)s (cid:2)0.0254 m(cid:7)s* 1 m(cid:7)s (cid:2)39.37 in.(cid:7)s
1 ft(cid:7)s (cid:2)0.3048 m(cid:7)s* 1 m(cid:7)s (cid:2)3.281 ft(cid:7)s
1 mi(cid:7)h (cid:2)1.609 km(cid:7)h 1 km(cid:7)h (cid:2)0.6241 mi(cid:7)h
Volume 1 in3(cid:2)16.39(103) mm3 1 mm3(cid:2)61.02(10(cid:3)6) in3
1 ft3(cid:2)0.028 32 m3 1 m3(cid:2)35.31 ft3
Work;energy 1 lb (cid:4)ft (cid:2)1.356 J 1 J (cid:2)0.7376 lb (cid:4)ft
Temperature2 T(°C) (cid:2) 5[T(°F) (cid:3)32] 32(cid:5)F (cid:2)0(cid:5)C (cid:2)273.15K
9
1°C(cid:2) 1K 70°F(cid:2) 21°C(cid:2) 294K
T(K) (cid:2)T((cid:5)C) (cid:6)273.15 212(cid:5)F (cid:2)100(cid:5)C(cid:2) 373K
*Exact value
1After conversion,the resulting value should be rounded off to an accuracy comparable to that of the original number.
2Use of (cid:5)C is permissible in SI.
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Finite Element Analyses s
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1
0
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2
The solid mechanics principles 6/
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and the computational proce- 0

dures presented in this Mechan- 5
:
ics of Materials textbook form 2
3
the basis for the Finite Element P
M
Method,which was used to create

these color photos. Pa
g
e

C
P
-
1
CP-1 V-22 Osprey tilt-rotor air-
craft structure. Shown are the
complete aircraft and a wing-tip
engine-mount section with finite
element grids, and a wing-tip
section that illustrates the use of
color graphics to interpret strain
contours.(MSC/NASTRANfinite
element analysis by Bell Heli-
copter Textron. Reprinted with
the permission of the American
Institute of Aeronautics and
Astronautics.)
color_inserts.qxd 10/26/10 5:23 PM Page CP-2
CP-2 An example of the use of finite element analysis in
support of the design of a mechanical latch member from a
Space Shuttle payload. (MSC/NASTRAN finite element
analysis with SDRC 1-DEAS postprocessing. Courtesy
NASA-Johnson Space Center.)
CP-3 Finite element analysis of the stress concentration due
to a hole in an axially loaded flat bar,as described in Section
12.2.The adjacent color bar indicates that the stress depicted
is the von Mises stress, which is discussed in Section 12.3.
(ABAQUS finite element analysis by Courtesy Greg
Swadener.)
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MECHANICS
OF MATERIALS
Third Edition
ROY R. CRAIG, JR.
with
MDSolids software
by
TIMOTHY A. PHILPOT
JOHN WILEY & SONS
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Library of Congress Cataloging-in-Publication Data:
Craig,Roy R.,Jr.1934-
Mechanics of materials / Roy R.Craig,Jr.-- 3rd ed.
p.cm.
ISBN 978-0-470-48181-3 (hardback)
1. Strength of materials. I.Title.
TA405.C89 2011
620.1'1292--dc22
2010047234
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
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PREFACE
TO THE STUDENT
This textbook is an introduction to the topic of mechanics of materials,an engineer-
ing subject that also goes by the names mechanics of solids,mechanics of deformable
bodies,and strength of materials.You should already have a thorough background
in statics,that is,you should know how to analyze the equilibrium of ‘‘rigid’’ bodies
by constructing free-body diagrams and formulating and solving the appropriate
equilibrium equations. In this course you will learn how to extend equilibrium
analysis to deformable bodies,specifically to various members that make up struc-
tures and machines.This requires not only careful attention to equilibrium require-
ments,but also consideration of the behavior of the material (e.g.,aluminum,steel,
or wood) of which the member is made,and consideration of the geometry of de-
formation. Therefore, you will learn to apply the three fundamental concepts of
solid mechanics:(1)Equilibrium,(2) Force-Temperature—Deformation Behavior of
Materials, and(3)Geometry of Deformation.
You will learn a number of important new topics, such as: how the external
forces that are applied to a body are distributed throughout the body,and whether
the body will fail under the action of the applied forces (the topic of stress);how the
body will deform under the action of the applied external forces and temperature
changes (the topic of strain); what material properties affect the way that the
body responds to the applied forces and temperature changes (the topic of stress-
strain-temperature behavior of materials);and other important solid-mechanics topics.
With the aid of this textbook you will learn systematic problem-solving methods,
including ways to assess the probable accuracy of your homework solutions.You
will enjoy using the computer program MDSolids that is available for use with this
textbook. Its intuitive graphical interface will help you develop problem-solving
skills by showing you the important factors affecting various problem types,by help-
ing you visualize the nature of internal stresses and member deformations,and by
providing you an easy-to-use means of investigating a greater number of problems
and variations.Nevertheless,the emphasis in this textbook remains on your devel-
oping an understanding of the fundamentals of elementary solid mechanics,not on
writing computer programs or on using an existing computer program just to get
immediate answers.
Please take time now to look at the color photographs that are included as a
color-photo insert in Chapter 1.They illustrate how the Finite Element Method,a
direct extension of this introduction to solid mechanics,is used to design and ana-
lyze everything from airplanes to cars, from skyscrapers and bridges to bicycle
frames and tennis racquets,from offshore oil rigs to computer chips.The goal of this
iii
FMTOC.qxd 12/13/10 9:02 AM Page iv
iv book is to prepare you to study further courses in solids and structures that will en-
able you to carry out such complex analyses,opening the door to the exciting world
Preface of Computer-Aided Engineering, whether your application is to aerospace engi-
neering,architectural engineering,civil engineering,mechanical engineering,petro-
leum engineering,or even to electrical engineering.
SPECIAL FEATURES
The philosophy guiding the development of this introductory solid-mechanics text-
book has been that students learn engineering topics best:(1) when they are made
aware of the fundamental concepts involved in the subject,(2) when they are taught
systematic problem-solving procedures and are provided many example problems
that are solved in a systematic manner and are complete,(3) when they have ample
opportunity for drill and practice in solving problems and obtaining feedback,and
(4) when they are given real engineering examples and shown the relevance of what
they are studying.To implement this philosophy,the following features have been
incorporated in this textbook.
• A Strong Emphasis on the Three Basic Concepts of Deformable-Body
Mechanics.Throughout this book students are reminded that solid mechan-
ics problems involve three fundamental concepts: Equilibrium, Material
Behavior, and Geometry of Deformation. In the Example Problems, the
equations that correspond to each of these three concepts are highlighted
and identified by name,so that the student should thoroughly understand the
important role played by each one of these three fundamental concepts.
• A Four-Step Problem-Solving Procedure. The following four steps are in-
cluded in the solution of most of the Example Problems in this book.
• State the Problem
• Plan the Solution
• Solve the Problem
• Review the Solution
Once an engineering student leaves the university environment and be-
comes a practicing engineer,with powerful computer programs to carry out
the detailed solution of complex problems,the importance of being able to
Plan the Solution and Review the Solution for probable accuracy will be-
come readily apparent.
• Example Problems;Systematic Problem-Solving Procedures.In this textbook,
over 140 Example Problems provide the student with detailed illustrations of
systematic procedures for solving solid-mechanics problems. In addition,
as part of the accompanying MDSolids software,there are an additional
90 Example Problems, with complete solutions provided in the same nota-
tion and style as the solutions in the textbook itself.
As noted above,the distinct contribution of each of the three fundamental
concepts—Equilibrium,Material Behavior,and Geometry of Deformation—is
highlighted and identified by name. Once the basic equations have been
written down, solutions are completed by combining these equations to
obtain the final answer(s).Procedure listsindicate convenient and system-
atic procedures for solving problems, and flow charts summarize these
procedures graphically. These problem-solving procedures, labeled the
Basic Force Method,the Displacement Method,and the Force Method, are
first presented in Chapter 3.
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Sign conventions for forces,displacements,etc.are established and are v
consistently followed, and wherever equilibrium equations are required, a
complete free-body diagram is drawn. Because equilibrium analysis plays Preface
such a central role in mechanics of solids,a special section in Chapter 1 is de-
voted to reviewing statics of rigid bodies and to introducing the concept of
internal resultants for deformable bodies.
• Computer Exercises and Computer Software.Thirty computer exercises are
included as homework problems;these are identified by a C-superscripted
problem number. Students are presented the opportunity to develop their
own computer programs,and the award-winning MDSolidssoftware is avail-
able via download for use on PCs running the Windows operating system.1
Appendix G describes the software that accompanies this textbook. To
download the software,you must register on the Wiley Student Companion
Site for this book at www.wiley.com/college/craig.For details,see the regis-
tration card provided in the book.
• Design.There is a multifaceted treatment of the topic of design.For exam-
ple,Section 2.8 discusses the philosophy of design,introduces the student to
straightforward allowable-stress design,and closes with an example of opti-
mum (minimum-weight) design of a simple statically determinate truss.The
final chapter,Chapter 12,discusses three special design-related topics:stress
concentrations,failure theories,and fatigue and fracture.Throughout the text
and among the special MDSolids Example Problems there are design-related
examples. Homework problems with design content are identified by a
D-superscripted problem number.
• Accuracy.Special efforts have been made to provide as error-free a book as
possible.At least two independent solutions have been obtained for every
homework problem,and the Solutions Manual was prepared directly by the
author in order to insure consistency and accuracy.
• Communication with the Authors. Comments regarding the book or the
Solutions Manual may be addressed to the author at the following e-mail ad-
dress:[email protected] address your comments or inquiries
regarding MDSolids by e-mail to Dr.Timothy Philpot:[email protected].
NEW IN THIS EDITION
This third edition of Mechanicsof Materials retainsthe hallmark features of the first
two editions—a strong emphasis on the three fundamental types of equations of solid
mechanics and on systematic procedures for solving problems.Listed below are the
new features of the Third Edition,followed by the major modifications that have
been incorporated into this edition
• From the student’s standpoint,the most significant new feature is the addi-
tion of a Chapter Review table at the end of each chapter.These Chapter
Reviews summarize the key points of the chapter,and they include the major
equations and figures from the chapter.In addition,students will find a list
of problems that will be useful to them in reviewing the chapter and prepar-
ing for examinations.
1The MDSolids software suite,developed by Dr.Timothy A.Philpot,was awarded the 1998 Premier
Award for Excellence in Engineering Education Courseware.