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Instructor’s Solutions Manual
MECHANICS
OF MATERIALS
EIGHTH EDITION
R. C. HIBBELER
Prentice Hall
Boston Columbus Indianapolis New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto
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FM_TOC 46060
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Page ii
Vice President and Editorial Director, ECS: Marcia Horton
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Media Director: Daniel Sandin
Copyright © 2011, 2008, 2005, 2003, 2001 by R. C. Hibbeler. Published by Pearson Prentice Hall. All rights reserved.
Manufactured in the United States of America. This publication is protected by Copyright, and permission should be
obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any
form or by any means, electronic, mechanical, photocopying, recording, or likewise. To obtain permission(s) to use
material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, 1 Lake
Street, Upper Saddle River, NJ 07458.
Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks. Where
those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been
printed in initial caps or all caps.
10 9 8 7 6 5 4 3 2 1
ISBN 10: 0-13-602312-6
ISBN 13: 978-0-13-602312-8
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CONTENTS
To the Instructor
iv
1 Stress
1
2 Strain
73
3 Mechanical Properties of Materials
92
4 Axial Load
122
5 Torsion
214
6 Bending
329
7 Transverse Shear
472
8 Combined Loadings
532
9 Stress Transformation
619
10 Strain Transformation
738
11 Design of Beams and Shafts
830
12 Deflection of Beams and Shafts
883
13 Buckling of Columns
1038
14 Energy Methods
1159
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To the Instructor
This manual contains the solutions to all the problems in Mechanics of Materials, Eighth Edition. As stated
in the preface of the text, the problems in every section are arranged in an approximate order of increasing
difficulty. Be aware that answers to all but every fourth problem, which is indicated by an asterisk (*), are
listed in the back of the book. Also, every fourth problem has an additional hint for the solution and is
indicated with a bullet (•). Finally, those problems indicated by a square (■) will require additional
numerical work.
You may wish to use one of the lists of homework problems given on the following pages. Here you will find
three lists for which the answers are in the back of the book, a fourth list for problems without answers, and a
fifth sheet which can be used to develop your own personal syllabus. The prepared lists generally represent
assignments with an easy, a moderate, and sometimes a more challenging problem.
If you have any questions regarding the solutions in this manual, I would greatly appreciate hearing from
you.
R. C. Hibbeler
[email protected]
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Page v
ANSWER ASSIGNMENT
Section
Title
Assignment 1 with Hints
1.1–1.2
1.3–1.5
1.6–1.7
2.1–2.2
3.1–3.5
3.6–3.8
4.1–4.2
4.3–4.5
4.6
4.7
4.8–4.9
5.1–5.3
5.4
5.5
5.6
5.7
5.8
5.9–5.10
6.1–6.2
6.3–6.4
6.5
6.6–6.7
6.8
6.9
6.10–6.11
7.1–7.3
7.4
7.5–7.6
8.1
8.2
9.1–9.2
9.3
9.4–9.6
9.7
10.1–10.2
10.3
10.4–10.5
10.6
10.7
11.1–11.2
11.3
11.4
12.1–12.2
12.3
12.4
12.5
12.6–12.7
12.8
12.10
13.1–13.3
13.4–13.5
13.6
13.7
14.1–14.2
14.3
14.4
14.5–14.6
14.7
14.8
14.9
Equilibrium of a Deformable Body
Average Normal and Shear Stress
Design of Simple Connections
Strain
The Stress Strain Diagram
Poisson’s ratio, Shear Stress-Strain Diagram
Deformation of an Axially Loaded Member
Statically Indeterminate Member
Thermal Stresses
Stress Concentrations
Inelastic Deformation and Residual Stresses
Torsion Stress and Power
Angle of Twist
Statically Indeterminate Members
Noncircular Shafts
Thin-Walled Tubes
Stress Concentrations
Inelastic Torsion and Residual Stresses
Shear and Moment Diagrams
Bending Stress
Unsymmetric Bending
Composite Beams
Curved Beams
Stress Concentrations
Inelastic Bending
Shear Stress
Shear Flow in Built-up Members
Shear Center
Thin-Walled Pressure Vessels
Stress Due to Combined Loadings
Stress Transformation
Princ. Stress and Max. In-Plane Shear Stress
Mohr’s Circle
Absolute Maximum Shear Stress
Strain Transformation
Mohr’s Circle
Abs. Maximum Shear Strain, Strain Rosettes
Material Property Relations
Theories of Failure
Prismatic Beam Design
Fully Stressed Beams
Shaft Design
Slope and Displacement by Integration
Discontinuity Functions
Moment-Area Theorems
Method of Superposition
Indet. Beams-Method of Integration
Indet. Beams-Mom. Area Theorems
Indet. Beams-Method of Superposition
Buckling of an Ideal Column
The Secant Formula, Inelastic Buckling
Design of Columns for Concentric Loading
Design of Columns for Eccentric Loading
Elastic Strain Energy
Conservation of Energy
Impact
Principle of Virtual Forces-Trusses
Principle of Virtual Forces-Beams
Castigliano’s Theorem-Trusses
Castigliano’s Theorem-Beams
1–5, 1–9, 1–21
1–37, 1–45, 1–53, 1–61
1–73, 1–81, 1–85, 1–97
2–5, 2–13, 2–21
3–5, 3–9, 3–17
3–25, 3–29, 3–33
4–5, 4–13, 4–17, 4–21
4–33, 4–41, 4–49, 4–61
4–69, 4–73, 4–77
4–89, 4–93
4–101, 4–105, 4–113
5–5, 5–13, 5–25, 5–29, 5–37
5–49, 5–57, 5–61, 5–69
5–81, 5–85, 5–93
5–101, 5–105
5–109, 5–117
5–121, 5–125
5–133, 5–137
6–5, 6–9, 6–17, 6–29, 6–41, 6–45
6–53, 6–57, 6–69, 6–85
6–113, 6–117, 6–121, 6–125
6–129, 6–133, 6–137
6–145, 6–149, 6–153
6–157, 6–161
6–169, 6–173, 6–177
7–5, 7–13, 7–25
7–33, 7–41, 7–45
7–53, 7–57, 7–69
8–5, 8–13
8–21, 8–33, 8–45, 8–53, 8–57
9–5, 9–9, 9–21
9–17, 9–25, 9–33
9–61, 9–65, 9–73
9–85, 9–93
10–5, 10–9
10–21, 10–17
10–25, 10–29
10–33, 10–41, 10–49
10–61, 10–73, 10–81, 10–89
11–5, 11–9, 11–17, 11–25
11–33, 11–37
11–41, 11–45
12–5, 12–9, 12–17, 12–25
12–37, 12–41, 12–49
12–57, 12–61, 12–73
12–93, 12–97, 12–101
12–105, 12–113
12–117, 12–120
12–121, 12–125, 12–129
13–5, 13–13, 13–25
13–49, 13–57, 13–65
13–89, 13–97, 13–105
13–109, 13–121, 13–125
14–5, 14–13, 14–21
14–29, 14–33, 14–41
14–45, 14–49, 14–57
14–73, 14–81, 14–85
14–89, 14–101, 14–109
14–125, 14–129, 14–133
14–137, 14–141, 14–145
V
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ANSWER ASSIGNMENT
Section
Title
Assignment 2
1.1–1.2
1.3–1.5
1.6–1.7
2.1–2.2
3.1–3.5
3.6–3.8
4.1–4.2
4.3–4.5
4.6
4.7
4.8–4.9
5.1–5.3
5.4
5.5
5.6
5.7
5.8
5.9–5.10
6.1–6.2
6.3–6.4
6.5
6.6–6.7
6.8
6.9
6.10–6.11
7.1–7.3
7.4
7.5–7.6
8.1
8.2
9.1–9.2
9.3
9.4–9.6
9.7
10.1–10.2
10.3
10.4–10.5
10.6
10.7
Equilibrium of a Deformable Body
Average Normal and Shear Stress
Design of Simple Connections
Strain
The Stress Strain Diagram
Poisson’s ratio, Shear Stress-Strain Diagram
Deformation of an Axially Loaded Member
Statically Indeterminate Member
Thermal Stresses
Stress Concentrations
Inelastic Deformation and Residual Stresses
Torsion Stress and Power
Angle of Twist
Statically Indeterminate Members
Noncircular Shafts
Thin-Walled Tubes
Stress Concentrations
Inelastic Torsion and Residual Stresses
Shear and Moment Diagrams
Bending Stress
Unsymmetric Bending
Composite Beams
Curved Beams
Stress Concentrations
Inelastic Bending
Shear Stress
Shear Flow in Built-up Members
Shear Center
Thin-Walled Pressure Vessels
Stress Due to Combined Loadings
Stress Transformation
Princ. Stress and Max. In-Plane Shear Stress
Mohr’s Circle
Absolute Maximum Shear Stress
Strain Transformation
Mohr’s Circle
Abs. Maximum Shear Strain, Strain Rosettes
Material Property Relations
Theories of Failure
1–1, 1–7, 1–17, 1–25
1–31, 1–42, 1–51, 1–67
1–74, 1–82, 1–86, 1–90
2–2, 2–11, 2–17, 2–26, 2–31
3–1, 3–10, 3–18, 3–22
3–26, 3–30, 3–34
4–6, 4–7, 4–15, 4–25
4–34, 4–42, 4–45, 4–55
4–70, 4–74, 4–75
4–90, 4–95
4–97, 4–103, 4–111
5–3, 5–9, 5–27, 5–39
5–50, 5–53, 5–63, 5–67
5–77, 5–87, 5–91
5–95, 5–99
5–113, 5–118
5–122, 5–123
5–127, 5–135, 5–139
6–1, 6–2, 6–6, 6–10, 6–19, 6–22, 6–27, 6–35
6–50, 6–54, 6–63, 6–70, 6–94
6–109, 6–114, 6–126
6–127, 6–134, 6–141
6–146, 6–150, 6–154
6–158, 6–162
6–165, 6–171, 6–178
7–1, 7–14, 7–23
7–34, 7–42, 7–47
7–54, 7–63, 7–66
8–1, 8–11
8–18, 8–26, 8–43, 8–55, 8–70
9–2, 9–6, 9–18
9–14, 9–26, 9–30, 9–42
9–59, 9–67, 9–82
9–86, 9–94
10–2, 10–10
10–18, 10–19
10–22, 10–26
10–31, 10–43, 10–50
10–63, 10–69, 10–77, 10–86
11.1–11.2
11.3
11.4
12.1–12.2
12.3
12.4
12.5
12.6–12.7
12.8
12.10
13.1–13.3
13.4–13.5
13.6
13.7
14.1–14.2
14.3
14.4
14.5–14.6
14.7
14.8
14.9
Prismatic Beam Design
Fully Stressed Beams
Shaft Design
Slope and Displacement by Integration
Discontinuity Functions
Moment-Area Theorems
Method of Superposition
Indet. Beams-Method of Integration
Indet. Beams-Mom. Area Theorems
Indet. Beams-Method of Superposition
Buckling of an Ideal Column
The Secant Formula, Inelastic Buckling
Design of Columns for Concentric Loading
Design of Columns for Eccentric Loading
Elastic Strain Energy
Conservation of Energy
Impact
Principle of Virtual Forces-Trusses
Principle of Virtual Forces-Beams
Castigliano’s Theorem-Trusses
Castigliano’s Theorem-Beams
11–1, 11–7, 11–13, 11–23
11–31, 11–38
11–39, 11–42
12–6, 12–11, 12–15, 12–23
12–38, 12–47, 12–50
12–58, 12–66, 12–69
12–87, 12–91, 12–95
12–103, 12–110
12–115, 12–119
12–122, 12–127, 12–134
13–1, 13–7, 13–17, 13–31
13–50, 13–55, 13–63, 13–67
13–82, 13–95, 13–106
13–107, 13–111, 13–119
14–6, 14–10, 14–15
14–25, 14–30, 14–35
14–50, 14–54, 14–63
14–73, 14–79, 14–86
14–90, 14–103, 14–113
14–123, 14–126, 14–134
14–135, 14–138, 14–142
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ANSWER ASSIGNMENT
Section
Title
Assignment 3
1.1–1.2
1.3–1.5
1.6–1.7
2.1–2.2
3.1–3.5
3.6–3.8
4.1–4.2
4.3–4.5
4.6
4.7
4.8–4.9
5.1–5.3
5.4
5.5
5.6
5.7
5.8
5.9–5.10
6.1–6.2
6.3–6.4
6.5
6.6–6.7
6.8
6.9
6.10–6.11
7.1–7.3
7.4
7.5–7.6
8.1
8.2
9.1–9.2
9.3
9.4–9.6
9.7
10.1–10.2
10.3
10.4–10.5
10.6
10.7
Equilibrium of a Deformable Body
Average Normal and Shear Stress
Design of Simple Connections
Strain
The Stress Strain Diagram
Poisson’s ratio, Shear Stress-Strain Diagram
Deformation of an Axially Loaded Member
Statically Indeterminate Member
Thermal Stresses
Stress Concentrations
Inelastic Deformation and Residual Stresses
Torsion Stress and Power
Angle of Twist
Statically Indeterminate Members
Noncircular Shafts
Thin-Walled Tubes
Stress Concentrations
Inelastic Torsion and Residual Stresses
Shear and Moment Diagrams
Bending Stress
Unsymmetric Bending
Composite Beams
Curved Beams
Stress Concentrations
Inelastic Bending
Shear Stress
Shear Flow in Built-up Members
Shear Center
Thin-Walled Pressure Vessels
Stress Due to Combined Loadings
Stress Transformation
Princ. Stress and Max. In-Plane Shear Stress
Mohr’s Circle
Absolute Maximum Shear Stress
Strain Transformation
Mohr’s Circle
Abs. Maximum Shear Strain, Strain Rosettes
Material Property Relations
Theories of Failure
1–2, 1–11, 1–18, 1–22
1–34, 1–46, 1–55, 1–62
1–77, 1–83, 1–89, 1–99
2–6, 2–10, 2–18, 2–22
3–3, 3–11, 3–19, 3–23
3–27, 3–31
4–2, 4–11, 4–18, 4–22
4–31, 4–46, 4–53, 4–58
4–71, 4–78, 4–85
4–87, 4–91, 4–94
4–106, 4–109, 4–110
5–6, 5–11, 5–22, 5–31
5–47, 5–54, 5–62, 5–66
5–79, 5–82, 5–83
5–93, 5–102
5–114, 5–117
5–120, 5–123
5–130, 5–134, 5–139
6–7, 6–13, 6–21, 6–23, 6–24, 6–31, 6–37, 6–42
6–51, 6–58, 6–66, 6–82, 6–99
6–111, 6–118, 6–122
6–130, 6–135, 6–138
6–147, 6–151, 6–155
6–159, 6–163
6–170, 6–174, 6–182
7–6, 7–11, 7–27
7–35, 7–43, 7–48
7–50, 7–58, 7–61
8–3, 8–7
8–22, 8–35, 8–42, 8–58
9–7, 9–10, 9–13
9–19, 9–22, 9–31, 9–37
9–63, 9–71, 9–83
9–87, 9–95
10–3, 10–11
10–18, 10–19
10–23, 10–27
10–34, 10–39, 10–47
10–66, 10–74, 10–82, 10–91
11.1–11.2
11.3
11.4
12.1–12.2
12.3
12.4
12.5
12.6–12.7
12.8
12.10
13.1–13.3
13.4–13.5
13.6
13.7
14.1–14.2
14.3
14.4
14.5–14.6
14.7
14.8
14.9
Prismatic Beam Design
Fully Stressed Beams
Shaft Design
Slope and Displacement by Integration
Discontinuity Functions
Moment-Area Theorems
Method of Superposition
Indet. Beams-Method of Integration
Indet. Beams-Mom. Area Theorems
Indet. Beams-Method of Superposition
Buckling of an Ideal Column
The Secant Formula, Inelastic Buckling
Design of Columns for Concentric Loading
Design of Columns for Eccentric Loading
Elastic Strain Energy
Conservation of Energy
Impact
Principle of Virtual Forces-Trusses
Principle of Virtual Forces-Beams
Castigliano’s Theorem-Trusses
Castigliano’s Theorem-Beams
11–3, 11–6, 11–11, 11–22
11–34, 11–35
11–43, 11–46
12–3, 12–7, 12–18, 12–25
12–35, 12–43, 12–53
12–55, 12–63, 12–74
12–89, 12–94, 12–98
12–106, 12–114
12–118, 12–119
12–123, 12–126, 12–130
13–3, 13–9, 13–18, 13–26
13–47, 13–53, 13–59, 13–70
13–83, 13–99, 13–103
13–110, 13–117, 13–126
14–3, 14–11, 14–14
14–27, 14–31, 14–34
14–51, 14–58, 14–67
14–74, 14–77, 14–82
14–87, 14–97, 14–110
14–125, 14–127, 14–129
14–139, 14–141, 14–143
VII
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Page viii
ANSWER ASSIGNMENT
Section
Title
Assignment without Answers
1.1–1.2
1.3–1.5
1.6–1.7
2.1–2.2
3.1–3.5
3.6–3.8
4.1–4.2
4.3–4.5
4.6
4.7
4.8–4.9
5.1–5.3
5.4
5.5
5.6
5.7
5.8
5.9–5.10
6.1–6.2
6.3–6.4
6.5
6.6–6.7
6.8
6.9
6.10–6.11
7.1–7.3
7.4
7.5–7.6
8.1
8.2
9.1–9.2
9.3
9.4–9.6
9.7
10.1–10.2
10.3
10.4–10.5
10.6
10.7
Equilibrium of a Deformable Body
Average Normal and Shear Stress
Design of Simple Connections
Strain
The Stress Strain Diagram
Poisson’s ratio, Shear Stress-Strain Diagram
Deformation of an Axially Loaded Member
Statically Indeterminate Member
Thermal Stresses
Stress Concentrations
Inelastic Deformation and Residual Stresses
Torsion Stress and Power
Angle of Twist
Statically Indeterminate Members
Noncircular Shafts
Thin-Walled Tubes
Stress Concentrations
Inelastic Torsion and Residual Stresses
Shear and Moment Diagrams
Bending Stress
Unsymmetric Bending
Composite Beams
Curved Beams
Stress Concentrations
Inelastic Bending
Shear Stress
Shear Flow in Built-up Members
Shear Center
Thin-Walled Pressure Vessels
Stress Due to Combined Loadings
Stress Transformation
Princ. Stress and Max. In-Plane Shear Stress
Mohr’s Circle
Absolute Maximum Shear Stress
Strain Transformation
Mohr’s Circle
Abs. Maximum Shear Strain, Strain Rosettes
Material Property Relations
Theories of Failure
1–4, 1–12, 1–20, 1–28
1–36, 1–40, 1–52, 1–60
1–76, 1–88, 1–92, 1–100
2–4, 2–8, 2–16, 2–24
3–4, 3–8, 3–16, 3–20
3–28, 3–32
4–4, 4–12, 4–16, 4–20
4–32, 4–40, 4–44, 4–52
4–68, 4–76, 4–84
4–88, 4–92, 4–96
4–100, 4–104, 4–112
5–4, 5–8, 5–20, 5–36
5–52, 5–56, 5–64, 5–72
5–80, 5–88, 5–92
5–96, 5–104
5–108, 5–116
5–120, 5–124
5–132, 5–136
6–4, 6–8, 6–12, 6–18, 6–20, 6–28, 6–36
6–52, 6–56, 6–68, 6–84
6–112, 6–116, 6–120
6–128, 6–132, 6–140
6–144, 6–152, 6–156
6–160, 6–164
6–168, 6–176, 6–184
7–4, 7–12, 7–24
7–32, 7–40, 7–44
7–52, 7–60, 7–68
8–4, 8–8
8–20, 8–28, 8–36, 8–56, 8–68
9–4, 9–8, 9–20
9–16, 9–28, 9–32, 9–36
9–60, 9–68, 9–76
9–84, 9–92
10–4, 10–8
10–16, 10–20
10–24, 10–28
10–32, 10–40, 10–44
10–60, 10–72, 10–76, 10–88
11.1–11.2
11.3
11.4
12.1–12.2
12.3
12.4
12.5
12.6–12.7
12.8
12.10
13.1–13.3
13.4–13.5
13.6
13.7
14.1–14.2
14.3
14.4
14.5–14.6
14.7
14.8
14.9
Prismatic Beam Design
Fully Stressed Beams
Shaft Design
Slope and Displacement by Integration
Discontinuity Functions
Moment-Area Theorems
Method of Superposition
Indet. Beams-Method of Integration
Indet. Beams-Mom. Area Theorems
Indet. Beams-Method of Superposition
Buckling of an Ideal Column
The Secant Formula, Inelastic Buckling
Design of Columns for Concentric Loading
Design of Columns for Eccentric Loading
Elastic Strain Energy
Conservation of Energy
Impact
Principle of Virtual Forces-Trusses
Principle of Virtual Forces-Beams
Castigliano’s Theorem-Trusses
Castigliano’s Theorem-Beams
11–4, 11–12, 11–20, 11–28
11–32, 11–36
11–40, 11–44
12–8, 12–12, 12–20, 12–24
12–36, 12–44, 12–48
12–56, 12–64, 12–72
12–88, 12–96, 12–100
12–104, 12–112
12–116, 12–120
12–124, 12–128, 12–136
13–4, 13–8, 13–16, 13–24
13–48, 13–56, 13–64, 13–72
13–88, 13–96, 13–104
13–108, 13–116, 13–120
14–4, 14–16, 14–20
14–28, 14–32, 14–40
14–48, 14–52, 14–64
14–72, 14–80, 14–84
14–88, 14–96, 14–104
14–124, 14–128, 14–132
14–136, 14–140, 14–144
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Page ix
ANSWER ASSIGNMENT
Section
Title
1.1–1.2
1.3–1.5
1.6–1.7
2.1–2.2
3.1–3.5
3.6–3.8
4.1–4.2
4.3–4.5
4.6
4.7
4.8–4.9
5.1–5.3
5.4
5.5
5.6
5.7
5.8
5.9–5.10
6.1–6.2
6.3–6.4
6.5
6.6–6.7
6.8
6.9
6.10–6.11
7.1–7.3
7.4
7.5–7.6
8.1
8.2
9.1–9.2
9.3
9.4–9.6
9.7
10.1–10.2
10.3
10.4–10.5
10.6
10.7
Equilibrium of a Deformable Body
Average Normal and Shear Stress
Design of Simple Connections
Strain
The Stress Strain Diagram
Poisson’s ratio, Shear Stress-Strain Diagram
Deformation of an Axially Loaded Member
Statically Indeterminate Member
Thermal Stresses
Stress Concentrations
Inelastic Deformation and Residual Stresses
Torsion Stress and Power
Angle of Twist
Statically Indeterminate Members
Noncircular Shafts
Thin-Walled Tubes
Stress Concentrations
Inelastic Torsion and Residual Stresses
Shear and Moment Diagrams
Bending Stress
Unsymmetric Bending
Composite Beams
Curved Beams
Stress Concentrations
Inelastic Bending
Shear Stress
Shear Flow in Built-up Members
Shear Center
Thin-Walled Pressure Vessels
Stress Due to Combined Loadings
Stress Transformation
Princ. Stress and Max. In-Plane Shear Stress
Mohr’s Circle
Absolute Maximum Shear Stress
Strain Transformation
Mohr’s Circle
Abs. Maximum Shear Strain, Strain Rosettes
Material Property Relations
Theories of Failure
11.1–11.2
11.3
11.4
12.1–12.2
12.3
12.4
12.5
12.6–12.7
12.8
12.10
13.1–13.3
13.4–13.5
13.6
13.7
14.1–14.2
14.3
14.4
14.5–14.6
14.7
14.8
14.9
Prismatic Beam Design
Fully Stressed Beams
Shaft Design
Slope and Displacement by Integration
Discontinuity Functions
Moment-Area Theorems
Method of Superposition
Indet. Beams-Method of Integration
Indet. Beams-Mom. Area Theorems
Indet. Beams-Method of Superposition
Buckling of an Ideal Column
The Secant Formula, Inelastic Buckling
Design of Columns for Concentric Loading
Design of Columns for Eccentric Loading
Elastic Strain Energy
Conservation of Energy
Impact
Principle of Virtual Forces-Trusses
Principle of Virtual Forces-Beams
Castigliano’s Theorem-Trusses
Castigliano’s Theorem-Beams
Assignment
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