cơ học vật liệu -instructor''''s solutions manual mechanics materials - R. C. hibbrler

MECHANICS
OF MATERIALS
EIGHTH EDITION
R. C. HIBBELER
Prentice Hall
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Instructor’s Solutions Manual
FM_TOC 46060 6/22/10 11:26 AM Page i
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Copyright © 2011, 2008, 2005, 2003, 2001 by R. C. Hibbeler. Published by Pearson Prentice Hall.All rights reserved.
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Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks.Where

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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
FM_TOC 46060 6/22/10 11:26 AM Page ii
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
CONTENTS
FM_TOC 46060 6/22/10 11:26 AM Page iii
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

FM_TOC 46060 6/22/10 11:26 AM Page iv
ANSWER ASSIGNMENT V
Section Title Assignment 1 with Hints
1.1–1.2 Equilibrium of a Deformable Body 1–5, 1–9, 1–21
1.3–1.5 Average Normal and Shear Stress 1–37, 1–45, 1–53, 1–61
1.6–1.7 Design of Simple Connections 1–73, 1–81, 1–85, 1–97
2.1–2.2 Strain 2–5, 2–13, 2–21
3.1–3.5 The Stress Strain Diagram 3–5, 3–9, 3–17
3.6–3.8 Poisson’s ratio, Shear Stress-Strain Diagram 3–25, 3–29, 3–33
4.1–4.2 Deformation of an Axially Loaded Member 4–5,4–13, 4–17, 4–21
4.3–4.5 Statically Indeterminate Member 4–33, 4–41, 4–49, 4–61
4.6 Thermal Stresses 4–69, 4–73, 4–77
4.7 Stress Concentrations 4–89, 4–93
4.8–4.9 Inelastic Deformation and Residual Stresses 4–101, 4–105, 4–113
5.1–5.3 Torsion Stress and Power 5–5, 5–13, 5–25, 5–29, 5–37
5.4 Angle of Twist 5–49, 5–57, 5–61, 5–69
5.5 Statically Indeterminate Members 5–81, 5–85, 5–93
5.6 Noncircular Shafts 5–101, 5–105
5.7 Thin-Walled Tubes 5–109, 5–117
5.8 Stress Concentrations 5–121, 5–125
5.9–5.10 Inelastic Torsion and Residual Stresses 5–133, 5–137
6.1–6.2 Shear and Moment Diagrams 6–5, 6–9, 6–17, 6–29, 6–41, 6–45

6.3–6.4 Bending Stress 6–53, 6–57, 6–69, 6–85
6.5 Unsymmetric Bending 6–113, 6–117, 6–121, 6–125
6.6–6.7 Composite Beams 6–129, 6–133, 6–137
6.8 Curved Beams 6–145, 6–149, 6–153
6.9 Stress Concentrations 6–157, 6–161
6.10–6.11 Inelastic Bending 6–169, 6–173, 6–177
7.1–7.3 Shear Stress 7–5, 7–13, 7–25
7.4 Shear Flow in Built-up Members 7–33, 7–41, 7–45
7.5–7.6 Shear Center 7–53, 7–57, 7–69
8.1 Thin-Walled Pressure Vessels 8–5, 8–13
8.2 Stress Due to Combined Loadings 8–21,8–33, 8–45, 8–53, 8–57
9.1–9.2 Stress Transformation 9–5, 9–9, 9–21
9.3 Princ. Stress and Max. In-Plane Shear Stress 9–17, 9–25, 9–33
9.4–9.6 Mohr’s Circle 9–61, 9–65, 9–73
9.7 Absolute Maximum Shear Stress 9–85, 9–93
10.1–10.2 Strain Transformation 10–5,10–9
10.3 Mohr’s Circle 10–21, 10–17
10.4–10.5 Abs. Maximum Shear Strain, Strain Rosettes 10–25, 10–29
10.6 Material Property Relations 10–33, 10–41, 10–49
10.7 Theories of Failure 10–61, 10–73, 10–81, 10–89
11.1–11.2 Prismatic Beam Design 11–5, 11–9, 11–17, 11–25
11.3 Fully Stressed Beams 11–33, 11–37
11.4 Shaft Design 11–41, 11–45
12.1–12.2 Slope and Displacement by Integration 12–5, 12–9, 12–17, 12–25
12.3 Discontinuity Functions 12–37, 12–41, 12–49
12.4 Moment-Area Theorems 12–57, 12–61, 12–73
12.5 Method of Superposition 12–93, 12–97, 12–101
12.6–12.7 Indet. Beams-Method of Integration 12–105, 12–113
12.8 Indet. Beams-Mom.Area Theorems 12–117, 12–120
12.10 Indet. Beams-Method of Superposition 12–121, 12–125, 12–129

13.1–13.3 Buckling of an Ideal Column 13–5, 13–13, 13–25
13.4–13.5 The Secant Formula, Inelastic Buckling 13–49, 13–57, 13–65
13.6 Design of Columns for Concentric Loading 13–89, 13–97, 13–105
13.7 Design of Columns for Eccentric Loading 13–109, 13–121, 13–125
14.1–14.2 Elastic Strain Energy 14–5, 14–13, 14–21
14.3 Conservation of Energy 14–29, 14–33, 14–41
14.4 Impact 14–45, 14–49, 14–57
14.5–14.6 Principle of Virtual Forces-Trusses 14–73, 14–81, 14–85
14.7 Principle of Virtual Forces-Beams 14–89, 14–101, 14–109
14.8 Castigliano’s Theorem-Trusses 14–125,14–129, 14–133
14.9 Castigliano’s Theorem-Beams 14–137, 14–141, 14–145
FM_TOC 46060 6/22/10 11:26 AM Page v
VI ANSWER ASSIGNMENT
Section Title Assignment 2
1.1–1.2 Equilibrium of a Deformable Body 1–1, 1–7, 1–17, 1–25
1.3–1.5 Average Normal and Shear Stress 1–31, 1–42, 1–51, 1–67
1.6–1.7 Design of Simple Connections 1–74, 1–82, 1–86, 1–90
2.1–2.2 Strain 2–2, 2–11, 2–17, 2–26, 2–31
3.1–3.5 The Stress Strain Diagram 3–1, 3–10, 3–18, 3–22
3.6–3.8 Poisson’s ratio, Shear Stress-Strain Diagram 3–26, 3–30, 3–34
4.1–4.2 Deformation of an Axially Loaded Member 4–6, 4–7, 4–15, 4–25
4.3–4.5 Statically Indeterminate Member 4–34, 4–42, 4–45, 4–55
4.6 Thermal Stresses 4–70, 4–74, 4–75
4.7 Stress Concentrations 4–90, 4–95
4.8–4.9 Inelastic Deformation and Residual Stresses 4–97, 4–103, 4–111
5.1–5.3 Torsion Stress and Power 5–3, 5–9, 5–27, 5–39
5.4 Angle of Twist 5–50, 5–53, 5–63, 5–67
5.5 Statically Indeterminate Members 5–77, 5–87, 5–91
5.6 Noncircular Shafts 5–95, 5–99
5.7 Thin-Walled Tubes 5–113, 5–118

5.8 Stress Concentrations 5–122, 5–123
5.9–5.10 Inelastic Torsion and Residual Stresses 5–127, 5–135, 5–139
6.1–6.2 Shear and Moment Diagrams 6–1, 6–2, 6–6, 6–10, 6–19, 6–22, 6–27, 6–35
6.3–6.4 Bending Stress 6–50, 6–54, 6–63, 6–70, 6–94
6.5 Unsymmetric Bending 6–109, 6–114, 6–126
6.6–6.7 Composite Beams 6–127, 6–134, 6–141
6.8 Curved Beams 6–146, 6–150, 6–154
6.9 Stress Concentrations 6–158, 6–162
6.10–6.11 Inelastic Bending 6–165, 6–171, 6–178
7.1–7.3 Shear Stress 7–1, 7–14, 7–23
7.4 Shear Flow in Built-up Members 7–34, 7–42, 7–47
7.5–7.6 Shear Center 7–54, 7–63, 7–66
8.1 Thin-Walled Pressure Vessels 8–1, 8–11
8.2 Stress Due to Combined Loadings 8–18,8–26, 8–43, 8–55, 8–70
9.1–9.2 Stress Transformation 9–2, 9–6, 9–18
9.3 Princ. Stress and Max. In-Plane Shear Stress 9–14, 9–26, 9–30, 9–42
9.4–9.6 Mohr’s Circle 9–59, 9–67, 9–82
9.7 Absolute Maximum Shear Stress 9–86, 9–94
10.1–10.2 Strain Transformation 10–2,10–10
10.3 Mohr’s Circle 10–18, 10–19
10.4–10.5 Abs. Maximum Shear Strain, Strain Rosettes 10–22, 10–26
10.6 Material Property Relations 10–31, 10–43, 10–50
10.7 Theories of Failure 10–63, 10–69, 10–77, 10–86
11.1–11.2 Prismatic Beam Design 11–1, 11–7, 11–13, 11–23
11.3 Fully Stressed Beams 11–31, 11–38
11.4 Shaft Design 11–39, 11–42
12.1–12.2 Slope and Displacement by Integration 12–6, 12–11, 12–15, 12–23
12.3 Discontinuity Functions 12–38, 12–47, 12–50
12.4 Moment-Area Theorems 12–58, 12–66, 12–69
12.5 Method of Superposition 12–87, 12–91, 12–95

12.6–12.7 Indet. Beams-Method of Integration 12–103, 12–110
12.8 Indet. Beams-Mom.Area Theorems 12–115, 12–119
12.10 Indet. Beams-Method of Superposition 12–122, 12–127, 12–134
13.1–13.3 Buckling of an Ideal Column 13–1, 13–7, 13–17, 13–31
13.4–13.5 The Secant Formula, Inelastic Buckling 13–50, 13–55, 13–63, 13–67
13.6 Design of Columns for Concentric Loading 13–82, 13–95, 13–106
13.7 Design of Columns for Eccentric Loading 13–107, 13–111, 13–119
14.1–14.2 Elastic Strain Energy 14–6, 14–10, 14–15
14.3 Conservation of Energy 14–25, 14–30, 14–35
14.4 Impact 14–50, 14–54, 14–63
14.5–14.6 Principle of Virtual Forces-Trusses 14–73, 14–79, 14–86
14.7 Principle of Virtual Forces-Beams 14–90, 14–103, 14–113
14.8 Castigliano’s Theorem-Trusses 14–123,14–126, 14–134
14.9 Castigliano’s Theorem-Beams 14–135, 14–138, 14–142
FM_TOC 46060 6/22/10 11:26 AM Page vi
ANSWER ASSIGNMENT VII
Section Title Assignment 3
1.1–1.2 Equilibrium of a Deformable Body 1–2, 1–11, 1–18, 1–22
1.3–1.5 Average Normal and Shear Stress 1–34, 1–46, 1–55, 1–62
1.6–1.7 Design of Simple Connections 1–77, 1–83, 1–89, 1–99
2.1–2.2 Strain 2–6, 2–10, 2–18, 2–22
3.1–3.5 The Stress Strain Diagram 3–3, 3–11, 3–19, 3–23
3.6–3.8 Poisson’s ratio, Shear Stress-Strain Diagram 3–27, 3–31
4.1–4.2 Deformation of an Axially Loaded Member 4–2, 4–11, 4–18, 4–22
4.3–4.5 Statically Indeterminate Member 4–31, 4–46, 4–53, 4–58
4.6 Thermal Stresses 4–71, 4–78, 4–85
4.7 Stress Concentrations 4–87, 4–91, 4–94
4.8–4.9 Inelastic Deformation and Residual Stresses 4–106, 4–109, 4–110
5.1–5.3 Torsion Stress and Power 5–6, 5–11, 5–22, 5–31
5.4 Angle of Twist 5–47, 5–54, 5–62, 5–66

5.5 Statically Indeterminate Members 5–79, 5–82, 5–83
5.6 Noncircular Shafts 5–93, 5–102
5.7 Thin-Walled Tubes 5–114, 5–117
5.8 Stress Concentrations 5–120, 5–123
5.9–5.10 Inelastic Torsion and Residual Stresses 5–130, 5–134, 5–139
6.1–6.2 Shear and Moment Diagrams 6–7, 6–13, 6–21, 6–23, 6–24, 6–31, 6–37, 6–42
6.3–6.4 Bending Stress 6–51, 6–58, 6–66, 6–82, 6–99
6.5 Unsymmetric Bending 6–111, 6–118, 6–122
6.6–6.7 Composite Beams 6–130, 6–135, 6–138
6.8 Curved Beams 6–147, 6–151, 6–155
6.9 Stress Concentrations 6–159, 6–163
6.10–6.11 Inelastic Bending 6–170, 6–174, 6–182
7.1–7.3 Shear Stress 7–6, 7–11, 7–27
7.4 Shear Flow in Built-up Members 7–35, 7–43, 7–48
7.5–7.6 Shear Center 7–50, 7–58, 7–61
8.1 Thin-Walled Pressure Vessels 8–3, 8–7
8.2 Stress Due to Combined Loadings 8–22,8–35, 8–42, 8–58
9.1–9.2 Stress Transformation 9–7, 9–10, 9–13
9.3 Princ. Stress and Max. In-Plane Shear Stress 9–19, 9–22, 9–31, 9–37
9.4–9.6 Mohr’s Circle 9–63, 9–71, 9–83
9.7 Absolute Maximum Shear Stress 9–87, 9–95
10.1–10.2 Strain Transformation 10–3,10–11
10.3 Mohr’s Circle 10–18, 10–19
10.4–10.5 Abs. Maximum Shear Strain, Strain Rosettes 10–23, 10–27
10.6 Material Property Relations 10–34, 10–39, 10–47
10.7 Theories of Failure 10–66, 10–74, 10–82, 10–91
11.1–11.2 Prismatic Beam Design 11–3, 11–6, 11–11, 11–22
11.3 Fully Stressed Beams 11–34, 11–35
11.4 Shaft Design 11–43, 11–46
12.1–12.2 Slope and Displacement by Integration 12–3, 12–7, 12–18, 12–25

12.3 Discontinuity Functions 12–35, 12–43, 12–53
12.4 Moment-Area Theorems 12–55, 12–63, 12–74
12.5 Method of Superposition 12–89, 12–94, 12–98
12.6–12.7 Indet. Beams-Method of Integration 12–106, 12–114
12.8 Indet. Beams-Mom.Area Theorems 12–118, 12–119
12.10 Indet. Beams-Method of Superposition 12–123, 12–126, 12–130
13.1–13.3 Buckling of an Ideal Column 13–3, 13–9, 13–18, 13–26
13.4–13.5 The Secant Formula, Inelastic Buckling 13–47, 13–53, 13–59, 13–70
13.6 Design of Columns for Concentric Loading 13–83, 13–99, 13–103
13.7 Design of Columns for Eccentric Loading 13–110, 13–117, 13–126
14.1–14.2 Elastic Strain Energy 14–3, 14–11, 14–14
14.3 Conservation of Energy 14–27, 14–31, 14–34
14.4 Impact 14–51, 14–58, 14–67
14.5–14.6 Principle of Virtual Forces-Trusses 14–74, 14–77, 14–82
14.7 Principle of Virtual Forces-Beams 14–87, 14–97, 14–110
14.8 Castigliano’s Theorem-Trusses 14–125,14–127, 14–129
14.9 Castigliano’s Theorem-Beams 14–139, 14–141, 14–143
FM_TOC 46060 6/22/10 11:26 AM Page vii
VIII ANSWER ASSIGNMENT
Section Title Assignment without Answers
1.1–1.2 Equilibrium of a Deformable Body 1–4, 1–12, 1–20, 1–28
1.3–1.5 Average Normal and Shear Stress 1–36, 1–40, 1–52, 1–60
1.6–1.7 Design of Simple Connections 1–76, 1–88, 1–92, 1–100
2.1–2.2 Strain 2–4, 2–8, 2–16, 2–24
3.1–3.5 The Stress Strain Diagram 3–4, 3–8, 3–16, 3–20
3.6–3.8 Poisson’s ratio, Shear Stress-Strain Diagram 3–28, 3–32
4.1–4.2 Deformation of an Axially Loaded Member 4–4, 4–12, 4–16, 4–20
4.3–4.5 Statically Indeterminate Member 4–32, 4–40, 4–44, 4–52
4.6 Thermal Stresses 4–68, 4–76, 4–84
4.7 Stress Concentrations 4–88, 4–92, 4–96

4.8–4.9 Inelastic Deformation and Residual Stresses 4–100, 4–104, 4–112
5.1–5.3 Torsion Stress and Power 5–4, 5–8, 5–20, 5–36
5.4 Angle of Twist 5–52, 5–56, 5–64, 5–72
5.5 Statically Indeterminate Members 5–80, 5–88, 5–92
5.6 Noncircular Shafts 5–96, 5–104
5.7 Thin-Walled Tubes 5–108, 5–116
5.8 Stress Concentrations 5–120, 5–124
5.9–5.10 Inelastic Torsion and Residual Stresses 5–132, 5–136
6.1–6.2 Shear and Moment Diagrams 6–4, 6–8, 6–12, 6–18, 6–20, 6–28, 6–36
6.3–6.4 Bending Stress 6–52, 6–56, 6–68, 6–84
6.5 Unsymmetric Bending 6–112, 6–116, 6–120
6.6–6.7 Composite Beams 6–128, 6–132, 6–140
6.8 Curved Beams 6–144, 6–152, 6–156
6.9 Stress Concentrations 6–160, 6–164
6.10–6.11 Inelastic Bending 6–168, 6–176, 6–184
7.1–7.3 Shear Stress 7–4, 7–12, 7–24
7.4 Shear Flow in Built-up Members 7–32, 7–40, 7–44
7.5–7.6 Shear Center 7–52, 7–60, 7–68
8.1 Thin-Walled Pressure Vessels 8–4, 8–8
8.2 Stress Due to Combined Loadings 8–20,8–28, 8–36, 8–56, 8–68
9.1–9.2 Stress Transformation 9–4, 9–8, 9–20
9.3 Princ. Stress and Max. In-Plane Shear Stress 9–16, 9–28, 9–32, 9–36
9.4–9.6 Mohr’s Circle 9–60, 9–68, 9–76
9.7 Absolute Maximum Shear Stress 9–84, 9–92
10.1–10.2 Strain Transformation 10–4,10–8
10.3 Mohr’s Circle 10–16, 10–20
10.4–10.5 Abs. Maximum Shear Strain, Strain Rosettes 10–24, 10–28
10.6 Material Property Relations 10–32, 10–40, 10–44
10.7 Theories of Failure 10–60, 10–72, 10–76, 10–88
11.1–11.2 Prismatic Beam Design 11–4, 11–12, 11–20, 11–28

11.3 Fully Stressed Beams 11–32, 11–36
11.4 Shaft Design 11–40, 11–44
12.1–12.2 Slope and Displacement by Integration 12–8, 12–12, 12–20, 12–24
12.3 Discontinuity Functions 12–36, 12–44, 12–48
12.4 Moment-Area Theorems 12–56, 12–64, 12–72
12.5 Method of Superposition 12–88, 12–96, 12–100
12.6–12.7 Indet. Beams-Method of Integration 12–104, 12–112
12.8 Indet. Beams-Mom.Area Theorems 12–116, 12–120
12.10 Indet. Beams-Method of Superposition 12–124, 12–128, 12–136
13.1–13.3 Buckling of an Ideal Column 13–4, 13–8, 13–16, 13–24
13.4–13.5 The Secant Formula, Inelastic Buckling 13–48, 13–56, 13–64, 13–72
13.6 Design of Columns for Concentric Loading 13–88, 13–96, 13–104
13.7 Design of Columns for Eccentric Loading 13–108, 13–116, 13–120
14.1–14.2 Elastic Strain Energy 14–4, 14–16, 14–20
14.3 Conservation of Energy 14–28, 14–32, 14–40
14.4 Impact 14–48, 14–52, 14–64
14.5–14.6 Principle of Virtual Forces-Trusses 14–72, 14–80, 14–84
14.7 Principle of Virtual Forces-Beams 14–88, 14–96, 14–104
14.8 Castigliano’s Theorem-Trusses 14–124,14–128, 14–132
14.9 Castigliano’s Theorem-Beams 14–136, 14–140, 14–144
FM_TOC 46060 6/22/10 11:26 AM Page viii
ANSWER ASSIGNMENT IX
Section Title Assignment
1.1–1.2 Equilibrium of a Deformable Body
1.3–1.5 Average Normal and Shear Stress
1.6–1.7 Design of Simple Connections
2.1–2.2 Strain
3.1–3.5 The Stress Strain Diagram
3.6–3.8 Poisson’s ratio, Shear Stress-Strain Diagram
4.1–4.2 Deformation of an Axially Loaded Member

4.3–4.5 Statically Indeterminate Member
4.6 Thermal Stresses
4.7 Stress Concentrations
4.8–4.9 Inelastic Deformation and Residual Stresses
5.1–5.3 Torsion Stress and Power
5.4 Angle of Twist
5.5 Statically Indeterminate Members
5.6 Noncircular Shafts
5.7 Thin-Walled Tubes
5.8 Stress Concentrations
5.9–5.10 Inelastic Torsion and Residual Stresses
6.1–6.2 Shear and Moment Diagrams
6.3–6.4 Bending Stress
6.5 Unsymmetric Bending
6.6–6.7 Composite Beams
6.8 Curved Beams
6.9 Stress Concentrations
6.10–6.11 Inelastic Bending
7.1–7.3 Shear Stress
7.4 Shear Flow in Built-up Members
7.5–7.6 Shear Center
8.1 Thin-Walled Pressure Vessels
8.2 Stress Due to Combined Loadings
9.1–9.2 Stress Transformation
9.3 Princ. Stress and Max. In-Plane Shear Stress
9.4–9.6 Mohr’s Circle
9.7 Absolute Maximum Shear Stress
10.1–10.2 Strain Transformation
10.3 Mohr’s Circle
10.4–10.5 Abs. Maximum Shear Strain, Strain Rosettes

10.6 Material Property Relations
10.7 Theories of Failure
11.1–11.2 Prismatic Beam Design
11.3 Fully Stressed Beams
11.4 Shaft Design
12.1–12.2 Slope and Displacement by Integration
12.3 Discontinuity Functions
12.4 Moment-Area Theorems
12.5 Method of Superposition
12.6–12.7 Indet. Beams-Method of Integration
12.8 Indet. Beams-Mom.Area Theorems
12.10 Indet. Beams-Method of Superposition
13.1–13.3 Buckling of an Ideal Column
13.4–13.5 The Secant Formula, Inelastic Buckling
13.6 Design of Columns for Concentric Loading
13.7 Design of Columns for Eccentric Loading
14.1–14.2 Elastic Strain Energy
14.3 Conservation of Energy
14.4 Impact
14.5–14.6 Principle of Virtual Forces-Trusses
14.7 Principle of Virtual Forces-Beams
14.8 Castigliano’s Theorem-Trusses
14.9 Castigliano’s Theorem-Beams
FM_TOC 46060 6/22/10 11:26 AM Page ix