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MECHANICS

OF MATERIALS

EIGHTH EDITION

R C HIBBELER

Prentice Hall

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Instructor’s Solutions Manual

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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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10 9 8 7 6 5 4 3 2 1

ISBN 10: 0-13-602312-6 ISBN 13: 978-0-13-602312-8

To the Instructor iv

CONTENTS

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

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

hibbeler@bellsouth.net

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

V I ANSWERASSIGNMENT

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

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

V I I I ANSWERASSIGNMENT

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

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