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Mechanics of Materials: An Integrated Learning System, 4th Edition
Timothy A. Philpot
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Chapter 1Stress
 
1.1Introduction   
1.2Normal Stress Under Axial Loading    
1.3Direct Shear Stress   
1.4Bearing Stress   
1.5Stresses on Inclined Sections   
1.6Equality of Shear Stresses on Perpendicular Planes   
 
Chapter 2Strain
 
2.1Displacement, Deformation, and the Concept of Strain   
2.2Normal Strain   
2.3Shear Strain   
2.4Thermal Strain   
 
Chapter 3Mechanical Properties of Materials
 
3.1The Tension Test   
3.2The Stress–Strain Diagram    
3.3Hooke’s Law   
3.4Poisson’s Ratio   
 
Chapter 4Design Concepts
 
4.1Introduction   
4.2Types of Loads  
4.3Safety   
4.4Allowable Stress Design  
4.5Load and Resistance Factor Design 
 
Chapter 5Axial Deformation
 
5.1Introduction   
5.2Saint-Venant’s Principle    
5.3Deformations in Axially Loaded Bars  
5.4Deformations in a System of Axially Loaded Bars  
5.5Statically Indeterminate Axially Loaded Members   
5.6Thermal Effects on Axial Deformation   
5.7Stress Concentrations   
 
Chapter 6Torsion
 
6.1Introduction   
6.2Torsional Shear Strain  
6.3Torsional Shear Stress   
6.4Stresses on Oblique Planes  
6.5Torsional Deformations   
6.6Torsion Sign Conventions    
6.7Gears in Torsion Assemblies   
6.8Power Transmission    
6.9Statically Indeterminate Torsion Members   
6.10Stress Concentrations in Circular Shafts Under Torsional Loadings    
6.11Torsion of Noncircular Sections    
6.12Torsion of Thin-Walled Tubes: Shear Flow   
 
Chapter 7Equilibrium of Beams
 
7.1Introduction   
7.2Shear and Moment in Beams   
 
7.3Graphical Method for Constructing Shear and Moment Diagrams   
7.4Discontinuity Functions to Represent Load, Shear, and Moment   
 
Chapter 8Bending
 
8.1Introduction   
8.2Flexural Strains    
8.3Normal Stresses in Beams   
8.4Analysis of Bending Stresses in Beams   
8.5Introductory Beam Design for Strength   
8.6Flexural Stresses in Beams of Two Materials   
8.7Bending Due to Eccentric Axial Load  
8.8Unsymmetric Bending  
8.9Stress Concentrations Under Flexural Loadings
8.10Bending of Curved Bars
 
Chapter 9Shear Stress in Beams
 
9.1Introduction   
9.2Resultant Forces Produced by Bending Stresses   
9.3The Shear Stress Formula   
9.4The First Moment of Area Q   
9.5Shear Stresses in Beams of Rectangular Cross Section   
9.6Shear Stresses in Beams of Circular Cross Section   
9.7Shear Stresses in Webs of Flanged Beams    
9.8Shear Flow in Built-Up Members   
9.9Shear Stress and Shear Flow in Thin-Walled Members   
9.10Shear Centers of Thin-Walled Open Sections  
 
Chapter 10Beam Deflections
 
10.1Introduction   
10.2Moment-Curvature Relationship   
10.3The Differential Equation of the Elastic Curve  
10.4Deflections by Integration of a Moment Equation   
10.5Deflections by Integration of Shear-Force or Load Equations  
10.6Deflections Using Discontinuity Functions   
10.7Method of Superposition   
 
Chapter 11Statically Indeterminate Beams
 
11.1Introduction   
11.2Types of Statically Indeterminate Beams  
11.3The Integration Method   
11.4Use of Discontinuity Functions for Statically Indeterminate Beams  
11.5The Superposition Method   
 
Chapter 12Stress Transformations
 
12.1Introduction   
12.2Stress at a General Point in an Arbitrarily Loaded Body  
12.3Equilibrium of the Stress Element    
12.4Plane Stress   
12.5Generating the Stress Element  
12.6Equilibrium Method for Plane Stress Transformations   
12.7General Equations of Plane Stress Transformation   
12.8Principal Stresses and Maximum Shear Stress   
12.9Presentation of Stress Transformation Results  
12.10Mohr’s Circle for Plane Stress  
12.11General State of Stress at a Point   
 
Chapter 13Strain Transformations
 
13.1Introduction   
13.2Plane Strain   
13.3Transformation Equations for Plane Strain   
13.4Principal Strains and Maximum Shearing Strain   
13.5Presentation of Strain Transformation Results  
13.6Mohr’s Circle for Plane Strain  
13.7Strain Measurement and Strain Rosettes   
13.8Generalized Hooke’s Law for Isotropic Materials   
13.9Generalized Hooke’s Law for Orthotropic Materials
 
Chapter 14Pressure Vessels
 
14.1Introduction   
14.2Thin-Walled Spherical Pressure Vessels   
14.3Thin-Walled Cylindrical Pressure Vessels   
14.4Strains in Thin-Walled Pressure Vessels   
14.5Stresses in Thick-Walled Cylinders
14.6Deformation in Thick-Walled Cylinders
14.7Interference Fits
 
Chapter 15Combined Loads
 
15.1Introduction   
15.2Combined Axial and Torsional Loads    
15.3Principal Stresses in a Flexural Member   
15.4General Combined Loadings    
15.5Theories of Failure    
 
Chapter 16Columns
 
16.1Introduction   
16.2Buckling of Pin-Ended Columns   
16.3The Effect of End Conditions on Column Buckling    
16.4The Secant Formula    
16.5Empirical Column Formulas— Centric Loading    
16.6Eccentrically Loaded Columns   
 
Chapter 17Energy Methods
 
17.1Introduction   
17.2Work and Strain Energy   
17.3Elastic Strain Energy for Axial Deformation
17.4Elastic Strain Energy for Torsional Deformation   
17.5Elastic Strain Energy for Flexural Deformation
17.6Impact Loading   
17.7Work-Energy Method for Single Loads  
17.8Method of Virtual Work    
17.9Deflections of Trusses by the Virtual-Work Method    
17.10Deflections of Beams by the Virtual-Work Method    
17.11Castigliano’s Second Theorem    
17.12Calculating Deflections of Trusses by Castigliano’s Theorem    
17.13Calculating Deflections of Beams by Castigliano’s Theorem    
 
Appendix AGeometric Properties of an Area
 
A.1Centroid of an Area   
A.2Moment of Inertia for an Area    
A.3Product of Inertia for an Area   
A.4Principal Moments of Inertia   
A.5Mohr’s Circle for Principal Moments of Inertia   
 
Appendix BGeometric Properties of Structural Steel Shapes
Appendix CTable of Beam Slopes and Deflections
Appendix DAverage  Properties of Selected Materials
Answers to Problems
Index 
Chapter 1 Stress
 
1.1 Introduction   
1.2 Normal Stress Under Axial Loading    
1.3 Direct Shear Stress   
1.4 Bearing Stress   
1.5 Stresses on Inclined Sections   
1.6 Equality of Shear Stresses on Perpendicular Planes   
 
Chapter 2 Strain
 
2.1 Displacement, Deformation, and the Concept of Strain   
2.2 Normal Strain   
2.3 Shear Strain   
2.4 Thermal Strain   
 
Chapter 3 Mechanical Properties of Materials
 
3.1 The Tension Test   
3.2 The Stress–Strain Diagram    
3.3 Hooke’s Law   
3.4 Poisson’s Ratio   
 
Chapter 4 Design Concepts
 
4.1 Introduction   
4.2 Types of Loads  
4.3 Safety   
4.4 Allowable Stress Design  
4.5 Load and Resistance Factor Design 
 
Chapter 5 Axial Deformation
 
5.1 Introduction   
5.2 Saint-Venant’s Principle    
5.3 Deformations in Axially Loaded Bars  
5.4 Deformations in a System of Axially Loaded Bars  
5.5 Statically Indeterminate Axially Loaded Members   
5.6 Thermal Effects on Axial Deformation   
5.7 Stress Concentrations   
 
Chapter 6 Torsion
 
6.1 Introduction   
6.2 Torsional Shear Strain  
6.3 Torsional Shear Stress   
6.4 Stresses on Oblique Planes  
6.5 Torsional Deformations   
6.6 Torsion Sign Conventions    
6.7 Gears in Torsion Assemblies   
6.8 Power Transmission    
6.9 Statically Indeterminate Torsion Members   
6.10 Stress Concentrations in Circular Shafts Under Torsional Loadings    
6.11 Torsion of Noncircular Sections    
6.12 Torsion of Thin-Walled Tubes: Shear Flow   
 
Chapter 7 Equilibrium of Beams
 
7.1 Introduction   
7.2 Shear and Moment in Beams   
7.3 Graphical Method for Constructing Shear and Moment Diagrams   
7.4 Discontinuity Functions to Represent Load, Shear, and Moment   
 
Chapter 8 Bending
 
8.1 Introduction   
8.2 Flexural Strains    
8.3 Normal Stresses in Beams   
8.4 Analysis of Bending Stresses in Beams   
8.5 Introductory Beam Design for Strength   
8.6 Flexural Stresses in Beams of Two Materials   
8.7 Bending Due to Eccentric Axial Load  
8.8 Unsymmetric Bending  
8.9 Stress Concentrations Under Flexural Loadings
8.10 Bending of Curved Bars
 
Chapter 9 Shear Stress in Beams
 
9.1 Introduction   
9.2 Resultant Forces Produced by Bending Stresses   
9.3 The Shear Stress Formula   
9.4 The First Moment of Area Q   
9.5 Shear Stresses in Beams of Rectangular Cross Section   
9.6 Shear Stresses in Beams of Circular Cross Section   
9.7 Shear Stresses in Webs of Flanged Beams    
9.8 Shear Flow in Built-Up Members   
9.9 Shear Stress and Shear Flow in Thin-Walled Members   
9.10 Shear Centers of Thin-Walled Open Sections  
 
Chapter 10 Beam Deflections
 
10.1 Introduction   
10.2 Moment-Curvature Relationship   
10.3 The Differential Equation of the Elastic Curve  
10.4 Deflections by Integration of a Moment Equation   
10.5 Deflections by Integration of Shear-Force or Load Equations  
10.6 Deflections Using Discontinuity Functions   
10.7 Method of Superposition   
 
Chapter 11 Statically Indeterminate Beams
 
11.1 Introduction   
11.2 Types of Statically Indeterminate Beams  
11.3 The Integration Method   
11.4 Use of Discontinuity Functions for Statically Indeterminate Beams  
11.5 The Superposition Method   
 
Chapter 12 Stress Transformations
 
12.1 Introduction   
12.2 Stress at a General Point in an Arbitrarily Loaded Body  
12.3 Equilibrium of the Stress Element    
12.4 Plane Stress   
12.5 Generating the Stress Element  
12.6 Equilibrium Method for Plane Stress Transformations   
12.7 General Equations of Plane Stress Transformation   
12.8 Principal Stresses and Maximum Shear Stress   
12.9 Presentation of Stress Transformation Results  
12.10 Mohr’s Circle for Plane Stress  
12.11 General State of Stress at a Point   
 
Chapter 13 Strain Transformations
 
13.1 Introduction   
13.2 Plane Strain   
13.3 Transformation Equations for Plane Strain   
13.4 Principal Strains and Maximum Shearing Strain   
13.5 Presentation of Strain Transformation Results  
13.6 Mohr’s Circle for Plane Strain  
13.7 Strain Measurement and Strain Rosettes   
13.8 Generalized Hooke’s Law for Isotropic Materials   
13.9 Generalized Hooke’s Law for Orthotropic Materials
 
Chapter 14 Pressure Vessels
 
14.1 Introduction   
14.2 Thin-Walled Spherical Pressure Vessels   
14.3 Thin-Walled Cylindrical Pressure Vessels   
14.4 Strains in Thin-Walled Pressure Vessels   
14.5 Stresses in Thick-Walled Cylinders
14.6 Deformation in Thick-Walled Cylinders
14.7 Interference Fits
 
Chapter 15 Combined Loads
 
15.1 Introduction   
15.2 Combined Axial and Torsional Loads    
15.3 Principal Stresses in a Flexural Member   
15.4 General Combined Loadings    
15.5 Theories of Failure    
 
Chapter 16 Columns
 
16.1 Introduction   
16.2 Buckling of Pin-Ended Columns   
16.3 The Effect of End Conditions on Column Buckling    
16.4 The Secant Formula    
16.5 Empirical Column Formulas— Centric Loading    
16.6 Eccentrically Loaded Columns   
 
Chapter 17 Energy Methods
 
17.1 Introduction   
17.2 Work and Strain Energy   
17.3 Elastic Strain Energy for Axial Deformation
17.4 Elastic Strain Energy for Torsional Deformation   
17.5 Elastic Strain Energy for Flexural Deformation
17.6 Impact Loading   
17.7 Work-Energy Method for Single Loads  
17.8 Method of Virtual Work    
17.9 Deflections of Trusses by the Virtual-Work Method    
17.10 Deflections of Beams by the Virtual-Work Method    
17.11 Castigliano’s Second Theorem    
17.12 Calculating Deflections of Trusses by Castigliano’s Theorem    
17.13 Calculating Deflections of Beams by Castigliano’s Theorem    
 
Appendix A Geometric Properties of an Area
 
A.1 Centroid of an Area   
A.2 Moment of Inertia for an Area    
A.3 Product of Inertia for an Area   
A.4 Principal Moments of Inertia   
A.5 Mohr’s Circle for Principal Moments of Inertia   
 
Appendix B Geometric Properties of Structural Steel Shapes
Appendix C Table of Beam Slopes and Deflections
Appendix D Average  Properties of Selected Materials
Answers to Problems
Index 
 

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