Applications of the principles of mechanics of materials have increased considerably over the last 25 years. Author takes its place as a standard text for civil, mechanical, and aerospace engineering majors, as well as for any other engineering discipline that includes mechanics of materials as a basic course. 

Vable’s distinct pedagogical approach translates into exceptional features that enhance student participation in learning. It assumes a complementary connection between intuition, experimental observation, and mathematical generalization, suggesting that intuitive development and understanding need not be at odds with mathematical logic, rigor, and generalization. This approach also emphasizes engineering practice without distracting from the main point of the text. 
With strong practical examples and real-life engineering problems praised by reviewers, Mechanics of Materials promises to provide the skills and principles that students need to organize, integrate, and make sense of the flood of information emerging in the world of modern engineering.

CONTENTS
PREFACE 
ACKNOWLEDGEMENTS 
A NOTE TO STUDENTS 
A NOTE TO THE INSTRUCTOR 
CHAPTER ONE STRESS
Section 1.1 Stress on a Surface 
Section 1.1.1 Normal Stress 
Section 1.1.2 Shear Stress 
Section 1.1.3 Pins 
Problem Set 1.1 
MoM in Action: Pyramids 
Section 1.1.4 Internally Distributed Force Systems 
Quick Test 1.1 
Problem Set 1.2 
Section 1.2 Stress at a Point 
Section 1.2.1 Sign convention 
Section 1.3 Stress Elements 
Section 1.3.1 Construction of a Stress Element for Axial Stress 
Section 1.3.2 Construction of a Stress Element for Plane Stress 
Section 1.4 Symmetric Shear Stresses 
Section 1.5* Construction of a Stress Element in 3-dimension 
Quick Test 1.2 
Problem Set 1.3 
Section 1.6* Concept Connector 
History: The Concept of Stress 
Section 1.7 Chapter Connector 
Points and Formulas to Remember 
CHAPTER TWO STRAIN
Section 2.1 Displacement and Deformation 
Section 2.2 Lagrangian and Eulerian Strain 
Section 2.3 Average Strain 
Section 2.3.1 Normal Strain 
Section 2.3.2 Shear Strain 
Section 2.3.3 Units of Average Strain 
Problem Set 2.1 
Section 2.4 Small-Strain Approximation 
Section 2.4.1 Vector Approach to Small-Strain Approximation 
MoM in Action: Challenger Disaster 
Section 2.5 Strain Components 
Section 2.5.1 Plane Strain 
Quick Test 1.1 
Problem Set 2.2 
Section 2.6 Strain at a Point 
Section 2.6.1 Strain at a Point on a Line 
Section 2.7* Concept Connector
Section 2.7.1 History: The Concept of Strain 
Section 2.7.2 Moiré Fringe Method 
Section 2.8 Chapter Connector 
Points and Formulas to Remember
Section 2.8 Chapter Connector 
Points and Formulas to Remember 
CHAPTER THREE MECHANICAL PROPERTIES OF MATERIALS
Section 3.1 Materials Characterization 
Section 3.1.1 Tension Test 
Section 3.1.2 Material Constants 
Section 3.1.3 Compression Test 
Section 3.1.4* Strain Energy 
Section 3.2 The Logic of The Mechanics of Materials 
Quick Test 3.1 
Section 3.3 Failure and Factor of Safety 
Problem Set 3.1 
Section 3.4 Isotropy and Homogeneity 
Section 3.5 Generalized Hooke’s Law for Isotropic Materials 
Section 3.6 Plane Stress and Plane Strain 
Quick Test 3.2 
Problem Set 3.2 
Section 3.7* Stress Concentration 
Section 3.8* Saint-Venant’s Principle 
Section 3.9* The Effect of Temperature 
Problem Set 3.3 
Section 3.10* Fatigue 
MoM in Action: The Comet / High Speed Train Accident 
Section 3.11* Nonlinear Material Models 
Section 3.11.1 Elastic–Perfectly Plastic Material Model 
Section 3.11.2 Linear Strain-Hardening Material Model 
Section 3.11.3 Power-Law Model 
Problem Set 3.4 
Section 3.12* Concept Connector 
Section 3.12.1 History: Material Constants 
Section 3.12.2 Material Groups 
Section 3.12.3 Composite Materials 
Section 3.13 Chapter Connector 
Points and Formulas to Remember 
CHAPTER FOUR AXIAL MEMBERS
Section 4.1 Prelude To Theory 
Section 4.1.1 Internal Axial Force 
Problem Set 4.1 
Section 4.2 Theory of Axial Members 
Section 4.2.1 Kinematics 
Section 4.2.2 Strain Distribution 
Section 4.2.3 Material Model 
Section 4.2.4 Formulas for Axial Members 
Section 4.2.5 Sign Convention for Internal Axial Force 
Section 4.2.6 Location of Axial Force on the Cross Section
Section 4.2.7 Axial Stresses and Strains 
Section 4.2.8 Axial Force Diagram 
Section 4.2.9* General Approach to Distributed Axial Forces 
Quick Test 4.1 
Problem Set 4.2 
Section 4.3 Structural Analysis 
Section 4.3.1 Statically Indeterminate Structures 
Section 4.3.2 Force Method, or Flexibility Method 
Section 4.3.3 Displacement Method, or Stiffness Method 
Section 4.3.4 General Procedure for Indeterminate Structure 
Problem Set 4.3 
MoM in Action: Kansas City Walkway Disaster 
Section 4.4* Initial Stress or Strain 
Section 4.5* Temperature Effects 
Problem Set 4.4 
Section 4.6* Stress Approximation 
Section 4.6.1 Free Surface
Section 4.6.2 Thin Bodies 
Section 4.6.3 Axisymmetric Bodies 
Section 4.6.4 Limitations 
Section 4.7* Thin-Walled Pressure Vessels 
Section 4.7.1 Cylindrical Vessels 
Section 4.7.2 Spherical Vessels 
Problem Set 4.5 
Section 4.8* Concept Connector 
Section 4.9 Chapter Connector 
Points and Formulas to Remember 
CHAPTER FIVE TORSION OF SHAFTS
Section 5.1 Prelude to Theory 
Section 5.1.1 Internal Torque
Problem Set 5.1 
Section 5.2 Theory of torsion of Circular shafts 
Section 5.2.1 Kinematics 
Section 5.2.2 Material Model 
Section 5.2.3 Torsion Formulas 
Section 5.2.4 Sign Convention for Internal Torque 
Section 5.2.5 Direction of Torsional Stresses by Inspection
Section 5.2.6 Torque Diagram 
Section 5.2.7* General Approach to Distributed Torque 
Quick Test 5.1 
MoM in Action: Drill, the Incredible Tool 
Problem Set 5.2 
Section 5.3 Statically Indeterminate Shafts 
Problem Set 5.3 
Section 5.4* Torsion of Thin-Walled Tubes 
Problem Set 5.4 
Section 5.5* Concept Connector 
Section 5.5.1 History: Torsion of Shafts 
Section 5.6 Chapter Connector 
Points and Formulas to Remember
CHAPTER SIX SYMMETRIC BENDING OF BEAMS
Section 6.1 Prelude to Theory 
Section 6.1.1 Internal Bending Moment 
Problem Set 6.1 
Section 6.2 Theory of Symmetric Beam Bending 
Section 6.2.1 Kinematics 
Section 6.2.2 Strain Distribution 
Section 6.2.3 Material Model 
Section 6.2.4 Location of Neutral Axis 
Section 6.2.5 Flexure Formulas 
Section 6.2.6 Sign Conventions for Internal Moment and Shear Force 
MoM in Action: Suspension Bridges 
Problem Set 6.2 
Section 6.3 Shear and Moment by Equilibrium 
Section 6.4 Shear and Moment Diagrams 
Section 6.4.1 Distributed Force 
Section 6.4.2 Point Force and Moments 
Section 6.4.3 Construction of Shear and Moment Diagrams
Section 6.5 Strength Beam Design 
Section 6.5.1 Section Modulus 
Section 6.5.2 Maximum Tensile and Compressive Bending Normal Stresses 
Quick Test 6.1 
Problem Set 6.3 
Section 6.6 Shear Stress In Thin Symmetric Beams 
Section 6.6.1 Shear Stress Direction 
Section 6.6.2 Shear Flow Direction by Inspection 
Section 6.6.3 Bending Shear Stress Formula 
Section 6.6.4 Calculating Qz 
Section 6.6.5 Shear Flow Formula 
Section 6.6.6 Bending Stresses and Strains 
Problem Set 6.4 
Section 6.7* Concept Connector 
Section 6.7.1 History: Stresses in Beam Bending 
Section 6.8 Chapter Connector 
Points and Formulas to Remember 
CHAPTER SEVEN DEFLECTION OF SYMMETRIC BEAMS
Section 7.1 Second-Order Boundary-Value Problem 
Section 7.1.1 Boundary Conditions 
Section 7.1.2 Continuity Conditions 
MoM In Action: Leaf Springs 
Problem Set 7.1 
Section 7.2 Fourth-Order Boundary-Value Problem 
Section 7.2.3 Boundary Conditions 
Section 7.2.4 Continuity and Jump Conditions 
Section 7.2.5 Use of Template in Boundary Conditions or Jump Conditions 
Problem Set 7.2 
MoM in Action: Skyscrapers 
Section 7.3* Superposition 
Section 7.4* Deflection by Discontinuity Functions
Section 7.4.1 Discontinuity Functions 
Section 7.4.2 Use of Discontinuity Functions 
Section 7.5* Area-Moment Method 
Problem Set 7.3 
Section *7.6 Concept Connector 
Section 7.6.1 History: Beam Deflection 
Section 7.7 Chapter Connector 
Points and Formulas to remember 
CHAPTER EIGHT STRESS TRANSFORMATION
Section 8.1 Prelude to Theory: The Wedge Method 
Section 8.1.1 Wedge Method Procedure 
Problem Set 8.1 
Section 8.2 Stress Transformation by Method of Equations 
Section 8.2.1 Maximum Normal Stress 
Section 8.2.2 Procedure for determining principal angle and stresses 
Section 8.2.3 In-Plane Maximum Shear Stress 
Section 8.2.4 Maximum Shear Stress 
Quick Test 8.1 
Section 8.3 Stress Transformation by Mohr’s Circle 
Section 8.3.1 Construction of Mohr’s Circle 
Section 8.3.2 Principal Stresses from Mohr’s Circle 
Section 8.3.3 Maximum In-Plane Shear Stress 
Section 8.3.4 Maximum Shear Stress 
Section 8.3.5 Principal Stress Element 
Section 8.3.6 Stresses on an Inclined Plane 
Quick Test 8.2 
MoM in Action: Sinking of Titanic 
Problem Set 8.2 
Quick Test 8.3 
Section *8.4 Concept Connector 
Section 8.4.1 Photoelasticity 
Section 8.5 Chapter Connector 
Points and Formulas to Remember 
CHAPTER NINE STRAIN TRANSFORMATION
Section 9.1 Prelude to Theory: The Line Method 
Section 9.1.1 Line Method Procedure 
Section 9.2.2 Visualizing Principal Strain Directions 
Problem Set 9.1 
Section 9.2 Method of Equations 
Section 9.2.1 Principal Strains 
Section 9.2.2 Visualizing Principal Strain Directions 
Section 9.2.3 Maximum Shear Strain 
Section 9.3 Mohr’s Circle 
Section 9.3.1 Construction of Mohr’s Circle for Strains 
Section 9.3.2 Strains in a Specified Coordinate System 
Quick Test 9.1 
Section 9.4 Generalized Hooke’s Law in Principal Coordinates 
Problem Set 9.2
Section 9.5 Strain Gages 
Quick Test 9.2 
MoM in Action: Load Cells 
Problem Set 9.3 
Section *9.6 Concept Connector 
Section 9.6.1 History: Strain Gages 
Section 9.7 Chapter Connector 
Points and Formulas to Remember 
CHAPTER TEN DESIGN AND FAILURE
Section 10.1 Combined Loading 
Section 10.1.1 Combined Axial and Torsional Loading 
Section 10.1.2 Combined Axial, Torsional, and Bending Loads about z Axis 
Section 10.1.3 Extension to Symmetric Bending about y Axis 
Section 10.1.4 Combined Axial, Torsional, and Bending Loads about y and z Axes 
Section 10.1.5 Stress and Strain Transformation 
Section 10.1.6 Summary of Important Points in Combined Loading 
Section 10.1.7 General Procedure for Combined Loading 
Problem Set 10.1 
Section 10.2 Analysis and Design of Structures 
Section 10.2.1 Failure Envelope 
Problem Set 10.2 
MoM in Action: Biomimetics 
Section 10.3 Failure Theories 
Section 10.3.1 Maximum Shear Stress Theory 
Section 10.3.2 Maximum Octahedral Shear Stress Theory 
Section 10.3.3 Maximum Normal Stress Theory 
Section 10.3.4 Mohr’s Failure Theory 
Problem Set 10.3 
Section 10.4 Concept Connector 
Section 10.4.1 Reliability 
Section 10.4.2 Load and Resistance Factor Design (LRFD) 
Section 10.5 Chapter Connector 
Points and Formulas to Remember 
CHAPTER ELEVEN STABILITY OF COLUMNS
Section 11.1 Buckling Phenomenon 
Section 11.1.1 Energy Approach 
Section 11.1.2 Eigenvalue Approach 
Section 11.1.3 Bifurcation Problem 
Section 11.1.4 Snap Buckling 
Section 11.1.5 Local Buckling 
Section 11.2 Euler Buckling 
Section 11.2.1 Effects of End Conditions
Section 11.3* Imperfect Columns 
Quick Test 11.1 
Problem Set 11.2 
MoM in Action: Collapse of World Trade Center 
Section *11.4 Concept Connector 
Section 11.4.1 History: Buckling
Section 11.5 Chapter Connector 
Points and Formulas to Remember 
APPENDIX A STATICS REVIEW
Section A.1 Types of Forces and Moments 
Section A.1.1 External Forces and Moments 
Section A.1.2 Reaction Forces and Moments 
Section A.1.3 Internal Forces and Moments 
Section A.2 Free-Body Diagrams 
Section A.3 Trusses 
Section A.4 Centroids 
Section A.5 Area Moments of Inertia 
Section A.6 Statically Equivalent Load Systems 
Section A.6.1 Distributed Force on a Line 
Section A.6.2 Distributed Force on a Surface 
Quick Test A.1 
Static Review Exam 1 
Static Review Exam 2 
Points to Remember 
APPENDIX B ALGORITHMS FOR NUMERICAL METHODS
Section B.1 Numerical Integration 
Section B.1.1 Algorithm for Numerical Integration 
Section B.1.2 Use of a Spreadsheet for Numerical Integration 
Section B.2 Root of a Function 
Section B.2.1 Algorithm for Finding the Root of an Equation 
Section B.2.2 Use of a Spreadsheet for Finding the Root of a Function 
Section B.3 Determining Coefficients of a Polynomial 
Section B.3.1 Algorithm for Finding Polynomial Coefficients 
Section B.3.2 Use of a Spreadsheet for Finding Polynomial Coefficients 
APPENDIX C REFERENCE INFORMATION
Section C.1 Support Reactions 
Table C.1 Reactions at the support 
Section C.2 Geometric Properties of Common Shapes 
Table C.2 Areas, centroids, and second area moments of inertia 
Section C.3 Formulas For Deflection And Slopes Of Beams 
Table C.3 Deflections and slopes of beams 
Section C.4 Charts of Stress Concentration Factors 
Figure C.4.1 Finite Plate with a Central Hole 
Figure C.4.2 Stepped axial circular bars with shoulder fillet 
Figure C.4.3 Stepped circular shafts with shoulder fillet in torsion 
Figure C.4.4 Stepped circular beam with shoulder fillet in bending 
Section C.5 Properties Of Selected Materials 
Table C.4 Material properties in U.S. customary units 
Table C.5 Material properties in metric units 
Section C.6 Geometric Properties Of Structural
Table C.6 Wide-flange sections (FPS units)
Table C.7 Wide-flange sections (metric units) 
Table C.8 S shapes (FPS units) 
Table C.9 S shapes (metric units) 
Section C.7 Glossary 
Section C.8 Conversion Factors Between U.S. Customary System (USCS) and the Standard International (SI) System 
Section C.9 SI Prefixes 
Section C.10 Greek Alphabet 
APPENDIX D SOLUTIONS TO STATIC REVIEW EXAM 
APPENDIX E ANSWERS TO QUICK TESTS 
APPENDIX H ANSWERS TO SELECTED PROBLEMS 
FORMULA SHEET