"Mechanics of Materials" by Madhukar Vable

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

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