Preface
Chapter 1: Mechanics of Materials
1.1 Statics
1.2 Vector algebra
1.3 Newton’s laws and equilibrium equations
1.4 Boundary conditions and static determinacy
1.5 Internal forces
1.6 Geometry
1.6.1 Centroids, centers of mass, and centers of gravity
1.6.2 First and second area moments
1.7 Deformable body mechanics
1.7.1 Stress and strain
1.7.2 Average stress and strain
1.7.3 Stress concentrations and Saint-Venant’s principle
1.7.4 Mechanical properties of materials
1.7.5 Elasticity and plasticity
1.7.6 Generalized Hooke’s law
1.7.7 Strain energy
1.7.8 Ductility
1.7.9 Directional properties
1.7.10 Thermal strains
1.8 Analysis and surrogate models
1.8.1 Note on applied forces
1.8.2 Differential models
1.8.3 Normal strain
1.8.4 Shear strain
1.8.5 Equilibrium
Chapter 2: Bar Analysis
2.1 Fundamentals of bar models
2.2 Deformation of bars
2.2.1 Internal forces
2.2.2 Applications of the bar equation
2.3 Statically indeterminate bars
2.4 Strain energy
2.5 Thermal effects
2.6 Superposition
2.7 Differential relation for bars
2.8 Chapter summary
2.8.1 List of symbols
Chapter 3: Shaft Analysis
3.1 Fundamentals of shaft models
3.2 Torsion of circular shafts
3.2.1 Internal torques
3.2.2 Application of torsion formula
3.3 Statically indeterminate shafts
3.4 Transmission of power
3.4.1 Strain energy
3.5 Thin-walled tubes
3.6 Chapter summary
3.6.1 List of symbols
Chapter 4: Beam Analysis
4.1 Fundamentals of beam models
4.1.1 Vocabulary and beam anatomy
4.2 Bending of beams
4.3 Normal stress in beams
4.3.1 Assumptions
4.3.2 Non-prismatic beams
4.4 Non-uniform bending
4.4.1 Transverse shear stress
4.4.1.1 Sign convention
4.4.2 Shear stress in non-rectangular sections
4.4.3 Shear stress in composite sections
4.5 Internal shear force and bending moment
4.6 Shear and moment diagrams
4.7 Euler-Bernoulli beam theory
4.7.1 Applications
4.7.2 Boundary and continuity conditions
4.8 Beam tables
4.9 Chapter summary
4.9.1 List of symbols
Chapter 5: Two-Dimensional Loading
5.1 Fundamentals of plane stress models
5.1.1 Hooke’s law
5.2 Plane stress transformations
5.3 Principal and max shear stresses
5.3.1 Triaxial stress
5.4 Mohr’s circle
5.4.1 General 3D problems
5.5 Thin-walled pressure vessels
5.5.1 Cylindrical
5.5.2 Spherical
5.6 Combined loading
5.6.1 Stress under combined loading
5.6.1.1 Determination of reactions
5.6.1.2 Deconstruction of geometry
5.6.1.3 Decomposition of loads
5.6.1.4 Application of surrogate models
5.6.1.5 Superposition
5.6.2 Deformation under combined loading
5.6.3 Discussion
5.7 Plane strain
5.7.1 Strain gauges
5.8 Chapter summary
5.8.1 List of symbols
Appendix A: Planar Geometry
A.1 Rectangle
A.2 Triangle
A.3 Regular polygon
A.4 Circle
A.5 Circular sector
A.6 Circular segment
A.7 Ellipse
A.8 Thin circular arc
Appendix B: Material Properties
Appendix C: Beam Tables
C.1 Cantilever with couple
C.2 Cantilever with point force
C.3 Cantilever with uniform load