Chapter 1

Analysis of Stress and Strain

Concept of stress and strain at a point

medium • 1 min read

Stress and strain tensors

medium • 2 min read

Principal stresses and strains, invariants

medium • 3 min read

Mohr's circle for 3D stress and strain

medium • 4 min read

Equations of equilibrium and compatibility conditions

medium • 5 min read

Chapter 2

Constitutive Relations

Generalized Hooke's Law

medium • 1 min read

Elastic symmetry and material properties

medium • 2 min read

Isotropic, orthotropic, and anisotropic materials

medium • 3 min read

Strain energy density function

medium • 4 min read

Theories of failure and yield criteria

medium • 5 min read

Chapter 3

Two-Dimensional Problems in Elasticity

Plane stress and plane strain conditions

medium • 1 min read

Airy's stress function

medium • 2 min read

Polynomial solutions for 2D problems

medium • 3 min read

Thick cylinders and rotating disks

medium • 4 min read

Stress concentration around holes

medium • 5 min read

Chapter 4

Torsion of Non-Circular Shafts

St. Venant's torsion theory

medium • 1 min read

Prandtl's stress function approach

medium • 2 min read

Torsion of elliptical and rectangular bars

medium • 3 min read

Membrane analogy

medium • 4 min read

Torsion of thin-walled multi-cell sections

medium • 5 min read

Chapter 5

Bending of Curved Beams and Plates

Winkler-Bach formula for curved beams

medium • 1 min read

Stresses in crane hooks and rings

medium • 2 min read

Symmetrical bending of thin rectangular plates

medium • 3 min read

Navier's and Levy's solutions for plates

medium • 4 min read

Membrane theory of thin shells

medium • 5 min read