Syllabus

Syllabus
Prerequisites: Undergraduate level courses on strength of materials & structural analysis.
Module I: Analysis of Stress (8 hours)
Introduction, Stress components at an arbitrary plane, Principal stresses, Stress invariants, Construction of Mohr’s circle, Differential equation of equilibrium, Plane stress problem, Boundary conditions.
Module II: Analysis of Strain (6 hours)
Introduction, Principal strains, Strain deviator and its invariants, Plane strain problem, Compatibility conditions.
Module III: Stress-strain relations (4 hours)
Stress-strain relations: Introduction, Generalized Hooke’s law, Stress-strain relations for isotropic and orthotropic materials, Displacement equations of equilibrium.
Module IV: Two Dimensional Problems in Elasticity (6 hours)
Stress function, Solution by polynomials, Saint-Venant’s Principle, Concentrated force acting on a beam, Effect of circular holes on stress distribution of a plate, Thick-walled cylinder subjected to internal and external pressure, Rotating disks of uniform thickness.
Module V: Torsion (6 hours)
Introduction, Torsion of general prismatic bars, Torsion of circular and elliptical bars, Torsion of equilateral triangular bars, Membrane analogy, Torsion of a thin-walled tubes, Torsion of a thin-walled multiple-cell closed section, Torsion or rolled sections.
Module VI: Introduction to Plasticity (6 hours)
Introduction, Nonlinear stress-strain behavior, Theories of failure, Criterion of yielding, Strain-hardening postulates, Rule of plastic flow.

To make students understand the concepts of stresses, strains and stress-strain relationships, basic theory of elasticity and plasticity and failure criteria.

To expose students to two dimensional problems in Cartesian and polar coordinates .

To make student familiar with problem formulations and solution techniques.

To familiarize students with the principle of torsion of prismatic bars of non circular sections.

1. Students will be able to understand the concepts and theories about the stress at a point for 2D and 3D elasticity problems.
2. Students will learn about the concepts of strain and different material constitutive relations for linear elastic systems.
3. Students will be able to appreciate the broader 2D multidisciplinary context of the underlying theory of elasticity.
4. Students will be able to find solutions for practical problems involving torsion in the theory of elasticity.
5. Students will be able to learn applications of theories of failure, the criterion of yielding & plasticity theorems to engineering analysis and design.

S P Timoshenko and J N Goodier, Theory of Elasticity, McGraw Hill,2006

L S Srinath, Advanced Mechanics of Solids, Tata McGraw-Hill

Martin H. Saad, Elasticity: Theory, Applications, and Numerics, Academic Press Inc 3rd edition, 2014

Chen and Han, Plasticity for Structural Engineers, Springer Verlag