**Description:**

Also known as Intermediate Solid Mechanics, this is an advanced level course on Solid Mechanics.This course provides Mechanical Engineering students with an awareness of various responses exhibited by solid engineering materials when subjected to mechanical and thermal loadings; an introduction to the physical mechanisms associated with design-limiting behavior of engineering materials, especially stiffness, strength, toughness, and durability; an understanding of basic mechanical properties of engineering materials, testing procedures used to quantify these properties, and ways in which these properties characterize material response; quantitative skills to deal with materials-limiting problems in engineering design; and a basis for materials selection in mechanical design.

**Course Contents:**

- Introduction and mathematical preliminaries. Index notation.
- Displacements in beams using different methods. Energy methods: minimum potential energy, Castigliano, principle of virtual work, Rayleigh-Ritz, reciprocal theorem, uniqueness.
- Plane problems: Airy stress function, 2d polar coordinates,axisymmetric problems, curved beams, thermal expansion.
- Elastic stability: energy approach to beam buckling, beam-columns with transverse loads, secant formula.
- Torsion of non-circular prisms, thin closed and open-walled sections, non-prismatic circular shaft, multiply connected sections.

(Fracture mechanics: approach to brittle cracks, mode III crack and stress intensity factor, mixed-mode fracture, stable and unstable crack growth. Experimental mechanics: strain gages and photo-elasticity)

**Motivation**:

Mechanics of solids has direct applications in product development. In any industrial or research based application, whenever one is required to develop a product or even a small machine part design of any component should be done so that the maximum stress is minimized. For this, one must have a clear understanding of the stresses and strains on the body. This course will develop the basics of calculating the stresses/ strains for different types of bodies and forces.

**Useful resources**:

While it is a good practice to refer to textbooks or video lectures besides your class notes, it is also important to remember that these sources may not be flawless. Reference material should only be used as a tool to strengthen concepts and not as a substitute for your class notes.

**Books**:

1. Crandall, S.H., Dahl, N.C. and Lardner, T.J., An Introduction to the Mechanics of Solids

2. Engineering Mechanics of Solids, E. Popov

3. Theory of Elasticity, S. P. Timoshenko and J. N. Goodier

4. Mechanics of Materials, J. M. Gere and S. P. Timoshenko

5. Elasticity Theory Applications, and Numerics, M. H. Sadd

**Internet Resources**:

## a) Prof.Dnyanesh Pawaskar ‘s Blog : http://solidmechanics2.blogspot.com/

**b) MIT Open Courses : 1. mechanics-and-materials-ii-spring-2004/
2. mechanics-materials-i-fall-2006/
c) Applied Mechanics of Solids, Allan F. Bower**

Interesting Trivia:

- Pin-Pin and Pin-Clamped Buckling Demonstration
- A Cantilevered Glass House
- Stress & Strain – Concentration
- Massive waves on a bridge
- Failure Analysis of WTC
- Analysis of a Cantilever Beam
- Buckling of an axially compressed cylindrical shell

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