501402: ADVANCED SOLID MECHANICS
Teaching Scheme: Examination Scheme:
Lectures : 3 Hrs/Week Theory Paper : 100 Marks
Duration 4 Hrs.
Unit 1: Analysis of Stress and Strains
Concept of stress at a point, stress tensor, stress on inclined plane, stress components on a rectangular parallelepiped in Cartesian coordinate system, derivation of stress equilibrium equations, transformation of stresses, stress invariants. The state of strain at a point, strain displacement relations, strain compatibility condition and stress compatibility conditions.
Unit 2: Stress-Strain Relationship
Generalized Hook’s law for Isotropic, Orthotropic, Transversely Isotropic materials, plane stress, plane strain and axisymmetric problems, Problems in 2D Cartesian coordinate system, Airy’s stress function, bending of beams.
Unit 3: Polar Coordinate System
Relationship between Cartesian and Polar coordinate system, Equilibrium quations, Strain displacement relations, Stress-strain relationship, Strain-displacement relationship for plane stress and plane strain conditions, Bending of curved bar, Stress concentration problems.
Unit 4: Axisymmetric Problems
Equilibrium equations, Strain displacement relations, Stress-strain relationship, Stresscompatibility equations, Plane stress and Plane strain conditions. Cylinders subjected to internal and external pressure.
Unit 5: Torsion
Assumptions and Torsion equation for general prismatic solid bars, Warping of Non-circular sections and St. Venant’s theory. Prandtle’s stress function approach. Torsion of Circular, Elliptical and Triangular cross-section bar. Torsion of thin-walled structures by membrane analogy, Torsion of rolled sections and shear flow.
Unit 6: Beams on Elastic Foundation
Differential equation, Infinite beams with concentrated load, concentrated moment, and finite uniformly distributed load. Semi-Infinite beams with free end subjected to finite uniformly distributed load, hinged end. Finite beams with free end and hinged end.
1. Timoshenko and Goodier - Theory of Elasticity, McGraw-Hill Publications
2. S. Crandall, N. Dahl and T. Lardner - Mechanics of Solids, McGraw Hill Publications
3 Wang - Applied Elasticity, Dover Publications
4. Irving Shames, Mechanics of deformable solids, Prentice Hall
5. Scholer, Elasticity in Engineering, McGraw-Hill Publications
6. Sadhu Singh – Theory of Elasticity, Khanna Publishers
7. L.S.Sreenath – Advanced Mechanics of Solids, Tata McGraw-Hill Publications
8. S M A Kazimi – Solid Mechanics, Tata McGraw-Hill Publications
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