Concepts of continuum, Stress at a point, Components of stress, Differential equations of equilibrium, Stress transformation, Principal stresses, Maximum shear stress, Stress invariants.
Strain at a point, Infinitesimal strain, Strain-displacement relations, Components of strain, Compatibility Equations, Strain transformation, Principal strains, Strain invariants, Measurement of surface strains, strain rosettes
Generalized Hooke’s Law, Stress-strain relationships, Equilibrium equations in terms of displacements and Compatibility equations in terms of stresses, Plane stress and plane strain problems, St. Venant’s principle, Principle of superposition, Uniqueness theorem, Airy’s stress function, Stress polynomials (Two Dimensional cases only).
Two-dimensional problems in rectangular coordinates, bending of a cantilever beam subjected to concentrated load at free end, effect of shear deformation in beams, Simply supported beam subjected to Uniformly distributed load. Two-dimensional problems in polar coordinates, strain-displacement relations, equations of equilibrium, compatibility equation, stress function.
Axisymmetric stress distribution - Rotating discs, Lame’s equation for thick cylinder, Effect of circular hole on stress distribution in plates subjected to tension, compression and shear, stress concentration factor.
Torsion: Inverse and Semi-inverse methods, stress function, torsion of circular, elliptical, triangular sections
Course outcomes:
After studying this course, students will be able to:
1. Ability to apply knowledge of mechanics and mathematics to model elastic bodies as continuum
2. Ability to formulate boundary value problems; and calculate stresses and strains
3. Ability to comprehend constitutive relations for elastic solids and compatibility constraints;
4. Ability to solve two-dimensional problems (plane stress and plane strain) using the concept of stress function.
Text Books:
1. S P Timoshenko and J N Goodier, “Theory of Elasticity”, McGraw-Hill International Edition, 1970.
2. Sadhu Singh, “Theory of Elasticity”, Khanna Publish ers, 2012
3. S Valliappan, “Continuum Mechanics - Fundamentals”, Oxford & IBH Pub. Co. Ltd., 1981.
4. L S Srinath, “Advanced Mechanics of Solids”, Tata - McGraw-Hill Pub., New Delhi, 2003.
Reference Books:
1. C. T. Wang, “Applied Elasticity”, Mc-Graw Hill Book Company, New York, 1953
2. G. W. Housner and T. Vreeland, Jr., “The Analysis o f Stress and Deformation”, California Institute of Tech., CA, 2012. [Download as per user policy from http://resolver.caltech.edu/CaltechBOOK:1965.001]
3. A. C. Ugural and Saul K. Fenster, “Advanced Strength and Applied Elasticity”, Prentice Hall, 2003.
4. Abdel-Rahman Ragab and Salah EldininBayoumi, “Engineering Solid Mechanics: Fundamentals and Applications”, CRC Press,1998