Introduction: Components of stresses, equations of Equilibrium, Principal stresses and Mohr's diagram in three dimensions. Boundary conditions. Stress invariants, Octahedral stresses, Decomposition of state of stress, Stress transformation. Introduction to Strain : Deformation-Strain Displacement relations, Strain components, The state of strain at a point, Principal strain, Strain transformation, Compatibility equations, Cubical dilatation. Stress -Strain Relations and the General Equations of Elasticity: Generalized Hooke's. Formulation of
elasticity Problems. Existence and uniqueness of solution, Saint -Venant's principle, Principle of super position and reciprocal thermo. Two Dimensional Problems in Cartesian Co-Ordinates: Airy's stress function, investigation for beam problems. Use of Fourier series to solve two dimensional problems. Two Dimensional Problems in Polar Co-Ordinates: General equations, stress distribution symmetrical about an axis, Pure bending of curved bar, Strain components in polar co - ordinates, Rotating disk and cylinder, Concentrated
force on semi-infinite plane, Stress concentration around a circular hole in an infinite plate. Thermal Stresses: Introduction, Thermo-elastic stress -strain relations. Torsion of Prismatic Bars: Torsion of Circular and elliptical cross section bars, Soap film analogy, Membrane analogy, Torsion of thin walled open and closed tubes. Elastic Stability: Axial compression of prismatic bars, Elastic stability, Buckling load for column with constant cross section.