Syllabus : 

Basic equations of Elasticity, Stress at a point with respect to a plane - normal and tangential components of stress - stress tensor - Cauchy’s equations - stress transformation - principal stresses and planes - strain at a point - strain tensor - analogy between stress and strain tensors - constitutive equations - generalized Hooke’s law - relation among elastic constants – equations of equilibrium -strain-displacement relations . Compatibility conditions - boundary conditions - Saint Venant’s principle for end effects –uniqueness condition. 2-D problems in elasticity. Plane stress and plane strain problems – Airy’s stress function – solutions by polynomial method – solutions for bending of a cantilever with an end load and bending of a beam under uniform load. Equations in polar coordinates - Lame’s problem - stress concentration problem of a small hole in a large plate. Axisymmetric problems - thick cylinders - interference fit - rotating discs. Special problems in bending: Unsymmetrical bending - shear center - curved beams with circular and rectangular cross-section .Energy methods in elasticity: Strain energy of deformation - special cases of a body subjected to concentrated loads, due to axial force, shear force, bending moment and torque – reciprocal relation -Maxwell reciprocal theorem - Castigliano’s first and second theorems - virtual work principle -minimum potential energy theorem - complementary energy .Torsion of non-circular bars: Saint Venant’s theory - Prandtle’s method - solutions for circular and elliptical cross-sections - membrane analogy - torsion of thin walled open and closed sections- shear flow