Week 1: Mathematical preliminaries and notation; Concept of Traction vector; Concept of Stress tensor
Week 2: Stress tensor and its representation in Cartesian coordinate system; Transformation of stress matrix; Equations of equilibrium; Symmetry of stress tensor
Week 3: State of stress in simple cases; Principal stress components and principal planes; Maximizing shear component of traction; Mohr’s circle
Week 4: Stress invariants; Octahedral Plane; Decomposition of stress tensor; Concept of strain and strain tensor
Week 5: Longitudinal, shear and volumetric strains; Local infinitesimal rotation; Strain compatibility condition
Week 6: Linear stress-strain relation for isotropic bodies; Relation between material constants
Week 7: Stress and strain matrices in cylindrical coordinate system; Equations of equilibrium in cylindrical coordinate system
Week 8: Axisymmetric deformations: combined extension-torsion-inflation of a cylinder
Week 9: Bending of beams having symmetrical and non-symmetrical cross-section
Week 10: Shear center, Shear flow in thin and open cross-section beams; Euler Bernouli and Timoshenko beam theories; beam buckling
Week 11: Energy methods, Reciprocal relations, Castigliano’s theorem, Deflection of straight and curved beams using energy method
Week 12: Various theories of failure and their application
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