Mechanics of Solids

The course introduces the fundamental concept of stress-strain behavior of ductile and brittle material, yield stress, and ultimate stress. Then, the participants are introduced to the state of stress in 2D and 3D space, stress transformation, eigen analysis for principal stress, and principal plane. It is followed by the definition of strain tensor, compatibility conditions, and their role in strain-displacement relation, principal strain, and different elastic constants for homogeneous, isotropic, and elastic material. Once the 3D stress and strain fields are explained, plane stress and plane strain problems are discussed along with the construction of Mohr's circle with numerical examples. With this background of 3D stress and strain field, different failure theories are explained with examples. Then, the bending and shear stress distribution across different cross-sections are explained, followed by the Euler-Bernoulli theory for beams undergoing bending deformation. A series of examples are presented at this stage to correlate the theory developed for different engineering problems. Then, the concepts of pure torsion and torsional rigidity are introduced, followed by energy formulation, i.e., the principle of virtual work and Castigliano's theorem for determinate and indeterminate structures. Finally, the column buckling theory, Euler's critical buckling load for different boundary conditions, and the beam-column problem formulation are covered.