MECHANICS OF SOLIDS

Tension, compression & shear

Types of external loads, self weight, internal stresses, normal and shear stresses, strain, Hooke’s law, Poisson’s ratio, relationship between elastic constants, stress strain diagrams working stress, elongation of bars of constant and varying sections, statically indeterminate problems in tension and compression, assembly and thermal stresses, strain energy in tension, compression and shear.

Analysis of stress and strain

Stress on inclined planes for axial and biaxial stress fields, principal stresses, Mohr’s circle of stress, principal strains, strain rosette, principal stress strain problem as an eigenvalue problem.

Bending moment and shear force

Different types of beams, shear force and bending moment diagrams for simply supported overhanging and cantilever beams, relationship connecting intensity of loading, shearing force and bending moment, shear force and bending moment diagrams for statically determinate plane frames.

Stresses in laterally loaded symmetrical beams

Theory of simple bending, limitations, bending stresses in beams of different cross sections, moment of resistance, beams of uniform strength, beams of two materials, shearing stresses in bending, principal stresses in bending, strain energy due to bending.

Unsymmetrical bending

Shear flow, shear centre, determination of shear centre for simple sections

Theory of columns

Axial loading of short strut, long columns, differential equation of the elastic curve, Euler’s formula, eccentric loading, direct and bending stresses, buckling load as an eigenvalue problem

Torsion

Torsion of circular solid and hollow shafts, power transmission, strain energy in shear and torsion, close coiled and open coiled helical springs

Thin and thick cylinders

Lame’s equation, stresses in thick cylinders due to internal and external pressures, compound cylinders, shrink fit, wire wound pipes and cylinders