Mechanics of Solids (PCMET302) Syllabus

Introduction to analysis of deformable bodies. Types of external loads — normal, shear, bending and bearing stress, linear and shear strains. Hooke's law, stress-strain diagrams, concepts of isotropy, orthotropy, anisotropy. Young's modulus, bulk modulus and rigidity modulus. Poisson's ratio, relationship between elastic constants.

Deformation in axially loaded bars — uniform cross section, varying cross section, dissimilar materials, principle of superposition. Thermal effects — simple and composite bars. Torsion: shafts, torsion theory of elastic circular bars, assumptions and limitations, polar modulus, torsional rigidity, shaft design for torsional load. Beams: classification, diagrammatic conventions, differential equations between load/shear force/bending moment, SFD and BMD of cantilever and simply supported beams with point load/UDL, point of inflection.

Stresses in Beams: pure bending, flexure formula for beams, section modulus, flexural rigidity (derivation and problems for rectangular section only). Deflection of Beams: moment-curvature relation, double integration method, Macaulay's method.

Stress on an inclined plane due to uniaxial and biaxial stress, stress on an inclined plane due to two normal stresses accompanied by shear stresses, principal planes and stresses, Mohr's circle of stress. Buckling and stability of long columns: Euler's buckling/crippling load for different end conditions, Euler equation derivation (both ends hinged only), Rankine's formula.