Mechanics of Solids | Department of Mechanical Engineering

Mechanics of Solids

UNIT-I Introduction: Concept of stress and strain, Hooke’s law, stress at a point, stresses and strains in bars subjected to axial loading. Elongation of Circular bar of uniformly varying cross section, Superposition theorem, Elongation of trapezoidal plate of constant thickness, Elastic Constants: Young’s modulus, Poisson ratio, modulus of rigidity, bulk modulus, Relationship between elastic constants, volumetric strain. Compound Stress: Stress on inclined plane, Principal stresses and principal planes, Mohr’s circle of stress.
UNIT-II Shear Force & Bending Moment: Beam & its type, type of loading, shear force & bending moment. SFD & BMD diagram for cantilever, simply supported beam for different types of loading, point load, uniformly distributed load, varying distributed load. Bending and Shear Stress in a Beam: Theory of Simple Bending, Bending Equation & its practical applications , section modulus, composite beams, beam of uniform strength, eccentric loading, middle third rule, middle quarter rule, shear stress in beam, rectangular, circular, I section.
UNIT-III Deflection of Beams: Differential equation of Flexure, Relationship between shear force, bending moment & deflection, double integration method, Macaulay’s method. Torsion of Shaft: Theory of torsion, polar modulus, power transmitted by shaft, torsional rigidity, shaft in series, shaft in parallel, tapered shaft
UNIT-IV Cylinders: Thin cylinders, stresses & strains in cylinders, Thick cylinders, Lame’s theory, compound cylinder, stresses & strain. Column: Classifications of column, nature of failure, Euler’s column theory, Column with both ends hinged, one end fixed and other free, both end fixed, one fixed and other hinged, effective lengths of columns.

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