SOM1 (B-TECH Mechanical Engineering 4th)

Unit 1 Simple Stresses & Strains: Concept & types of Stresses and strains, Poison’s ratio, stresses and

strain in simple and compound bars under axial loading, stress strain diagrams, Hooks law, elastic

constants & their relationships, temperature stress & strain in simple & compound bars under

axial loading, Numerical.

Unit II Compound Stresses & Strains: Concept of surface and volumetric strains, two dimensional stress

system, conjugate shear stress at a point on a plane, principle stresses & strains and principalplanes,

Mohr’s circle of stresses, Numerical.

Unit III Shear Force & Bending Moments: Definitions, SF & BM diagrams for cantilevers, simply

supported beams with or without over-hang and calculation of maximum BM & SF and the point

of contra-flexure under (i) concentrated loads, (ii) uniformly distributed loads over whole span or

a part of it, (iii) combination of concentrated loads and uniformly distributed loads, (iv)

uniformly varying loads and (v) application of moments, relation between the rate of loading, the

shear force and the bending moments, Problems.

Unit IV Torsion Of Circular Members: Torsion of thin circular tube, Solid and hollow circular shafts,

tapered shaft, stepped shaft & composite circular shafts, combined bending and torsion,

equivalent torque, effect of end thrust. Numericals.

Unit V Bending & Shear Stresses in Beams: Bending stresses in beams with derivation & application to

beams of circular, rectangular, I,T and channel sections, composite beams, shear stresses in

beams with combined bending, torsion & axial loading of beams. Numericals.

Unit VI Columns & Struts: Column under axial load, concept of instability and buckling, slenderness

ratio, derivation of Euler’s formulae for the elastic buckling load, Eulers, Rankine, Gordom’s

formulae Johnson’s empirical formula for axial loading columns and their applications, eccentric

compression of a short strut of rectangular & circular sections, Numerical.

Unit VII Slope & Deflection: Relationship between bending moment, slope & deflection, Mohr’s theorem,

moment area method, method of integration, Macaulay’s method, calculations for slope and

deflection of (i) cantilevers and (ii) simply supported beams with or without overhang under

concentrated load, Uniformly distributed loads or combination of concentrated and uniformly

distributed loads, Numerical.

Unit VIII Fixed Beams: Deflections, reactions and fixing moments with SF & BM calculations & diagrams

for fixed beams under (i) concentrated loads, (ii) uniformly distributed load and (iii) a

combination of concentrated loads & uniformly distributed load.