Strength of Materials
Strength of Materials for GATE Mechanical and Civil Engineering, one topic per lesson: the theory in plain words, the formulas, a solved example, and GATE-style questions (MCQ, MSQ and NAT) whose numerical answers are recomputed by a program when the site is built.
1Stress and Strain
- Stress, Strain and Elastic ConstantsNormal and shear stress, strain, Hooke's law, the stress-strain curve, elastic constants E, G, K and Poisson's ratio, bars of varying section, composite bars and thermal stress.
- Mohr's Circle, Principal Stress, Thin CylindersStress transformation, principal stresses and planes, maximum shear stress, Mohr's circle, strain gauges, and hoop and longitudinal stresses in thin cylinders and spheres.
2Beams
- Shear Force and Bending Moment DiagramsSign conventions, shear force and bending moment diagrams for cantilevers and simply supported beams under point loads, UDL and moments, the load-shear-moment relations and points of contraflexure.
- Bending and Shear Stresses in BeamsThe flexure formula M/I = σ/y = E/R, section modulus, beams of uniform strength, shear stress distribution in rectangular and circular sections, and the shear centre.
- Deflection of BeamsThe elastic curve EI y'' = M, double integration, Macaulay's method, moment-area theorems, and standard slope and deflection results for cantilevers and simply supported beams.
3Torsion and Columns
- Torsion of Shafts and SpringsThe torsion equation T/J = τ/r = Gθ/L, solid and hollow shafts, power transmission, combined bending and torsion, and close-coiled helical springs in series and parallel.
- Columns, Strain Energy and Theories of FailureEuler buckling load and effective lengths, slenderness ratio and Rankine's formula, strain energy, impact loading, Castigliano's theorem, and the theories of failure.