Strength of Materials

Stress, strain and deformation of beams, shafts and columns. How structural members respond to load: axial stress and strain, shear, bending of beams, torsion, deflection limits and column buckling — the checks behind every beam, column and connection in a building or bridge.

• Stress — Stress is internal force per unit area. Learn normal (tensile/compressive) stress, bearing stress, allowable stress and factor of safety, stress concentrations, and thin-walled pressure vessels.
• Strain — Strain is deformation per unit length. Learn normal and shear strain, microstrain, the stress–strain curve, ductility, lateral strain and Poisson's ratio, and how strain gauges measure it.
• Bending — Bending creates tension on one side of a beam and compression on the other. Learn the flexure formula σ = My/I, neutral axis, section modulus, beam selection and combined bending and axial load.
• Torsion — Torsion is twisting. Learn shear stress τ = Tr/J, angle of twist θ = TL/GJ, power transmission P = Tω, solid vs hollow shafts, and designing shafts for strength and stiffness.
• Shear — Shear stress acts parallel to a surface. Learn direct shear in pins and bolts (single and double shear), punching, shear strain and modulus, and the shear-stress distribution in beams (VQ/Ib).
• Deflection — Deflection is how far a beam moves under load. Learn the elastic curve EI·y″ = M, standard formulas for cantilevers and simply supported beams, superposition, and serviceability limits.
• Buckling — Slender members in compression can suddenly bow sideways at loads far below their crushing strength. Learn Euler's critical load, effective length, slenderness ratio, Johnson's formula and design against instability.