Mechanics of materials

Mechanics of materials — also called strength of materials — studies how solid bodies respond internally to external loads. Where statics treats bodies as rigid, mechanics of materials asks what happens inside the material: how much it stretches, twists, or bends, and when it breaks.

The core quantities are stress and strain. Stress (σ) is internal force per unit area — axial stress is σ = P/A for a load P on cross-sectional area A. Strain (ε) is normalized deformation — change in length divided by original length. For elastic materials the two are proportional through Hooke's law, σ = Eε, where E is the modulus of elasticity that measures a material's stiffness. Loading a member beyond its yield strength causes permanent deformation, and the stress-strain diagram maps the full journey from elastic behavior through yielding to ultimate strength and fracture.

Each loading mode has its own analysis. Axial members carry tension or compression; shafts in torsion develop shear stress τ = Tc/J; and beams in bending develop flexural stress σ = Mc/I, maximum at the outer fibers, along with transverse shear. Combined loadings are resolved with stress transformation and Mohr's circle to find principal stresses, and slender columns are checked against Euler buckling. Design wraps these results in a factor of safety comparing allowable stress to expected stress.

The FE Civil exam includes mechanics of materials as a major topic. Expect problems computing stresses and deformations in axial members, shafts, and beams, reading stress-strain diagrams, applying Mohr's circle, and checking columns for buckling.