Mechanics of Materials

Define normal and shear stress, relate stress to strain through Hooke's law and elastic constants, and apply allowable-stress design with factors of safety.

Calculate deformations in axially loaded members, solve statically indeterminate bars using compatibility equations, and account for thermal expansion and stress concentrations.

Apply the torsion formula to circular shafts, calculate angle of twist and polar moment of inertia, and analyze power transmission and shear flow in thin-walled sections.

Determine bending stresses using the flexure formula, locate neutral axes and centroids of composite sections, and apply the parallel-axis theorem for beam design.

Calculate transverse shear stress distributions in beams using the shear formula and understand how shear varies across common cross-section shapes.

Transform plane stress and strain states to find principal values and maximum shear using Mohr's circle, and analyze thin-walled pressure vessels under combined loading.

Determine beam deflections and elastic curves using integration methods and apply strain-energy techniques to analyze deformations under various loading conditions.

Predict column buckling loads using Euler's formula, determine effective lengths for various end conditions, and assess column stability under axial compression.