Foundations: Bending Moment & Strain Energy

Calculate support reactions for a statically determinate beam under point, uniform (UDL), and varying (UVL) loads.

Write the internal bending moment expression, M(x), for beam segments under various load types by making sectional cuts.

Define bending strain energy (U) and state its formula: U = ∫ M²/(2EI) dx.

State Castigliano's Second Theorem and its practical application for beam deflections: δ = ∫ (1/EI) * M * (∂M/∂P) dx.

Set up the moment expression M(x) and its partial derivative ∂M/∂R for a simple indeterminate beam where R is the redundant reaction.