Slope at free end of cantilever with UDL = wL³/(3EI). Deflection at free end = wL⁴/(8EI).

Maximum 3 members can be cut in a 2D truss to maintain a determinate section with 3 equilibrium equations available.

For a simply supported beam with central point load, maximum bending moment occurs at the center (L/2) and equals PL/4.

Superposition principle applies only to linear elastic systems with small displacements where strain-displacement and stress-strain relationships are linear.

A hinged/pin support prevents translation in both horizontal and vertical directions (2 restraints), thus has 2 unknown reactions (Hx and Vy). Rotation is free.

In method of sections for trusses, we can cut maximum 3 members (one truss has 3 equilibrium equations: ΣFx=0, ΣFy=0, ΣM=0) to find member forces.

Flexibility method removes redundant reactions/members equal to degree of indeterminacy to create a primary determinate structure, then applies compatibility equations.

Castigliano's second theorem: ∂U/∂P = deflection at point of load application. U is strain energy and P is the applied load.

Virtual work method applies imaginary (virtual) displacements to calculate real deflections and support reactions in statically determinate and indeterminate structures.

For a cantilever beam, maximum bending moment always occurs at the fixed support where the reaction moment is maximum. BM = W × L = 20 × 5 = 100 kN-m at fixed end.