Virtual work principle: For equilibrium, ΣδW_external + ΣδW_internal = 0. External work by real forces through virtual displacements equals internal work.

For a 2D truss: m = number of members, n = number of joints. Condition m = 2n - 3 ensures static determinacy (3 reactions for 2D frame).

Influence line for shear force in a segment without concentrated loads remains constant (horizontal). Between segments with point loads, it's linear.

Portal frame columns experience both axial forces (from vertical loads) and bending moments (from lateral loads and frame action), resulting in combined stresses.

Method of sections allows cutting maximum 3 members in a 2D truss because we have 3 equilibrium equations (ΣFx=0, ΣFy=0, ΣM=0) to solve for 3 unknowns.

Beam deflection formula δ = f(W,L,E,I) depends on all four parameters: load, span, elastic modulus, and second moment of inertia.

Three-hinged arch has 4 reaction components (2 at each support) and 3 equilibrium equations plus 1 condition that moment at internal hinge = 0, making it statically determinate.

For cantilever with UDL, deflection at free end = wL⁴/(8EI) and slope = wL³/(3EI). The option given represents deflection which is commonly asked.

Superposition principle applies for linear elastic systems with small deformations where effects are additive and independent of loading sequence.

For a simply supported beam with central point load, maximum bending moment occurs at the center due to symmetry. BM_max = WL/4 = 40×8/4 = 80 kNm