Energy Methods MCQ with answer and solution

Concept

Reciprocity of deflections in elastic structures

Formula

Δ₁₂ = Δ₂₁

Step-by-step solution

1. Betti's generalized reciprocal theorem states that the virtual work done by system 1 forces acting through system 2 displacements equals the work done by system 2 forces through system 1 displacements. 2. Maxwell's reciprocal deflection theorem is the single-load case of Betti's theorem: Δ_jk = Δ_kj. 3. This establishes direct reciprocity between applied loads and resulting deflections. 4. Thus, Maxwell-Betti's theorem relates load-deflection reciprocity. Answer: A

Explanation

The Maxwell-Betti reciprocal theorem establishes that in any linear elastic system, the deflection at point 1 due to a unit load at point 2 is equal to the deflection at point 2 due to a unit load at point 1. It fundamentally relates load-deflection reciprocity.

Why the other options are wrong

B) Stress-strain relationships are governed by constitutive equations (Hooke's law). C) Buckling modes are determined by eigenvalue stability analysis. D) Plastic hinges pertain to limit state plastic collapse theory.

Shortcut

Maxwell-Betti = Reciprocal theorem for load-deflection (Δ₁₂ = Δ₂₁).

Common mistake

Thinking the theorem relates stress and strain directly instead of generalized loads and deflections.