In the 'mechanism method' of plastic analysis, the 'virtual work' equation for a beam mechanism gives:
Choose the correct answer
Equilibrium of moments at one cross-section
External virtual work (load × displacement) equals internal plastic hinge work (ΣMp×θ) — gives collapse load
Settlement of supports
Elastic deflection only
Correct Answer
B. External virtual work (load × displacement) equals internal plastic hinge work (ΣMp×θ) — gives collapse load
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Mechanism (kinematic) method: postulate a collapse mechanism, apply virtual displacement, equate external virtual work to internal plastic hinge work. External: Σ(W×δ); Internal: Σ(Mp×θ). At collapse: Mp = minimum value satisfying W×δ = Σ(Mp×θ). For propped cantilever (UDL w, span L): collapse needs 2 hinges → Mp = wL²/11.66. Multiple mechanisms checked; governing = lowest load.
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