The 'Castigliano theorem Part II' states that the partial derivative of total strain energy U with respect to force Qi gives:
Choose the correct answer
The force at point i
Displacement δi at the point and direction of Qi — ∂U/∂Qi = δi (Castigliano Part II for deflection)
The moment of inertia
Rate of change of load
Correct Answer
B. Displacement δi at the point and direction of Qi — ∂U/∂Qi = δi (Castigliano Part II for deflection)
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Castigliano II: ∂U/∂Qi = δi (displacement in direction of Qi). Used to find displacements. For bending: U = ∫M²/(2EI) dx; ∂U/∂P = ∫(M/EI)×(∂M/∂P) dx. Powerful for redundant structures (virtual force = 1 to find any deflection). Castigliano I (less used): ∂U/∂δi = Qi (force from displacement). Very useful for trusses: U = ΣF²L/(2AE).
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