Castigliano''s second theorem states that the deflection at a loaded point is:
Choose the correct answer
Equal to total strain energy divided by load
Equal to the partial derivative of total strain energy with respect to that load (∂U/∂P)
Equal to product of load and span
Found only from moment distribution
Correct Answer
B. Equal to the partial derivative of total strain energy with respect to that load (∂U/∂P)
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Castigliano''s 2nd theorem: δ_i = ∂U/∂P_i where U = total strain energy in structure, P_i = applied load (force or moment) at the point and in the direction of the desired displacement. Applies to linear elastic structures. Used to find deflections without drawing elastic curve — particularly useful for trusses and curved members.
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