Castigliano's second theorem is used to find the deflection (or rotation) at a point in a structure. It states that the deflection delta_i at the point of application of force P_i is:
Choose the correct answer
delta_i = partial U / partial P_i (partial derivative of total strain energy U with respect to that force)
delta_i = U / P_i
delta_i = P_i x L / AE
delta_i = M_i / EI
Correct Answer
A. delta_i = partial U / partial P_i (partial derivative of total strain energy U with respect to that force)
AI Detailed Explanation & IS Code Reference
Unlock the reasoning, formula path and code-linked notes inside your student dashboard.
Castigliano's second theorem: delta_i = dU/dP_i, where U = total strain energy stored in the structure. For beams: U = integral(M^2/(2EI) dx). Method: compute M in terms of P_i (actual or dummy), differentiate w.r.t. P_i, integrate dU/dP_i. If no force at desired point, add dummy force Q, find dU/dQ, then set Q = 0.
ScoreCardAI links this solution with subject, topic and difficulty signals so your scorecard can identify weak areas after a full mock test.
Practice more Civil Engineering questions
This MCQ belongs to AE Level Premium Test Series. Full tests include timed attempts, rank comparison and subject-wise analysis.