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)
Why is this the answer?
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.
Related Engineering Mechanics MCQs
More solved Engineering Mechanics questions for AE/JE Civil Engineering exams.
- The centroid of a semicircular area of radius R from its diameter is:
- Second moment of area (moment of inertia) of a rectangle (b wide, d deep) about its...
- For a column of length L with both ends pinned, the Euler critical buckling load Pcr is:
- Which of the following about rigid body under coplanar forces is correct?
- D'Alembert's principle converts a dynamics problem into an equivalent statics form by...
- In the Bow notation system for graphical truss analysis (force polygons):
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.