Question

Which of the following statement(s) is/are correct?

• A. If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the deflection at any point is equal to the load applied at that point.
• B. If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the load at any point is equal to the deflection at that point.
• C. If a structure is acted upon by two force system \(P_a\) and \(P_b\), in equilibrium separately, the external virtual work done by a system of forces \(P_b\) during the deformations caused by another system of forces \(P_a\) is equal to the external virtual work done by the \(P_a\) system during the deformation caused by the \(P_b\) system.
• D. The shear force in a conjugate beam loaded by the \(M/EI\) diagram of the real beam is equal to the corresponding deflection of the real beam.

Hint:

The principle of virtual work is widely used in structural analysis, where the virtual displacement and work are related to forces and deflections.

Answer 1

The Correct Option is A, B, C

- (A) and (B) are correct as they represent the basic principle of the variational formulation in structural mechanics. In linear elasticity, the derivative of strain energy with respect to displacement gives the force, and the derivative with respect to the force gives the displacement.
- (C) is the principle of virtual work, which is also correct in the case of elastic deformations under different force systems. The external virtual work is equal for the systems in equilibrium.
- (D) represents the conjugate beam method, which is also correct as it relates shear force in a conjugate beam to the bending moment of the real beam.
Thus, the correct answer is:
\[ \boxed{\text{(A), (B), (C)}}. \]