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Which of the following statement(s) is/are correct?
- 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.
- 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.
- If a structure is acted upon by two force system Pₐ 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 Pₐ is equal to the external virtual work done by the Pₐ system during the deformation caused by the P_b system.
- 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.
Correct answer: 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.
Solution
This statement is correct because it reflects the principle of virtual work in linear elasticity, where the change in strain energy with respect to an applied load gives the corresponding deflection at that point, demonstrating the relationship between load and displacement in elastic structures.
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