Question

In the solution of statically indeterminate problems, Castigliano’s second theorem employs the

• A. principle of virtual work
• B. virtual displacement method
• C. virtual force method
• D. principle of least work

Hint:

1. Use Castigliano’s second theorem for calculating displacements in statically indeterminate structures.
2. Remember that the principle of least work helps simplify the solution of such problems by minimizing strain energy.

Answer 1

The Correct Option is D

Step 1: Understanding Castigliano’s second theorem. Castigliano’s second theorem is used to determine the displacements in statically indeterminate structures. It states that the displacement of a point in a structure is equal to the partial derivative of the total strain energy with respect to the force applied at that point. Step 2: Principle employed. The principle of least work is applied in conjunction with Castigliano’s second theorem to solve for the unknown forces in statically indeterminate structures. The principle states that the strain energy in the structure is minimized when the equilibrium conditions are satisfied. Conclusion: Castigliano’s second theorem employs the principle of least work, which matches option \( \mathbf{(D)} \).