Question

Redundant frames may be analysed by using

• A. Castigliano's first theorem
• B. Castigliano's second theorem
• C. Moment-area theorem
• D. Funicular polygon

Hint:

Remember: \[ \boxed{ \delta=\frac{\partial U}{\partial P} } \] where \(U\) is the strain energy and \(P\) is the applied load. This theorem is extensively used for the analysis of statically indeterminate structures.

Answer 1

The Correct Option is B

Step 1: Recall Castigliano's second theorem. Castigliano's second theorem relates the partial derivative of strain energy to the corresponding displacement. \[ \delta = \frac{\partial U}{\partial P}. \]

Step 2: State its application. The theorem is widely used for determining unknown redundant forces and reactions in statically indeterminate structures and redundant frames. Hence, \[ \boxed{\text{Castigliano's second theorem}} \] is the correct answer. Therefore, \[ \boxed{(B)} \] is the correct answer.