Question

Match LIST-I with LIST-II: \[\begin{array}{|c|l|} \hline \textbf{LIST-I (Assumption/ theorem)} & \textbf{LIST-II (Type of analysis/ strength determination)} \\ \hline \text{A. Plane section remains plane before and after bending} & \text{I. Elastic analysis and superposition} \\ \hline \text{B. Material is elastic and deformations/ deflection is small} & \text{II. Linear strain distribution} \\ \hline \text{C. Uniqueness theorem} & \text{III. Non-linear analysis and buckling load} \\ \hline \text{D. Large deformation} & \text{IV. Collapse load} \\ \hline \end{array}\] Choose the most appropriate match from the options given below:

• A. A - I, B - II, C - III, D - IV
• B. A - I, B - II, C - IV, D - III
• C. A - II, B - I, C - III, D - IV
• D. A - II, B - I, C - IV, D - III

Hint:

Remember: - Linear strain assumption → Bending theory. - Elasticity + small deflection → Superposition valid. - Uniqueness theorem → Non-linear stability. - Large deformation → Plastic collapse load.

Answer 1

The Correct Option is C

Step 1: Analyze A.
The core principle of bending theory (Bernoulli's assumption) states that a "plane section remains plane before and after bending." This principle leads to a linear strain distribution. Consequently, A corresponds to II.

Step 2: Analyze B.
The conditions "material is elastic and deflections are small" indicate an elastic analysis where the principle of superposition is applicable. Therefore, B corresponds to I.

Step 3: Analyze C.
The "uniqueness theorem" guarantees a singular solution in structural analysis, particularly relevant in non-linear stability and buckling scenarios. Hence, C corresponds to III.

Step 4: Analyze D.
The concept of "large deformation" is employed in plastic analysis for the determination of the collapse load. Thus, D corresponds to IV.

Step 5: Conclusion.
The accurate matching is as follows: \[A - II, B - I, C - III, D - IV\]