Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): In the analysis of rigid frames, the usual practice is to consider the strain energy due to flexure only.
Reason (R): The strain energies due to axial and shear forces are usually quite small compared to that of flexure.
In the light of the above statements, choose the most appropriate answer from the options given below:

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

This simplification is valid for "slender" members. For "deep beams," shear deformation becomes significant and cannot be ignored in strain energy calculations.

Answer 1

The Correct Option is A

Concept: The total strain energy in a structural member is the sum of energy due to bending (flexure), axial force, shear, and torsion.

Step 1: Evaluate the Assertion (A).
In standard structural analysis of rigid frames (like portal frames), engineers primarily focus on bending moments. The deformations due to bending are significant, and therefore, the strain energy associated with flexure is the dominant term. Thus, Assertion (A) is correct.

Step 2: Evaluate the Reason (R).
For typical beam and frame members where the span-to-depth ratio is large, the contributions of axial deformation and shear deformation to the total displacement are negligible (often less than 5%). Since strain energy is proportional to these deformations, the energy from axial and shear forces is indeed very small compared to flexural energy. Thus, Reason (R) is correct.

Step 3: Establish the connection.
The reason (the small magnitude of other energy types) directly justifies the practice described in the assertion.