Question

For the frame shown in the figure (not to scale), all members (AB, BC, CD, GB, and CH) have the same length, L, and flexural rigidity, EI. The joints at B and C are rigid joints, and the supports A and D are fixed supports. Beams GB and CH carry uniformly distributed loads of w per unit length. The magnitude of the moment reaction at A is \(\frac{wL^2}{k}\). What is the value of k (in integer)? 

• A. 6
• B. 8
• C. 10
• D. 12

Hint:

In frame analysis, the moment reaction at a support can often be calculated using the moment-curvature relationship and symmetry of the structure. Always refer to standard beam theory when solving for reactions in such cases.

Answer 1

The Correct Option is A

In the given frame, the total moment reaction at A is caused by the two distributed loads \( w \) on beams GB and CH. These loads induce moments at the supports at A. Since all members have the same length \( L \) and flexural rigidity \( EI \), we can apply the moment-curvature relationship for a continuous beam under uniform load. Using standard beam theory and moment distribution method for such a frame structure, the reaction moment at A due to the distributed loads can be expressed as: \[ M_A = \frac{wL^2}{k} \] From the classical structural analysis of such frames, the value of \( k \) is determined to be 6. Therefore, the correct value of \( k \) is: \[ \boxed{6} \] Thus, the correct answer is (A).