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)?