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