Consider the linearly elastic plane frame shown in the figure. Members HF, FK, and FG are welded together at joint F. Joints K, G, and H are fixed supports. A counter-clockwise moment \( M \) is applied at joint F. Consider flexural rigidity \( EI = 10^5 \, \text{kN-m}^2 \) for each member and neglect axial deformations.
\includegraphics[width=0.35\linewidth]{image51.png}
If the magnitude (absolute value) of the support moment at H is 10 kN-m, the magnitude (absolute value) of the applied moment \( M \) (in kN-m) to maintain static equilibrium is \(\underline{\hspace{1cm}}\) (round off to the nearest integer).