A thin$-$walled prismatic beam with a channel section shown in figure is subjected to equal transverse shear forces $P$ in the positive $x$ and $y$ directions. Assume that the wall thickness $t$ is uniform.

$($a$)$ Show that the solution for the shear flow distribution obtained in class satisfies equilibrium; i$.$e$.$ the net resultant shear force in the $x$ and $y$ directions are equal to $P.$

$($b$)$ Determine the location and magnitude of the maximum shear stress in the crosssection plane.