$(35$ points$)$ The forces are shown in the figure.

a$)$ Calculate the internal forces and internal moments at a cross$-$sectional plane cutting through H and K $.$

b$)$ Calculate the normal stress and shear stress$($es$)$ acting at point K$,$ which is located on the outer surface of the solid shaft. State the direction of the shear stress and whether the normal stress is in tension or compression.

The solid, circular shaft has a radius of $20$ mm $,$ giving it a polar moment of inertia, $J=2\mathrm{.}523{10}^{5}m{m}^4,$ and an area moment of inertia, $I=1\mathrm{.}257{10}^{5}m{m}^4.$