$3.$ A thin$-$walled cylindrical pressure vessel has an outer radius of $100$ mm and a wall thickness of $5$ mm $.$ It is subjected to an internal pressure of $5$ MPa and an axial compression load of $85$ kN at its end caps. Determine the following $(11$ points$)$:

$($a$)$ The maximum in$-$plane shear stress in MPa

$($b$)$ The associated normal stress in MPa

$\backslash [$

r$=1\backslash$mathrm$\{$~m$\}$

$\backslash ]$