Question$2$: $(12$ points$)$ A cylindrical pressure vessel is subjected to internal pressure $p=5000$kPa, and outer torque $T=400kN.m$ and an axial compressive force $F=300kN$ as shown. The vessel's properties are $E=180$GPa and $v=0,3.$ Hint: In your computation take $r=400mm$ as the outer radius of the cylinder.

A$.(3-$points$)$ Find the stresses ${}_x,{}_y$ and ${}_{xy}($in MPa$)$ noting that the sign of the shear stress is opposite to that indicated on the infinitesimal element shown in the figure.

B$.(2-$points$)$ Find the principle stresses at the outer wall of the cylinder $($in MPa$)$:

C$.(2-$points$)$ Find the maximum shear stress ${}_{\text{m}\text{a}\text{x}}$ at the outer wall of the cylinder $($in MPa$).$

D$.(3-$points$)$ Find the normal and shear stresses on the plane of the weld that is ${}_v$ and ${}_v.$

E$.(2-$points$)$ Find the change in thickness $($in mm$)$ of the cylinder due to the normal stresses at the outer boundary.