Yielding $($Stress$)$ Q$80$

A thin$-$walled vessel is subject to an internal pressure of $225\mathrm{.}08$bar and an external positive torque $($Right Hand Rule$)$ of $3563$Nm$.$

The vessel wall$-$thickness is $4$ mm and its external diamter is $211$ mm $.$

The vessel is made from a ductlie metal with a Yield Strength of $630\mathrm{.}36$MPa, Using clockwise positive polar co$-$ordinates:

Determine for an element of stress on the external surface:

the Maximum in$-$plane Principal Stress $($Answer in MPa only$).$

the Minimum in$-$plane Principal Stress $($Answer in MPa only$).$

the Tresca in$-$plane Effective Stress $($Answer in Pa only$).$

the von Mises in$-$plane Effective Stress $($Answer in MPa only$).$

the Maximum in$-$plane Shear Stress $($Answer in Pa only$)$