A pressure vessel with a $150$ psig internal pressure is fabricated from a section of $\backslash (48^\{\backslash$prime $\backslash$prime$\}\backslash )($nominal$)$ diameter steel pipe. The pipe outside diameter is $48$ inches and the inner diameter is $47\mathrm{.}25$ inches. A torque about the longitudinal axis of $\backslash (5\backslash$times $10^\{5\}\backslash$mathrm$\{$ft$\}1\backslash$mathrm$\{$lb$\}\backslash )$ is also being applied to the pressure vessel. The steel material has a $35$ ksi Yield Strength and $\backslash (15\backslash \%\backslash )$ ductility.

Find: The factor of safety with respect to the yield strength $-$ by applying the Distortion Energy theory.

Schematic Diagram $-$ Not to Scale