Problem $3-$B

A thin$-$walled pressure vessel has an outside diameter of $10$ inches and wall thickness of $0\mathrm{.}05$ inches. The pressure vessel is $30$ inches long. Both ends are capped and one end is fixed. The other end is subjected to a torque. What is the maximum torque and pressure for the pressure vessel if it is made of G$10400$ HR steel and the relationship between pressure and torque is $T=0\mathrm{.}5P$ where $T$ is in in lb and $P$ is in psi? Hints:

Draw a sketch of the problem.

Determine the equations for Axial stress, tangential stress, and shear stress in terms of $P$ or $T$

Using the $2-$D Mohrs Circle, find the principal stresses in terms of $P$ or $T$

Draw a $3-$D Mohrs Circle of the $3$ principal stresses.

From $4$ Determine the maximum shear stress and compare it with $S_{sy}=\frac{S_y}{2}$