Problem $1(15$ pts$)$

A cylindrical pressure vessel $($inner radius of $10$ in $.$ and thickness of $\frac{1}{4}in.),$ shown below, is fabricated from a spirally welded pipe. The angle of the welds is $=20,$ as shown below. The pressure vessel is fitted with end caps, and pressurized to $p=200$ psi.

Using Mohr's circle or otherwise, determine:

$($a$)$ the normal stress perpendicular to the weld.

$($b$)$ the maximum $($out of plane$)$ shear stress