$14\mathrm{.}6$ Thin$-$walled Pressure Vessels $($sort of $...)$

Each of two A$-36$ steel bands is $2$ in $.$ wide and is secured around the smooth rigid cylinder. If the bolts are tightened so that the tension in them is $400$ lb $,$ determine

a$)$ the pressure exerted on the cylinder,

b$)$ the normal stress in the band,

c$)$ the distance half the band stretches.

Hint: This is actually a "hoop stress" problem!

Start by calling the pressure between the cylinder and the band P $,$ and then DRAW YOUR FBDs of the bands to derive your own equation for relating pressure and tension in the bands.

Also, don't forget our earlier homework had tables of material properties $($like A$-36$ steel$).$