Problem $8\mathrm{.}3\mathrm{.}12$

A pressurized steel tank is constructed with a helical weld that makes an angle $=55$ with the longitudinal axis $($see figure$).$ The tank has radius $r=0\mathrm{.}6m,$ wall thickness $t=18mm,$ and internal pressure $p=2\mathrm{.}8$MPa. Also, the steel has modulus of elasticity $E=200$GPa and Poisson's ratio $v=0\mathrm{.}30.$ Determine the following quantities for the cylindrical part of the tank.

$($a$)$ The circumferential and longitudinal stresses.

$($b$)$ The maximum in$-$plane and out$-$of$-$plane shear stresses.

$($c$)$ The circumferential and longitudinal strains.

$($d$)$ The normal and shear stresses acting on planes parallel and perpendicular to the weld $($show these stresses on a properly oriented stress element$).$