Problem HW $4\mathrm{.}1$: A closed$-$end thick$-$walled cylinder with an inner diameter of $50$ mm and outer diameter of $200$ mm is subjected to the following combined loading scenario. The internal pressure is $=150$MPa while an external pressure is also applied with $Po=20$MPa. The cylinder also experiences a torque around the longitudinal axis of $5kN-m.$

a$)$ Sketch the pressures and torque acting on a cross section of the cylinder

b$)$ Calculate the components of stress at the radial location of $r=45mm$ that are resolved in a cylindrical coordinate system. Give your answer in matrix notation and use units of MPa for your answer.

Checkpoint: sigma$\_$theta $=31\mathrm{.}5$MPa