A thick$-$walled cylinder with $0\mathrm{.}25$ m internal diameter and $0\mathrm{.}4$ m external diameter is fabricated of a material whose elastic limit is $350$ MPa and Poisson's ratio $v=0\mathrm{.}30.$

a$)$ Determine for an internal pressure $p_i=0$ the maximum external pressure to which the cylinder may be subjected according to the maximum shear stress theory.

b$)$ Determine for an external pressure $p_0=0$ the maximum internal pressure to which the cylinder may be subjected according to the maximum distortion energy criterion.