Problem #$5-$ Column Analysis $(20$ points, $6$ parts$)$

A $2\mathrm{.}5-$in$.$ diameter steel bar is used as an axially loaded pin$-$connected compression member. The ASTM A$36$ structural steel has a proportional limit of $36,000$ psi and a modulus of elasticity of $29,000,000$ psi. Complete the following:

Part A $(4$ points$)$: Find the moment of inertia of the column.

Part B $(4$ points$)$: Find the cross$-$sectional area of the column.

Part C $(4$ points$)$: Find the radius of gyration of the column.

Part D $(4$ points$)$: Calculate the shortest length for which Euler's formula applies.

Part points$)$: Calculate the critical load if $L=48$ in$.$

Part $F(2$ points$)$: Calculate the critical stress if $L=48$ in$.$