$2\mathrm{.}2-1$D A hollow, circular, cast$-$iron pipe $12,000$ksi supports a brass $)=(14,000$ksi and weight $W=2$kips, as shown. The outside diameter of the pipe is $d_c=6in.$

$($a$)$ If the allowable compressive stress in the pipe is $5000$ and the allowable shortening of the pipe is $0\mathrm{.}02$ in$.,$ what is the minimum required wall thickness $t_{c,\text{m}\text{i}\text{n}}?($Include the weights of the rod and steel cap in your calculations.$)$

$($b$)$ What is the elongation of the brass rod${}_r$ due to both load $W$ and its own weight?

$($c$)$ What is the minimum required clearance $h?$