A long, rectangular copper bar under a tensile load $P$ hangs from a pin that is supported by two steel posts $($see figure$).$ The copper bar has a length of $2\mathrm{.}0m,$ a cross$-$sectional area of $4800m{m}^2,$ and a modulus of elasticity $E_c=120$GPa. Each steel post has a height of $0\mathrm{.}5m,$ a cross$-$sectional area of $4500m{m}^2,$ and a modulus of elasticity $E_s=200$GPa.

$($a$)$ Determine the downward displacement $$ of the lower end of the copper bar due to a load $P=180kN.$

$($b$)$ What is the maximum permissible load $P_{\text{m}\text{a}\text{x}}$ if the displacement $$ is limited to $1\mathrm{.}0mm?$

$($c$)$ what is the maximum stress in the bar$/$post system?