A square plastic bar $($length $L_{p1}$ side dimension $s_p=193mm)$ is inserted in side a hollow, square, cast$-$iron fube $($length $L_r=400mm,$ side dimension $s_c=200mm$ and wall thickness $t=3mm).$ What is the force $P$ required so that when compressed, the final length of the bar is equal to the length of the tube $($ L $)$ and, at the same time, the gap between the plastic bar and the cast$-$iron tube is closed?

Assume: $E_c=170$GPa,$v_c=0\mathrm{.}3,E_p=3\mathrm{.}8$GPa,$v_p=0\mathrm{.}4$