A high$-$density polyethylene $E=128$ksi;$=88\frac{{10}^{-6}}{}F$;$v=0\mathrm{.}4$ bar is positioned between two rigid

supports. The bar is square with cross$-$sectional dimensions of $2\mathrm{.}50$ in $.$ by $2\mathrm{.}50$ in $.$ and length $L=48in.$ At

room temperature, a gap of $=0\mathrm{.}25in.$ exists between the block and the rigid support at B $.$

$($a$)$ Determine the lowest temperature at which the $0\mathrm{.}25$ in gap closes.

$($b$)$ If the temperature increases by $120F,$ determine the normal stress in the bar and the longitudinal strain in

the bar.