The two cylindrical rod segments shown in the figure below $($Figure $1)$ are fixed to the rigid walls such that there is a gap of

$0\mathrm{.}01in$ between them when $T_1=55F.$ Each rod has a diameter of $1\mathrm{.}5in.$ Take ${}_{al}=13\frac{{10}^{-6}}{}F,$

$E_{al}=10({10}^3)ksi,({}_Y{)}_{al}=40$ksi,${}_{cu}=9\mathrm{.}4\frac{{10}^{-6}}{}F,({}_Y{)}_{cu}=50$ksi, and $E_{cu}=15({10}^3)ksi.$

Figure