Problem $1$: $[$Required$]$

The $40$ foot long steel rails on a train track are laid with a small gap between them to allow for thermal

expansion. Determine the required gap, $,$ so that the rails just touch one another when the temperature

increased from $T_1=-30F$ to $T_2=70F?$ Using the gap, what would be the axial force in the rails

if the temperature would rise to $T_3=100F?$ The cross$-$sectional area of each rail is $4\mathrm{.}25i{n}^2.$

Assume the rail is made of stainless $304$ steel $(=9\mathrm{.}6{10}^{-6}i\frac{n}{i}\frac{n}{}F,E=28,000$ksi$).$