The $40-$ft long A$-36$ steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the total required gap, $2**,$ so that the rails just touch one another when the temperature is increased from $T_1=-20F$ to $T_2=90F.$ If the rails were installed at $-20F$ with this gap, what would be the axial force in the rails if the temperature were to rise to $T_3=110F.$ The cross sectional area of each rail is $6\mathrm{.}10i{n}^2.E_{st}=29,000$ksi. What is the total required gap to allow thermal expansion? What is the force in the rail due to the additional expansion?