A solid disk of radius $5$ inch needs to be assembled with a hollow steel tire of thickness $0\mathrm{.}15$ inch. The inner radius of the hollow tire is $4\mathrm{.}99$ inch at room temperature $T_o=70F.$

To what temperature. To what temperature $T_1$ should the tire be heated so that it slips in place over the solid disk. Find the stress field in the assembly after it has been cooled back to room temperature. Use the following general solution to help solve the problem.

${}_{rr}=A+\frac{B}{r^2}$

${}_{}=A-\frac{B}{r^2}$

The properties in both metals are $E=30{10}^6,v=0\mathrm{.}3,=7\frac{{10}^{-6}}{}F.$