Problem $2\mathrm{.}5-14$

A brass sleeve $S$ is fitted over a steel bolt $B($see figure$),$ and the nut is tightened until it is just snug. The bolt has

a diameter $d_B=25mm,$ and the sleeve has inside and outside diameters $d_1=26mm$ and $d_2=36,$

respectively.

Calculate the temperature rise $T$ that is required to produce a compressive stress of $25$MPa in the sleeve.

Use material properties as follows:

For sleeve, ${}_S=21\frac{{10}^{-6}}{}C$ and $E_S=100$GPa;

For the bolt, ${}_B=10\frac{{10}^{-6}}{}C$ and $E_B=200$Gba.