$20-\mathrm{mm}$ diameter steel rod
$\mathrm{A}=314.16 {\mathrm{mm}}^2$
$\mathrm{E}=200 \mathrm{GPa}$
$\mathrm{\alpha }=12.0\times {10}^{-6}{/}^{\circ }\mathrm{C}$

A $20-\mathrm{mm}$ diameter steel rod is held snugly between rigid walls as shown above.

Calculate the temperature drop $∆\mathrm{T}$ at which the shear stress in the $15-\mathrm{mm}$ diameter bolt becomes $70 \mathrm{MPa}$.