(Solved): A rod consisting of two cylindrical portions AB and BC is restrained at both ends. Portion AB is m ...

A rod consisting of two cylindrical portions $AB$ and $BC$ is restrained at both ends. Portion $AB$ is made of steel $(E_s=200\mathrm{GPa}$, ${\alpha }_s=11.7\times 10^{-6}/{}^{\circ }\mathrm{C})$ and portion $BC$ is made of brass $(E_b=105\mathrm{GPa}$, ${\alpha }_b=20.9\times 10^{-6}/{}^{\circ }\mathrm{C}$ ). Knowing that the rod is initially unstressed, determine the compressive force induced in $ABC$ when there is a temperature rise of $50^{\circ }\mathrm{C}$.