$14$

A $2m$ long beam AB is connected by the help of two rigid disk at both ends. The core of the beam is aluminum $,{}_{al}=24**{10}^{-6},\frac{1}{}C)$ and the cover of the beam is steel $(E_{st}=200GP,{}_{st}=12**{10}^{-6}\frac{1}{}C).$ Initially, there is no stress or no strain in the beam. An axial force $P=5kN$ is applied to the rigid disks and the temperature of the beam is decreased by $40C.$ Find the stresses in the aluminum and steel components.

$($a$-$a Cross$-$section$)$