Question $2($CLO $2-100\%)$

A rod consisting of two cylindrical portions $AB$ and $BC$ is fixed supported at both ends at $T_1=20C.$

Portion $AB$ is made of brass $(E_b=105$GPa,$a_b=21{10}^{-6}{}^C)$ and portion $BC$ is made of aluminum $(E_a=70$

$GP{a}_2{}_3=24{10}^{-6}$@$C).$ Knowing that the rod is initially unstressed, determine:

a$)$ The normal stress induced in portions $AB$ and $BC,$ if temperature is changed to $T_2=50C.$

b$)$ The corresponding deflection of point $B.$