Bar $500mm]$ having a cross$-$sectional area of $A_1=350m{m}^2$ is connected at flange $B$ to $84$GPa;$=12\mathrm{.}5\frac{{10}^{-6}}{}C$;$L_2=500mm]$ with a cross$-$sectional area of $A_2=450m{m}^2.$ The assembly is connected to rigid supports at A and $D.$ The assembly is subjected to a temperature increase of $130C.$ When the assembly is subjected to an external force of $50kN$;

$($a$)$ Compute the internal force in both members

$($b$)$ Compute the induced stress in both members $($state whether compressive or tensile$)$