The pin$-$connected structure shown in the

figure consists of a rigid bar ABCD and two

axial members. Bar $(1)$ is steel $[$E$=200$ GPa $,=11\mathrm{.}7\frac{{10}^{-6}}{}C]$ with a cross$-$sectional area of A$1=400m{m}^2.$ Bar $(2)$ is an aluminum alloy $[E=70$ GPa $,=22\mathrm{.}5*\frac{{10}^{-6}}{}$C $]$ with cross sectional area of $A_2=400m{m}^2.$ The bars are

unstressed when the structure is assembled.

After a concentrated load of $P=36kN$ is

applied and the temperature is decreased by

$50C,$ determine:

$($a$)$ the normal stresses in bars $(1)$ and $(2).$

$($b$)$ the deflection of point $D$ on the rigid bar.