A load $P$ will be supported by a structure consisting of a rigid bar ABCD, a steel $E=29,000$ksi;$=6\mathrm{.}5\frac{{10}^{-6}}{}F$ bar $(1)$ and an

aluminum alloy $E=10,000$ksi;$=12\mathrm{.}5\frac{{10}^{-6}}{}F$ bar $(2).$ The bars have cross$-$sectional areas of $A_1=0\mathrm{.}75i{n}^2$ and $A_2=1\mathrm{.}25in.{?}^2,$

respectively. Dimensions of the structure are $a=3\mathrm{.}8ft,b=4\mathrm{.}1ft,c=5\mathrm{.}9ft,L_1=13ft,$ and $L_2=21ft.$ The bars are unstressed when the

structure is assembled. After a concentrated load of $P=30$kips is applied and the temperature has been increased by $70F,$

determine:

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

$($b$)$ the magnitude of the vertical deflection of joint $D.$