A load $P$ will be supported by a structure consisting of a rigid bar ABCD, a steel A load $P$ will be supported by a structure consisting of a rigid bar ABCD, a steel

$\{$:$F]$ bar $(1)$ and an aluminum alloy $E=10,000$ksi;$a=12\mathrm{.}5\frac{{10}^{-6}}{}F$ bar $(2).$ The bars have cross$-$sectional

areas of $A_1=0\mathrm{.}60in.{?}^2$ and $A_2=1\mathrm{.}35in.{?}^2,$ respectively. Dimensions of the structure are $a=2\mathrm{.}0ft,b=2\mathrm{.}3ft,c=$

$4\mathrm{.}0ft,L_1=8ft,$ and $L_2=19ft.$ The bars are unstressed when the structure is assembled. After a concentrated

load of $P=39$ kips is applied and the temperature has been increased by $50F,$ determine:

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

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

Part $1$

Consider the deflected shape of the rigid bar. Determine the deformation of bar $(1)$ in terms of the

deformation of bar $(2).$

$\{$:$F]$ bar $(1)$ and an aluminum alloy $[\{$:$E=10,000$ksi;$a=12\mathrm{.}5\frac{{10}^{-6}}{}F]$ bar $(2).$ The bars have cross$-$sectional

areas of $A_1=0\mathrm{.}60in.{?}^2$ and $A_2=1\mathrm{.}35i{n}^2,$ respectively. Dimensions of the structure are $a=2\mathrm{.}0ft,b=2\mathrm{.}3ft,c=$

$4\mathrm{.}0ft,L_1=8ft,$ and $L_2=19ft.$ The bars are unstressed when the structure is assembled. After a concentrated

load of $P=39$kips is applied and the temperature has been increased by $50F,$ determine:

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

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

Part $1$

Consider the deflected shape of the rigid bar. Determine the deformation of bar $(1)$ in terms of the

deformation of bar $(2).$