Rigid bar ABCD is supported by a pin connection at A and by two axial bars $(1)$ and $(2).$ Bar $(1)$ is a $28-$in$.-$long bronze $[E=14800$ksi, $[$:$=9\mathrm{.}7\frac{{10}^{-6}}{}F\}$ bar with a cross$-$sectional area of $1\mathrm{.}50i{n}^2\frac{.}{B}ar(2)$ is a $44-$in$.-$long aluminum alloy $\frac{{10}^{-6}}{}F]$ bar with a cross$-$sectional area of $2\mathrm{.}50i{n}^2.$ Both bars are unstressed before the load $P$ is applied. Assume $L_1=28$ in$.,L_2=44$ in$.,a=36$ in$.,b=52$ in$.,$ and $c=12$ in$.$ If a concentrated load of $P=31$ kips is applied to the rigid bar at $D$ and the temperature is decreased by $100.$

$1.$Assuming members in tension, relate the force in the members and the applied force P by summing moments about the pin A$.$

$2.$Relate the deflections of points B and C$.$

$3.$ Relate the deformations of member $1$ and member $2.$

$4.$ Using the relationship of deformation in yerms of force and temperature change for each member together with equation $(3),$ derive a compatibility equation for the structure.

$5.$Solve for F$1$ and F$2$ using the results of parta $1$ and $4.$

$6.$ Determine the normal stress in each bar.

$7.$ Determine the normal strain in each bar.

$8.$ Determine the defelction of the ridig bar ABCD at point C$.$

$9.$ Determine the defelction of the rigid bar ABCD at point D$.$