Consider the same truss structure shown in Problem $3.$ It is statically indeterminate. Point A has pin support, and points C and D have roller support. The area of all bars is $\backslash (5\backslash$mathrm$\{$in$\}^\{2\}\backslash )$ and $\backslash ($ E$=\backslash )30000$ kips$/$in $\backslash (\{\}^\{2\}\backslash )$

In addition to the downward vertical load of $120$ kips at point E $,$ all the elements of the truss are subjected to temperature increase of $\backslash (60^\{\backslash$circ$\}$ F $\backslash ).$ In addition, element $\backslash ($ A B $\backslash )$ is fabricated $0\mathrm{.}1$ inches too short and element BC is fabricated $0\mathrm{.}05$ inches too long. Given the coefficient of thermal expansion $\backslash (\backslash$alpha$=6\mathrm{.}5\backslash$times $10^\{-6\}\backslash$quad$\{\}^\{\backslash$circ$\}$ F$^\{-1\}\backslash ).$ Just like problem $3,$ Consider the reaction $\backslash ($ R$\_\{$C$\}\backslash )$ at the roller C as redundant support. Using the method superimposition, neatly break down the structure into two statically determinate structures$-$one consisting of external forces $($the primary structure$),$ and the second consisting of the redundant force $\backslash ($ R$\_\{$C$\}\backslash )$ only. Given this new information on thermal loading and fabrication error in addition to the external load, and the using the work that you did in part $3$:

a$.$ Obtain $\backslash (\backslash$Delta$\_\{$C$\}\backslash )$ using the unit load method. Here, $\backslash (\backslash$Delta$\_\{$C$\}\backslash )$ is the displacement at point $\backslash ($ C $\backslash )$ of the primary structure subjected to external load only. Hint: Since the $\backslash ($ Q $\backslash )$ structure depends on what is the primary unknown, it stays same as the $\backslash ($ Q $\backslash )$ structure used to obtain $\backslash (\backslash$Delta$\_\{$C$\}\backslash )$ of the primary structure in part b of problem $3.$ You can use the values of $\backslash ($ Q$\_\{$i$\}\backslash )$ that you obtained while calculation $\backslash (\backslash$Delta$\_\{$C$\}\backslash )$ in part b of problem $3.$ In addition, the $\backslash ($ P $\backslash )-$system has three effects: $($a$)$ external loading at point E$,($b$)$ thermal stresses, $($c$)$ fabrication error. Make sure to consider all three effects in the P$-$system. As far as external load at point E is concerned, you can borrow the member force results from part a of problem $3.$

$(20$ points$)$

b$.$ Obtain $\backslash ($ R$\_\{$C$\}\backslash )$ using compatibility equation for point C $.$ Make sure to specify the direction of $\backslash ($ R$\_\{$C$\}\backslash ).$ You can use the value of $\backslash ($ a$\_\{$c c$\}\backslash )$ obtained in part c of problem $3.$

$(5$ points$)$

c$.$ Use equilibrium equations to find out the remaining reaction forces at points A$,$ and D$.$

Once you have found all the reactions, obtain and tabulate the member forces $(5$ points$)$