For the following truss:

a$)$ Without performing a structural analysis indicate whether each bar is in tension or compression under the loading shown.

b$)$ Compute the forces in Bars A$-$B$,$ A$-$D$,$ and B$-$C$.$

c$)$ Determine how much Bar B$-$D contributes to the deflection at point $C($assume the bar's area is $4\mathrm{.}0i{n}^2$ and $E=10,000$ksi $)$

Note: $[$Difficulty $=10$ minutes