Q$4.[0\mathrm{.}6\backslash \%]$

A $180$ kN load is applied to a steel truss as shown. The cross$-$sectional area and the length of each of the members is shown. Determine the following:

$($a$)$ The strain energy $\backslash ($ U $\backslash )$ on each of the members U$\_$BC$,$ U$\_$CD and U$\_$BD$.$

$($b$)$ The total strain energy on the entire truss in Joules. $($Note: $1$ Joule $\backslash (=1\backslash$mathrm$\{$Nm$\}\backslash ))$

$($c$)$ The total deflection on the entire truss in millimeters. $\backslash (\backslash$mathrm$\{$E$\}=200\backslash$mathrm$\{$GPa$\}\backslash ).$