For the pin$-$jointed plane frame $($truss$)$ shown in Figure Q$2,$ use the method of virtual work to determine the vertical deflection at joint D and the horizontal deflection at joint C $.$ The values for $($W$),($P$)$ and $($a$)$ are indicated in Table $2$ shown below.

Assume all members of the truss have a constant EA of $\backslash (2\backslash$times $10^\{5\}\backslash$mathrm$\{$kN$\}\backslash ).$

$(50$ marks$)$

Values of the loads and dimensions for Q$2.$

$\backslash$begin$\{$tabular$\}\{$c$|$c$|$c$\}$

$\backslash$hline $\backslash (\backslash$mathbf$\{$W$\}\backslash )$ & $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ & $\backslash (\backslash$mathbf$\{$a$\}\backslash )\backslash \backslash$

$\backslash ((\backslash$mathrm$\{$kN$\})\backslash )$ & $\backslash ((\backslash$mathrm$\{$kN$\})\backslash )$ & $\backslash ((\backslash$mathrm$\{$m$\})\backslash )\backslash \backslash$

$20$ & $10$ & $1$

$\backslash$end$\{$tabular$\}$