$2.$ A continuous beam ABCD covers three spans, $\backslash (\backslash$mathrm$\{$AB$\}=1\mathrm{.}5\backslash$mathrm$\{$~L$\},\backslash$mathrm$\{$BC$\}=3\backslash$mathrm$\{$~L$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$CD$\}=\backslash$mathrm$\{$L$\}\backslash )$ as shown in figure. It carries uniformly distributed loads of $\backslash (2\backslash$mathrm$\{$~W$\},\backslash$mathrm$\{$~W$\}\backslash )$ and $3$ W per metre run on $\backslash (\backslash$mathrm$\{$AB$\},\backslash$mathrm$\{$BC$\}\backslash )$ and CD respectively. If the beam is of the same cross$-$section throughout, find the bending moments at supports B and C and the reactions on each support. Also plot bending moment and shear force diagrams.