A continuous beam ABCDE, with uniform flexural rigidity throughout has roller supports at $B,C$ and $D,$ a built$-$in support $E$ and an overhang $AB$ as shown in Figure. It carries a uniformly distributed load of intensity of $2k\frac{N}{m}$ on $AB$ and another of intensity of $3k\frac{N}{m}$ over BCDE. In addition to it$,$ a point load of $8kN$ is placed midway between $C$ and $D.$ The span lengths are $AB=2m,BC=CD=DE=5m.$ Obtain the support moments by the moment distribution method and sketch the B$.$M$.$ diagram giving values at salient points.