$(15$ points$)$ For the loadings shown on the beam with $P=3KN$ and $Q=8KN,$ determir $($a$)$ the reactions at hinge $C$ and roller $B,$ and $(b)$ the internal shear and bending mom at $0\mathrm{.}45$ m from point $A($i$.$e$.$ at the mid$-$point between point $C$ and point $D).$