$4\mathrm{.}5\mathrm{.}8$ A beam ABC is simply supported at A and B$,$ and

has an overhang BC $($see figure$).$ The beam is loaded by

two forces P and a clockwise couple Pa at D acting on the assembly shown.

a$)$ Sketch the shear and bending moment diagrams for beam ABC.

b$)$ If the moment Pa at D is replaced by the moment M$,$

find an expression for M in terms of the variables P

and a such that the reaction at B is zero. Sketch the associated shear and bending moment diagrams for

beam ABC. and add beam slopes and deflection by the method of cuts PROB. $4\mathrm{.}5\mathrm{.}8$