Q$3)(40$ points$)$ For the given structure in the figure, members $AB$ and $BC$ are rigidly connected to each other at B; BC and CD are pin connected to each other at C $($there is an internal hinge at C$)$; members CD$,$ DE and DF are rigidly connected to each other at D; BF is a truss member:

a$)$ Determine the axial force in truss bar BF$,$ and state whether it is in tension or compression.

b$)$ Plot the axial force, shear force and bending moment diagrams for the frame members of the structure only $($exclude truss member BF in your plots$).$ Clearly indicate the local axis for each member and the sign convention in drawing your diagrams, and show all critical values on the plots.