$(25$pts$)$ A beam is loaded as shown. Support A is a frictionless roller. Support B is an anchored frictionless pin.

a$.$ Show that $Ay=22$kip up$,By=4$kip up$,$ and $Bx=0.$

b$.$ Find the expressions for the internal shear Vint across the beam.

c$.$ Find the expressions for the internal moment Mint across the beam.

d$.$ Sketch the shear diagram, noting any maxima, minima, zero crossing, slopes, and if nonlinear whether concave or convex.

e$.$ Sketch the moment diagram, noting any maxima, minima, zero crossing, slopes, and if non$-$linear whether concave or convex.