A concrete beam with rectangular cross section, b $=10$ in$,=26\mathrm{.}5$ in$,$c $=6$ ksi and $=60$ ksi. The beam carries factored dead load and factored live load of $1\mathrm{.}9$ kip$/$ft$,6$ kip$/$ft$,$ respectively, over the span of $20$ ft and is reinforced with $6$#$7$ bars and you have only #$3$ bars to design stirrups. Assume the beam is sitting on bearings with $10$ in width.

a$)$ Find $$ shear envelope

b$)$ Determine if minimum shear reinforcement is required

c$)$ Determine maximum stirrup spacing

d$)$ Design the stirrups along the length of beam