Problem $2.(35$ points$)$

A uniform live load of $400l\frac{b}{f}t$ and a single concentrated live load of $1200$ lb are to be placed on the beam. The beam has a weight of $50l\frac{b}{f}t.$ Determine

$($a$)$ the maximum negative vertical reaction at support F Answer: $q,$

$($b$)$ the maximum positive moment at B Answer: $q,$

$($c$)$ maximum negative shear force at $E$ Answer: $q,$

$A$ is a pin support, $D$ and $F$ are roller supports and $C$ is an internal pin.