$2.)$ A fixed$-$fixed beam with a length of $20$ ft is subjected to the following combination of loads:

Distributed Dead Load: $425$ plf

Distributed Live Load: $300$ plf

Distributed Snow Load: $200$ plf

Distributed Rain Load: $100$ plf

Point Dead Load: $5400$ lbs

Find the following:

a$)$ The factored design LRFD moments and controlling load combinations

b$)$ The factored design LRFD shear and controlling load combination

c$)$ The reduction factors from ACl $318$ for both Bending and Shear in this configuration