Please show all working $,$ make refrence to tables used. Thanks for answering

$-$ The beam shown in Figure $3$ is part of a roof system. Assume that there is partial lateral

support equivalent to bracing at the ends and at midspan. The loading consists of

$180l\frac{b}{f}t$ dead load $($not including the weight of the beam$),95l\frac{b}{f}t$ roof live load, $275$

$l\frac{b}{f}t$ snow load, and $180l\frac{b}{f}t$ wind load acting upward. The dead, live, and snow loads

are gravity loads and always act downward, whereas the wind load on the roof will

always act upward. Use A$992$ steel and select a shape. The total deflection must not

exceed $\frac{L}{180}.$

a$.$ Use LRFD$.$

b$.$ Use ASD.