$(30-$points$)$ The following beam is under a uniformly distributed load, is ${36}^{\text{'}}$ long and is constructed of a W$36$x$194$ section and A$992$ steel. It is laterally supported at the supports and at midspan $(18\text{'}).($i$)$ determine $C_b$ for the beam, $($ii$)$ determine the moment capacity of the beam, $M_n,($iii$)$ calculate the maximum moment acting on the beam, $M_u,$ in terms of $w_u,($iv$)$ calculate the maximum value of $w_u$ that can be supported by the beam, and $($v$)$ assuming $w_u$ is the service load and that the live load is twice the dead load, determine the maximum possible values of the dead and live load for the beam.