Perform the following computations for a W $1636$ steel beam:

a$)$ Compute the limiting plastic length $($Lp$)$ and the second limiting length $($Lr$).$

b$)$ Determine the nominal resisting moment capacity $($Mn$)$ for an unbraced length of $5$ ft$.$

c$)$ Determine the nominal resisting moment capacity $($Mn$)$ for an unbraced length of $10$ ft$.$