Problem $5(24$ pts$)$

A simply supported steel beam carries a concentrated dead load $(P_D)$ of $40$ kips and

a concentrated live load $(P_L)$ of $25$ kips $,$ as shown in the figure below. The steel is

A$992$ Grade $50(F_y=50$ksi$).$ Beam length is $20$ ft $.$ The beam is assumed to be

laterally supported. Use LRFD design method $({}_b=0\mathrm{.}9).$

$($a$)$ Ignoring the self$-$weight of the beam,

i$)$ Find $P_u(3$ points$)$

ii$)$ Find $M_u$ considering $P_u$ only $(3$ points$)$

iii$)$ Find required $Z_x(3$ points$)$

iv$)$ Use Table provided in next page to find the most economical section for this beam. $(3$ points$)$

$($b$)$ Use the weight of the section you designed in part $($a$)$ and

i$)$ Find the distributed load due to the weight of the beam $(w_u(3$ points$)$

ii$)$ Find $M_u$ considering both $P_u$ and $w_u(3$ points$)$

iii$)$ Find the required $Z_x$ for new $M_u(3$ points$)$

iv$)$ Is the section adequate with the beam self$-$weight included? $(3$ points$)$