Select the lightest W $($A$992$ steel$)$ for the simply supported girder shown below. Use LRFD$.$

The member is laterally braced at points $F,G,H,$ and I.

Consider the self$-$weight of the girder for all calculations.

Maximum depth of girder $=19$ in

Maximum deflection due to live load $$ Span$/360$

Maximum deflection due to dead plus live loads $$ Span$/240$

Calculate the deflections at mid$-$span.

You may use the AISC Manual aids to select the section.

Verify the flexural strength and shear strength of the girder using the AISC Specification formulas.

Service load R:

$R(dead),=6k,R(live),=13k$

Service uniform distributed load W:

$W($dead$),=$ self$-$weight of girder $+0\mathrm{.}175\frac{k}{f}t,W($live$),=$ none

The service loads include the self$-$weight of beams $($P$)$ and $($R$).$