Select the lightest W shape beam for the load distribution shown in the image below. The live load is $8$ kip $(8,000$ lb$)$ and the dead load is $2$ kip $(2,000$ lb$).$ The beam is simply supported and the span is $30$ ft$.$ Deflection is not to exceed span$/240$ for the live load. E $=29,000$ ksi, Fy $=36$ ksi. Use the method described in the Solved Example video and check for bending moment including self$-$weight, deflection, and shear. Make sure to include the values for each failure mode and the capacity that you are comparing with for each failure mode, as was done in the video.