The beam supports the roof made from asphalt shingles and wood sheathing boards. If the...

The beam supports the roof made from asphalt shingles and wood sheathing boards. If the boards have a thickness of in. and a specific weight of 50 lb/ft³, and the roof’s angle of slope is 30°, determine the dead load of the roofing—per square foot—that is supported in the x and y directions by the purlins.