S.7-1: A cantilevered HSS 2x2x3/16 tube beam is 2 ft long and supports a sign from the side of a building. The sign weighs 800 lb, and its center of gravity is offset from the center of the tube by 12 inches, causing a torsional moment to be induced in the tube from the weight of the sign. Check the design strength of this beam with the load case presented, considering all limit states and interaction. Assume the tube is A500 Grade B steel.

A steel beam is 24 inches tall, has a length, L, of 32ft, and has a yield stress of 36ksi. The simply supported beam supports a single load, P, of 17 kips at its midspan. If the theoretical maximum deflection of this beam is -(PL^3)/(48EI), determine the required moment of inertia such that the actual deflection of the beam will not exceed a value of L/360, and the actual stress will have a factor safety of 1.5 with respect to yielding.