A flat-bed trailer is to be designed with a curvature such that when loaded to capacity the

Question:

A flat-bed trailer is to be designed with a curvature such that when loaded to capacity the trailer bed is flat. The load capacity is to be 3000 lbf/ft between the axles, which are 25 ft apart, and the second-area moment of the steel structure of the bed is I = 485 in4. Determine the equation for the curvature of the unloaded bed and the maximum height of the bed relative to the axles.