I am designing a 4'x12' trailer frame. 8' of it will support weight, the balance will be the tongue. My area of concern is bending at the ends of the long supports. There will be a wheel assembly located 4' from the frames end that will support all but the tongue weight of 100 -120 lbs. I plan to use commercial steel tubing so the moment of inertia ($I$) and Section Modulus ($Z$) are known quantities.
What I need is a formula that is suited to this design - ie. something that will tell me how much the frame might bend under load. I have some knowledge of simple design as well as an AISC and Machinery's handbooks
Its going to be a 4' x 8' with a 4' tongue, the tongue weight should be 50 to 80 lbs. I'm designing it to keep the weight below 900 lbs. I want it to have 15" wheels. I'm using components for a design weight of 2000 lbs. and plan on using axle-less wheel hubs. There will be a close to a uniform load spaced over the wheels. The wheel assembly will be off center to improve tracking.
I'm looking for a suitable "Beam Diagram" to ensure I stay within a reasonable deflection. I have seen them designed with 2" x 2", and 2" x 3" tubing.