The loads on this bridge would actually be pretty small just because the length is so short. While it is true a triaxle truck or fire engine might roll across it, bridge calculations are done on length and weight. In this case, even if a tri-axle truck did roll across the bridge, because the bridge is only 13 feet long, that means the entire weight of the truck is never fully on the bridge. (The front axle is on the bridge, or the rear axles are on the bridge, but never the full weight of the truck.
It still leaves the three rear axles over the bridge granted, but then that load is spread over 12 tires.
The best way to deal with that is, to put down (4) I beams at truck width, angle irons welded x fashion between them so they do not twist under load, then plank the bridge over with 3x8 planking. I would add bumpers on the outside, or railings depending on height. (Just to limit the liability of kids or grand kids falling off if it is high).
I would not over-think this too much.
That is why I discussed highest single axle load.