There might well be problems with the supports, but I'm surprised that there are no beams in this design. Steel beams would be the most practical for this size, but I don't see any pre-stressed concrete beams either. Concrete deck is poured in place with non-stressed reinforcement, so it isn't very resistant to bending, and is rarely expected to span such a distance by itself. I know of a shorter one-lane bridge that never has more than one tractor or big truck on it at one time, that nevertheless has a 6" steel beam under the concrete deck under each tire track. Perhaps it was over-engineered, but then again perhaps the bridge in TFA was under-engineered...