I don't expect any more than 10,000 lbs of weight per bay. Loading it up with hay would be heavier. At the moment, the design is for 100 psf.

Here's my latest thinking:

Floor Joist Layout

On Craig's suggestion (and knowing that it was the way in many old barns), I looked at configurations of sleepers. The part I didn't like, however, was embedding the ends of the sleepers in the concrete. I also wanted to keep the beam size a bit smaller than the sleepers would require. I've ended up (for the moment) with the configuration in the link above. By adding a post to the middle of the central span I can get the loads supported without having to resort to a giant member in the middle of the drive bay. It's been an evolving puzzle. Thanks for your input.