Good idea to stiffen the joists. If the space is not being used below, I would build a 2x4 wall, pressure treated bottom plate and double or triple top plate. Space the studs at 32" on center, or 16"o.c., under each joist with one top plate. You don't know the slab thickness or hidden bearing (if any) for a post and beam frame. The blocks in this case are required to hold the joists from rotation, because the rim doesn't extend the full thickness of the joist.
http://www.bssconline.org/Homebuilders_Guide/Chapter4.pdf Page 5. Be safe, G
http://www.bssconline.org/Homebuilders_Guide/Chapter4.pdf Page 5. Be safe, G