taldridg
This is a tough one. One way concrete joists are my favorite structural system. But with the older constructions like the one you are working with, the slab thickness was usually pretty thin and the design was always based on a uniform load situation.
A 3000 lb. concentrated load would really concern me with the slab you describe.
You could check the one-way shear, [φ]Vc per the ACI code using between 20" to 40" for the effective width, b, but the thin-ness of the slab, coupled with the age and the fact that these older joist systems rarely had distribution cross-ribs built in them.
Without the cross ribs, this means that you may have longitudinal cracking along the slab/joist interface due to one joist deflecting relative to the other and the cross rib not there to minimize its effects. So this crack may be present to diminish your shear capacity despite your calculations.
The idea Lutfi presented can work, but man, that's a lot of steel to buy to resist the load. If its a moving load, that would tell me that you might have a bit of fatigue factor to consider as well (fatigue in crack development, not in the rebar).
A few other mitigation options:
1. Bolt some angled brackets with one leg attached to the under side of the slab and the vertical leg attached to the joist web side. These angles could run down the length of the slab and provide some additional shear capacity at the slab/joist interface.
2. Add a reinforced topping to add strength to span over the ribs and transfer the concentrated load. Might not be a good option as it raises the floor and adds dead load that may be too much for the existing joists to handle.
3. Load test a few areas with the point load to see what happens (see IBC chapter 17 or ACI Chapter 5?)
4. Tell the owner the 3000 lb load can't be applied to the floor.