This is what I would try, before calculating anything:
1. Get as much detail information on the joist as possible, all the dimensions, the span and spacing, are ends visible so you can see the reinforcing bar or stran?
2. Try to find out when the structure was built. That gives an indication of what codes it was designed under, what companies might have manufactured it etc.
3. Send a note outlining all you know about the joist, with a sketch of the details, to all the precasters within a reasonable trucking distance of the site, to see if they may have any information. If the structure is a bridge, check with the highway department that has juristiction.
4. If all that fails, then you have to get your slide ruler out (sorry, that was just for effect), your calculator or computer. All you can do is make some reasonable assumptions of loading and materials and see if the section will support them. The tough part is trying to find out what the reinforcing is. You may have to do some probing or non distructive testing.
This is the path I would take, hope it is some help.