professional opinions

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The best opinion you can get, probably for free, is to talk with the engineer / designer at a local truss fabricator (look in Yellow pages under Trusses - Construction, just above Trust Services)LOL. At our local fab shops they will usually take enough time to discuss what they feel are appropriate uses for their product. I think they will steer you away from installing a floor, but who knows, they might suggest a floor truss system that would work better than conventional joists. Take a picture or draw the trusses and take measurements of the span, and height, and I think someone will help.

Heres the deal. For use as an attic with a 30 psf live load (storage and people) and 10 psf dead load (joists, flooring, insulation, drywall), a 2x4 joist is only rated for a span of 7 feet 3 inches assuming 16 inch centers. It takes a 2x12 to span over 23 feet for a typical garage, so most garages with storage above, use a beam to cut the span to 12 to 13 feet and use 2x8 joists.

Here is a link to a simplified DIY span calculator that might be helpful.
http://www.cwc.ca/design/design_tools/calcs/SpanCalc2002/index.php

For a fee, a construction consultant or structural engineer could provide design plans for a separate joist system. This is not sistering the bottom chord, but installing separate loadbearing joists supported on the load bearing walls.