Gym retrofits on second floors can be tricky. One thing that should also be considered is vibration. I've had occasion to review an existing retail space with bar joists and form deck/concrete for the purpose of adding group exercise class/aerobic rooms. Vibration considerations - particularly with an adjacent other tenant space not owned by the gym - would have required some sort of structural retrofit (like adding joists).
I had one project (new construction) years ago with a work-out room adjacent to apartments on every floor (it was a desirable amenity). If I recall correctly we recessed the floor structure several inches in order to put in a special vibration and impact-absorbing floor mat. I don't recall the name of that system at the moment, but a similar type system might be useful in a retrofit situation. If you have an architect on your project, the floor finish/need for impact resistance would definitely be something to discuss with them.
------------------------------
Stephanie Slocum P.E., M.ASCE
Founder
Engineers Rising LLC
State College, PA
------------------------------