I can help.
They're spanning 31.5' with no intermediate support?
WOW. They will either need an intermediate support (or two, I will check) or you will need to put the properly sized joists in between or next to each of the original joists. Which option do you prefer?
Are they supporting a single floor only with no load bearing walls above?
Will they support any ceramic tile?
For the single floor only and without ceramic tile, you will need 16" TJI 560 at 16" on center.
If you have ceramic tile, you will need LVL 3.5" x 18" 2.0E at 16" on center.
Hello. Do you have any other questions for me on this topic. If you could rate my answer, I would appreciate it.