We are building a hand hewn old oak log home (yes pioneer style not kit log). We want exposed solid timber beams in the ceiling of the main floor. We are having oak sawn into 2x6 tongue & groove ceiling/floor for on top of these beams. Our roof load will not rest on this floor system, its weight will be on the log walls. There will be bedrooms above so weight load will just be living space. One room will have a 16ft open span, one 12 ft, the kicker will be the 20x20 open living room. We were thinking these beams would need to be on 30inch centers. Our question is what species of wood and what size beams? We can saw our own pine, oak, poplar.
This question is a bit on (or over) the edge of what's sensible to ask here. Even those who might be structural engineers (I'm not) can't do your structural engineering over the internet. People get hurt when buildings fall down.
Hopefully you have some big trees available.
Running it through a basic wood beam calculator (DAGS, which will keep any links from getting old), the 20 ft span on 30" spacing will need to be at least 4x16, and if you are sawing (or hewing) it yourself you're going to have to learn to grade your lumber for beams (a knot or split in the wrong place can make a much larger beam unsuitable for the load, depending where it is on the beam.) Or you do what the old-time old builders of your old oak log home would have more likely have done, and put two posts in the room supporting a central beam, rather than trying to span 20 feet. Few barns even had spans over 12 feet...
If you mean "tulip poplar" AKA tuliptree (wood tends to be greenish), it might be usable. It's a somewhat respectable wood. White poplar (young bark can be greenish, but the wood is dead white) aka cottonwood aka popple - I believe is generally considered unsuitable for beams - it's a lovely soft white wood to carve, you can cut wall panels from it, but it's weak as can be. Pine or oak are both fine.