My cabin is 24' x 24' and with three RPSLs, my minimum diameter on the Ridge Pole is 16". We have a 6' eve on the back and 8' eve on the front, our snow load is 200 lbs. per square foot, quite heavy. I had to look long and hard to get a 40' log with 16" at the small end. My point is the only one to tell you how to support your roof, is your engineer.
Of course it was "free" like the rest of my logs, just had to get it myself.

If you can get a larger ridgepole, I would advise it for a house that large. Structural members that must carry a load by themselves should have room for error built in, and a 12" diameter log doesn't have much room for error, even if you have 4 support logs. One hidden pocket of rot and your roof could wind up in your living room.

By the way, 12" at the butt or the top?

Poplar from the woods, or from around the home?

Poplar will (should) work fine for the wall logs, but
I'm not brave enough to use it for a ridgepole or
rafters. You would be surprised at the low strength
of home-grown Poplar. Regular watering makes them
grow fast, but they are not something I would use as
a structural element.

Was just at the new place. About 1/2 way home it hit
me that I wanted to bring home some of my Poplar (have
about 2000 bd ft) to make some light-weight fruit boxes.
May have to go to Home Depot for pine. It's several hundred
miles to go back and get my Poplar lumber.

BTW...you may consider milling your own wood if the wood is
free and plentiful. I could have milled my Poplar for about 5 -10
cents. I had a friend mill the logs, and while he was away building
and wiring a post & beam house, the guys who were supposed to
be milling were taking day long coffee breaks. I could have milled
in less than 20 hours. They took about 125 (or so) hours. That hurt
the ol' checkbook.

-Rick

I remember Ellsworth in class telling me that slow growth(i think tighter rings) is best for logs to build with. Rick is right --ok for walls-like Rick said--not for structure on main bearing loads--or at least better safe than sorry.

At least in the Northwest. Stuff rots faster than bread. Skip specifically mentioned several times to never use poplar or mix media. I could see in a pinch using poplar (like Donner party survival hut) but the stuff is grown as a crop to make toilet paper for a reason. Fast, soft and rots like crazy. Instant pulp. If you are going to invest in a good log home, poplar for any use would be a mistake in my opinion.

It is an abused description of many trees however. Here, mostly cotton woods and the ilk. Grows faster than grass. Rings so big looks like cocentric doughnuts. Snaps like pretzel sticks. Nuts, I cut them down and chip them up and in two years another 20' plus tree grows out of the stump. I consider them weeds.

I was told by an elderly fellow once, they called them poplar because the sound they make when they bust. Probably not so, but the do indeed pop real easy.

Build with a good fir or pine or cedar. Use the poplar for firewood or cabinets. :0) Makes pretty furniture.

Depending on the part of the country you are from, poplar is either aspen, cottonwood, tulip tree, tulip poplar, and there are probably other names trees that are called poplar.

Yellow poplar, also called tulip poplar, or Liriodendron tulipifera, has been used in log homes in kentucky for 200 years. There are 150 year old log homes, built out of this species, still standing within 10 miles of where I'm building. Of course, they were old growth poplar which can't be gotten now, but with adequate protection from water they do not rot, termites have very little interest, and they grow straight and tall. As I've mentioned before, it does check more than a lot of species but again, with adequate overhangs these checks are of no real consequence, as the do not "check through".

I would not use poplar for structural elements unless it is oversized for the job. My ridgepole is 24" diameter at the butt.