This is a great place to find out properties of different woods in North America.
Softwoods of North America
There is also one for hardwoods.
Very informative paper and a very helpful site on understand wood in general.
Those span tables from AWC.org could work as long as the log encloses the cut lumber shape (I think this is what Cactus Rex mentioned earlier) since roundwood is stronger that dimensional lumber. Not the most material efficient, but it would work!
Sadly those span tables www.uaf.edu/et cetera... are only for trees in Alaska.

I am not in Alaska. Otherwise those would work.
I got Ben Laws new book
Roundwood Timber Framing (I believe it is called) but have not found anything on engineering . . .
He did give reference to a paper that went into the structural properties of wood. Mabye I can dig that out of my computer files later.
Good book though. He really builds those buildings natural. No nails. He just uses wood oak pegs help hold the roundwood together. Mostly the fancy mortise and tenon joints to the work. The guy is amazing. The Log Construction Manual wips out the chainsaws and such

Still, if you get the general idea from the book I think an axe can work.
Okay, back to research . . .