I thought I read somewhere, can't remember where or when, that said cottonwood was not good for timber framing. I could be totally wrong. But as mentioned more research is necessary. There are formulas for figuring out the amount of shrinkage a beam will have. One book that has them is by Steve Chappell called "A Timber Framer's Workshop". I believe it's available through the online store. If not it's available through foxmaple.com
I just review his chapter on this and cotton wood is not listed on his chart of shrinkage values.
Good luck, Jim