Thank you to Gregory Huber for his definitions, paraphrased from those he wrote for the Saucon Valley Barn Tour guide.
Basement. The ground level of a two or more level barn, usually devoted to stabling animals.
Bay. The space or area between adjacent framing units or bents. For example, in a wood-framed barn with four bents, there are three bays.
Bent.One of the major transverse framing units on the second level of a barn that consists of partial barn width tie beams, vertical side wall posts, mid-point posts, braces of varying lengths, and often, built-in ladders. Bents were assembled on the barn floor or ground and were raised during barn raisings.
Brace.These diagonal members are either relatively short or quite long.
Fore-Bay. That part of the second level of a Pennsylvania barn that cantilevers over the stable wall of the basement.
Hay Mow.The "attic" level of a barn in which hay is stored.
To be continued.