I have a 4x6x16 beam that I would like to use on a new swing set. If I span 12 feet between supports, can I leave one or both ends cantilevered to support an additional swing?
Yes - I have a swing set that we purchased that was exactly that construction with 4x6 legs and a 16' 4x6 main beam with one swing cantilevered on one end. Ours was made by Woodplay
4x6x16 is a good sized beam. Enough for a swing set anyway. As for the cantilever, how large of a cantilever are you talking? The general rule of thumb in architecture is no more than 30%. So for example, a 30% of a 16' beam is 4.8', which would be just under 2 1/2 feet on each side. Thats a little tight but in this case you could probably get away with 3 feet on each side as the moment is still very near or over the support. You can do some quick beam calculations here.