Beam size and material for 15 feet long swing

I would refrain from using that type of fastener. I believe it will allow a lot of movement. I made a sketch to show what I have made before, many years ago. It does not have any hangers just angled notches that allow the legs to fit tightly and notches that act as a setting for the beam to bear on. A single bolt will draw it all together, or two could be used.

The legs are also splayed to help stabilize the swingset, and give more room for the swings.

7/12/2016 Edit

All it really takes is a circular saw set at 5 degrees or so. No set angle, just something that would draw tight as the bolt tightens. The notches on the beam are the same depth alll the way through. Just determine the angle you want the legs to splay at and make sure the overall width of the cut on the side is no wider than the leg material, otherwise the fit may be loose. The legs are what is cut at the angle. I added some sketches to help elaborate a little.

I hope it helps.

With the narrower angle (15), they add cross supports. The wider angle (30) is given with no supports.

Making a stable swing set is no joke. Unless it is part of a larger structure that weighs it down, the legs need to be anchored in concrete. When I was a kid I used flimsy backyard swing sets and could easily rock the whole swing set, frame and all, back and forth. Also, the swing set should be 10 feet from any fence, wall or hard surface (like pavement) if you want to avoid injuries. Some children (like myself) will swing out to the maximum height (about 8 feet) then leap out of the seat and go flying. When I was a kid this was a game we played, the object being to see who could catapult themself the furthest distance.

There is no hard and fast rule about the angle. It depends on the design of the swing set, especially the height, the material and the way it is joined. You can use a narrow angle, but the beams must be correspondingly stronger and better anchored.