I'm planning to build a post and beam swingset out of 6x6 pressure
treated lumber. I want to have 2 swings and one tire swing. The top
beam will be 16 feet, the posts 12 footers probably 4 feet into the
ground making it 8 feet high. The challenge is the tire swing. I have
two possible designs:

one ----- cantilevered with the middle post centered somewhere around 8 feet. The tire swing would mount at the end of the cantilever with the swings inbetween the two beams. This allows both swings and the tire swing to be used at one time. I prefer this design, but my concern is the amount of force on the connection point with the middle post and beam.

two ----- post and beam (not cantilevered). The tire swing would go in the middle with a swing on each side. In this design, the two swings would need to be set up on hooks while the tire swing is used. The advantage is the elimination of the severe stress on the middle beam with the cantilevered approach.

so, being the curious type, I snooped around a little and found some momemt of intertia and modulus of rupture calculations, like this...

moment of inertia, l = (W x H^3)/12 and strength, inch lbs = modulus of rupture x moment of intertia

so for me.... l = 5.5^4/12 = 76.3 strength = 76.3 X 8000 = 686,700 inch lbs

ok, so I'm a computer programmer, not an engineer. I have no idea what this number means to me. Doesn't the modulus of rupture depend on the span? Also this applies to the beam and I'm guessing my bigger concern is the post with approach #1.

Also, I originally wanted to use mortis and tenon joints mainly because I've always wanted to do that, but (especially with approach #1), I thought it might be better to drill 4 holes straight down thru the beam into the post and pound rebar or something similar down thru beam into the post.

The real question here is how do I calculate whether the middle post/beam connection will hold in design #1. I'm kinda assuming the second approach won't be a problem.

Any help on this would be appreciated.

one ----- cantilevered with the middle post centered somewhere around 8 feet. The tire swing would mount at the end of the cantilever with the swings inbetween the two beams. This allows both swings and the tire swing to be used at one time. I prefer this design, but my concern is the amount of force on the connection point with the middle post and beam.

two ----- post and beam (not cantilevered). The tire swing would go in the middle with a swing on each side. In this design, the two swings would need to be set up on hooks while the tire swing is used. The advantage is the elimination of the severe stress on the middle beam with the cantilevered approach.

so, being the curious type, I snooped around a little and found some momemt of intertia and modulus of rupture calculations, like this...

moment of inertia, l = (W x H^3)/12 and strength, inch lbs = modulus of rupture x moment of intertia

so for me.... l = 5.5^4/12 = 76.3 strength = 76.3 X 8000 = 686,700 inch lbs

ok, so I'm a computer programmer, not an engineer. I have no idea what this number means to me. Doesn't the modulus of rupture depend on the span? Also this applies to the beam and I'm guessing my bigger concern is the post with approach #1.

Also, I originally wanted to use mortis and tenon joints mainly because I've always wanted to do that, but (especially with approach #1), I thought it might be better to drill 4 holes straight down thru the beam into the post and pound rebar or something similar down thru beam into the post.

The real question here is how do I calculate whether the middle post/beam connection will hold in design #1. I'm kinda assuming the second approach won't be a problem.

Any help on this would be appreciated.