And I think I figured it out driving home from work.

The 2x6 is rated to carry 20 lbs per sq ft at a 12 foot span. In my simple mind, I am imagining a single 2x6 spanning 12 feet with a row of 1 foot by 1 foot squares on them. Each square is 20 lbs. So twelve of them weigh 240 lbs. Therefore, a single joist can carry 240 lbs with acceptable deflection.

Since I am planning to hang the swing from four eye bolts attached to 2x6's or 4x4's perpendicular to the joist span and going on top of three joists, they should be able to carry 3 X 240 lbs, or 720 lbs. Each side of my swing may weigh up to 500 lbs, so the three joists should not be over stressed since three joists should be able to carry 720 lbs.

(Actually more than that since the math I am using is based on a 12 foot span and my actual span is 10 feet.)

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