Calculate load on pipe supported on multiple points

I am planning to use a steel SCH 40 pipe (using this material for cost and availability) to distribute a load across a ceiling. I will attach a 21' stick of pipe to each joist (16" on center; 15 joists). I'm trying to figure out what size pipe I need to buy, and to do this I want to calculate how good of a job the pipe will do distributing the load. So, I want to calculate:

If a load (say, 2000 lb) is placed exactly between two load points ( for symmetry to keep the math simpler we can assume 7 support points on each side of load, at 8" from load, 24", 40", etc.), how much of that load will be applied to the two nearest support points?

Thanks

Vernon