I am planning on putting a shed roof on my 6x20 wood deck that is on the gable end of my house. I plan to use 2x4 joists by running 8 foot joists 16 inches on center and using a 4x4 as a beam to rest them on. The roof would pitch about 3/12. I would use joist hangers against the house. Is 2x4's OK for the estimated 6.5 foot span? Is the 4x4 strong enough for the beam? How far apart should I space the posts?