I have a need for two beams that will allow me to hang 2 X 6's off one side and 2 X 8's off the other so that my ceiling is flat. The span for the beam is 15 ' 3 ", and the span for the joists is 12 '. I'm building this room inside my present pole barn, which has a shed roof above where I'll be building my "room". It has a concrete floor and is 32 ' long and 24 ' wide. Will three 2 X 12 X 16's be enough beam to support those joists, insulation, a sheetrock ceiling and four sheets of plywood on top of the 2 x 8's for lightweight storage?