do not sandwich the ply wood to the joist = waste of time and adds 0 to the spanabilty! your 2x6 construction in weak...u need to run a header board and split that span in 1/2.. ..not enough space for a wood beam then move to steel. add- any flex in the floor is going to make cracks in the tile joints... tgi/bci's only add stiffness > as there height increases.... u can sandwich all day and do yourself no good.
atv has it figured out. Split the span.
