Rigid foam, continuous raised floor structure without wooden supports

A building sub-floor construction comprising a plurality of elongated beams formed of rigid polymer foam material, wherein the elongated beams comprise similar cross-sectional shapes, and wherein the elongated beams are configured to snuggly engage one another along their lengths to produce a continuous slab, and wherein one or more of said plurality of elongated beams is hollow and configured to function as an air duct, and wherein the construction further includes header joists on sill plates around a perimeter of the sub-floor providing a snug fit for said beams.