Retrofitting a horizontal building roof having a pre-existing, composite-strength concrete roof having a corrugated steel deck with concrete poured over the deck top. Replacing the pre-existing roof with a dry-installed composite-strength roof having a rigid sheet installed over a corrugated steel deck, the rigid sheet attached to the deck by mechanical fasteners extending through the rigid sheet and the upper ribs of the corrugated deck. The newly installed roof restrains the upper ribs against lateral distortion under loading, thus forcing the corrugated deck to maintain shape and operate to composite capacities in excess of predictable flexural load capabilities of its components considered alone.