A precast composite flooring system utilizes girders and floor panels having steel lower structures placed in tension and concrete upper structures places in compression. Openings through a stem wall allow ducts, pipes, and conduits to be run therethrough. The system provides reduced weight over conventional precast or pour in place systems, allowing further reduction in the weight and size of other building components. The floor deck does not use tensioning strands, allowing openings to be formed at nearly any stage of construction and with reduced concern over cutting steel reinforcement. The floor panels and girders bolt together and bolt to a steel column frame, allowing for more efficient assembly.