Abstract: A system for constructing multi-story building is disclosed. The system can include a plurality of vertical beams and a base beam section. The base beam section can be supported horizontally between the plurality of vertical column members and can include a composite shear connector attached thereto. The framing system can further include a plurality of concrete plank sections spanning perpendicularly to, and supported by, either side of the base beam. The plurality of concrete plank sections can be assembled in pairs. The framing system can also include grout material applied to the composite shear connector and the concrete plank sections to fill the cavities of the assembly to provide an integral framing system. A method for assembling such a system is also disclosed.