A floor system for a building includes prefabricated grid sections attached to framing members of the building and a plurality of panels mounted to the grid to form a structurally integrated floor. The panels are removable to provide access to space below the floor that would otherwise be inaccessible in a conventional floor. A subfloor deck below the floor separates one building story from another and encloses the space between the floor and the deck, which can be used for temporary and permanent installations including, for example, pipes for water, laboratory gases, and compressed air, and power, telephone, and data cables; and as a plenum for HVAC. Either or both of the floor and the subfloor deck can be attached to the building frame to function as a diaphragm. The floor system replaces conventional permanent structural floors and raised accessible flooring systems.