A floating offshore structure having a buoyant hull with an open truss frame having heave plates vertically spaced along the truss frame. One or more of the heave plates include a skirt plate that is attached around the outer perimeter of the heave plate and increases the effectiveness of the heave plate at trapping water mass between the heave plates for reducing heave motions of the floating offshore structure. A skirt plate is attached to one or more heave plates at essentially a right angle to the heave plate. The skirt plate may extend beyond the upper and lower surfaces of the heave plate or be positioned so as to be flush with the one surface of the heave plate and extend only beyond the opposite surface of the heave plate.