Abstract: A system and method of preparing residential and commercial screen enclosures using box beams having a two-piece construction from identical extruded parts, which are self-mating and connected with fasteners, or snap-fitted together without fasteners. The box beam so formed is strong and easy to construct, and preferred in the front walls and roof designs of gable, mansard, dome, and flat screen enclosures. Both extruded parts of the box beam have a planar central member with two substantially perpendicular side pieces each having an exterior-facing spline and screen-edge retaining groove. In addition, an interior-facing gusset-retaining slot is created between each spline groove and the planar central member, with each pair of opposed slots configured and positioned to receive a tightly-fitting gusset plate that provides stronger and more precise box beam joints than is possible with gusset plates secured only by fasteners, as is common in prior art beam construction.