A support structure flange preform (11) resembles the Greek letter "pi" and has a base (13) with two legs (15, 17) extending therefrom. The perform is composed of a composite material that is formed from tows of woven or braided fiber. The tows are oriented to extend throughout each the base and legs. The perform may be either impregnated with a suitable thermoset resin, or may be unimpregnated so that resin may be infused at a later step of the overall manufacturing process. Two of the preforms are joined to a sine wave-shaped web (31) of the structural beam. The web is formed from uncured, thermoset resin sheets that are reinforced with oriented fibers. The web has two outer laminates that sandwich a syntactic or foamed resin layer in between. The legs of each perform straddle one edge of the web and are shaped to both sides to the precise contours of the web. A laminate strip (33) is positioned against the base of each preform to create a pair of flanges for the structural support member. The assembled structure is then heated and cured. The web and/or flanges of the structure also may be configured with alternating beads, tapered in either the vertical or horizontal direction, or inclined at non-orthogonal angles.