Beams are among the most frequently used structural members in constructions. Presently composite beams are not available wherein the web(s) have integrated fibre assemblies oriented in bias (+/-theta degrees) directions relative to the beam's length direction, the flange/s have integrated fibre assemblies oriented in the beam's length and width (0 degrees/90 degrees) directions, and the web(s) - flange(s) have mutual through-thickness integrity at their junctions. Consequently, the competitive potential of composite beams is not fully utilised with respect to conventional counterparts built from isotropic materials. To overcome this shortcoming and bring composite beams to a new level of competitiveness, an innovative Add-on Weaving technique has been specifically developed recently. This Paper introduces the novel woven preform architecture and presents the initial results demonstrating the performance of new composite I-beams developed for the purpose. This advancement reflects maturing of the new weaving technique and its 3D fabric reinforcements and also supports its transit from lab to industry.