Composite industry has long been seeking practical solutions to boost laminate through-thickness strengths and interlaminar shear strengths (ILSS), so that composite primary structures, such as stiffeners, can bear higher complex loadings and be more delamination resistant. Three dimensional (3D) woven fabrics were normally employed to render higher transverse and shear strengths, but the difficulty and high expense in producing such fabrics make it a hard choice. Based on a novel idea that the warp yarns that interlock layers of the weft yarns might provide adequate fiber crimps that would allow the interlaminar shear or radial stresses to be transferred and borne by the fibers, rather than by the relatively weaker matrix resin, thus improving the transverse strengths, this work provided a two point five dimensional (2.5D) approach as a practical solution, and demonstrated the superior transverse performances of an economical 2.5D shallow-bend woven fabric (2.5DSBW) epoxy composites, over the conventional two dimensional (2D) laminates and the costly 3D counterpart composites. This approach also produced a potential candidate to fabricate high performance stiffeners, as shown by the test results of L-beams which are common structural components of any stiffeners. This study also discovered that an alternative structure, namely a 2.5D shallow-straight woven fabric (2.5DSSW), did not show any advantages over the two control structures, which were a 2D plain weave (2DPW) and a 3D orthogonal woven fabric (3DOW) made out of the same carbon fibers. Composites of these structures in this study were conveniently fabricated using a vacuum-assisted resin infusion process (VARI). The L-beams were tested using a custom-made test fixture. The strain distribution and failure mode analysis of these beams were conducted using Digital Image Correlation (DIC) and X-ray Computed Tomography Scanning (CT). The results demonstrated that the structures containing Z-yarns or having high yarn crimps or waviness, such as in cases of 3DOW and 2.5DSBW, respectively, were shown to withstand high loadings and to resist delamination, favorable for the applications of high-performance structural composites.