A novel shear reinforcing system, Wound Fiber Reinforced Polymer (W-FRP), is proposed that capitalizes on the flexibility of carbon fiber to create durable reinforcement cages for geometrically optimized concrete structures, thereby unlocking new potential to minimize carbon emissions associated with new concrete structures. FRP shear design methods have been extensively validated against prismatic beam tests, but variations in geometry are not yet considered. This paper proposes revised design methods, validated against tests on eight W-FRP reinforced variable-depth concrete beams, to examine the contributing factors to shear capacity. It is shown that the corner strength, orientation, and compression concrete confinement provided by W-FRP links, along with the contribution to shear of longitudinal bars are key design parameters. Optimizing the W-FRP pattern is found to provide as much as 50% shear capacity enhancement. The variable-depth geometry tested in this paper use 19% less concrete than an equivalent strength prismatic beam. Both reinforcement and geometry optimizations are the key steps towards achieving minimal material use for concrete structures