The pursuit of structurally efficient elements that minimize material consumption while meeting structural performance requirements is becoming increasingly important due to escalating global environmental concerns. This relevance is particularly pronounced for high-performance concrete elements with high-strength FRP reinforcement, such as epoxy-impregnated carbon fabrics or rebars, which have up to six times the tensile strength of steel but are often underutilized at ultimate bending conditions. In order to establish an explicit link between the design parameters and the resource efficiency of the design of a rectangular cross-section, we present closed-form formulas that inherently satisfy the requirement of full utilization of both, concrete and reinforcement. As a result, this derivation offers a direct means of delineating the range of parameters that lead to an efficient cross-sectional design. The design equations are derived using a novel analytical flexural model, which is based on an energetically equivalent bilinear approximation of a nonlinear concrete material law. The accuracy of the flexural capacity and design efficiency formulas is validated using three data sources: (i) a series of tests conducted in-house on carbon-fabric reinforced and steel-carbon hybrid-reinforced beams in three-point and four-point bending configurations; (ii) comparative studies of material utilization ratios for varying reinforcement ratios, using a general numerical model of a cross-section; (iii) a broad collection of data from published studies. The flexural model used in the closed-form design equations achieves an average fit of 97% between the analytically predicted and experimentally measured flexural capacities, representing an improvement over the ACI 440 code, which has a corresponding value of 89%. The efficiency-oriented evaluation and flexural design concepts presented here provide a conceptual foundation for quantifying and enhancing the design efficiency of carbon-reinforced concrete elements, marking a significant step towards sustainable construction.