Design Aids for a Reinforced Concrete Beam with the Minimum Cost Concept

In reinforced concrete design, structural member sizes and amount of reinforcing steel areas are usually selected based on the structural designers' experience. Most existing charts provided for the design of reinforced concrete structural members were developed mainly based on force equilibrium conditions and some serviceability criteria. Sections selected from these charts may not result in an economic solution in terms of material costs as well as construction costs. Practical design aids are developed and suggested in this study for the economical design of reinforced concrete beam under flexural loading. With the beam width fixed, the depth of a beam, positive steel areas and negative steel areas are found from Khun-Tucker necessary conditions with Lagrangian multipliers to minimize the sectional cost of a beam. The developed design aids might be useful in selecting optimum reinforced concrete beam sections. Theoretical derivations and use of the developed design aids are described in this paper.