Eccentricity-Based Optimization Procedure for Strength Design of RC Sections under Compression and In-Plane Bending Moment

The strength design of reinforced concrete (RC) rectangular sections for combined compression and in-plane bending with two levels of reinforcement is indeterminate: three unknowns are to be solved, but with only two equilibrium equations; an additional condition is necessary to solve the problem. The additional condition leads to the finding of a minimum reinforcement-concrete ratio. This paper proposes a new approach based on the equivalent eccentricity of the applied compressive load. Different domains are reported, each of which is associated with given values of eccentricity and axial load. Analytical expressions for the domain boundaries are established, and a simple procedure is described to outline the conditions corresponding to the optimal reinforcement. The main advantage of this procedure is its simplicity, which allows manual computations. Some examples employing reinforcement sizing diagrams illustrate the validity of this approach.