Analytical formulation for biaxial curvature domains of rectangular reinforced concrete sections

This study proposes a novel closed-form analytical model for defining the biaxial ultimate curvature domains of rectangular reinforced concrete (RC) sections under combined axial load and biaxial bending. The model is derived through a hybrid approach that couples high-fidelity fiber-based sectional analysis with data-driven calibration. A comprehensive parametric database, covering a wide range of geometric configurations, reinforcement ratios, and material properties, is generated and used to calibrate a super-ellipse-based formulation for the curvature domain. The key innovation lies in the derivation of an explicit expression for the super-ellipse shape exponent, obtained via a multi-population Genetic Programming (GP) symbolic regression algorithm. This expression accounts for the combined effects of axial load, reinforcement layout, and reinforcement ratio, thereby improving accuracy compared to existing models that rely on simplified assumptions. The resulting closed-form solution efficiently captures the direction-dependent inelastic deformation capacity of RC sections without requiring computationally intensive numerical analyses. Its applicability is demonstrated through extensive validation against the numerical database, showing excellent agreement. The proposed model offers structural engineers a practical tool for ductility verification and plastic hinge calibration, advancing performance-based seismic design methodologies.