Closed-form biaxial curvature and ductility domains for reinforced concrete rectangular sections

Abstract

The accurate yet practical assessment of deformation capacity of reinforced concrete (RC) members under axial load and biaxial bending is a key challenge in performance-based seismic engineering. This study develops a new set of closed-form analytical expressions for the analytical approximation of the biaxial elastic curvature, ultimate curvature and curvature ductility domains of rectangular RC cross-sections. An extensive parametric dataset of curvature domains is generated, spanning a wide range of geometrical configurations, reinforcement ratios, and axial load levels. The resulting directional capacity data are then approximated using a super-ellipse equation with the shape exponents calibrated via symbolic regression using a multi-population genetic programming (GP) algorithm. The resulting closed-form equations accurately capture the complex direction-dependent nature of the domains, showing superior accuracy and generality when compared to existing formulations. The proposed model successfully balances high fidelity while maintaining computational efficiency of a closed-form solution, ensuring compactness and ease of integration into structural analysis and design tools. The results will show that the model can balance accuracy and usability for performance-based assessment, displacement-based design, and the calibration of lumped-plasticity nonlinear models of RC columns.