Keywords: strength capacity of cross-sections, bi-axial bending, fire analysis, composite steel-concrete, full-range fire, strain-driven.

This study presents a unified computational framework for the direct assessment of the post-fire strength capacity of steel-reinforced concrete (SRC) cross-sections subjected to biaxial loading under geometric and thermal asymmetry. In contrast to conventional interaction-surface approaches, the proposed methodology reformulates strength assessment as a direct equilibrium–failure problem solved along prescribed loading paths, eliminating the need for interaction surface construction. The framework is built upon a hierarchical operator-based solution strategy comprising: (i) a predictor-based localization stage driven by a reduced sectional stiffness matrix, which identifies both the governing control pivot and a bracketing interval containing the failure point, (ii) an outer bisection procedure acting on a control strain parameter, and (iii) an inner damped Newton solver enforcing sectional equilibrium. To improve robustness under severe thermal degradation and material softening, an Adaptive Plastic Centroid (APC) formulation is introduced, providing a stable reference configuration and extending the solvability domain in regimes where classical formulations may become ill-conditioned. The framework consistently captures irreversible degradation and path-dependent thermo-mechanical effects throughout heating, cooling, and post-fire stages. Numerical results demonstrate excellent robustness and accuracy, while highlighting the critical influence of the cooling phase on the residual strength capacity of asymmetrically heated SRC cross-sections.

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