Second‐Order Flexibility‐Based Element for Fire‐Exposed Structural Member Analysis

Abstract This paper presents an advanced computational method for analyzing structural members exposed to fire, using a novel second‐order flexibility‐based fiber beam‐column element. Developed using the complementary strain energy approach and the Engesser‐Crotti theorem, the formulation captures geometric and material nonlinearities—including biaxial bending–axial force interaction, thermal elongation, and slenderness effects. Its key innovation lies in the explicit coupling of plasticity, geometric nonlinearity, and thermal effects, enabling accurate simulation of stiffness degradation and internal force redistribution with a single element per member. The method traces plasticity evolution using the uniaxial temperature‐stress‐strain response of fibers. Tailored for RC and composite steel‐concrete members, the model captures their unique fire behavior. It employs the Finite Analytic Method (FAM) for element integration and a co‐rotational framework for global geometric nonlinearity. The nonlinear analysis framework supports both isothermal analysis for generating strength interaction diagrams and anisothermal analysis for predicting fire resistance time under progressive heating. Validation against benchmarks confirms its accuracy and computational efficiency.