This paper presents an advanced computational method that incorporates the combined effects of geometrical and distributed plasticity into a fiber beam-column element for analysing steel reinforced concrete (SRC) frames exposed to fire. A novel second-order flexibility-based element has been developed using the complementary strain energy approach in conjunction with the Engesser-Crotti theorem to compute incremental force-deflection relationships at the element level. The formulation accounts for critical factors such as the coupling between bi-axial bending and axial force, thermal elongation, and slenderness effects under fire conditions. Moreover, the model efficiently traces the gradual spread of plasticity by following the uniaxial temperature-stress-strain behaviour of individual fibres at integration points, allowing for an accurate representation of the evolving resistance and failure mechanisms under fire [1]. Specifically developed for steel reinforced concrete elements, including Concrete Encased Steel (CES) and Concrete Filled Steel Tubular (CFST) members, the model accurately captures their unique material properties and interaction effects in fire conditions. The second-order flexibility-based formulation, employing the Finite Analytic Method (FAM) [2] for numerical integration, provides a comprehensive framework for integrating both material (distributed plasticity) and geometrical nonlinearities using a single element per member. Additionally, it is formulated as a co-rotational (CR) beam-column element, allowing for global geometrically nonlinear analysis. A general nonlinear thermal incremental-iterative solution scheme, based on the Newton-Raphson algorithm, is developed to address nonlinearities due to thermal expansion and material degradation at both the element and structural levels. Validation through benchmark problems and comparative studies demonstrates the accuracy and computational efficiency of the proposed method, making it suitable for performance-based fire design and assessment of composite structures.