This study provides a comprehensive evaluation of the strength capacity of bi-axially loaded steel-reinforced concrete (SRC) cross-sections under full fire exposure, including the heating, cooling, and post-fire phases. An advanced computational method is developed for direct strength assessment, using a strain-driven iterative approach combined with an adaptive plastic centroid. This “fail-safe” method improves global convergence properties through bisection and damped Newton techniques, ensuring accuracy and preventing convergence errors. The analysis considers temperature-induced material strength reductions and potential failure modes, highlighting the importance of explicit models for heating-cooling cycles and varying stress conditions throughout all fire stages. Unlike traditional methods that focus solely on ultimate or nominal capacity, this approach allows for a more thorough strength assessment. Validation is performed through comparisons with numerical data from the literature, extending benchmarks for assessing SRC cross-sections exposed to high temperatures.