Computational issues in biaxial bending capacity assessment of RC and composite cross-sections exposed to fire

This paper introduces an advanced computational method for assessing the biaxial bending capacities of arbitrary-shaped reinforced concrete and steel–concrete composite cross-sections under fire conditions. The proposed approach involves a strain-driven iterative method coupled with an adaptive plastic centroid providing a “fail-safe” methodology by combining the bisection and damped Newton methods to improve its global convergence properties. Several key computational issues are addressed: (1) strength assessment criteria and its impact on computational outcomes, (2) the pathological behavior of local convergent iterative methods causing divergence or spurious solutions in stress-resultant space, (3) the softening behavior of concrete in compression affecting solution uniqueness and interaction diagram convexity, (4) non-planar vertical interaction diagrams induced by a mobile centroid, and (5) computational challenges related to solution non-uniqueness or non-existence in M-M stress resultant space when axial force falls outside the iso-load contour. An additional notable feature and novelty of the proposed method lie in its unique capability to assess true plane vertical interaction diagrams enabling also both ultimate and nominal strength assessment. Validation includes comparisons with other numerical results and experimental data from international literature, extending the benchmark results for the strength capacity assessment of composite cross-sections exposed to high temperatures.