Interaction Surfaces for Post-Fire Analysis Based on Minkowski Sum

: The primary aims of this paper are twofold: firstly, to employ Minkowski sum to assess the interaction surfaces of a reinforced concrete section in a post-fire analysis, and secondly, to investigate the impact of fire length on load-bearing capacity for a simple example of a beam under four-point bending. The approach used in this study has previously been utilized for fire scenarios and can be easily adapted for post-fire analysis purposes. The Minkowski sum method is utilized to generate interaction surfaces by combining multiple basic geometric shapes into a more intricate shape. In this case, the simpler shapes used are ellipsoids, and they approximate the contribution of a cross-sectional part. By dividing the section into parts, various material characteristics can be assigned to them, which is crucial for analyzing fire and post-fire bearing capacity. Once the interaction surfaces are formulated, the procedure of evaluating utilization of sections is explained based on the inputted sectional forces. The study compares the experimental and numerical results. The findings obtained utilizing this methodology demonstrate good conformity with outcomes obtained through both experimental data and finite element analysis. The investigation illustrates that fire exposure duration has the most substantial influence on compression and bending load-bearing capacity, particularly when subjected to small eccentricity.