# Study on the Fire Resistance of Axially Restrained H-Shaped Steel Beams Under Real Fire
## 5 Conclusions  
This paper uses the validated finite element model to conduct a parametric analysis of the fire resistance performance of Q460 steel beams, analyzing the impacts of loading patterns, longitudinal maximum temperature in the early fire stage, and load ratio on the critical temperature of steel beams. A theoretical analysis of the real fire response of Q460  
Figure 18: Comparison of critical temperatures between calculated and simulated results.  
steel beams during the heating stage is conducted, and the simplified calculation formula for the critical temperature is revised based on finite element analysis results. The following main conclusions are drawn:  
(1) Under consideration of longitudinal temperature non-uniformity in the early fire stage, the critical temperatures of steel beams in all scenarios exhibit a significant increase compared to those under direct ISO 834 heating. The average increase was 100-120 \({}^{\circ}\)C. When the vent area is expanded to 4 m2, the transverse temperature difference of the steel beam is reduced to less than 50 \({}^{\circ}\)C, and the difference between the critical temperature and the ISO 834 working condition is reduced to less than 5%. The height of the ventilation openings has a minimal effect on the critical temperature of steel beams, as the distribution patterns and temperature differences of non-uniform temperature fields in steel beams during the early fire stage show little variation under various scenarios, thus exerting similar influences on the critical temperature of steel beams.  
(2) Under the same scenario, for every 0.1 increase in load ratio, the critical temperature decreases by about 25 \({}^{\circ}\)C. When the load ratio increases from 0.2 to 0.8, the critical temperature decreases from 670 \({}^{\circ}\)C to 565 \({}^{\circ}\)C, with a decrease of 15.7%. Under the condition of a fixed load ratio, the failure temperature decreases by 8-12 \({}^{\circ}\)C for every 100 \({}^{\circ}\)C increase in the early maximum temperature. When the load ratio is fixed, as the maximum temperature in the early fire stage increases, the failure temperature of steel beams exhibits a moderate decrease, and the difference from the critical temperature under ISO 834 heating conditions gradually diminishes.  
(3) The critical temperature of steel beams is modified, and the simplified calculation formula of critical temperature under different load ratios is proposed. Using the simplified calculation formula for steel beams, the critical temperature was calculated and compared with finite element analysis results; it was found that the calculation results were in good agreement with the finite element analysis results, and the difference was within 5%. Therefore, the simplified calculation method of the critical temperature of the constrained Q460 steel beam proposed in this paper can be used in practical engineering projects as an effective reference for calculating the critical temperature, and it can provide practical suggestions for related design work.  
Conceptualization, W.C. and T.Y.; methodology, Q.Q. and X.W.; software, X.W.; validation, Q.Q. and X.W.; data curation, M.L. and Z.C.; writing--original draft preparation, Q.Q.; writing--review and editing, W.C.; visualization, J.L. All authors have read and agreed to the published version of the manuscript.  
This study was supported by Shandong Higher Education Institutions Young Creative Talents Science and Technology Support Program (TJY2303).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
The authors declare no conflict of interest.