# Parametric Study on the Buckling of Unbraced Steel Frames under Fire Situation
## 4 Conclusions  
Steel frames exposed to fire lose strength and stiffness. Therefore, designers must adequately assess the behavior of steel frame elements in fire, trying to be as realistic as possible.  
For the studied cases, it can be concluded that:  
* Through a linear buckling analysis that considers the effect of temperature on the reduction in steel stiffness, it was found that the critical load of a steel frame in fire decreases as a function of the increase in temperature. All steel frames studied in this research presented lateral displacement of their joints at some point during the fire. For that reason, the most consistent manner to classify steel structures in fire is into braced and unbraced structures. In this study, braced frames were considered by simply restraining the lateral displacements, and in real situations, such restraint should be provided by the bracing system. The influence of the fire and its impact on the bracing system might have a significant influence on the behavior of the frames in case of fire. Further studies on this particular matter should be carried out but are outside the scope of the present paper. The instability of the steel frame during fire is not always controlled by the critical column at normal temperature;
* With this study, we concluded that it is possible to propose approximate buckling lengths to verify the safety of regular and irregular unbraced steel frames. For cases 1, 2, 5, 6, 9, 10, 11, and 12 (defined in Section 2.4), fire was located in one story at a time or in two stories, simultaneously. For the columns in the ground story, it is recommended a buckling length of \(l_{fi}=1.0\ l\) and \(l_{fi}=2.0\ l\) for frames with fixed or pinned supports, respectively; for the remaining columns of the remaining stories, a buckling length of \(l_{fi}=1.0\ l\) is suggested.  
Figure 18: Fire resistance time results for cases 4 and 8 with fire in one story at a time (simplified design method vs. advanced design method).  
* It was observed that, for different geometries of steel frames (i.e., regular and irregular), as well as for various fire cases, the differences between the values of the buckling factors have not shown to be significant.
* Considering the second-order stresses calculated at room temperature and taking into account the respective geometrical imperfections for pinned frames, it was concluded that adopting a buckling coefficient of 1.0 yielded results outside safety parameters. Such conclusion is possible when compared with the advanced design method. Therefore, such buckling coefficients used in case of fire are not recommended.
* Finally, it follows that a global first-order analysis of steel frames in fire without including the effects of imperfections in the verification of an equivalent column in relation to buckling phenomena and considering buckling lengths corresponding to the global mode of instability of the structure in fire is the best methodology for a simplified analysis of steel structures in fire.  
Conceptualization, T.S. and C.C.; methodology, C.C.; software, T.S. and C.C.; validation, C.C., P.V.R. and N.L.; investigation, T.S.; data curation, C.C.; writing--original draft preparation, T.S.; writing--review and editing, C.C., N.L. and P.V.R.; visualization, T.S.; supervision, C.C., P.V.R. and N.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by national funds through FCT--Fundacao para a Ciencia e a Tecnologia, I.P., under the Scientific Employment Stimulus-Institutional Call-awarded to the second author (CEECINST/00026/2018).  
The data will be made available upon reasonable request to the corresponding author.  
The authors declare no conflict of interest.