# Parametric Study on the Buckling of Unbraced Steel Frames under Fire Situation
## 3 Results and Discussion
### Fire Resistance Analysis  
This section reports the fire resistance analyses conducted in the steel frames studied for the various fire cases described in Section 2.4. The analyses used the simplified design method and the formulations proposed by EN1993-1-2 [15]. The results will be later compared with those yielded by finite element method (FEM) analyses with the software SAFIR [34]. The abscissa axis represents the fire resistance times obtained with SAFIR [34], i.e., using an advanced design method based in the FEM. The ordinate axis shows the fire resistance time results calculated using the simplified method, considering first-order internal forces and using the buckling coefficients proposed in Section 3.1.4. The simplified design method results are deemed safe when lower fire resistance is obtained when compared to the resistance predicted by SAFIR and unsafe otherwise.  
for frames with pinned supports and fire in the lower story. In other cases, results are within the safety margin.  
Figure 12: Variation of the buckling factor with the temperature of the most critical column in all frames for scenario 6 with fixed supports.  
Figure 13: Variation of the buckling factor with the temperature of the most critical column in all frames for scenario 6 with pinned supports.  
Regarding cases 3-(CE,cold-CI,4S-B4S) and 7-(CE,cold-CI,4S-B3S) (see Figure 16), it was found that these were too conservative for the cases in question. In other words, fire resistance times calculated by the simplified design method using a buckling factor of \(l_{fi}/l=1.0\) for all columns (except those belonging to story 0 of the pinned frame, for which \(l_{fi}/l=2.0\) was used) were well below the values calculated with the advanced FEM design. Moreover, it is observed in Figure 17 that, when the buckling coefficient used tends to  
Figure 14: Fire resistance time results for cases 6, 9, 10, 11, and 12, with fire in 1 story and 2 stories simultaneously at a time (1 st simplified design method) vs. advanced design method).  
Figure 15: Fire resistance time results for case 6 with fire in one story at a time (second simplified design method vs. advanced design method).  
\(l_{fi}/l=0.5\) for all columns (except those belonging to story 0 of the pinned frame, for which \(l_{fi}/l=1.0\) was used), the results were quite satisfactory.  
In all fire cases wherein the columns were heated, those were responsible for the collapse of the structure. However, in fire cases 4 and 8, in which the external and internal  
Figure 16: Fire resistance time results for cases 3 and 7 with fire in one story and two stories simultaneously at a time (second simplified design method (K = 1.0 and 2.0) vs. advanced design method).  
Figure 17: Fire resistance time results for cases 3 and 7 with fire in one story and two stories simultaneously at a time (simplified design method (K = 0.5 and 1.0) vs. advanced design method).  
columns are at room temperature and only the beams are heated on 3 or 4 sides, the collapse of the structure was governed by the beams. According to Figure 18, it was found that in most cases the results were satisfactory and well within safety margins.