## 3 Results
### Frame A  
The temperature increase in the following minutes of fire duration and related reduction factors for yield strength and Young's modulus [6] for frame A are presented in Tables 2 and 3. These show the values of effect of action and bending moment resistance in following minutes of fire duration. In the table, only the values for the most stressed elements (nodes) are presented. The number of nodes is consistent with that presented in Figure 3. The analysis was carried out with timesteps of 5 min. For frame A in the 45 th minute of the fire duration, the bending moment resistance was exceeded; therefore, the previous step was analyzed. The most stressed elements were nodes no. 2 and 12 (corners of the frame). After introducing their hinges, the moment distribution in the 40 th minute of fire would look similar to that shown in Figure 4a. It is easy to notice (see Table 3) that in this case, the bearing capacity in the ridgepole area was exceeded, which decided the failure of the structure. Nevertheless, before introducing hinges, the moment distribution looked like that shown in Figure 4b. The highest values of the bending moments occurred in the columns' bases and in the corners. Therefore, in the reliability computation, two mechanisms that combined these nodes (M1, M2--Figure 3a) were analyzed. Of course, in the case of frame structures there is an unlimited number of \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fire Duration**} & \multicolumn{4}{c}{**IPE 100**} & \multicolumn{4}{c}{**HEB 100**} \\ \cline{2-7}  & **Ta [\({}^{\circ}\)C]** & **k\({}_{\text{F}}\) [-]** & **k\({}_{\text{E}}\) [-]** & **Ta [\({}^{\circ}\)C]** & **k\({}_{\text{y}}\) [-]** & **k\({}_{\text{E}}\) [-]** \\ \hline
0 & 20 & 1 & 1 & 20 & 1 & 1 \\ \hline
5 & 40 & 1 & 1 & 37 & 1 & 1 \\ \hline
10 & 94 & 1 & 1 & 79 & 1 & 1 \\ \hline
15 & 153 & 1 & 0.95 & 125 & 1 & 0.97 \\ \hline
20 & 210 & 1 & 0.89 & 163 & 1 & 0.93 \\ \hline
25 & 265 & 1 & 0.83 & 217 & 1 & 0.88 \\ \hline
30 & 317 & 1 & 0.78 & 260 & 1 & 0.84 \\ \hline
35 & 366 & 1 & 0.73 & 301 & 1 & 0.80 \\ \hline
40 & 410 & 0.98 & 0.70 & 341 & 1 & 0.76 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Temperature analysis of elements of frame A. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Fire Duration**} & \multicolumn{4}{c}{**M\({}_{\text{Rd}}\)**} & \multicolumn{4}{c}{**M\({}_{\text{Ed}}\)**} \\ \cline{2-5}  & **2, 12 Node** & **1, 13 Node** & **2, 12 Nodes** & **7 Node** & **1, 13 Node** \\ \hline
5 & 9.3 & 24.5 & 8.4 & 4.58 & 5.3 \\ \hline
10 & 9.3 & 24.5 & 8.4 & 4.43 & 6.2 \\ \hline
15 & 9.3 & 24.5 & 8.5 & 4.29 & 7.0 \\ \hline
20 & 9.3 & 24.5 & 8.6 & 4.17 & 7.8 \\ \hline
25 & 9.3 & 24.5 & 8.6 & 4.07 & 8.4 \\ \hlinefailure paths, because plastic hinges may be created in any point of frame. But it is generally known and checked by the experiment mentioned in the Introduction that the most typical are sway and beam mechanisms. Therefore, those mechanisms were particularly chosen for further analysis. According to the method presented in the previous chapter, at the beginning of the fire (0-15 min), the reliability of the structure (according to mechanism M1) was so high that it was mathematically impossible to compute the value of the reliability index. The reliability indices for the following minutes of fire duration are presented in Figure 5. Between the 35 th and 40 th minutes, a rapid decrease in the reliability index is observed (according to the M1 mechanism). This is the direct result of the \(k_{y}\) reduction coefficient that influences the decrease in the bending moment resistance value. On the other hand, the analysis of the beam mechanism (M2) shows that the reliability increases slightly with the fire duration, which is the result of unburdening the bent. It is noteworthy that the combined mechanism (M1M2) computed according to Equation (12) gave the same results as the mechanism M2.