## 3 Results
### Computational Study
#### 3.1.2 Example 2: Statically Indeterminate Truss with Six Degrees of Freedom
In the case of Truss 2 (Figure 8), due to the blockage of thermal elongation in the bottom chord, under temperature influence, huge axial forces were generated (Table 5), so the whole analysis was stopped before the fifth minute of the duration of the fire. It is worth noticing that not only the two cross-braces (no. 20, 31) exceeded the limit state, but also all the elements that create the bottom chord (no. 1-6). They are marked in red in Figure 8 and highlighted in Table 5, which presents the effect of action and the load-bearing capacity in each element in the fifth minute of fire duration. What is important, even in the case without taking into account temperature (0 min), is the reliability index for the structure was very low (see Table 6). It was caused by the fact that the obtained cut-sets (Figure 8) are connected in a series way. It should be explicitly underlined that such a behavior of indeterminate structure is extremely unexpected. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Fire Duration [min]**} & \multicolumn{3}{c}{**Reliability Index \(\beta\) [-]**} \\ \cline{2-4}  & **Truss 1** & **Truss 2** & **Truss 3** \\ \hline
0 & - & 0.84 & - \\
5 & 7.77 & - & - \\
10 & 7.94 & - & - \\
15 & 4.7 & - & - \\
20 & 4.52 & - & 6.22 \\
25 & 4.33 & - & 0.34 \\
30 & 3.53 & - & 1.88 \\
35 & 2.08 & - & 1.59 \\
40 & 3.42 & - & 1.19 \\
45 & 2.98 & - & 0.64 \\
50 & 2.43 & - & 0.06 \\
55 & 1.05 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Reliability indices for trusses 1, 2, 3 in the following minutes of fire duration. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Tuss**} & \multirow{2}{*}{**Number of Cut-Sets**} & \multicolumn{3}{c}{**Time of Searching**} \\  & & & & & & & & & & & Cut-Sets [h] \\ \hline
**Truss 1** & 325 & \(\approx\)11 \\
**Truss 2** & 4888 & \(\approx\)19 \\
**Truss 3** & 14,160 & \(\approx\)98 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The number and time of cut-sets searching for Trusses 1, 2, 3. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No. of Element**} & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** \\ \hline
**Effect of action [kN]** & \(-222\) & \(-201\) & \(-195\) & \(-195\) & \(-201\) & \(-222\) & \(-2\) & \(-33\) & \(-44\) & \(-44\) & \(-33\) \\
**Load bearing capacity [kN]** & \(173\) & \(173\) & \(173\) & \(173\) & \(173\) & \(173\) & \(254\) & \(254\) & \(245\) & \(254\) & \(254\) \\ \hline
**No. of Element** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** & **21** & **22** \\ \hline
**Effect of action [kN]** & \(-2\) & \(-7\) & \(17\) & \(14\) & \(17\) & \(14\) & \(17\) & \(-7\) & \(-46\) & \(-27\) & \(-15\) \\
**Load bearing capacity [kN]** & \(254\) & \(75\) & \(158\) & \(158\) & \(158\) & \(158\) & \(158\) & \(75\) & \(35\) & \(32\) & \(30\) \\ \hline
**No. of Element** & **23** & **24** & **25** & **26** & **27** & **28** & **29** & **30** & **31** & \\ \hline
**Effect of action [kN]** & \(-13\) & \(-5\) & \(2\) & \(2\) & \(-5\) & \(-13\) & \(-15\) & \(-27\) & \(-46\) & \\
**Load bearing capacity [kN]** & \(32\) & \(35\) & \(158\) & \(158\) & \(35\) & \(32\) & \(30\) & \(32\) & \(35\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The effect of action and load-bearing capacity for Truss 2 in the fifth minute of fire duration. It is well-known that in a series system, the static weakness is observed. It means that the reliability of the whole structure is lower than the reliability of the weakest element. That is the reason why the obtained reliability index for the structure is very low. The truss in Figure 9 was the last structure analyzed. In this case, the intermediate support in the half of the bottom chord span was introduced. In the Figure 9, cut-sets corresponding to the presented static scheme are shown.