## 3 Results
### Computational Study
#### 3.1.2 Example 2: Statically Indeterminate Truss with Six Degrees of Freedom  
The method presented in the first example is useful also for more complex structures, as this is presented in Figure 6. Particularly, this structure was analyzed in the paper [37], where the method with the use of full cut-sets was used. The very serious disadvantage of this method is that it is very time-consuming. Searching for all potential cut-sets, without taking into account the effect of action and load-bearing capacity, took more than 11 h.  
To make the method more efficient, the procedure with searching reduced cut-sets was used. It is worth noting that the groups of elements are designed to be made from the same profiles. In the case of Truss 1, cross-braces were designed to be made from SHS 60 \(\times\) 60 \(\times\) 3, bottom chord from HEA 100, and top chord-from HEA 120. It is obvious, then, that some cross-braces are in compression and the other are in tension; they have the very low ratio effect of action/load bearing capacity, so their reliability is equal to 1. This fact allows for reducing the number of cut-sets, which is the main issue of the presented paper. The task of system analysis with full cut-sets was analyzed in detail in the article [38]; in the following paper, the full cut-sets for Truss 1 are attached in Appendix A. The analysis of efficiency and correctness of the proposed method was checked on Truss 1 (Figure 6). Without thermal influence on the structure, no mechanism was found. The elements 20, 21, 30, and 31 (Figure 6) were the only ones which reliability was different from 1. It is obvious, then, removing any combination of this set of elements causes changes of the truss' static scheme, in such a way that only the degree of statically indeterminacy decreases. There is no possibility of transforming the structure into a mechanism. The structure analyzed in the following minutes of fire duration several times changed a static scheme as the result of exceeding the limit state of some elements. All these schemes with corresponding reduced cut-sets are shown in Figure 7. The results obtained using the proposed method were compared with these obtained previously with using full cut-sets [37]. Both were exactly the same, which confirms the correctness of the proposed method. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Fire Duration [min]** & 0 & 5 & 10 & 15 & 20 \\ \hline
**Reliability index \(\beta\) [-]** & 7.62 & 6.89 & 7.04 & 3.68 & 1.15 \\ \hline \end{tabular}
\end{table} 
Table 3: The results of reliability analysis of the two degrees of freedom structure in the following minutes of fire duration. Figure 6: Statically indeterminate structure with six degrees of freedom (Truss 1). In the previous research, the author took an attempt to conduct the system analysis for two structures, which was different from Truss 1 only in support type. For the structures which are the same as this in Figure 6, but supported in the different way (Figures 8-11), the method of searching all possible cut-sets is useless. First, this generates a very large number of cut-sets (Table 4). In addition, it is very time consuming. Introducing the reduced method allows us to get results within a few seconds (for analyzed structures). Figure 7: Static schemes of Truss 1 in subsequent minutes of fire duration and corresponding cut-sets. Figure 8: Statistically indeterminate structure with six degrees of freedom, with two nonsliding supports (Truss 2) and corresponding cut-sets. Figure 10: Statistically indeterminate structure with six degrees of freedom with intermediate support (after 1 st reduction) and corresponding cut-sets. Figure 9: Statistically indeterminate structure with six degrees of freedom with intermediate support (Truss 2) and corresponding cut-sets. The proposed new method enables us to conduct system analysis for structures with additional blocked degree of freedom (Figures 8 and 9).