## 3 Results  
Because the article focuses mainly on the description of the methods, a simple example has been chosen. The analysis of the statically indeterminate truss presented in Figure 4 was conducted. The basic assumptions were as follows: the temperature and node forces presented in the figure are the only load, the structure is made of S235 steel, elements 1-12 are made of IPE300, elements 13-25 are made of SHS 60 \(\times\) 60 \(\times\) 5, the vermiculite spray-applied fire insulation with a thickness of 2 cm was applied. All results presented below concern the truss in the 30 th minute of fire duration.  
With continued fire duration, the effect of action in elements of statically indeterminate truss increases, but the bearing capacity decreases. In the analyzed structure, the bearing capacity of external cross-traces (18 and 25 according to Figure 4) was exceeded before the 30 th minute of fire duration. Therefore, it is necessary to consider the new static scheme presented in Figure 5. The digits in the truss scheme correspond to numeration of bars. To  
Figure 4: The static scheme of the analyzed truss.  
Figure 3: The algorithm of computation.\(\{\)displaystyle \(\backslash\)Theta = 2\(\backslash\)pi U_[2].\(\backslash\).\(\}\).  
conduct the system reliability analysis, it is essential to find the so-called \"cut-sets\". In the simplest way, it can be defined as the failures of single elements which lead to transforming the structure into a mechanism. In the paper, stiffness matrix spectral analysis was used to find cut-sets. In this method, all possible combinations of truss elements are removed from the stiffness matrix and its determinant is examined [41; 45]. If it is equal to zero, it means the structure is geometrically variable and the cut-set was found. This method is quite time consuming when we check all possibilities, so a good idea is to limit the number of bars, for example by the method proposed in [46]. In this case, all truss elements whose reliability is equal to 1 are neglected. For the analyzed truss, reliabilities of single elements in the 30 th minute of fire duration are presented in Appendix A. In Figure 5, elements in red are those bars whose reliability is different to 1, so they were taken into account during searching cut-sets. This task was realized with the usage of C++ code [46]. The searching of cut-sets was realized in the deterministic way, because according to authors, taking into account the randomness would not change the group of neglected elements (which are mostly elements intension).  
The analyzed truss in the 30 th minute of the duration of the fire can be transformed into a mechanism in two ways (Figure 5). The first corresponds to series systems, which means that failure of any element of the following set: 7, 8, 9, 10, 11, 12, 20, 21 will result in the failure of the whole structure. The second presented system is parallel-series, which means that the failure of the whole structure may be the result of the following elements failures: (9 **AND 18) OR (10 AND 23)**.  
In the SYSREL program where the system reliability analysis with FORM was performed, the logical model is the cut-sets representation is depicted in Figure 6.