## 2 Materials and Methods
Generally, the load-bearing capacity is computed as follows:  
\[N_{fi,\theta,Rd}=k_{y,\theta}N_{Rd}\Big{[}\gamma_{M,0}/\gamma_{M,fi}\Big{]} \tag{3}\]  
\[N_{b,fi,t,Rd}=\chi_{fi}Ak_{y,\theta}f_{y}/\gamma_{M,fi} \tag{4}\]  
where:  
\(N_{fi,\theta,Rd}\)--the design load-bearing capacity of a tension member with a uniform temperature \(\theta_{a}\);  
\(N_{fi,t,Rd}\)--the design buckling capacity at time, \(t\), of a compression member;  
\(N_{Rd}\)--the design-bearing capacity of the cross-section, \(N_{pl,Rd}\), for normal temperature design, according to EN-1993-1-1 [31];  
\(k_{y,\theta}\)--the reduction factor for the yield strength of steel at the temperature, \(\theta_{a}\), reached at time, \(t\), according to Table 3.1 in EC-1993-1-2 [29],  
an elemental area of the cross-section;  
\(f_{y}\)--yield strength;  
\(\gamma_{M,0}\), \(\gamma_{M,\theta}\)--partial safety coefficient (in the paper they are neglected, because to conduct the reliability analysis characteristic values are needed);  
\(\chi_{fi}\) is the reduction factor for flexural buckling in a fire design situation and is defined as follows:  
\[\chi_{fi}=\frac{1}{\varphi_{\theta}+\sqrt{\varphi_{\theta}^{2}-\overline{ \lambda}_{\theta}^{2}}} \tag{5}\]  
where:  
\[\varphi_{\theta}=\frac{1}{2}\Big{[}1+\alpha\overline{\lambda}_{\theta}+ \overline{\lambda}_{\theta}^{2}\Big{]} \tag{6}\]  
\[\alpha=0.65\sqrt{235/f_{y}} \tag{7}\]  
\[\Delta\theta_{a,t}=\frac{\lambda_{p}A_{p}/V\big{(}\theta_{g,t}-\theta_{a,t} \big{)}}{d_{p}c_{a}\rho_{a}(1+\phi/3)}\Delta t-\Big{(}e^{\phi/10}-1\Big{)} \Delta\Theta\theta_{g,t} \tag{2}\]0  
In the Equation (8), \(k_{E,\theta}\) is the reduction factor for the slope of the linear elastic range at the steel temperature, \(\theta_{a}\), reached at time, \(t\), according to \[\Delta\theta_{a,t}=\frac{\lambda_{p}A_{p}/V\big{(}\theta_{g,t}-\theta_{a,t} \big{)}}{d_{p}c_{a}\rho_{a}(1+\phi/3)}\Delta t-\Big{(}e^{\phi/10}-1\Big{)} \Delta\Theta\theta_{g,t} \tag{2}\]11 in EN-1993-1-2 [29], \(k_{y,\theta}\) is defined the same as in Equations (3) and (4). To conduct the reliability analysis, it is essential to know not only the load-bearing capacity of each member but also the values of the effect of action in each element. In the case of truss structures, these are axial forces. They were obtained as the results of computation, conducted in the Robot Structural Analysis program. From the structural reliability point of view, three basic structural systems, i.e., series, parallel, and mixed systems can be identified. The series system corresponds to the statically determinate structures, and its characteristic feature is that the whole system is reliable as long as all of the system components are reliable. In other words, the structure will fail if in any of elements' effects of action will exceed the load-bearing capacity. It is so called the weakest link conception. The reliability of the series system is computed according to the following formula:  
\[\Delta\theta_{a,t}=\frac{\lambda_{p}A_{p}/V\big{(}\theta_{g,t}-\theta_{a,t} \big{)}}{d_{p}c_{a}\rho_{a}(1+\phi/3)}\Delta t-\Big{(}e^{\phi/10}-1\Big{)} \Delta\Theta\theta_{g,t} \tag{2}\]2  
where:  
\(R_{i}\)--the reliability of the \(i\)-th element;  
\(n\)--number of system elements. The parallel system is typical for some simple statically indeterminate structures. The structures that correspond to a parallel system are reliable until all of the components become unreliable. The reliability of parallel system is equal to:  
\[\Delta\theta_{a,t}=\frac{\lambda_{p}A_{p}/V\big{(}\theta_{g,t}-\theta_{a,t} \big{)}}{d_{p}c_{a}\rho_{a}(1+\phi/3)}\Delta t-\Big{(}e^{\phi/10}-1\Big{)} \Delta\Theta\theta_{g,t} \tag{2}\]3  
where \(R_{i}\) and \(n\) are defined the same as in Equation (9). The models of series and parallel systems are presented in Figure 1a,b. The mixed system can be of two types: parallel-series or series-parallel. The same examples of such a system are presented in Figure 1c,d.