## 2 Materials and Methods  
The presented method combines fire and reliability analysis of a plane steel frame. As the task is very complex, some reductive assumptions had to be made. They are as follows:  
* The temperature of fire gases is uniformly distributed and computed according to standard fire curve. * The temperature of steel elements is uniformly distributed in all directions and is computed according to the Eurocode. * The structure will become unreliable because of the formation of plastic hinges, before exceeding bearing capacity in any rod. * Randomness is not taken into account during temperature computation. * The geometric and mechanical characteristics are assumed to be random values with a normal distribution. * Random variables are assumed to be not correlated. Changes in the rigidity of the nodes under temperature are neglected. The assumptions presented above are very strong, and in the obvious way introduce some discrepancy between obtained theoretical results and realistic situation. Nevertheless, they are essential to narrow down the task, find out some fundamental dependencies, and identify potential problems that may occur during system reliability analysis of frame structures under fire influence. Modeling the temperature of fire gases is a separate, extensive field of science; this is why it was computed according to Eurocode, without probabilistic description. This article focuses on the structural response of the frame, not on fire modeling. Because of the formulation of the research, where bearing capacity and effect of action are values used for the reliability index assessment, the choice of random variables seems to be quite natural. The last two assumptions (uncorrelated variables and neglecting the changes in the nodes' rigidity) may generate the biggest doubts. They are introduced to focus directly on the system reliability method. In further research, the author will resign from them and compare the results with those obtained currently. In this paper, two types of plane, one-story single-nave steel frames, are analyzed (Figure 3). They are assumed to have the same dimensions and fire insulation, but different loads and steel profiles of the top chord, which is essential due to another concentrated load in this area. Figure 3: Steel frames analyzed: (**a**) frame A, (**b**) frame B. The calculations were made in three steps. First, the temperature of the fire gases and the single elements was calculated according to Eurocode [6]. The temperature of fire gases was assumed to be uniformly distributed according to the standard fire curve, and the fire insulation was assumed to have the following characteristics: \(\lambda_{p}=0.12\ \frac{W}{\text{mK}}\), \(d_{p}=0.02\ \text{m}\), \(c_{p}=1100\ \frac{\text{J}}{\text{kgK}}\). Then, static analysis in following minutes of fire duration was conducted in the Robot Structural Analysis program. Self-weight, temperature load, and concentrated forces (according to Figure 3) were taken into account. In the schemes (Figure 3), the analyzed mechanism are presented (M1, M2), but they will be described later in this article. Finally, the principal part of the research-system reliability analysis was carried out. The set of random variables is presented in Table 1, and their characteristics were assumed according to [30]. All other variables were treated as deterministic. Additionally, the displacement analysis was conducted in the following minutes of the fire duration. In the presented research, the failure of the whole frame was analyzed as the result of creating plastic hinges in the most stressed nodes, which finally leads to transforming the structure into mechanisms. To realize this task, it is essential to know the bending moment resistance (\(M_{fi,\theta,Rd}\)) for individual cross-sections.