## 3 Result and Discussion  
The structure shown in Figure 1a is a steel, industrial hall with lattice girders pinned jointed to prefabricated reinforced concrete columns. The bracing system commonly used in this type of building makes it possible to model lattice girds as flat trusses (Figure 1b). This approach is widely used in design practice. The connection of a steel lattice girder and a column is implemented as pinned. For this reason, it was assumed that the truss is simply supported. The system was loaded only with concentrated forces applied to the nodes of the top chord. In Figure 1b, the compression elements are marked in red and the tension members are marked in green. This structure was analysed with respect to basic and accidental (i.e., fire design) situations. It was assumed that all structural elements are made of S275 steel and heated from all sides. The top and bottom chords were made from I-sections, whereas bracing members were made from square tubing. The selected profiles and the effect of actions, i.e., forces arising in individual elements of the structure, are shown in Table 2.  
In the static analysis, by means of FEM, we used a flat truss element, which is a simple two-node element with two degrees of freedom in each node. The shape functions of the displacement field are linear. The displacement field of an element contains two translational components: horizontal u and vertical v. The strain tensor is reduced to one non-zero component of [PERSON]'s strain tensor \(\varepsilon_{11}\), which characterizes the elongation of the bar. Other components of the strain's tensor are equal to zero. The stress tensor is represented by component \(\sigma_{11}\) of [PERSON]'s second stress tensor. The detailed mathematical formulations of the stress-strain relationship for steel at elevated temperatures are given in [30]. In Figure 2, this relationship is shown for steel S275. \begin{table}
\begin{tabular}{c c c} \hline
**Section** & **Effect of Actions** \\ \hline
**Bottom chord** & 1100 & N1 = N6 = 0 kN; N2 = N3 = N4 = N5 = 53 kN \\
**Top chord** & IPE 140 & N2 = N8 = N11 = N2 = -38 kN; N0 = N10 = -54 kN \\
**Bracing** & RHS50x50x5 & N13 = N19 = -36 kN; N14 = N16 = N18 = -12 kN; N19 = N2 = 0 kN \\  & N20 = N25 = 46 kN; N21 = N24 = -21 kN; N22 = N23 = 1 kN \\ \hline \end{tabular}
\end{table} 
Table 2: Truss sections and the effect of actions. Figure 1: (**a**) Example of an industrial hall with steel lattice girders [31]. (**b**) Static scheme of the truss model. The starting point of a full fire analysis is to define fire scenarios. It is assumed that the structure is in the fully developed fire phase, so the standard fire curve (Equation (1)) is adopted. For unprotected and insulated steel members, the temperature increment was estimated in accordance with the formulas in Equations (2) and (3). The temperature field is uniform along the member length and along the cross-section height. Next, the mechanical properties that influence the resistance of tension and compression members are calculated. The most important mechanical properties of steel elements are yield strength and Young's modulus of elasticity. A decrease in the values of mechanical parameters leads directly to a reduction in the resistance of tension and compression members, as per Equations (5) and (6), which finally results in the limit state being exceeded. Thermal load is brought into the nodes as an additional load, in accordance with the incremental FEM method. For thermal load defined in this way, the stiffness matrix of the truss element is determined for Young's modulus as a function of temperature. The fire analysis is not intended to determine the value of the limit load but that of fire resistance, i.e., to specify the time of the structure's failure. In this particular case, static loads are constant, whereas additional axial forces can be created in the truss elements under thermal load.