# The Impact of Support Type on the Reliability of Steel Trusses Subjected to the Action of a Fire
## 3 Results
### Thermal-Static Analysis  
The presented analysis began with calculations of the temperature of combustion gases and elements of the structure in the passing minutes of a fire duration. In the analyzed examples, an increase in temperature leads to an exceeding the limit state of the bearing capacity of some rods, which results in a change in the static scheme of the structure. For truss \"0\", consequently exceeded Ultimate Limit State ULS can be observed in symmetrically positioned cross-braces, starting from outermost elements (Figure 3a-c). Ultimately, after the 59 th minute of the fire, the outermost posts buckle, which is equivalent to conversion of the structure into a mechanism. Figure 2: Geometry of analyzed trusses: (**a**) a truss with one hinged movable support and one hinged nonmovable support (truss “0”); (**b**) a truss with an additional intermediate support (truss “A”); and (**c**) a truss with the blockade of free thermal deformations (truss “B”). In the case of truss \"A\", the first change in the static scheme occurs after 20 min of the fire duration (\(\mathrm{t_{fi}}=20.05\) min (1203 s)). Buckling cross-braces belong to the outermost and central frames of the truss (Figure 4a). During the next several minutes (\(\mathrm{t_{fi}}=29.2\) min (1752 s)), ULS is exceeded in the central post and another pair of diagonals (Figure 4b). The current scheme (Figure 4b) is geometrically variable, which decides the conversion of the structure into a mechanism and the end of calculations. In the case of truss \"B\", changes of the static scheme occur in a much earlier phase of the fire (Figure 5). The buckling of outermost diagonals (Figure 5a) occurs already after 4 min of the combustion gases exposition (\(\mathrm{t_{fi}}=4.12\) min (247 s)). During the following minutes (\(\mathrm{t_{fi}}=5.75\) min (345 s)), the structure is converted into a mechanism due to the exceeding bearing capacity of the outermost elements of the bottom chord (Figure 5b). Under the fire load, the significant changes in the value of axial forces (which are in the analyzed task associated with the effect of action) and bearing capacity are observed. Figures 6 and 7 present changes in axial forces in the passing seconds of fire duration for the selected elements of truss, which were the deciding ones for static scheme change. The numeration of rods is compliant with this presented in Figure 2. In the case of \"A\" truss, 23 and 28 elements exceeded ULS first with fire duration (Figure 6a). Directly after that, extreme cross-braces exceeded bearing capacity (Figure 4a). In the following seconds of fire, rods numbered 21 and 30 (Figure 6b) were \"the weakest\" elements, and then middle post-element 16 exceeded collapse criterion (buckling) (Figure 4b). For the \"B\" truss, with only a few minutes of fire duration, the elements numbered 20 and 31 exceeded failure criterion (buckling) (Figure 7a). In the few following seconds of fire duration, the ULS of extreme elements of bottom chord (Figures 5b and 7b) was exceeded and the structure became the mechanism. The analysis of the changes  
Figure 4: Change in the static scheme of truss “A” along with the fire duration: (**a**) \(t_{\text{fi}}\) = 20.05 min (1203 s) and (**b**) \(t_{\text{fi}}\) = 29.2 min (1752 s). Figure 5: Change in the static scheme of a truss with the blockade of free thermal deformations along with the fire duration: (**a**) \(t_{\text{fi}}\) = 4.12 min (247 s) and (**b**) \(t_{\text{fi}}\) = 5.75 min (345 s). of axial forces during fire for all elements of both trusses is presented in Appendix A. In the case of truss \"A\" (Figure 6), changes are not too abrupt, and they are closely related to changes in the static scheme. Entirely reversed dynamics of changes are observed in the case of truss \"B\" (Figure 7). In this case, the value of axial forces in the elements of the bottom chord increases rapidly with every passing minute, which decides the very fast conversion of the structure into a mechanism.