# Numerical Investigation of the Collapse of a Steel Truss Roof and a Probable Reason of Failure
## 4 Results and Discussion
### Global Analysis with Mechanical Loads and Thermal Effects
Figure 17 shows the equivalent stresses of von Mises occurring in the space truss systems and columns. It can be seen that the stresses coming out of this figure are quite safe. However, it has been found that the stress values in the support joints reach values exceeding the safety limits, and the supports reaching these values are concentrated in the areas where damage occurred. The reason for the great stress values in this global model is that the model is simple and gives a general idea. It would be appropriate to consider separately the situations in the supports with large stresses. It is also to be noted that the \"U\" shaped connections between the steel truss structures and the supports on the walls display the greatest stresses, which is not realistic, as these connections do not exist in the real structures. Therefore, those stress values were disregarded. Figure 18 shows the resultant displacements that occurred throughout the system. From this figure, it can be seen that displacements are suitable and larger displacements occurred in the regions where the damage occurred. Figure 19: Displacements in the long-edge direction caused by load and thermal effects in the space frame and steel-reinforced concrete column system. Figure 17: Stresses due to load and thermal effects in the space frame and steel-reinforced concrete column system. Furthermore, Figure 19 shows the displacements in the long-edge direction, x-direction. This figure clearly shows that there were large displacements in the areas where the damage occurred. Figure 20 shows the displacements in the direction of the short edge of the building, the so-called y-direction. It is to be noted that the larger displacements were observed in the direction along the shorter edge, whereas the larger displacements due to thermal expansion were expected in the direction of the long edge. The reason behind this can be explained with different stiffness levels of the structure in different directions and boundary conditions of the supports. As can be seen from Figure 6, the number of columns in the first two rows of the halls B, D, and F are much more intensively positioned than that seen in the rest of the building. Moreover, the intensity of the columns in the x-direction is greater than the intensity of columns in the y-direction. Therefore, the stiffness in the x-direction is expected to be greater than the stiffness in the y-direction. The sliding supports and the stiffness of the structure allow the structure to deform in the y-direction more than it can in the x-direction, even though the tendency to deform is more in the x-direction than in the y-direction. This leads to the storage of a larger amount of energy in the x-direction. Additionally, since, there was no damage in the spherical supports themselves, as can be seen in Figure 15, the excessive displacements caused larger stress values in the bolt connections between the spherical parts and the members. Therefore, it was found plausible that this mechanism caused the actual failure. The displacements of the structure in the vertical direction are given in Figure 20. Comparing the vertical displacements of the previous global analysis and this one (Figures 11 and 21), both cases display very similar distribution trends but the new one exhibits larger displacements. This is because  
Figure 21: Displacements in the vertical direction caused by the loads in the space frame and steel-reinforced concrete column system. Figure 20: Displacements in the short-edge direction caused by load and thermal effects in the space frame and steel-reinforced concrete column system. there is a synergy effect based on the complex loading, and the thermal expansion leads to extra loading and elongation in horizontal directions.