*4.4. Global Analysis with Mechanical Loads and Thermal E*ff*ects*

With these results obtained from the global analysis it was found that increasing horizontal forces may cause damage, various damage scenarios were investigated by changing the loads applied to the space frame system. As the first case, the vertical load was increased considerably and no damage was predicted in the real damaged zones A and F, as given in Figure 1. As the next case, the structure was tested by increasing the horizontal load. Although the horizontal load value was increased to a level that cannot be reached by wind and similar factors, the damage that occurred cannot be explained with these combinations of loads. However, the structure was found to be more sensitive and vulnerable to the horizontal loads. Finally, it was understood that the space frame system with the columns is safe against vertical loads (snow, water, etc.) and horizontal loads (wind, etc.).

It is obvious that different factors must have been present in order to explain the real damage in the structure. Therefore, considering the natural events occurring on the night of the event, their effects on the structure were considered. It was assumed that reasons such as heavy rain that leads to ponding on the roof with a slope of 1% and a plausibly clogged water discharging drainage system would not cause damage similar to that which occurred. Besides, around the rooftop surface there are several scuppers with 15 cm height. Even with the assumption of full ponding of the roof with 15 cm height, it can be confidently claimed that the chosen loads for the analysis were on the cautious side and led to conservative results, which do not point out any damage predictions similar to the real damage.

On the other hand, a large number of lightning strikes were detected on the night of the incident. The effects of lightning depend on the energy of the lightning itself. The energy of lightning, which is impossible to fully determine, depends on many parameters, such as the altitude of the cloud where the lightning originates. It is well known that this discharged energy heats up a considerable amount of air surrounding the core of the lightning. The temperature rise is so rapid and significant that it can start fires near the location where lightning strikes [37]. Furthermore, when lightning strikes a building, the electric current passes through the structure, which leads to a sudden heat generation and a rapid increase of temperature [29,37,38]. Besides, quite large shock forces occur due to the interaction of large masses of hot and cold air around it, and also due to the humidity of the air and the ground, which is called the blast effect. In addition, it is known that the presence of water amplifies the blast effect and interacts with the structure under electric current [34]. Therefore, it is thought that these great shock forces can cause instant damage.

Even though it is judged that the structure is heated, it is impossible to predict or evaluate the exact or even approximate rise of temperature. For the purpose of understanding the underlying factors that led to the damage shown in Figure 1, the effects of temperature change on the structure were investigated using a simplified approach. The space frame system was given a temperature increase of 50 ◦C. Lightning is most likely to cause a local thermal shock and not heat up the entire structure. However, it is impossible to know the number of lightning strikes, the generated heat, the temperature rise, generated blast, etc.

Based on these assumptions, a 50 ◦C temperature increase was applied to the global model alongside the external loads as described in the previous global analysis. A new static model was built and the results are given in Figures 17–21. 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 17.** Stresses due to load and thermal effects in the space frame and steel-reinforced concrete column system.

**Figure 18.** Resultant displacements due to load and thermal effects in the space frame and steel-reinforced concrete column system.

**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 20.** Displacements in the short-edge direction caused by load and thermal effects in the space frame and steel-reinforced concrete column system.

**Figure 21.** Displacements in the vertical direction caused by the loads 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 there is a synergy effect based on the complex loading, and the thermal expansion leads to extra loading and elongation in horizontal directions.
