## 4 Conclusions  
This paper uses the probabilistic seismic demand model to investigate the seismic vulnerability of transmission towers in terms of the maximum Inter-Storey Drift Ratio (ISDR) and the intensity measure related to spectral acceleration. Incremental dynamic analysis is performed to estimate the capacity limit state for the transmission tower, and the IDAs are utilised to obtain the fragility functions and the Collapse Margin Ratio (CMR). Finally, three seismic scenarios (Far-Field, Near-Field, and Repeated Earthquakes) are used to estimate the tower seismic performance of multi-component seismic excitations using NL-THA. Based on the results, the following significant conclusions are drawn:  
1. For the failure mechanism for the structures, the deformation and failure mode for far-field is buckling failure in its frame members. For the near-field case, it is tensile failure with fracture material, which becomes worse when subjected to repetitive aftershock excitation that results in a combination of tensile failure with material fracture and compression buckling at the base of the columns. 2. From the IDA curves, for both far-field and near-field, repetitive earthquakes are more damaging to the structure than single events; the far-field case results in CP damage state at 1.10 g and the near-field at 0.80 g, while aftershock results in CP damage state  
Figure 15: Collapse fragility curves, far-field, near-field, and repetitive earthquakes. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Seismic Scenarios** & **IMCE (g)** & **I\({}_{\text{500}}\)**s (g)** & **CMR** \\ \hline
**Far-Field** & 0.30 & 3.5 & 11.67 \\
**Near-Field** & 0.30 & 2.0 & 6.67 \\
**Repeated Earthquakes** & 0.30 & 1.4 & 4.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: CMR values for three seismic scenarios. at 0.71 g. However, the transmission tower performs far better in the case of far-field ground motions than near-field. It can be concluded that the frame elements of the transmission steel tower suffer significant damages under near-field and repetitive ground motion than under far-field ground motion, despite the fact that the damage probability at far-field ground motion is greater than near-field ground motion before achieving 1.0 g.
3. From the fragility curves, the occupancy and life safety limit states are considered crucial in monitoring the seismic performance for the possibility of capacity recovery post seismic events. The structure rapidly loses occupancy during near-field and repetitive seismic events and is more life threatening compared to far-field excitations. As long as the intensity does not exceed 2.50 g, the structure can be repaired. When structures are subjected to near-field seismic occurrences, the structures can benefit from repair attempts if the intensity measure is 1.50 or less, and 1.20 g or less in the case of several seismic scenarios. The radar view provides a clear view of the difference between the three seismic scenarios. 4. From CMR, the rate of collapse for the transmission steel tower is lower under far-field ground motion than under near-field and repetitive ground motions. This is because the CMR for the far-field ground motion is greater than that of the near-field ground motion; the CMR values are 11.67, 6.67, and 4.67 for the far-field, near-field, repetitive ground motions, respectively. When considered as a single event, the analyses show that the transmission steel tower is more likely to collapse than a tower under far-field ground motion excitation and that the tower is more likely to damage during multiple seismic events, demonstrating that the tower can withstand the desired seismic performance or MCE of 0.30 g according to the Lebanese seismic norm. This verifies the accuracy of the results of the IDA and fragility analyses. This work shows the existence of research opportunities to determine the limit states through incremental dynamic analysis and fragility curves.