## 6 Seismic Performance of the Case Study
### SD Limit State
#### 6.2.3 Nonlinear Dynamic Time-History Analysis  
To evaluate the impact of ground motion directionality and to assess the seismic performance of structural elements and the building as a whole, we conducted a comparative analysis under two seismic input cases: XY and YX. In addition to ground motion directionality, 14 bidirectional ground motions covering a wide range of characteristics were analysed to study the comprehensive seismic performance. Tables 10 and 11 report essential parameters of the adopted ground motions: the arias intensity varies from 0.2 to 1.9 m/s with the corresponding predominant period spanning between 0.16 and 0.86 s, representing different varieties in the energy content as well as spectral composition of ground motions. This diversity ensures that the seismic response of the building is assessed for a wide range of conditions reflecting real-world variability. Although specific ground motion characteristics cannot, in general, be associated with individual capacity-to-demand ratios because of the averaging approach, the selection process ensures the critical structural responses are captured. For each beam and column, we calculated the capacity-to-demand (C/D) ratios for both rotation (ductile mechanism) and shear (brittle mechanism) in both cases. In determining the demands, we considered the maximum response from the two local axes of each element (i.e., taking the maximum of \(Rot_{2}\) and \(Rot_{3}\) for rotations, and \(V_{2}\) and \(V_{3}\) for shears; here, 2 and 3 refer to the local axes of the element). Additionally, to account for the variability in seismic inputs, we averaged the maximum responses obtained from 14 different ground motions for each element. By generating separate bar charts for the XY and YX cases, we effectively presented the C/D ratios of individual elements, which were organised by floor levels. This approach enhances clarity and reduces visual clutter, allowing for the straightforward identification of elements where the demand exceeds capacity (i.e., C/D ratio less than one). Highlighting these critical elements is essential for assessing the seismic adequacy and safety of the structure. Furthermore, to quantify the influence of changing the ground motion direction, we computed the normalised percentage differences in the C/D ratios between the XY and YX cases for each element. This was achieved by taking the absolute difference between the C/D ratios of the two cases, dividing it by the C/D ratio from the XY case to normalise, and expressing it as a percentage. Presenting these normalised differences in bar charts enables us to clearly identify elements significantly affected by the change in seismic input direction. A threshold percentage (e.g., 10%) was established to highlight elements with substantial differences, which are indicated in the plots through distinct color coding. This method of result presentation not only provides a visual comparison of structural performance under different seismic inputs but also serves the broader objective of assessing the seismic performance of individual elements and the building as a whole. By focusing on both the individual components and their collective behaviour, we gain comprehensive insights into the structural integrity and resilience of the building. Employing normalised percentage differences and clear visual markers facilitates an intuitive and scientifically robust interpretation of the data, supporting informed decision making in seismic design, assessment, and retrofitting strategies. Figures 20 and 21 present the C/D ratio plots of beams and columns, regarding the seismic performance of the building under a rotation-ductile mechanism, and a shear-brittle mechanism for seismic input cases in both the XY and YX directions. For beams (Figure 20), the first floor demonstrates a significant rotational capacity relative to demand with several beams showing exceptionally high C/D ratios.