## 6 Seismic Performance of the Case Study
### SD Limit State
#### 6.2.3 Nonlinear Dynamic Time-History Analysis
This indicates that these beams possess considerable reserve capacity for ductile deformation, thereby reducing the likelihood of rotational failure during seismic events. In contrast, on the second and third floors, the rotational C/D ratios decrease considerably. While most beams on the thirdfloor maintain a reasonable safety margin, many beams on the second floor show C/D ratios closer to the threshold, indicating that these beams are more susceptible to reaching their rotational capacity under seismic loading. The shear performance in beams reveals a more uniform distribution across floors, with C/D ratios generally remaining above the threshold, especially on the first and third floor. A few beams on the second floor also approach the shear capacity threshold, suggesting potential areas of concern for brittle failure. This suggests that while most beams have adequate shear capacity, certain beams on the upper floors may be more vulnerable to shear-induced brittle failure under severe seismic forces. For columns (Figure 21), the rotation C/D ratios reveal a clear pattern: the first floor exhibits the highest values, suggesting a substantial reserve capacity for ductile behaviour. However, the second and third floors show markedly lower rotational C/D ratios with values closer to or even below the threshold for some columns. This decrease in rotational capacity indicates that columns on the upper floors are more likely to experience high demand relative to their rotational capacity, making them more susceptible to ductile failure. The YX case similarly shows reduced rotational C/D ratios on upper floors, underscoring the importance of accounting for directional seismic input when evaluating ductile performance. Shear C/D ratios for columns follow a similar trend with higher values on the first floor and significantly lower values on floors 2 and 3. Some first-floor columns show ratios near the threshold, signalling a potential shear vulnerability, but columns on the second and third floors exhibit more widespread proximity to the threshold, especially in both the XY and YX cases. This suggests that the upper floors, particularly the columns, may be at a higher risk of brittle failure under shear forces, which is a critical consideration in seismic design. The findings highlight that while the lower floors maintain robust ductile and shear capacities, the upper floors, especially columns in shear, may require further assessment or strengthening measures to enhance the structure's seismic resilience. Figures 22 and 23 illustrate the normalised percentage differences in capacity-to-demand (C/D) ratios for both rotation and shear in beam and column elements across the structure, considering the two seismic input cases (XY and YX). The results are categorised by floor levels and assess elements where ground motion directionality significantly affects performance. Elements with a normalised difference exceeding the 10% threshold are highlighted in red, identifying those that demonstrate a substantial response variation between the XY and YX seismic cases. For beams (Figure 22), rotation differences show prominent sensitivity to seismic input direction, particularly on floor 2 and floor 3, where several elements exceed the threshold, indicating a higher rotational demand discrepancy between the two cases. This sensitivity to directionality is less pronounced in shear demands for beams, with fewer elements surpassing the threshold, suggesting that rotational ductility may be more direction-sensitive than shear strength. In the analysis of the columns (Figure 23), on floor 1, there are no columns with a normalised percentage difference above the 10% threshold for rotation capacity-to-demand ratios. For shear capacity-to-demand ratios on floor 1, only two columns exceed the 10% threshold, indicating that the shear response of these specific columns shows sensitivity to the change in seismic input direction (XY vs. YX).