## 6 Seismic Performance of the Case Study
### SD Limit State
#### 6.2.4 Comparison of the Performed Analysis  
This section provides an extensive comparative analysis of the seismic performance of structural elements by examining their capacity-to-demand ratios (CDRs) using pushover analysis, response spectrum analysis (RSA), and time-history (TH) analysis in both the XY and YX directions. We determine CDRs for rotations and shears for each beam and column on all floors by dividing the elements' capacities from design specifications by the demands from the analyses. To identify the most critical conditions, we take the minimum CDRs and compare them with those from the pushover and TH analyses; RSA results are shown only for shear CDR values due to its linear nature. Results are presented in tailored plots with specific Y axis limits to enhance readability and highlight differences. This method enables a comprehensive evaluation of the structural elements' performance under various seismic conditions, pinpointing weaknesses and assessing the effectiveness of each analytical approach. Figures 24 and 25 present a comparative evaluation of the capacity-to-demand ratios (CDRs) across three analysis types: pushover analysis, response spectrum analysis (RSA), and time-history (TH) analysis in both the XY and YX directions. This comparison serves to highlight the differences in predicted structural responses, allowing an assessment of each method's capability in capturing realistic seismic demands. Notably, while pushover analysis tends to produce higher CDR values, suggesting greater element capacities under seismic loading, this method may not accurately capture the dynamic effects associated with actual earthquake events. RSA, being a linear analysis method, often yields lower CDR values but still fails to fully represent the nonlinear response. TH analysis, with results shown separately for XY and YX directions, demonstrates more nuanced performance outcomes, suggesting that it better captures the directional sensitivity and complexity of seismic loading. This study reveals that pushover and RSA may overestimate structural capacity, while TH analysis provides a more conservative and realistic assessment. For beams (Figure 24), the figures indicate that pushover and RSA analyses tend to predict higher CDRs for shear, whereas TH analysis often yields lower, more critical CDRs, particularly in the YX direction. This pattern highlights the dynamic influence of seismic loading on shear demands with TH analysis revealing potentially vulnerable conditions that static or linear analyses may overlook. Additionally, for rotational demands, pushover analysis again demonstrates relatively high CDRs, reflecting a potentially optimistic perspective on rotational capacity under static loading. This optimistic result may not hold under the dynamic conditions of a real seismic event, as seen by the more conservative CDRs in TH analysis. These trends remain consistent across floors, suggesting that TH analysis, especially when considering bidirectional loading, is more effective at identifying the critical performance of beams. This assessment emphasises the importance of dynamic analysis to capture both rotation and shear vulnerabilities across various structural levels. In the case of columns (Figure 25), particularly when assessing shear demands, RSA often produces elevated CDRs, which may not accurately capture the complex nonlinear behaviour of columns under seismic loading. TH analysis again highlights more critical conditions, especially when comparing results across the XY and YX directions, indicating a significant sensitivity to the orientation of the loading. Columns subjected to TH analysis in the YX direction generally exhibit lower CDRs than in the XY, suggesting directional dependencies that are crucial for a realistic assessment of seismic performance. This observation is especially relevant in identifying potential structural vulnerabilities that static analyses, such as pushover, might overlook.