## 6 Seismic Performance of the Case Study
### SD Limit State
#### 6.2.1 Response Seismic Analysis (RSA)  
The seismic response of the case study was assessed using the spectral acceleration values corresponding to the four modal periods identified through modal analysis. The combined effects were then calculated based on their modal participation factors. Since the elastic spectra did not meet the EC8 applicability conditions, the seismic input was represented using reduced spectra. To account for different behaviours, two \(q\)-factors were applied: 3.0 for ductile mechanisms and 1.5 for brittle mechanisms.  
The verification of ductile mechanisms was performed by evaluating the bending moment. Figures 17 and 18 show the capacity-to-demand (C/D) ratios for moment and shear in beams and columns across three floors for RSA analyses with reduction factors \(q=1.5\) and \(q=3\). Each sub-plot series in this chart shows moment and shear C/D ratios--both for beams and columns--with the red-dotted line indicating the threshold value of C/D = 1. Values above this threshold indicate that elements have sufficient reserve capacity to withstand the applied seismic demands, while values near or below this line suggest areas that may be of concern.  
In beams (Figure 17), general patterns of increase in C/D ratios are observed from floor 1 to floor 3, especially for \(q=3\); this would imply a greater reserve capacity in upper floors where seismic demands are generally lower. Shear C/D ratios also develop in a somewhat more uniform manner along the floors, which indicates that shear demands within the structure are more evenly distributed. Among the beams, most of them have C/D ratios much larger than the threshold, showing that they have an adequate or even higher capacity to resist seismic forces.  
In the columns (Figure 18), we observe a mix of high and borderline C/D ratios. The columns in floor 1 are especially high in the C/D values for the moment capacity. This is probably due to the more conservative estimate of column design to strengthen the base against high seismic forces. The columns in floors 2 and 3 have a somewhat lower C/D ratio, and in some, the C/D ratios are close to or slightly below the threshold line. This is particularly conspicuous in the moment capacity for a few columns located on floors 2 and 3, indicating that those elements could be more vulnerable under seismic demands and may need closer examination or additional reinforcement to ensure safety requirements.  
This close review has pointed out that the existence of some columns with C/D ratios close to, or lower than, 1--in particular, on the top floors--requires special attention at those locations. However, in a general consideration, the large majority of the columns have sufficient reserve capacity above the limiting threshold, which means globally the design is strong and ready to resist seismic demands for situations of RSA \(q=1.5\) and \(q=3\). In structural elements such as these, the high value of C/D provides confidence in the stability of the structure, although a few cases call attention to areas that may need more care with a view to maintaining uniform safety performance on all the floors.  
Figure 17: Distribution of moment and shear capacity-to-demand ratios for beam elements across floors under RSA (\(q=1.5\)) and RSA (\(q=3\)) analyses.  
Figure 18: Distribution of moment and shear capacity-to-demand ratios for columns elements across floors under RSA (\(q\) = 1.5) and RSA (\(q\) = 3) analyses.