## 5 Global Structural Response of the Case Study  
The case study features a rectangular plan and exhibits structural asymmetry along both the X and Y axes (Figure 2). Additionally, the heights of the storeys vary. To measure in-plan irregularity, eccentricity along these principal directions has been assessed in terms of stiffness and strength. The centre of mass at each storey has been determined by considering the mass of both the floors and the infill panels. The centre of strength has been identified (Figure 13) as the centre point of ultimate shear forces in columns and walls, while the centre of stiffness has been established using the simplified method proposed by [PERSON] et al. (2010) (2010) and [PERSON] et al. (2014, 2015) (2014, 2015) (2016, 2017). Table 12 presents the percentage eccentricities of strength and stiffness centres with respect to the mass centre for each storey in both the X and Y directions. It shows the variation in eccentricities across storeys, providing insight into the distribution of stiffness and strength relative to the mass centre. From Table 12, we observe that the eccentricity of strength is generally higher than that of the stiffness for both the X and Y directions across all storeys. In the X direction, storey 1 exhibits the largest strength eccentricity (14.98%), indicating a notable misalignment between the mass and strength centres, which could lead to increased torsional effects under lateral loading. The stiffness eccentricity in the X direction is much lower, peaking at storey 2 with 4.75%. This suggests that the structure's stiffness is better aligned with the mass centre compared to the strength distribution. In the Y direction, the eccentricity values for both strength and stiffness are relatively low, with storey 1 again showing the highest strength eccentricity (8.02%). The stiffness eccentricity decreases significantly across the storeys, reaching 0.25% at storey 4. This implies that in the Y direction, the mass and stiffness centres are well aligned, minimising potential torsional responses. Other important information regarding the effects of in-plan irregularity on the seismic response of buildings is given by the participation mass related to each vibrational mode. Table 13 presents the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Storey**} & **Strength** & **Stiffness** & **Strength** & **Stiffness** \\  & **Eccentricity** & **Eccentricity** & **Eccentricity** & **Eccentricity** \\  & **(X)** & **(X)** & **(Y)** & **(Y)** \\ \hline
1 & 14.98\% & 2.71\% & 8.02\% & 4.26\% \\
2 & 3.32\% & 4.75\% & 2.53\% & 0.86\% \\
3 & 7.23\% & 2.87\% & 4.87\% & 0.10\% \\
4 & 3.59\% & 1.36\% & 0.25\% & 0.25\% \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Percentage eccentricity of strength and stiffness centres with respect to the mass centre in both X and Y directions for each storey (Figure 13). Figure 13: Mass, strength and stiffness centres of the model. first four periods of the case study along with the associated participant masses, which were determined through the modal analysis. The modal analysis results in Table 13 provide valuable insights into the dynamic behaviour of the structure. The first mode exhibits a dominant participation in the X direction (53.66%) with a corresponding natural frequency of 4.67 Hz, indicating that the structure primarily responds in the X direction during this mode. In the second mode, the Y direction dominates with 43.07% of the modal mass at a natural frequency of 5.71 Hz. The third mode, with significant rotational participation about the Z axis (38.27%), highlights the potential for torsional response, with a frequency of 6.59 Hz. The higher frequency modes, like the fourth mode (13.05 Hz), show minimal participation in all directions, implying that higher modes contribute less to the global seismic response.