## 4 Seismic Analysis
### Structural Response  
We evaluated the structural response of the case study using three types of analysis: linear response spectrum (RSA), nonlinear static (pushover), and nonlinear dynamic (TH). The seismic behaviour was analysed by referring to global and local parameters. Within global parameters, both top displacement (either top displacement or inter-storey drift ratio) and torsional effects were considered. Moreover, the latter was described using the Torsional Drift Ratio, TDR, characterising torsional irregularities by the ratio between the maximum and minimum lateral displacement along the storey perimeter. Larger TDR values correspond to higher torsional irregularities and, therefore, high inter-storey lateral displacement differences. For seismic performance definition--according to what was debated in the previous section--local parameters based on ECS [50] have been considered. In the response spectrum analysis (RSA) performed in this study, the seismic response of the hospital building was evaluated using spectral accelerations corresponding to the first four vibrational modes, which were obtained through a preliminary modal analysis. Each mode was weighted according to its participation factor, and the elastic response spectrum was employed as the seismic input. The elastic response spectrum was adjusted using a behaviour factor (\(q\)) of 1.5 for brittle behaviour and 3.0 for ductile behaviour, aligning with the latest seismic code requirements. The structural response evaluation according to code provisions included the application of lateral forces in both principal directions, considering the combination of one directional response with 30% of seismic action from the perpendicular direction. This method provided a thorough assessment of the building's overall seismic response, adhering to the original design principles (just for simplicity, we excluded the 5% accidental eccentricity). Nonlinear static (pushover) analysis generally requires creating a pushover curve that relates base shear to the lateral roof displacement at a reference point, which is often defined as the centre of mass. At a minimum, two vertical load distributions should be applied. For asymmetric buildings, inelastic torsional responses are highly sensitive to load distribution, higher modal contributions, and accidental mass eccentricity. Additionally, torsional rotations can create significant differences in lateral displacement between the stiff and flexible sides. Thus, the selection of a reference point for monitoring target  
Figure 11: Limit values of the SD response quantities of the beams and columns. displacement impacts capacity evaluation. Solely using the roof centre of mass may lead to a non-conservative estimate of seismic capacity by neglecting these torsional effects in asymmetric buildings. Using multiple reference points is recommended to capture this behaviour more accurately. This research investigates how the torsional inelastic response is influenced by lateral force distribution and the chosen control point for monitoring target displacement. The study uses two criteria to vary pushing forces along the building height: (i) proportional to storey mass and height, forming a triangular shape, and (ii) proportional only to storey mass, leading to a more uniform distribution [50; 54]. To assess the influence on displacement control, four points are considered: (A) flexible side, (B) centre of mass of the building, (C) stiff side, and (D) semi-flexible side (see Figure 12).This analysis evaluates how the reference location impacts the determination of torsional demands and capacities in asymmetric structures exhibiting inelastic behaviour. In addition to the linear pseudo-dynamic and nonlinear static analyses, a nonlinear time-history analysis was conducted to capture the detailed dynamic response of the hospital building under real earthquake records.