## 5 Proposed Design Procedure  
The previous sections discussed the key aspects for evaluating the seismic response of a structure with an ADS. This section provides a detailed explanation of the proposed procedure. The proposed procedure is based on the capacity spectrum method (CSM), and the design objective is expressed in terms of a displacement limit. It is crucial to emphasize that existing buildings, often designed without seismic considerations, tend to be irregular and sensitive to higher modes. This condition can significantly affect the effectiveness of a  
Figure 4: Evaluation of the equivalent viscous damping needed to achieve the target performance point. capacity-spectrum-based design procedure, such as the one presented herein. Therefore, when deemed suitable for a specific application, the use of a standard pushover analysis can be more efficiently replaced by alternative approaches, such as incremental modal pushover analysis (IMPA) [23]. IMPA extends the well-known modal pushover analysis (MPA) [29; 30] to obtain a multimodal capacity curve, which proves valuable for seismic assessment or design implementation. As dissipative towers alter the structural response of the original building, the procedure is inherently iterative. The capacity curve must be continually updated to reflect the characteristics of the new coupled structure (building + tower). According to the CSM, considering the energy dissipated by the ADS (in addition to the dissipative capacity of the structure, which is computed from the capacity curve of the original structure), the structural response is obtained by reducing the design spectrum based on the damping (\(\xi_{tot}\)) of the \(S\)+\(ADS\). \[\xi_{tot}=\xi_{I}+\xi_{eq,S+A} \tag{8}\]  
To execute this procedure, the designer must define the desired performance. Because this is a displacement-based procedure, the definition is based on a target displacement, typically corresponding to a chosen limit state under specific seismic conditions. Subsequently, the total effective damping required to match the actual maximum displacement and the target displacement can be determined. The additional damping provided by the ADS (e.g., a dissipative tower) is estimated as the difference between the total damping and the hysteretic damping of the original structure. The characteristics of the ADS are then determined to meet the required additional damping. Although the procedure is iterative, it converges after only a few iterations. The key steps are outlined below. Step 1. The seismic action was defined in terms of the elastic response acceleration spectrum (\(T-S_{a}\)). Step 2. The target displacement was selected (e.g., the top displacement, \(D_{t}\)*) according to the desired performance (limit state). Step 3. The capacity curve for the retrofitted structure, \(S\)+\(ADS\), considering the top displacement (\(D_{t}\)) and base shear (\(F_{b}\)), was established through a pushover analysis. A pushover analysis can be conducted by adopting one of the various force distribution methods outlined in the building codes and literature. It is advisable to employ a multimodal procedure. When a modal pushover analysis is performed, it is important to note that the modal shape is influenced by the interaction between the building and the tower. Consequently, at each iteration (in Step 3, from iterations 1 to \(n\)), the load profile must be adjusted to match the modal shape of the current braced structure. It is worth noting that during the initial iteration, the existing building is considered, and the capacity curve obtained at this stage is crucial for assessing the contribution provided by the existing framing structure. Step 4. The capacity curve obtained in Step 3 can be approximated by a simpler bilinear curve that is completely defined by the yielding point (\(D_{S}+A_{DS,y}\), \(F_{S+ADS,y}\)) and the hardening ratio (\(\beta_{S+ADS}\)). (At the first iteration, these parameters correspond to \(D_{S,y}\), \(F_{S,y}\), and \(\beta_{S}\) of the existing building).