## 6 Conclusions  
In this study, a tuned mass damper (TMD) was designed to be installed on the rooftop of a medium-rise building in order to change the building's behavior from dissipative to non-dissipative under seismic action. The application of the TMD was aimed at reducing stresses in structural members and floor displacement in order to avoid damage to structural and non-structural elements under strong earthquakes. Thereby, the building with TMD would not need reparation interventions after such earthquakes.  
In the proposed solution, the mass of the TMD is made by an RC slab laying on flat surface sliders (FSSs) installed on the building rooftop. Two different solutions were proposed to provide the TMD with design stiffness and damping. In one solution (TMD1), stiffness and damping are both provided by lead rubber isolators (LRIs), while in the other solution (TMD2), stiffness and damping are provided by low-damping rubber isolators (LDRIs) and viscous linear dampers (VLDs), respectively.  
Starting from the TMD mass value obtained from the adopted design method, the optimal masses of TMD1 and TMD2 were 25% and 12% of the total mass of the building, respectively.  
The proposed solutions led to very similar results. It was observed that the TMD significantly changes the main vibrational modes of the building, reducing the spectral accelerations. Consequently, a reduction in flexural and shear actions of at least 50% at the base of the walls and of at least 55% at the base of the columns was achieved. The flexural demand over capacity ratios were strongly reduced, bringing the maximum from 7.38 (OB) to 1.41 and 1.56 with TMD1 and TMD2, respectively. Based on this result, it can be concluded that the designed TMDs are effective in reducing the stresses in the structural elements of the considered medium-rise building, almost to the substantially elastic bound. Both TMDs involve an increase in the input energy, but most of it is dissipated through damping by TMD devices, hence halving the energy dissipated through modal damping by the building.  
A base isolation system (BIS) was also designed to compare its effectiveness in reducing the stresses in the building's structural members with that of TMD1 and TMD2. BIS proved to be the most effective strategy, as expected, since it radically increased the periods of the building's vibration modes. This produces a reduction in the shear actions at the base of the building of at least 90%, leading the strength verifications of structural members to all be largely satisfied.  
However, from the results obtained for the case study, it can be concluded that a TMD can be used for the retrofit of existing buildings as a valid alternative to base isolation when the latter is technically unfeasible.  
Conceptualization, methodology, M.P., L.M. and G.F.; software, validation, formal analysis, investigation, data curation, writing--original draft preparation, visualization, L.M.; writing--review and editing, L.M. and G.F.; resources, supervision, project administration, funding acquisition, M.P. All authors have read and agreed to the published version of the manuscript.  
The research has been partially funded by: (1) the Italian Department of Civil Protection, within the framework of Executive Project DPCRe-LUIS 2022-2024; (2) the European Union Next-GenerationEU (PIANO NAZIONALE DI RIPRESA E REISILENZA (PNRR)-MISSIONE 4 COMPONENTE 2, INVESTIMENTO 1.5-D.D. 1058 23/06/2022, ECS0000043), within the Interconnected Nord-Est Innovation Ecosystem (iNEST). This manuscript reflects only the authors' views and opinions, neither the European Union nor the European Commission can be considered responsible for them; (3) the strategic plan of University of Udine within the framework of the project \"ESPeRT\", whose support is greatly appreciated.  
Not applicable.  
The authors declare no conflict of interest.