## 5 Conclusions  
This study conducted a detailed parametric analysis using Finite Element (FE) simulations to evaluate the behavior of steel beam-to-column joints equipped with FREEDAM dampers, with a focus on European Moment Resisting Frames (MRFs). Through rigorous calibration with experimental data from the RFCS Project FREEDAM, the accuracy of our simulation results has been ensured. The investigation has led to several key findings:  
* The behavior of moment-rotation curves in both hogging and sagging conditions follows four distinct phases, indicating the critical phases of joint performance.
* Consistent stiffness was observed in the first elastic phase across different assemblies, with the D2B assembly showing slightly higher stiffness, highlighting the importance of the assembly configuration.
* Joints with multiple-slot dampers exhibited increased stiffness in the second elastic phase due to the engagement of a larger number of bolts, underscoring the effectiveness of the damper design.
* The calibration of hole sizes, tailored to the damper's geometry and positioning, is crucial for optimizing performance, emphasizing the need for precise design considerations.
* Based on the insights gained from this research, the primary recommendation is to carefully size the slots according to the detailed explanations provided in Section 2 with reference to Equation (3).
* Future experimental testing, particularly focusing on multiple-slot configurations, is advocated to validate these findings and further refine damper designs for enhanced seismic resilience of steel structures.  
Conceptualization, V.P., E.N. and R.M.; Methodology, M.D., V.P. and R.M.; Software, M.D. and P.T.; Validation, E.N., M.D. and P.T.; Formal analysis, E.N. and P.T.; Investigation, E.N. and P.T.; Writing--original draft, E.N. and P.T.; Writing--review and editing, M.D. and P.T.; Supervision, M.D., V.P. and R.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by RFCS Dreamers, grant number 101034015.  
Not applicable.  
The data presented in this study are available in the article.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Haunch (Direction)**} & \(k_{1}\) & \(k_{2}\) & \(m_{1}\) & \(m_{2}\) & \(m_{0,04}\) \\ \cline{2-7}  & **[rad\({}^{-1}\)]** & **[rad\({}^{-1}\)]** & **[-]** & **[-]** & **[-]** & **[-]** \\ \hline \multirow{4}{*}{D2C} & Single (up) & 66.86 & 23.11 & 0.38 & 0.94 & 0.38 \\  & Multiple (up) & 57.15 & 40.95 & 0.37 & 0.97 & 0.37 \\  & Single (down) & 74.09 & 29.73 & 0.40 & 1.10 & 0.46 \\  & Multiple (down) & 64.70 & 45.76 & 0.40 & 1.17 & 0.47 \\ \hline \multirow{4}{*}{D3B} & Single (up) & 100.76 & 17.82 & 0.49 & 0.78 & 0.80 \\  & Multiple (up) & 113.29 & 28.98 & 0.48 & 0.77 & 0.79 \\ \cline{1-1}  & Single (down) & 126.88 & 20.87 & 0.63 & 1.59 & 1.10 \\ \cline{1-1}  & Multiple (down) & 95.03 & 35.43 & 0.64 & 1.51 & 0.89 \\ \hline \hline \end{tabular}
\end{table}
Table 6: _Cont._