## 2 Description of the Investigated Joints and Relevant Damper Configurations
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Assembly**} & \multicolumn{6}{c}{**Haunch**} & \multicolumn{6}{c}{**T-stub**} & \multicolumn{6}{c}{**L-stub**} \\ \cline{2-19}  & \(b_{s,H}\) & \(b_{i,H}\) & \(h_{H}\) & \(b_{f,H}\) & \(t_{f,H}\) & \(t_{w,H}\) & \(b_{T}\) & \(h_{f,T}\) & \(t_{f,T}\) & \(t_{w,T}\) & \(b_{L}\) & \(h_{f,L}\) & \(t_{f,L}\) & \(t_{w,L}\) \\  & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** \\ \hline D1A & 440 & 251 & 245 & 135 & 15 & 15 & 205 & 170 & 25 & 345 & 20 & 75 & 180 & 20 & 296 & 20 \\ D2B & 555 & 424 & 340 & 180 & 20 & 20 & 270 & 190 & 30 & 405 & 25 & 90 & 220 & 30 & 399 & 30 \\ D2C & 720 & 504 & 392 & 195 & 30 & 25 & 270 & 210 & 40 & 480 & 30 & 90 & 286 & 35 & 569 & 35 \\ D3B & 795 & 582 & 492 & 195 & 30 & 25 & 290 & 250 & 40 & 555 & 30 & 90 & 364 & 45 & 637 & 35 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dimensions of the upper and lower connections. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Beam Size**} & \multicolumn{6}{c}{**Bending Utilization Factor (\(\overline{m}\)) [-]**} \\ \cline{2-5}  & \(\overline{m}\)\(\leq\)**0.3** & **0.3**\(<\)\(\overline{m}\)\(\leq\)**0.4** & **0.4**\(<\)\(\overline{m}\)\(\leq\)**0.5** & **0.5**\(<\)\(\overline{m}\)\(\leq\)**0.6** \\ \hline IPE 270 & - & - & D1 & D1 \\ IPE 300 & - & D1 & D1 & D1 \\ IPE 360 & D1 & D1 & D2 & D2 \\ IPE 400 & D1 & D2 & D2 & D2 \\ IPE 450 & D2 & D2 & D3 \\ IPE 550 & D2 & D3 & D3 & D4 \\ IPE 600 & D2 & D3 & D4 \\ IPE 750 \(\times\) 147 & D3 & D4 & D5 & D5 \\ IPE 750 \(\times\) 161 & D3 & D4 & D5 & D5 \\ IPE 750 \(\times\) 173 & D3 & D4 & D5 & D5 \\ IPE 750 \(\times\) 196+ & D4 & D5 & D5 & D5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Design chart: bending utilization factor and the beam size. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Assembly**} & \multirow{2}{*}{**Beam**} & \multirow{2}{*}{**Column**} & \(L_{beam}\)**/2** & \(L_{column}\) & \(\overline{m}\) & **Bolts (10.9 class)** \\ \cline{3-8}  & & **[mm]** & **[mm]** & **[mm]** & **[-]** & **[-]** & **[-]** \\ \hline D1A & IPE 270 & HE 240 B & 3000 & 3500 & 0.47 & M16 & 4 \\ D2B & IPE 450 & HE 360 B & 3000 & 3500 & 0.47 & M20 & 6 \\ D2C & IPE 600 & HE 320 M & 3000 & 3500 & 0.35 & M20 & 8 \\ D3B & IPE 550 & HE 500 M & 3000 & 3500 & 0.47 & M20 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Features of the analyzed dampers. The friction shim has the same width and height as the L-stub web and a thickness of 8 mm. The hole dimensions for the plates of the various components, given the size of the bolts, have been calculated according to EN 1993-1-3 standards [20]. The lengths of the horizontal slotted holes in the multiple-slotted haunches was calculated assuming a  
Figure 4: Schematic representation of the beam-to-column joints and relevant geometric parameters. Figure 3: Details of the upper and lower connections. minimum rotation value of the connection greater than 0.035 radians in order to comply with highly ductile systems according to [16]. In particular, the rotation value used in the examined configurations was set to 0.04 rad to provide extra ductility. Given the rotation value, the maximum stroke that each bolt can undergo was calculated, based on simple geometric considerations. In fact, according to Figure 5, the maximum stroke per bolt is conservatively equal to the product of the distance between the center of rotation and the bolts centroid (\(d_{1,b},\ d_{2,b}\)) and the predefined rotation value (\(\varphi_{max}\)). Table 5 reports the half-lengths of the slots obtained according to the previous assumptions and their design values established with a 1% tolerance to ensure at least the predefined rotation \(\varphi_{max}\) (Equation (3)), accounting for assembly and manufacturing defects in the various components of the joint.