## 2 Beam-to-Column Connections
### BCC-1: Device with Crossed-Slotted Holes  
The first solution analyzed consists of a friction device with a pin on the top of the connection to the column and an assembly of steel plates with crossed holes with slotted shape on the lower part of the connection. This device is here indicated as BCC-1 and the details of all constituent parts are reported in Figure 1a. In the case of BCC-1, six preloaded bolts are used, type M16, class 10.9; the internal lever arm \(z_{1}\) is equal to 399 mm, while the angle \(\alpha_{1}\) between the sliding-force application point and the axis of the beam measures 61\({}^{\circ}\).  
The system is modelled through the finite element (FE) method. The FE software used for the simulation is Abaqus/CAE [27]. A cross-section of 250 \(\times\) 300 mm\({}^{2}\) for the beam and 300 \(\times\) 400 mm\({}^{2}\) for the column are assumed. In the joint model, the structural elements' length is 2500 mm for the beam and 3000 mm for the column. The latter is pinned at the ends, while a concentrated vertical force applies a cyclic displacement to the tip of the beam. The FE type used for the concrete parts is the first-order hexahedron named C3D8R, while the steel elements which constitute the connection are modeled with linear tetrahedra, type C3D4. This FE model is conducted under the simplified hypotheses of elastic behavior of all components and by neglecting the steel reinforcement of beam and column, thus, focusing only on the mechanism of the friction device. To this scope, the ideal fixed encastre is modelled for connecting the damping device to both beam and column while realistic constraints and interaction properties are simulated for the mechanism of the main top pin and for the sliding plates. A multi-point constraint of type \"beam\" is assumed between the longitudinal pin axes and the internal surfaces of the holes, while a friction mechanism  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Connection** & \(F_{d,i}\) **(kN)** & \(t_{s,i}\) **(\%)** & \(F_{pc,d}\) **(kN)** \\ \hline BCC-1 & 275.7 & 52.3 & 57.5 \\ BCC-2 & 289.5 & 53.8 & 72.3 \\ BCC-3 & 294.1 & 42.9 & 73.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Design sliding force, stress-level coefficient, and effective preload for the proposed BCCs.  
is introduced in the sliding plates, with a friction coefficient of 0.4. Rigid normal contacts are also modeled between the bolt shanks and the internal surfaces of both circular and slotted holes.  
A cyclic test is performed with displacements of \(\pm\)100 mm, whose results are reported in Figure 1b as a normalized moment-rotation curve. It can be noted that the clearance around the pin connection causes resistance between the friction plates when the pin moves before contact with the edges of the hole. This is an undesirable contribution, which negatively affects the system's stiffness and dissipation capacity. Finally, from Figure 1c, which shows the stress state at peak, it can be observed that stresses are under the elastic limit in the whole model with the exception of a limited stress concentration in the sliding plate, due to the localized contact against the bolt shank.