## 5 Results and Discussion  
### Description of the Connection  
The graphs below depict the relationship between the bending moment applied to the connection and the resulting rotation angle in the beam. The hysteresis curves were obtained from a finite element analysis developed with the help of the WORKBENCH 2021 R1 software, imposing the boundary conditions detailed in Figures 8 and 9. Similar calibrations were also applied in [32; 33; 34]. The hysteresis curve illustrates the connection's response to cyclic loading, indicating its strength, stiffness, and energy dissipation capabilities. The slope of the curve in the first phase corresponds to the initial stiffness of the connection. The slope decreases as the load increases and the structure deforms, indicating stiffness degradation throughout the loading cycles. The area bounded by the hysteresis curve reflects the capacity of the connection to dissipate seismic energy. The connection absorbs energy while undergoing loading cycles, preventing this energy from being transmitted to other parts of the structure and protecting the overall integrity of the frame. It is observed that the resistance of the connection at 0.04 radians is 432.3 kNm, a value greater than the yielding moment of the beam. It reflects the structure's ability to absorb seismic energy by resisting significant deformations before reaching plasticizing. Table 10 shows the analytical values of the plastic moment of each type of connection. The Mp value corresponds to the nominal plastic moment of the beam section.  
The 1-A beam-column connection experiences a maximum moment at 0.02 rad, which is equivalent to 98.39% of 0.8 Mp. It means that the material is close to its limit of deformation, but still has some capacity to resist additional forces. At 0.04 rad, the maximum moment in the connection drops to 85.98% of 0.8 Mp, reflecting the degradation of its strength as the connection experiences greater angular deformations. This also implies a reduced ability to dissipate seismic energy, as the connection absorbs energy as it undergoes loading cycles, but its ability to do so decreases as its stiffness degrades (Figure 11a).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Connection Type** & **Plastic Moment (kN m)** & **0.8 Mp (kN m)** \\ \hline
1-A & 588.15 & 470.52 \\
2-A & 504.45 & 403.56 \\
2-B & 504.45 & 403.56 \\
3-A & 504.45 & 403.56 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Analytical plastic moment for each connection type.  
At 0.02 rad, the maximum moment generated in connection 2-A is 95.94% of 0.8 Mp, meaning that the connection is close to its yielding limit but still retains some capacity to resist additional deformations. At 0.04 rad, the maximum moment in the connection is 86.39% of 0.8 Mp, reflecting the degradation of the connection strength as it experiences greater angular deformations. This illustrates a progressive reduction in stiffness, the ability to resist cyclic loading, and the ability to dissipate seismic energy (Figure 11b).  
The maximum moment generated in connection 2-B at 0.02 rad is 100.01% of 0.8 Mp; meanwhile, for 0.04 rad, the maximum moment is 90.91% of 0.8 Mp (Figure 11c). The maximum moment generated in connection 3-A at 0.02 rad is 100.86% of 0.8 Mp, and for 0.04 rad, the maximum moment is 90.15% of 0.8 Mp (Figure 11d).