# Unified Simplified Capacity Model for Beam-Column Joints into RC Moment Resisting Frame
## 3 Analytical Model
### Experiemntal Validation
The figure shows the analytical and experimental value of column shear, V\({}_{\text{j}}\) and V\({}_{\text{j}}\)exp, respectively. The diagonal black line represents the ideal condition where the experimental value coincides with the analytical prevision (line with unitary slope); the red represents the best interpolating line of the points crossing the origin. Furthermore, the coefficient of determination, R\({}^{2}\), is shown for each case. The same analysis was performed for T-shaped RC joints under negative column shear (Figure 8) and the X-shaped RC joints (Figure 9). Figure 8: Experimental and numerical comparison for T-shaped RC joints under negative column shear: minimum bond stress (blue), average bond stress (orange), and maximum bond stress (green). Figure 7: Experimental and numerical comparison for T-shaped RC joints under positive column shear: minimum bond stress (blue), average bond stress (orange), and maximum bond stress (green). The previous figures show the impact of the bond stress (minimum, average, and maximum value) on the ultimate capacity of RC-joints. It is worth noting that the analytical predictions slightly worsen when the bond stress decreases. However, this effect appears to be negligible in the entire population. Under positive or negative column shear, the coefficient of determination undergoes very small variations for T-shaped RC joints. Only for negative column shear does the coefficient of determination decrease, moving from the minimum to average bond stress, while it weakly increases when the maximum bond stress is considered. This effect is likely due to the characteristics of the experimentally tested specimens. Furthermore, the characteristics of the bond condition strongly depend on the construction of the RC joints. For this reason, the comparison was performed while changing parametrically the characteristics of bond conditions. Under both positive and negative column shear, the analytical predictions fit well with the experimental results. It is confirmed by the coefficient of determination, R\({}^{2}\), and slope of the interpolating line, which are both very close to 1. The same analysis was performed for X-shaped RC joints. The comparison between the experimental and the analytical predictions show a higher dispersion compared to the case of T-shaped RC joints. However, given the large number of specimens, it was noted that some specimens exhibited non-typical behavior. In fact, in analyzing some experimental results, it is clear that some values are not typical for the materials. These differences are apparently due to particular test conditions. A screening of some test values could be useful to eliminate unrealistic results; however, the authors preferred to consider the entire population instead of filtering data, since not all of the information is available. The dispersion changes slightly with the considered bond capacities; thus, the ultimate behavior of X-shaped joints appears to be weakly influenced by the bond capacity of the reinforcement layer. The proposed model allows the assessment of the failure mode to be linked to the ultimate capacity of RC joints. It is worth noting that the failure mode varies as some input parameters change. According to the experimental database, the impact of the bond stress on the ultimate capacity was noted. In particular, the bond stress has been changed according to the Equations (17)-(19) for the entire sample, and the related failure mode was assessed. Figure 10a,b refer to the T-shaped joints under positive and negative column shear, respectively, while Figure 10c shows the same result for X-shaped joints. Figure 9: Experimental and numerical comparison for X-shaped RC joints: minimum bond stress (blue), average bond stress (orange), and maximum bond stress (green). It is worth noting that the sign of column shear strongly influences the failure mode of T-shaped RC joints. Decreasing the bond stress value, the failure mode is due to the bond capacity exceedance for almost the entire population.