# Unified Simplified Capacity Model for Beam-Column Joints into RC Moment Resisting Frame
## 3 Analytical Model
### Experiemntal Validation  
Experimental tests performed on real T- and X-shaped RC joints have been used to validate the proposed analytical model. [PERSON] and [PERSON] [79] have compiled a database with 492 experimental results of beam-column joints from the literature. This database was used to validate the proposed analytical model. The full database is related to several types of RC joints. In particular, 270 specimens refer to T-shaped RC joints, while 222 specimens refer to X-shaped RC joints. The T-shaped joints were analyzed under positive and negative column shear, V\({}_{c}\). The several experimental programs provide the basic information for applying the proposed model. Unfortunately, not all information is available from the literature. In particular, for some specimens, the bond characteristic of the reinforcement bars was not disclosed. For this reason, the three levels of maximum bond stress, according to Equations (17)-(19), have been considered. Therefore, the impact of the bond stress on the ultimate capacity of the RC-joint has been assessed. This approach has been performed on the entire population. All information about the entire population has not been thoroughly discussed in this paper, due to the large number of specimens. For additional information, the reader could refer to the specific reference [79]. However, it is interesting to observe the main characteristics of the population. The main geometrical characteristics (depth and height) of the frame elements (beams and columns) are shown in Figure 4a,b for T- and X-shaped RC joints, respectively. The geometrical characteristics of the population embrace an ample range of typical values found in the existing building stock. Figure 5a,b show the amount of the longitudinal bars in the frame elements for the T- and X-shaped RC joints, respectively. The amount of reinforcement cross-section areas can be considered representative both of existing and new RC buildings. Finally, the mechanical characteristics of concrete are shown in Figure 6a,b for T- and X-shaped RC joints. The mechanical performance of concrete can be considered typically representative of existing and new RC buildings. Therefore, this large sample size provides a good database for validating the proposed analytical model; however, some specimens of the dataset are not usual, both in terms of geometrical and mechanical characteristics. The proposed model allows us to check the failure mode which occurred for the RC-joint. Unfortunately, this information is not available for some experimental tests. Figure 4: Geometrical characteristics of RC frame elements (column and beams): (**a**) T-shaped RC joints, (**b**) X-shaped RC joints. Figure 5: Geometrical characteristics of longitudinal reinforcements of RC frame elements (column and beams): (**a**) T-shaped RC joints, (**b**) X-shaped RC joints. Figure 6: Mechanical performance of material of RC frame elements (column and beams): (**a**) T-shaped RC joints, (**b**) X-shaped RC joints. Therefore, the comparison between the failure mode which was experimentally detected and the one which was numerically predicted has not been performed. The analytical results are shown by fixing the three values of bond stress according to Equations (17)-(19). The same bond stress yields to different bond capacities at different layers of bars (top and bottom) if different bars are present. Since, in X-shaped RC joints, the demands at the top and bottom layers of bars are equal, the bond capacity yielding to the failure is provided by the minimum amount of steel bars at the bottom or top layers. Conversely, for T-shaped RC joints, the bond demand depends on the sign of column shear; hence, the check should be performed both at the bottom and top layers of bars, because the bond capacity could also change at the two layers. Figure 7 shows the comparison between the experimental results and the analytical predictions related to the T-shaped joints under positive column shear.