## 4 Calculation Method of Shear Carrying Capacity of UHPFRC Beam-Column Joint  
### Shear Resistance Mechanism of UHPFRC Beam-Column Joint  
As a critical element in RC frame structures, beam-column joints in complicated stress conditions play the important role of transferring forces, including the bending moment, shear force, and axial force. Orthogonal diagonal compressive and tensile stresses exist along the diagonal direction of the joint core panel in the joint when they carry horizontal and vertical compression forces that are transferred from the beam as well as column. The diagonal compressive stress is resisted by UHPFRC diagonal strut in joint core, and the horizontal component force of the diagonal compression force is the horizontal shear strength of the joints. Therefore, the mechanical model can be simplified as a diagonal strut, as illustrated in Figure 8b. Unlike NC crushing under compressive load, the compression failure mode of UHPFRC is usually cracked in the compressive stress direction and bulges in the other direction because of the existence of fiber, so diagonal strut UHPFRC never crushes, and contributes to a large proportion of the shear carrying capacity of joints, even in the failure stage. The reinforced stresses are very small before joint cracking, and the diagonal compressive stress and tensile stress are mainly resisted by the UHPFRC in the joint core. When the diagonal tensile stress exceeds the tensile strength of UHPFRC, an initial crack is formed. The higher tensile strength and peak tensile strain of UHPFRC cause beam-column joints to exhibit higher initial cracking strength. Following cracking, the diagonal tensile stress is mainly resisted by the stirrup and steel fibers in the UHPFRC fracture surface, as illustrated in Figure 8c,d. The stirrup, steel fiber, and longitudinal steel bar across joints' core form a truss. The stirrup and steel fibers constitute the horizontal tie, and vertical reinforced bars (if they exist) and steel fibers constitute the vertical tie. With a further increase in the displacement and cycle, the joint diagonal strut mechanism gradually undergoes degradation in carrying the diagonal compressive stress, owing to UHPFRC cracking. Therefore, the horizontal shear force is resisted by the UHPFRC friction resistance and the dowel force of the steel bars and steel fibers. However, the aggregate interlock forces of UHPFRC joint are smaller than those of RC joint, because there is no coarse aggregate in UHPFRC.  
Figure 7: Strain of stirrups in joint cores: (**a**) specimen EJ-5 and (**b**) specimen J-4.  
Based on the above analysis, the shear carrying capacity of the examined joint is the summation of the shear resistance of the UHPFRC diagonal strut, fibers, and stirrup, the calculation model of which is illustrated in Figure 8. Thus, the shear carrying capacity expression can be defined in the form of Equation (3); that is,  
\[V_{j}=V_{c}+V_{f}+V_{sv} \tag{3}\]  
in which \(V_{j}\) is the shear carrying capacity of the UHPFRC joint, \(V_{c}\) is the horizontal component force of the diagonal compression force resisted by the UHPFRC diagonal strut in the joint core, \(V_{f}\) is the shear carrying capacity of the steel fibers, and \(V_{sv}\) is the shear carrying capacity of the stirrup.