## 5 Calculation Method of Shear Capacity Based on Truss-Arch Model  
The investigation of the shear resistance mechanism for reinforced concrete members in inclined sections remains one of the most significant challenges in structural mechanics. This complexity primarily arises from the evolution of discontinuous stress fields, which are induced by the redistribution of stresses within the cross-section following cracking. In recent years, advancements in computational mechanics have facilitated a deeper understanding of shear resistance mechanisms. Scholars have successively introduced analytical frameworks, including the truss-arch model [37], Modified Compression Field Theory [38], and fixed-angle softened-truss models [39], thereby gradually constructing a comprehensive theoretical foundation for the shear force transmission mechanism in cracked concrete. This paper employs a simplified superposition approach and applies the truss-arch theory to investigate and analyze the shear behavior of the original concrete beam and the high-toughness epoxy mortar overlay. Furthermore, a calculation formula for the shear capacity of the high-toughness epoxy mortar-reinforced beam is proposed. The truss-arch model, proposed by [PERSON] et al. [40] and [PERSON] et al. [41], is an extension of the truss model that incorporates the arching action of concrete. [PERSON] et al. [42] undertook a meticulous theoretical analysis of the truss-arch model and derived a calculation formula for the shear capacity based on the truss-arch model. They contrasted the calculated values with the current codes in China and the United States. The results indicate that, in comparison with the codes of the two countries, the shear capacity calculated based on the truss-arch model is in better agreement with the test values, and the truss-arch model can serve as a theoretical model for the shear failure of RC beams. The truss-arch model assumes that the shear forces in the members are shared by both the truss and arch models, meaning that the compressed concrete in the member serves as both the compression flange and the inclined compression member, as well as the arch itself, as shown in Figure 14.  
Figure 14: The truss arch model. The truss model is shown in Figure 15. In this model, the tensile longitudinal reinforcement and stirrup are treated as tension bars, the concrete is treated as the oblique compression bar, and the strengthening layer epoxy mortar serves as both a tension bar and an oblique compression bar. Together, the stirrups, concrete, and epoxy mortar transfer the shear force to the supports. T is the tension in the oblique tie rod, P is the compression in the oblique compression bar, h is the height of the RC beam, and z is the distance between the upper and lower stringers in the truss model. 1. Shear capacity provided by oblique tie rod  
The oblique tie rod model is shown in Figure 16, where the stirrups and epoxy mortar work together to bear the truss tension. \[T=\Big{(}\rho_{s}f_{yo}b+f_{t}b_{m}\Big{)}z\cot\varphi \tag{1}\]  
where \(\rho_{s}\) and \(f_{yo}\) are the stirrup ratio and stirrup yield strength, respectively; \(f_{t}\) is the tensile strength of epoxy mortar; \(b\) and \(b_{m}\) are the original beam and reinforcement layer widths, and \(\varphi\) is the angle between the truss diagonal compression rod and the beam axis; \(\alpha\) is the angle of the oblique tie rod, and \(\alpha=90^{\circ}\) because the stirrups were arranged vertically along the beam axis. The vertical projection of the truss tension \(T\) constitutes the shear force borne by the truss tie rod. \[V_{tu}=T\sin\alpha=\big{(}\rho_{s}f_{yo}b+f_{t}b_{m}\big{)}z\cot\varphi \tag{2}\]
2. Shear capacity provided by oblique compression bar  
The oblique compression bar model is shown in Figure 17.  
Figure 16: Truss model for RC beam under tension. Figure 15: The truss model for RC beam.