## 2 Stress Analysis Method of the Arch Ring Section
### Analysis of the Initial Stress State of the Arch Ring Section Considering Prestressing Effect  
The prestressing effect analysis is carried out for reinforced concrete arches equipped with prestressing, and the formula for calculating the stresses at the top and bottom flanges of each section of the arch section is derived by combining the diagonal tension buckle cantilever casting process. The following assumptions are made before the derivation of the formula. 1. Flat section assumption. 2. The neutral layer and the neutral axis assumptions. 3. The assumption of linear elasticity by Hooke's law. The arch ring segments with straight lines instead of curves, ignoring the effect of curvature. * The arch ring section is straight instead of curved to ignore the effect of bending. The formulae for the calculation of the post-tensioning prestressing effect in the \"Specifications for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts\" (JTG3362-2018) [21] were used to analyze the stresses at the top and bottom flanges of the arch section caused by the prestressing force. The stresses in the cross-section of the concrete member generated by the prestressing force are \(\sigma_{pc}\) at the top flanges and \(\sigma_{pt}\) at the bottom flanges. The specific expressions are shown in Equation (3) and Equation (4), respectively. The simplified calculation model of prestressing concrete members is shown in Figure 1.  
\[N_{p}=\sigma_{pe}\cdot A_{p}+\sigma_{pe}^{\prime}\cdot A_{p}^{\prime} \tag{1}\]  
Eccentric distance:  
\[e_{pn}=\frac{\sigma_{pe}\cdot A_{p}\cdot y_{pn}-\sigma_{pe}^{\prime}\cdot A_{p }^{\prime}\cdot y_{pn}}{N_{p}} \tag{2}\]  
The top flanges:  
\[\sigma_{pc}=\frac{N_{p}}{A_{n}}+\frac{N_{p}\cdot e_{pn}}{I_{n}}\cdot y_{n} \tag{3}\]  
The bottom flanges:  
\[\sigma_{pt}=\frac{N_{p}}{A_{n}}-\frac{N_{p}\cdot e_{pn}}{I_{n}}\cdot y_{n} \tag{4}\]  
where \(A_{n}\) is the net cross-sectional area, \(N_{p}\) is the combined force of prestressing and common reinforcement in post-tensioned members, \(M_{p2}\) is the secondary bending moment generated by the prestressing force, \(N_{p}\) is a super-stationary structure such as a prestressed concrete continuous beam, \(I_{n}\) is the net cross-sectional moment of inertia, \(e_{pn}\) is the distance from the center of gravity of the net cross-section to the point of the combined force of prestressing and common reinforcement in the body, \(y_{n}\) is the distance from the center of gravity of the net section to the calculation fiber, \(y_{pn}\), \(y_{pn}^{\prime}\) is the distance from the point of the combined force of prestressing bars in the tension zone and compression zone to the axis of the center of gravity of the net section, \(\sigma_{pe}\), \(\sigma_{pe}^{\prime}\) is the effective prestressing stress of prestressing bars in the tension zone and compression zone, \(A_{p}\), \(A_{p}^{\prime}\) is the cross-sectional area of prestressing reinforcement in the tension and compression zones, \(\sigma_{pc}\) is the stress at the top flange of the main arch rim section under the prestressing effect, and \(\sigma_{pt}\) is the stress at the bottom flange of the main arch rim section under the prestressing effect. During the construction of the cantilever cast arch bridge, the structural system is relatively complex, and the calculation of stress at the top and bottom flanges of the main arch section is more complicated considering the prestressing effect, and the coupling effect of cable force and prestressing will occur after buckle tensioning. Three crucial construction conditions are highlighted during the process of cantilever casting of the main arch ring considering prestressing: concrete casting, prestressing tensioning and buckle cable tensioning, and the stress formula of the top and bottom flanges of the arch ring  
Figure 1: Simplified calculation model of prestressing concrete members.