# Proposed New Analytical Method of Tower Load in Large-Span Arch Bridge Cable Lifting Construction
## 4 Application in Tower Analysis
### Stability Analysis  
The restraining action of the wind cable on the tower is considered as the elastic support. Stability analysis is performed focusing mainly on the upstream, midstream, and downstream main cable lifting rated loads at the mid-span position. A total of eight load conditions were calculated for the buckling analysis, and their specific load combinations are shown in Table 8 for conditions 1 to 8.  
Considering all the loads that may occur in the arch rib lifting, the first six orders of buckling modes are calculated for each load condition. The calculation takes into account geometrical nonlinear influences, including a P-Delta effect and large displacement effect.  
Table 9 lists the first-order buckling factor for each load condition of the towers. From Table 9, it can be seen that the first-order buckling factor of the tower under the action of load condition 5 is the smallest. Since the calculated load is the actual load, the buckling factor is the safety factor, and the minimum stability safety factor 7.52 is greater than the critical value 4, and the safety factor for the other load conditions is greater. The cable lifting system is carried in a level ten wind load in the maximum cantilever state before the  
Figure 11: Buckle cables acting on the tower.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Load Condition** & **Load Combination** & **Load Condition** & **Load Combination** & **Load Condition** & **Load Combination** \\ \hline
1 & (1) + (2) + (3) + (6) & 5 & (1) + (2) + (5) + (6) & 9 & (3) \\
2 & (1) + (2) + (3) + (8) & 6 & (1) + (2) + (5) + (8) & 10 & (4) \\
3 & (1) + (2) + (4) + (6) & 7 & (1) + (2) + (7) & 11 & (5) \\
4 & (1) + (2) + (4) + (8) & 8 & (1) + (2) + (9) & — & — \\ \hline \hline \end{tabular}
\end{table}
Table 8: Load conditions and load combinations.  
arch rib is closed, which has a stability safety factor of 22.91. This shows that the overall stability of the towers is safe at all stages of the arch rib installation process.  
The first-order instability mode of the towers in each load condition is the overall longitudinal overturning instability of the cable towers. Figure 12 shows the first six orders of the buckling mode of the towers under the action of load condition 5. The first-order buckling mode is the longitudinal overall instability of the cable tower at the right bank (see Figure 12a). The second-order buckling mode is the longitudinal overall instability of the cable tower at the left bank (see Figure 12b). The third-order buckling mode is the twisted instability of the tower at right bank (see Figure 12c). The fourth- and fifth-order buckling modes are bending instability under compression of the steel pipe column of the tower at the right bank (see Figure 12d,e). The sixth-order buckling mode is the lateral moving instability of the right bank tower (see Figure 12f). The most likely instability of the towers is still through overall overturning. To improve the overall stability performance of a tower, the stability coefficient of the tower can be improved by setting the wind cable and adjusting the wind cable force.