# Proposed New Analytical Method of Tower Load in Large-Span Arch Bridge Cable Lifting Construction
## 3 Accuracy Verification of Calculation Method
### Numerical Model  
#### 3.2.1 Establishment of Numerical Model  
Wind cables and towers are simulated by a spatial rod-frame structure using the general-purpose finite-element analysis software SAP2000. Figure 7 shows the overall numerical calculation model. The overall coordinate system of the numerical model takes the cross-bridge direction as the \(X\) axis, the along-bridge direction as the \(Y\) axis, and the vertical direction as the \(Z\) axis. The wind cable is considered as the cable element in the calculation model, and its constraints are simulated as hinged at both ends; the connection with the Earth is a fixed hinge, and its initial tension is added according to strain load. The individual component parts of the tower are simulated using a frame element. The \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(Q\) & \(\Delta H\) & \(L\) & \(L_{1}\) & \(L_{2}\) & \(L_{3}\) & \(L_{4}\) & \(L_{5}\) & \(\alpha_{1}\) & \(\alpha_{1}\) & \(f_{0}\) \\ (**kN/m**) & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **(\({}^{\circ}\))** & **(\({}^{\circ}\))** & **(\({}^{\circ}\))** & **(m)** \\ \hline
1.346 & 2.5 & 430 & 207.5 & 15 & 68 & 65 & 360 & 23.0 & 34.1 & 20.5 \\ \hline \(f_{1}\) & \(f_{2}\) & \(F\) & \(\beta\) & \(\eta\) & \(\theta_{1}\) & \(\theta_{2}\) & \(P\) & \(\mu\) & \(q\) & \(f_{q}\) \\ (**m**) & **(m)** & **(kN)** & **(\({}^{\circ}\))** & & **(\({}^{\circ}\))** & **(\({}^{\circ}\))** & **(ton)** & & **(kN/m)** & **(m)** \\ \hline
18.9 & 21.3 & 71.7 & 0.33 & 0.98 & 22.6 & 34.3 & 67.5 & 0.012 & 0.196 & 24 \\ \hline \end{tabular} Note: The meanings of parameters have been given in Section 2.  
\end{table} 
Table 1: Parameters of the cable system when carrying to mid-span. Figure 6: Overall layout of cable lifting system. connection between the tower column and the Earth is simulated by a fixed hinge. The connections between the universal rods are simulated as hinged at both ends. The foot of the cable tower is hinged to the top of the buckle tower. The foot of the buckle tower is fixed to the Earth. The size of the tower element is 0.5 m and the size of the wind cable element is 1 m. The whole numerical model has 2212 nodes and 6214 frame elements. Figure 8 shows the numerical model of the right bank tower and its component members. The structures of the towers on both banks are basically the same; both are in the form of a cable tower and buckle tower combined into one (see Figure 8a). The height of cable tower is 21.6 m, the transverse width of the top is 44 m, and the transverse width of the tower foot is 40 m. The cable tower is assembled into a truss structure using M-type universal rods. The main column adopts double columns with a single column size of 4 m \(\times\) 2.56 m in plan (see Figure 8d). A steel-box distribution beam is set at the top of the tower to support the main cable and cable saddles and to distribute loads transferred from the suspension cable system to each node at the top of the tower (see Figure 8b). The cable tower bottom is hinged with the buckle tower top; the cable tower bottom hinge seat distribution beam adopts a steel box beam (see Figure 8f). Each column of the buckle tower is made of 60630 \(\times\) 14 mm steel pipes and connected by a ring flange to ensure the strength and stiffness of the buckle tower. Diagonal rods adopt universal rods and connect with the welded plate on the column steel pipe through bolts (see Figure 8c). The full width of the buckle tower top is 47.6 m, and an H-type distribution beam is set at the top of the buckle tower (see Figure 8e). The universal rods of the tower are made of Q235 steel, and the steel pipe columns, H-beams, and distribution beams are made of Q345 steel. The material physical and mechanical characteristic parameters are shown in Table 2.