## 4 Analysis of Influencing Factors of Crossing Cable
### Tower Height  
In order to study the influence of the tower height on the restraining effect of the crossing cables, the tower height below the deck is adjusted on the basis of the three-tower cable-stayed bridge, and six pairs of crossing cables are set up in the main span. The maximum vertical deflection of the deck and the bending moment of the mid tower bottom under a uniform load with and without crossing cables are calculated, respectively. In the original model, the height of the tower below the deck is 70 m, and the height of the tower below the deck is adjusted to 120 m and 170 m. Table 3 shows the maximum vertical  
Figure 16: Vertical deflection of the deck (\(L=1000\) m).  
Figure 17: Vertical deflection of the deck (\(L=1500\) m).  
deflection of the deck under different tower heights. It is noted that increasing the tower height can still effectively improve the vertical stiffness of the deck by setting crossing cables. Therefore, in a multi-tower cable-stayed bridge across deep valleys, crossing cables are still an effective measure to improve the structural stiffness.  
Table 4 shows the bending moment of the mid-tower bottom under different tower heights. When the span of the main span is 1000 m, the reduction degree of the bending moment at the mid-tower bottom gradually decreases with the increase in the tower height. This is because when the tower height is increased without crossing cables, the ability of the tower to resist bending decreases, and the restraint effect of longitudinal restraint cables on the tower increases, which significantly reduces the bending moment of the tower below the deck. When the main span is 1500 m, increasing the tower height will not reduce the improvement effect of the crossing cable on the stress at the mid-tower bottom.  
Figure 19: Bending moment of the mid tower (\(L\) = 1500 m).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Main Span**} & \multirow{2}{*}{\begin{tabular}{c} **Tower Height** \\ **Below Deck** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **0 Pairs of** \\ **Crossing Cables** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **6 Pairs of** \\ **Crossing Cables** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Deflection** \\ **Reduction** \\ \end{tabular} } \\ \hline \multirow{3}{*}{\(L\) = 1000 m} & 70 & 3.33 & 1.48 & 55.55\% \\  & 120 & 3.40 & 1.50 & 56.11\% \\  & 170 & 3.44 & 1.50 & 56.37\% \\ \hline \multirow{3}{*}{\(L\) = 1500 m} & 70 & 5.05 & 2.83 & 43.96\% \\  & 120 & 5.47 & 2.93 & 46.52\% \\ \cline{1-1}  & 170 & 5.77 & 2.99 & 48.17\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: The maximum vertical deflection of the deck under different tower heights.  
Figure 18: Bending moment of the mid tower (\(L\) = 1000 m).  
In this paper, the anchorage position with the largest constraint stiffness of the crossing cable is given, and the influence of the crossing cable on the static performance of the long-span three-tower cable-stayed bridge is analyzed. However, in the theoretical derivation stage, the bending stiffness of the deck is not considered, and the applicability of the crossing cable stiffness formula in cable-stayed bridges with a high-stiffness deck such as steel truss girders needs to be further improved.