# Geometric Nonlinear Analysis of the Catenary Cable Element Based on UPFs of ANSYS
## 4 Verification and Numerical Examples
### Engineering Example Validation and Analysis
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**West Bank** & **Initial** & **West Bank** & **Initial** & **East Bank** & **Initial** & **East Bank** & **Initial** & **Area of** \\
**Buckle** & **Tension** & **Anchor** & **Tension** & **Buckle** & **Tension** & **Anchor** & **Tension** & **Buckled** \\
**Number** & **(kN)** & **Cable** & **Number** & **(kN)** & **Number** & **(kN)** & **Anchor** \\ \hline X1 & 1402 & XMS1 & 920 & D1 & 1402 & DMS1 & 9  
Table 8 and Figure 12 show that the relative error between the maximum buckling force and the measured value of the buckling anchor cable calculated using the newly developed element user101 is 5.6%. In comparison, the maximum relative error of element link10 is 5.7%. The maximum buckling force simulated by element link10 is smaller than the measured value and is smaller than the maximum buckling force simulated by element link10, which is due to the increase in the sag effect caused by the larger buckling length, resulting in a smaller buckling force and an increase in the lower deflection of the arch. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Location of Measurement** & **Experiment/mm** & \
\begin{tabular}{c} **Numerical Values (Development** \\ **Element User101)/mm** \\ \end{tabular} &
\begin{tabular}{c} **Numerical Values (Ansys** \\ **Element Link10)/mm** \\ \end{tabular} \\ \hline Section 2 & \(-6\) & \(-6.1\) (1.7) \({}^{*}\) & \(-5.5\) (8.3) \\ Section 3 & \(-11\) & \(-10.3\) (6.4) & \(-9.5\) (13.6) \\ Section 4 & \(-14\) & \(-14.3\) (2.1) & \(-15.2\) (8.6) \\ Section 5 & \(-16\) & \(-17.2\) (7.5) & \(-14.4\) (10.3) \\ Section 6 & \(-24\) & \(-26.0\) (8.3) & \(-25.3\) (5.4) \\ Section 7 & \(-31\) & \(-33.6\) (8.4) & \(-29.6\) (4.5) \\ Section 8 & \(-37\) & \(-39.0\) (5.4) & \(-39.2\) (5.8) \\ Section 9 & \(-48\) & \(-51.7\) (7.7) & \(-49.6\) (3.3) \\ Section 10 & \(-56\) & \(-59.8\) (6.8) & \(-52.8\) (5.8) \\ Section 11 & \(-67\) & \(-67.9\) (1.3) & \(-69.3\) (3.5) \\ Section 12 & \(-78\) & \(-82.7\) (6.0) & \(-82.2\) (5.4) \\ Section 13 & \(-85\) & \(-89.3\) (5.1) & \(-89.1\) (4.8) \\ Section 14 & \(-94\) & \(-97.5\) (3.7) & \(-97.9\) (4.1) \\ Section 15 & \(-98\) & \(-103.7\) (5.8) & \(-93.1\) (5.0) \\ Section 16 & \(-109\) & \(-110.9\) (1.7) & \(-113.9\) (4.5) \\ Section 17 & \(-124\) & \(-124.9\) (0.7) & \(-120.5\) (2.8) \\ Section 18 & \(-136\) & \(-139.6\) (2.6) & \(-127.8\) (6.0) \\ \hline \hline \end{tabular} \({}^{*}\)Numbers in parentheses indicate the absolute error percentage with respect to experimental results.  
\end{table} 
Table 7: Maximum vertical deflection of each segment of the arch ring. Figure 11: Comparison of maximum deflection values for each section of the arch ring: (**a**) Comparison of different elements with experimental values; (**b**) Comparison of the absolute error of different elements. Figure 13 shows that the maximum tensile stress in the top slab is more significant, and the maximum tensile stress in the bottom slab is less than that in the link10 element and is more in line with the measured converted tensile stress values due to the buckling effect of the buckling anchor cable causing a greater deflection in the cast section of the arch ring and a smaller buckling anchor cable force.