# Form-Finding Analysis of the Rail Cable Shifting System of Long-Span Suspension Bridges
## 4 Testing Results of Model Test  
After the completion of the rail cable tensioning, the finite element results, experimental results and the analytical results are compared. The responses of several representative locations are compared in Table 1, and the cable forces at the anchor points of the main cable are shown in Table 2.  
From Table 1, it can be seen that the deviation of the results gained by the analytical method from measured values and finite element values in the Y direction is small, the maximum deviation values are 4.36% and 4.00%, respectively. It is shown in Table 2 that the deviation of the main cable force at the anchorage point is small, with a maximum of 2.34%. The deviations of the main cable displacement of the mid-span, the 1/4 span on the Jishou side, and the 1/4 span on the Chadong side in X-direction are relatively large, mainly due to the small deformation value in the X direction and the test system accuracy. The comparison between the test results and the analytical results shows that the presented method can be applied to the form-finding computational analysis of the RCS system  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Items**} & \multicolumn{2}{c}{**Main Cable Displacement**} & \multicolumn{2}{c}{**Main Cable Displacement**} & \multicolumn{2}{c}{**Main Cable Displacement**} \\  & \multicolumn{2}{c}{**at Mid-Span**} & \multicolumn{2}{c}{**at 1/4 Span on the**} & \multicolumn{2}{c}{**at 1/4 Span on the**} \\  & & & & & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\ \hline Finite element solution & 1.4 & 28.6 & \(-\)0.6 & 9.0 & 3.6 & 7.7 \\ Model test measured value & 1.5 & 27.5 & \(-\)0.5 & 8.9 & 3.5 & 7.5 \\ Analytical calculation results & 1.6 & 26.3 & \(-\)0.6 & 8.7 & 3.7 & 7.2 \\ Deviation of the finite element solution & 6.67 & 4.00 & 20.00 & 1.12 & 2.86 & 2.67 \\ from the measured value (\%) & 6.67 & 4.36 & 20.00 & 2.25 & 5.71 & 4.00 \\ \hline \multicolumn{7}{l}{Note: The measured value is the average of the upstream and downstream measuring points. The value is negative} \\ \multicolumn{7}{l}{when the X-direction measuring point moves to Jishou side and when the Y-direction measuring point moves to the upstream, and vice versa.} \\ \end{tabular}
\end{table}
Table 1: Effects of the working condition of rail cable tensioning on the systematical line shape.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Main Cable Force at**} & \multirow{2}{*}{**Finite Element**} & \multirow{2}{*}{**Model Test**} & \multirow{2}{*}{**Analytical**} & \multirow{2}{*}{**Deviation of the Finite**} & \multirow{2}{*}{**Deviation of the Analytical**} \\  & & & & & \\  & & & & & \\
**the Anchor Point** & **Solution/KN** & **Value/KN** & **Results/KN** & **the Measured Value/\%** & **Value/\%** \\ \hline Jishou side & 61.7 & 59.9 & 61.3 & 3.01 & 2.34 \\ Chadong side & 58.5 & 57.1 & 58.2 & 2.45 & 1.93 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Effects of the working condition of rail cable tensioning on the force of main cable.  
under the non-loading condition, which can simplify the analysis of the RCS system. The deviations of the simplified analytical results with the finite element results and model test results are less than 5%, which validates that the proposed method can be used in engineering practice.