## 4 Conclusions  
The precise displacement control of the bridge deck at the lower end of the hanger is very critical during the hanger replacement process of half-through arches with a suspended deck by cable hangers by using the pocket hanging method. The method of hanger replacement based on precise displacement control is proposed in this paper. Firstly, the variation coefficient of shear versus displacement on both sides of the hanger to be replaced were calculated and the hanger was separated from the overall model in order to establish the equivalent model of the hanger to be replaced. Secondly, the structural response of the hanger replacement process and the new hanger installation process were obtained on the basis of the equivalent model. Finally, an actual hanger replacement of an arch bridge was adopted to verify the correctness and feasibility of the proposed method. The following conclusions can be drawn:  
1. The adopted equivalent model of hanger replacement by separating from the overall model in this paper was accurate, and only partial boundary conditions need to be considered in practical application to get accurate results. 2. In the hanger replacement process of an arch bridge based on the pocket hanging method, the cumulative displacement increased and decreased alternately, and the corresponding variation values were basically the same during the new hanger installation process using equal step tensioning and unloading, which would achieve a satisfactory result and meet the requirements. 3. Although the trend of the finite element calculation results was consistent with the measured results, the deviation between them was still large. By comparison, the calculated result using the proposed method were fast and accurate enough through the practical engineering verification, and the hanger replacement was feasible under the precise displacement control. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Working Condition** & **1+** & **1–** & **2+** & **2–** & **3+** & **3–** & **4+** & **4–** & **5+** & **5–** \\ \hline Measured [mm] & 1.88 & 0.42 & 2.1 & 0.49 & 2.12 & 0.54 & 2.34 & 0.63 & 2.56 & 0.77 \\ FEM [mm] & 1.75 & 0.4 & 2.16 & 0.47 & 2.24 & 0.59 & 2.53 & 0.6 & 2.61 & 0.7 \\ FMD [\%] & \(-6.8\) & \(-6\) & 3.02 & \(-3.3\) & 5.26 & 9.68 & 8.11 & \(-4.5\) & 2.26 & \(-9.8\) \\ Present paper [mm] & 1.88 & 0.43 & 2.02 & 0.48 & 2.18 & 0.56 & 2.37 & 0.65 & 2.6 & 0.76 \\ PMD [\%] & \(-0.1\) & \(-0.1\) & 3.94 & 1.18 & \(-2.5\) & \(-3.5\) & \(-1.1\) & \(-3.1\) & \(-1.6\) & 0.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculation results of the bridge deck displacement at the lower end of the hanger under different working conditions during hanger removal. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Working Condition** & **1+** & **1–** & **2+** & **2–** & **3+** & **3–** & **4+** & **4–** & **5+** & **5–** \\ \hline Measured [mm] & 2.83 & 1.43 & 3.19 & 1.55 & 3.03 & 1.55 & 3.19 & 1.48 & 3.04 & 1.51 \\ FEM [mm] & 3.05 & 1.31 & 3.39 & 1.45 & 3.27 & 1.6 & 3.05 & 1.59 & 3.22 & 1.37 \\ FMD [\%] & 7.97 & \(-7.8\) & 6.54 & \(-6.8\) & 8.1 & 3.49 & \(-4.2\) & 7.19 & 6.07 & \(-9.7\) \\ Present paper [mm] & 2.9 & 1.45 & 3.1 & 1.52 & 3.12 & 1.52 & 3.12 & 1.52 & 3.12 & 1.52 \\ PMD [\%] & \(-2.5\) & \(-1.7\) & 2.74 & 2.37 & \(-3\) & 1.74 & 2.09 & \(-2.6\) & \(-2.8\) & \(-0.5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Calculation results of the bridge deck displacement at the lower end of the hanger under different working conditions in the new hanger installation. **Author Contributions:** Conceptualization, H.W., L.W. and X.W. ; methodology, H.W., [PERSON] and [PERSON]; validation, [PERSON] and K.H. ; formal analysis, [PERSON], [PERSON] and X.W. ; investigation, [PERSON], [PERSON] and X.W. ; writing--original draft preparation, [PERSON] and L.W. ; writing--review and editing, [PERSON] and W.W.; project administration, [PERSON] and W.W.; funding acquisition, [PERSON] and W.W. All authors have read and agreed to the published version of the manuscript.