## 4 Implementation Analysis of a Reasonable Completion State
### Multiple-Control Method for the Whole Process of System Transformation  
The girder jacking-up method [36] and hanger tensioning method [1; 2] are usually adopted for the system transformation of a self-anchored suspension bridge. The application of the later method is wider [21; 37]. The hangers are tensioned in several stages and the girder is transformed from the bracket support state to the cable suspension state [38; 39]. In addition, the hanger force, hanger elastic elongation, and the vertical displacements of girder and cable can be chosen as the control parameters of the system transformation process [40]. However, only one of them is usually chosen as the single control parameter currently, or the target hanger force and tag line position were chosen as the dual control parameters for part of the hanger tensioning process [41]. Moreover, the control accuracy of the hanger tensioning process is affected by the ambient temperature changes, operation errors, and measuring errors [42]. Especially for the later tensioning stages, the influences on hanger force brought by the measuring error of cable displacement are more significant because of the large cable stiffness. The final adjustment of hanger force might be more complex. In this paper, the multiple-control method for the whole process of the system transformation was proposed. The hanger tensioning force, exposed the amount of hanger anchor cup, and the tag line position were chosen as the multi-control parameters. The hanger tensioning and the mutual check between the multiple parameters were synchronized. The tensioning error accumulations were basically avoided. The calculation schematic is shown in Figure 17. The tag line was prefabricated on the surface of hanger, and \(L_{ta}\) was the initial distance between the tag line and the bottom surface of the hanger anchor cup. The hanger tensioning force \(P_{ij}\) of tensioning step \(i\) for hanger \(j\) was used to calculate the elevation value \(H_{aij}\) at the bottom surface of the hanger anchor cup. \[H_{aij}=H_{cij}-\Delta H_{cij}-L_{c}-L_{sj}-\frac{P_{ij}L_{sj}}{E_{j}A_{j}} \tag{6}\]  
Figure 16: Erection alignment of north cable. (**a**) Cable alignment. (**b**) Error percentage. where \(H_{cij}\) is the measured cable alignment at hanger \(j\) and \(\Delta H_{cij}\) is the vertical displacement of the cable caused by hanger tensioning. \(L_{c}\) is the distance from the cable center to the hanger fork ear center and \(L_{sj}\) is the unstressed hanger length. \(E_{j}\) and \(A_{j}\) are the elastic modulus and cross-sectional areas of the hanger, respectively. The target distance \(L_{dij}\) from the tag line to the top of the hanger tube was calculated based on the vertical displacement \(\Delta H_{gij}\) of the girder caused by hanger tensioning, as well as the target value of the exposed amount \(L_{saij}\) of the hanger anchor cup. \[\left\{ \begin{array}{l}L_{dij}=H_{aij}+L_{ta}(1+\frac{p_{ij}}{E_{i}A_{j}})- H_{dij}-\Delta H_{gij}\\ L_{saij}=H_{dij}-L_{dj}-T_{p}-T_{s}+\Delta H_{gij}-H_{aij}\end{array} \right. \tag{7}\]  
where \(H_{dij}\) is the measured elevation of the hanger tube top, \(L_{dj}\) is the measured length of the hanger tube, and \(T_{p}\) and \(T_{s}\) are the thicknesses of the anchor plate and nut, respectively. The principles of the multiple-control method are detailed as follows. 1. The prefabricated tag line should be convenient for observation. The value of \(L_{ta}\) for the Hunan Road Bridge was 3.5 m. The elastic elongation of the hanger segment from the tag line to the bottom surface of the hanger anchor cup cannot be ignored. 2. The target position of the tag line in each tensioning step should be calculated based on the hanger tensioning force, instead of the target hanger force. Thus, the synchronization of hanger tensioning and multiple-check can be realized. The tensioning errors can then be eliminated basically before dismantling the tensioning equipment.