# Form-Finding Analysis of the Rail Cable Shifting System of Long-Span Suspension Bridges
## 1 Introduction  
Suspension bridges [1; 2; 3; 4; 5; 6; 7] are widely used to cross long-span barriers in engineering; their mechanical behaviors during construction have attracted the special attention of researchers [8; 9; 10; 11; 12; 13; 14; 15]. Girder erection is the key and difficult step for the construction of the long-span suspension bridges in mountainous areas. To facilitate transportation and erection, structural types of girders are often designed as steel trusses. Mature construction methods include the deck crane construction method [16], and the cable crane construction method, among others [8; 9]. Rail cable shifting (RCS) is a new, recently invented method, and it was firstly used in the successful erection of the girder of the Aizhai Bridge [17; 18; 19; 20; 21; 22; 23]. The erection of the 1000.5-m steel truss girder required only two and a half months [16]. With RCS, the construction period is greatly shortened, and the amount of steel used for the steel truss girder is significantly reduced. However, this technology is still new in terms of practical use, and its widespread promotion requires the accumulation of more experience. Meanwhile, knowledge and research on this technology remains to be further developed, for example to learn whether the analysis process of RCS system can be further simplified, whether the technological process can be further optimized, and whether the equipment and operations can be standardized. All of these restrict the widespread promotion and application of RCS technology.  
In the presented technology, the shifting system is a double-layer flexible suspended cable system that consists of the main cables, hangers, saddles, and rail cables. With the tension of the track cable and the cable system under stress, the system will undergo obvious deformation, through which the load will be distributed according to the stiffness in the cable system [24; 25; 26; 27; 28; 29; 30; 31; 32]. For the long andflexible sling structure, deviation and elongation will appear in the process of the rail cable tensioning, and variations should not be ignored. The rail cable force during the tensioning process of the rope sling is unknown, and an implicit solution needs to be derived with respect to the deformation coordination relation of the system. These issues all these bring difficulties and complexity to the static analysis. During the process of the research and development, the finite element method is used to compute the main cable and the rail cable that are regarded as segmental catenaries, and the computational process is complicated. Moreover, the rail cable has a large pretension force, which is different from the force of the suspension cable segment obtained when only the weight force and sling force on both ends are considered.  
In this paper, to simplify the form-finding [33] analysis of the RCS process under the non-loading condition, an analytical method is developed to establish the global mechanical model of the main cable, sling, and rail cable and to solve the equation, under the condition that the sling force is unknown. Here, the basic assumptions of the mechanical analysis of flexible cables are introduced and the elastic elongation of the sling is considered. The comparisons among the analytical results, the finite element results, and model test results show the presented analytical method is correct and it can be used in the computation and analysis of similar structures.