# A New Method for Finding the Shape of the Main Cable in the Special Cable Plane
## 1 Introduction  
In recent years, a variety of new bridge structures have emerged in the world, and the spatial special-shaped suspension bridge is one of them [1]. Different from the parallel cable plane, the main cable and suspender of the spatial special-shaped cable plane are under spatial stress, and the stress of the overall structure is more complex [2]. The main cable is the main load-bearing component of the suspension bridge, and the main cable shape is one of the main size parameters to be considered in the design of the suspension bridge. Therefore, the reasonable main cable shape has always been the focus of research workers. According to the main cable alignment, suspension bridges can be divided into plane cable plane suspension bridges and space cable plane suspension bridges [3]. Spatial cable plane suspension bridges can also be subdivided into spatial cable plane suspension bridges and spatial special-shaped cable plane suspension bridges [4]. At present, the calculation theory and method of the main cable alignment of suspension bridges with parallel cable planes have been relatively mature, and some valuable results have been achieved. In terms of theory, [PERSON] [5] put forward the calculation model of finding the main cable shape in the parallel cable plane on the basis of analyzing the main cable stress in the parallel cable plane. [PERSON] [6] introduced the finite element method into the calculation ofsuspension structures and proposed the basic process of finding the shape of the main cable in the parallel cable plane. In recent years, there have also been some valuable advances in computational methods. [PERSON] [7] applied the heuristic algorithm to form a finding calculation of the main cable. [PERSON] [8] proposed an optimization algorithm considering the influence of cable clamps. [PERSON] [9] proposed a new form-finding finite element analysis method for the main cable. Suspension bridges with a spatial cable plane are a common structural form of the spatial cable plane. The main cables of the plane suspension bridge with spatial cables are in the state of spatial stress, and the suspenders are in the state of plane stress. The stress of the structure is more complex than that of the suspension bridge with a parallel cable plane. In recent years, the research of the space main cable has made some progress. In terms of the calculation theory of space main cable, [PERSON] [10] analyzed the force on the main cable of the space cable plane and proposed the calculation model of space main cable bridge alignment. In terms of the calculation method of the space main cable, [PERSON] [11] summarized the forces on the space main cable and proposed the Steffens Newton method with adjustable parameters. [PERSON] [12] found that the existing space main cable calculation models rely on high-precision iterative initial values, and the traditional influence matrix method faces the problem of nonconvergence in some cases. To solve this problem, he proposed the modified Marquardt least squares method. [PERSON] [13] proposed a nonlinear GRG method. [PERSON] [14] proposed a form-finding method considering the thermal effect of the main cable. [PERSON] [15] proposed a finite element method to solve the shape of main cable with the Euler method. [PERSON] [16] proposed a finite element method with unknown parameters of cable node coordinates and element internal forces. [PERSON] [17] proposed a form-finding algorithm considering cable saddle friction. The research on finding the shape of the main cable of a spatial special-shaped suspension bridge has also made some progress in recent years. [PERSON] [18] proposed a modeling method that uses the Midas modeling assistant to repeatedly modify the cable inclination. [PERSON] [2], based on the catenary theory, proposed an analytical expression for the completed alignment of the main cable with a spatial special-shaped cable plane considering the coupling between the main cable and the suspender.