## 2 Modeling of Long-Span CRS  
As described above, the CRS was composed of suspension cable, conductor, insulator and anchorage while guyed masts towers were removed. The suspension cable supported the conductors and was anchored on both ends. The suspension cable and conductor, the main components of CRS, made a complex flexible structural system. It was always an issue \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Design Parameters** & **Rope for Conductor** & **Quad-Bundle Conductor** & **Tension Insulator** \\ \hline Span (m) & 1000 & 800 & 10 in total \\ Total cross section area (mm\({}^{2}\)) & 766.50 & 425.24 & 125,600 \\ External diameter (mm) & 36 & 26.82 & 400 \\ Weight per length (kg/m) & 59.52 & 1.35 & 100 \\ Elastic modulus (N/mm\({}^{2}\)) & 180,000 & 65,000 & 190,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Recommended design parameters of long-span CRS. Figure 2: Diagram of long-span cross-rope suspension line. modeling complex flexible structural systems with large deformation due to convergence problems when considering geometrical nonlinearity. This paper presents an assembly modeling approach where the components of the CRS and their deformed shape and loading states were separately analyzed and finally assembled. Commercial finite element software, ANSYS, was adopted for the mentioned modeling process. All members were modeled by a two-node link element type in three-dimensional space, which means only tensile force and strain were considered for each element, and the bending and torsion stiffness were ignored. Regarding the frequency of principal vibration mode, a minimum of 100 divisions for a whole segment of cable or conductor was essential [20]. In order to obtain stable and accurate computation, the whole structure was divided into several individual parts, including suspension cables and conductors. Those substructures were computed separately and then assembled into a whole system. Consequently, displacement and deformation of each node and element were calculated in their substructures and inputted as initial conditions for the whole assembled structural system. Therefore, stability and accuracy of computation were achieved in this way. The deformed shape of the suspension cable and conductor under initial static load were calculated, respectively. The initial shape function of conductor with uniform load was simplified to a parabola, which was defined by a sag in middle span, and was given as follows:  
\[y=4 xf_{m}(1-x/l)/l \tag{1}\]  
where \(x\) is the distance from starting point (m), \(l\) is the span (m) and \(f_{m}\) is the sag in the midspan (m):  
\[f_{m}=\gamma l^{2}/8\sigma_{0}\cos\beta \tag{2}\]  
where \(\gamma\) is uniform load in per length and section (N/m mm\({}^{2}\)), \(\sigma_{0}\) is horizontal stress of the conductor (N/mm\({}^{2}\)), \(\beta\) is the angle of height difference, \(\tan\beta=h/l\), where \(h\) is the height difference between two suspension points (m). It was noticed that horizontal stress \(\sigma_{0}\) could be calculated from design tensile force \(T\), which was considered as the control parameter for calculating the deformed shape of the suspension cable and conductor. Approximated parabola shapes of each substructure were calculated by taking tensile force \(T\) into Equation (2) and then Equation (1). Coordinates of nodes and tensile stress of each element were input to finite element software program as initial conditions for static analysis. Then, the approximate shape of each substructure obtained was exported for further calculation. The process of an assembly modeling approach for the CRS transmission line is shown in Figure 3. Firstly, the finite element models of conductor and suspension cable were established, respectively, the material properties were input, and the initial shapes of the conductor and suspension cable were calculated with the design tension or sag as the control parameters.