## 5 Numerical Simulation  
A long-span suspension bridge over a deep gorge, as shown in Figure 6, in the Hunan Province of China [34] was adopted in the present study to evaluate the fatigue reliability of the suspenders. The suspension bridge has a span arrangement of 242 m + 1176 m + 116 m. The truss girder is 27 m wide and 7.5 m high. A three-dimensional (3D) finite element model was set up on the ANSYS platform to simulate the suspension bridge, in which the steel truss girder and concrete pylon were idealized as the 3D-beam element, BEAM4, and the cables and suspenders are simplified as a 3D-link element, LINK10. The stiffness contributions due to the pavement and railing were neglected and their masses were equally distributed to the steel truss girder using the mass-only element MASS21. The bearings implemented at both ends of bridge girder were modeled by swing rigid links and horizontal rigid links to restrict the vertical and horizontal movement, while the viscous fluid dampers installed at both ends of the bridge girder, to mitigate the longitudinal movement, were simulated with the control element COMBIN37. Additionally, the main cables and pylons are fixed at the bases.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Random Variables** & **Notation** & **Mean** & **COV** & **Distribution** & **Source** \\ \hline Critical fatigue damage & \(D_{\Delta}\) & 1.0 & 0.3 & Lognormal & [33] \\ Fatigue detail coefficient & \(A\) & \(7.99\times 10^{12}\) MPa\({}^{3}\) & 0.34 & Lognormal & [29] \\ Predicted effective stress range & \(S_{re}^{*}\) & Equation (13) & 0.2 & Lognormal & Equation (13) \\ Predicted Average daily number of cycles & \(N_{avg}^{*}\) & Equation (14) & 0.2 & Lognormal & Equation (14) \\ Slope constant & \(m\) & 3.0 & – & Deterministic & [29] \\ \hline \hline \end{tabular}
\end{table}
Table 5: Random variables for fatigue reliability evaluation of suspenders.  
There is a total of 71 pairs of suspenders distributed along the longitudinal axis of the bridge. Among which, 3 pairs are anchored on the ground directly, (denoted as ground suspenders hereafter) with an equal distance of 29 m, and the other 68 pairs are anchored on the steel truss girder (denoted as girder suspenders hereafter) with an equal distance of 14.5 m. As shown in Figure 6, the 71 pairs of suspenders are labeled as Si (\(i\) = 1,2,..., 71), in which S1, S70, and S71 denote the ground suspenders and S2 to S69 denote the girder suspenders. Since the suspension bridge is symmetric about the longitudinal axis, for each pair of suspenders, the suspender at the windward side has a pretty similar fatigue performance as that of the susender at the leeward side. Additionally, the preliminary analysis reveals that the suspenders S1, S2, S19, and S36 can be used to represent all the suspenders under various loading scenarios. Therefore, the suspenders S1 (ground susender), S2 (suspender at the girder end), S19 (suspender at 1/4 span), and S36 (suspender at mid-span) at the windward side were selected for the subsequent analysis.  
For each suspender, the upper end directly crosses the main cable, while the lower end is attached with a pin connection to the anchorage plate on the upper chord of the truss girder. Steel wire ropes with an elasticity modulus of \(1.15\times 10^{5}\) MPa are adopted for all the suspenders. Two types of cross sections are adopted for the suspenders, as follows: (1) A cross section with a diameter of 88 mm was used for suspenders S1, S2, S36, S69-S71 and (2) a cross section with a diameter of 62 mm was used for the rest suspenders. As illustrated in Figure 7, the steel wire rope in the suspender consists of eight outer strands and eight middle strands laid helically and symmetrically in two layers around a straight core strand, and the core strand itself is made of several wires regularly arranged around a central wire.  
Figure 6: Layout of the prototype suspension bridge (m).  
Figure 7: Wire rope suspenders (**a**) configuration and (**b**) cross sections.