## 5 Buffeting Fatigue Damage Analysis of CFRP Stay Cables
### CFRP Cable Fatigue Damage Analysis
Through the rainflow counting method and fatigue damage accumulation calculations, the fatigue damage of each CFRP cable under different wind speeds and angles of attack was obtained, as shown in Figure 23. The results indicate that, when the mean wind speed at deck height was 20 m/s, the fatigue damage of the CFRP cables varied minimally and decreased with increasing cable length. However, at a mean wind speed of 30 m/s, the damage distribution showed significant changes, with the maximum fatigue damage occurring at cables J17 and B17 under a \(-3^{\circ}\) angle of attack. As seen in Figure 17, these cables were close to the 1/4 span of the main girder and the mid-span of the side span, respectively. As the wind speed further increased, the fatigue damage of all cables grew nonlinearly, but the maximum damage remained concentrated at J17 and B17, significantly exceeding that at other locations. At the design wind speed, under a \(-3^{\circ}\) angle of attack, the fatigue damage of cable B17 far surpassed that of the other cables. This phenomenon likely arises because, under turbulent wind loads covering multiple frequencies, the main girder's vibration at specific higher-order frequencies forces cables near these positions to endure substantially larger stress amplitudes than others, accelerating fatigue damage accumulation and rendering these cables the most vulnerable. Based on the above computational results, this study estimated the fatigue damage of CFRP stay cables induced by turbulent wind loads. The analysis adopted a mean wind speed of 30 m/s at deck height. While a \(3^{\circ}\) angle of attack was more critical for structural deformation, the \(-3^{\circ}\) angle induced greater cable stress amplitudes and was thus selected as the adverse angle of attack for fatigue life assessment. Taking the most vulnerable cable B17 as an example, its annual fatigue damage value under turbulent wind loads at 30 m/s and \(-3^{\circ}\) angle of attack was approximately 1.42 \(\times\)\(10^{-19}\), which is far below the critical fatigue damage threshold of 1.0. This indicates that CFRP cables will not experience fatigue failure due to buffeting wind loads during their service life. Nevertheless, despite the CFRP cables' exceptional fatigue resistance, bridge design and maintenance protocols should rigorously address the fatigue performance of cables at critical locations such as B17. Where necessary, appropriate vibration mitigation measures including cross-ties or dampers should be implemented to prevent long-term damage accumulation under stochastic loads such as traffic or wave-induced vibrations. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**AOA (deg)**} & \multirow{2}{*}{**Scheme**} & \multicolumn{6}{c}{**Serial Number of Stay Cable**} \\ \cline{3-8}  & & **B01** & **B17** & **B34** & **J34** & **J17** & **J01** \\ \hline \multirow{3}{*}{\(-3\)} & STEEL & \(3.592\times 10^{-7}\) & \(3.432\times 10^{-6}\) & \(2.826\times 10^{-8}\) & \(9.981\times 10^{-9}\) & \(7.437\times 10^{-7}\) & \(3.450\times 10^{-7}\) \\  & CFRP & \(8.604\times 10^{-15}\) & \(7.595\times 10^{-12}\) & \(1.587\times 10^{-17}\) & \(1.492\times 10^{-18}\) & \(1.335\times 10^{-12}\) & \(6.641\times 10^{-13}\) \\  & STEEL & \(8.368\times 10^{-8}\) & \(1.786\times 10^{-6}\) & \(1.543\times 10^{-8}\) & \(3.064\times 10^{-9}\) & \(5.903\times 10^{-7}\) & \(7.542\times 10^{-7}\) \\  & CFRP & \(5.868\times 10^{-16}\) & \(2.515\times 10^{-13}\) & \(1.351\times 10^{-18}\) & \(2.555\times 10^{-19}\) & \(5.618\times 10^{-14}\) & \(5.004\times 10^{-15}\) \\  & STEEL & \(4.460\times 10^{-9}\) & \(8.554\times 10^{-8}\) & \(1.493\times 10^{-9}\) & \(9.057\times 10^{-11}\) & \(5.213\times 10^{-8}\) & \(2.405\times 10^{-8}\) \\  & CFRP & \(2.621\times 10^{-19}\) & \(1.112\times 10^{-17}\) & \(5.958\times 10^{-21}\) & \(2.601\times 10^{-21}\) & \(1.124\times 10^{-17}\) & \(6.662\times 10^{-19}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Buffeting-induced fatigue damage of cable under \(U_{d}\) within 1000 s for both schemes.