## 5 Buffeting Fatigue Damage Analysis of CFRP Stay Cables
### CFRP Cable Fatigue Damage Analysis  
As shown in Figure 18, the analysis focused on stay cables B01, B17, and B34 from the side spans and J01, J17, and J34 from the main span of the CFRP cable-stayed bridge scheme. These cables were uniformly distributed along the longitudinal axis of the bridge, covering a range of lengths and stress amplitudes. The stress time histories of these cables under varying wind speeds and angles of attack were extracted. The comparative analysis revealed that the windward-side cables exhibited larger stress amplitudes and more intense buffeting responses. Therefore, this study conducted a statistical analysis of fatigue damage based on stress variations in windward-side cable elements. The stress time histories of these cables under varying wind speeds and angles of attack were extracted. Due to space constraints, only the stress time histories of cable J01 under the design wind speed at AOA of \(0^{\circ}\), \(3^{\circ}\), and \(-3^{\circ}\) are presented in Figure 19.  
To statistically analyze the cyclic stress amplitudes and the corresponding cycle counts of the bridge stay cable elements under buffeting forces, a rainflow counting algorithm [31] was programmed in MATLAB R2024a to process the stress time histories of multiple critical stay cables across various loading conditions. Distribution plots of the stress amplitudes were generated to illustrate the relationships among stress amplitude, cycle count, and mean stress. To conserve space, Figures 20-22 present the stress amplitude distributions of the J01 stay cable under three angles of attack (\(-3^{\circ}\), \(0^{\circ}\), \(3^{\circ}\)) and varying wind speeds, derived from the rainflow counting method. These results illustrate the relationships among stress amplitude, cycle count, and mean stress under different wind-load combinations. Figure 18: Layout of selected stay cables. By statistically processing the stress amplitudes and cycle counts obtained from the rainflow counting method and combining the \(S\)-\(N\) curve Equation (15) with the fatigue damage accumulation formula Equation (14), the cumulative fatigue damage of stay cables at various locations under different wind conditions can be calculated. This study compared the fatigue damage of critical cables in both schemes under the design wind speed over a 1000 s duration across different angles of attack. The results, summarized in Table 4, demonstrate that, under identical wind loads, the steel stay cables exhibited significantly higher fatigue damage caused by turbulent wind than the CFRP stay cables. Additionally, at a \(-3^{\circ}\) angle of attack, cables at all locations in both the schemes showed greater fatigue damage than under other angles. This phenomenon may arise because, at negative angles of attack, the aerodynamic lift coefficient and aerodynamic moment coefficient of the main girder both become negative. Consequently, the aerodynamic load on the girder manifests as a downward pressure and a torsional moment that forces the girder cross-section to face the incoming flow. Simultaneously, the stay cables experience larger lateral deformations than the crack-like ones. Figure 21: Stress amplitude distribution of the CFRP stay cable No. J01 under AOA of \(0^{\circ}\): (a) U = 20 m/s; (b) U = 30 m/s; (c) U = 40 m/s; (d) U = 52.97 m/s. Figure 20: Stress amplitude distribution of the CFRP stay cable No. J01 under AOA of \(-3^{\circ}\): (a) U = 20 m/s; (b) U = 30 m/s; (c) U = 40 m/s; (d) U = 52.97 m/s. due to aerodynamic drag. The combined effects of these factors result in significantly higher cable stresses at \(-3^{\circ}\) than at other angles of attack. After performing dynamic calculations on the CFRP cable-stayed bridge structure under varying wind speeds and angles of attack, the stress time histories of the stay cables at characteristic positions were extracted.