# Flutter Reliability Analysis of Xiangshan Harbor Highway Cable-Stayed Bridges in Service
## 4 Flutter Reliability Analysis of Xiangshan Harbor Bridge  
### Flutter Reliability Analysis  
According to the analysis of the influence law for flutter instability parameters, it could be found that the influences of main beam stiffness, wire breaking rate, damping ratio and cable breakage location on flutter stability cannot be ignored. Therefore, the flutter reliability of Xiangshan Harbor Bridge was analyzed considering these four parameters and the actual situation. For the flutter uncertainty analysis of Xiangshan Harbor Bridge, according to the results of the above parameters affect, there are four random parameters, including the main beam stiffness, the wire breaking rate, the damping ratio and the cable breakage location. The design value of the stiffness of the main beam was 0.75 times that of the bridge under initial state, and the stiffness of the main beam was changed by adjusting the elastic modulus \(E\) of the steel material, so the design value of the main beam stiffness was 1.575 \(\times\) 10\({}^{5}\) MPa and the variation coefficient was 0.05. The wire breaking rate was 20% for reliability analysis, so the design value of the overall cable cross-sectional area was 0.20085 m\({}^{2}\), and its variation coefficient was 0.05. The variation coefficient of main beam stiffness and cable cross-sectional area was determined in accordance with the relevant literature on bridge reliability and relevant suggestions in _Uniform Standard for Reliability  
Figure 16: Schematic diagram of cable breakage position (m). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cable Breakage Position** & **Condition 1** & **Condition 2** & **Condition 3** & **Initial State** \\ \hline Critical flutter wind speed & & & & \\ (m/s) & 53 & 60 & 63 & 64 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Flutter critical wind speed of Xiangshan Harbor Bridge at different cable breakage location. Design of Engineering Structures_[43]. The design value of the damping ratio was 0.3%, and its variation coefficient is often assumed to be in the range of 0.15 to 0.88 because the structural damping ratio is lower and the variation coefficient is higher, so the variation coefficient of damping ratio in this study took the middle value 0.4. However, there is no corresponding standard for the cable breakage location, so in order to make the sampling result more consistent with the actual situation the design value was set as five and the variation coefficient was 0.5. According to the above description, using MATLAB and the Latin hypercube sampling method, the parameters were sampled 30 times, and the accuracy could meet the requirements. These four uncertain parameters and their distribution types are summarized in Table 6.  
MATLAB software was used to realize the sampling of LHS, and 30 random sampling times are listed in Table 7. In the process of flutter instability analysis, the actual value of each parameter was equal to the design value multiplied by the sampling value in Table 7, and then the actual values were input into the finite element model to calculate the critical flutter wind speed. When calculating the critical flutter wind speed of the bridge, if a certain parameter took the sampling value for calculation, other parameters took the design value. Then, the flutter instability of the deterministic analysis of the cable-stayed bridge was finished, and the critical wind speed of flutter instability was obtained on the basis of Section 3.3. The 30 groups of deterministic analysis results are listed in Table 8, and the statistic parameters of the flutter critical wind speed are listed in Table 9.