# Static Wind Reliability Analysis of Long-Span Highway Cable-Stayed Bridge in Service
## 4 Case Analysis of Static Wind Instability and Parameter Influence of Xiangshan Harbor Bridge  
### Finite Element Model of Xiangshan Harbor Bridge  
The main bridge of Xiangshan Harbor Bridge in Ningbo City in China is a five-span continuous semi-floating cable-stayed bridge with double towers and double cable planes in Figure 4. The main girder section is a streamlined closed steel box shape, the detailed sizes are marked in Figure 5, and the bridge tower is diamond-shaped. The auxiliary pier and transition pier are rectangular thin-walled types. The foundations of the bridge tower and piers are all bored pile foundations. Vertical and lateral bearings are set between the cable tower and the main beam, and viscous dampers with the function to limit displacement are installed in the longitudinal direction. In this analysis, the limit of dampers on the longitudinal motion of the main beam is ignored, and the main beam is only restrained in the lateral and vertical directions. The longitudinal sliding bearing is set on one side of the transverse bridge direction between the main beam and the transition pier and the auxiliary pier, and the longitudinal sliding bearing on the other side can limit the lateral relative movement at the same time, so it is simplified to constrain the main beam in the lateral and vertical directions, and only coupling the degrees of freedom in the lateral and vertical directions when building the finite element model. And the bottom of the cable tower and piers is consolidated to constrain all degrees of freedom.  
The finite element model of Xiangshan Harbor Bridge is established by ANSYS software. This bridge is simulated as a single-ridge girder model as a \"fish bone spur\" form. The whole modeling process is finished by APDL (ANSYS Parametric Design Language). The main beam, bridge tower, and piers are simulated by BEAM188 element which can give the cross-section shape, the connection between the main girder and stay cables is realized by rigid arms that are modeled by BEAM4 element with high rigidity. The stay cables are modeled by the LINK10 element, and the ballast and the second-stage dead load are substituted by the mass point MASS21 element. The connection between the main beam, the bridge tower, and the pier is simulated by coupling constraint, and the bottom of the bridge tower and bridge piers are consolidated. The complete finite element model of Xiangshan Harbor Bridge is shown in Figure 6.  
The dynamic characteristic analysis of this bridge is conducted in accordance with the modal analysis function in ANSYS software, and the natural vibration frequency and mode shape results of the bridge can be extracted. The analysis results of the first ten-order natural vibration frequencies are listed in Table 1 and compared with the measured frequencies of Xiangshan Harbor Bridge by dynamic load tests [21] whose detailed contents are from [28]. It can be found from Table 1 that the difference between the calculated value by the numerical simulation and the measured value by tests is acceptable. Therefore, the established numerical model meets the engineering requirements and can be used for structural response analysis.  
Figure 4: Layout of main bridge (m).  
Figure 5: Cross-section layout of steel box girder (mm).  
Figure 6: Finite element model of Xiangshan Harbor Bridge.