The aerodynamic stability of a new type of Multi-tower cable-stayed bridge with rhombic stiffening cables

Aerodynamic stability is an important problem in the design and research of long-span multi-tower cable-stayed Bridges. The three-dimensional nonlinear aerodynamic stability analysis method is used to qualitatively analyze the aerodynamic stability of a new type of rhombic stiffened cable-stayed bridge in this paper, and compared with conventional cable-stayed bridges. The results show that the new rhombus stiffener can greatly increase the longitudinal stiffness of the structure and reduce the vibration period of the structure. The maximum lateral displacement, vertical displacement and torsion Angle of the structure under wind load are reduced, and the critical unstable wind speed of the structure is increased. It can be seen that the aerodynamic stability of the new type of rhombus cable-stayed bridge is better than conventional cable-stayed bridge.


Introduction
Long-span multi-tower cable-stayed bridge is a flexible structure [1], which is easy to vibrate and deform under wind load. In history, the damage accidents of cable-stayed Bridges due to wind vibration often occur, so the influence of wind load on cable-stayed Bridges should be paid attention to.
It is of great significance to study the strength, stiffness and carrying capacity of long-span multitower cable-stayed bridge under natural wind load so that it can still play the role of transportation in the process of high wind. Because of the difficulty in anchorage of the middle tower, the longitudinal stiffness of the long-span multi-tower cable-stayed bridge is low and vibration and deformation are more likely to occur under wind load. A new type of rhombic stiffener cable-stayed bridge which can increase the directional stiffness of a multi-tower cable-stayed bridge was proposed in this paper. The aerodynamic stability of the new type of rhombic stiffener cable-stayed bridge and the conventional cable-stayed bridge under the wind load was compared and analyzed by considering the wind attack Angle, vertical wind load and cross wind load in this paper. It is a reference for the application of the new cable-stayed bridge in practical engineering.

Dynamic characteristics of a new type of rhombus cable-stayed bridge
The stiffness control of multi-tower cable-stayed bridge is very important in design. Through reasonable layout of stiffening cables can improve the overall stiffness of multi-tower cable-stayed bridge [2]. But the conventional methods of stiffening cables have many deficiencies, the new stiffening cables system (rhombic Cables) was performed in this paper (as shown in Figure 1): Figure 1. Multi-tower Cable bridge with rhombic cables As shown in Figure 1, because one end of Tie-down cables was anchored on the top and root of tower and the other end is anchored on the girder, it causes that tower and girder are validly connected to become a balanced system and increase the overall stiffness of the structure.
The actual bridge design parameters were used in this paper, and diamond stiffeners were set on each tower. Compared with the conventional cable-stayed bridge, the influence of rhombic stiffening cables on the wind resistance of the bridge was analyzed.
The total length of Bridge is 1327.6m. This bridge has three towers and four spans whose midspan is 460m, side span is 203.8m and height of tower is 247.5m. The calculation model is shown in figure  2.
a. The conventional cable-stayed bridge b. The cable-stayed bridge with rhombus cable

Figure 2. Calculation model
The above models were analysed by using the finite element software Ansys, and the first 6 order natural vibration frequencies and formations obtained were shown in As shown in table 1, the self-vibration period of rhombus cable-stayed bridge decreases from 15 seconds to 9 seconds, and the frequency increases from 0.1045 to 0.1841, indicating that the rhombus greatly increases the stiffness of the structure along the bridge. Moreover, the vertical bending formation of the main girder is relatively late compared with the traditional cable-stayed bridge, so the vertical rigidity of the main girder can be increased.

The aerodynamic stability of the new rhombus stiffening cable-stayed bridge
In -3°, 0° and 3° initial wind Angle of attack, the conventional cable-stayed bridge and rhombus stiffening cable-stayed bridge had carried on the aerodynamic stability analysis by three dimensional nonlinear analysis method [3]. The bridge model was simplified to the bar model. The bridge deck main beam and bridge tower were simulated by spatial beam element. The cable-stayed cable was simulated by spatial rod element. The calculation model is shown in figure 2.The main beam takes into account the action of three components of static force. Because the main girder size of the bridge in this paper was similar to that of Taizhou Changjiang river bridge, static three-component force [4]of Taizhou Changjiang river bridge was adopted in this analysis.   As shown in figure 4, under 0 ° angle of attack wind, when wind speed is low, the conventional cable-stayed bridge and the rhombus stiffening cable-stayed bridge of displacement are close to in all directions. When the wind speed reaches 110m/s, conventional cable-stayed bridge vertical and torsional displacement sudden increase sharply, structure began to enter a state of instability, and the displacement difference between the two structures is large. The critical wind speed of rhombic stiffener cable-stayed bridge is about 130m/s. The instability of the two cable-stayed Bridges is mainly manifested by the spatial flexural and torsional coupled instability of the main girder in vertical bending and torsional deformation, and it is also associated with lateral bending deformation. It can be seen that under the same conditions, the aerodynamic stability of rhombus cable-stayed bridge is better than that of conventional cable-stayed bridge [9].
Under 3 ° and + 3 ° angle of attack wind, the displacement changing law of different wind speeds is similar. In the same wind speed, the vertical and horizontal displacement and torsion angle of the rhombic stiffening cable-stayed bridge are smaller than conventional cable-stayed bridge. As the wind speed is higher, the displacement of the rhombic stiffening cable-stayed bridge in all directions is reduced obviously. It further states that in the same case, the structure stiffness of rhombus stiffening cable-stayed bridge is larger than that of conventional cable-stayed bridge, and the aerodynamic stability of rhombus stiffening cable-stayed bridge is better than that of conventional cable-stayed bridge [10].

Conclusion
The three-dimensional nonlinear aerodynamic stability analysis method is used to qualitatively analyze the aerodynamic stability of a new type of rhombic stiffened cable-stayed bridge in this paper, and compared with conventional cable-stayed bridges.
The results show that the new rhombus stiffening can greatly increase the longitudinal stiffness of the structure and reduce the vibration period of the structure. The maximum lateral displacement, vertical displacement and torsion Angle of the structure under wind load are reduced, and the critical unstable wind speed of the structure is increased. It can be seen that the aerodynamic stability of the new type of rhombus cable-stayed bridge is better than conventional cable-stayed bridge.