Flutter characteristics of twin-box girder bridges with vertical central stabilizers
Introduction
Twin-box girders with a center gap between two girders has been proven to be one of the effective aerodynamic countermeasures for improving the aerodynamic performance of long-span cable-supported bridges, and so its implementation becomes increasingly popular for long-span, or even super long-span bridges [1], [2], [3], e.g., Xihoumen Bridge with the main span of 1650 m (China) and Gwangyang Bridge with the main span of 1545 m (Korea). Nevertheless, twin-box girders with various Slot Width Ratios (SWRs, for example, the 20% SWR refers to D/Bs = 0.2, where D is slot width and Bs is the width of two decks) may exhibit different flutter performance [4], [5]. Although the maximum growth rate of Critical Flutter Wind Speed (Ucr) could reach more than 20% after slotting for twin-box girders, the aerodynamic stability of the bridges becomes uncertain when the length of the growing span of the bridge is over certain limit [4], [6]. Therefore, the implementation of practicable aerodynamic countermeasures (e.g. Vertical Central Stabilizers (VCS)) becomes necessary for further enhancing the flutter performance of super long-span bridges.
VCS could play an important role in the airflow separation and have been applied in many long-span bridges with different geometrical shapes to improve flutter performance. For example, the Akashi Kaikyo Bridge (the length of the longest span is 1991 m) with a 2.15 m height VCS installed in the centerline of the truss-type stiffening girder [7] and the Runyang Yangtze River Bridge (the length of the longest span is 1490 m, China) with a 0.65 m height VCS on the top of the closed box girder [8]. Based on the numerical simulation, VCS have been verified to be an effective aerodynamic measure to improve the flutter performance of long-span bridges either with an open cross section or with a streamlined box cross section [9]. The results from wind tunnel tests also confirm that both the VCS on the top of two-isolated-girder section and box girders with cantilevered slabs could increase the Ucr by approximately 11% [10]. Moreover, the flutter performance of twin-box girders could be significantly improved when installing a reasonable scheme of VCS [11], [12], [13].
Over the last decades, a lot of research work has been carried out to investigate the control effectiveness of VCS on the flutter performance of long-span bridges with box girders. It has been found that the flutter control effect of VCS is closely related to the height and location of VCS. The flutter performance of box girders will decrease if the height of VCS exceeds a critical limit [10]. The installation of central stabilizer on the top of a box girder (Type A) appears to be one of the best ways of stabilizing box girders aerodynamically, while the optimal height of VCS depends on the types of VCS (three types of stabilizers were studied in present study: Type A-only one VCS installed on the top of deck; Type B - only one VCS installed on the bottom of deck; Type AB – one VCS installed on the top of deck, while another one installed below the bottom of deck) [8]. Flutter performance of a multi-box girder section gradually improves with the increase of the height of VCS on the top of girder section, whereas the Ucr decreases when the height of VCS is greater than 0.5 h/H [14]. As for the twin-box girders, Type C has the best flutter-controlling effect for a twin-box girder among three basic types of Type A, B and C (i.e. Type C – installing VCS under the central slotting), and the combination schemes of VCS (Type A + B and Type C + B) are more effective with the about 15% growth rate of Ucr [10]. However, the control effect of VCS with various positions and configurations flutter performance for twin-box girder bridges with various SWR is still not well understood. Therefore, further research work on identifying the optimal height and location of VCS for twin-box girder bridges with various SWR is required.
To further understand the role of VCS in the improvement of flutter performance, the present study mainly focuses on the flutter instability taking into consideration flutter derivatives and the coupling effects of heaving and torsional degree, as well as the effect of flow structures around girders. Matsumoto et al. [15] proposed a new approach in studying the flutter instability of flutter branches. Their results suggested that the controlling flutter derivatives is a way of controlling the flutter mechanism. Chen et al. [16] found that the aerodynamic damping with the reference of flutter derivative A2∗ is the most important stabilizing term among five flutter derivatives, and the use of VCS could produce a higher level of heaving degree participation and greater critical wind speed for a truss-girder section. In addition, many studies have successfully employed the Computational Fluid Dynamics (CFD) technique for simulating the flow structures around oscillating bridge sections with the aim of exploring the flutter mechanism and predicting the critical flutter wind speed [17], [18], [19], [20], [21], [22], [23]. CFD simulation results based on Random Vortex Method also showed that the Ucr could be increased by using VCS since the strength of the large vortices’ structure become weakened and its rhythmic motion is destroyed [9]. CFD simulation results showed that the VCS control the stream around the girder as well as the vortex generation [16]. However, the relevant studies on the flutter mechanism of twin-box girders with VCS are limited and need to be further investigated. In the present study, we aim to investigate the flutter characteristics of twin-box girders with various schemes of SWRs and VCS. Firstly, wind tunnel tests were firstly conducted to demonstrate the influence of bridge geometry in the flutter performance of twin-box girders with six representative height and four types of VCS. The measured Ucr corresponding to these schemes of aerodynamic countermeasures, such as different combination of five SWRs and VCS, were analyzed and compared, respectively. Secondly, a Two-Dimensional Three Degree of Freedom (2D-3DOF) flutter analysis method has been adopted to quantify the flutter mechanism with regard to aerodynamic damping and DOF participation level of three types of VCS. Accordingly, the velocity filed and pressure distributions from CFD simulations were used to further understand the aerodynamic behavior of twin-box girder bridges with various VCS. In addition, both the Lorentz function and Sine function were employed to estimate the correction coefficient of the modified Selberg formula, which is of importance for estimating the Ucr of twin-box girders with various SWRs and VCS.
Section snippets
Experimental set-up
The measurement of the Ucr of twin-box girders with different combination schemes of SWR and VCS is the purpose of this experimental investigation. As shown in Fig. 1(a) and (b), a series of 1:80 simplified section models of twin-box girders without consideration of the deck secondary structures were performed in the TJ-1 Wind Tunnel of Tongji University to accommodate the size of sectional models and testing section. Since the SWR plays an important role in the aerodynamic performance of
Theoretical analysis of stabilizing mechanism
A two-dimensional three-degree-of-freedom (2D-3DOF) flutter analysis method was developed to quantify the effects of flutter derivatives, aerodynamic damping, and flutter modality on flutter performance [4], [8]. In this study, 2D-3DOF was applied to theoretically analyze the stabilization mechanism of twin box girders under various VCS. Three typical types, including the 20% SWR for Types A and B and the 40% SWR for Type AC, were given as the example, and the stabilization mechanism of the
Flow structures simulation
In this section, the aerodynamic instability mechanism of the VCS was further investigated through CFD simulation in term of instantaneous velocity field and vortex structures.
Empirical expression
Selberg formula is widely utilized to calculate the critical flutter wind speed of streamlined cross sections for design purpose [29]. A modified Selberg formula was further developed to calculate the Ucr of a closed box girders with Type A of VCS, wherein Lorentz peak-value function was utilized [8]. Subsequently, the Lorentz peak-value function was also used to estimate the Ucr of twin-box girders with various SWR [4]. In order to quantitatively evaluate the control effects of VCS on the
Conclusions
In this study, the flutter characteristics of twin-box girders bridges with the combination schemes of various slot width ratios and vertical central stabilizers were studied through experimental investigation in conjunction with theoretical analysis. The major conclusions are as follows:
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The height variation of VCS significantly affects the Ucr and β of a twin-box girder bridge with 20% SWR. However, under a relatively large SWR (e.g. >60%), the change of the height of VCS has little impact on
Acknowledgments
The authors gratefully acknowledge the support for the research work jointly provided by the National Key Basic Research Program of China (973 Program) (No. 2013CB036300), the National Science Foundations of China (No. 91215302, 51078276, and 51678436).
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