• Wind and Structures
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• v.11 no.3
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• pp.209-220
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• 2008

Flutter derivatives provide the basis of predicting the critical wind speed in flutter and buffeting analysis of long-span cable-supported bridges. Many studies have been performed on the methods and applications of identification of flutter derivatives of bridge decks under wind action. In fact, strong wind, especially typhoon, is always accompanied by heavy rain. Then, what is the effect of rain on flutter derivatives and flutter critical wind speed of bridges? Unfortunately, there have been no studies on this subject. This paper makes an initial study on this problem. Covariance-driven Stochastic Subspace Identification (SSI in short) which is capable of estimating the flutter derivatives of bridge decks from their steady random responses is presented first. An experimental set-up is specially designed and manufactured to produce the conditions of rain and wind. Wind tunnel tests of a quasi-streamlined thin plate model are conducted under conditions of only wind action and simultaneous wind-rain action, respectively. The flutter derivatives are then extracted by the SSI method, and comparisons are made between the flutter derivatives under the two different conditions. The comparison results tentatively indicate that rain has non-trivial effects on flutter derivatives, especially on and $H_2$ and $A_2$thus the flutter critical wind speeds of bridges.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.2A
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• pp.97-104
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• 2011

This study presents the aerodynamic admittance function of bridge girder under turbulent flow generated from wind velocity spectrum measured at bridge site. Three dimensional buffeting analysis of concrete cable-stayed bridge were performed considering aerodynamic admittance functions obtained from four different methods. It is revealed from the analysis that vertical buffeting responses considering proper aerodynamic admittance functions were just half of that neglecting aerodynamic admittance function. Grid turbulence was found to relatively lower the aerodynamic admittance function at low frequency range, and to underestimate the buffeting wind forces. It is recommended to use the aerodynamic admittance function evaluated from flutter derivatives or measured at active turbulence in order to properly predict the buffeting responses of bridges.

• Wind and Structures
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• v.7 no.6
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• pp.421-447
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• 2004

This paper presents a time domain approach for predicting buffeting response of long suspension bridges under skew winds. The buffeting forces on an oblique strip of the bridge deck in the mean wind direction are derived in terms of aerodynamic coefficients measured under skew winds and equivalent fluctuating wind velocities with aerodynamic impulse functions included. The time histories of equivalent fluctuating wind velocities and then buffeting forces along the bridge deck are simulated using the spectral representation method based on the Gaussian distribution assumption. The self-excited forces on an oblique strip of the bridge deck are represented by the convolution integrals involving aerodynamic impulse functions and structural motions. The aerodynamic impulse functions of self-excited forces are derived from experimentally measured flutter derivatives under skew winds using rational function approximations. The governing equation of motion of a long suspension bridge under skew winds is established using the finite element method and solved using the Newmark numerical method. The proposed time domain approach is finally applied to the Tsing Ma suspension bridge in Hong Kong. The computed buffeting responses of the bridge under skew winds during Typhoon Sam are compared with those obtained from the frequency domain approach and the field measurement. The comparisons are found satisfactory for the bridge response in the main span.

• Wind and Structures
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• v.20 no.2
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• pp.275-292
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• 2015

The presence of traffic on a slender long-span bridge deck will modify the cross-section profile of the bridge, which may influence the flutter derivatives and in turn, the critical flutter wind velocity of the bridge. Studies on the influence of vehicles on the flutter derivatives and the critical flutter wind velocity of bridges are rather rare as compared to the investigations on the coupled buffeting vibration of the wind-vehicle-bridge system. A typical streamlined cross-section for long-span bridges is adopted for both experimental and analytical studies. The scaled bridge section model with vehicle models distributed on the bridge deck considering different traffic flow scenarios has been tested in the wind tunnel. The flutter derivatives of the modified bridge cross section have been identified using forced vibration method and the results suggest that the influence of vehicles on the flutter derivatives of the typical streamlined cross-section cannot be ignored. Based on the identified flutter derivatives, the influence of vehicles on the flutter stability of the bridge is investigated. The results show that the effect of vehicles on the flutter wind velocity is obvious.

• Wind and Structures
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• v.10 no.1
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• pp.1-22
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• 2007

The suppression of aerodynamic response of long-span suspension bridges during erection and after completion by using single TMD and multi TMD is presented in this paper. An advanced finite-element-based aerodynamic model that can be used to analyze both flutter instability and buffeting response in the time domain is also proposed. The frequency-dependent flutter derivatives are transferred into a time-dependent rational function, through which the coupling effects of three-dimensional aerodynamic motions under gusty winds can be accurately considered. The modal damping of a structure-TMD system is analyzed by the state-space approach. The numerical examples are performed on the Akashi Kaikyo Bridge with a main span of 1990 m. The bridge is idealized by a three-dimensional finite-element model consisting of 681 nodes. The results show that when the wind velocity is low, about 20 m/s, the multi TMD type 1 (the vertical and horizontal TMD with 1% mass ratio in each direction together with the torsional TMD with ratio of 1% mass moment of inertia) can significantly reduce the buffeting response in vertical, horizontal and torsional directions by 8.6-13%. When the wind velocity increases to 40 m/s, the control efficiency of a multi TMD in reducing the torsional buffeting response increases greatly to 28%. However, its control efficiency in the vertical and horizontal directions reduces. The results also indicate that the critical wind velocity for flutter instability during erection is significantly lower than that of the completed bridge. By pylon-to-midspan configuration, the minimum critical wind velocity of 57.70 m/s occurs at stage of 85% deck completion.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.5
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• pp.402-409
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• 2004

Numerical analysis of static and dynamic wind effects on civil engineering structures was performed. Long-span suspension bridges are flexible structures that are highly sensitive to the action of the wind. Aerodynamic effect often becomes a governing factor in the design process of bridges and aeroelastic stability boundary becomes a prime criterion which should be confirmed during the structural design stage of bridges because the long-span suspension bridges are prone to the aerodynamic instabilities caused by wind. If the wind velocity exceeds the critical velocity that the bridge can withstand, then the bridge fails due to the phenomenon of flutter. Buffeting caused by turbulence results in structural fatigue, which could lead to the failure of a bridge. Navier-Stokes equations are used for the aeroelastic analysis of bridge girder section. The aeroelastic simulation is carried out to study the aeroelastic stability of bridges using both Computational Fluid Dynamic (CFD) and Computational Structural Dynamic (CSD) schemes.

• Wind and Structures
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• v.1 no.1
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• pp.67-75
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• 1998

Tiger Gate Bridge, a steel suspension bridge with a main span of 888 m and a stiffening box girder, is located at the Pearl River Estuary, Guangdong Province, one of the typhoon-prone area in China. Focusing on the developing of the full aeroelastic model of the bridge and simulation of the wind field of the bridge site in a large boundary wind tunnel at Tongji University, Shanghai, China, some main results about the wind resistant properties of the bridge including aerodynamic instability, buffeting responses both being in operation and erection stages by using of a full aeroelastic model wind tunnel testing are introduced. Some of analytical approaches to those aerodynamic behaviours are also presented, and compared with experimental data of the testing.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.36 no.3
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• pp.349-359
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• 2016

In order to analytically evaluate buffeting responses, the analysis of wind characteristics such as turbulence intensity, turbulence length, gust, roughness coefficient, etc must be a priority. Static aerodynamic force coefficients, flutter coefficients, structural damping ratios, aerodynamic damping ratios and natural frequencies affect the analytical responses. The bridge interested in this paper has being been used for 32 years. As the time passes, current terrain conditions around the bridge are different markedly from the conditions it was built 32 years ago. Also, wind environments were considerably varied by the climate change. For this reason, it is necessary to evaluate the turbulence intensity, length, spectrum and roughness coefficient of the bridge site from full-scale measurements using the structural health monitoring system. The evaluation results indicate that wind characteristics of bridge site is analogous to that of open terrain although the bridge is located on the coastal area. To calculate buffeting responses, the analysis variables such as damping ratios, static aerodynamic force coefficients and natural frequency were evaluated from measured data. The analysis was performed with regard to 4 cases. The evaluated variables from measured data are applied to the first and second analysis cases. And the other analysis cases were performed based on Design Guidelines for Steel Cable Supported Bridges. The calculated responses of each analysis cases are compared with the buffeting response measured at less than 25m/s wind speed. It is verified that the responses by the numerical analysis applying the estimated variables based on full-scale measurements are well agreed with the measured actual buffeting responses under wind speed 25m/s. Also, the extreme wind speed corresponding to a recurrence interval 200 years is derived from Gumbel distribution. The derived wind speed for return period of 200 years is 45m/s. Therefore the buffeting responses at wind speed 45m/s is determined by the analysis applying the estimated variables.

• Journal of Korean Society of Steel Construction
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• v.9 no.2 s.31
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• pp.259-267
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• 1997

Wind tunnel test results and their interpretations focused on the behavior of girder, which were performed to study the aerodynamic stability of a self-anchored suspension bridge with lateral sag of main cable, are presented in this paper The shape of the girder which has the best aerodynamic stability was selected based on the section model test under uniform and turbulent flow conditions. Good performance of the selected section was confirmed in the full bridge model test. Measured flutter derivatives are presented for further study. Buffeting response was investigated to check the fatigue problem and serviceability of the bridge but it was found to be acceptable from the engineering point of view. Even though the drag coefficient of the girder had high value, the amplitude of the lateral vibration was found to be very low. This may be due to the restraint provided by the lateral sag of the cables.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.5A
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• pp.887-899
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• 2006

The aim of this study is to investigate a correlation between fundamental data on aerodynamic characteristics of bridge girder cross-sections, such as aerodynamic force coefficients and flutter derivatives, and their aerodynamic behaviour. The section model tests were carried out in three stages. In the first stage, seven deck configurations were studied, namely; Six 2-edge girders and one box girder. In this stage, changes in aerodynamic force coefficients due to geometrical shape of girders, incidence angle of flow, wind directions and turbulence intensities were studied by static section model tests. In the second stage, the dynamic section model tests were carried out to investigate the relativity of static coefficients to dynamic responses. And finally, the two-dimensional (lift-torsion) aerodynamic derivatives of three bridge deck configurations were investigated by dynamic section model tests. The aerodynamic derivatives can be best described as a representation of the aerodynamic damping and the aerodynamic stiffness provided by the wind for a given deck geometry. The method employed here to extract these unsteady aerodynamic properties is known as the initial displacement technique. It involves the measurement of the decay in amplitude with time of an initial displacement of the deck in heave and torsion, for various wind speeds, in smooth flow. It is suggested that the proposed aerodynamic force coefficients and flutter derivatives of bridge girder sections will be potentially useful for the aeroelastic analysis and buffeting analysis.