A finite-element-based framework for buffeting analysis of long-span cable-supported bridges under skew winds is developed in the frequency domain utilizing the linear quasi-steady theory and the strip theory of aerodynamics in conjunction with the pseudo excitation method. A set of universal expressions for six components of buffeting forces is first derived in association with oblique cross-sections of bridge components, in which the buffeting forces are formed with respect to the wind coordinate system and then converted to those with respect to the structural coordinate system. Skew mean wind and three orthogonal components of velocity fluctuations can thus be easily handled without any further decomposition. The coherence between velocity fluctuations of wind turbulence at any two arbitrary spatial points is considered in the global wind coordinate system rather than in the global structural coordinate system. Aeroelastic stiffness and damping matrices due to self-excited forces are then taken into consideration in terms of the 18 flutter derivatives with respect to the oblique cross-sections. The pseudo-excitation method is finally employed to solve efficiently the fully coupled 3D buffeting problem of long-span cable-supported bridges under skew winds with the effects of multi-modes and spatial modes, inter-mode coupling and aerodynamic coupling, and the interaction among major bridge components being naturally included.

s paper addresses the measurement of eight flutter derivatives of a typical oblique strip of the Tsing Ma bridge deck under skew winds. The wind tunnel test technique developed for this measurement includes the design of oblique sectional model, the development of a dynamic test rig, and the application of unifying least-square (ULS) method for identification. The eight identified flutter derivatives of discrete values are first fitted to obtain eight flutter derivative curves as functions of both wind inclination and yaw angle. Based on these curves, the effects of wind inclination and yaw angle on aeroelastic damping and stiffness, in particular on critical wind speed, are then discussed. Furthermore, the measured flutter derivatives of the bridge deck under skew winds are compared with those obtained from the empirical formulae derived from the skew wind theory. Finally, the critical wind speeds from the measured flutter derivative A2• curves are also compared with those from the A2•curves estimated by the empirical formulae. © 2002 Elsevier Science Ltd. All rights reserved.

The finite-element-based framework for buffeting analysis of long-span cable-supported bridges under skew winds has been presented in Part 1 of this paper. The framework is now applied to the Tsing Ma Suspension Bridge in Hong Kong as a case study. The wind velocities and bridge responses measured by the Wind and Structural Health Monitoring System (WASHMS) of the bridge during Typhoon Sam in 1999 are first analyzed to find the skew wind characteristics surrounding the bridge, the modal damping ratios and acceleration responses of the bridge. The buffeting responses of the bridge under skew winds during Typhoon Sam are then computed using the wind characteristics and modal damping ratios measured from the field and the aerodynamic coefficients and flutter derivatives of the bridge deck and tower measured from the wind tunnel under skew winds. The computed acceleration responses of the bridge deck and cable are finally compared with the responses measured from the field. The comparison is found to be satisfactory in general and the case study forms a good practical demonstration for the verification of the proposed method for buffeting analysis of long-span cable-supported bridges under skew winds.

In the modal analysis of cable-stayed bridges using the finite element approach, the single-girder model or the double-girder model is often adopted for modeling the bridge deck. These two models are simple and easy to embody in commercial software packages, but the warping stiffness (constant) of bridge deck cannot be properly taken into consideration. This paper thus presents a triple-girder model consisting of one central girder and two side girders symmetrically connected to each other by transverse links. The proposed triple-girder model can easily consider the warping stiffness and other section properties of the bridge deck, and at the same time keep the user-friendly features in the single-girder model. The Nanpu cable-stayed bridge, built recently in China, is then taken as a case study to verify the rationality of the proposed triple-girder model through a comparison with measured data. The study shows that the modal properties of the cable-stayed bridge obtained from the modal analysis using the triple-girder model are more reasonable and close to the measured data. Further studies of four more cable-stayed bridges in China highlight that the extent of the warping effect depends greatly on the type of bridge deck and on the type of bridge tower–cable system. A simple approach for estimating some section properties of typical open-section decks is also suggested to further facilitate the use of the triple-girder model. © 2000 Elsevier Science Ltd. All rights reserved.

This paper aims to measure six static aerodynamic coefficients, while a companion paper addresses the measurement of eight flutter derivatives, of a typical oblique strip of the Tsing Ma suspension bridge deck under skew winds. The wind tunnel test technique developed for the aerodynamic coefficient measurement includes the design of oblique sectional models, the development of a test rig and a measurement system, and the analysis of test results. The effects of model end angle on the aerodynamic coefficients are investigated and found to be very small on lift, drag and pitching moment coefficients. The measured results are then fitted to obtain the six aerodynamic coefficient curves as functions of both wind inclination and yaw angle, which will be used in a later comparison of buffeting response of the bridge between field measurement and analysis. The measurement results reveal that the drag, lift and pitching moment coefficients are much larger than the crosswind force, rolling moment and yawing moment coefficients. The variation of lift coefficient with wind yaw angle is small, but the value of drag coefficient decreases with increasing wind yaw angle and the value of pitching moment coefficient increases with increasing wind yaw angle. The obtained six aerodynamic coefficient curves are also used to examine the currently used cosine rule for buffeting analysis of a bridge under yaw winds. It is found that the traditional cosine rule is generally inadequate, particularly in the cases of large wind yaw angle.

提出了用一个人工低风速的紊流场作为主要环境随机振动源的环境随机振动试验方法，并用该试验方法和随机振动信号频域分析方法对南京长江三桥全桥气弹模型进行了模态识别。经与有限元计算结果比较后可知,所识别的全桥气弹模型固有频率和振型结果令人满意。

介绍了所编制的实桥环境随机振动测试数据处理及固有模态识别程序EDPFDM。该程序以频域法为基础，可对经实桥分组环境随机振动测试而得的大量数据进行快速自谱、互谱及相位差和凝聚性分析，从而识别出桥梁的固有模态及对应的结构阻尼比的估计范围。以香港汲水门大桥固有模态环境随机振动测试为实例，结合用MSC- NASTRAN通用程序的模态分析结果，证明了程序EDPFDM的效率和可靠性。

汲水门大桥是一座主跨430米、双塔平行双索面、公铁两用双层斜拉桥，横跨香港马湾岛和大屿山岛之间的汲水门水道。在通车之前对该桥进行了实桥环境随机振动试验研究，以获得对桥梁抗震、抗风、健康监测、故障诊断等非常重要的结构固有模态(包括固有频率、振型及对应的阻尼比)。对主梁上的11个测站(33个测点)和两桥塔上的4个测站(16个测点)分4组进行了环境随机振动信息的记录，并利用自编的模态识别程序EDPFDM对所记录的信号进行了处理。在0～6Hz范围内共识别出主梁竖向弯曲振动为主的模态10阶，主梁横向弯曲振动为主的模态4阶，主梁扭转振动为主的模态6阶。经比较，固有频率和振型的试验结果与MSC-NAS-TRAN程序的分析结果十分接近。

节段模型风洞试验是研究涡激共振风速锁定范围和最大振动幅值的一种重要手段。基于一个具有自激特性的经验线性涡激力模型，从涡激共振微分方程出发，推导了涡激共振试验节段模型质量系统模拟公式，并建立了相应的模型与实桥之间涡激共振幅值的换算关系，给出了涡激共振幅值的振型修正系数和阻尼修正系数公式。由此，通过合理的质量系统模拟和响应幅值换算，可在二维的涡激共振节段模型试验中考虑实桥的结构和振动的三维特性的影响。

扁平箱形截面桥梁的颤振临界风速与风偏角的关系明显地受到风攻角的影响。在0°风攻角情况下，扁平箱形截面流线性好，其颤振性能与平板接近,颤振临界风速随风偏角的增加而增加，用传统的平均风分解方法可以获得较好的结果；而对于非0°风攻角的情况，扁平箱形截面的流线性变差，随着风偏角的增加其颤振临界风速呈起伏变化，最低值一般在斜风的情况下出现，此时，传统的平均风分解方法不再适用。