Time domain vs. frequency domain characterization of aeroelastic forces for bridge deck sections

The characterization of unsteady transverse wind forces of bridge sections under oscillatory motion is commonly addressed in the frequency domain by means of the so-called flutter derivatives. Thin airfoil theory suggests that for streamlined bodies a time domain treatment is equivalent; in this case small-amplitude motions are assumed and superposition of effects can still be accepted. This observation led researchers to postulate the extension of this methodology to bridge sections, based on the analytical transformation of aeroelastic derivatives into time-dependent functions, to be used in step-by-step finite-element or equivalent simulations. In this paper the procedure for obtaining these functions from data in the frequency domain is reviewed, fully extended to the complete set of derivatives and applied both to streamlined and bluff deck sections. The validity of this approach has been only partially investigated in the past; assessment for bridge deck sections and its convenience with respect to frequency domain analyses are discussed, and applied to relative to a range of typical examples.     

Time domain formulation of self-excited forces on bridge deck for wind tunnel experiment

Time domain formulation of the self-excited wind forces on bridge decks employs indicial functions. In bridge aeroelasticity, these functions are obtained by transforming the flutter derivative model to time domain. Studies have suggested, however, that the relative amplitude effect, i.e. the effect of structural oscillation amplitude relative to the amplitude of response to ambient wind, on flutter derivatives needs to be considered. This effect indicates the difference between the two cases, where the pulse response of an elastically supported body is smooth and where the motion is significantly affected by ambient wind forces. The non-linearity may affect the transformation of flutter derivative model to time domain. An alternative to obtaining the time domain formulation for the self-excited force is to treat the self-excited force as a separate dynamic system, so that the relative amplitude effect can be evaluated in more detail. In this paper, a self-excited force generation system coupled with the rigid bridge deck system is proposed to overcome the difficulties in the measurement and derivation of the time domain representation of self-excited force on bridge decks. This expression can be linked to a flutter derivative model, and a transform relationship between the two models is suggested.     

A methodology for the experimental extraction of indicial functions for streamlined and bluff deck sections

This paper addresses the experimental derivation of step-response non-stationary forces in the time domain (indicial functions), to be used in iterative numerical simulations (convolution techniques) for flutter instability analyses of suspension bridges, as an alternative to aeroelastic derivatives evaluated in the frequency domain. In particular a system, conceived for the direct extraction of these coefficients, has been designed, built and tested in wind tunnel. The study has investigated the experimental procedure of measurement and the statistical analysis of the recorded data. Both airfoil-type models (NACA) and a bluff section, simulating the behavior of bridge section, have been considered.     

桥梁气动导纳识别的阶跃函数拟合法

基于桥梁主梁断面气动导数、阶跃函数与气动导纳之间的关系,提出一种获取气动导纳的阶跃函数拟合法。首先根据紊流风场中的抖振响应,识别桥梁结构气动导数和等效气动导纳,然后由气动导数可拟合得到阶跃函数,并根据阶跃函数系数计算得到竖向脉动风对应的气动导纳,最后结合等效气动导纳计算水平向脉动风对应的气动导纳。阶跃函数拟合法直接根据抖振响应完成了桥梁断面完整气动导纳的识别,实例研究表明,该方法对于桥梁断面气动导纳识别而言是可行的。     

On the vortex shedding forcing on suspension bridge deck

Vortex-induced vibrations are not negligible while evaluating the aerodynamic and aeroelastic behavior of a long-span suspension bridge. This kind of forcing, that can produce high vibration levels, occurs at very low reduced velocities concerning low wind speed and high-frequency modes. This work presents results of experimental tests performed on the multibox deck shape of the Messina Strait bridge investigating vortex shedding phenomena and developing a numerical model to reproduce the vortex shedding forcing. The experimental tests, focused on low reduced velocities, highlight the typical non-linear pattern of the vortex shedding.     

Effect of relative amplitude on bridge deck flutter

Self-excited wind forces on a bridge deck can be non-linear even when the vibration amplitude of the body is small. This phenomenon is evaluated in this paper. Experiments detecting the nonlinearity are performed first, with the concept of “relative amplitude”, i.e. the amplitude of the externally triggered free vibration relative to the envelope of the ambient response of an elastically supported rigid sectional model. Two types of sectional model, a twin-deck bluff model (model A) and a partially streamlined box girder model (model B) are tested with two extreme cases of relative amplitude. Based on the flutter derivatives of model B, a flutter boundary prediction is subsequently carried out on a cable-supported bridge to manifest the changes of critical flutter wind velocity due to different relative amplitudes. The effect of relative amplitude on flutter derivatives and on the flutter boundary reveals, from the structural point of view, a complex relationship between the self-excited forces and the “structural vibration noise” due to turbulence that is inherent in the interaction of the ambient wind with the structure. Although the aeroelastic forces are linear when the body motion due to an external trigger is not affected significantly by this turbulence, they are postulated to be nonlinear when this “vibration noise” cannot be neglected.     

Modal analysis of suspension bridge deck units in erection stage

A long suspension bridge located in a typhoon region may be exposed to a high risk of wind-induced large vibrations during the construction stage because of its long construction period. The dynamic properties of the bridge in different construction stages therefore have to be well understood in bridge design, so that a proper wind tunnel test or further dynamic response analysis can be performed. To this end, this paper presents a detailed finite element modeling and modal analysis of the Tsing Ma long suspension bridge when the first few deck units are erected at the bridge midspan. The three-dimensional finite element model includes not only the deck units but also the main cables to which the deck units are suspended through hangers, the bridge towers, and the side span cables. The results from the numerical analysis show a clear picture of how dynamic properties are transformed from the tower-cable system to the tower-cable-deck unit system. The results indicate that wind-induced vibration of a cable suspension bridge during the construction stage may be more critical than that of the completed bridge. The predicted natural frequencies and mode shapes of the tower-cable-deck unit system are also compared with the measured results, and the comparison is satisfactory.     

Forced motion and free motion aeroelastic tests on a new concept dynamometric section model of the Messina suspension bridge

The work presents a new original experimental rig to more deeply investigate the aerodynamic behaviour of long span suspension bridges. Set-up and model are designed to grant an accurate study on main aeroelastic phenomena in bridge engineering. More in details, experimental set-up and a 1:60 scale sectional model of Messina bridge deck are presented. The complete rig—composed by dynamometric model, suspension set, experimental set-up and active turbulence generator—is designed in order to execute both forced and free motion tests, allowing to change the average position in terms of angle of attack and yaw angle and to investigate flutter derivatives, admittance functions and vortex-induced vibrations.     

Weighting ensemble least-square method for flutter derivatives of bridge decks

In this paper, a reliable but simple identification method, here called the weighting ensemble least-square method (WELS), has been developed to extract all eight flutter derivatives of bridge deck from free vibration records. For every wind speed, free vibration test of section model is generally repeated several times in order to obtain more reliable parameter estimates. In the WELS method, many free vibration records at the same wind speed are regarded as an ensemble. The common mode parameters are then identified simultaneously from the ensemble data. The parameter fit is obtained by a nonlinear least-square method. Weighting factors are proposed to make each experiment record with the same weight in total residual error analysis. The ensemble composed of many records can reduce the effect of the colored noise of few records on the convergence of least-square iteration process. The flutter derivatives of two section models are identified to indicate the reliability and effectiveness of the WELS method.     

Identification of flutter derivatives of bridge decks with free vibration technique

The flutter derivatives of bridge decks can be determined in a unique manner on condition that the complex modal parameters of the system at one reduced frequency are obtained. Based on the idea, a new method of identifying the flutter derivatives of bridge decks is proposed and it can overcome some shortcoming of the existing method and extend the applicability of the free vibration technique at high wind velocity. The identified results have agreements with the target ones of an ideal thin-plate section and those of a thin-plate section measured by the forced vibration technique. The proposed method is reliable and effective to extract the flutter derivatives from coupled free vibration.     

Structural behavior of strengthened bridge deck specimens under fatigue loading

The deterioration of concrete bridge decks that have been directly damaged by traffic loads affects their durability, safety, and function. It is therefore necessary to strengthen the damaged concrete structures. Even though there have been many experiments performed to investigate the static behavior of strengthened structures, few experiments or analyses have considered their fatigue behavior.

In this study, fatigue tests were conducted on bridge decks strengthened using various fiber-reinforced polymer plastics, such as carbon fiber sheet, glass fiber sheet, and grid-type carbon fiber reinforced plastic. All of the strengthened specimens were shown to have an improved resistance to crack propagation and better stress distributions. The Weibull distribution was adopted to analyze the fatigue life of the decks. The fatigue life limits of the strengthened bridge decks were determined at higher stress levels, and the grid-type carbon reinforced plastic specimens proved to be the most effective.     

钢桥面铺装局部修复方案试验研究

钢桥面铺装的修复技术是钢桥面铺装技术研究的重要组成部分,其复杂性在一定意义上远大于新建大跨径钢箱梁桥的桥面铺装研究。江阴大桥为主跨1385m的钢箱梁悬索桥,钢桥面采用47 mm浇注式沥青混凝土铺装,通车三年多后钢桥面出现大面积破坏。对江阴大桥钢桥面铺装出现的破坏类型以及钢箱梁构造等特点进行研究,在室内试验研究如弯曲试验、拉拔试验、车辙试验、复合梁疲劳试验的基础上,提出了5.0 cm、5.5 cm、6.0 cm不同厚度的双层环氧沥青混合料与“浇注式沥青混合料 环氧沥青混合料”4种结构方案,并利用江阴大桥钢桥面铺装大修的机会,选取代表性梁段作了试验段。研究表明双层环氧沥青混合料性能优于其他方案,此研究为我国钢桥面铺装局部修复方案的确定以及成功实施提供基础依据。     

大跨斜拉桥索力监测研究——以乌江二桥为例

大跨斜拉桥拉索索力状态是衡量桥梁是否处于正常运营状态的一个重要标志。本文首先对斜拉桥拉索索力监测的方法和原理进行了阐述;然后,结合乌江二桥对监测系统、索力监测的设计做了介绍;最后对乌江二桥索力监测的结果进行了分析,从而对拉索索力的状态进行了评估,为斜拉桥桥梁状态的评估提供了依据。     

Data-driven stochastic subspace identification of flutter derivatives of bridge decks

Most of the previous studies on flutter derivatives have used deterministic system identification techniques, in which the buffeting forces and the associated responses are considered as noises. In this paper, one of the most advanced stochastic system identification, the data-driven stochastic subspace identification technique (SSI-DATA) was proposed to extract the flutter derivatives of bridge decks from the buffeting test results. An advantage of the stochastic method is that it considers the buffeting forces and the responses as inputs rather than as noises. Numerical simulations and wind tunnel tests of a streamlined thin plate model conducted under a smooth flow by the free decay and the buffeting tests were used to validate the applicability of the SSI-DATA method. The results were compared with those from the widely used covariance-driven SSI method. Wind tunnel tests of a two-edge girder blunt type of Industrial-Ring-Road Bridge deck (IRR) were then conducted under both smooth and turbulent flows. The identified flutter derivatives of the thin plate model based on the SSI-DATA technique agree well with those obtained theoretically. The results from the thin plate and the IRR Bridge deck helped validate the reliability and applicability of the SSI-DATA technique to various experimental methods and wind flow conditions. The results for the two-edge girder blunt type section show that applying the SSI-DATA yields better results than those of the SSI-COV. The results also indicate that turbulence tends to delay the onset of flutter compared with the smooth flow case.     

桥面抛丸处理技术在临连高速公路中的应用

结合工程实例,研究了桥面抛丸处理技术的工作原理、抛丸设备的技术参数以及抛丸处理的关键控制参数,并叙述了其具体施工过程及安全、环保注意事项,通过采用抛丸处理工艺,提高了桥面铺装的耐久性。     

Estimation of torsional-flutter probability in flexible bridges considering randomness in flutter derivatives

Torsional-flutter instability is an aeroelastic phenomenon of interest to the bridge engineer, corresponding to a torsionally unstable vibration regime of the deck driven by wind excitation and appearing beyond a certain critical wind velocity. In this study a method for the derivation of the flutter probability for long-span bridges with bluff decks is proposed.In the first part of this study the deterministic problem is addressed. In contrast with the classical solution method in the frequency domain based on a numerical procedure for assessing the critical wind velocity, a single-mode “closed-form” algorithm for the derivation of the critical velocity was investigated. A polynomial representation of the aeroelastic-loading coefficients (flutter derivatives), necessary for torsional-flutter analysis, was utilized.In the second part an algorithm for estimating the torsional-flutter probability was developed, considering randomness in bridge properties, and flutter derivatives in particular due to their preeminent role in torsional-flutter velocity estimation.Experimental errors in the extraction of flutter derivatives from wind tunnel tests were analyzed. The “closed-form” algorithm, developed in the first part, allowed for a direct numerical solution of the flutter probability in a simple way.The torsional-flutter probability for three simulated bridge models with rectangular closed-box and truss-type girder deck was numerically determined. A set of experimental data, available from the literature, was employed. The simulations enabled the validation of the proposed algorithm.     

Response of a continuous, skewed, steel bridge during deck placement

An investigation was conducted to study environmental, material and deck placement effects on the behavior of a continuous, skewed, High Performance Steel (HPS), integral abutment bridge during construction using field data and three-dimensional finite element models. The finite element models were calibrated against girder strain measurements recorded during deck placement. During calibration, the effects of temperature changes during deck placement were clearly evident and were shown to have a significant effect on the accuracy of the finite element results. Effects from hardening of the concrete deck as the pour progressed were shown to be less evident. A calibrated model was used to compare stress variations and deflections of the two outer girders when concrete was placed (1) perpendicular to the girders and (2) parallel to the skew. The influence of various parameters on numerical model results was postulated and a deck placement method was recommended.     

Fatigue behavior and statistical evaluation of the stress category for a steel-concrete composite bridge deck

The maintenance cost of bridges is rapidly increasing since many existing bridges are deteriorating or reaching their design life all over the world. Moreover, as many long-span bridges are under construction and planning in Korea, research and development on bridge decks with high load-resistance capacity as well as high fatigue strength has become a growing concern. This research gives experimental results of the fatigue behavior of a new-type of steel-concrete composite bridge deck being developed under such circumstances. The proposed composite bridge deck consists of corrugated steel plate, welded steel ribs, stud shear connectors, and reinforced concrete filler. Fatigue tests were conducted under a four-point bending test with four different stress ranges in constant amplitude. In order to determine the influence of the concrete filling, fatigue tests on partial steel specimens containing only plain corrugated steel plates were performed in advance. The partial steel specimens and the steel-concrete composite deck specimens both showed fatigue failure in the tension part concerning the fillet welding part between the corrugated steel plate and steel rib. Finally, the stress category of the fillet welding part of each specimen is evaluated based on a statistical approach of Albrecht’s probability model. The research concludes that the fatigue behavior of such steel-concrete composite decks under sagging moment can be estimated based on the classical S-N approach, focusing on steel components.     

水泥密封防水剂在桥面防水中的应用

阐述了对桥面采取防水措施的必要性，结合盐城经济开发区开发大桥工程实例，介绍了SJM-1500水泥密封防水剂在桥梁防水中的应用技术。