Buffeting Response Of Long-span Bridges Research Articles

Full long-term buffeting analysis of suspension bridges using Gaussian process surrogate modelling and importance sampling Monte Carlo simulations

Recent findings from full-scale measurements campaigns and analytical investigations of the design buffeting response of long-span bridges suggest that the assumptions adopted in most wind-resistant design guidelines are not strictly conservative. In such cases, a full long-term analysis is the most accurate alternative for reliability-based design. However, the application of such methodology becomes unfeasible due to the corresponding computational demand. Notably, many evaluations of the buffeting response are required, and time-consuming numerical integration is traditionally used to evaluate the long-term response. To overcome these drawbacks, this paper proposes a framework to increase the computational efficacy of long-term analyses for the wind-resistant design of long-span bridges by combining two strategies. First, the buffeting response is estimated with a Gaussian process regression that requires less time than the traditional multimodal buffeting response estimation. Then, long-term analysis is carried out using importance sampling Monte Carlo simulations that converge faster than the traditional analysis based on numerical integration. The computational framework is demonstrated in a case study of a proposed super-long suspension bridge subjected to loads induced by wind buffeting. The advantage of the proposed framework is verified, as it requires less than 1% of the computational demand of the traditional full long-term analysis.

Investigations of the long-term extreme buffeting response of long-span bridges using importance sampling Monte Carlo simulations

Several studies have shown that site measurements of the buffeting responses of long-span bridges do not always agree with predictions from analytical models. The observed discrepancy is believed to be explained by the variability in the wind’s turbulence field, which is ignored in the current design guidelines. Additionally, the guidelines neglect the true variability in the buffeting response, as this parameter is considered to be deterministically dependent on the mean wind speed only, and a single short-term-averaged wind condition is assumed to be representative of the bridge’s behaviour over its lifetime. Such assumptions underestimate the design buffeting response. Alternatively, a full long-term analysis is regarded as the most accurate approach to handling extreme response estimations. Applications of this analysis in the wind engineering literature are scarce due to its large computational demand. With the objective of alleviating such demand, this paper proposes a full long-term analysis framework based on importance sampling Monte Carlo (ISMC) simulations and investigates, for the first time, the extreme buffeting response of a suspension bridge in its design phase with this framework. The results were compared with available formulations based on reliability methods and numerical integration. The proposed ISMC framework requires fewer simulations than the other formulations while maintaining a good degree of accuracy. The results show that the estimated extreme response is 30% larger than the current design guidelines suggest, showing the importance of considering the turbulence parameters' and loading effects' variabilities when calculating extreme responses.

Buffeting Response Prediction of Long-Span Bridges Based on Different Wind Tunnel Test Techniques

The traditional method for calculating the buffeting response of long-span bridges follows the strip assumption, and is carried out by identifying aerodynamic parameters through sectional model force or pressure measurement wind tunnel tests. However, there has been no report on predicting the buffeting response based on the sectional model vibration test. In recent years, the author has proposed a method, based on the integrated transfer function, for predicting the buffeting response of long-span bridges through theoretical and full-bridge tests. This provided an idea for predicting the buffeting response based on the sectional model vibration test. Unfortunately, the effectiveness and accuracy of this method have not been proven or demonstrated through effective tests. To solve this problem, a long-span suspension bridge was taken as a background. Parameters such as aerodynamic admittance were identified through a sectional model force measurement test and the integrated transfer functions were identified through a sectional model vibration test. A taut strip model test was also conducted. Furthermore, the buffeting response prediction results based on three kinds of wind tunnel test techniques were compared. The results showed that if the strip assumption was established, the results of the three methods aligned well, and that selecting a reasonable model aspect ratio for the test could effectively reduce the influence of the 3D effect; moreover, identifying the integrated transfer function by the sectional model vibration test could effectively predict the long-span bridge buffeting response. Furthermore, when the strip assumption failed, the results of the traditional calculation method using 3D aerodynamic admittance became smaller. A larger result would be obtained by neglecting the influence of aerodynamic admittance.

Nonuniform wind characteristics and buffeting response of a composite cable-stayed bridge in a trumpet-shaped mountain pass

Due to the spatial differences in wind fields in mountainous areas, it is an urgent problem to accurately estimate the buffeting response of long-span bridges in mountainous areas. In this paper, the spanwise variations in the mean and fluctuating wind characteristics of a bridge site are obtained based on a terrain wind tunnel test of a trumpet-shaped mountain pass. Additionally, the aerodynamic admittance function of a Π-shaped composite girder under different wind attack angles is measured in the wind tunnel. The buffeting response calculation theory considering the spanwise variations in the mean wind and fluctuating wind characteristics along the main girder is established. The influence of the nonuniform wind characteristics on the buffeting response of the main girder is analyzed. The results show that the spanwise variation in wind characteristics at the bridge site is affected by the direction of inflow and can be described by a quadratic polynomial. Nonuniform wind parameters have obvious effects on the buffeting response, and a nonuniform wind attack angle is a key factor affecting the buffeting response. It may not be appropriate to predict the buffeting response by using the single-point wind field observation results in mountainous areas.

Generalized framework for identification of indicial response functions from flutter derivatives of long-span bridges

The hypothesis that the Wagner and Kussner functions, conventionally used in the thin-airfoil aerodynamics, can also be used in the bridge aerodynamics, is often suggested in the literature. However, this assumption may lead to an inaccurate prediction of the buffeting response of bridges with increasing spans, which calls into question the validity of this assumption. This paper presents a generalized framework for the identification of bridge-related aerodynamic and aeroelastic indicial response functions (IndRFs) to simulate the buffeting response of long-span bridges under turbulent winds. For that, the direct relationships between IndRFs and experimental data of flutter derivatives are developed with the help of the Fourier transform, followed by the extraction of IndRFs through an optimization technique. Compared with the conventional Wagner and Kussner functions, the identified IndRFs exhibit the overshooting behavior, which can change the bridge aerodynamics significantly. To check the efficacy of the proposed framework, the numerical example of a suspension bridge is presented, and buffeting analysis is performed for two cases considering ① the identified aeroelastic and aerodynamic IndRFs, and ② the Wagner and Kussner functions. The simulation results are also compared with the field measurements, showing that the identified IndRFs are adequately reliable and unique functions for a bridge deck to simulate its buffeting response accurately.

Development of nonlinear framework for simulation of Typhoon-induced buffeting response of Long-span bridges using Volterra series

This paper presents a nonlinear time-domain analysis framework to simulate the buffeting response of long-span bridges subjected to the typhoon winds. The analysis framework separates the aerodynamic forces generated on the bridge deck into low- and high-frequency components modelled by the quasi-steady and Volterra series-based wind load models, respectively. The aerodynamic nonlinearity and non-stationary wind effects existing in the wind-bridge interaction are incorporated in the analysis framework in terms of the ① static force coefficients measured at low-frequency effective angle of attack, ② flutter derivatives identified at varying angles of attack, ③ higher order fluid memory terms of the Volterra series and ④ time-varying mean wind speed. The efficacy of the proposed framework is verified by presenting the numerical example of a suspension bridge fully immersed in the typhoon winds with aerodynamic characteristics sensitive to the effective angle of attack. The dynamic analysis results show good agreement in the simulation of the typhoon-induced buffeting response of the bridge deck. Moreover, the simulation results are also compared with the measurements, and the existing linear and nonlinear wind load models to elucidate the efficiency of the proposed framework.

Numerical simulation of buffeting response of long-span bridges in time-domain using Volterra based wind load model

Numerical simulation of buffeting response of long-span bridges in time-domain using Volterra based wind load model

Integrated transfer function for buffeting response evaluation of long-span bridges

An experimental approach to the prediction of the buffeting response of long-span bridges is presented, and the concept of the integrated transfer function, which directly relates the fluctuation characteristics of turbulent flow to the buffeting response of bridge structures, is introduced in this paper. The integrated transfer function is independent of the characteristics of turbulent flow, so once the integrated transfer function is identified in wind tunnel experiments, it can be directly used to calculate the buffeting response of the actual bridge in the atmospheric boundary layer. To verify the presented approach, a long-span suspension bridge is taken as an example and a series of experiments are carried out in a wind tunnel. Experiments in two different flow fields at the design wind velocity are performed to investigate the effects of turbulent flow characteristics on the integrated transfer functions, and the results measured at another wind velocity are given for comparison. The results show that the integrated transfer functions of the bridge measured in the two flow fields are almost identical, which confirms that it is independent of the flow field. An application example is also performed to evaluate the buffeting response with the use of the measured integrated transfer functions. Compared to the traditional approach, the presented experimental approach based on the integrated transfer function avoids errors caused by the inaccurate simulation of the turbulent flow (such as the integral scales, wind spectra and wind spatial correlations) and provides a more accurate prediction of the buffeting response of long-span bridges.

Tropical Storm–Induced Buffeting Response of Long-Span Bridges: Enhanced Nonstationary Buffeting Force Model

AbstractAn enhanced nonstationary buffeting force model for calculating tropical storm (i.e., typhoon/hurricane)–induced buffeting response of long-span bridges is presented. The evolutionary power...

Analysis of Multimode Coupled Buffeting Response of Long-Span Bridges to Nonstationary Winds with Force Parameters from Stationary Wind

AbstractThis paper presents a general frequency domain framework for predicting multimode coupled buffeting response of long-span bridges to nonstationary winds. Within this framework, the wind speed field, aerodynamic forces, and bridge response are separated into deterministic time-varying mean and evolutionary random fluctuating components. Under the assumption of low variation rate of mean wind speed, the time-varying mean and self-excited and buffeting forces are modeled in static force coefficients, flutter derivatives, and admittance functions, determined in a wind tunnel under stationary wind, but with consideration of nonstationary wind characteristics in a quasi-steady manner. The time-varying mean bridge response is calculated through static analysis at each time instant. The random buffeting response is expressed in generalized modal displacements governed by the equations of a frequency-dependent linear time-variant (LTV) system. An equivalent frequency-independent LTV system is introduced, w...

Extreme value of typhoon-induced non-stationary buffeting response of long-span bridges

This paper concerns the extreme value of typhoon-induced non-stationary buffeting response of long-span bridges. The framework of non-stationary buffeting analysis is briefly introduced first, in which the non-stationary buffeting response is regarded as the summation of a time-varying mean response and a dynamic response that can be represented by a zero-mean evolutionary Gaussian process characterized by an evolutionary power spectral density (EPSD) function. The formulas for determining approximate probabilistic characteristics of extreme non-stationary responses are then derived by extending the currently-used Poisson and Vanmarcke approximations. By comparing with the Monte Carlo solution, the extended approximations for extreme value of non-stationary responses are found reliable and accurate enough. Particularly, the extended Vanmarcke approximation can give closer results to the Monte Carlo solution than the extended Poisson approximation. The extended Vanmarcke approximation is finally applied to the Stonecutters Bridge to find the extreme value of non-stationary buffeting response of the bridge to a strong typhoon. The results show that the extreme displacement responses of the bridge from the non-stationary buffeting analysis are larger than those predicted by the conventional stationary buffeting analysis, and therefore the non-stationary buffeting analysis is necessary.

Typhoon-induced non-stationary buffeting response of long-span bridges in complex terrain

This paper presents a framework for predicting typhoon-induced non-stationary buffeting response of long-span cable-supported bridges located in a complex terrain. First, a non-stationary typhoon wind model is proposed based on observations from measured typhoon wind data. The wind model includes mainly time-varying mean wind speed, mean wind speed profile and evolutionary power spectral density (EPSD) function. Typhoon-induced wind loading on a bridge deck is then represented by time-varying mean wind forces, non-stationary buffeting forces associated with time-dependent aerodynamic coefficients and self-excited forces characterized by time-dependent aerodynamic derivatives. A nonlinear static analysis is performed to determine time-varying mean wind response, whereas the pseudo excitation method is employed to compute the EPSD-expressed non-stationary buffeting response of a long-span cable-supported bridge. The proposed framework is finally applied to predict non-stationary buffeting responses of a long-span cable-stayed bridge located in a complex terrain during a strong typhoon as a case study. The case study demonstrates how to apply the proposed framework and the results show that the proposed framework is feasible and necessary.

New estimation methodology of six complex aerodynamic admittance functions

This paper describes a new method for the estimation of six complex aerodynamic admittance functions. The aerodynamic admittance functions relate buffeting forces to the incoming wind turbulent components, of which the estimation accuracy affects the prediction accuracy of the buffeting response of long-span bridges. There should be two aerodynamic admittance functions corresponding to the longitudinal and vertical turbulent components, respectively, for each gust buffeting force. Therefore, there are six aerodynamic admittance functions in all for the three buffeting forces. Sears function is a complex theoretical expression for the aerodynamic admittance function for a thin airfoil. Similarly, the aerodynamic admittance functions for a bridge deck should also be complex functions. This paper presents a separated frequency-by-frequency method for estimating the six complex aerodynamic admittance functions. A new experimental methodology using an active turbulence generator is developed to measure simultaneously all the six complex aerodynamic admittance functions. Wind tunnel tests of a thin plate model and a streamlined bridge section model are conducted in turbulent flow. The six complex aerodynamic admittance functions, determined by the developed methodology are compared with the Sears functions and Davenport`s formula.

Influence of uncertainty in selected aerodynamic and structural parameters on the buffeting response of long-span bridges

Multimode-analysis methods for the study and derivation of flutter instability and buffeting response are readily available from the literature and have been successfully applied to the assessment of the susceptibility of long-span bridges to wind loading. In both cases flutter critical velocity and buffeting oscillation are usually estimated from deterministic analyses. However, the probabilistic nature of the problem is latent since uncertainties, especially those associated with the definition of wind and aerodynamic characteristics, are intrinsically present. These quantities include, for example, wind-turbulence power spectral density, static coefficients and aerodynamic derivatives, usually derived from either site observations or experimental analysis. Their effects are often neglected or usually addressed through sensitivity analyses only. While in the past uncertainty in flutter estimates has been analyzed by researchers (for example through reliability analysis), little attention has been devoted to buffeting. In this paper the effects associated with the random nature of wind and structural characteristics are analyzed through the derivation of a closed-form solution associated with the single-mode buffeting problem with selected random parameters. A specific example is provided to clarify the role of wind power spectral density, damping and selected aeroelastic derivatives.

Coupled buffeting response analysis of long-span bridges by the CQC approach

Based on the modal coordinates of the structure, a finite-element and CQC (complete quadratic combination) method for analyzing the coupled buffeting response of long-span bridges is presented. The formulation of nodal equivalent aerodynamic buffeting forces is derived based on a reasonable assumption. The power spectral density and variance of nodal displacements and elemental internal forces of the bridge structure are computed using the finite-element method and the random vibration theory. The method presented is very efficient and can consider the arbitrary spectrum and spatial coherence of natural winds and the multimode and intermode effects on the buffeting responses of bridge structures. A coupled buffeting analysis of the Jiangyin Yangtse River Suspension Bridge with 1385 in main span is performed as an example. The results analyzed show that the multimode and intermode effects on the buffeting response of the bridge deck are quite remarkable.

A tuned mass damper for suppressing the coupled flexural and torsional buffeting response of long-span bridges

The purpose of this paper is to present a tuned mass damper which simultaneously reduces the vertical and torsional buffeting responses of long-span bridges. The proposed damper has two frequencies, which are tuned to the frequencies of the first flexural and torsional structural modes, to suppress the resonant effects. The aerodynamic coupling is taken into account for the formulation of the bridge-damper system, and this model is thus applicable to those bridges with significant mode coupling. The buffeting response reduction and the increase of the critical velocity are investigated through a parametric analysis. Based on this parametric study, the design procedures of the tuned mass damper for the wind-excited bridges are proposed. The results show that the proposed tuned mass damper is at least as effective as the usual tuned mass damper for suppressing buffeting response; furthermore it appreciably increases the stability of the bridge with either a single-degree-of-freedom flutter or a coupled flutter.

Aerodynamic Coupling Effects on Flutter and Buffeting of Bridges

The effects of aerodynamic coupling among modes of vibration on the flutter and buffeting response of long-span bridges are investigated. By introducing the unsteady, self-excited aerodynamic forces in terms of rational function approximations, the equations of motion in generalized modal coordinates are transformed into a frequency-independent state-space format. The frequencies, damping ratios, and complex mode shapes at a prescribed wind velocity, and the critical flutter conditions, are identified by solving a complex eigenvalue problem. A significant feature of this approach is that an iterative solution for determining the flutter conditions is not necessary, because the equations of motion are independent of frequency. The energy increase in each flutter motion cycle is examined using the work done by the generalized aerodynamic forces or by the self-excited forces along the bridge axis. Accordingly, their contribution to the aerodynamic damping can be clearly identified. The multimode flutter generation mechanism and the roles of flutter derivatives are investigated. Finally, the coupling effects on the buffeting response due to self-excited forces are also discussed.

Flutter and Buffeting Analysis. I: Finite-Element and RPE Solution

A finite-element formulation is developed for analyzing flutter instability and buffeting response of long-span bridges and their interaction. The flutter derivatives, instead of the indicial functions used by previous researchers, are applied in the random parametric excitation (RPE) analysis. This application makes finite-element formulation possible and results in much less computational effort in RPE analysis than those of previous analyses. With the finite-element program developed in the present study, as many modes as desired can be easily included in the flutter and buffeting analyses. Users have the choice of RPE or eigenvalue method for flutter analysis and RPE or spectral method for buffeting analysis.

Optimization of TMD for suppressing buffeting response of long-span bridges

A mathematical model is developed for optimizing the parameters of TMD (tuned mass damper) used for suppressing buffeting response of long-span bridges. The parameters of the TMD with which Nanpu Cable-Stayed Bridge under construction in Shanghai, China, is suggested to be equipped are calculated by using the computer program made by the authors based on the method.