Analysis Of Long-span Bridges Research Articles

Radial force analysis of long span bridge with trapezoidally corrugated steel webs

The study numerically and theoretically investigates the radial force effect of long span prestressed concrete (PC) box girders with trapezoidally corrugated steel webs (TCSWs). It reveals that under the influence of radial forces, the curved prestressing tendons in the bottom slab in long span box girder bridges with TCSWs exhibited higher levels of stress and deflection compared to conventional concrete box girder bridges due to the accordion effect of the TCSWs. Furthermore, this study simplifies the radial forces as concentrated forces of PC box girder with TCSWs. Based on this simplification, a formula is derived to accurately calculate the magnitude of these radial forces. Through parameter analysis of the power exponent in the equation defining the curve profile of the bottom slab, it was observed that lower power exponents result in more significant radial force effects. Finally, to eliminate the radial force effect, the study innovatively proposed an optimized structural scheme by adopting horizontal bottom slab at midspan and arranging horizontal diaphragms uniformly across the entire longitudinal span of the bridge. A contrastive study suggested that the horizontal arrangement of internal prestressing tendons in the bottom slab at midspan could effectively eliminate the negative impact of the radial force effects and greatly improve the overall bearing capacity of the box girders with TCSWs.

Joint distribution of wind speed and direction in the context of field measurement

The joint distribution of wind speed and wind direction at a bridge site is vital to the estimation of the basic wind speed, and hence to the wind-induced vibration analysis of long-span bridges. Instead of the conventional way relying on the weather stations, this study proposed an alternate approach to obtain the original records of wind speed and the corresponding directions based on field measurement supported by the Structural Health Monitoring System (SHMS). Specifically, SHMS of Sutong Cable-stayed Bridge (SCB) is utilized to study the basic wind speed with directional information. Four anemometers are installed in the SHMS of SCB: upstream and downstream of the main deck center, top of the north and south tower respectively. Using the recorded wind data from SHMS, the joint distribution of wind speed and direction is investigated based on statistical methods, and then the basic wind speeds in 10-year and 100-year recurrence intervals at these four key positions are calculated. Analytical results verify the reliability of the recorded wind data from SHMS, and indicate that the joint probability model for the extreme wind speed at SCB site fits well with the Weibull model. It is shown that the calculated basic wind speed is reduced by considering the influence of wind direction. Compared to the design basic wind speed in the Specification of China, basic wind speed considering the influence of direction or not is much smaller, indicating a high safety coefficient in the design of SCB. The results obtained in this study can provide not only references for further wind-resistance research of SCB, but also improve the understanding of the safety coefficient for wind-resistance design of other engineering structures in the similar area.

Numerical Analysis of Interaction of Single Pile and Soil Based on ADINA

The interaction between pile and soil can not be ignored in the seismic analysis of long-span bridges. Earthquake action in the form of lateral load apply on the pile through the soil, the analysis of pile under lateral load is very important in aseismatic analysis of bridge. Analysis of the horizontal load pile-soil interaction by using finite element analysis software ADINA, establishing the three-dimensional contact model of pile-soil interaction and the analysis model by using p-y curve model of soil-pile interaction respectively. Comparing the displacement of the top of pile with the actual measurements to verify the numerical method is right. It shows that the feasibility of using ADINA for pile-soil interaction analysis.

Prediction of bridge flutter under a crosswind flow

This paper presents a number of approximated analytical formulations for the flutter analysis of long-span bridges using the so-called uncoupled flutter derivatives. The formulae have been developed from the simplified framework of a bimodal coupled flutter problem. As a result, the proposed method represents an extension of Selberg\' s empirical formula to generic bridge sections, which may be prone to one of the aeroelastic instability such as coupled-mode or single-mode (either dominated by torsion or heaving mode) flutter. Two approximated expressions for the flutter derivatives are required so that only the experimental flutter derivatives of (H*2A*1) are measured to calculate the onset flutter. Based on asymptotic expansions of the flutter derivatives, a further simplified formula was derived to predict the critical wind speed of the cross section, which is prone to the coupled-mode flutter at large reduced wind speeds. The numerical results produced by the proposed formulas have been compared with results obtained by complex eigenvalue analysis and available approximated methods show that they seem to give satisfactory results for a wide range of study cases. Thus, these formulas can be used in the assessment of bridge flutter performance at the preliminary design stage.

Condition Assessment on Thermal Effects of a Suspension Bridge Based on SHM Oriented Model and Data

This paper aims to carry out the condition assessment on temperature distribution and thermal effects of a long span suspension bridge. The structural health monitoring (SHM) oriented data analysis is first performed and several indices are developed to process the time-varying temperature, displacement, and strain responses. An analytical procedure based on heat transfer theory is presented to determine the temperature distributions within the bridge. The fine finite element models of the deck plate, the cross frame, and the bridge tower are constructed for thermal analysis. A new approach to the thermal-structural coupling analysis of long span bridges is proposed to examine the structural thermal effects. The feasibility and validity of the proposed data process method and the new approach for thermal-structural coupling analysis are examined through detailed numerical simulation. The numerical results are compared with the field measurement data obtained from the long-term monitoring system of the bridge and they show a very good agreement, in terms of temperature distribution in different time and in different seasons. This exercise verifies the accuracy of the heat transfer analysis employed and the effectiveness and validity of the proposed approaches for data processing and thermal-structural coupling analysis.

Development of computational software for flutter reliability analysis of long span bridges

The flutter reliability analysis of long span bridges requires use of a software tool that predicts the uncertainty in a flutter response due to uncertainties in the model formulation and input parameters. Existing flutter analysis numerical codes are not capable of dealing with stochastic uncertainty in the analysis of long span bridges. The goal of the present work is to develop a software tool (FREASB) to enable designers to efficiently and accurately conduct flutter reliability analysis of long span bridges. The FREASB interfaces an open-source Matlab toolbox for structural reliability analysis (FERUM) with a typical deterministic flutter analysis code. The paper presents a brief introduction to the generalized first-order reliability method implemented in FREASB and key steps involved in coupling it with a typical deterministic flutter analysis code. A numerical example concerning flutter reliability analysis of a long span suspension bridge with a main span of 1385 m is presented to demonstrate the application and effectiveness of the methodology and the software.

Aeroelastic analysis of long span bridges via indicial functions considering geometric and material nonlinearity

A time domain approach for predicting the flutter response of long-span bridges was presented. The unsteady aerodynamic forces were presented by the indicial functions through a convolution integral, whereas the nonlinear least square method was used to calculate the aerodynamic indicial parameters. The nonlinear dynamic analysis which includes both the geometric and material nonlinearities due to the unsteady self excited aerodynamics force was considered. Numerical analyses were then performed using three dimensional finite element model of the suspension bridge. The results show that the geometric and material nonlinearities have a significant influence on the critical velocity and the response of long-span bridges.

Peak Factors for Bridges Subjected to Asynchronous Multiple Earthquake Support Excitations

지진에 대한 장대 교량의 정확한 반응 해석은 지진 방재에 있어서 중요한 역할을 한다. 본 논문은 비동기 다지지점 지진입력에 의한 교량의 반응을 진동수 영역방법과 시간 영역방법으로 해석하였으며 그 결과를 동기 입력 결과와 비교하였다. 시간영역방법에서는 선형모드 중첩 법으로 최대반응 값을 계산하였다. 진동수영역방법에서는 선형랜덤진동 이론을 사용하여 교량 성능에 영향을 미치는 모드와 다지지점 지진입력의 상호상관관계를 고려한 반응의 제곱평균근(RMS값)을 계산하였다. 교량 성능 반응 중, 변위 및 부재의 내력에 대한 시간 영역해석 결과와 진동수영역 해석 결과로부터 최대반응 값과 RMS값의 비로 정의된 최대반응 계수의 실용적인 값과 계산 방법을 요약하였다. 신뢰 있는 최대 반응계수가 있으면, 교량의 성능기반설계에서 구체적인 임의의 입력을 고려한 시간영역방법보다 결과의 일반성 및 수치적인 장점을 갖은 진동수영역방법이 더 효율적이다. Accurate response analysis of long span bridges subjected to seismic excitation is important for earthquake hazard mitigation. In this paper, the performance of a typical four span continuous reinforced concrete bridge model subjected to asynchronous multiple seismic excitations at the supports is investigated in both the time and frequency domains and the results are compared with that from a relevant uniform support excitations. In the time domain analysis, a linear modal superposition approach is used to compute the peak response values. In the frequency domain analysis, linear random vibration theory is used to determine the root mean square response values where the cross correlation effects between the modal and the support excitations on the seismic response of the bridge model are included. From the two sets of results, a practical range of peak factors which are defined to be the ratio of peak and the root mean square responses are suggested for displacements and forces in members. With reliable practical values of peak factors, the frequency domain analysis is preferred for the performance based design of bridges because of the computational advantage and the generality of the results as the time domain analysis only yields results for the specific excitation input.

Digital Simulation of Bridge Wind Fields Based on Wavelet Method

Digital simulation of stochastic wind velocity field is prerequisite to flutter or buffeting analysis of long-span bridges in time-domain. Wavelet method was applied to the simulation of the stochastic wind field, performing the effective simulation of spatial stochastic wind field. According to the idea of multi-resolution analysis and orthonormal wavelets, relationship between wavelet coefficients and PSD(power spectral density)function is deduced , then the wavelet coefficients on each and every scale are obtained from the given PSD function, the intermittency was introduced into wavelet coefficients while at the same time preserves the target spectral characters. As a result, the inverse wavelet transform is applied to generate stationary wind velocity history through the given wavelet coefficients. A numerical example to illustrate the application of the proposed method for the simulation of a bridge wind velocity field is provided.

Seismic Reliability of Long-Span Bridges Based on the First Order Reliability Method

In this paper, first order reliability method (FORM) is generalized to the seismic reliability analysis of long-span bridges and the first excursion probability of a single tower cable-stayed bridge is studied. The seismic motivation is firstly dispersed as a series of random variables. Then the cross velocities on the dispersed time points can be obtained by solving the motivation of the design checking points with FORM. The upper bound of first excursion probability is also obtained by integrating the cross velocities at different time. The results show that the seismic reliability analysis method based on the FORM is feasible and effective to solve the first excursion probability problem. The single tower cable-stayed bridge studied in this paper has a higher reliability under strong seismic.

Discussion on “Full-order and multimode flutter analysis using ANSYS” [Finite elements in analysis and design 44(9–10) (2008) 537–551

This discussion has pointed out that when doing the flutter analysis of long span bridge using ANSYS, enough data of the external file (flutter derivatives) should be given. Otherwise, the inaccuracy even the wrong result will be obtained.

Computational study on aerodynamics of long-span bridges

A numerical procedure for aerodynamic load analysis of long span bridges is presented. The preconditioned Reynolds averaged Navier-Stokes equations are adopted to compute flows over the bridges. To capture the turbulent characteristics of the flows, two equation turbulence models, Coakley’s q − ω model and Menter’s k − ω SST model, are used to compute the turbulent viscosity. A dual time stepping method in conjunction with the AF-ADI method is used to advance the solution in time. A loosely coupled method of the preconditioned RANS equations with the turbulence model equations is employed for fast computation without losing numerical stability. The numerical method for the aerodynamic load analysis is verified against well-known benchmark problems. Aerodynamic loads of two real bridges are computed with the method to demonstrate the usefulness of the method.

Nonstationary Response Analysis of Long Span Bridges under Spatially Varying Differential Support Motions Using Continuous Wavelet Transform

An input-output relation for the nonstationary response of long-span bridges subjected to random differential support motions is proposed in the present study. The proposed methodology is more general than the existing ones, in the sense that it can evaluate nonstationarity in both the intensity and frequency content of the response statistics for spatially correlated multipoint random excitations. Furthermore, because the input-output relation is established through the transfer functions of dynamic systems, the proposed wavelet-based methodology can easily be used to predict the stochastic response of any structural systems in conjunction with available finite-element software. The input-output formulation is also not restricted to a particular wavelet basis function, since it has been derived by following a general wavelet-based description of input nonstationary processes. The bridge has been modeled as a simply supported beam with multispans in a finite-element framework to obtain the dynamic propert...

Seismic spatial effects on dynamic response of long-span bridges in stationary inhomogeneous random fields

The seismic analysis of long-span bridges subjected to multiple ground excitations is an important problem. The conventional response spectrum method neglects the spatial effects of ground motion, and therefore may result in questionable conclusions. The random vibration approach has been regarded as more reliable. Unfortunately, so far, computational difficulties have not yet been satisfactorily resolved. In this paper, an accurate and efficient random vibration approach — pseudo excitation method (PEM), by which the above difficulties are overcome, is presented. It has been successfully used in the three dimensional seismic analysis of a number of long-span bridges with thousands of degrees of freedom and dozens of supports. The numerical results of a typical bridge show that the seismic spatial effects, particularly the wave passage effect, are sometimes quite important in evaluating the safety of long-span bridges.

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 state space method for coupled flutter analysis of long-span bridges

A state-space method is proposed to analyze the aerodynamically coupled flutter problems of long-span bridges based on the modal coordinates of structure. The theory about complex modes is applied in this paper. The general governing equation of the system is converted into a complex standard characteristic equation in a state space format, which contains only two variables. The proposed method is a single-parameter searching method about reduced velocity, and it need not choose the participating modes beforehand and has no requirement for the form of structure damping matrix. The information about variations of system characteristics with reduced velocity and wind velocity can be provided. The method is able to find automatically the lowest critical flutter velocity and give relative amplitudes, phases and energy ratios of the participating modes in the flutter motion. Moreover, the flutter analysis of Jiangyin Yangtse suspension bridge with 1385 m main span is performed. The proposed method has proved reliable in its methodology and efficient in its use.

Multimode coupled flutter and buffeting analysis of long span bridges

In this paper, the equations of structural motion are expressed in time-invariant state-space equations by expressing the frequency dependent self-excited forces in terms of rational functions. Accordingly, the multimode coupled flutter analysis is reduced to evaluate the eigenvalues of a constant matrix at each prescribed wind velocity. This formulation is computationally efficient in comparison with the conventional iterative approach. The complex mode approach is utilized for analyzing efficiently the coupled buffeting response. This approach is computationally more efficient than the conventional scheme in which a matrix inversion is required to evaluate the system transfer function at each frequency. A long span cable-stayed bridge and a suspension bridge are used to investigate the coupled flutter. The effect of the aerodynamic coupling among modes on the buffeting response is ascertained and compared to conventional mode-by-mode approach.

Prediction Method of Aerodynamic Admittance Functions using Flutter Derivatives

This paper describes the comparison between analysis and measurement of aerodynamic admittance functions for lift and moment. Sears' function which is a theoretical expression for the aerodynamic admittance for a thin airfoil is conventionally applied to the gust response analysis of long span bridges. Comparing to the experimental results of the aerodynamic admittance function for deck sections, the measured aerodynamic admittance functions are different from Sears' function and some experimental formulas have been suggested. However, these formulas are not sufficient to apply to various sections. Then we propose new prediction method of aerodynamic admittance functions for lift and moment utilizing flutter derivatives and these functions obtained by our method have been compared with the measured ones and verified to be accurate.

A practical engineering method for the flutter analysis of long span bridges

Abstract This paper presents a practical method for the determination of the onset of wind induced Flutter instabilities for long span bridges. The method is illustrated by presenting the results of analyses performed on suspension bridge structures subjected to aerodynamic loading. Finally, the paper presents and discusses the significance of the results obtained to date.

Buffeting analysis of long span bridges: a new algorithm

This paper presents a new algorithm for buffeting analysis of long span bridges, featured mainly by a complete finite element approach and a pseudo-excitation method. Aeroelastic forces on a bridge deck are first converted into nodal forces to form element aeroelastic damping and stiffness matrices. Aerodynamic forces are then converted into nodal forces to obtain an element loading vector. After the system equation of motion is assembled, the pseudo-excitation method is finally applied to determine the buffeting response, which naturally includes inter-mode and multi-mode contributions. The accuracy of the new algorithm is examined by comparison with the Scanlan's method through an example bridge deck. The potential advantages of the algorithm are also pointed out.