Simplified prediction of wind-induced response and stability limit of slender long-span suspension bridges, based on modified quasi-steady theory: A case study

The Hardanger Bridge is currently under construction in Norway. It will have a main span of 1310 m and a girder that is only 18.3 m wide, which implies that wind-induced vibration is a major concern in the design. Buffeting response and flutter analysis of the Hardanger Bridge are treated in this paper. The self-excited forces are modelled using aerodynamic derivatives obtained from free vibration tests, quasi-steady theory, and a suggested modified quasi-steady theory. The stability limit predicted using aerodynamic derivatives corresponded well with the wind tunnel results, while the quasi-steady theory severely underestimated the critical mean wind velocity for the section model used in the wind tunnel tests. A new set of modified quasi-steady coefficients are suggested, where the experimental results of the aerodynamic derivatives are used to obtain frequency-independent model coefficients. The critical velocities predicted by the modified quasi-steady coefficients differ only by 4-5% from estimates based on the aerodynamic derivatives. The response predicted by the suggested simplified aerodynamic model is also presented, and the results indicate that adequate estimates are achieved.     

Relationships among aerodynamic admittance functions, flutter derivatives and static coefficients for long-span bridges

Wind actions on long-span bridges are commonly considered as the superimposition of buffeting forces and self-excited forces, depending on the aerodynamic admittance functions and on the flutter derivatives, respectively. Since bridge deck sections are bluff bodies, the aerodynamic admittance functions and the flutter derivatives have to be determined experimentally by wind tunnel tests. This paper introduces a generalized quasi-static theory, defining new relationships among the flutter derivatives and the aerodynamic admittance functions. All the relationships are theoretically verified for the zero circular frequency; based upon experimental results, the validation of the relationships among the flutter derivatives is also provided for non-zero values of the frequency.     

Fatigue analysis of long-span suspension bridges under multiple loading: Case study

Long-span suspension bridges are often subject to multiple types of dynamic loads, especially those located in wind-prone regions and carrying both trains and road vehicles. Fatigue assessment shall be performed to ensure the safety and functionality of the bridges. This paper proposes a framework for fatigue analysis of a long-span suspension bridge under multiple loading by integrating computer simulation with structural health monitoring system. By taking the Tsing Ma Bridge in Hong Kong as an example, a computationally efficient engineering approach is first proposed for dynamic stress analysis of the bridge under railway, highway and wind loading. The fatigue-critical locations are then determined for key bridge components, and databases of the dynamic stress responses at the critical locations are established. The time histories of dynamic stresses induced by individual loading during the design life of the bridge are generated based on the databases. The corresponding stress time histories due to the combined action of multiple loading are also compiled. Finally, fatigue analysis is performed to compute the cumulative fatigue damage over the design life of 120 years. The results indicate that it is necessary to consider the combined effect of multiple loading in the fatigue analysis of long-span suspension bridges.     

Reliability analysis of long span steel arch bridges against wind-induced stability failure

An efficient method for reliability assessment of long span steel arch bridges against wind-induced stability failure is presented in this paper. The prediction of wind-induced stability of such bridge structures is performed by an eigenvalue method and the reliability estimates are determined by a generalized first-order reliability algorithm. A software strategy for interfacing the present method with ANSYS is developed via a freely available MATLAB software tool (FERUM). A numerical example involving a detailed computational model of a long span steel arch bridge with a main span of 550 m is presented to demonstrate the applicability and merits of the present method and the software strategy. Finally, the most influential random variables on the reliability of long span steel bridges against wind-induced stability failure are identified by a sensitivity analysis.     

Aerodynamic investigations for the tender design concepts of the Øresund cable-stayed bridge

For the Øresund link project two alternative tender designs were proposed, one single-level box girder solution and a double-level truss girder solution. Aerodynamic investigations, comprising wind tunnel section model tests as well as full-scale predictions, were carried out for the cable-stayed part of the two design alternatives. The section model tests covered static and dynamic tests for various configurations of bridge deck equipment, aiming at the detection of possible instabilities or vortex shedding effects and recording of the buffeting response. Cross-sectional admittance functions and aerodynamic derivatives have been estimated, and employed for full-scale predictions of dynamic displacements at a chosen value of the characteristic mean wind speed.     

Flutter reliability analysis of suspension bridges

A reliability analysis method is proposed in this paper through a combination of the advantages of the response surface method (RSM), finite element method (FEM), first-order reliability method (FORM) and the importance sampling updating method. The method is especially applicable for the reliability evaluation of complex structures of which the limit state surfaces are not known explicitly. After the accuracy and efficiency of the method are demonstrated through numerical examples, the method is used to estimate the flutter reliability of a suspension bridge. The uncertainties such as material properties, geometric parameters, structural damping ratio, flutter derivatives and extreme wind velocity at the bridge site are considered. The example suspension bridge is the Jiang Yin Bridge with a main span length of 1385 m built in China. The results show that the proposed method based on an empirical formula in which the limit state function is explicitly represented as a function of variables overestimates the flutter reliability of suspension bridges. The actual flutter reliability should be more accurately analyzed using the proposed method based on the deterministic finite element method in which the limit state function is implicitly represented as a function of variables. Finally, the most influential random variables on flutter reliability of suspension bridges are identified by using a sensitivity analysis.     

Stability analysis of wind-induced torsional motion of slender bridges

The paper presents a numerical, simulation-based approach to investigate the stability of torsional motion of slender suspension bridges under stochastic wind turbulence. The torsional bridge motion is represented by a linear, single degree of freedom oscillator. Stochastic turbulence in wind velocity is considered in the form of a periodic excitation with random phase modulation. The stability condition refers to the asymptotic sample stability, for which the necessary and sufficient condition is that the largest Lyapunov exponent be negative. Monte Carlo simulation is performed to evaluate the largest Lyapunov exponent, and stochastic differential equations of motion are integrated in polar coordinates using Euler's scheme. Unlike earlier analytical approximations, a quadratic noise term is retained in the present analysis. The turbulence intensity is shown to have a small stabilizing effect on the bridge stability in a sense that an increase in the turbulence intensity moderately increases the critical mean wind velocity beyond the deterministic flutter velocity. The stabilization effect is limited to the case of narrowband detuned excitation. In the proximity of the parametric resonance frequency, an increase in the bandwidth of the excitation process tends to stabilize the bridge motion.     

Fatigue life estimation of steel girder of Yangpu cable-stayed Bridge due to buffeting

As the main span of modern cable-stayed bridges becomes longer and longer, the buffeting-induced fatigue damage problem of steel girders located in strong wind regions may have to be taken into consideration in the design of the bridge. This paper presents a method in the mixed frequency–time domain for estimating the fatigue life of steel girders of the Yangpu cable-stayed Bridge due to buffeting. In the suggested method, the joint probability density function of wind speed and wind direction at the deck level of the bridge is first established. The power spectra of the critical stress of the girder are then derived from the power spectra of the generalized coordinates of the bridge for different wind speeds and wind directions. The derived stress spectra are no longer a narrow spectrum when the background component of stress response is included. Thus, the time histories of the critical stress are simulated from their power spectra and the stress cycle distributions are estimated in terms of rainflow count method. The formulae derived based on the modified Miner law and the random vibration theory are finally used for estimating the fatigue life of the bridge girder. The results show that the effects of wind direction on the fatigue life of the Yangpu Bridge are significant. The predicted fatigue life due to buffeting is much longer than the design life of the bridge.     

Performance of steel bridges during the 1995 Hyogoken–Nanbu (Kobe, Japan) earthquake-a North American perspective

A large number of steel bridges were damaged by the January 17, 1995, Hyogoken-Nanbu (Kobe, Japan) earthquake. This damage is particularly relevant to Eastern North America where considerably more steel bridges exist than in Western North America where bridges exposed to past earthquakes were mostly of reinforced concrete. Therefore, in light of the Kobe earthquake, a comparison of the steel design practice and design requirements in Japan and North America is instructive. In this paper, such a comparison is first presented, followed by a review of the observed damage to steel bridges and a review of the causes for this damage. Then, the relevance of these observations to North American bridge design practice is examined.     

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.     

结构健康监测和可靠性评估

对美国最大跨度桁架桥中的主要桁架构件以及整个结构系统的可靠性进行评估。根据构件和系统的可靠性指标,可以采用随机方法评估大跨桥的安全水平。然而,大多数旧的大跨桥是基于允许应力设计的,其可靠性不可能被保证。本研究的可靠性分析基于对恒荷载、活荷载和风载分布的评估。通过收集大量的输入和响应数据,对大桥进行长期结构健康监测。根据外部荷载影响的模式和大小,长期监测数据清楚揭示了不同结构的性能。案例显示,采用传统的分析方法难以确定由于温度引起的结构响应。为探讨温度对结构的影响以及在可靠性评估中考虑长期监测数据的作用,也对温度引起的响应进行分析。研究显示：温度导致的响应对整个系统的可靠性具有明显的影响。     

Database-assisted design methodology to predict wind-induced structural behavior of a light-framed wood building

This study investigates the applicability of the database-assisted design (DAD) methodology to predict structural reactions in a light-framed wood structure subjected to fluctuating wind pressures. Structural influence functions were determined on a 1/3-scale light-frame wood structure, which was then subjected to a wind flow, while the surface pressures and structural reactions at roof-to-wall and wall-to-foundation connections were simultaneously recorded. There was a good agreement between the DAD-predicted structural reactions and experimentally measured reactions, confirming that the DAD method is suitable for predicting the structural reactions in light-frame wood buildings. Subsequently structural reaction time histories at several connections within the building were generated using a 1:50 scale wind tunnel model of the structure and the peak structural reactions determined using the DAD method and previously obtained influence functions. When the DAD-estimated reactions were compared with reactions predicted by the ASCE 7-05 main wind force resisting system (MWFRS) method, they showed the ASCE 7 reactions were highly non-conservative(i.e. smaller than the DAD method predictions), by as much as 39% at the gable end truss. The components and cladding method showed reasonable agreement with the DAD method for the gable end and first interior truss reactions but it too underestimated the reaction loads at the second and third interior trusses by 30% and 12% respectively.     

Back calculation and model calibration for earthquake damaged bridges - a general procedure and its application to a highway viaduct

Seismic back calculation in structural engineering consists in the interpretation and reproduction of observed earthquake-induced damage patterns of structures. This article provides an overview of the methods used to this end in bridge engineering and presents a procedure for the back calculation. The methodological aspects, regarding investigations and modelling steps, are presented by a set of flowcharts. The procedure is applied on an existing Italian viaduct damaged during the L’Aquila 2009 earthquake. The damage state observed has been reproduced by an acceptable degree of precision indicating that the method can be a suitable tool for engineers facing this kind of problems.     

Pedestrian wind comfort around a large football stadium in an urban environment: CFD simulation, validation and application of the new Dutch wind nuisance standard

Three-dimensional steady Reynolds-averaged Navier–Stokes (RANS) Computational Fluid Dynamics (CFD) simulations are used in combination with the new Dutch wind nuisance standard to assess pedestrian wind comfort around a large football stadium in Amsterdam, before and after the addition of new high-rise buildings. The focus of the study is on the elevated circulation deck and the surrounding streets and squares. CFD validation is performed by comparison of the simulated mean wind speed at the deck with full-scale measurements. The important effect of local ground roughness specification on the simulated wind speed values is indicated. Application of the Dutch wind nuisance standard shows that wind comfort at the elevated circulation deck is only slightly influenced by the new buildings. Wind comfort at the surrounding streets and squares however significantly deteriorates. Finally, the results obtained by the Dutch wind nuisance standard are compared to those obtained by a more simplified procedure for the transformation of wind statistics to the building site, as used in earlier studies. The more sophisticated transformation procedure in the Dutch standard was successfully validated based on full-scale measurements in earlier research. Comparison of the Dutch standard results in this study with those of the simplified procedure shows that the latter provides overestimations by up to 25% for the highest discomfort probabilities. This type of large discrepancies can significantly change the outcome of wind comfort studies.     

On interference between two circular cylinders in staggered arrangement at high subcritical Reynolds numbers

The results of a wind-tunnel investigation on the interference between two identical parallel circular cylinders arranged in staggered configurations, carried out in a uniform smooth flow at high subcritical Reynolds number, are presented. On the basis of the pressure measurements and the flow visualization, three main flow patterns are classified and discussed. Close attention is paid to the switching phenomenon of two different pressure patterns at critical angles. This switching creates discontinuity of large lift forces on cylinders. With measurements of velocity profiles and power spectral analysis in the gap between the two cylinders, the mechanism of the appearance of this extreme aerodynamic force is discussed.     

Effects of soil‐structure interaction and lateral design load pattern on performance‐based plastic design of steel moment resisting frames

The effects soil‐structure interaction (SSI) and lateral design load‐pattern are investigated on the seismic response of steel moment‐resisting frames (SMRFs) designed with a performance‐based plastic design (PBPD) method through a comprehensive analytical study on a series of 4‐, 8‐, 12‐, 14‐, and 16‐story models. The cone model is adopted to simulate SSI effects. A set of 20 strong earthquake records are used to examine the effects of different design parameters including fundamental period, design load‐pattern, target ductility, and base flexibility. It is shown that the lateral design load pattern can considerably affect the inelastic strength demands of SSI systems. The best design load patterns are then identified for the selected frames. Although SSI effects are usually ignored in the design of conventional structures, the results indicate that SSI can considerably influence the seismic performance of SMRFs. By increasing the base flexibility, the ductility demand in lower story levels decreases and the maximum demand shifts to the higher stories. The strength reduction factor of SMRFs also reduces by increasing the SSI effects, which implies the fixed‐base assumption may lead to underestimated designs for SSI systems. To address this issue, new ductility‐dependent strength reduction factors are proposed for multistory SMRFs with flexible base conditions.     

既有高陡挡墙下深基坑开挖支护设计与分析

通过对高度为62 m的既有高陡肋板式锚杆挡墙墙脚开挖15 m的基坑支护设计作为实例，对超限高边坡的特殊性及其在支护设计中存在的问题进行了分析，在此基础之上采用建筑边坡工程技术规范（GB50330-2002）、数值模拟、工程类比法相结合的方法对支护结构进行了优化设计和效果评价。监测结果表明，本工程支护设计经济有效地保护了既有高陡挡墙及其顶部大型公共建筑的安全，对其它类似工程具有较强的参考意义。     

某引水工程大口径管材应用的关键技术探析

本文介绍大口径预应力钢筒混凝土管（PCCP）在长距离输水管线中的应用,以及工程设计时,对管材的选择、管材结构设计标准的选择、配件设计、管道软土地基的沉降分析及处理、止推设计及沟槽支护的做法等的研究和讨论,供类似工程参考。     

基于CFD及《绿色校园评价标准》优化景观要素格局——以“2013全国大学生绿色校园概念设计大赛”一等奖作品为例

随着对教学环境重要性认识的不断增强,校园室外环境的优化与建设改造问题已引起教育工作者和建筑设计人员的广泛关注.基于《绿色校园评价标准》并利用CFD动态模拟技术对实有校园——沈阳建筑大学进行考察,通过对其景观要素格局的优化设计,强调从各种景观要素的生态效应角度出发,推进校园绿色生态化发展的必要性和建设发展绿色校园的重要意义.     

Re-examination of the effect of a plane boundary on force and vortex shedding of a circular cylinder

The hydrodynamic forces and vortex shedding of a smooth circular cylinder immersed in different boundary layers were experimentally investigated at Reynolds numbers from 1.30×10⁴ to 1.45×10⁴. The effects of the bed proximity, the thickness of the boundary layer, and the velocity gradient in the boundary layer on the pressure distribution, the hydrodynamic forces and the vortex shedding behavior were examined. The experimental results show that both the drag and lift coefficients strongly depend on the gap ratio, and are affected by the boundary layer. A downward lift is observed at certain gap ratios in rod-generated boundary layers, and an explanation of this downward lift is given. Two different criteria for calculating the Strouhal number in the literature are discussed in this paper. It is found that the variation of the root-mean-square (RMS) lift coefficient reveals the onset or suppression of the vortex shedding. A quantitative method for identifying the vortex shedding suppression point is proposed. The observations show that the vortex shedding is suppressed at a gap ratio of about 0.2–0.3, depending on the thickness of the boundary layer. This critical gap ratio decreases as the thickness of the boundary layer increases.