Response of circular bridge decks to moving vehicles

This paper discusses the dynamic response of a curved bridge deck to a moving vehicle. The bridge deck is idealized as a set of annular sector plates and circular rings rigidly jointed together. On the basis of classical plate and ring theories a method has been developed to obtain the response to a moving vehicle idealized as a spring mass system. After obtaining the normal modes and frequencies and establishing the orthogonality conditions, the problem of the forced motion of the deck is solved by the method of spectral representation. Numerical results have been presented to illustrate the effect of several vehicle and bridge parameters on the response.     

Soil–structure interaction in resonant railway bridges

This paper explores dynamic soil–bridge interaction in high speed railway lines. The analysis was conducted using a general and fully three-dimensional multi-body finite element–boundary element model formulated in the time domain to predict vibrations caused by trains passing over the bridge. The vehicle was modelled as a multi-body system, the track and the bridge were modelled using finite elements and the soil was considered as a half-space by the boundary element method. The dynamic response of bridges to vehicle passage is usually studied using moving force and moving mass models. However, the multi-body system allows to consider the quasi-static and dynamic excitation mechanisms. Soil–structure interaction was taken into account by coupling finite elements and boundary elements. The paper presents the results obtained for a simply supported short span bridge in a resonant regime under different soil stiffness conditions.     

考虑约束扭转的斜拉桥车激横向振动分析

利用有限单元法,基于力学原理和几何协调条件,导出了非对称箱型截面梁单元的弯扭耦合刚度矩阵,建立了斜拉桥在车辆荷载作用下的横向动力分析模型。由于考虑了箱梁的约束扭转,该模型能够分析复线或多线铁路桥在偏载作用下的横向振动问题。以桥梁轨道随机不平顺作为激振源,进行了机车过桥的实例分析。计算结果表明,桥梁的车激横向动力响应随车速及轨道不平顺样本的不同而变化,并随桥跨的增加而快速变得显著,车辆偏载对箱梁扭转振动有显著影响,所建立的力学模型是斜拉桥车桥耦合振动分析的实用模型。     

防撞梁在超高车辆撞击铁路桥梁中的防撞性能研究

作为交通运输工程中不可或缺的一部分,铁路桥梁在生命线及基础设施系统中发挥着重要的作用,一旦被超高车辆撞击,将会造成难以估计的生命及财产损失。提出4个不同配置（横梁、支撑）防撞梁,作为一种缓冲机制安装于桥梁可能发生撞击的主梁底部区域,并通过1:5缩尺模型对防撞梁的防撞性能及工作原理进行研究,并提出基于数值模拟的简化分析方法,实验结果表明:4个防撞梁对于降低桥梁在冲击荷载下的动力响应均有很好效果,能够有效降低桥梁结构在冲击荷载下的动力响应,塑性变形折减至50%,变形能力较好的防撞梁防撞性能更好,此外,基于数值模拟的简化分析方法是有效的。     

AN ITERATIVE SOLUTION METHOD FOR DYNAMIC RESPONSE OF BRIDGE–VEHICLES SYSTEMS

An iterative solution method is presented and illustrated to analyse the dynamic response of bridge–vehicle systems. The method consists in dividing the whole system into 2 subsystems at the interface of the bridge and vehicles; these 2 subsystems are solved separately; their compatibility at the interface is achieved by an iterative procedure with under-relaxation or with Aitken acceleration. The characteristics of this method are explained on a simplified system with 2 degrees of freedom (DOF). The numerical results for a simple example demonstrate the high performances of the proposed method: good convergence rate and high accuracy. Finally, the method is applied to a practical example: the linear dynamic response of the Yangtze-River Bridge at Wuhan under a moving train with 2 locomotives and 4 freight cars. The efficiency is attained because neither formation nor factorisation of the coefficient matrices for the equations of the system are needed at every time step in linear analysis. The Aitken acceleration technique is more efficient in systems with multi-degrees of freedom than the relaxation technique. The proposed method will be even more efficient in non-linear dynamic response because, in this case, the iterations are necessary whether the system is solved as a whole or not.     

Bridge dynamic loading due to road surface irregularities and braking of vehicle

Single span highway bridges of composite construction are idealized as beams as well as orthotropic plates. A standard HS–20–44 highway vehicle is represented by a planar, two-axle, sprung mass system with frictional device. The response equations are derived in terms of the natural modal co-ordinates of the bridge and of displacement co-ordinates of the vehicle. The road surface irregularities, generally found at the junctions of the approach road and bridge ends, are idealized as a 45° ramp. The maximum impact factors for bending moment and deflection are obtained due to the ramp and in combination with the braking of vehicle for symmetric as well as essentric loading of the vehicle.     

基于运营环境和提升小波变换的桥梁损伤检测研究

根据损伤桥梁在车辆荷载作用下的动力响应特点,以及提升小波变换对信号突变信息的放大功能,提出了利用桥梁运营荷载作用下加速度响应提升小波变换系数的分布特性对结构损伤进行识别的方法。首先,采集桥梁在行车荷载作用下的加速度响应信号;然后,对加速度响应信号进行提升小波变换,分别利用加速度响应信号、加速度响应信号差,提升小波变换系数空间变化的峰值识别损伤位置;最后,对行车速度、损伤位置、损伤程度和测量噪声对损伤识别效果的影响进行了分析讨论。结果表明：在行车速度8m/s以下、测量噪声不高于5%情况下,利用运营荷载作用下桥梁单点动力响应信号提升小波变换,可以实现桥梁多处损伤的检测和识别。     

Spatially coupled vibrations of a suspension bridge under random highway traffic

The problem of spatial dynamic response of a suspension bridge to the passage of trains of concentrated forces with random values is considered. The arrival of forces at the bridge is assumed to constitute a Poisson process of events. Such an excitation process is an appropriate model of vehicular traffic loads acting on the bridge. The bridge is idealized by a single-span thin-walled beam underslung to two cables. The response of the bridge in the space-time domain is described by a coupled system of non-linear, integro-differential equations. The dynamic influence functions of vertical and horizontal deflections at each cross-section point are obtained for the linear case. Cumulants and probability density functions of response are determined. Numerical methods have been used to develop a computer-oriented algorithm aimed at the numerical solution of the problem. As examples, numerical results for a particular bridge with some practical load cases are presented and illustrated by graphs.     

地震作用下储罐与管道连接波纹管的动力响应

针对储罐与管道连接这个抗震薄弱环节进行研究，考虑了储罐与地基、管道与地基的相互弹性作用及流固耦合作用，使计算模型比较符合工程实际情况。将储罐罐壁看作为刚体，将波纹管部分和管道部分分别用旋转锥壳单元和空间梁单元离散化，通过分析得到波纹管与储罐连接接合面、波纹管与管道连接接合面不同单元之间的位移协调约束方程，并用罚函数法进行处理。根据流体力学速度势理论和有限元法的基本理论，利用哈密尔顿变分原理推导出储罐与管道连接波纹管系统动力分析方程，编制了系统动力分析有限元程序，计算了垂直地震激励不同场地土地基条件下储罐与管道连接波纹管位移响应。     

Bridge response with tractor-trailer vehicle loading

A method for the calculation of dynamic response and loading of single span multigirder bridges due to vehicle loads is described. The analysis takes account of vehicle acceleration or braking, road surface roughness and eccentric placement of the vehicle on the bridge. The analysis is presented for a three-axle tractor-trailer vehicle and the bridge is modelled as an orthotropic plate using higher order finite strips. As an example application, the loadings produced with braking of the three-axle vehicle and a nominally equivalent two-axle vehicle on a bridge were computed. Previous theoretical studies of bridge loading with vehicle braking had employed a two-axle idealization of a three-axle vehicle. The results of the present study show that this approximation is not valid for braking studies as the behaviour of the two vehicle models is significantly different. The loadings produced by a three-axle vehicle are generally less severe than those due to an ‘equivalent’ two-axle vehicle.     

Dynamic performance analysis of a seismically isolated bridge under braking force

In order to study the dynamic performance of seismically isolated bridges under the most unfavorable loads in the longitudinal direction,a dynamic equation for vehicle braking in the longitudinal direction is established.A four or fiveorder Runge-Kutta method is adopted to obtain the time-history response of a wheel set under braking force.The quadratic discretization method is then used to transform this time-history into a braking and bending force time-history of a structural fixed node,and a dynamic response analysis of the seismically isolated bridge under the vehicle’s braking force is carried out using ANSYS,a universal finite element analysis software.According to the results,seismic isolation design results in a more rational distribution of braking force among piers;the influence of the initial braking velocity on the vehicle braking force is negligible;the location where the first wheel set leaves the bridge is the most unfavorable parking location;a seismic isolation bridge bearing constructed according to typical design methods enters into a yield stage under the braking force, while the shearing force at the bottom of the pier declines as the isolation period is extended;the design requirements can be met when the yield displacement of the seismic isolation bearing is less than 5 mm and the yield strength is greater than the braking force.     

A simplified fragility analysis of fan type cable stayed bridges

A simplified fragility analysis of fan type cable stayed bridges using Probabilistic Risk Analysis (PRA) procedure is presented for determining their failure probability under random ground motion. Seismic input to the bridge support is considered to be a risk consistent response spectrum which is obtained from a separate analysis. For the response analysis, the bridge deck is modeled as a beam supported on springs at different points. The stiffnesses of the springs are determined by a separate 2D static analysis of cable-tower-deck system. The analysis provides a coupled stiffness matrix for the spring system. A continuum method of analysis using dynamic stiffness is used to determine the dynamic properties of the bridges .The response of the bridge deck is obtained by the response spectrum method of analysis as applied to multidegree of freedom system which duly takes into account the quasi - static component of bridge deck vibration. The fragility analysis includes uncertainties arising due to the variation in ground motion, material property, modeling, method of analysis, ductility factor and damage concentration effect. Probability of failure of the bridge deck is determined by the First Order Second Moment (FOSM) method of reliability. A three span double plane symmetrical fan type cable stayed bridge of total span 689 m, is used as an illustrative example. The fragility curves for the bridge deck failure are obtained under a number of parametric variations. Some of the important conclusions of the study indicate that (i) not only vertical component but also the horizontal component of ground motion has considerable effect on the probability of failure; (ii) ground motion with no time lag between support excitations provides a smaller probability of failure as compared to ground motion with very large time lag between support excitation; and (iii) probability of failure may considerably increase for soft soil condition.     

Dynamic response of circular bridge decks

A method has been developed for the study of the dynamic response of curved bridge decks on the basis of plate equations in polar co-ordinates. A general solution for the forced motion of annular sector plates has been obtained by the method of spectral representation. The specific problem of a moving force on the bridge deck is discussed in detail. A method for obtaining the static response from dynamic analysis is suggested. Numerical results are presented to illustrate the influence of the speed of travel of the force and of the physical parameters of the bridge decks on the deformation. A detailed discussion on the numerical results is also included.     

Dynamic response of single-span beam bridges to a series of moving loads

The paper makes a contribution to the problem of a stream of loads crossing a single-span beam bridge. There are considered the basic load models, in the form of a stream of fixed amplitude forces, unsprung masses and viscoelastic oscillators. The matrix equations of motion of the system are formulated and discussed. The problem of dynamic stability and steady-state response of a bridge carrying a periodic stream of inertial loads is formulated and solved. The paper also includes a vibration study of a beam bridge subjected to a uniform stream of moving loads, of a limited or unlimited number of load cycles.     

Effect of train dynamics on seismic response of steel monorail bridges under moderate ground motion

This study is intended to investigate the seismic response of steel monorail bridges using three‐dimensional dynamic response analysis. We particularly consider monorail bridge–train interaction when subjected to ground motion that occurs with high probability. A monorail train car with two bogies with pneumatic tires for running, steering and stabilizing wheels is assumed to be represented sufficiently by a discrete rigid multi‐body system with 15 degrees of freedom (DOFs). Bridges are considered as an assemblage of beam elements with 6 DOFs at each node. Modal analysis is used for dynamic response analysis under moderate earthquakes. The seismic response of an advanced monorail bridge that adopts a simplified structural system and composite girders is investigated through comparison with seismic responses of a conventional bridge. The acceleration response of a monorail train is also calculated to investigate the effect of structural types of bridges on the train's dynamic response during earthquakes. Results show that the seismic responses of the advanced bridges are greater than those of the conventional monorail bridge because of the simplified structural system and increased girder weight that is attributable to composite girders of the advanced bridge. Moreover, the train on the advanced bridge shows greater dynamic response than that on the conventional bridge. Observations reveal that the dynamic monorail train system acts as a damper on the monorail bridge. That fact shows that the existing design, which considers a train as additional mass, yields a conservative result. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic response analysis of road vehicle-bridge system for continuous rigid frame bridges with high piers

The objective of this study is to investigate the effects of earthquakes on road vehicle-bridge coupling vibration systems. A two-axle highway freight vehicle is treated as a 13 degree-of-freedom system composed of several rigid bodies, which are connected by a series of springs and dampers. The framework of the earthquake-vehicle-bridge dynamic analysis system is then established using an earthquake as the external excitation. The equivalent lateral contact force serves as the judgment criteria for sideslip accidents according to reliability theory. The entire process of the vehicle crossing the bridge is considered for a very high pier continuous rigid frame bridge. The response characteristics of the vehicle and the bridge are discussed in terms of various parameters such as earthquake ground motion, PGA value of the earthquake, incident angle, pier height, vehicle speed and mass. It is found that seismic excitation is the most influential factor in the responses of the vehicle-bridge system and that the safety of vehicles crossing the bridge is seriously impacted by the dual excitations of earthquake and bridge vibration.     

澳门澳凼第三大桥斜拉桥地震反应分析

结合一座澳门澳凼第三大桥斜拉桥的工程设计实例,采用大型有限元分析程序ANSYS,选取空间BEAM188、BEAM4及SHELL63单元建立动力计算模型,对比研究了主塔墩底在假定固结和考虑桩土共同工作这两种边界约束处理方式下的动力特性;并选取三条地震波在桥的纵、横向分别进行桥梁地震作用下的时程分析,给出了主梁和中塔的内力、位移及时程响应。     

A study of railway bridge/vehicle interaction and evaluation of fatigue life

A new vehicle model and the partial bridge model were used to study the dynamic interaction between an open deck steel truss bridge and a moving freight train. The responses in terms of dynamic stresses in certain critical members in the bridge were generated to predict their fatigue lives by using a reliability-based methodology.     

双向地震作用下互通式斜交桥梁地震响应及碰撞效应分析

斜交桥梁由于其不规则的结构形式使其受力规律与规则桥梁相比具有特殊性和复杂性,在地震作用下梁体的平动与转动存在弯扭耦合效应,导致结构动力响应分析复杂。针对斜交桥梁的结构特点,建立包含桩土相互作用的三维有限元模型,在考虑水平双向地震作用下,采用反应谱法及时程分析法对京包高速公路某互通式斜交桥梁进行地震反应分析。结果表明:互通式简支斜交桥梁的地震响应受地震动输入方向的影响较大,在考虑碰撞效应后,碰撞涉及结构部位的地震位移显著增加,地震内力也出现较大差异,即说明在斜交桥梁抗震设计时有必要适当考虑地震动输入方向和梁端与墩台及相邻梁端的碰撞效应。     

强震区非对称连续梁桥地震响应及性能评价

为研究高烈度地区不等跨连续梁桥的抗震性能，依托某高速公路上一座主跨为（40+60+35）m的典型不等跨连续梁桥，建立其动力分析有限元模型，获得该桥的模态特性。在E1概率和E2概率两种地震水平作用下，同时采用反应谱分析和时程分析法，对不等跨桥梁结构的地震响应进行分析。最后根据桥墩验算截面的弯矩-曲率关系曲线，探讨该桥梁的抗震性能。研究结果表明：动态时程反应分析与反应谱分析所得的结果基本吻合，由于反应谱分析假定结构线弹性状态而时程反应分析考虑了材料的弹塑性，在E2概率水平下，两者个别响应值有较大差别；由于反应谱法是对各阶模态下最大响应的组合，动态时程反应分析是同一时刻各地震波引起的结构响应的组合，因而时域和频域计算结果会存在一些误差，频域结果偏于保守；E1、E2概率地震作用下，主桥桥墩检算截面仍然在弹性范围内工作，满足弹性设计要求。