Modelling three‐dimensional non‐linear seismic performance of elevated bridges with emphasis on pounding of girders

Unseating of bridge girders/decks during earthquakes is very harmful to the safety and serviceability of bridges. Evidence from recent severe earthquakes indicates that in addition to damage along longitudinal direction, lateral displacement and rotation of bridge girders caused by pounding to adjacent girders can also lead to unseating. To simulate this effect, 3D modelling of the dynamic performance of whole bridge structures, including pounding, is needed strongly. This paper presents a 3D model that is practically suitable to precisely analyse pounding between bridge girders. Experiments have been conducted to verify the proposed pounding model. The 3D non‐linear modelling of steel elevated bridges is also discussed. A general‐purpose dynamic analysis program for bridges, namely dynamic analysis of bridge systems (DABS) has been developed. Seismic analyses on a chosen three‐span steel bridge are conducted for several cases including pounding as a case study. The applicability of the proposed pounding model is illustrated by the computations. The effects of poundings on the response of bridge girders are discussed and the computation results are given. Copyright © 2002 John Wiley & Sons, Ltd.     

双层板桁钢梁应力分析

以跨度最大的双层斜拉桥闵浦大桥为背景,研究了双层板桁钢梁桥面板的受力特性,阐述了精细壳单元与梁单元结合的整体有限元模型,并分析了上、下桥面间腹杆的受力特性与桥面板的应力分布特性;采用桥面纵横梁间带U肋精细桥面模型,分析了桥面板和U肋在车辆荷载作用下的应力分布。研究表明,上、下层桥面横桥向应力小于纵桥向应力,并且横桥向应力的不均匀性明显大于纵桥向;车轮荷载作用下,正交异性桥面板应力分析时,荷载位置对纵横向应力峰值的影响很小,并且横桥向应力起控制作用,峰值均出现在U肋与顶板交接处。     

Required separation distance between decks and at abutments of a bridge crossing a canyon site to avoid seismic pounding

Major earthquakes in the past indicated that pounding between bridge decks may result in significant structural damage or even girder unseating. With conventional expansion joints, it is impossible to completely avoid seismic pounding between bridge decks, because the gap size at expansion joints is usually not big enough in order to ensure smooth traffic flow. With a new development of modular expansion joint (MEJ), which allows a large joint movement and at the same time without impeding the smoothness of traffic flow, completely precluding pounding between adjacent bridge decks becomes possible. This paper investigates the minimum total gap that a MEJ must have to avoid pounding at the abutments and between bridge decks. The considered spatial ground excitations are modelled by a filtered Tajimi‐Kanai power spectral density function and an empirical coherency loss function. Site amplification effect is included by a transfer function derived from the one‐dimensional wave propagation theory. Stochastic response equations of the adjacent bridge decks are formulated. The effects of ground motion spatial variations, dynamic characteristics of the bridge and the depth and stiffness of local soil on the required separation distance are analysed. Soil–structure interaction effect is not included in this study. The bridge response behaviour is assumed to be linear elastic. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

近断层地震动对上承式拱桥动力响应的影响

为了揭示近断层地震作用下上承式钢筋混凝土拱桥的动力响应特点,以西南山区某上承式拱桥为背景,用OpenSEES平台建立了全桥非线性动力分析模型,探讨了近断层地震动的输入方式、脉冲效应和竖向地震动等三个关键因素对桥梁动力响应的影响规律。研究结果表明:地震输入方式对拱圈地震响应的影响较小,但对拱上立柱地震响应的影响很大,尤其是拱顶附近的短立柱,在抗震分析中,建议偏安全地采用三向地震输入方式;脉冲效应对拱桥地震响应的影响非常大,会导致拱圈、拱上立柱和桥面板地震响应大幅增加,桥面板残余平面转角甚至增大6倍以上;竖向地震动对拱圈轴力和面内弯矩、拱上立柱纵向弯矩和剪力的影响很大,拱顶处的面内弯矩放大倍数最大可达2.95,总体来说,采用规范所建议的方法考虑竖向地震是偏保守的。     

Dynamic response of skew bridge decks

In this paper the dynamic response of a skew bridge deck has been investigated, treating it as an orthotropic plate and using the finite strip method. Employing the normal mode method, the response of the deck due to a moving force has been calculated. Williams' method has been used to accelerate the convergence of the solution. Numerical work has been done for different skew angles and speed ranges. In this study, the history curves and the maximum amplification spectra for deflection and bending moment are presented.     

A parametric study of the required seating length for bridge decks during earthquake

During the recent major earthquakes, some bridges suffered severe damage due to the pull-off-and-drop collapse of their decks. This is due to the large differential movements of the adjacent spans of bridges during strong shaking compared to the seating lengths provided. The differential movements are primarily due to the different vibration properties of adjacent spans and non-uniform ground excitations at the bridge supports. This paper analyses the effects of various bridge and ground motion parameters on the required seating lengths for bridge decks to prevent the pull-off-and-drop collapse. The random vibration method is used in the analysis. A two-span bridge model with different span lengths and vibration frequencies and subjected to various spatially varying ground excitations is analysed. Non-uniform spatial ground motions are modelled by the filtered Tajimi–Kanai power spectral density function and an empirical coherency function. Ground motions with different intensities, different cross-correlations and different site conditions are considered in the study. The required seating lengths for bridge decks are calculated. Numerical results are presented and discussed with respect to different bridge vibration and ground motion properties. © 1998 John Wiley & Sons, Ltd.     

Dynamic response of single span highway bridges

The dynamic response of single span simply supported bridge decks subjected to the passage of vehicles is examined. A modal analysis approach is adopted that is based upon a finite strip idealization of the deck. The vehicle is modelled as a rigid body supported at two points by a suspension idealization that accounts for the effect of tyre stiffness and the frictional nature of real suspension systems. Results are presented for an orthotropic slab deck and a box girder deck that illustrate the effects of (i) the initial precompression of the suspension system as the vehicle enters the span, (ii) the ratio of the vehicle's natural frequency to that of the bridge deck and (iii) a bridge deck surface profile that is not perfectly horizontal.     

考虑流固耦合的桥墩地震反应方法

跨海桥梁地震反应中,作用于桥墩上的动水压力具有明显的流固耦合特征。依据张量理论,推导时变区域散度变换关系及微分形式的几何守恒律;基于任意拉格朗日一欧拉描述,从采用欧拉描述的流体运动Navier—Stokes方程出发,推导时变区域的流体运动控制方程;给出流固耦合问题中的结构计算模型、耦合面接触条件、耦合场计算方法以及流场网格运动控制方法。以某跨海大桥为例说明桥墩地震反应方法,重点突出地震动输入、流场初始条件模拟等问题。计算结果表明：流固耦合理论能够模拟桥梁墩台地震反应中的流场和结构特性;流场初始条件的正确模拟可保证计算稳定性,并减少运算量;横向地震动激励下,桥墩基底剪力较大,纵向地震动激励下,结构运动剧烈;流固耦合系统中的线弹性结构在地震反应中具有明显的非线性特征。     

非对称单侧混合梁斜拉桥多点激励地震响应分析

以一座主跨为820 m的双塔非对称单侧混合梁斜拉桥为研究对象,对其进行动力特性分析。运用相对运动法进行多点激励地震响应计算,分析行波效应对塔顶、主梁、塔底等关键位置动力响应的影响,同时对比分析入射角方向（即斜拉桥两侧相对方向）对其动力响应的影响。结果表明：与一致激励分析结果相比,多点激励使得主塔内力结果偏小,而使得主梁内力结果偏大;不同入射角地震激励对非对称大跨度斜拉桥的内力也会产生较大影响,内力变化可达20%。因此,在进行该类型非对称混合梁斜拉桥设计中,应考虑非一致激励效应和地震动输入方向的影响因素。     

新型形状记忆合金阻尼器的试验研究

本文在对形状记忆合金(SMA)的力学性能研究的基础上，设计和制造出一种性能良好的SMA阻尼器，介绍了其工作原理及有关试验结果，将该阻尼器安装在斜拉桥模型上，进行了斜拉桥模型振动试验。试验结果表明该阻尼器的耗能效果明显，在工程结构振动控制方面具有比较好的应用前景。     

Modelling of shear keys in bridge structures under seismic loads

Shear keys are used in the bridge abutments and piers to provide transverse restraints for bridge superstructures. Owing to the relatively small dimensions compared to the main bridge components (girders, piers, abutments, piles), shear keys are normally regarded as secondary component of a bridge structure, and their influences on bridge seismic responses are normally neglected. In reality, shear keys are designed to restrain the lateral displacements of bridge girders, which will affect the transverse response of the bridge deck, thus influence the overall structural responses. To study the influences of shear keys on bridge responses to seismic ground excitations, this paper performs numerical simulations of the seismic responses of a two-span simply-supported bridge model without or with shear keys in the abutments and the central pier. A detailed 3D finite element (FE) model is developed by using the explicit FE code LS-DYNA. The bridge components including bridge girders, piers, abutments, bearings, shear keys and reinforcement bars are included in the model. The non-linear material behaviour including the strain rate effects of concrete and steel rebar are considered. The seismic responses of bridge structures without and with shear keys subjected to bi-axial spatially varying horizontal ground motions are calculated and compared. The failure mode and damage mechanism of shear keys are discussed in detail. Numerical results show that shear keys restrain transverse movements of bridge decks, which influence the torsional–lateral responses of the decks under bi-axial spatially varying ground excitations; neglecting shear keys in bridge response analysis may lead to inaccurate predictions of seismic responses of bridge structures.     

Nonlinear seismic response analysis of arch dam-foundation systems- part II opening and closing contact joints

A time-domain method for the analysis of arch dam-foundation rock dynamic interaction during earthquake was proposed, and the dynamic relaxation technique was adopted to obtain the initial static response for dynamic analysis by [Du et al. (2005). The paper has been contributed to Bulletin of earthquake engineering]. In this paper, a nonlinear explicit method in time domain considering the opening and closing effect of contact joints on arch dam during earthquake is further proposed by introducing the dynamic contact force model into the method. The simulation accuracy of dynamic contact force model is verified by comparing its calculation result and test result of scale model on shaking table. Finally, the influence of joints on the seismic response of Xiaowan arch dam is studied by the proposed method and some conclusions are given.     

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。     

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.     

Earthquake simulation test of circular reinforced concrete bridge column under multidirectional seismic excitation

1 Introduction Since the 1971 San Fernando earthquake, a signi?cant amount of research has been conducted on the ductility capacity of reinforced concrete bridge columns, resulting in signi?cant advances in the seismic design of bridges. Since most tests have been done in static or quasistatic conditions and unidirectional loading conditions, however, no method that properly evaluates the effect of multidirectional dynamic loading has been developed, and design recommendations on this effect a…     

超大跨度斜拉桥考虑行波效应的地震动随机响应研究

斜拉桥地震反应不同于其它桥型,具有明显的空间耦合效应.利用有限元理论对苏通长江公路大桥的空间抗震性能进行分析,重点研究行波效应对结构响应的影响,并与一致激励计算的结果进行比较,为大跨度斜拉桥抗震分析采用随机方法提供了一定的参考依据.研究结果表明,行波效应对斜拉桥结构内力有显著的影响,大跨度斜拉桥抗震性能分析必须考虑行波效应.而行波效应的影响与结构自身动力特性、视波速、构件位置及研究响应类型(位移与内力)相关.     

Vertical oscillations due to axial-bending coupling during seismic response of RC bridge piers

The paper presents a numerical investigation on the behaviour of reinforced concrete bridge piers subjected to horizontal seismic input. The scope of the investigation is to quantify the phenomenon of bending-induced axial vibrations. The results of a set of analyses conducted on single-column bent systems indicate that flexural cracking produces, in fact, significant axial vibrations. This effect is particularly relevant in squat elements with low axial force where the sway of the cross-sectional neutral axis under alternate bending causes strong hammering impulses at crack closure. Quantification of the effects related to this phenomenon can be determinant for the seismic assessment of existing bridges as well as for the design of new bridges. Likewise, performance and design forces of bearings and other anti-seismic devices can be estimated with more accuracy, based on the expected level of combined vertical and horizontal acceleration response on decks. The pier overall flexural response is not significantly altered by the fluctuation in axial force associated to these impulses, although local moment–curvature behaviour is, due to axial–bending interaction. Shear resisting mechanisms should be more sensitive to these vibrations and shear failure anticipated when a reduction in the axial contribution to the section shear capacity occurs. A tentative equation for the prediction of this flexural-induced vertical acceleration component is proposed based on simplified section kinematics and elastic impact analysis. Copyright © 1999 John Wiley & Sons, Ltd.     

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.