大跨高墩连续刚构桥三维动力响应的时程分析
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摘要
预应力混凝土连续刚构桥，因为其地形适应性强、设计、施工技术成熟，跨越能力大，造价合理，近年来被广泛采用，已成为预应力混凝土桥梁的主要桥型。随着大跨高墩连续刚构桥在我国的不断发展和应用，与此桥型相关的问题也在被深入的研究和探讨。
桥梁结构的动力问题一直是桥梁工作者们所关心的问题，桥梁结构的动力问题包括桥梁结构的自由振动和桥梁结构的动力响应这两个方面的问题。本文以内昆线上的李子沟特大铁路桥为研究对象，首先用实体结构有限元法分析了其空间自振特性。分析结果表明用实体模型计算的连续刚构桥的自振频率具有很高的精度。接着在李子沟特大桥的瞬态动力学时程分析中，分别建立了实体模型和三维空间梁单元模型，在移动荷载作用下进行了桥梁结构的一系列的对比分析。在建立动力学方程的基础上，采用Newmark积分法，考虑移动荷载速度和桥梁刚度的影响，对移动荷载作用下桥梁的动态响应进行了研究。桥梁主梁在两种不同材料的情况下分别模拟列车以90km／h，120km／h，160km／h三种不同速度通过全桥的情况，分别得出桥梁五跨跨中的挠度，以及跨中截面上下缘的应力时程曲线。
结果表明：该桥自振以纵桥向的弯曲为主，理论计算频率和实测频率很吻合；四个高墩的自振周期满足1959年高墩会议上对高墩自振周期的限制标准；移动荷载作用下挠度曲线是以一定的频率围绕静挠度线的一种类正弦波；从移动荷载对主梁上下缘截面引起的应力时程曲线来看，截面上缘与下缘的应力时程曲线大致关于时间轴对称，应力时程有些滞后，从不同列车速度下时程曲线比较可以发现，速度大小对应力峰值大小的影响不明显。通过对两种模型的计算结果很好的吻合发现：用三维空间梁单元可以很好的模拟桥梁的空间响应，避免了三维实体建模的繁杂，可以节省大量机时。
Because of the strong adaptability of terrain, the maturity of design and construction technology, long-span capability and the reasonable cost, the continuous rigid frame bridge of prestressed concrete is widely adopted and has already become the main bridge type of the prestressed concrete bridge in recent years. With the constant development and application of the long-span and high piers continuous rigid frame bridge in our country, the corresponding issues have been researched and discussed deeply.
The dynamic problems of bridge structures have always been cared for by bridge workers. It consists of two aspects: one is free vibration and another is dynamic response of the bridge structure. Firstly, combined with Lizigou long-span railway bridge of the Neikun railway line, its space free-vibration is analyzed with the FEM(finite element method) of solid element in this thesis. The analysis result is very precise. Secondly, solid model and three-dimensional beam element model are built up respectively in the transient-dynamic response time history analysis of Lizigou long-span railway bridge, and then a series of contrast analysis are done under the moving load. On the base of dynamic equation, with the Newmark integral method, taking into account influence of the moving load, velocity and stiffness, the dynamic response of the bridge are discussed under the effect of moving load. The process of the train through the bridge at three different velocities of 90km/h, 120km/h, 160km/h are simulated separatel
y in two different girder material. Middle-span deflection time response graph of five spans and the time history response stress graph of the top and bottom flange in the middle-span section are given.
According to the calculation, the following results can be obtained: the free-vibration of the bridge is mainly the longitudinal bend and the calculation frequency is coincident with the measured result; The free-vibration period of four high piers can fit the limiting criterion which is established at the high-pier meeting in 1959; the deflection graph under the moving load is a kind of analogous sine wave, which surround the static-deflection graph with certain frequency; From the time history response stress graph induced by the moving load on the top and bottom flange of the girder section, the time history response stress graph at the top and bottom is approximately symmetry to the time axis and time response stress is a little lagged. From the contrast of the different time history response graph at different speed, it can be noticed that the stress peak value is not evidently influenced by the change of the velocity. Through the calculated results of the two models, both are very consistent. Obviously
, the space response of the bridge can be well simulated with the three-dimensional beam element and the complexity of the three-dimensional solid modeling can be avoided and much calculation time can be saved.
桥梁结构的动力问题一直是桥梁工作者们所关心的问题，桥梁结构的动力问题包括桥梁结构的自由振动和桥梁结构的动力响应这两个方面的问题。本文以内昆线上的李子沟特大铁路桥为研究对象，首先用实体结构有限元法分析了其空间自振特性。分析结果表明用实体模型计算的连续刚构桥的自振频率具有很高的精度。接着在李子沟特大桥的瞬态动力学时程分析中，分别建立了实体模型和三维空间梁单元模型，在移动荷载作用下进行了桥梁结构的一系列的对比分析。在建立动力学方程的基础上，采用Newmark积分法，考虑移动荷载速度和桥梁刚度的影响，对移动荷载作用下桥梁的动态响应进行了研究。桥梁主梁在两种不同材料的情况下分别模拟列车以90km／h，120km／h，160km／h三种不同速度通过全桥的情况，分别得出桥梁五跨跨中的挠度，以及跨中截面上下缘的应力时程曲线。
结果表明：该桥自振以纵桥向的弯曲为主，理论计算频率和实测频率很吻合；四个高墩的自振周期满足1959年高墩会议上对高墩自振周期的限制标准；移动荷载作用下挠度曲线是以一定的频率围绕静挠度线的一种类正弦波；从移动荷载对主梁上下缘截面引起的应力时程曲线来看，截面上缘与下缘的应力时程曲线大致关于时间轴对称，应力时程有些滞后，从不同列车速度下时程曲线比较可以发现，速度大小对应力峰值大小的影响不明显。通过对两种模型的计算结果很好的吻合发现：用三维空间梁单元可以很好的模拟桥梁的空间响应，避免了三维实体建模的繁杂，可以节省大量机时。
Because of the strong adaptability of terrain, the maturity of design and construction technology, long-span capability and the reasonable cost, the continuous rigid frame bridge of prestressed concrete is widely adopted and has already become the main bridge type of the prestressed concrete bridge in recent years. With the constant development and application of the long-span and high piers continuous rigid frame bridge in our country, the corresponding issues have been researched and discussed deeply.
The dynamic problems of bridge structures have always been cared for by bridge workers. It consists of two aspects: one is free vibration and another is dynamic response of the bridge structure. Firstly, combined with Lizigou long-span railway bridge of the Neikun railway line, its space free-vibration is analyzed with the FEM(finite element method) of solid element in this thesis. The analysis result is very precise. Secondly, solid model and three-dimensional beam element model are built up respectively in the transient-dynamic response time history analysis of Lizigou long-span railway bridge, and then a series of contrast analysis are done under the moving load. On the base of dynamic equation, with the Newmark integral method, taking into account influence of the moving load, velocity and stiffness, the dynamic response of the bridge are discussed under the effect of moving load. The process of the train through the bridge at three different velocities of 90km/h, 120km/h, 160km/h are simulated separatel
y in two different girder material. Middle-span deflection time response graph of five spans and the time history response stress graph of the top and bottom flange in the middle-span section are given.
According to the calculation, the following results can be obtained: the free-vibration of the bridge is mainly the longitudinal bend and the calculation frequency is coincident with the measured result; The free-vibration period of four high piers can fit the limiting criterion which is established at the high-pier meeting in 1959; the deflection graph under the moving load is a kind of analogous sine wave, which surround the static-deflection graph with certain frequency; From the time history response stress graph induced by the moving load on the top and bottom flange of the girder section, the time history response stress graph at the top and bottom is approximately symmetry to the time axis and time response stress is a little lagged. From the contrast of the different time history response graph at different speed, it can be noticed that the stress peak value is not evidently influenced by the change of the velocity. Through the calculated results of the two models, both are very consistent. Obviously
, the space response of the bridge can be well simulated with the three-dimensional beam element and the complexity of the three-dimensional solid modeling can be avoided and much calculation time can be saved.
引文
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[2] 易日．使用ANSYS6.1进行结构力学分析．北京大学出版社．2002
[3] 李景涌．有限元法．北京邮电大学出版社．1999
[4] 刘作霖，徐兴玉等．预应力T型刚构式桥．人民交通出版社．1982
[5] 曾庆元，郭向荣．列车桥梁时变系统振动分析理论与应用．中国铁道出版社，1999
[6] 徐岳，王亚君，万振江．预应力混凝土连续梁桥设计．人民交通出版社．2000
[7] 博嘉科技编著．有限元分析软件ANSYS融会与贯通．中国水利水电出版社．2002
[8] 嘉木工作室．ANSYS5.7有限元实例分析教程．机械工业出版社．2002
[9] 李国豪．桥梁结构稳定与振动 中国铁道出版社 1996
[10] 赵国藩．高等钢筋混凝土结构学 中国电力出版社 1999
[11] 宋一凡．公路桥梁动力学．人民交通出版社．1999
[12] 陈精一，蔡国忠．电脑辅助工程分析ANSYS使用指南．中国铁道出版社．2001
[13] 郝超，强士中，马栋君译．移动荷载作用下桥梁的振动控制．国外桥梁．1999．第3期
[14] 范立础．预应力混凝土连续梁桥．人民交通出版社．1988．8
[15] 马建敏，吕景林．用ANSYS对复杂结构进行动态响应计算．机械科学与技术．1998．第6期
[16] 肖新标，沈火明．移动荷载速度对简支梁动态响应的影响．西南交通大学学报．2001．增刊
[17] 韩景泉，王鑫．简支梁在动荷载作用下竖向动挠度的计算理论研究．森林工程．2000．第6期
[18] 项贻强，胡峰强．V型墩预应力连续刚构桥结构动力分析和试验研究．中国市政工程．2003．第1期
[19] 沈光玉．炳草岗金沙江大桥自振特性分析计算．辽宁交通科技．2003．第3期
[20] 李清海，谭笃光．车辆荷载作用下桥梁动力效应的有限元分析．振动与冲击．1994．第1期
[21] 刘春华，项海帆，顾明．大跨度桥梁抖振响应的空间非线性时程分析法．同济大学学报．1996．第4期
[22] 杨岳民，潘家英，程庆国．大跨度铁路桥梁车桥动力响应理论分析及试验
研究．中国铁道科学．1995．第4期
[23] 夏禾，徐幼麟，阎全胜．大跨度悬索桥在风与列车荷载同时作用下的动力响应分析．铁道学报．2002．第4期
[24] 王永平，陈彦江，傅金科．单车荷载下简支梁桥的动力特性和响应的试验研究．土木工程学报．1995．第5期
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