基于Newmark-β显式直接积分法的三塔斜拉桥非线性地震响应分析
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摘要
三塔单索面斜拉桥在空间动力行为方面有其独特之处。以济南建邦黄河公路大桥为例,运用有限元方法建立桥梁的空间动力数值分析模型,构建结构特征方程,在频率范围1 600～0cps,频移为1cps基础上运用lanczos法解此方程获得结构空间动力特性;进而利用拟相对速度反应谱SV和拟绝对加速度反应谱SA之间的数学关系,在大量地震记录中选择与场地特征周期基本一致的波谱,对其峰值加速度和持续时间进行调整后直接输入动力数值模型;采用质量和刚度因子法计算结构各振型阻尼比,以恒载作用下结构受力状态作为初始状态,运用Newmark-β显式直接积分法迭代求解结构动力微分方程组,并取γ≥0.5且β≥γ/2以满足其无条件稳定;考虑恒载作用在地震发生过程中对结构产生的二阶效应,获得非线性地震响应数值解,并由此总结出该类桥型的地震响应一般规律。结果可为该类桥型的抗震设计提供参考。
Cable-stayed bridge with three towers and single cable plane has uniqueness on dynamic behavior in space.In this paper,the Jianbang Yellow River Highway Bridge in Jinan is taken,as example,using finite element method to build spatial dynamic numerical analysis model of the bridge,and to form a structural characteristic equation,the space dynamic characteristics of the structure is obtained with frequency range of 1 600~0 cps and frequency shift 1 cps by using lanczos methods for the solution of the equation.The mathematical relationship between pseudo relative velocity response spectrum SV and pseudo absolute acceleration response spectrum SA is used to select the spectra with basically same characteristic site period in a large number of seismic records,whose peak acceleration and duration are adjusted to directly be input to the dynamic numerical analysis model.Using mass and stiffness factor method in calculation on damping ratio of every vibration type,taking stressed state of the structure under dead load as the initial state,Newmark-β explicit scheme direct integration method with γ≥0.5 and β≥γ/2 which make the method being no-conditional stable is used to the solution of the structure dynamic differential equations.Considering the second order effect from dead load in the structure during an earthquake,the numerical solution of nonlinear seismic response is obtained.Furthermore,general laws on seismic response of such bridge type is concluded to provide a feasible basis for seismic design of such bridge type.
Cable-stayed bridge with three towers and single cable plane has uniqueness on dynamic behavior in space.In this paper,the Jianbang Yellow River Highway Bridge in Jinan is taken,as example,using finite element method to build spatial dynamic numerical analysis model of the bridge,and to form a structural characteristic equation,the space dynamic characteristics of the structure is obtained with frequency range of 1 600~0 cps and frequency shift 1 cps by using lanczos methods for the solution of the equation.The mathematical relationship between pseudo relative velocity response spectrum SV and pseudo absolute acceleration response spectrum SA is used to select the spectra with basically same characteristic site period in a large number of seismic records,whose peak acceleration and duration are adjusted to directly be input to the dynamic numerical analysis model.Using mass and stiffness factor method in calculation on damping ratio of every vibration type,taking stressed state of the structure under dead load as the initial state,Newmark-β explicit scheme direct integration method with γ≥0.5 and β≥γ/2 which make the method being no-conditional stable is used to the solution of the structure dynamic differential equations.Considering the second order effect from dead load in the structure during an earthquake,the numerical solution of nonlinear seismic response is obtained.Furthermore,general laws on seismic response of such bridge type is concluded to provide a feasible basis for seismic design of such bridge type.
引文
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[2]叶爱君.桥梁抗震[M].北京:人民交通出版社,2002.
[3]Newmark N M.A Method of Computation for Structural Dy-namics[J].Journal of the Engineering Mechanics Division,ASCE,1959,85(2):67-94.
[4]翟婉明.大型结构动力分析的Newmark-β显式算法[J].重庆交通学院学报,1991,10(2):33-41.
[5]中华人民共和国建设部,国家质量监督检验检疫总局.GB50011-2001.建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.
[6]华孝良,徐光辉.桥梁结构的非线性分析[M].北京:人民交通出版社,1997.
[7]任慧,尚守平,李刚.非匀质场地地震反应的模态叠加法解[J].西北地震学报,2009,31(1):26-30
[8]Wang P H,Yang C G.Parametric studies on cable-stayedbridges[J].Computers and Structures,1996,60(2):243-260.
[9]高大峰,刘伯栋,张静娟.中承式钢筋混凝土拱桥自振特性分析[J].西北地震学报,2009,31(1):75-79.
[10]翟婉明.非线性结构动力分析的Newmark顶测——校正积分模式[J].计算结构力学及其应用,1990,7(2):51-58.
[11]Clough R W,Penzien J.王光远,译.结构动力学[M].北京:科学出版社,1985.
[12]Park K C.An Improved Stiffly Stable Method for Direct Inte-gration of Nonlinear Structural Dynamic Equations[J].Jour-nal of Applied Mechanics,ASME,1975,42(2):464-470.
[13]梁庆国,韩文峰.强震区岩体地震动力破坏特征[J].西北地震学报,2009,31(1):15-20.
[14]重庆交通科研设计院.JTG/T B02-01-2008.公路桥梁抗震设计细则[S].北京:人民交通出版社,2008.
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