喻明秋，祝 兵，张斗龙

（1．攀枝花市规划和建设局，四川攀枝花 617000；2．西南交通大学土木工程学院，四川成都 610031；3．檀慕信息技术（上海）有限公司成都分公司，四川成都 610031）

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①

喻明秋1，祝 兵2，张斗龙3

（1．攀枝花市规划和建设局，四川攀枝花 617000；2．西南交通大学土木工程学院，四川成都 610031；3．檀慕信息技术（上海）有限公司成都分公司，四川成都 610031）

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。

三塔单索面斜拉桥；动力特性；无条件稳定；二阶效应；Newmark－β显式直接积分法

Abstract：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 1 600～0cps and frequency shift 1cps by using lanczos methods for the solution of the equation．The mathematical relationship between pseudo relative velocity response spectrum SVand pseudo absolute acceleration response spectrum SAis 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－βexplicit scheme direct integration method withγ≥0．5andβ≥γ／2which 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．

Key words：Cable－stayed bridge with three towers and single cable plane；Dynamic characteristics；No－conditional stable；Second order effect；Newmark－βexplicit scheme direct integration method

0 引言

大跨度桥梁结构准确的地震响应计算是其抗震设计的前提和基础，而地震响应计算结果的可信度与计算方法息息相关。……