多维地震激励下曲线梁桥简化模型及最不利输入方向研究

曲线梁桥只有在某一特定方向输入地震动时,结构某点或某截面的内力(或应力)才能达到最大值,需要沿多个可能方向输入计算才能确定地震动最不利输入方向。根据隔震曲线梁桥受力特点,将桥梁上部结构和桥墩简化均具有两个水平自由度和一个围绕质量中心轴扭转自由度的堆积质量模型,建立双质点六自由度简化分析模型,通过求解曲线梁桥的动力学方程研究结构的动力特性和地震动行为。算例表明,双质点模型计算结果与传统的有限元模型基本一致,且计算方法简单,可以考虑各种敏感因素的影响,借助编程更适合提出规律性的设计方法。进而在双质点模型基础上应用MATLAB编程探讨多维地震作用下曲线梁桥地震波最不利输入方向的问题,针对不同参数的隔震曲线梁桥,改变相关参数后只需运行一次就可以实现最不利输入角度的确定,可为有限元法最不利地震波输入方向的确定提供参考,并大大减少多个方向输入试算的工作量。

A Simplified Model of, and Critical Angles for Curved Bridgesunder Multi-dimensional Earthquake Excitation

The internal force or stress of a certain point or section of a curved girder bridge can reach its maximum value only when earthquake motion is sourced from a certain direction. Therefore, it is necessary to input ground motions in multiple possible directions so that the critical angle can be determined. Based on the mechanical characteristics of isolated curved girder bridges, this study simplified bridge superstructure and piers into an accumulated mass model with two horizontal degrees of freedom and one torsional degree of freedom around the mass center axis. Thus, a simplified analytical model with two particles and six degrees of freedom was established. Dynamic characteristics and ground motion behavior of the curved girder bridge were studied by solving the dynamical equation of the structure. The experimental sample showed that the calculated results of the two-particle model were basically consistent with those of the traditional finite element model. The method was simple and the influence of various sensitivity factors was considered. With the help of programming, a more regular design method is put forward. Based on the model, the critical angle of curved girder bridges under multi-dimensional earthquake action was investigated using MATLAB programming. For isolation curved girder bridges with different parameters, the critical angle could be determined only by running the program once after changing relevant parameters. The model provided a reference for determining the critical angle of seismic waves by a finite element method, and greatly reduced the workload of trial calculations of multi-directional input.