波形钢腹板组合箱梁扭转振动的矩阵分析方法

Matrix Analysis Method for Torsional Vibration of Composite Box Girders with Corrugated Steel Web

为精确计算简支波形钢腹板组合箱梁的扭转振动频率,在考虑波形钢腹板剪切变形的基础上,运用动力学势能不变值原理及形成矩阵的“对号入座”法则,推导组合箱梁在扭转振动时的单元刚度矩阵。基于推导结果,编写扭转振动频率计算程序,给出该桥型结构剪切系数、有效剪切模量以及扭转刚度的计算方法,并分析波形钢腹板型号和剪切变形对扭转振动频率的影响。结果表明:工程中常用的四种型号的简支波形钢腹板组合箱梁的扭转振动频率较为接近,在实际计算中可忽略波形钢腹板型号对扭转振动频率的影响;剪切变形对简支波形钢腹板组合箱梁的扭转振动频率造成高达41.11%的影响,并且超过了对其弯曲振动频率的影响,在实际工程计算中必须考虑剪切变形的影响。

In order to accurately calculate the torsional vibration frequency of simply supported corrugated steel web composite box girders,on the basis of considering the shear deformation of corrugated steel webs,the principle of invariant value of dynamic potential energy and the“set-in-right-position”rule of forming a matrix are used to derive the element stiffness matrix of composite box girders during torsional vibration.Based on the derivation results,a program for calculating the torsional vibration frequency was written,and the calculation methods for the shear coefficient,effective shear modulus and torsional stiffness of the bridge structure were given.Subsequently,the effects of corrugated steel web type and shear deformation on the torsional vibration frequency were analyzed.The results show that the torsional vibration frequencies of the four types of simply supported corrugated steel web composite box girders commonly used in engineering are relatively close,and the influence of the corrugated steel web type on the torsional vibration frequency can be ignored in actual calculations;the influence of shear deformation on the torsional vibration frequency of simply supported corrugated steel web composite box girders is as high as 41.11%,and exceeds the influence on its bending vibration frequency.Therefore,the influence of shear deformation must be considered in practical engineering calculations.