连续梁桥冲击系数与频率的对应关系

Relation between frequencies and impact coefficients of continuous beam bridges

为明确在计算连续梁桥主梁不同荷载效应(位移、正负弯矩和剪力)的冲击系数时,采用哪一阶频率计算更加合理,以分联长度为r×30 m(跨数r=3,4,5,6)的预应力混凝土连续梁桥为研究对象,运用理论分析与有限元数值模拟相结合的手段,研究了位移冲击系数、正负弯矩冲击系数和剪力冲击系数与前3阶频率的对应关系。首先运用动力学和曲率模态理论得到了位移冲击系数、正负弯矩冲击系数和剪力冲击系数与各阶振型的关系式;接着运用梁格法分别建立r×30 m预应力混凝土连续梁桥的MIDAS Civil有限元数值模型,然后利用傅里叶级数分别对有限元分析中得到的前3阶竖弯振型进行拟合,最后将拟合得到的振型函数代入不同效应的冲击系数与各阶振型的关系式,从而分别得到前3阶竖弯模态对不同效应冲击系数的贡献百分比,并与已有研究成果进行对比,对该理论分析正确性进行了验证。研究结果表明:位移冲击系数、正弯矩冲击系数和剪力冲击系数根据第1阶竖弯频率来计算更加合理,在前3阶竖弯模态中,第1阶模态贡献了跨中最大动位移的84.4%~99.5%、跨中截面最大正动弯矩的77.2%~98.7%、支座截面最大动剪力的84.1%~99.1%;负弯矩冲击系数则根据第2阶竖弯频率来计算更加合理,在前3阶竖弯模态中,第2阶模态贡献了支座截面最大负动弯矩的70.0%~98.2%。

In order to clarify which order frequency was more reasonable when calculating the impact coefficients of different load effects(displacement, positive and negative bending moment and shear force) of the girder of a continuous beam bridge, the prestressed concrete(PC) continuous beam bridges with spans-unite length of r×30 m(span number r=3, 4, 5, 6) were taken as the research object. By using the theoretical analysis and finite element numerical simulation simultaneously, the relation between displacement impact coefficient, positive and negative moment impact coefficient and shear impact coefficient and the first three order frequencies were studied. Firstly, the relationship between displacement impact coefficient, positive and negative moment impact coefficient, shear impact coefficient and models of each order were obtained by using dynamics and curvature modal theory. Then the beam grid method was used to establish the MIDAS Civil finite element modes of r×30 m PC continuous beam bridges. And the Fourier series were used to fit the first three order vertical bending modes obtained from the finite element analysis. Finally, the fitting mode function was substituted into the relationship between the impact coefficients of different effects and the modes of each order, so that the contributing percentages of the first three orders of vibration modes to the impact coefficients of different effects were obtained. The theoretical analysis conclusions were verified by comparing with the existing research results. The research results show that the displacement impact coefficient, positive bending moment impact coefficient, and shear impact coefficient can be calculated more reasonably according to the first order vertical bending frequency. Among the first three order vertical bending modes, the first order mode contributes 84.4% to 99.5% of the largest dynamic displacement in the mid-span section, 77.2% to 98.7% of the maximum dynamic positive bending moment in the mid-span section, and 84.1% to 99.1% of the maximum dynamic shear force of the bearing section. The negative moment impact coefficient is calculated more reasonably according to the second order vertical bending frequency. Among the first three order vertical bending modes, the second order mode contributes 70.0% to 98.2% of the maximum negative dynamic bending moment of the support section. 9 tabs, 2 figs, 31 refs.