基于Timoshenko梁理论的钢-混组合梁动力折减系数

doi:10.13229/j.cnki.jdxbgxb20210742

摘要/Abstract

摘要：

基于Timoshenko梁理论，推导了考虑剪切滑移影响的钢-混组合梁的运动微分方程，得到了简支钢-混组合梁的自振频率和振型的显式解析表达式。提出了更适用于钢-混组合梁动力分析的动力折减系数，并给出了“刚度折减系数”和“频率折减系数”的解析表达式。与已有基于Euler-Bernoulli梁理论的动力折减系数进行了对比分析，讨论了剪力键刚度、剪切变形、转动惯量、跨高比对频率折减系数的影响。结果表明：当进行钢-混组合梁动力分析时，尤其是跨高比较小的组合梁，可以忽略转动惯量的影响，但不可忽略剪切变形的影响。

关键词: 桥梁工程, 钢-混组合梁, 动力折减系数, 剪切变形, 界面剪切滑移, 解析解

Abstract:

The motion differential equation of steel-concrete composite beams considering the shear slip effect was derived based on the Timoshenko beam theory. And the analytical expressions of eigenfrequencies and modes for simply-supported steel-concrete composite beams were obtained. The dynamic reduction coefficients which were more suitable for dynamic analysis of steel-concrete composite beams were proposed， and the analytical expressions of "stiffness reduction coefficient" and "frequency reduction coefficient" were given. Then the dynamic reduction coefficients were compared with the existing one based on Euler-Bernoulli beam theory. The effects of shear connector stiffness， shear deformation， rotary inertia， and span-to-depth ratio on the frequency reduction coefficient were discussed. The results show that the effect of the rotary inertia can be ignored， but that of the shear deformation must be considered in the dynamic analysis of steel-concrete composite beams with smaller span-to-depth ratios.

Key words: bridge engineering, steel-concrete composite beam, dynamic reduction coefficient, shear deformation, shear slip, analytical expression

中图分类号:

U441

孙琪凯,张楠,刘潇,周子骥. 基于Timoshenko梁理论的钢-混组合梁动力折减系数[J]. 吉林大学学报(工学版), 2023, 53(2): 488-495.

Qi-kai SUN,Nan ZHANG,Xiao LIU,Zi-ji ZHOU. Dynamic reduction coefficients of steel⁃concrete composite beam based on Timoshenko beam theory[J]. Journal of Jilin University(Engineering and Technology Edition), 2023, 53(2): 488-495.

图/表 8

图1

图2

表1

图3

图4

图5

图6

表2

钢-混组合梁自振特性对比表"

阶次	实测值	ANSYS	文献［9］模型		本文模型
阶次	实测值	ANSYS	$f n E B$	$γ n E B$	$f n T$	$γ n T$
1	19.38	21.08	22.27	0.88	21.28	0.84
2	63.13	62.48	75.96	0.75	67.02	0.66
3	-	114.48	156.09	0.69	126.07	0.56

表2

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阶次	SD/RI梁	仅SD梁	E-B梁
1	158.29	158.69 （0.3%）	165.29 （4.4%）
2	542.04	546.49 （0.8%）	618.90 （14.2%）
3	1077.90	1093.73 （1.5%）	1373.02 （27.4%）
4	1709.64	1745.80 （2.1%）	2428.52 （42.0%）
5	2408.85	2474.51 （2.7%）	3785.50 （57.1%）