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基于Timoshenko梁理论的钢-混组合梁动力刚度矩阵法

孙琪凯 张楠 刘潇

孙琪凯, 张楠, 刘潇. 基于Timoshenko梁理论的钢-混组合梁动力刚度矩阵法[J]. 工程力学, 2022, 39(8): 149-157. doi: 10.6052/j.issn.1000-4750.2021.04.0301
引用本文: 孙琪凯, 张楠, 刘潇. 基于Timoshenko梁理论的钢-混组合梁动力刚度矩阵法[J]. 工程力学, 2022, 39(8): 149-157. doi: 10.6052/j.issn.1000-4750.2021.04.0301
SUN Qi-kai, ZHANG Nan, LIU Xiao. A DYNAMIC STIFFNESS MATRIX METHOD FOR STEEL-CONCRETE COMPOSITE BEAMS BASED ON THE TIMOSHENKO BEAM THEORY[J]. Engineering Mechanics, 2022, 39(8): 149-157. doi: 10.6052/j.issn.1000-4750.2021.04.0301
Citation: SUN Qi-kai, ZHANG Nan, LIU Xiao. A DYNAMIC STIFFNESS MATRIX METHOD FOR STEEL-CONCRETE COMPOSITE BEAMS BASED ON THE TIMOSHENKO BEAM THEORY[J]. Engineering Mechanics, 2022, 39(8): 149-157. doi: 10.6052/j.issn.1000-4750.2021.04.0301

基于Timoshenko梁理论的钢-混组合梁动力刚度矩阵法

doi: 10.6052/j.issn.1000-4750.2021.04.0301
基金项目: 中央高校基本科研业务费专项资金项目(2020YJS121)
详细信息
    作者简介:

    孙琪凯(1992−),男,河北人,博士生,主要从事钢-混组合结构动力学研究(E-mail: qikai.sun@outlook.com)

    刘 潇(1996−),女,四川人,博士生,主要从事钢-混组合结构噪声与振动研究(E-mail: m18782030990@163.com)

    通讯作者:

    张 楠(1971−),男,北京人,教授,博士,博导,主要从事结构动力学研究(E-mail: nzhang@bjtu.edu.cn)

  • 中图分类号: U441+.3

A DYNAMIC STIFFNESS MATRIX METHOD FOR STEEL-CONCRETE COMPOSITE BEAMS BASED ON THE TIMOSHENKO BEAM THEORY

  • 摘要: 基于Timoshenko梁理论提出了适用于分析钢-混组合梁自振特性的动力刚度矩阵法,该计算模型中考虑了钢-混结合面剪切滑移、剪切变形和转动惯量的综合影响。动力刚度矩阵推导过程中未引入近似位移场或力场,因此,计算结果是准确的。与其他Timoshenko梁模型最大的不同是假设混凝土子梁和钢梁分别具有独立的剪切角,这个假设更加符合组合梁的实际运动,因此,计算结果更加准确。与已发表文章中的试验梁频率计算结果作对比分析;并讨论了不同剪力键刚度、跨高比时,剪切变形和转动惯量对钢-混组合梁自振频率的影响。结果表明:相对于已有的Euler-Bernoulli组合梁、子梁转角相同假设的Timoshenko组合梁模型,文中计算方法具有更高的计算精度,尤其是对于高阶频率;频率越高、剪力键刚度越大或跨高比越小,Euler-Bernoulli组合梁模型计算结果误差越大;对于1阶、2阶和3阶频率,高跨比分别大于10、18和25后,Euler-Bernoulli组合梁模型计算结果误差小于5%。
  • 图  1  钢-混组合梁构造图

    Figure  1.  Structural drawing of steel-concrete composite beam

    图  2  剪切滑移量示意图

    Figure  2.  Schematic diagram of shear slip

    图  3  动力刚度矩阵法计算流程图

    Figure  3.  Calculation flow chart of dynamic stiffness matrix method

    图  4  实验梁构造图 /mm

    Figure  4.  Structural drawing of experimental beam

    图  5  前5阶振型

    Figure  5.  First five modes

    图  6  前3阶自振频率随剪力键刚度的变化情况

    Figure  6.  Effect of shear connector stiffness on first three eigenfrequencies

    图  7  前3阶自振频率随跨高比的变化情况

    Figure  7.  Effect of depth-to-span on first three eigenfrequencies

    表  1  梁材料参数

    Table  1.   Material parameters of composite beam

    参数实验梁
    混凝土子梁钢梁
    Ei/MPa3.0×1042.06×105
    Gi/MPa1.4375×1047.9231×104
    ρi/(kg/m3)26007850
    ki0.830.38
    Ai/m20.510.0406
    Ii/m43.825×10−32.495×10−3
    下载: 导出CSV

    表  2  实验梁2自振频率分析结果对比表

    Table  2.   Comparison of eigenfrequencies obtained by different methods for experimental beam 2

    阶数测试结果ANSYS理论计算结果
    文献[23]文献[24]本文理论
    119.38 21.0822.86 (4.9)22.04 (1.2)21.79
    263.1363.0973.99 (12.9)72.92 (11.3)65.52
    3116.71156.37 (24.0)143.63 (13.9)126.07
    4172.08263.46 (35.6)231.45 (19.2)194.23
    5224.48402.66 (48.2)333.06 (22.6)271.65
    注:文献[23]为Euler-Bernoulli组合梁模型;文献[24]为Timoshenko组合梁模型,但假设混凝土子梁和钢梁具有相同的剪切角。括号中数值为相对于本文理论计算结果的误差/(%)。
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-21
  • 修回日期:  2021-06-30
  • 网络出版日期:  2021-09-02
  • 刊出日期:  2022-08-01

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