潘旦光, 付相球, 韦杉杉, 陈钒, 杨少平. 变高度悬臂箱梁剪力滞效应的半解析解[J]. 工程力学, 2018, 35(9): 207-213. DOI: 10.6052/j.issn.1000-4750.2017.08.0643
引用本文: 潘旦光, 付相球, 韦杉杉, 陈钒, 杨少平. 变高度悬臂箱梁剪力滞效应的半解析解[J]. 工程力学, 2018, 35(9): 207-213. DOI: 10.6052/j.issn.1000-4750.2017.08.0643
PAN Dan-guang, FU Xiang-qiu, WEI Shan-shan, CHEN Fan, YANG Shao-ping. SEMI-ANALYTIC SOLUTION FOR SHEAR LAG EFFECT OF CANTILEVER BOX GIRDERS WITH VARYING DEPTH[J]. Engineering Mechanics, 2018, 35(9): 207-213. DOI: 10.6052/j.issn.1000-4750.2017.08.0643
Citation: PAN Dan-guang, FU Xiang-qiu, WEI Shan-shan, CHEN Fan, YANG Shao-ping. SEMI-ANALYTIC SOLUTION FOR SHEAR LAG EFFECT OF CANTILEVER BOX GIRDERS WITH VARYING DEPTH[J]. Engineering Mechanics, 2018, 35(9): 207-213. DOI: 10.6052/j.issn.1000-4750.2017.08.0643

变高度悬臂箱梁剪力滞效应的半解析解

SEMI-ANALYTIC SOLUTION FOR SHEAR LAG EFFECT OF CANTILEVER BOX GIRDERS WITH VARYING DEPTH

  • 摘要: 以等截面Euler梁的自由振动模态为Ritz基函数,提出了一种求解变高度箱梁剪力滞微分方程组的Ritz法。该方法首先进行与箱梁相同跨度相同边界条件等截面欧拉梁模态分析,然后将箱梁的竖向挠度和剪切转角用模态及其导数的线性组合来表达,从而将变分法所得箱梁剪力滞微分方程组转化为线性代数方程组进行求解。在此基础上,研究了参与计算模态阶数和截面高度变化率对计算误差的影响,算例分析结果表明:箱梁高度变化越大,Ritz法的收敛速度越慢;但随着参与计算模态阶数的增加,Ritz法将收敛到解析解。采用12阶以上模态进行计算,所得的剪力滞系数误差小于5%。

     

    Abstract: By using the free vibration mode of an Euler beam as Ritz base function, a new Ritz method is proposed to solve the set of shear lag differential equations of a varying depth box girder. Firstly, the modal analysis of a uniform cross-sectional Euler beam which is the same length and boundary condition with the box girder is carried out. The vertical deflection and the shear rotation of the box girder are expressed by the linear combination of the model and its derivative. And then the set of shear-lag differential equations of the box girder obtained by the calculus of variations are transformed into a set of linear algebraic equations. Then, the influences of the number of modes and variation ratio of section height on the errors are investigated. The numerical examples show that:the more significant the height of the box girder varies, the slower the Ritz method converges; but the results by Ritz method would converge to the analytic solution with the increasing of the number of modes. The errors of shear lag coefficients are less than 5%, when more than 12 of modes are included.

     

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