多级阶梯柱侧向刚度与轴压临界力的精确分析及其实用算式
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摘要
汽车起重机的伸缩臂或高空消防车的多级油缸是工程中常见的多级阶梯柱,为确定其侧向刚度与轴压稳定性,通过纵横弯曲理论建立了计及二阶效应的多级阶梯柱模型的挠曲微分平衡方程,对多级阶梯柱侧向刚度和纵向稳定性进行分析,得到了多级阶梯柱侧向挠曲方程和轴压失稳特征方程的精确表达,并给出了工程常用的5级及5级以下精确表达的显示形式;针对工程应用,给出多级阶梯柱稳定性分析的等效构件法;引入挠度影响系数,给出多级阶梯柱侧向刚度分析的实用算式,从而为工程应用提供了高效便捷的侧向刚度与轴压稳定性分析计算公式。分别以5级、8级阶梯柱模型为例,利用该文精确表达式与实用算式对其进行刚度与稳定性计算,得到了阶梯柱模型的臂端挠度与计算长度系数,通过将计算结果与标准文献精确结果进行比较,验证了该文精确表达式的正确性和实用算式的精度与适用性。
Telescopic crane booms and multistage cylinders of large fire trucks are typical stepped column structures. To analyze their vertical stiffness and stability status under axial loadings, differential equations of the deflection of stepped column structures based on the vertical and horizontal bending theory are established in this study. Precise expressions of the lateral deflection and buckling characteristic equations with second-order effects are obtained. More specifically, formulations for columns of less than six levels of steps are derived for practical engineering application. An equivalent component method is proposed for the stability analysis of stepped column structures, and a formulation for lateral stiffness analysis is derived by introducing the deflection influence coefficient. Examples with 5 and 8 levels of stepped column are used for the stability and stiffness analysis, and the effective length factor and the deflection at the column ends are calculated. Results calculated from the proposed formulations in this study agree well with those from literature, which demonstrates the credibility and accuracy of the proposed formulations and their applicability in engineering practice.
Telescopic crane booms and multistage cylinders of large fire trucks are typical stepped column structures. To analyze their vertical stiffness and stability status under axial loadings, differential equations of the deflection of stepped column structures based on the vertical and horizontal bending theory are established in this study. Precise expressions of the lateral deflection and buckling characteristic equations with second-order effects are obtained. More specifically, formulations for columns of less than six levels of steps are derived for practical engineering application. An equivalent component method is proposed for the stability analysis of stepped column structures, and a formulation for lateral stiffness analysis is derived by introducing the deflection influence coefficient. Examples with 5 and 8 levels of stepped column are used for the stability and stiffness analysis, and the effective length factor and the deflection at the column ends are calculated. Results calculated from the proposed formulations in this study agree well with those from literature, which demonstrates the credibility and accuracy of the proposed formulations and their applicability in engineering practice.
引文
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[3]Kukla S.Free vibrations and stability of stepped columns with cracks[J].Academic Press,2009,319:1301―1311.
[4]陆念力,孟丽霞.基于二阶理论的弹性约束变截面悬臂梁刚度与稳定性分析[J].工程力学,2012,29(12):365―369.Lu Nianli,Meng Lixia.The stiffness and stability analysis of a tapered beam with elastic restraint considering second-order effects[J].Engineering Mechanics,2012,29(12):365―369.(in Chinese)
[5]Vasquez Jorge,Riddell Rafael.A simple stepped column buckling model and computer algorithm[J].American Institute of Steel Construction Inc,2011,48:19―30
[6]刘古岷.关于阶梯柱状构件稳定性的近似计算公式[J].建筑机械,1995,1(10):12―15.Liu Gumin.The approximate formulas of stepped column stability[J].Construction Machinery,1995,1(10):12―15.(in Chinese)
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[8]GB/T3811-2008,起重机设计规范[S].北京:中国标准出版社,2008.GB/T3811-2008,Design rules for cranes[S].Beijing:China Standard Press,2008.(in Chinese)
[9]陆念力,兰朋,白桦.起重机箱形伸缩臂稳定性分析的精确理论解[J].哈尔滨建筑大学学报,2000,33(2):89―93.Lu Nianli,Lan Peng,Bai Hua.Precise stability analysis of telescopic boom[J].Journal of Harbin University of Civil Engineering and Architecture,2000,33(2):89―93.(in Chinese)
[10]孟丽霞,陆念力,王佳.基于静力凝聚的高精度变截面梁单元及其几何非线性分析研究[J].工程力学,2013,30(10):257―263.Meng Lixia,Lu Nianli,Wang Jia.The geometric nonlinearity analysis of high accuracy tapered beam element based on the static condensation[J].Engineering Mechanics,2013,30(10):257―263.(in Chinese)
[11]陆念力,刘士明,兰朋.具有伸缩液压缸的起重机伸缩臂之整体稳定性[J].工程机械,2008,9(39):46―51.Lu Nianli,Liu Shiming,Lan Peng.Overall stability of telescopic crane booms with retractable hydraulic cylinders[J].Construction Machinery and Equipment,2008,9(39):46―51.(in Chinese)
[2]Park J S,Stallings J M.Lateral torsional buckling of stepped beams with continuous bracing[J].Journal of Bridge Engineering,2005,10(1):87―95.
[3]Kukla S.Free vibrations and stability of stepped columns with cracks[J].Academic Press,2009,319:1301―1311.
[4]陆念力,孟丽霞.基于二阶理论的弹性约束变截面悬臂梁刚度与稳定性分析[J].工程力学,2012,29(12):365―369.Lu Nianli,Meng Lixia.The stiffness and stability analysis of a tapered beam with elastic restraint considering second-order effects[J].Engineering Mechanics,2012,29(12):365―369.(in Chinese)
[5]Vasquez Jorge,Riddell Rafael.A simple stepped column buckling model and computer algorithm[J].American Institute of Steel Construction Inc,2011,48:19―30
[6]刘古岷.关于阶梯柱状构件稳定性的近似计算公式[J].建筑机械,1995,1(10):12―15.Liu Gumin.The approximate formulas of stepped column stability[J].Construction Machinery,1995,1(10):12―15.(in Chinese)
[7]斯尼科夫H K.杆系的稳定性[M].北京:建筑工程出版社,1956:186―202.Snikov H K.The stability of the truss[M].Beijing:Construction Engineering Press,1956:186―202.(in Chinese)
[8]GB/T3811-2008,起重机设计规范[S].北京:中国标准出版社,2008.GB/T3811-2008,Design rules for cranes[S].Beijing:China Standard Press,2008.(in Chinese)
[9]陆念力,兰朋,白桦.起重机箱形伸缩臂稳定性分析的精确理论解[J].哈尔滨建筑大学学报,2000,33(2):89―93.Lu Nianli,Lan Peng,Bai Hua.Precise stability analysis of telescopic boom[J].Journal of Harbin University of Civil Engineering and Architecture,2000,33(2):89―93.(in Chinese)
[10]孟丽霞,陆念力,王佳.基于静力凝聚的高精度变截面梁单元及其几何非线性分析研究[J].工程力学,2013,30(10):257―263.Meng Lixia,Lu Nianli,Wang Jia.The geometric nonlinearity analysis of high accuracy tapered beam element based on the static condensation[J].Engineering Mechanics,2013,30(10):257―263.(in Chinese)
[11]陆念力,刘士明,兰朋.具有伸缩液压缸的起重机伸缩臂之整体稳定性[J].工程机械,2008,9(39):46―51.Lu Nianli,Liu Shiming,Lan Peng.Overall stability of telescopic crane booms with retractable hydraulic cylinders[J].Construction Machinery and Equipment,2008,9(39):46―51.(in Chinese)