秦力一, 许德刚, 王本瑞, 刘习军. 求解阶梯连续梁的通用方程[J]. 力学与实践, 2006, 28(6). DOI: 10.6052/1000-0992-2006-015
引用本文: 秦力一, 许德刚, 王本瑞, 刘习军. 求解阶梯连续梁的通用方程[J]. 力学与实践, 2006, 28(6). DOI: 10.6052/1000-0992-2006-015
GENERAL EQUATION FOR SOLVING STEPPED CONTINUOUS BEAMS[J]. MECHANICS IN ENGINEERING, 2006, 28(6). DOI: 10.6052/1000-0992-2006-015
Citation: GENERAL EQUATION FOR SOLVING STEPPED CONTINUOUS BEAMS[J]. MECHANICS IN ENGINEERING, 2006, 28(6). DOI: 10.6052/1000-0992-2006-015

求解阶梯连续梁的通用方程

GENERAL EQUATION FOR SOLVING STEPPED CONTINUOUS BEAMS

  • 摘要: 考虑阶形变化截面及不等跨度的情况,建立了求解多跨连续梁变形的通用方程.根据挠曲微分方程并采用奇异函数求解,给出了分析此类连续梁位移的边界参数方程. 该参数方程中含有若干待定的初参数和支反力.进一步导出计算变刚度不等跨连续梁位移的递推格式.最后考虑了位移协调条件及平衡条件而得到求解支反力的代数方程组.其计算的实例表明该方法适于编程运算.

     

    Abstract: A general equation is established to calculate thedeformation of continuous beams on many supports taking into considerationthe stepped cross sections and unequal spans. From the differential equation ofthe deflection and by using singular functions, the boundaryparametric equation, in which a certain number of undetermined initialparameters and the reactions of supports are contained, is derived foranalyzing the displacements of the continuous beams. And further, therecurrence formula is developed for calculating the displacements ofthe continuous beams with variable stiffness and unequal spans. Finally, inconsideration of the compatible conditions of displacements and equilibriumconditions as well , the system of algebraic equations is obtained for solvingthe reaction of support. A numerical example indicates that the present method may be adapted for programming.

     

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