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力学与实践 ›› 2006, Vol. 28 ›› Issue (6): 0-0.doi: 10.6052/1000-0992-2006-015

• 应用研究 •    

求解阶梯连续梁的通用方程

秦力一 许德刚 王本瑞 刘习军   

  1. 郑州工业大学工程力学系 450002 郑州大学工学院工程力学系 郑州工业大学工程力学系 450002 天津大学机械学院力学系
  • 收稿日期:2006-01-11 修回日期:1900-01-01 出版日期:2006-12-10 发布日期:2006-12-10

GENERAL EQUATION FOR SOLVING STEPPED CONTINUOUS BEAMS

  • Received:2006-01-11 Revised:1900-01-01 Online:2006-12-10 Published:2006-12-10

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.

关键词: 通用方程, 连续梁, 变刚度, 不等跨

Abstract: A general equation is established to calculate the deformation of continuous beams on many supports taking into consideration the stepped cross sections and unequal spans. From the differential equation of the deflection and by using singular functions, the boundary parametric equation, in which a certain number of undetermined initial parameters and the reactions of supports are contained, is derived for analyzing the displacements of the continuous beams. And further, the recurrence formula is developed for calculating the displacements of the continuous beams with variable stiffness and unequal spans. Finally, in consideration of the compatible conditions of displacements and equilibrium conditions as well , the system of algebraic equations is obtained for solving the reaction of support. A numerical example indicates that the present method may be adapted for programming.

Key words: general equation, continuous beam, variable stiffness, unequal