中间铰支加固的悬臂梁稳定性试验分析

Stability Analysis of Cantilever Beam Reinforced by Middle Hinge Support

杆的稳定性理论公式仅适用于两端约束(或仅一端)的情况,而在实际的结构设计时,往往会对杆件的中间部位进行加固。基于小挠度曲线的微分方程,对中间铰支加固的悬臂梁进行分析,从而导出其特征方程。通过对特征方程进行求解拟合,最终得到中间铰支加固的悬臂梁压杆稳定性公式。该公式仍然保持传统欧拉梁的计算形式,杆件中间铰支加固的效果通过长度因数“μ”进行体现。拟合公式的计算结果与有限元软件的计算结果对比,误差在0.5%以内,满足实际工程的精度要求。

The theoretical formula for the bar stability normally applies to the situation in which the two ends of bar are restrained or just one end is restrained.In the generally structural design,the middle part of the bar is always reinforced.In this paper,based on the differential equation of small deflection curve,the cantilever reinforced in the middle by a hinged shoe is analyzed so as to derive its characteristic equation.The characteristic equation is derived from the analysis of above differential equation;at last,the stability formula of the cantilever beam compression bar reinforced by the middle hinge is obtained by solving and fitting the characteristic equation.This formula still remains traditional calculation form of the Euler beam,and the effect of the bar which was reinforced in the middle by a hinged shoe is decided by the length factor"μ".Comparing the computation results of the fitting equation with that of the finite element method,the error is less than 0.5%,which is far below the accuracy requirements in the actual projects.