求解阶梯连续梁的通用方程

GENERAL EQUATION FOR SOLVING STEPPED CONTINUOUS BEAMS

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．

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.