GENERAL EQUATION FOR SOLVING STEPPED CONTINUOUS BEAMS
求解阶梯连续梁的通用方程

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.