GENERAL EQUATION FOR SOLVING STEPPED CONTINUOUS BEAMS

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.