The Lateral Buckling of the Beams with Cross Section which discontinuosly changes by Steps

Abstract

In these papers, writer deals with the lateral buckling of beam with cross scction which discontinuosly changes by steps. The differential equation of equilibrium for the small angle of twist is used as follows : -[numerical formula] B and C are the flexural and torsional rigidity of the beam sections. The angle and its first derivative θ' can be found by integration, and takes the form as the next expression for the portion of the beam. [numerical formula] The boundary conditions have two kinds in this case. The one is that of beam ends, and the other is that of the continuation of the seams in the portions. At the k th sections and k+1 th sections, the next relations are formed. [numerical formula] Elliminating the integration constants, we can determine the critical moment expressed as follows : -[numerical formula] where μ is the coefficient depending upon the kind of load, the state of the beam sections, and number of their steps. It can be found by trial-error-method in general. As the numerical examples, the critical moment and critical load of the beam with two steps in the sections are determined.