Buckling Loads for Stepped Columns

The formulation of exact characteristic buckling load equations for ideal stepped columns is shown. The method is based on the three-step moment equation. This expression, analogous to the well-known three-moment equation, relates the bending moments at three adjacent steps of a slightly buckled column. Modified moment equations are developed for various types of supports. The string polygon method and known load-slope relationships for simply supported struts are used in the development. The bounds of the buckling load are established by inspection of the poles of the characteristic equation. The characteristic equation is solved by trial and error. The solution is expedited by algebraic approximations for the transcendental functions (end slope magnification factors).