Diagram Method Of Determining Effective Length Of Multilayer Columns With Different Axis Forces

A key step in the stability computation of multilayer column is determining the effective length of columns. Therefore calculation formulas and tables are given in the Standard of "Code for design of steel structures", which are applicable for regular cases but not for special cases, such as with large difference of axial force between the columns connected each other. For the special cases the Standard’s method will lead to unsafe or too conservative results. In this regard, this article carried on the thorough research, and proposed a new calculation chart method.In this paper, introduces three kinds of second order elastic stability analysis method first. Including balance differential equation method, second-order force method And second-order displacement method, According to three different analysis way, determined the basic equations, the necessary parameters, and applicable range, lay the theoretical foundation for the graphic method.Select four column model:①two-tier column with articulated upper and lower end;②two-tier column with the articulated upper end and the lower end fixed;③two-tier column with the free upper end and the fixed lower end;④single stage column with the free upper end and the fixed lower end. Based on those calculation models, choose suitable analysis method to deduce the buckling stability critical state equation.In the process of derivation, introduce two dimensionless parameters which can comprehensively reflect the characteristics of the stick:Line stiffness ratio v and stick characteristic coefficient ratio P.Observed the relationship between the two parameters and the effective length. Using the corresponding relationship, Selection of parameters v and P value range from zero to go to infinity, and made the graphic witch can reflect this relationship, the graphic can not only quickly determine the effective length, but also show graphically its trend with the relevant parameters.In order to verify the reliability of new Graphic method, using finite element analysis software ANSYS, Suckling Analysis the four selected model, get the stick buckling critical load, contrast the results come from new Graphic method, both difference is within1%, proved the Graphic method in this paper is a kind of reliable method for definite the stick effective length.The graphics of the paper can be considered as a supplementary to formulas and tables of the relevant standards.