The Study of Elastic Buckling Load of Uniform & Non-Uniform Columns Under Non-Uniform Axial Loading Using Finite Element Method

Abstract

The need to use non-uniform members in the structures from the past till now had been proposed although the subjects and research references in this case are insufficient. Therefore the use of non-uniform members is inevitable and should be carefully examined. About this members the main subject that should be investigated is buckling that if it occures it leads to member failure which may leads to collapse of the local or entire structure. So the exact solution of buckling load of non-uniform columns is available only for simple cases. In this paper a method based on finite element method is used for studing the problem of elastic buckling load of non-uniform columns with general cases of cross-section and axial loading. In first the column is devided to arbitrary numbers of finite elements. Then the stiffness matrix and geometric stiffness matrix is obtained based on existing relationship for each element and then for overall column. After applying boundary conditions using the eigenvalue equation to obtain the critical buckling load .It is clear that the effects of changes in cross-section of a column appear in stiffness matrix and changes in axial loading in geometric stiffness matrix. The proposed method in addition to high accuracy is general and could be used by th Matlab codes. Results obtained from this method are compared to ones that presented by Serna et al. The procedure in this paper is rating as a exact solutions but Serna’s method is a closed form method that is from approximated solutions. The results are presented for uniform columns under non-uniform axial loading and non-uniform columns under non-uniform axial loading. Different non-uniform columns contain single web-tapered columns, double web-tapered columns and web-tapered & flange-tapered columns. Also results are presented for various end boundary conditions that contain hinged-hinged, clamped-clamped, hinged-clamped and clamped-free

Keywords

• elastic buckling
• uniform and non-uniform columns
• axial load
• eigenvalue
• finite element