Buckling analysis of nonuniform columns with elastic end restraints

Since compression members, such as columns in a multistory building, are mostly the key elements in a structure, even a small decrease in their load carrying capacity can lead to catastrophic failure of the structure. A compression member has to be designed to satisfy not only the strength and serviceability requirements, but also the stability requirements. In fact, the behavior of a slender column is mostly governed by the stability limit states. In an attempt to construct ever-stronger and ever-lighter structures, many engineers currently design slender high strength columns with variable cross sections and various end conditions. Even though buckling behavior of uniform columns with ideal boundary conditions have extensively been studied, there are limited studies in the literature on buckling analysis of nonuniform columns with elastic end restraints since such an analysis requires the solution of more complex differential equations for which it is usually impractical or sometimes even impossible to obtain exact solutions. This paper shows that variational iteration method (VIM) can successfully be used for this purpose. VIM results obtained for columns of constant cross sections, for which exact results are available in the literature, agree with the exact results perfectly, verifying the efficiency of VIM in the analysis of this special type of buckling problem. It is also shown that unlike exact solution procedures, variational iteration algorithms can easily be used even when the variation of column stiffness along its length and/or the end conditions are rather complex.