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.
