Abstract Buckling loads for tapered and stepped columns have been determined by a finite difference method using a matrix iteration solution technique (a BASIC program for which is appended). Errors which can arise with the finite difference approach are discussed namely, that convergence towards the correct buckling load as the number of segment sub-divisions is increased may not be monotonic, that simple averaging of the second moments of area to either side of a change of section is hardly adequate and that correct formulation of the problem using a fourth order differential equation is difficult. It is shown that consistent and correct results can be obtained using only a small number of segment subdivisions coupled with extrapolation procedures. A simple expression is derived for an “effective” value of second moment of area at a change of section.
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