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Abstract

The finite Fourier sine transform method was used in this work to solve the elastic buckling problem of thin-walled beams for the case of pinned ends, and uniform moments applied at the ends. The problem is a boundary value problem given by a fourth order ordinary differential equation and Dirichlet boundary conditions at the pinned ends. The Dirichlet boundary conditions at the pinned ends make the finite Fourier sine transform method ideally suited for the solution. The transformation of the governing domain equation converted the problem to an algebraic eigen-value problem. The condition for nontrivial solution was used to obtain the characteristic buckling equation as a fourth degree polynomial. The eigen-values of the characteristic buckling equation were used to obtain the n buckling moments. The critical buckling moment was found to correspond to the first buckling mode. The expressions obtained for the n buckling modes and the critical buckling moment were identical to those by other researchers who used other methods of analysis.