The Picard’s successive iteration method is applied to determine the Euler critical force for a slender column. The initial approximation of the buckling mode of the column is a polynomial function that satisfies the boundary conditions. A numerical example is solved and the obtained result is compared with that obtained by the Euler formula. An assessment of the accuracy of the solution is made at each iteration step. In the paper is shown that the Picard’s iteration method could also be used for obtaining the closed form exact solution of the buckling load. The investigated column is hinged at its upper end and supported by a Q- apparatus at the other. It is loaded with a compressive force at the upper end.
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