Solution of the Generalised Elastic Column Buckling Problem by the Galerkin Variational Method
Journal Title: International Journal for Research in Applied Science and Engineering Technology (IJRASET) - Year 2017, Vol 5, Issue 1
Abstract
In this paper, a system of three differential equations describing the generalized elastic column buckling problem for axial compressive load, Nx acting through the centroid of the cross-section; and such that the bimoment is zero is solved by the Galerkin variational method for columns with two pinned ends. The problem was found to reduce to an algebraic eigen-value problem for which the characteristic buckling equation was found. Two specializations of the buckling problem – doubly symmetric cross-sections and singly symmetric cross-sections were considered. For doubly symmetric cross-sections, it was found that the buckling modes are uncoupled resulting in three possibilities for the failure – Euler flexural buckling failure load in the z axis, Euler flexural buckling failure load in the y axis and the critical load in torsional buckling. The least value of the three buckling loads governs the buckling mode of failure. For columns with singly symmetric cross-sections, one of the governing equations becomes uncoupled while the other two become coupled. The characteristic buckling equation shows the column can fail by Euler flexural buckling in the yy direction and torsional – flexural buckling mode. The values of the buckling load (eigen-values) obtained using the Galerkin variational method were found to be identical with solutions for the same problem obtained in the literature using the method of undetermined parameters.
Authors and Affiliations
Ike C. C. , Nwoji C. U. , Ikwueze E. U. , Ofondu I. O.
Keywords
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