Abstract: For a thin-walled box column with varable cross-section, the three governingequations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients, so if is very difficult to solve them bymeans of an analytic method. In this paper, polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differentialequations. Based on the energy principle and the Galerkin’s method the approximateformulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively, and numerical examples are used to verify the correctness of the soltuions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box colunns wiht variable corsssection. This paper is of practical value.

Key words: thin-walled box column with variable cross-section, torsionalflexural buckling, approximate solutions for buckling loads