On torsional buckling of thin walled I columns with variable cross-section

Abstract

The problem of extreme critical conservative loads of torsional buckling for axially compressed thin walled I columns with variable, within given limits, bisymmetric cross-section, is considered. Basing on the Pontryagin's maximum principle, it has been shown that the critical load of a column with variable cross-section may exceed the bounds defined by critical loads for columns with constant extreme cross-section. On the other hand the extreme loads for flexural buckling are the critical ones for columns with extreme constant cross-section. In the numerical example, enclosed, the extreme critical loads for simply supported I column with variable width of flanges and corresponding optimal shapes of flanges are the object of analysis. Moreover, it has been shown that these bifurcation points are symmetric and stable.