The first order variation of critical buckling load of thin-walled columns with bisymmetric open cross-section due to some variations of the design variables such as: cross-section dimensions, or material characteristics is derived. The considerations are based on the classical linear theory of thin-walled beams with non-deformable cross-section. The influence of the residual welding stresses is taken into account. In the numerical examples dealing with I-column the functions describing the effect of the variation of the dimensions of the flange and some parameters describing the residual welding stresses on the critical load of torsional buckling are found. The linear approximation of the exact relationship of the critical load of torsional buckling due to variations of the design variable is determined and the approximation error is discussed.
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