The effective length factor is a familiar concept for practicing engineers and has long been an approach for column stability evaluations. Neglecting the effects of axial force in the restraining members, in the case of sway prevented frames, is one of the simplifying assumptions which the Alignment Charts, the conventional nomographs for K-Factor determination, are based on. A survey on the problem reveals that the K-Factor of the columns may be significantly affected when the differences in axial forces are taken into account. In this paper a new iterative approach, with high convergence rate, based on the general principles of structural mechanics is developed and the patterns for detection of the critical member are presented and discussed in details. Such facilities are not available in the previously presented methods. A constructive methodology is outlined and the usefulness of the proposed algorithm is illustrated by numerical examples.