Calculation of Effective Lengths and Effective Slenderness Ratios of Stepped Columns

The analysis of stepped columns arises in the design of heavy mill buildings. Such columns are generally loaded at the top and at the section where the cross section changes. The application of the AISC Specification requires that the engineer determine the effective length of each section of the column. This is a problem in elastic stability theory, and the results are dependent not only on the end fixities, but also on the ratio of the end axial load to the intermediate axial load, the ratio of the length of the upper segment to the length of the lower segment, and the ratio of the upper moment of inertia to the lower moment of inertia. In this paper the authors have extended the analysis to three cases of practical interest, not previously considered. Consistent non-dimensional characteristic equations are given for all five cases.