Column Effective Length considering the Inter-Story Interaction

Abstract

Through an analysis of a simple two-story frame, this paper revealed that the assumptions used in conventional effective length method led to an unrealistic distribution of beam restraints among the connected columns. With three assumptions of the conventional approach discarded, a new approach is proposed by which column effective length considering inter-story interaction can be obtained in unbraced two- or three-story frames. A quadratic equation for two-story frames and a cubic equation for three-story frames are derived from which the rotational restraints provided to each column may be solved and the effective length factors can then be determined by the traditional formula or tables. For frames of more than 3 stories, the weakest story is selected and a three-story sub-assemblage including the weakest column is taken out, and the proposed method is applied, the effective length of the weakest column is thus obtained, the effective length of the remaining columns are computed through a predefined relations. Because the sub-assemblage included beams at far ends of the columns above and below the column under consideration, the far end condition (hinged or fixed) may be considered easily.