Buckling of stepped columns considering the interaction effect among columns

Abstract

The effective length factors of stepped columns, as provided by the current design codes, are not suitable for certain situations, such as multi-bay frames and pitched-roof portal frames, because the interaction effect among the columns and the influence of the roof inclination angle are not considered. This paper proposes a simple but accurate hand calculation method to evaluate the effective length factors and second-order effects on framed stepped columns. In this approach, the expression of the negative lateral stiffness for stepped columns is first determined and then used to determine the effective length factors considering the interaction effects among columns. This is followed by a theoretical analysis to evaluate second-order effects, and expressions for calculating the deflection and moment amplification factors are developed. A practical method to account for the influence of the roof inclination angle for frames with stepped columns is also presented. The results of the performed eigenvalue and nonlinear static analyses demonstrate the validity of the proposed method. Based on the presented analysis, recommendations are made for the improvement of current design codes. Finally, the values of the key factors, αs0 and αsN, for some common cases are determined. The findings will assist in the development of reliable and cost-efficient designs of stepped columns in mill buildings.