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.

中文翻译：

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考虑柱间相互作用的阶梯柱屈曲

摘要 现行设计规范规定的阶梯柱有效长度系数不适用于某些情况，如多开间框架和斜屋顶门式框架，因为柱之间的相互作用和屋顶的影响。不考虑倾角。本文提出了一种简单但准确的手工计算方法来评估框架阶梯柱的有效长度因素和二阶效应。在这种方法中，首先确定阶梯柱的负侧向刚度表达式，然后在考虑柱间相互作用的影响下确定有效长度因子。然后进行理论分析以评估二阶效应，并开发了计算挠度和力矩放大系数的表达式。还介绍了一种用于考虑带阶梯柱的框架屋顶倾角影响的实用方法。所执行的特征值和非线性静态分析的结果证明了所提出方法的有效性。基于所提出的分析，提出了改进当前设计规范的建议。最后，确定一些常见情况的关键因素αs0 和αsN 的值。研究结果将有助于在工厂建筑中开发可靠且具有成本效益的阶梯柱设计。提出了改进当前设计规范的建议。最后，确定一些常见情况的关键因素αs0 和αsN 的值。研究结果将有助于在工厂建筑中开发可靠且具有成本效益的阶梯柱设计。提出了改进当前设计规范的建议。最后，确定一些常见情况的关键因素αs0 和αsN 的值。研究结果将有助于在工厂建筑中开发可靠且具有成本效益的阶梯柱设计。