Buckling lengths of steel circular arches respecting non-uniform arch axial forces

Abstract

The non-dimensional buckling length factors of circular arches under various support conditions, different types of uniform loadings and closed or open cross sections are presented. The extensive numerical study based on the linear bifurcation analysis (LBA) respected the relevant variable distribution of axial arch forces for determination of the buckling length factors which are related to the maximal (support) axial arch forces used as a constant in the fictitious Euler‘s strut. Various aspect ratios H/L (the arch rise to the arch span) in the range of 0.1 ≤H/L≤ 0.5 are studied. While the in-plane stability (and the respective buckling length factors) are nearly independent on the arch cross-sections, the out-of-plane stability (and respective buckling length factors) strongly depends on both the support conditions and the ratio of the second moment of area about horizontal axis and St. Venant torsional constant of the arch cross sections. The results are presented in the graphs and the received data may serve for a preliminary or simple design of steel arches using the relevant interaction formulas covering elastic–plastic behaviour and required imperfections.