Predicting equation of quasi-static and dynamic failures of steel columns under fire

•Critical axial restraint stiffness ratio (βl,cr) was defined to differentiate quasi-static and dynamic failures of columns under fire.•Effects of sectional width-thickness ratio b/t, length–width ratio D/B, sectional size, axial load ratio, and bending moment load ratio on βl,cr were numerically investigated.•Dynamic effects and βl,cr of box-section steel columns both increase with the enlargement of b/t, D/B or sectional size.•Effect of bending moment load ratio on dynamic effects of column failure is negligible.•A predicting equation of βl,cr was proposed for steel columns under fire. Steel columns may fail in dynamic or quasi-static types under fire. The quasi-static failure of steel column could be considered as gradual column removal in the collapse assessment of structures, while the dynamic failure cannot. Hence, it is meaningful if the failure type of the column could be predicted. To identify the failure types of box-section steel columns under fire simply, this paper adopted a validated numerical model to conduct a systematic parametric analysis. The critical axial restraint stiffness ratio (βl,cr), which is used to predict the failure type of columns under fire conditions, is the main focus. Firstly, the values of βl,cr of columns with a representative section were studied, with various slenderness ratios and load ratios being considered. Then, the effects of width-thickness ratio, length–width ratio, sectional size, and bending moment load ratio on βl,cr were studied. The results indicate that βl,cr of columns with the representative section increases with the rise of the load ratio, and increases sharply after the load ratio exceeds a certain level. Besides, the dynamic effect during column buckling and βl,cr both increase with the rise of either the width-thickness ratio, length–width ratio, or sectional size. Moreover, based on the results, a predicting equation for βl,cr of box-section steel columns was proposed. The failure type of a steel column under fire can be easily predicted by the proposed equation. Finally, the proposed equation was verified by an additional series of case studies, and good agreement was achieved.