Direct evaluation of fire resistance for restrained steel columns in frames using consistent rigid-plastic models and energy formulations

•Consistent rigid-plastic models are developed to determine the collapse temperature of restrained steel columns in fire.•The M−N interaction is considered for the plastic devices, modelled as pure plastic hinges or as “exact” plastic piston-hinge devices.•The degradation of the mechanical properties with heating is accounted for.•The developed methodologies excel in predicting the column’s collapse temperature. The paper develops a simple and expeditious numerical methodology to evaluate directly the resistance of restrained steel columns in fire conditions. During fire, the column expands due to heating and a compressive restraining force is applied by the surrounding frame, which makes the column prone to buckling. Besides, the column’s mechanical properties degrade with heating. The column’s resistance in fire is defined by its collapse temperature, at which the column is no longer capable to carry the serviceability load applied prior to the fire event. The collapse temperature occurs deeply in the plastic range, along the thermal post-buckling path. Based on the critical thermal buckling mode, a plastic mechanism is adopted to represent the column at collapse. This plastic mechanism is analysed by means of a consistent energy formulation. The methodology is able to represent a wide range of cases in practice, such as longitudinal gradients of temperature, general supporting conditions, any level of longitudinal restraining stiffness and a serviceability load with any adequate magnitude. The expeditious procedure computes the collapse temperature always within a small and acceptable error when compared to more sophisticated numerical tools – in some cases, it surpasses commercial Finite Element packages and it is always much more precise than the simplified method presented in the European code of practice. Predictably, it will become a quite useful tool at the engineering office.