Simple analytical models for restrained steel columns in fire

•The behaviour of restrained columns in fire is analysed by means of two simple models, accounting for all nonlinearities.•These models are the adapted Shanley model and a two rods system joined by a plastic hinge.•The methodologies enable a simple and easy strategy to compute the critical temperature within a minimum error. In structural engineering, two distinct types of computational strategies can be used to analyse a frame under the action of forces. The first type applies to any general structure and incorporates all involved complexities in the mathematical model. It aims to represent as accurately as possible all involved phenomena and leads usually to very complex numerical models, such as the Finite Elements ones. In contradistinction to this, the alternative strategies adopt simple but representative mathematical models that focus on a specific phenomenon. Despite their limited range of application, simple mathematical models enable an easier analysis of the key phenomena without forfeiting accuracy. They also provide a good depiction of the true physical response. Within this latter context, the present work presents two simplified structural models for the analysis of restrained elasto-plastic steel columns under fire conditions: i) an adapted Shanley model and ii) a two rigid rods frame joined by a plastic hinge. Only uniform heating is considered, as reference, and all nonlinear properties are taken into account, namely the degradation of the steel’s properties with heating, the nonlinear constitutive behaviour and the instability effects arising from the restraining of the thermal elogation. These two models enable the computation of the critical temperature, which defines the column’s strength in case of fire, with minimum effort and within an acceptable accuracy.