On the use of Bernstain-Bézier functions for modelling the post-fire stress-strain relationship of ultra-high strength steel (Grade 1200)

Ultra-high strength steels (UHSS) have significant potential applications in the engineering fields due to their unique specifications. In recent years, it has been experimentally shown that the post-fire stress-strain response of this material is highly dependent on the maximum steel temperature and the sustained load applied to it during fire. This paper employs the Bernstain-Bézier functions to present the relationship between the stress, strain, the maximum fire temperature and the sustained axial load ratio (β) for Grade 1200 UHSS cooled for fire temperatures to room temperature. The experimental results are used to verify and validate the proposed model throughout the paper. The model showed to be capable of not only interpolating the stress-strain curves, but also extrapolating them out of the range of the available experimental tests data. Also, taking advantage of the stress-strain-temperature response of the UHSS tested at elevated temperatures, the instantaneous stress-induced strain and consequently the creep strain of UHSS subjected to different constant sustained load values during transient fire are obtained.