A general theoretical formulation of deformation of steel structures exposed to fire

Abstract

This paper presents a proposal for the formulation of a mathematical model of a fire resistance testing process for steel beams subject to bending, carried out experimentally in a test furnace. The model for the formulation was created with a balance method by describing with the fundamental laws of thermomechanics the phenomena occurring during the experiment analysed for the formulation. The viscoplastic behave our of steel at high temperatures was described with constitutive relationships proposed by Perzyna (which form the so-called “overload model”). The general mathematical model of the experiment analysed, obtained in the form of a system of differential equations, is discussed. The authors considered the impact of known physical properties of the test material and the impact of the results of the observations made during the research on the behaviour of individual terms of the model’s equations. Based on these considerations, simplifications were proposed which optimized the mathematical description and facilitated its adaptation to a special case. As a result of the investigation, a system of equation was obtained which described the processes present during the fire resistance test. It is postulated here to accept the system of equations as the mathematical model. Keywords: thermomechanical analysis, fire resistance test, viscoplastic constitutive laws, Perzyna model