Criteria of limiting temperature and parametric analysis of the large deflection behavior for fully restrained steel beams in fire

Abstract

This paper mainly involve 3 parts: 1) To apply the minimum principle of acceleration in dynamics of elastic-plastic continua at finite deformation to the statics problems, a computing model is presented for the restrained steel beams exposed to the fire. In this model, both effects of large deflection and thermal expansion deformation are taken into account, and the constitutive equations with the temperature effects are used. Then a dynamic finite difference (DFD) method is presented by using the discrete technique, which can be used in simulating the response of the steel beams at elevated temperature, and the large deflection behavior and catenary action effects of the beams can be adequately expressed. The primary numerical results show that the method is valid and credible. Compared with other methods, this technique is very simple, and it can also be further developed to simulate the behavior of steel beams subjected to the coupling loading of explosion and fire when both effects of strain rate and inertia are considered. 2) By using this DFD method, detailed parametric analysis are presented so as to check the consistency of response results for several different formulas of thermal expansion deformation and retention factors of steel at elevated temperature, the influence of these parameters on the critical temperature is examined. 3) Based on the analysis for the curves of temperature-generalized yield function comprised by the axial force and bending moment, both criteria to determine the limiting temperature (or failure temperature) of large deflection steel beams are presented more explicitly, that is, both limiting temperatures can be determined by if the catenary force begins to appear or arrives at the maximum value, respectively. It is shown by numerical results that both limiting temperatures are close to the both critical temperatures which are corresponding to the maximum deflections equal to span/20 and span/10, respectively. This conclusion may be helpful to make rational fire resisting design for the steel beams.