Distribution of temperature in steel and composite beams and joints under natural fire

The present article describes the existing methods and recommendations for the evaluation of temperature profiles in steel beams and joints covered by a concrete slab. Then, modifications and improvements to the existing methods are proposed in order to predict more accurately temperatures at the level of the top flange of the beam by accounting for heat fluxes between the steel elements and the concrete slab.
The two methods presented in this article differ by the degree of simplicity, the field of applicability and the accuracy of the predicted results. Comparisons with numerical simulations
performed in the finite element program SAFIR have been described for the validation of these new methods. It is assumed in these numerical models that the contact between the steel
profile and the concrete slab is perfect.
The “original” Lumped Capacity Method gives globally good predictions of temperature in steel and composite beams and joints but does not integrate heat fl uxes between the steel elements and the concrete slab. This leads to an over-estimation of temperature in the steel elements during the heating phase and to an under-estimation of temperature during the cooling phase. In order to take these fluxes into consideration in the evaluation of the top flange temperature, it is suggested in the first proposed method to integrate a part of the concrete slab into the heated surface or volume considered in the Lumped Capacitance Method. The Composite Section Method correctly predicts temperature at the level of the top flange under ISO fire or during the
heating phase of parametrical fire curves but a delay is observed between these analytical results and those obtained from numerical simulations performed in SAFIR software. In
a second method, called Heat Exchange Method, it is proposed to calculate separately the heat fluxes between, on one side, the top flange and, on the other side, the gases of the compartment, the rest of the steel section and the concrete slab. The temperatures given by this latter method are in very good agreement with those obtained from FE models.
The use of this method is really less fastidious than the use of FE models, especially for joints, but is limited to a certain type of fire curves (parametrical fire curves defined in the Annex A of the EN 1991-1-2).
Finally, a bilinear temperature profi le has been proposed to interpolate the analytically-calculated temperatures at the level of the top and bottom flanges on the total height. This procedure is simple and shows a good agreement with the numerical results in 2-D beam sections and 3-D joint zones during the heating and cooling phases of parametric fire curves.