Analytical study on the distribution of temperature and bearing strength of slim-floor beams under fire

In this paper, a detailed analytic solution of the 1-D heat equation is presented to determine the distribution of temperature within a steel section integrated into a concrete slab, known as composite slim-floor beams (CoSFB). At first, the previous studies about the thermo-mechanical behavior of the slim-floor beams in the scale of experimental campaigns and numerical modeling have been investigated. Then, an analytical method, function of space and time, is suggested to determine the temperature distribution within the SFB section. Therefore, a steel section integrated into a concrete slab which is subjected to a time-dependent heat flux according to the standard fire curve will be examined. The proposed method is an analytical solution of the general form of the heat equation for transient conduction that simplified in order to calculate the load bearing resistance of SFB. This non-homogeneous differential equation is solved by applying the method of variation of parameters, setting up a homogenous problem and applying the separation of variables to get the homogeneous system. Hence, according to the results of FE modeling, the method has been based on assumptions to retain the accuracy of the calculations as well as to reduce the complications in the analytical method. At last, the results of the simplified analytical solution are compared with the numerical simulation, which confirms the logical process. Contrary to numerical methods, the newly proposed method can pragmatically be solved the heat equation with the moving boundary.