Temperature prediction for multi‐dimensional domains in standard fire

Abstract

SUMMARYThe existing 1D analytical solution for heat conduction inside structural members plays an important role in the estimation of temperature field and prediction of member strength in fire. In this paper, the novelty lies in a set of proposed analytical formulations for the conduction heat transfer within multi-dimensional (2D and 3D) domains subjected to a particular time-varying boundary condition, i.e. the standard fire conditions. Solutions of multi-dimensional conduction are based on the eigenfunction approach using the technique of separation of variables. The multi-dimensional effect is incorporated by the product of respective solutions of 1D transient heat conduction (1D step functions) of the plate and the infinite cylinder that serve as a set of basis for derivation of analytical solutions. Fire boundary conditions are incorporated using the Duhamel's principle, where the time-varying fire temperature curve is imposed on the step functions. In this paper, the boundary conditions of the first and the third kind are considered, respectively. The analytical solutions are compared with results obtained from finite element analysis for verification.

Prediction of the Thermal Contact Resistance at the Steel-Concrete Interface of CFST Columns with Circular Cross-Section

“…Due to the world-wide trend towards the performance-based design approach to buildings, research on structure fire analysis has become increasingly important in recent years. Methods to predict the temperature field of structural components under fire conditions have been developed using different mathematical techniques, including the classical methods of separating the variables [4], Laplace transform [5], Green's function approach [6][7][8], and Galerkin spatial discretization method and fully implicit Crank-Nicolson method [9]. In traditional prescriptive codes, such as EC3 [10] and EC4 [11], the temperature field analyses of the structural members is largely based on empirical relations.…”