Temperature prediction for contour-insulated concrete-filled CHS subjected to fire using large time Green’s function solutions

An accurate numerical approach is developed in this paper for thermal analysis of contour-insulated concrete-filled circular hollow sections subjected to fire, based on analytical solutions of transient diffusion equations in radial coordinate system obtained using the Green’s function approach. The steel layer is conveniently treated as a thin film with lumped heat capacitance, i.e. the temperature distribution inside the steel section is assumed to be uniform. Perfect contact conditions are assumed at both of the insulation–steel and the steel–concrete interfaces. Solutions of the heat equations are represented by large time series expansions obtained from homogeneous boundary conditions using the eigenfunction approach. The time-varying boundary conditions, i.e. the fire conditions are incorporated in terms of Stieltjes integral by means of Duhamel’s theorem. Numerical models are developed using temporal discretization, while no spatial discretization is required since spatial variables are analytically tractable. The proposed numerical scheme is not restricted to any specific fire conditions, and can be used in conjunction with parametric fire as proposed in the Eurocode.