Derivation of a new temperature calculation formulation for heavily fire insulated steel cross-sections

Equations are given in the Eurocode standard EN 1993-1-2 on the estimation of temperature in insulated steel cross sections when assuming uniform steel section temperature, sometimes called a lumped heat capacity assumption. When deriving these equations the temperature of the exposed insulation surface is assumed equal the surrounding fire gas temperature. That is a simplification that may provide inaccurate results for heavily insulated steel sections, when the heat capacity of the insulation is considerably higher than that of the steel section. Therefore, a new lumped mass formulation suited for heavily insulated steel sections is proposed in this paper. It accounts for the heat transfer resistance between the fire and the insulation surface as well as for the heat capacity of the insulation. The accuracy of the predictions made with the proposed new formulation are compared with results of accurate 1-D finite element numerical analyses considering insulation materials with several combinations of thermal properties and thicknesses. Analyses with the proposed formulation is shown to yield accurate and generally on the safe side estimations of steel temperature in comparison to the finite element (FE) calculations. The new formulation is applicable to lightly as well as heavily insulated steel sections.