Thermal Response to Fire of Insulated Cylindrical Steel Elements
Standard calculation methods are used in current design practice in the United States to determine the fire resistance rating of structural steel elements protected with spray-applied fire resistive materials (SFRMs). These calculation methods are based on simplified analysis of heat transfer through the SFRM material to the steel substrate. This analysis assumes one-dimensional heat transfer in Cartesian coordinates, i.e., a flat plate. Based on this analysis, the ratio of the weight per unit length to the surface area per unit length, expressed in terms of the 'W/D ratio,' is the governing parameter for heating of the steel element. For cylindrical rods, such as those used in steel bar joists, and other small structural shapes, this analysis is inappropriate because the surface area of the insulated element increases with increasing insulation thickness, thus increasing the surface area for heat transfer to the insulated assembly. Simplified and detailed numerical heat transfer analyses have been performed in both Cartesian and cylindrical coordinates that demonstrate the reduced level of fire resistance associated with a given thickness of insulation on a cylindrical rod relative to a wide-flange element with the same W/D ratio.