The effect of a shear bond in the Rankine method for the fire resistance of RC columns

The Rankine formula has been adopted by many natural codes for designing columns and frames at ambient temperature. The method had recently been adapted for structural fire resistance prediction by Tan and co-workers [Tang CY, Tan KH. Basis and application of a simple interaction formula for steel frames under fire conditions. J Struct Engrg ASCE 2001;127(10):1206–13; Tang CY, Tan KH, Ting SK. Basis and application of a simple interaction formula for steel columns under fire conditions. J Struct Engrg ASCE 2001;127(10): 1214–20; Tan KH, Tang CY. Interaction formula for reinforced concrete columns in fire conditions. ACI Struct J 2004;101(1):19–28; Tan KH, Tang CY. Interaction model for unprotected concrete filled steel columns under standard fire conditions. J Struct Eng 2004;130:1405–13]. The conventional Rankine method considers a linear interaction of two failure modes: plastic squashing and linear elastic buckling, ignoring the coupling interaction between the two modes. Consequently, the conventional method gives lower bounds to actual failure loads. This paper discusses the physical meanings of the Rankine approach and the effect of coupling interaction (termed “shear bond” for consistency with our earlier publications) between the collapse modes on the ultimate failure load. The purpose is to demonstrate that the Rankine method is a conservative, robust, and rational method for the structural design of columns under either ambient or elevated temperatures. The approach can be further adapted to provide more accurate failure load predictions by incorporating the shear bond effect into the Rankine formula. Material deterioration at elevated temperature and the resulting effects on the strength and stability of columns are also quantified. A computer code (SAFIR), developed at the University of Liege, was used to calibrate the modified Rankine method.