Effects of thermal gradients on membrane stresses in thin slabs
The Building Research Establishment (BRE) of the United Kingdom has developed a simple design method for the determination of the capacity of composite slabs in fire. The method, based on ambient temperature large-deflection plastic theory, predicts the capacity by calculating the enhancement added by tensile membrane action to the theoretical yield-line load of the slab. Tensile membrane action is a load-carrying mechanism experienced by thin slabs undergoing large vertical deflections, where stretching of the midplane produces a central area of tensile force balanced by a peripheral ring of compressive force. The use of this mechanism in structural fire engineering introduces safety and economy, as a large number of floor beams can be left unprotected. The method, developed on the assumption that the slabs are simply-supported, also assumes that the development of the tensile membrane mechanism is maintained at elevated temperatures. An analytical procedure for the determination of this membrane capacity has recently been developed by the University of Edinburgh. It argues that the development of tensile membrane action at elevated temperatures differs from that at ambient temperature, and that the tensile forces developed in the centre of the slab can only be balanced by sufficient anchorage along the slab’s boundaries. Experimental investigations on large-deflection behaviour of simply-supported slabs at ambient and elevated temperatures, conducted at the University of Sheffield, have confirmed the variation in the mechanism at ambient and elevated temperatures, but have identified that the load-carrying capacity can be effectively developed without the horizontal anchorage along the slab’s boundaries. These observations have led to the belief that thermal gradients, acting alone through the depth of the slab, can induce considerable amounts of tensile membrane action. This paper therefore investigates this phenomenon in simply-supported thin slabs. It examines displacements and stresses developed at ambient and elevated temperatures, using the Rayleigh-Ritz approach. Good comparisons are made with finite element analyses.