Calculation of tensile membrane effects of concrete slabs

Significant experimental and theoretical research work showed that, concrete slabs at large vertical displacements could support loads considerably greater than those calculated by the well-established yield-line approach. The mechanism for supporting the load was shown to be tensile membrane action, which could form within the slab irrespective of whether it was restrained or unrestrained horizontally at its boundaries. Most of these research works were based on work method. Combining of previous research work and segment equilibrium method, Bailey (2001) proposed a simplified design method, which took account the membrane action of composite floor slabs at large displacements. This model considered the slab with no in-plane horizontal restraint at its edges, can carry a load greater than that calculated using normal yield-line theory, is partly due to in-plane tensile stresses developing at the centre of the slab and partly due to the increase in yield moment in the outer regions of the slab, where compressive stresses occur. The enhancement included two parts, one is due to membrane action and another is due to membrane forces, of yield line load for each element. Typically the enhancements of 2 elements are not equal, and the difference was explained by the effects of vertical shear or the in-plane shear. Because Bailey's theoretical derivation was based on in-plane resultant moment equilibrium equations, and assumed the fracture failure model of reinforcements occurred through the depth of the slab across the short span at first, so it is not unified with the yield-line theory, and may lead to tedious calculations. Based on the additive decomposition theory of deformation gradients, this paper presents an energy-based model to determine the limit carrying capacity of concrete slab at large displacement, which considered the membrane effects and unified with the conventional plastic line theory. The model could predict the load-carrying capacity of either rectangular or square concrete slabs with both orthotropic and isotropic reinforcement, and could interpret why for similar reinforcement the square slabs always fail at a lower vertical displacement compared to the rectangular slabs, and the reason of fracture of reinforcement along the short span of rectangular slab. Comparison between the developed model and test results shows good correlation.