Calculation of tensile membrane effects of concrete slabs

Significantexperimental and theoretical research work showed that, concreteslabs at large vertical displacements could support loadsconsiderably greater than those calculated by the well-establishedyield-line approach. The mechanism for supporting the load wasshown to be tensile membrane action, which could form within theslab irrespective of whether it was restrained or unrestrainedhorizontally at its boundaries. Most of these research works werebased on work method. Combining of previous research work andsegment equilibrium method, Bailey (2001) proposed a simplifieddesign method, which took account the membrane action of compositefloor slabs at large displacements. This model considered the slabwith no in-plane horizontal restraint at its edges, can carry aload greater than that calculated using normal yield-line theory,is partly due to in-plane tensile stresses developing at thecentre of the slab and partly due to the increase in yield momentin the outer regions of the slab, where compressive stressesoccur. The enhancement included two parts, one is due to membraneaction and another is due to membrane forces, of yield line loadfor each element. Typically the enhancements of 2 elements are notequal, and the difference was explained by the effects of verticalshear or the in-plane shear. Because Bailey's theoreticalderivation was based on in-plane resultant moment equilibriumequations, and assumed the fracture failure model ofreinforcements occurred through the depth of the slab across theshort span at first, so it is not unified with the yield-linetheory, and may lead to tedious calculations.Based on the additive decomposition theory of deformationgradients, this paper presents an energy-based model to determinethe limit carrying capacity of concrete slab at largedisplacement, which considered the membrane effects and unifiedwith the conventional plastic line theory. The model could predictthe load-carrying capacity of either rectangular or squareconcrete slabs with both orthotropic and isotropic reinforcement,and could interpret why for similar reinforcement the square slabsalways fail at a lower vertical displacement compared to therectangular slabs, and the reason of fracture of reinforcementalong the short span of rectangular slab. Comparison between thedeveloped model and test results shows good correlation.