Yield-line plasticity and tensile membrane action in lightly-reinforced rectangular concrete slabs

The paper provides the systematic derivation of a new analytical approach to tensile membrane action of lightly-reinforced thin concrete slabs at large deflections. The basic motivation for the work comes from the recent use of tensile membrane action as an enhancement, in the fire condition, of the capacity of the thin concrete slabs which are normally made composite with downstand steel beams, at temperatures which have substantially degraded the contribution of these steel beams. The method accepts as a premise that such slabs form a pattern of localized yield lines as an initial small-deflection failure mechanism, and that these yield lines retain their positions as subsequent deflection occurs. As the slab deflects, maintaining the correct kinematics of the articulation and displacement of the system of slab facets, interacting across the yield lines, is extremely important to the horizontal equilibrium of the slab. In this process it becomes necessary to re-think the basic assumption of traditional yield-line theory that any local cross-section of unit width along a yield line equilibrates the force of its concrete compression block with the yielded steel's tension force, producing constant plastic moment capacities for the mesh in either direction along any yield line. In the approach set out in this paper only overall equilibrium of the system of facets needs to be maintained. As in normal rigid-plastic analysis, concrete acts only when compressed, and then at its compressive strength, and steel acts at its tensile yield strength whilst it remains intact. However, steel in either direction can fracture when the local crack-width causes its local strain to exceed its fracture ductility. When the rebar crossing the diagonal yield lines begins to fracture this generally indicates that the slab's capacity is about to reduce with further deflection. The paper does not attempt to address how a rebar's free length across a discrete crack is generated, or the limiting crack widths implied, but this is shown in a range of examples to be a major issue if tensile membrane action is to be used in practice to enhance the capacity of slabs, for example in hazard loading situations. It is important that principles be established in future to quantify this aspect of rebar ductility.