Development and Modification of Yield Line Patterns in Thin Slabs Subjected to Tensile Membrane Action

It is widely recognized that composite floor slabs experiencing large displacement develop a central zone of hydrostatic membrane tension, surrounded and equilibrated by a ring of membrane compression around the periphery. This mechanism, known as tensile membrane action, can greatly enhance the load-bearing capacity of a slab compared with that defined by yield line analysis. This is a very useful effect in cases where large deflections can be accepted, particularly in fire-resistance design of composite slabs, since the strength enhancement permits some beams to be left unprotected. Studies of tensile membrane action in the 1960s led to the development of several methods to define slab load capacity under large displacement. The method due to Hayes [5] has become the most widely accepted, and was adopted by Bailey [1, 2] in developing the BRE method for fire-safe design of composite floors. Based on observations from the Cardington fire tests and on assumptions concerning yield line patterns and membrane stresses, it calculates the load-carrying enhancement of a slab as a function of its deflection [2]. It also postulates a deflection limit at which the maximum acceptable strain in the rebar is reached. On close examination, however, several hypotheses, such as the assumed failure mechanisms, seem illogical. The BRE method assumes that a common observation, of a through-depth crack forming across the central short-span of the slab, represents the limit state for such slabs. However, it has been observed that similar cracks can also appear at the intersections of the yield lines, or even not appear at all [3]. This paper proposes a simple way to define the deflection at which the through-depth crack forms, and where on the slab it appears. Based on consistent kinematic assumptions, it calculates the tensile stresses at key points of the slab [4], and predicts the position and displacement at which through-depth cracking occurs.