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        8 Yield Line Theory

        8.1 The essentials

        Yield Line Design is a well-founded method of designing reinforced concrete slabs, and similar types of elements. It uses Yield Line Theory to investigate failure mechanisms at the ultimate limit state. The theory is based on the principle that:

        work done in yield lines rotating = work done in loads moving

        Yield Line Design is easy to grasp but there are several fundamental principles that need to be understood. Yield Line Design is a plastic method: it is different from ‘normal’ elastic methods.

        8.1 .1 A short history of Yield Line Theory

        Yield Line Theory as we know it today was pioneered in the 1940s by the Danish engineer and researcher K W Johansen.

        As early as 1922, the Russian, A Ingerslev presented a paper to the Institution of Structural Engineers in London on the collapse modes of rectangular slabs. Authors such as R H Wood, L L Jones, A Sawczuk and T Jaeger, R Park, K O Kemp, C T Morley, M Kwiecinski and many others, consolidated and extended Johansen’s o riginal work so that now the validity of the theory is well established making Yield Line Theory a formidable international design tool.

        In the 1960s 70s and 80s a significant amount of theoretical work on the application of Yield Line Theory to slabs and slab-beam structures was carried out around the world and was widely reported.

        To support this work, extensive testing was undertaken to prove the validity of the theory. Excellent agreement was obtained between the theoretical and experimental Yield Line patterns and the ultimate loads.

        The differences between the theory and tests were small and mainly on the conservative side. In the tests where restraint was introduced to simulate continuous construction, the ultimate loads reached at failure were significantly greater than the loads predicted by the theory due to the beneficial effect of membrane forces.

        8.1 .2 What is a yield line?

        A yield line is a crack in a reinforced concrete slab across which the reinforcing bars have yielded and along which plastic rotation occurs.

        8.1 .3 What is Yield Line Theory?

        Yield Line Theory is an ultimate load analysis. It establishes either the moments in an element (e.g. a loaded slab) at the point of failure or the load at which an element will fail. It may be applied to many types of slab, both with and without beams. Consider the case of a square slab simply supported on four sides as illustrated by Figure 8.1.1. This slab is

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