Yield line theory and concrete plasticity

Abstract

This paper reviews the relationship between yield line theory, developed for reinforced concrete slabs by Johansen in the 1930s and 1940s, and limit analysis, formulated by the Hodge–Hill–Prager school around 1950. Recalling work from the 1970s, it is shown that not only is yield line theory fully compatible with limit analysis, but the Johansen ‘stepped’ yield criterion is in fact the only yield condition for the slab that allows coinciding upper and lower bounds in the sense of limit analysis to be derived by yield line theory. The yield condition for an arbitrarily reinforced slab is reproduced in closed form, obviating the need for coordinate transformations, and allowing the permissibility of stress states to be checked for anisotropic slabs with non-coinciding principal directions of top and bottom reinforcement.