Unified geometrical framework for the plastic design of reinforced concrete structures

Although the analysis and design of structures in static equilibrium can be intuitively carried out using simple equilibrium-based methods such as graphic statics, the application of these methods to engineering problems that take into consideration specific material properties is generally limited. Within the domain of reinforced concrete, existing geometric approaches for developing stress fields and yield lines based on the theory of plasticity are especially useful. However, these approaches usually rely on iterative constructions and are generally limited to two-dimensional cases. By taking advantage of graphic statics, this article introduces the theoretical basis for an entirely geometrical method to generate discrete stress fields and yield line patterns in two- and three-dimensional reinforced concrete structures. The proposed approach is based on the use of reciprocal stress functions and the relationship between form and force diagrams.