Applications of graphic statics to analysis and design of reinforced concrete: Stress fields and yield lines

Abstract

© Fédération Internationale du Béton – International Federation for Structural Concrete. Graphic statics can be effectively used for the analysis and design of structures in static equilibrium and for solving engineering problems related to specific materials, most notably, reinforced concrete. In this regard, methods for the construction of stress fields and yield lines, based on the theory of plasticity, are particularly valuable; however, their automation and generalisation to the third dimension are still open research topics. This paper introduces a unified method based on graphic statics for the generation of discrete stress fields of 2D and 3D reinforced concrete structures and the definition of admissible yield line patterns in concrete slabs. The presented approach relies on the construction of reciprocal stress functions, and the link between form and force diagrams through Minkowski sums.