Abstract
AbstractAlthough 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.
Highlights
KEYWORDS Airy stress function, graphic statics, reciprocal diagrams, reinforced concrete, stress fields, structural analysis and design, strut-and-tie models, yield line patterns
This article has highlighted the potential of graphic statics and its associated geometrical constructions as a design and analysis tool for the direct creation of discrete 2D and 3D stress fields, and compatible yield line mechanisms in reinforced concrete structures (Figure 18)
It has been shown how several important engineering problems related to reinforced concrete can be solved using reciprocal polyhedral Airy stress functions
Summary
KEYWORDS Airy stress function, graphic statics, reciprocal diagrams, reinforced concrete, stress fields, structural analysis and design, strut-and-tie models, yield line patterns In analogy to the approach of generating discrete stress fields explained, it is possible to define yield line patterns using form and force diagrams and reciprocal stress functions (Section 2.1).
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