This paper presents procedures for the generation of strut-and-tie models and stress fields for structural concrete components using the techniques of topology optimization and graphic statics. Strut-and-tie models are principally the discretized stress field patterns that rigorously simplify the dimensioning and detailing of reinforced concrete members. Over the past twenty years, extensive research has been carried out on the development of methodologies to mainly produce two-dimensional strut-and-tie models based on flow of stresses within a structure. The generation of stress field patterns currently relies on finite element analysis and topology optimization methods. This research addresses the limitations of topology optimization algorithms in producing reasonable strut-and-tie configurations. For example, in the case of continuum topology optimization, translation of the material distribution layout to a workable truss geometry is not trivial and may require iterations.
On the other hand, the method of graphic statics proved to be helpful in the generation of in-equilibrium truss patterns including a visual representation of force magnitudes or constant stresses in truss elements. This study will also highlight the potentials of using algebraic formulation of graphic statics in the creation of appropriate truss models and examines the reciprocal characteristics of the form and force diagrams for the visualization of their corresponding stress fields.
This research has established computational procedures to utilize graphic statics and discrete truss topology optimization (i.e. ground truss optimization) methods independently or cooperatively to create suitable truss models and stress fields for two-dimensional cases. The computational routines for three-dimensional problems are the work in progress and the challenges of the effort will be addressed. The examples presented in this article demonstrate the capabilities of the mentioned methods to produce the desired results for two- and three-dimensional scenarios.