Graphic Statics and Strut and Tie models


This research investigates procedures for the generation of strut-and-tie models and stress fields for structural concrete components, based on the techniques of layout 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 the flow of stresses within a structure. The generation of stress field patterns currently relies on finite element analysis and optimization methods. This research addresses the limitations of optimization algorithms in producing reasonable strut-and-tie configurations. For example, in the case of 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 the algebraic formulation of graphic statics to create a range 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 algebraic graphic statics and layout 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.


Salma Mozaffari

Masoud Akbarzadeh

Thomas Vogel