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Title: Developing a polyhedral graphic statics formulation for tetrahedral truss systems
This paper presents procedures to generate truss topologies as an input form for polyhedral graphic statics and develops an algebraic formulation to construct their force diagrams. The study's ultimate goal is to extend the authors' previous research in 2D [1] to generate 3D strut-and-tie models and stress fields for reinforced concrete design. The recent algebraic formulation constructs reciprocal polyhedral diagrams of 3D graphic statics with either form or force as input [2]. However, the input is usually a set of polyhedrons or self-stressed networks [3]. Another implementation of polyhedral graphic statics [4] includes general truss topologies. But the starting geometry is usually the global force diagram, and based on its modification or subdivision, a form diagram is constructed. Therefore, currently, there exists no formulation to analyze a spatial truss using polyhedral graphic statics. This paper develops an algorithm to build upon the algebraic 3D graphic statics formulation and notation [2, 5] to construct the force diagram for input geometries that do not include all closed cells. The article also shows how the proper definition of the external spaces between the applied loads and reaction forces and the tetrahedral subdivision of the truss makes it possible to construct the reciprocal force diagram. more » This technique can be further explored to generate various truss topologies for a given volume and identify an optimized solution as the strut-and-tie model for reinforced concrete. Figure 1 illustrates an example of a spatial truss with two vertical applied loads and four vertical supports, the subdivision of the inner and outer space, the constructed force diagram, and the Minkowski sum of the dual diagrams (i.e., the geometrical summation of the form and scaled force diagram). « less
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International Association of Shell and Spatial Structures
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National Science Foundation
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