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On the equilibrium of funicular polyhedral frames and convex polyhedral force diagrams |
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| Affiliation: | 1. Institute of New Imaging Technology, Universitat Jaume I, Castellón, Spain;2. I3BH, Universitat Politècnica de València, Valencia, Spain;3. Texas A&M University, Zachry Department of Civil Engineering, USA;4. Dpto. Ingeniería Mecánica y Construcción, Universitat Jaume I, Castellón, Spain;1. Department of Mechanical Engineering, Yokohama National University, Japan;2. JGC ?Corporation, Japan;3. IHI Corporation, Japan;1. Key Laboratory of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China;2. School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China;3. Chair of Structural Design, Institute of Technology in Architecture, ETH Zürich, 8093 Zürich, Switzerland;1. KU Leuven, Faculty of Engineering Science, Department of Architecture, Kasteelpark Arenberg 1 - box 2431, 3001 Leuven, Belgium;2. Vrije Universiteit Brussel, Faculty of Engineering, Department of Architectural Engineering, Belgium;3. ETH Zurich, Institute of Technology in Architecture, BLOCK Research Group, Switzerland;4. KU Leuven, Faculty of Engineering Science, Department of Civil Engineering, Belgium |
| Abstract: | This paper presents a three-dimensional extension of graphic statics using polyhedral form and force diagrams for the design of compression-only and tension-only spatial structures with externally applied loads. It explains the concept of 3D structural reciprocity based on Rankine’s original proposition for the equilibrium of spatial frames. It provides a definition for polyhedral reciprocal form and force diagrams that allows including external forces and discusses their geometrical and topological characteristics. This paper furthermore provides a geometrical procedure for constructing a pair of reciprocal polyhedral diagrams from a given polyhedron representing either the form or force diagram of a structural system. Using this method, this paper furthermore suggests a design strategy for finding complex funicular spatial forms in pure compression (or tension), based on the construction of force diagrams through the aggregation of convex polyhedral cells. Finally, it discusses the effect of changes in the geometry of the force diagram on the geometry of the form diagram and the distribution of forces in it. |
| Keywords: | Three-dimensional graphic statics Reciprocal diagrams Spatial systems of forces Convex force polyhedra Rankine’s principle of equilibrium of polyhedral frames |
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