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For vector-based 3D graphic statics, this reciprocity is generally not achieved. This paper presents transformations for vector-based 3D force diagrams that allow the associated 3D form diagram to adjust accordingly, covering global and local manipulations and supporting force-direction and magnitude control as a structural design 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problem does the paper address in vector-based 3D graphic statics?","Question",{"text":112,"@type":113},"It addresses that the reciprocity between form and force diagrams, which exists in 2D graphic statics, is generally not achieved in vector-based 3D graphic statics.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What kinds of transformations are proposed for the 3D force diagram?",{"text":117,"@type":113},"The paper describes two categories: global transformations affecting all elements simultaneously, and local transformations enabling manipulation of individual elements.",{"name":119,"@type":110,"acceptedAnswer":120},"How do the transformations support the structural design process?",{"text":121,"@type":113},"By adjusting the magnitude and direction of forces in vector-based 3D force diagrams, the designer can actively steer load-bearing behavior while the corresponding 3D form diagram adjusts 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net/publication/320101168)  \nVector-Based 3D Graphic Statics: Transformations of Force Diagrams  \nConference Paper · September 2017  \nCITATIONS 12  \nREADS 833  \n4 authors:  \nPierluigi D'Acunto  \nTechnische Universität München 58 PUBLICATIONS 269 CITATIONS  \nJean-Philippe Jasienski  \nUniversité Catholique de Louvain-UCLouvain 15 PUBLICATIONS 109 CITATIONS  \nPatrick Ole Ohlbrock  \nTechnische Universität München 29 PUBLICATIONS 203 CITATIONS  \nCorentin Fivet  \nÉcole Polytechnique Fédérale de Lausanne 108 PUBLICATIONS 671 CITATIONS  \nSome of the authors of this publication are also working on these related projects:  \n Construction with reclaimed materials and goods View project  \n Computational tools for creative structural design View project  \nAll content following this page was uploaded by Pierluigi D'Acunto on 29 September 2017.  \nThe user has requested enhancement of the downloaded file.  \nVector-Based 3D Graphic Statics: Transformations of Force Diagrams  \nPierluigi D’ACUNTO*a, Jean-Philippe JASIENSKIb, Patrick Ole OHLBROCKa, Corentin FIVETc  \n*a ETH Zürich, Institute of Technology in Architecture, Chair of Structural Design,  \nStefano-Franscini-Platz 1, 8093 Zürich (CH)  \ndacunto@arch.ethz.ch  \nb UCLouvain, LOCI – Structures & Technologies  \nc EPF Lausanne, ENAC, Structural Xploration Lab  \nAbstract  \nThe reciprocity between form and force diagrams in 2D graphic statics makes it possible to manipulate the form diagram while directly evaluating the redistribution of the forces within the force diagram. Conversely, after modifying the force diagram, the consequent transformation of the form diagram can be assessed at once. In the case of vector-based 3D graphic statics, the reciprocity between the diagrams is generally not achieved. This paper describes a series of transformations that can be applied to a vector-based 3D force diagram while allowing the corresponding 3D form diagram to adjust accordingly. Two categories of manipulations of the force diagram are described: global transformations that affect simultaneously all the elements of the diagram and local transformations, which permit the manipulation of individual elements of the diagram. Thanks to these transformations, the adjustment of the magnitude and the direction of the forces in vector-based 3D force diagrams can be used as an active operation in the structural design process.  \nKeywords: vector-based 3D graphic statics, 3D force diagram, global transformations, local transformations, parallel transformations, projective transformations, constraint-driven transformations  \n1. Introduction  \nOne of the most peculiar features of 2D graphic statics is the geometric reciprocity between form and force diagrams. This property has been investigated in depth by Maxwell [12], who discussed the case of reciprocal diagrams in which corresponding edges are perpendicular to each other. This has been followed by the findings of Cremona [6], who defined a geometric procedure to generate reciprocal diagrams with corresponding parallel edges. Thanks to the reciprocity of the diagrams, on the one hand, it is possible to manipulate the form diagram and evaluate directly the effects on the distribution of the forces in the force diagram. On the other hand, the magnitude and the direction of the forces can be modified in the force diagram while assessing the resulting transformation of the form diagram. As outlined by Huerta [9], the transformation of the diagrams has been used as a fundamental operation for structural design since the introduction of 2D graphic statics.  \nIn relation to 3D graphic statics, global parallel transformations that preserve the static equilibrium of a given form diagram have been extensively reviewed by Fivet [8], who has also introduced a geometric procedure to deal with non-parallel projective transfo","cbCaik0CH4sfwxol","https://ap.wps.com/l/cbCaik0CH4sfwxol","pdf",1149348,11,"English","# Abstract\n# 1. Introduction","[{\"question\":\"What problem does the paper address in vector-based 3D graphic statics?\",\"answer\":\"It addresses that the reciprocity between form and force diagrams, which exists in 2D graphic statics, is generally not achieved in vector-based 3D graphic statics.\"},{\"question\":\"What kinds of transformations are proposed for the 3D force diagram?\",\"answer\":\"The paper describes two categories: global transformations affecting all elements simultaneously, and local transformations enabling manipulation of individual elements.\"},{\"question\":\"How do the transformations support the structural design process?\",\"answer\":\"By adjusting the magnitude and direction of forces in vector-based 3D force diagrams, the designer can actively steer load-bearing behavior while the corresponding 3D form diagram adjusts accordingly.\"}]","Vector-Based 3D Graphic Statics - Transformations of Force Diagrams | PDF",28]