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Based on Rankine's proposition for equilibrium of polyhedral frames in 1864, this research provides a clear illustration of the theory of reciprocity between form and force diagrams in three dimensions. It explores the geometric relationship between three-dimensional networks to determine the equilibrium of general spatial frames. It extends graphic statics(More)
• Three-dimensional extension of graphic statics using polyhedral form and force diagrams. • Defining the topological and geometrical relationships of 3D reciprocal diagrams. • Design of compression and tension-only spatial structures with externally applied loads. • Designing complex funicular spatial forms by aggregating convex force polyhedral cells. •(More)
This paper introduces scissor-hinged retractable membrane structures, a system for retractable membrane roofs that require a fully retractable supporting structure and multiple stable roof-configurations. A vaulted, foldable, supporting structure is developed consisting of two scissor-hinged frames that can retract towards opposite sides of the space below.(More)
• General, non-procedural approach to graphical analysis of two-dimensional structures. • Equilibrium equations derived from reciprocal relation between form and force graphs. • States of stress of structural systems from analysis of equivalent unloaded networks. • Construction of planar straight-line drawings of planar form graphs. • Computational back-end(More)
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