Three-dimensional graphic statics: Initial explorations with polyhedral form and force diagrams. Issue 2 (June 2016)

• Record Type: Journal Article
• Authors: Akbarzadeh, Masoud; Van Mele, Tom; Block, Philippe
• Other Names: Block Philippe guest-editor.; Fivet Corentin guest-editor.; Van Mele Tom guest-editor.
• Is Part Of: International journal of space structures. Volume 31:Issue 2/3/4(2016)
• Page Start: 217
• Page End: 226
• Publication Date: 2016-06
• Subjects: constrained reciprocal diagrams -- graphic statics procedures -- Rankine's principle of equilibrium of polyhedral frames -- three-dimensional graphic statics; Space frame structures -- Periodicals; Space (Architecture) -- Periodicals; Space (Architecture); Space frame structures; Periodicals; 624.177
• DOI: 10.1177/0266351116660802
• Languages: English
• ISSNs: 0956-0599

Abstract

This article investigates how reciprocal form and force polyhedrons can be used to develop procedures for the design of three-dimensional trusses and funicular structures, analogous to the well-known techniques of graphic statics for two-dimensional structural systems. It demonstrates how global equilibrium of a system of forces can be established by constructing a closed force polyhedron, if the forces can be replaced by a resultant force alone, without a resultant couple. It also describes the three-dimensional equivalent of the "closing string, " which is the basis in graphic statics for the construction of funicular solutions for given loads and support locations. Furthermore, it provides a procedure for constructing a constrained funicular form for a simple, determinate boundary condition. Finally, it discusses some of the difficulties involved with similar constructions and procedures for non-concurrent forces and in particular with those systems of forces that can only be replaced by a resultant force and couple.