Three-dimensional Graphic Statics: Initial explorations with polyhedral form and force diagrams

Akbarzadeh M., Van Mele T. and Block P.
International Journal of Space Structures
doi: 10.1177/0266351116660802

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.


    author  = "Akbarzadeh, M. and Van Mele, T. and Block, P. ",
    title   = "Three-dimensional Graphic Statics: Initial explorations with polyhedral form and force diagrams",
    journal = "International Journal of Space Structures",
    year    = "2016",
    volume  = "31",
    number  = "2",
    pages   = "217-226",
    month   = "June",
    doi     = "10.1177/0266351116660802",
    note    = "",

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