3D Graphic Statics: Geometric Construction of Global Equilibrium

Graphic Statics provides a collection of procedures for the design and analysis of two-dimensional structural systems, involving only geometric operations on two-dimensional form and force diagrams. Unfortunately, the applicability of Graphic Statics to three-dimensional problems is limited. Only three-dimensional problems that can be replaced by an equivalent series of two-dimensional problems, can be addressed. It has been shown how the equilibrium of three-dimensional systems of forces can be described using polyhedral form and force diagrams [1, 2, 7]. However, procedures for solving specific design and analysis problems with these polyhedral diagrams have not yet been developed. One of the fundamental procedures in traditional (2D) Graphic Statics is to establish global equilibrium for given boundary conditions, and to use this information to construct different funicular solutions for the specified loads and supports. Therefore, in this paper, as a first step in the development of truly 3D Graphic Statics, we describe an equivalent procedure for given, three-dimensional boundary conditions. The procedure involves only geometric operations on polyhedral form and force diagrams. The method, as it is presented here, is only applicable to statically determined systems of forces in which the applied loads do not generate a resultant couple. We give an overview of the well known procedure in 2D Graphic Statics to identify its key concepts and constructive elements, and describe the different steps of the three-dimensional version in detail