Graphical method for the construction of pairs of 3D skew funiculars in equilibrium with coplanar loads and controlled supports' positions

Abstract

Two-dimensional (2D) funicular structures can be easily generated and controlled by means of simple geometric constructions. These geometric constructions derive from reciprocal relationships between the form and force diagrams of a structure, which form the basis of graphic statics. Unlike in 2D space, in 3D space, similar geometric constructions cannot always be established for the design of three-dimensional (3D) funicular structures. In some specific cases though, purely geometric procedures requiring no numerical approximations can be defined. In particular, this contribution explores the geometric transformation of 2D funicular structures as a means to graphically generate 3D funicular structures in equilibrium with coplanar loads. A fully graphical method for the construction of such pairs of 3D skew funiculars in equilibrium with coplanar loads and with control over the position of the supports is presented. It is based on geometrical linear relationships between the original and the transformed structures. Ultimately, it is shown how such pairs of 3D skew funiculars can be applied to the design of bridge and roof structures for instance. © 2020 fib. International Federation for Structural Concrete.