Design and exploration of externally post-tensioned structures using graphic statics

Funicular structures, which follow the shapes of hanging chains, work in pure tension (cables) or pure compression (arches), and offer a materially efficient solution compared to structures that work through bending action. However, the set of geometries that are funicular under common loading conditions is limited. Non-structural design criteria, such as function, program, and aesthetics, often prohibit the selection of purely funicular shapes, resulting in large bending moments and excess material usage. In response to this issue, this paper explores the use of a new design approach that converts non-funicular planar curves into funicular shapes without changing the geometry; instead, funicularity is achieved through the introduction of new loads using external post-tensioning. The methodology is based on graphic statics, and is generalized for any two-dimensional shape. The problem is indeterminate, meaning that a large range of allowable solutions is possible for one initial geometry. Each solution within this range results in different internal force distributions and horizontal reactions. The method has been implemented in an interactive parametric design environment, empowering fast exploration of diverse axial-only solutions. In addition to presenting the approach and tool, this paper provides a series of case studies and numerical comparisons between new post-tensioned structures and classical bending solutions, demonstrating that significant material can be saved without compromising on geometrical requirements