Externally post-tensioned structures: validation through physical modelsLeonardo Todisco and Caitlin Mueller, Proceedings of the 3rd International Conference on Structures and Architecture, 2016
Funicular structures, which follow the idealized shapes of hanging chains under a given loading, are recognized as materially efficient structural solutions because they exhibit no bending under normal loading conditions and minimize the amount of required members, often reducing the amount of material needed. However, non-structural conditions, such as aesthetics, functionality, and geotechnical issues, often prohibit selection of a structurally ideal funicular shape: bending moments inevitably arise, decreasing the structural efficiency of the design.
This paper briefly describes how a new design philosophy consisting in the introduction of additional loads, using external post-tensioning cables, can convert a non-funicular structure into a funicular one without changing its starting geometry. This system is based on the possibility of introducing external forces into the main structure through a system of stressed tension cables and compressive or tension struts resulting in changing internal force distribution.
The theoretical approach, based on graphic statics, has been generalized for any two-dimensional geometry. The method has been implemented in a parameterized and interactive environment allowing the fast exploration of different equilibrated solutions.
This paper focuses on the physical modeling, testing, and validation of structures implementing this approach. The structures are modelled through reduced-scale non-funicular geometries fabricated through additive manufacturing (3D printing), with the post-tensioning system constructed with thin cable and precise laser-cut struts. Slow motion video captures show how three different non funicular geometries (pointed-arch, circular arch and free form curve), made of discrete elements and without bending strength, stand only if the cable is working in the appropriate way, demonstrating the efficacy of the new system.
Furthermore, this paper introduces a built example on the scale of real building systems. The paper describes the design and construction process of a post-tensioned pavilion structure. This pavilion, called Funicular Explorations, serves as both a validation and demonstration of this new method, expressing the creative freedom of designers and the structural performance of the results. The design is an array of eight two-dimensional curves, made from custom-cut corrugated cardboard and nylon webbing. The array begins with a funicular parabolic arch, and progresses toward a visually expressive but structurally arbitrary shape. The external post-tensioning system contributes increasingly from one curve to the next, finally allowing the terminal free-form shape to be achieved with axial forces only.
The use of physical models, independent of their scale, is informative but also didactic, illustrating the possibilities and trade-offs in funicular explorations for architectural design. Furthermore such models demonstrate the structural concept behind the post-tensioning system in an intuitive way. The aim of this research is to allow architects and structural engineers a way to achieve high-performance, efficient, and safe designs, even when the global geometry departs from classical funicular shapes.