Making-of Pringle : equitangential, bending active, wooden frame and minimal surface membrane

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Membrane structures usually follow the principles of traditional formfinding methods. In analogy to soapfilm experiments, anticlastically curved, tension-only surfaces are form-found by predefining elements within the surface as well as predefining closed boundary conditions. Usually such elements are arches, eye-loops, ridge and valley cables, humps, in order to influence the resulting curvature of the surface. Edge cables, edge beams or frames create closed boundary conditions. In the realization, these boundary conditions represent essential structural elements, but mostly they are neglected in terms of architecturally designed, space defining elements. In 2009, the unrealized, competition winning entry (Filz) for a roof cover for the Guatemala relief map raises the architectural demand for an integrative solution, where the bordering frame-like structure and its enclosed membrane surface form an architectural and structural unity.

This paper presents the development from the 2009 bordering frame-like structure for the Guatemala relief map competition, to the temporary tensile cover for a historic courtyard at University of Innsbruck in 2011, to the research on the Pringle from 2014 on and its realization as equitangential, bending active, wooden frame in 2017.
The undulating boundary frame with elliptical cross-section of the Guatemala relief map competition represents the result of a multiobjective, architectural and structural optimization, whereas the proposed solution for the frame of the cover of the historic courtyard at the University of Innsbruck follows the idea of a geometrical simplification. This proposal has been aiming for a frame, which consists from circularly bent pieces resulting in simplified fabrication and assembly and simultaneously resulting in lower costs. The authors` expertise in minimal surfaces and research in bending active structures have been bundled into the experimental structure of the “Pringle” in 2017, a minimal surface within an actively bent, annular wooden stripe. Such a stripe is circular in planar state and it is divided at one or a couple of locations. At these divisions further segments with the same geometry are added, causing self overlapping overlenght. A closed elastic stripe with overlenght is frustrated by geometry, forcing it to buckle. The bidirectional interaction of minimal surface and its boundary - “Pringle” iteratively approximated the tangential direction of the minimal surface at the boundary and the transversal inclination, respectively torsion, of the stripe. This way the strong axis of the annular stripe perfectly absorbs all axial forces from the minimal surface. The annular stripe`s weak axis allowed for elastic bending into the desired shape. The dimensions and material of the experimental structure were as follows: annular stripe from three layers of 600mm x 6mm plywood, diameter 9m, total height 2,8m, cantilevering 2,5m, cable-net from Liros prestretch high performance yachting robe;
In retrospective, the structure is analyzed (collaborative accomplishment by Filz, Shahzad, Niiranen at Aalto University), firstly, by simulating the lifting process of the plywood frame forming the spatial configuration of the frame (quasi-static analysis with geometrically nonlinear, orthotropically layered shell finite elements). Secondly, a stress analysis for the final configuration of the frame with tensional ropes (geometrically nonlinear beam finite elements) will focus on comparing the stress states of the frame with and without initial stresses resulting from the (bending) deformations of the lifting process. This comparison aims at distinguishing and demonstrating the roles of geometry and initial stresses of the actively bent frame structure.
In conclusion, the consecutive project based research emphasizes on the various aspects of form-generating members and form-found membrane surface as coalesce, respectively bidirectionally informing elements.
However, the aim for an integrative solution of boundary and membrane has brought up different approaches and solutions, which again have been caused by differently weighted parameters. Whereas earlier proposals for the boundary frames can be categorized as “shaped” the bending active, wooden frame of the Pringle is a result of selforganization.
The use of wood facilitated the fabrication, assembly and erection processes. Creep and material fatigue of the wood, which have been triggered by elastic bending, are supposed to be structurally counterproductive. Nevertheless, long-term surveillance showed that the cable net geometrically and structurally blocked the whole system. Therefore, no major deformations of the structure have been observed.
Original languageEnglish
Publication statusPublished - 2019
MoE publication typeNot Eligible
EventInternational Conference on Structures and Architecture - Convention Centre of the Calouste Gulbenkian Foundation, Lisbon, Portugal
Duration: 24 Jul 201926 Jul 2019


ConferenceInternational Conference on Structures and Architecture
Abbreviated titleICSA
Internet address

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