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Funicular Funnel Shells
Matthias Rippmann and Philippe Block
Abstract This paper introduces a new typology of structurally efficient, funnel-shaped shells for light and open architectural applications. We discuss a novel approach for structural form-finding of funicular shell shapes by defining free boundaries that are balanced by continuous tension rings. Existing funnel-shaped structures illustrate the compelling possibilities for design variation in which vertical and horizontal structural elements transition smoothly, creating exciting spatial configurations. Initially, delicate designs are often executed using bulky cantilevers though, which derogate the true elegance of these shapes. The new techniques discussed in this paper demonstrate how the combination of compression-only shells with funicular tension rings leads to a great variety of efficient and expressive forms. The research demonstrates how compression and tension forces can be explicitly controlled and manipulated locally in such structures, using a fully implemented, digital form-finding tool based on Thrust Network Analysis. Thanks to the flexible implementation, resulting shell designs range from simple symmetric shapes to complex, configurations with perforations in the shell and undulating ridge edges. Independent of their complexity, all resulting shells are subject to the clear and comprehensible structural system. The structural system is tested and verified using a 3D printed, discrete, structural scale model. The elegance and delicate composition of form and force in compression and tension showcased in this funnel-shaped rib-vaulted model hints to the new possibilities for contemporary, architectural applications of the presented structural typology.
Matthias Rippmann, Philippe Block
ETH Zurich - Institute of Technology in Architecture, Switzerland
1 Introduction
1.2 Spatial Potential of Funnel-Shaped Architecture
The term funnel-shaped, or mushroom architecture discussed in this paper refers to structures that are supported centrally, forming a cantilevering canopy without columns along the outer edge. Visually, the vertical parts i.e. columns and the horizontal parts i.e. roof/ceiling of these structures often merge into one another, forming a continuous space that opens up towards its boundaries. Architectural applications range from large roof structures covering public spaces to smaller interior design projects. These funnel-shaped structures offer great spatial potential. They combine the organic and unique spatial potential of shells and vaults (Chilton 2000), with the openness and lightness associated to modern roof structures in steel and concrete. However, most applications are reduced only to formal considerations, disregarding the structural capacity of these shapes. Evidently, this is true for only decorative ceiling ribs or panels, as in the projects in Fig. 1, which can be applied to existing structures to visually change the perception of space.
Fig. 1 (a) Rogers Stirk Harbour + Partners, National Assembly for Wales (2005) (Photograph: Katsuhisa Kida); (b) Koichi Takada Architects, Restaurant [tree] (2010) (Photograph: Sharrin Rees)
In contrast to these decorative elements, the structures shown in Fig. 2 are based on fixed-end columns supporting the cantilevering horizontal elements. For example, a rib-mushroomed floor slab-construction was designed by Pier Luigi Nervi for the Palazzo del Lavoro in Turin, Italy (1961), covering a 7,900m2 exhibition space (Fig. 2a). Frank Lloyd Wright used connected lily-pad columns for the Johnson Wax Building in Racine, WI, USA (1936). Yet, these structures are featuring large cantilevering parts, which strongly depend on a relatively high bending capacity of the material and therefore large cross-sections toward the connection with the columns or supports.
Fig. 2 (a) Luigi Nervi, Palazzo del Lavoro (1961) (Photograph: Roberto Saba) (b) Frank Lloyd Wright, Johnson Wax Building (1936) (Photograph: Jack Boucher)
Nevertheless, these structures (Figs. 1-2) and numerous other examples from medieval times (Fig. 3a) show the potential of architectural applications and spatial configurations using funnel geometry (Clifford 2012). However, up to now, the structural potential of this building typology has not been fully exploited in order to extend its architectural vocabulary.
1.2 Structural Potential of Funicular Funnel-Shaped Shells
The structural efficiency of shells comes from the fact that their dominated load-bearing is membrane action, i.e. axial compressive or tensile force flows along its centre surface, which is inherently more efficient than carrying loads through bending.
Traditional vault construction demonstrates the use of efficient structural form in combination with funnel-shaped architecture, such as the rib vault of the chapel of Cluny Museum in Paris, France (1485-1510). This masonry vault of course stands efficiently in compression due to its funicular shape (Fig. 3a) resulting in a relatively filigree structure. The contemporary installation La Voûte de LeFevre (2012) by Matter Design is based on the same structural system, featuring a more irregular geometry thanks to digital, structural form finding and CNC fabrication (Fig. 3b).
Fig. 3 (a) Rib vault of the chapel of Cluny Museum (1485-1510); (b) Matter Design, La Voûte de LeFevre (2012)
Yet, these compression structures depend on fixed boundary conditions, which usually do not allow opening up the sides. The vaults in Fig. 3a are stable thanks to massive buttresses taking the horizontal thrust of the rib structure. The openness and lightness of the installation in Fig. 3b on the other hand can only be achieved by a steel frame suspended from the ceiling of the gallery space. The structure thus depends on this continues support, in contrast to the cantilevering structures in Fig. 2. The question arises how one can use the structural efficiency of funicular shapes to create open, funnel-shaped shells without the need of a secondary structural frame acting in bending or heavy buttresses.
This paper discusses a direct form-finding approach for funicular funnel shells, and demonstrates the manifold design space of