Mas­te­ring the Free Form

Incidental Space in the Swiss Pavilion: structural design

The Biennale Swiss Pavilion's concrete shell is, analogous to the architectural space it creates, the outcome of an intuitive, controlled process, with graphic statics methods used to illustrate the shell’s load-bearing behaviour. An experimental study object of ETH Zurich's Professor of Structural Design Joseph Schwartz.                            


At first glance, the Swiss Pavilion for the Architecture Biennale 2016 in Venice seems unfathomable, both as a load-bearing structure and as architectural space. The «randomly» created form follows no rules and is based on neither geometric considerations nor experimental structural-design criteria. It is a shell − nothing more and nothing less.

As in many of Christian Kerez' works, the load-bearing structure spans the architectural space without additional elements; everything merges into a single whole. This article is not about the search for or finding of form. Nevertheless, the dialogue with the architect seems important insofar as the implications of the fundamental decisions were invariably discussed. As usual, the discussions were not confined to the load-bearing behaviour but entailed a holistic approach covering other crucial aspects such as the choice of materials, the design principle, the production method including transportation and assembly, how the structure would be used and its economic viability.

The search for form and construction

What would be the implications of solid, heavyweight or lightweight construction? Should the structure be prefabricated or erected in situ? Whether prefabrication or concreting in situ is used, how can the construction joints be designed so as to preserve the shell's abstract character? Will the structure need to be dismantled and reassembled elsewhere afterwards? How can it be built at the lowest possible cost? How far will the choice of a mineral material affect spatial conditions in the exhibition hall? Will the concrete be sprayed, poured or applied? With or without discrete reinforcement, prestressing or fibres? Without or with formwork, and of what kind?

All of these questions are closely related to load-bearing behaviour and span a complex multidimensional matrix. As in the conventional architectural design process, a systematic analysis of such a matrix is neither appropriate nor expedient. Instead of scientific decision-making, an intuitive process comes to the fore, often based on gut instinct. A deductive approach is replaced by an inductive one  – not, however, like the form of the structure itself, left almost entirely to chance, but calibrated according to strict criteria of feasibility and economic viability. In this respect, discussions with the contractors involved in this highly intuitive process proved to be very valuable.

Stability provided by multiple warping

These issues are not unfamiliar either to the Chair of Structural Design at ETH Zurich or the engineers at Dr. Schwartz Consulting. They are, in fact, a recurring theme of their work, especially in their collaboration with the architect (see the articles Schulhaus Leutschenbach (Leutschenbach School) in TEC21 44/2009 and Stahlbau nackt (Steel construction laid bare) in TEC21 11/2015). No less familiar are the challenges associated with the load-bearing behaviour of the spatial shell developed here, which can be interpreted as a free-form structure. While the roof design for the Museum of Modern Art in Warsaw centred on geometric forms in the shape of extremely wide-span cylindrical shells, the Guangzhou Art Museum design in China entailed equally challenging free-form shells, which while freely developed in geometric terms adhered to clear structural-design principles. Here too, plausible solutions were devised to address the challenging issue of the construction method. Of particular interest is the fact that relatively thin shells possess extraordinary static efficiency thanks to their double curvature – something well-known to shell builders from Antiquity to modern times.

Here, a link can be made with the development of stone arch structures by the Ancient Romans, and in particular the principle underpinning the Pons Fabricius, the oldest Roman bridge in Rome. That principle was also instrumental in the design of the Biennale Pavilion shell. While the arch curvature carries the gravitational forces, the reaction forces generated in the foundations, which are just as evenly distributed, are transmitted by means of an inverted arch. Whereas in Roman round arches, it is the strength of the arches and the additional lateral pressures that keep the arches in balance in spite of their sub-optimal shape from a structural-design perspective. In the case of the Pavilion shell, it is the multiple, ubiquitous warping which gives the load-bearing structure its extraordinary rigidity. Furthermore, the arched bridges have lateral horizontal struts that are responsible for diverting the vertical arch forces. The Biennale design lacks the corresponding horizontal supporting forces halfway up; these are replaced by the ties indicated in the  picture at the start of the article, which counteract any lateral displacement of the wall parts.

Form-finding using graphic statics

The Biennale Pavilion project is a perfect fit for the Chair of Structural Design’s research interests. A central focus of its research investigates the relationship between architecture and engineering with a particular emphasis on the differing understanding of the role of form. This issue serves as a focal point for a wide range of projects with the shared objective of studying discipline-specific categories of thinking and the possibility of interdisciplinary interaction. Both teaching and research are driven by graphic statics, in which − unlike analytical statics – all mathematical operations are performed using vector geometry and therefore do not involve any numerical calculations. This reliance on geometry generates an interconnected set of diagrams, meaning that a change in any one diagram requires geometric adjustments to be made to the others. In this way, the relationships between force and form also become spatially visible, enabling not only analysis but also an active and hence synthetic form-finding process.1

A shell structure not formed according to the elementary criteria of a simple inner force flow is hard to grasp from a structural-design perspective as it is internally statically indeterminate to a large degree and goes beyond traditional typologies (see pictures below). With Discrete Analysis, a method has been developed to determine the internal forces and systemic behaviour of such structures by continuously varying the load-bearing system, according to the lower bound theorem of theory of plasticity, between a discrete gridshell with hinged bars, rigidly connected bars and a continuous shell. This method is perfectly suited for use in design and thus serves as a basis for interdisciplinary discourse when developing load-bearing forms which go beyond traditional typologies and are satisfactory from both an architectural and a design-engineering point of view.2 In this regard, the Biennale Pavilion is a welcome experimental study object.

(Translation: Rob Gartenberg, ttn)

Other research topics

The research projects of ETH Zurich's Chair of Structural Design devise geometry-based solutions for structural-design and architectural challenges.In this context, the internal forces within free-form structures are investigated using curved stress fields3, combinations of hypar elements4, interactive control of inner force flows5 and spatially folded structures6. Another research project adresses the production of prestressed free-form structures by means of prefabrication7.


(1) Maximilian Schrems: Zur Erweiterung der «grafischen Statik» in die dritte Dimension, Dissertation, 2016.

(2) Thomas Kohlhammer: Strukturoptimierung von stabförmigen Flächentragwerken mittels reziproker Analyse, Dissertation, 2013.

(3) Marco Bahr, Toni Kotnik: Strut and Tie Networks – An Approach to Numerical Curved Stress Fields, Proceedings of the IABSE-IASS Symposium, London 2011.

(4) Ting Cao, Joseph Schwartz, Chi Zhang: Prototypical Hypar: an operative form-making method based on Hyperbolic Paraboloids, Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium – Future Visions, Amsterdam 2015.

(5) Patrick Ole Ohlbrock, Joseph Schwartz: Combinatorial Equilibrium Modelling, Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium – Future Visions, Amsterdam 2015.

(6) Pierluigi D’Acunto, Juanjo Castellon: Folding Augmented: A Design Method for Structural Folding in Architecture, in: Origami 6: The Sixth International Meeting of Origami in Science, Mathematics, and Education, Koryo Miura, Toshikazu Kawasaki, Tomohiro Tachi, Ryuhei Uehara, Robert Lang, Patsy Wang-Iverson (eds.), 2014.

(7) Lluis Enrique, Philippe Block, Joseph Schwartz: Form-finding method for prestressed cable networks using graphic statics, Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium – Future Visions, Amsterdam 2015.