Beyond Bending: Reimagining Compression Shells [2 ed.] 9783955533915, 9783955533908

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Philippe Block, Tom Van Mele Matthias Rippmann, Noelle Paulson

Beyond Bending Reimagining Compression Shells

CONTENTS

6 Foreword La Biennale di Venezia 11  Reporting from the Front The War on Bending By Alejandro Aravena 12 In the Footsteps of Vitruvius By John Ochsendorf



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Beyond Bending

17 Beyond the Slab I 20 Building with Weak Material 33 Beyond the Slab II 42 Building with Less Material 55 Beyond the Dome 64 Exploring Form and Forces 79 Beyond Freeform 90 Extending Stereotomy 101

The Making of the Armadillo Vault

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Form and Structure

127 138

Stereotomy and Fabrication

147 170

Construction and Assembly

Engineering the Extreme A Conversation with Ochsendorf DeJong & Block

Informing Geometry A Conversation with the Block Research Group

Balancing Craft and Machine A Conversation with the Escobedo Group

178 Afterword  A New Research-Driven Architectural Practice By Gilles Retsin 184 186 187 188 190

Authors Contributors Exhibition and Object Credits Image Credits Bibliography

FOREWORD

La Biennale di Venezia For a world of beams and slabs built with steel-reinforced concrete, compression-only shell structures, which can be extremely thin constructions, offer the potential to drastically reduce material requirements. Building with fewer materials means in turn less environmental strain caused by the construction industry. Drawing from a revival of forgotten principles combined with the latest methods for reimagining the design, engineering, fabrication and construction of compression shells, this book advocates for the logic of such forms. Through in-depth background on the state-of-the-art research, advanced engineering, and highly-skilled masonry craft that resulted in the Armadillo Vault and other innovations exhibited at La Biennale di Venezia, the 15th International Architecture Exhibition in 2016, by the Block Research Group, ETH Zürich, Ochsendorf DeJong & Block, and the Escobedo Group, it demonstrates dramatic ways to move beyond bending. In August 2015, in his role as the newly appointed curator of La Biennale di Venezia, Alejandro Aravena wrote to Philippe Block and John Ochsendorf to invite them to contribute to his exhibition “Reporting from the Front”. Aravena specifically asked Block and Ochsendorf to submit a report from the front of their “War on Bending”. Ideas quickly coalesced to form the plan for an exhibition entitled Beyond Bending. Their goal was to show what can be achieved when reinforced concrete slabs, which normally work in bending, instead take on curved, compression-only forms. A team was formed to include the Block Research Group at ETH Zürich (led by Philippe Block and Tom Van Mele), the engineering consultancy of Ochsendorf DeJong & Block (comprised of John Ochsendorf, professor at MIT, Matthew DeJong, professor at the University of Cambridge, and Philippe Block) and the construction and masonry experts of the Escobedo Group (led by David and Matt Escobedo). Although the team members had been collaborating in various constellations for over 10 years, the invitation to exhibit at the Biennale represented their first opportunity on such a large scale and on the world’s premier stage for architectural innovation. Aravena’s initial invitation included the statement, “The battle for a better built environment is neither a tantrum nor a romantic crusade”. This sentiment also fittingly describes what the team accomplished in Venice. The objects that were displayed in the Beyond Bending exhibition – and whose precedents, principles, and potentials are described in greater depth on the pages that follow – represent efforts toward achieving a better built environment. With their focus on compression-only structures, they show methods for more ap6

propriate construction. They demonstrate more efficient use of materials and labour in various contexts from developing countries in Africa to prosperous, high-income countries like Switzerland. Rather than being romantic attempts at revival for revival’s sake, these structures draw upon historical examples and “lost” techniques that have been reinvigorated and adapted for current technological and fabricational possibilities. Thus, the exhibition carried the subtitle “Learning from the past to design a better future”. Beyond Bending filled an entire room in the Corderie dell’Arsenale, a former workshop for the production of naval ropes, the initial construction of which began as early as 1303. For this exhibition, four examples of vaulted floor systems displayed in two of the corners formed “Beyond the Slab I” and “Beyond the Slab II”; a canvas of 19 form and force diagrams covering one wall constituted “Beyond the Dome”; and the Armadillo Vault, the exhibition’s centrepiece under the rubric of “Beyond Freeform”, spanned an area of 75 square metres. Visitors could enter the exhibition from one of two large, arched doorways. To move through the room, they were forced to either walk around or under the Armadillo Vault, with each path providing different perspectives. The format of this book follows the structure of the exhibition and its headings. “Beyond Bending” describes the objects displayed in Venice. Each section begins with a short explanatory text taken from the original exhibition labels followed by photographs to provide visual context. Then, pages with a shaded background allow for more in-depth, theoretical analysis. These sections each present precedents, principles, and potentials. They indicate past or present references, describe the architectural, computational, and/or structural methods behind the objects, and propose future possibilities for development and innovation. The second section charts the “Making of the Armadillo Vault” through photographs, diagrams, texts, and conversations with the team leaders covering various aspects of the vault’s realisation. This variety of perspectives demonstrates how constraints informed the design, engineering, fabrication, and construction of this remarkable structural achievement.

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Top view and sections of the Beyond Bending exhibition in the Arsenale building of La Biennale di Venezia, showing its main components.

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Original proposal with hand-drawn sketches submitted to curator Alejandro Aravena in ­September 2015.

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Alejandro Aravena

Reporting from the Front The War on Bending When people look at modern buildings, they tend to describe them as boxes: rectilinear cubic volumes defined by vertical and horizontal lines and elements. It is true that we need flat horizontal surfaces to walk around and use rooms in a reasonably simple enough way, but we tend to assume that the lower side of such surfaces (slabs) and the associated structural components (beams) also have to be flat. For some reason, not only is a horizontal beam seen as something inevitable but it is even seen as structurally desirable. A rectilinear horizontal beam naturally tends to bend. In this bending there are two forces at play: compression in the upper part (particles pushing against each other) and tension in the lower part (particles trying to pull away from each other). The invention of reinforced concrete consists in the introduction of rebars to resist tension, a force that concrete alone cannot support. The problem is that the mass needed in that lower part of the beam is not there to perform any structural operation, but only to protect the steel from rusting; structurally speaking, it is dead weight. This was the starting point of these engineers’ research. They studied old structures like the King’s College Chapel and Guastavino vaults, and concluded that if bending could be avoided and the structure could work only in compression, then something like 70 % of the matter could be saved. This has huge consequences for the weight and amount of matter used in the overall system, with potentially dramatic savings in direct costs. But it also has consequences in the amount of energy saved because less matter is needed – there is less energy spent in the fabrication and less energy spent in the transportation. It even saves time since less material has to be put in place. Using state-of-the-art engineering, software, and robotic prefabrication technology, their research may open a path for a global shift in the building paradigm.

Text from the catalogue of the 15th International Architecture Exhibition - La Biennale di Venezia (May 28th – November 27th 2016). Used with permission.

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John Ochsendorf

In the Footsteps of Vitruvius Why build a stone vault in the 21st century? The Armadillo Vault may be perceived by some as a form of nostalgia, romanticising a past that we can never return to. This structure could also be measured by the timeless Vitruvian ideals of firmitas, utilitas, and venustas: solidity, utility, and beauty. It is useful to examine the vault through these Vitruvian lenses, both to frame the project and to evaluate its contribution to contemporary architecture. Firmitas Builders throughout time and space have chosen stone for monumental architecture precisely for its solidity and durability. As human settlements achieved greater wealth, buildings of earth and wood gave way to stone, from Çatalhöyük to Angkor Wat. Many cultures constructed stone shelters as a way of seeking permanence: safety from fire and the elements. Well-constructed stone pyramids, walls, and vaults are the most durable architecture ever created. The Armadillo Vault is constructed of stone in order to demonstrate new potential for one of the oldest and most durable building materials. The vault finds stability through geometry, with a double-curved shell to provide structural integrity. Hidden steel reinforcement is not required for the vault to stand. Stone stacked on stone creates a solid structure. In an age of 50-year building lifetimes, the Armadillo Vault is nearly permanent. If left outside in the rain and wind, its limestone would erode at the rate of approximately one millimetre per decade. Over 500 years, it could lose enough thickness by erosion to threaten the stability of the thin vault. While the use of dry-jointed stone achieves firmitas, the Armadillo Vault is more fragile than a traditional stone vault for two reasons. As a temporary installation at the Venice Biennale, it has not yet found a permanent home. And as a daring demonstration of the possibility of computation today, it can give the visual impression of fragilitas due to its remarkable thinness. Thus, the Armadillo Vault expresses both firmitas and fragilitas simultaneously, and its structural audacity is obvious to both stonemasons and casual observers. Utilitas But what is the utility of a stone vault? The oldest stone vaults in the world acted as shelters, whether for the tholos tombs at Mycenae, or the brick-vaulted grain storage sheds for the funerary complex of Ramses II, each built more than a thousand years before Vitruvius. Shelter is the most basic utility. However, 12

as an interior installation, the Armadillo Vault was not built to provide shelter from the elements. This project is an act of intellectual and technical exploration. It builds on millennia of exploration in masonry vaulting that flourished until the early 20th century, when the rise of steel and concrete structures led to a heavy reliance on the flexure of beams. The freeform stone vault demonstrates the potential for compression-only structures. It embraces extreme constraints in the formal exploration of design and digital fabrication. The vault was designed and built in less than six months based on more than a decade of intense research at MIT, ETH Zürich, and the University of Cambridge. It is an opportunity to put theory into practice by marrying new theoretical knowledge with new practical capabilities. Transferring research into practice is the ultimate utilitas of the Armadillo Vault. Venustas Beauty is subjective and reasonable opinions will differ. However, the proportions of the Armadillo Vault were created in response to extreme constraints: fitting inside an existing historic building with severe limitations on weight and construction. Within these constraints, the designers sought to create moments of discovery and surprise. From different viewpoints, the limestone vault oscillates between expected and unexpected. The limitations on time for fabrication required that only one side of each of the stones could be accurately machined. The flat exterior panels are a visual demonstration of this fabrication constraint, and the interior saw cuts illustrate the dominant flow of compression in the vault. Reading the flow of forces in the surface of the material is beautiful, at least to students of structural design. The material is unadorned, and the vault aims to be honest throughout. Limestone obeys gravity. The outward thrust of the vault is expressed in the steel tension ties, and the bearing pads demonstrate the limitations on floor loads in the soft soils of Venice. The Armadillo Vault is both simple and complex simultaneously. It finds beauty by embracing the constraints of Venice. The Beyond Bending installation was possible only because of years of collaboration and trust between all contributors. Each explored our own personal frontiers: both theoretical and practical. In the pages that follow, the details of the design and fabrication are outlined. We do not seek to revive dead traditions, but to discover new possibilities. And to explore our own Vitruvian Triad.

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Beyond Bending Throughout history, master builders have discovered expressive forms through the constraints of economy, efficiency, and elegance. There is much to learn from the architectural and structural principles they developed. Novel structural design tools that extend traditional graphical methods to three dimensions allow designers to discover a vast range of possible forms in compression. By better understanding the flow of compressive forces in three dimensions, excess steel can be eliminated, natural resources can be conserved, and humble materials like earth and stone can be reimagined for the future. By combining methods from the past with new technologies and fabrication techniques, this exhibition advocated for the logic of compression-only forms. It offered possibilities to move beyond the slab, beyond the dome, beyond freeform, and ultimately beyond bending.

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Beyond the Slab I An arch in compression with a tension tie makes more efficient use of material than a beam in bending. To create masterpieces in unreinforced masonry, great builders of the past discovered stable geometry in compression. The vaults and floor systems here demonstrate that compression geometry can be used to build with minimal steel and with relatively weak material. These structures can be visually exciting with lower cost, lower weight, and lower environmental impact than conventional concrete slabs. Ceramic Tile Vault  Builders have constructed thin tile vaults throughout the Mediterranean region for over 600 years. These vaults require minimal support from below during construction, making them economical to build. In this model, the doubly curved masonry shell carries loads efficiently in compression, and the horizontal thrust is resisted by steel tension ties. Stiffening ribs provide the required depth to carry concentrated loads and to ensure that the thin tiles remain in compression. This historical form serves as an inspiration for new designs in compression. Earthen Vault The masonry materials of a well-designed compression shell do not require high strength because stresses are low. To design for resource constraints, local soil can be used to create stabilised, unfired earth bricks. The earthen shell can serve as a low-cost floor system with dramatically lower environmental impact, up to 90 % less embodied CO₂ than conventional steel and concrete structures. Local masons can be trained in the production and construction of these systems, providing new economic livelihood as well.

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The tile-vaulted floor consists of diaphragms or spandrel walls on the top to stiffen the ­shallow, doubly curved shell underneath. The masonry shell is composed of two layers of thin ceramic tiles bonded with cement mortar

in a herringbone pattern. Four arches on the edges, initially supported by temporary falsework during construction, convey the loads to the supports.

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Building with Weak Material When building unreinforced masonry vaults, good geometry is essential for maintaining equilibrium through contact only – that is, principally through compression. These funicular ­geometries have the advantage that the stresses in them are very low. Current development of engineered materials, such as concrete, steel, and so on, is largely focused on making these materials stronger, on increasing their allowable stress. However, achieving stability through geometry, through funicular forms, for example, rather than through material strength, opens up the possibility of using weak materials. Particularly in developing contexts, such materials may be locally sourced and produced with lower environmental impact, thus offering more viable, sustainable alternatives to typical construction practice. Tile Vaulting  Originating in the Mediterranean region, the traditional building method of thin-tile vaulting has a long history that stretches back more than 600 years. Also known today as Catalan or Guastavino vaulting, this technique makes use of lightweight tiles and a fast-setting mortar. This allows the vaults to be built without support from below by temporarily cantilevering newly placed bricks from already stable sections. Starting from (arched) boundary conditions – often built on reusable falsework – the tiles are placed flat to build the vault’s surface in stable arches with minimal guidework describing the vault’s target geometry. When a self-supporting part of the shell has been completed, this first layer of tiles serves as permanent formwork upon which the additional layers of brick can be laid with conventionally setting mortar (at different angles to avoid obvious hinge lines), thus building up the section to the required structural depth. Nubian vaulting is another technique that allows unreinforced brick vaults to be built without falsework. This construction method, whose history dates to more than 3,000 years ago, uses air-dried adobe bricks and earthen mortars. Because it depends only on natural materials that can be found locally, Nubian vaulting is often the preferred vaulting technique for construction in 20

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Top: The main construction techniques for ­unreinforced brick vaults: the classic Roman vault with bricks laid on falsework, decentred after the vault is complete; and two techniques that can be constructed without formwork: Nubian and Catalan or tile vaulting.

Bottom left: A historical photograph of a ­ atalan mason placing a lightweight tile, C ­temporarily cantilevered using a fast-setting mortar, until a stable arch is constructed. ­Bottom right: The tile-vaulted ceilings of the Oyster Bar in Grand Central Terminal, New York, by the Guastavino Co. (1912): three layers of unreinforced tile, built without formwork for the main arches, supporting parts of the Vanderbilt Hall above.

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resource-constrained locations and developing-world contexts. This “pitchedbrick” method (as each new arched course leans on the previously built section) has seen an evolution in Mexico that offers more formal possibilities, going beyond the simply extruded barrel vault. However, due to the combination of lightweight bricks and fast-setting mortar – and the associated capacity for temporary cantilevers – the spectrum of forms achievable with thin-tile vaulting is much wider. Strength Through Geometry In 1675, the English scientist Robert Hooke discovered “the true […] manner of arches for building”, which he summarised with a single phrase: “As hangs the flexible line, so but inverted will stand the rigid arch”. Generalised, this means that the shape a string takes under a set of loads, when inverted, illustrates a path of compressive forces for an arched structure to support the same set of loads. The shape of the string, and the inverted arch, is called a funicular shape for these loads. In 1748, Poleni used Hooke’s hanging chain principle to assess the safety of the cracked dome of St. Peter’s in Rome. For this, he had to find a line of force, a thrust line, that lies everywhere within the masonry, to show the structure was safe for that set of loads. There are only three types of equations that can be used for structural analysis: equilibrium (statics); geometrical (compatibility), and materials (stresses). For historical masonry structures, the first two types of equations are most important, since stresses are typically an order of magnitude below the failure stress of the masonry. A stability or equilibrium approach will therefore be most valuable to assess the safety of masonry structures, and limit analysis provides a theoretical framework, introduced by Jacques Heyman in 1966. Unreinforced masonry demands compression-only load transfer for all loading cases. The safety of arched or vaulted structures in masonry is fundamentally a problem of geometry, not stress. Failure is caused mainly due to stability rather than material crushing. A thrust line traces and visualises a possible path of the resultant (compressive) forces in the section. An arch geometry with a thrust line staying inside its cross section everywhere thus has a possible force flow in equilibrium or load transfer through contact and in compression.

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Top: Material strength versus equilibrium ­stability. Galileo (1638) compares corresponding bones of mammals of different sizes to ­illustrate that for stress-driven problems, ­structures do not scale linearly (as mass relates to volume and stress to cross-sectional area, the applied load and the load-bearing capacity scale by the powers of 3 and 2 respectively)

Bottom: For given loads, a thrust line can be found by hanging weights, proportional to the loads to be carried, from a string ­model. If a thrust line can be found within the section of a structure, then it is in ­equilibrium through compression and friction (as used by Poleni [1748] for the analysis of the dome of St. Peter's Basilica in Rome, Italy).

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Top to bottom: A stiffened arch with ties: An arch carries a uniform load to the supports ­using only compressive forces. A large point load results in a thrust line that exits the ­section. Thus, the arch can no longer stand in compression only. Adding a stiffener allows

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the thrust line to be contained within the ­section of the structure. The hori­ zontal thrust of the arch can be equilibrated with tension ties, thus transforming the stiffened arch into a lightweight beam.

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Stiffened Arch For a vertical load, distributed uniformly along a horizontal line, the funicular geometry is a parabolic arch. As stresses are low, this arch can be materialised requiring a very small cross-sectional area. However, adding a further point load results in a thrust line that can no longer be contained in the thin arch’s cross-section. This means that forces can no longer be transferred through compression only, and bending capacity would be required to resist the combined, non-funicular loading case. However, for a thin arch, adding reinforcement would not be very effective. Since only a very small moment arm could be formed, bending moments would result in a force couple of extremely large magnitude. This, in turn, could lead to compressive stresses that would cause material crushing, if instability due to buckling had not yet occurred; the result is structural failure, that is, collapse. Locally adding structural depth using a stiffener in the form of spandrel walls allows the thrust line to travel to the supports in compression through the deepened section. Finally, absorbing the horizontal components of thrust with tension ties effectively transforms the stiffened arch into a lightweight version of a beam. Funicular geometry alone is thus not sufficient to build a safe and stable structure. The funicular geometry needs to be stiffened such that all loading cases can be carried to the supports through compression. The most efficient and effective approach is to provide sufficient positive double curvature. Stability then comes from the multiple load paths along which loads can travel to the supports and from the effective structural depth that the positive double curvature creates. However, in shallow floors, sufficient curvature cannot be provided. Additionally, a flat surface is needed to walk on. Other stiffening strategies in compression include adding self-weight (essentially rendering the effect of the live load negligible) and increasing effective structural depth by undulation, corrugation, or by adding stiffeners as explained above.

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Appropriate Construction Although thin-tile vaults are materially and structurally efficient, the technique lost popularity because it is quite labour-intensive in most contexts. In a developing world context, where labour is relatively cheap and unemployment is high, thin-tile vaulting projects can provide employment to workers who, after a bit of training, learn not only how to form or press the tiles but also how to lay them to build the vault. Of course, Africa’s vernacular architecture is based on local materials, with soil and loam playing a central role in many traditional construction methods. Providing assistance in devising a structurally sound and safe strategy to use these local materials to go beyond single-storey dwellings and offering solutions for multiple-storey housing (G+1 or G+2 are most relevant) are the challenges here. Introducing cement-stabilised, soil-pressed bricks for tile vaulting, the Mapungubwe Interpretive Centre in South Africa by Peter Rich, John Ochsendorf and Michael Ramage was a milestone project, showing that solutions based on materials associated by locals with vernacular, and thus often poor, architecture could look exciting and win international prizes. It clarified that “cheap solutions that do not look cheap” can be offered through clever use of compression shells. As a follow-up project, the Sustainable Urban Dwelling Unit (SUDU) prototype designed and constructed together with Dirk Hebel in Addis Ababa, Ethiopia, pushed the sourcing of local resources and labour one step further by being as pure as possible. By using local, earthen materials for 90 % of the structure and due to the availability of cheap labour, the cost of the modern-looking, two-storey box was only 40 euros per square metre. The fraction of imported materials was used in the tied concrete support beams that provide the boundary conditions for the unreinforced, soil-pressed brick floor and roof structures to thrust against. The project’s shallow floor used Catalan vaulting, while the large roof used Nubian/Mexican vaulting, employing stiffening through spandrel walls and a stabilised fill as opposed to positive double curvature.

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Top: The Guastavino Co.'s patented rib and dome system proposes spandrel walls or ­stabilised fill to stiffen the unreinforced tile shell for non-uniform loads, which then also forms a horizontal floor surface.

Bottom: Construction of low-cost housing in Addis Ababa, Ethiopia in 2009. Cement for concrete and reinforcement steel had to be imported and were therefore expensive. ­Dimensional timber is not available to make formwork and environmentally toxic eucalyptus wood is used in a non-recyclable, unsustainable manner.

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Top: As shown in the construction of the ­Mapungubwe Interpretation Centre, when the earthen tiles are placed following an arch with the right geometry, this extremely weak material can support the next, stronger layers to be placed by another mason, building up a safe structural floor. Tension ties connect the barrel vault's springings, resolving and absorbing its horizontal thrust.

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Bottom: Local workers being trained in tile ­vaulting to build the Sustainable Urban Dwelling Unit (SUDU). Right: Predominantly based on ­local resources and cheap labour, the final ­construction cost for this 5-by-8-metre, ­double-storey prototype was only 3,500 euros.

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The Block Research Group and ODB Engineering designed, engineered and managed the construction of the tile-vaulted prototype of a module for the Droneport project by the Norman Foster Foundation and EPFL / Redline, also shown at the 2016 Venice Architecture Biennale.

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Beyond the Slab II Inspired by historical tile vaults, contemporary fabrication methods move beyond masonry to create new design possibilities for ribbed vaults. Uninhibited by traditional fabrication constraints, novel structural form-finding and optimisation methods can result in more efficient geometry in compression. The compressive vaults thrust outward on the supports, which are stabilised by tension ties. As with their historical predecessors, such vaults demonstrate significant s­ avings in weight and environmental ­impact compared to conventional concrete slabs. Concrete Shell Floor  The two-centimetre-thick shell in unreinforced concrete follows the structural principles of the historic tile vault. Activating ­compressive shell ­action in the vault while externalising tension with ties can result in savings of over 70 % of concrete compared to a typical floor slab in bending. The complex geo­metry requires an expensive, two-part mould. However, this is cost-effective for repeated units and multiple casts. Structural optimisation is combined ­with ­ ramatic material savings in construction. innovative concrete casting to create d 3D-Printed Floor  New possibilities in 3D printing enable the fabrication of complex structures and components at competitive cost. With well-designed compression shapes that have low stresses, the formal freedom offered by such exciting digital fabrication technologies can be fully exploited. Like Robert Maillart’s pioneering three-hinged concrete bridges, this printed floor is discretised to control the compressive force flow for all loading cases. Such prefabricated components are opening new possibilities in the challenge to enclose space.

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The concrete shell floor was cast using a ­two-part mould made from high-density ­polyethylene, using a 5-axis CNC (Computer Numerical Control) router. The upper and ­lower mould parts are supported and fixed

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in position during the casting process using CNC-milled wooden cover panels. The upper cover and mould part have holes for pouring the concrete into the mould.

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The 3D-printed floor consists of five modules, forming a discrete shell without any mechanical connection between neighbouring elements. The additive manufacturing technique uses ­silica sand bonded by phenolic binders in a

l­ayered process with a resolution of 0.25 mm. The high precision and geometric flexibility of the production method facilitated the fabrication of the structurally optimised, intricate rib geometries in the first place.

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Building with Less Material As demonstrated by the previous examples of vaulted, unreinforced masonry structures, compressive forms can be built efficiently with limited resources. This is particularly relevant in developing contexts where engineered materials are often unavailable, while labour and local materials such as soil are abundant and inexpensive. In resource-constrained contexts, building with less material is a necessity. However, given the general need to use fewer natural resources or raw materials, and to reduce CO2 and greenhouse gas emissions, why are we not doing better in all contexts? To be able to exploit the efficiency of a shallow tile arch or vault in a technologically advanced construction environment, we have adapted the previously introduced concepts to tied and stiffened shell floor systems that can be prefabricated using concrete casting or even 3D printing with sand. Cracked Beam Because of the high cost of non-standard formwork, the structure of most (reinforced) concrete buildings is built as much as possible using standard, flat formwork parts. This unavoidably leads to the production of straight columns, walls, beams and floor slabs. Straight beams and slabs, which carry loads through bending, need a certain structural depth to prevent the internal forces from becoming too high. Additionally, as required by building code, the steel reinforcement in concrete construction elements has to be protected from corrosion (and fire) by a concrete cover of approximately four centimetres. Structurally speaking, this cover is dead weight. Large amounts of material in many parts of standard beams and slabs are not needed structurally and are therefore wasted. Just after being poured or cast, a simply supported, reinforced concrete beam works as a (linear) elastic element carrying load through continuous compressive and tensile principal stress directions inside its section. It deforms such that, towards the top of the section the concrete is compressed, while the bottom part is stretched. Due to the geometric incompatibility 42

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Top to bottom: Internal forces in a simply ­supported beam: An uncracked beam works as a (linear) elastic element with continuous stress lines. Bending causes the top of the beam to be compressed while its bottom is stretched. The steel reinforcement is only

­activated when the concrete (at the bottom) cracks. Using stirrups, the internal forces in a reinforced concrete beam are redirected around the cracks. Deformations and cracks due to tension can be avoided by prestressing the cross-section.

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of these deformations, as well as the limited tensile capacity of concrete, cracks occur perpendicular to the tensile stress direction. Once these bending cracks occur, the steel reinforcement on the bottom of the beam is activated. It picks up the tensile stress and prevents further deformation. Stirrups redirect the internal forces around the cracks by providing vertical tensile members, thus allowing compression struts to form inside the concrete. A truss system with equivalent structural behaviour can be imagined inside the concrete’s section. A more efficient internal load path can be obtained by prestressing or post-tensioning the beam, for example, with cables. This prevents the bending cracks and eliminates the need for stirrups. To further avoid cracks due to incompatibility of internal deformations, the prestressing cables are best inserted in sleeves so that compression and tension deformations can happen independently. Stiffened Funicular Shell Rather than pulling them through sleeves inside the straight beam or plate, post-tensioning cables can be externalised, leaving the “inside” of the structure in pure compression. When a beam or plate is allowed to act as a tied arch or a vault in this way, much of the wastefulness described above can be avoided or even eliminated entirely. The solid slab can be replaced by a doubly curved shell with stiffeners. The shape of the shell is funicular for the dead load, which is a combination of the slab’s own weight and the permanent loads above. The shell component of the floor thus supports those loads through a network of compression forces. As in the stiffened arch in “Building with Weak Materials” above, the stiffening ribs allow non-funicular loading cases to be carried to the corners through compression as well. For these loading cases, which are combinations of the dead load and non-permanent live loads, the locally increased structural depth offers additional paths for the thrust networks to develop within the boundaries of the material or cross-section of the structure. Steel ties absorb the (horizontal) thrusts of the stiffened shell. By externalising the steel components, they can be accessed, making fire-proofing, corrosion protection, and maintenance much easier. The steel can even be encased or integrated in the beams of a structural frame of the building. Furthermore, as in the post-tensioned beam, since the ties are no longer embedded in the concrete, they can elongate independently, thus preventing the otherwise unavoidable cracks due to incompatible deformations. Although these aspects increase the longevity of the structure quite significantly, the main reason to use externalised, post-tensioned ties is that this can lead to a dramatic reduction of structurally unnecessary concrete. The solid concrete 44

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Top: The vaulted bottom of the floor is shaped according to the thrust network for the dead load, which includes the floor's own weight. Middle: For combined dead and live load cases, the stiffeners provide additional structural depth such that a thrust network can be found within the boundaries of the material, carrying

these loads in compression to the supports. Bottom: By restraining the supports, for ­example by connecting them with tension ties, the floor unit can carry applied loads through compression alone. It is thus a three-dimensional version of the tied and ­stiffened arch.

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Top: Most of the weight of a high-rise building is in its structure. At least three-quarters of this is due to the floors. Reducing the weight of the floors results in additional material savings on the columns and foundation.

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Bottom: Rather than layering functions – s­ tructural, mechanical, technical etc. – the ­created cavities can be used to integrate some, if not all, of these additional media.

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slab is carved out, leaving only what is needed for efficient force transfer in compression for all load cases. For typical spans, when compared to standard, hollow-core floor systems, more than 70 % of concrete can be saved. Dramatic Benefits Since the building industry is one of the most significant sources of greenhouse gases, and its most commonly used building material – reinforced concrete – is an important contributor to the embodied energy of the built environment, the impact of compressive floor systems with externalised tension ties presented here is incredibly promising. In high-rises, most of the structure of a building is needed to support its own weight. Since the largest part of that weight is due to the floor slabs, significant weight reductions of the floors are multiplied as they percolate down, resulting in lower requirements on the primary structure (beams and columns) and the foundations. Finally, as the mass of the structure higher up decreases, the seismic response of the building also improves. Significant opportunities for the integration of building systems also emerge. Parts that would have been filled with material in typical beam or plate structures are instead cavities, and the stiffeners between those cavities can be perforated without reducing the structural performance of the floor. This means that pipes, wires, mechanical systems, etc. can be inserted and routed through volumes of the floor system that were previously inaccessible. Building systems thus no longer have to be placed in a separate layer. As a result, storey height can be reduced and much more real estate becomes available for the same total building height, especially in combination with novel climate control systems. Finally, recent research has demonstrated that vibro-acoustic dampening of low-frequencies is possible through structural stiffness. Interestingly, the same measures that improve the structural efficiency of the floor also improve noise dampening. They include (in order of importance): shape (curvature of the shell), topology (layout of the stiffening ribs), and size (distribution of mass). This means that the light floor units can be acoustically performant without requiring additional mass. While the potentials of such a floor system are manifold, its structural geometry is complex and its fabrication can be expensive. For example, a double-sided mould is required to cast the prefabricated concrete unit – a costly and wasteful process. However, if the moulds can be reused, for example in high-rise buildings, then economies of scale apply, and production becomes much more cost-effective.

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Above: After load testing the unreinforced concrete stiffened shell prototype, the section with its 2-centimetre-thick parts is revealed.

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Top right: The thin concrete shell allows the ­integration of efficient, low-energy, hydronic heating and cooling systems that activate the surface as a radiator, as shown in the research of Prof. Arno Schlüter and his group at ETH Zürich. Bottom right: The five-by-five-metre floor units will be part of the NEST HiLo unit in Dübendorf, Switzerland.

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Fabrication Technologies The drawbacks of prefabrication with concrete casting can be addressed with emerging fabrication developments such as 3D-printing. This technology allows for building up geometries, including locally undercutting or cantilevering parts, which would not be possible to achieve using two-part moulds. Thus, fully bespoke building elements can be produced. Further benefits enabled by 3D printing include that the results can be differentiated according to varying, local boundary conditions (loading, supports or openings, other media, etc.); ornamentation can be added at no additional cost; and features for HVAC (channels for cooling, heating, pipes, air outlets, etc.) can be integrated along with lighting fixtures, electric and other wires, and so on. As even more sophisticated geometries can be created, printed elements can be further optimised for structural and/or acoustical improvements. These advantages can be obtained to the precision of a grain of sand. However, 3D printing comes with challenges as well. The tensile strength and bending capacity of most currently available printing materials are negligible, and even their compressive strength is quite limited. In addition, the integration of (tensile) reinforcements during printing presents difficulties. The compression-only floor system thus represents an ideal application for these remarkable technological advances and new fabrication techniques.

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Top: The floor made out of weak, 3D-sand-printed material satisfies building codes from a structural point of view.

Bottom: Additive manufacturing at construction scale is rapidly developing, offering new possibilities to create bespoke geometry ­without needing moulds. Here, a large-scale, 3D-sand-printed piece is being taken from the printing bed.

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Half of the Block Research Group – that is, more than one ton of ETH Zürich nerds – crouching on the 3D-sand-printed, unreinforced floor ­prototype.

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Beyond the Dome Graphic statics is a powerful approach for relating the geometry of a structure to the forces acting in the structure. Master builders have used this simple yet powerful design methodology to discover structural form for over a century. Enhanced by computation, novel design approaches allow for geometrical exploration well beyond historical precedents. Even for highly constrained boundary conditions, infinite solutions are possible and new forms are waiting to be discovered. Form and Force Diagrams Thrust Network Analysis (TNA) extends graphic statics to 3D for contemporary design. Form and force diagrams provide explicit control over the geometry of a spatial network of compressive forces in equilibrium with a set of vertical loads shown on the top of each diagram. The form diagram in the middle defines the directions along which the horizontal thrust in the network can flow, and the lengths of the lines in the force diagram at the bottom represent the magnitude of those forces. Each of these solutions starts from a highly constrained problem: a compression-only form supported on a circular base. The form and force diagrams demonstrate the logical beauty of TNA-based form finding, going well beyond the classical dome.

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Exploring Form and Forces In engineering, design-by-analysis is common practice. Unfortunately, such an approach to the design and optimisation of structures does not foster creativity and rarely results in “new” structural solutions. Current trends advocate the adoption of methods that allow engineers to replace their tried-and-true spreadsheets with tools that allow for more exploratory and informed decision-making during the early design phase. Essential to informed structural design is the intuitive visualisation of results as feedback to the designer. The most effective feedback of structural information has been shown to be in the form of direction and length, rather than colour and density as is typical in structural analysis software. Graphical methods for the design and analysis of structures, by their nature, not only depict this information explicitly but also use geometric representations and relationships as the drivers and control mechanisms during the design and optimisation process. Graphic Statics Tracing back to Simon Stevin’s introduction of the parallelogram rule to construct force vector equilibria in 1568 and Varignon’s first use of a funicular polygon of forces in the eighteenth century, graphic statics became a powerful design and analysis method in the nineteenth century with protagonists such as Rankine, Maxwell and Bow in England, Culmann and Ritter in Switzerland and Cremona in Italy. Great engineers like Eiffel or Maillart used graphic statics to design their masterpieces, such as the Eiffel Tower in Paris, France, or the Salginatobel Bridge in Schiers, Switzerland. One of the primary advantages of graphic statics is the explicit representation of the relation between the shape of a structure and the equilibrium of internal and external forces with geometrically linked “form and force” diagrams. The magnitudes of forces in the structural system are represented by the lengths of segments in the force diagram; longer lines mean larger forces. This allows the designer to understand and visualise the relation between changes in geo64

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metry and the corresponding changes in the distribution and magnitude of forces, and the relation between nodal and global equilibrium of a structural system. These insights are not necessarily as easily understood through the horizontal, vertical and moment equilibrium equations, which essentially describe the same relationships. This intuitive appreciation of and control over the reciprocal relationship between form and forces makes graphic statics particularly useful, not only for the design and analysis of cables, arches and trussed structures, but also for beams and frames.

Early uses of graphic statics: The first appearance of funicular force polygons in Varignon’s Nouvelle mécanique ou statique (1725), graphically computing the internal forces in physical experiments with strings.

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An early drawing (1928) by Maillart shows his use of graphic statics to find thrust lines for all loading cases constrained to go through the three structural hinges, thus defining the profile of the Salginatobel Bridge in Schiers, Switzerland (1930).

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Bow (1873) explains the use of “Diagrams of Forces” to evaluate the “Economics of Construction related to Framed Structures”, which is also the title of his book on graphic statics in which he introduces the now widely adopted Bow’s notation.

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Design by Forces Computer-aided modelling and computation make it possible to use the form and force diagrams of graphic statics as bidirectional design drivers, control mechanisms that allow the designer not only to explore the effect of the ­geometry of a structural system on its performance, but also to do the opposite: to design a structure by controlling or constructing the geometry of its forces. Optimised structural geometry can thus be obtained explicitly and directly, rather than through trial-and-error iterations of an uninformed, brute-force, design-by-analysis approach. Exploiting the geometric representation of “form and forces” as a control mechanism of two-dimensional equilibrium even further, advanced optimisation and form finding can be achieved by extending the reciprocal relation between form and force diagrams with intuitive geometric constraints. Set up as a parametric model, the geometry of a constant-force truss, for example, can be explored interactively, simply by constraining some of the vertices of the force diagram to a circle or line. An insightful, surprising way to look at any force diagram in graphic statics is as the subdivision of a closed polygon representing the global equilibrium of external forces. Each subdivision of this global polygon corresponds to a different solution for the same boundary conditions. Furthermore, any subdivision with only convex faces will result in a system of forces that is either in pure compression or tension. This principle can thus be used to explore and discover various topologies and geometries of compression-only branching structures for given loads and supports.

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Left: Enforcing constant-force bottom or top chords of truss-like systems with just one circle or line constraint applied to specific nodes of the force diagram.

Right: Subdividing the global force polygon, which represents the equilibrium of the applied loads and the reaction forces compatible with the given support locations, allows for the discovery of compression-only branching structures without predefined topology.

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Top: Thrust Network Analysis extends graphic statics to the design and analysis of shell structures; a compression-only equilibrium solution for given vertical loads is defined by the reciprocal relation between form and force diagrams. The form diagram is the horizontal projection of the three-dimensional network and the force diagram represents its horizontal equilibrium.

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Bottom: As in graphic statics, the equilibrium of a node in the form diagram is represented by a closed polygon of force vectors in the force diagram. This means that corresponding edges in both diagrams are parallel and that the magnitude of (horizontal) force in an edge in the form diagram can be obtained by measuring the length of its corresponding edge in the force diagram.

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Exploring the Indeterminacy of Shells Thrust Network Analysis (TNA) is a method for generating compression-only vaulted structures. It provides a graphical and intuitive approach to explore discrete, funicular networks by using the form and force diagrams of graphic statics to control the geometry of the projection of a chosen force layout and its horizontal equilibrium for vertical loading cases. Used in form finding, this method provides control over the many degrees of freedom of highly indeterminate, three-dimensional equilibrium networks, allowing the designer to explore an infinite range of structural forms for the same layout of edges. The form diagrams represent the horizontal projections of the layout of edges in the three-dimensional equilibrium networks, while the force diagrams visualise the specific distributions of horizontal thrust that result in their expressive shapes. A simple geometric constraint requiring all faces of the force diagrams to be convex ensures that all solutions are in pure compression. This kind of highly constrained form finding would hardly be imaginable without a direct, graphical method.

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3D Graphic Statics In spatial structures, the equilibrium of a node can be represented geometrically with a closed (convex) polyhedron instead of a closed polygon. In this three-dimensional version of graphic statics, the forces applied to the node are perpendicular to corresponding faces of the polyhedron, and their magnitudes are proportional to the areas of these faces. By combining force polyhedrons into aggregations of polyhedral cells, three-dimensional funicular systems of forces can be designed. Furthermore, by requiring that those aggregations form a proper cell decomposition of space, i. e. a cellular diagram without overlapping cells, these structures can be easily constrained to be compression- or tension-­ only. And also here, starting from a single-cell force polyhedron describing the equilibrium of the externally applied loads and reaction forces, different types of subdivision schemes can be applied to create a variety of surprising, expressive, fully spatial branching structures.

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Top: In three-dimensional graphic statics using force polyhedra, the equilibrium of a spatial node can be computed and visualised using a closed force polyhedron. If the faces of the polyhedron are perpendicular to the members coming together at the node, then the face areas represent the magnitudes of the forces along the corresponding members.

Bottom: Fully spatial solutions in compression can be obtained by aggregating polyhedral cells into an equilibrated force diagram.

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Using three-dimensional graphic statics for designing a spatial structure in compression-only allows components made from a weak material – here mycelium, essentially mushroom roots – to be used as load-bearing elements. The installation, a project with Prof. Dirk Hebel of the Karlsruhe Institute of Technology and his team, was shown at the 2017 Seoul Biennale of Architecture and Urbanism.

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Beyond Freeform Like the spectacular Gothic vaults, the cut stone vault at the centre of the exhibition was stable because of its geometry. This piece is not a romantic attempt to revive the Gothic, but rather a direct critique of freeform architecture. Standing without steel reinforcement, the expressively flowing surface highlighted the misconception that complex geometry need go hand-in-hand with inefficient use of material. It demonstrated creative possibilities within very tight design constraints. The Armadillo Vault  The Armadillo Vault embodies the beauty of compression made possible through geometry. Its shape comes from the same structural and constructional principles as the stone cathedrals of the past, enhanced and extended by computation and digital fabrication. Comprised of 399 individually cut limestone voussoirs, unreinforced and without mortar, the vault spans 16 metres with a minimum thickness of only five centimetres. The tension ties equilibrate the form, and its funicular geometry allows it to stand in pure compression. This sophisticated form emerged from the computational, graphic statics-based design and optimisation methods developed by the team. The engineering of the discrete shell also used innovative computational approaches to assess stability. Each stone is informed by structural logic, by the need for precise fabrication and assembly, by the hard constraints of a historically protected setting, as well as by tight limitations on time, budget, and construction. To simplify the fabrication process and avoid the need to flip the stones during cutting, the voussoirs are planar and smooth on the exterior. Their interior sides are marked by a series of grooves resulting from initial rough cutting. Rather than mill these surfaces away, they remain as an expressive feature, aligned with purpose to serve as visual reminders of the force flow. After its initial fabrication and test assembly in Texas, the vault was disassembled and shipped to Venice, where it was reassembled on site in just two weeks. Like an intricate 3D puzzle, it can be deconstructed and built again at future locations. 79

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Extending Stereotomy The way architecture is designed, planned and built has changed dramatically with the emergence of digital tools in the last two decades. The possibilities of modern CAD software have led to an increasingly expressive formal language in architectural design, characterised by curvilinear geometry. Furthermore, mass customisation and digital fabrication processes have enabled the realisation of freeform architecture. Thanks to advances in technology and engineering methods in today’s construction industry, almost anything is possible. However, this freedom in design has come at a cost. Often the virtual design process fails to connect with the intrinsic nature of architectural production, in which materiality and structure are the two key elements. As a consequence, the design process becomes increasingly decoupled from the subsequent realisation of a building, resulting in heavy structures and bulky constructions, and thus contributes to the waste of materials and resources. In this respect, much can be learned from master builders, who were responsible for both design and construction following a holistic approach towards architectural production. Master Builders and Stereotomy Stone architecture, especially from the Gothic period, has always excited great fascination in architects and engineers alike. This shared interest originates from the interdisciplinary design approach that was needed to realise them, inherently coupling form, material and structure. Master masons had to cope with and ensure the interrelation of all aspects of such buildings, from their architectural expression and structural form to the fabrication techniques used and the strategies for their erection. They were stimulated by the latest developments within technology available at that time while simultaneously pushing limitations of these developments further, for example, by developing intricate design strategies for domes, vaults, and bridges such that stone blocks 90

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The extrados geometry of the voussoirs of the Henry VII Lady Chapel vaults (1519) bears witness to the holistic approach of master builders, combining and balancing constraints and requirements related to architectural expression and structural form as well as to fabrication and construction.

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could be assembled into self-supporting constructions. This set of geometrical knowledge and techniques of arranging, drawing, and cutting blocks of solid material, such as stone or wood, is referred to as stereotomy. Much can be learned from traditional stereotomic techniques, especially regarding the design of structurally informed tessellation geometries, defining the segmentation of funicular forms into smaller units while considering and balancing various requirements and constraints simultaneously. Ultimately, the essence of stereotomy is exactly about this balance to satisfy multiple objectives in complex planning and construction processes – a paradigm still highly relevant with regards to contemporary freeform architecture. The Masonry Model Although the modern architectural canon has nearly eliminated traditional stonework and any form of ornamentation from the vocabulary in modern structures, much inspiration can still be drawn from the traditional craft and techniques mastered and perfected by the ancient builders. The constraints imposed by building with materials that have essentially no tensile or bending capacity, and in a context or time where modern construction technology is not available, can be summarised into a “masonry model” that can be applied to other structural systems as well, as a form of rationalisation mechanism. The masonry model essentially imposes the logic of compression-only structures onto the materialisation of otherwise less constraining structural systems. For example, following the masonry model, the discretisation of volumetric structures should be such that only minimal mechanical connections are required at the interfaces, allowing the assembled discrete structure to stand as a masonry structure would. Discrete elements such as bricks or stone blocks can be assembled into stable structures without mechanical connections or glue at the interfaces, not only through the formation of arches, but also by using friction, corbelling, or balancing. When fully embracing all of these structural actions, even a box can become a vaulted, unreinforced discrete assembly, safely standing under its own weight.

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Top: Discrete structures can stand through arch action, corbelling, and friction or any combination of these structural principles. Bottom: The Sean Collier Memorial by Yoon + Höwler Architects in Cambridge, Massachusetts, USA, (2015) is made of 32 solid granite blocks. The discrete stone structure relies on arch action with five buttressing half-arches supporting the central part.

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Top: Gothic builders reduced the need for falsework by using a system of ropes and counterweights. Bottom: Robotic assembly of a discrete model structure using two collaborative robotic arms to temporarily support and position block elements until a new equilibrated configuration is formed.

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Reducing Falsework In combination with informed construction logics, falsework for discrete assemblies can be reduced or even eliminated. An igloo, for example, can be built without a supporting structure by cutting the ice blocks so they can be placed in a spiralling sequence. Masonry domes can also be built without falsework by working in stable sections; with every completed ring of bricks, the structure is stable, and during construction of the ring the mortar’s adhesion prevents the individual bricks from sliding. For geometries that cannot be built using a spiralling or circular logic, Gothic builders developed systems using ropes, counterweights and pulleys to assemble and construct vaults with minimal supports, effectively cantilevering out in space, providing temporary reaction forces with the ropes. Sometimes even robotic assistance proves to be useful to discover surprising new masonry forms and to develop efficient 3D-puzzle-building strategies to build them with only temporary supports. The objective behind this exercise with a two-armed robotic setup is to obtain knowledge that can be used to optimise the construction sequence of, for example, large-scale shell roofs such that they can be safely installed from large pieces without falsework and using only a limited number of cranes on site. The cupola of the Sports Palace in Tbilisi, Georgia, for example, was erected in 1961 according to a specially designed assembly sequence of precast modules with custom, stepped-element geometries, without scaffolding or falsework and using only two cranes placed inside the 75-metre-span building. Although the cupola has a simple, domical shape, it serves as an inspiration for how smart construction logics could be applied to more complex architectural forms to optimise the erection process. If discrete-element assemblies are designed to have only compressive and frictional contact forces at the interfaces between the discrete parts, the assembly process can be further simplified by designing the interfaces or even the entire parts so that they facilitate building in stable sections with little or no temporary support required. They can be designed, for example, to be self-registering to simplify placement and alignment of the discrete elements.

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Force Flow Discretising or pre-cracking a structure reduces the indeterminacy of the internal force equilibrium and thereby controls the force flow, keeping the structure in compression and avoiding crack generation. By doing so, the designer tells the structure where no bending can occur. Alternatively, the structure will show through the formation of cracks in zones of tension how it found a stable equilibrium compatible with the non-tension material it is made of. Examples of this are the simple beam in bending, cracked to activate the tension ties, a stone lintel on a Greek temple, cracked at mid span, if not collapsed, standing as a three-hinged arch thanks to friction at its base, or the Pantheon in Rome, with radial cracks up to 70 millimetres wide, standing as simple arches supporting a compression dome. The three-hinged arch is perhaps the simplest example of this principle. Used by Robert Maillart for the design of the Salginatobel Bridge, it guaranteed that no additional stresses would be induced later, when differential settlement of the supports occurred due to unavoidable uneven movements of the hills on both sides of the valley. Reduced to a statically determinate structure, the internal forces are kept constant and only dependent on geometry. The combination of form finding, discretising, and post-tensioning can form an effective strategy to control force flow, deformation, and cracking of continuous parts or hinging of an assembly. Form finding enables stability to be achieved through geometry, providing material based on the compressive load paths for all loading cases. Discretising a structure means lowering the degree of structural indeterminacy by locally taking away the capacity for bending moment transfer, and post-tensioning helps to impose compressive prestress to overcome the tensile parts of bending stresses. Together, these offer opportunities to safely use a material weak in bending/tension, as shown by the presented 3D-sand-printed floor prototype.

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The 3D-printed floor prototype consists of five discrete elements that form a shallow vault in compression without any mechanical connection between them. The male/female interlocking features at the interfaces guarantee proper alignment between neighbouring elements.

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Left: Surprising discrete-element assemblies can be designed by controlling the location and orientation of the interfaces between the elements; for example, an unreinforced, “vaulted” box standing only due to compressive and frictional contact forces.

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Right: Computational tools can help to find possible decompositions of, for example, a “vaulted” box by interactively providing visual feedback regarding the corresponding compression and frictional contact forces at the interfaces between neighbouring elements.

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The Making of the Armadillo Vault The Armadillo Vault is the result of extreme constraints in time, budget, weight, size, and geometry. Many of these constraints were determined by its location inside the Corderie dell’Arsenale in Venice, a historically protected building. In this context, designing, ­engineering, and assembling a self-supporting structure without any cranes or other heavy equipment presented challenges but also motivated innovations. The team combined their deep knowledge of traditional techniques in masonry with cutting-edge methods in computational form finding and analysis to create a soaring stone vault – proportionally as thin as a third of an eggshell – that seemed to grow out of the Arsenale itself. Furthermore, as the images, analyses, and conversations in this section demonstrate, the Armadillo Vault is truly an international structure – a vault of Texas limestone blocks, quarried and cut near Austin and shipped across the Atlantic to Venice. Combining the best of computation and craft, machine and handwork, researchers, engineers, and skilled master masons on two continents orchestrated the complexities of its form finding, fabrication, test assembly, shipment, and final assembly in the course of a few months. Although the exhibition in Venice was temporary, the team hopes the Armadillo will soon find a permanent home to stand again as an embodiment of what can be achieved when we move beyond bending.

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Form and Structure The Armadillo Vault is essentially a giant, intricate, three-dimensional puzzle of 399 limestone blocks. Its shape, which allows it to stand in pure compression, unreinforced and without mortar or mechanical connections between the stones, is the result of a form finding and optimisation process applying Thrust Network Analysis. This geometry-based approach to the exploration of structural forms – using computational inverted hanging models – facilitated the integration of assembly and fabrication constraints as well as architectural and functional requirements from the early design stages to create a dramatic and structurally surprising centrepiece for the exhibition.

Roughly triangular in plan, the stone surface wrapped around the existing columns in the exhibition space. Wide steel supports distributed the vault’s weight evenly over the historic floor. A system of ties connecting the outer supports absorbed the horizontal thrust, leaving only vertical reaction forces.

Design  Various designs for the vault were first sketched on paper, laying out different combinations of features in response to the distinct characteristics of the exhibition space in the Corderie dell’Arsenale. The spatial qualities and overall structural performance of selected alternatives were further investigated through three-dimensional equilibrium studies with RhinoVAULT, a form-finding tool based on Thrust Network Analysis, for the design of compression-only surface structures. The chosen design had a roughly triangular shape in plan, covering an area of approximately 75 square metres with only four supports: one in the middle of the structure and three along the boundary. Large edge arches spanning more than 15 metres in various directions allowed the exhibition space to flow freely underneath, while two of the old masonry columns of the historic building pierced through large, oval-shaped openings in the stone surface of the structure.

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Form Finding The dominant self-weight of the vault was taken as the design load to define the funicular geometry of the middle surface of the structure. As the weight itself is a function of the geometry of this surface and locally assigned non-uniform thicknesses, this was an iterative process during which the overall design of the vault was continuously refined. Each iteration consisted of three steps. First, a thrust network was generated using form and force diagrams to explicitly control the reciprocal relationship between the direction and layout of force paths in three-dimensional force networks and the magnitude of forces in equilibrium along those directions, respectively. From this, a smooth control mesh was generated that allowed for more sculptural modifications to the geometry. A key concern was to have high positive double curvature everywhere in the shell. Finally, since the previous step did not necessarily maintain (compression-only) equilibrium, the closest possible thrust network to this modified design was generated using a “best fit” algorithm. One of the openings in the surface was pulled towards the ground to increase local double curvature even further, while maintaining an overall shallow design that evenly distributed the weight over all four supports. Because of the stress limitations on the floor, it was crucial to reduce the weight of the stone shell as much as possible. By increasing curvature, the effective structural depth necessary to resist asymmetric live loads could be increased through geometry rather than by adding mass. Based on material tests, it was determined that the minimum required thickness of the blocks was five centimetres. With large safety factors applied, this was the limiting thickness at which spalling of the stone due to eccentric loads at the interfaces could start occurring. For aesthetic reasons and to increase stability, the thickness was gradually increased towards the supports to 8 centimetres at the linear supports and 12 centimetres at the springing points on the boundary and in the middle.

Top: The distribution of horizontal forces that “best fits” the designed shell geometry with a compression-only thrust network for the assigned stone thickness is represented by (and controlled with) a force diagram. This two-dimensional equilibrium corresponds to a specific distribution of the horizontal forces along the edges of the three-dimensional thrust network.

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Right: An overview of early design options sketched digitally with RhinoVAULT, the free software plugin based on Thrust Network Analysis for the exploration of compression-­ only geometry under vertical loading, developed by the Block Research Group.

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Top: Eccentric loads were applied to test cubes of the limestone material in the MIT Civil Engineering aboratory to determine the thickness at which the voussoirs would be in danger of spalling.

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Bottom: The three-dimensional thrust network was funicular for the chosen stone thickness distribution. From the forces in the thrust network and the thickness of the stone section, a lumped stress distribution was calculated to be compared to the allowable stress in the limestone.

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Analysis Offsets from the middle surface according to the locally assigned thicknesses defined the intrados and extrados surfaces of the vault. This stone envelope was divided into courses, and the courses into blocks. By staggering the blocks and aligning the courses to the force flow and the edge arches, firm interlocking of all blocks was guaranteed, hence also ensuring three-dimensional behaviour. The stresses under all loading cases were found to be an order of magnitude below that crushing strength of the soft stone. Furthermore, the stability of the unreinforced, dry assembly of stones when subjected to different forms of loading, including concentrated loads, settlements of the supports, and earthquake loads, was analysed in accordance with the Italian code and the requirements formulated by the engineers of the Biennale. The results were verified with structural analysis software implementing the Discrete Element Method. It was shown that the structure would remain stable if people were to climb on it, hang from the edge, or if a minor earthquake occurred.

Structural analysis based on the Discrete Element Method was carried out at the University of Cambridge to evaluate how the vault would behave when subjected to point loads, differential support settlements, seismic activity, and so on.

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Engineering The Corderie dell’Arsenale is a heritage-protected, historic building. Therefore, nothing could be attached or anchored to the walls, columns or floor. Additionally, the average bearing stress on the floor could not exceed 600 kilogrammes per square metre, which is roughly the weight of a tightly packed crowd of people. Even though the weight of the vault had been reduced to the absolute minimum, special stiff footings with 20-millimetre-thick steel base plates and dense arrays of triangular, vertical stiffening plates were developed to avoid stress concentrations by spreading the weight of the vault over a sufficiently large area. To remove the need for mechanical connections between the vault and the floor, these supports were then connected by a system of ties that absorbed the outward thrust of the vault such that only the vertical components of the reaction forces had to be transferred to the ground. Each support had two ties, which were connected to a triangular frame around (but not connected to) the central support, as that support was designed to have primarily vertical reaction forces under all loading cases. The exposed ties, served as visible reminders of how the structural system worked. To keep the tension ties on the desired level and avoid deformations while people walked over them and also to reduce the risk of tripping and provide wheel chair accessibility, a simple steel bridge connected to the bottom and sides of the ties was installed. This decision not to hide the tension ties, for example under a raised floor, was made in order to explicitly show that the elegance and extreme thinness of the unreinforced shell could only be achieved with the ties equilibrating the foundations. Bending moments do not disappear; instead, they are carried through efficient compression and tension.

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Top: Many stiffeners were added to distribute the stresses on the ground as equally as possible and remain below the limit of 600 kg/m² for the protected heritage floor. Bottom: Mortar was added to reduce peak stresses below the supports and avoid breaking the floor tiles.

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Initial hand sketches exploring different boundary conditions for the compression shell, reacting to the layout of the exhibition space in the Arsenale.

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The shell’s funicular geometry was carefully sculpted using advanced TNA-based form-finding and optimisation tools available through the Block Research Group’s open source computational framework, compas.

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Fabrication of the steel supports in the Escobedo Group’s workshop in Buda, Texas.

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Engineering the Extreme A Conversation with Ochsendorf DeJong & Block

The founding partners of Ochsendorf DeJong & Block (ODB Engineering), John Ochsendorf, Matthew DeJong and Philippe Block, discuss how their past experiences as engineers as well as their broader motivations as educators helped them confront the extreme challenges posed by the Armadillo Vault. Noelle Paulson:  In the context of Ara-

vena’s Biennale theme of “Reporting from the Front”, what was the message you wanted to convey with the Armadillo Vault? Aravena was effectively provoking you when he called it the “War on Bending”, asking you to share what you are doing on the front of architecture, and what you are battling there. Philippe Block:  First of all, I wanted

to show that there are other ways to ­design, that one can start from extremely hard constraints, that the material system can be the structural system as well, and that one can do exceptional things with humble materials. Also, that engineering doesn’t have to be just about solving a problem or about optimisation, but it can also be about discovering exciting forms. We had to drive the entire project through constraints, and we did this using graphic statics methods that we extended through computation. We used equilibri116

um analysis and Discrete Element Modelling to understand the range of stability of the unreinforced cutstone vault. Ultimately this became a demonstration or a summary of our many years’ working together – Matt’s and my PhDs at MIT and both of those growing out of John’s PhD work at the University of Cambridge. That we got to do this on the world’s main stage for architecture and managed to show another way to approach design, this was extremely rewarding. John Ochsendorf:  The biggest thing is the primacy of geometry – the importance of three-dimensional geometry both locally and globally. We live in an age of architecture where buildings are trying to be noticed, but we’re also part of an age in which we have an imperative to save resources. I think our message was very clear: you can do complex geometry within constraints. The Armadillo Vault was making a bold statement about what’s possible geometrically, but it

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was an extravagant motion, albeit far less extravagant than a lot of complex geometries we see in contemporary architecture practice. What we see from this is that geometry matters and that we can produce exciting designs when we combine structural and constructional constraints with architectural considerations. And we can lift the human spirit without devastating the planet. That really was important for me.

scale structural model was necessary to convey our message. As John often says, “Masonry does not lie”, so it was really the only way to avoid any remaining scepticism and show that through geometry, we can achieve exceptional shapes. Matthew DeJong: You really can’t cheat with dry, cut-stone blocks. NP:   What were the most challeng-

ing aspects of the project? And the most rewarding ones?

NP:   Why did you choose to present

your ideas in the form of a cut-stone, unreinforced vault? How was the material important in this statement? JO:   Again, geometry had primacy –

it was about explicitly demonstrating that it stands through geometry. Stone is a traditional material – one of the world’s oldest building materials – and remarkable in that it can last for centuries. Using stone was the cleanest way to show that the vault was standing purely through geometry because, in a way, these are stacked children’s blocks, whereas if we had cast it in a thin-shell concrete or built it out of anything that had mortar in between the joints, even in bricks, it would have conveyed a very different message. PB:   I agree. It was necessary to go that extreme. Even if we were to have added mortar, then some people would have argued that part of the structural capacity was in the mortar, not the geometry. In the end, we literally had a giant, purely discrete, dry-assembled 3D puzzle. This large-

JO:   For me, it was the timing. This

was such a huge constraint on every­ thing that to do something really innovative and out on the edge of engineering in such a short amount of time was definitely the most challenging aspect. The design, engineering, fabrication, and installation all had to happen in less than a year. PB:   Actually, it was only 5 months if you exclude the time needed for transport from Texas to Venice. MD:  I think bringing together a group of people with such different types of expertise at very short notice was challenging. As ODB, we work well together and have for a while, but then integrating the theory and ideas that we already know with ­construction in Texas on the other side of the world presented more challenges, also due to the time constraints. PB:   Most rewarding to me was that we managed to stay quite pure and true to ourselves, to our methods and how we approach engineering. Through our participation in the Biennale we had an opportunity to show that there is a different way to 117

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do engineering and design. And, finally, that we pulled it off and that, all in all, everything went quite smoothly given the tight constraints. It was challenging for sure, but we did bring very different disciplines and partners together. MD:   Regarding the most rewarding aspect: it is first of all the fact that the theory actually worked! Before we decentred in Texas there was still  a small doubt in the back of my mind.  We occasionally asked ourselves: “Is this actually going to stand up?” But the bigger picture is that the project served as a Proof of Concept, the Armadillo Vault showed what is possible on that scale – that all of the theory and analysis methods we worked on for many years were effective. To see that was extremely rewarding. PB:   We had confidence it would stand after decentring, but as you said, it was indeed a challenging aspect. There were so many unknowns, particularly because of the tight time constraints, for example with assembly tolerances, with the unknown boundary conditions in the Arsenale, with potential movements of the supports because of the old, constantly moving building – these things were absolutely impossible to model or predict or even to imagine. Because of this, we had to count quite a bit on our intuitions, our engineering gut feelings, our educated guesses at many points in the process. MD:   The issue of tolerances is a good example, because that can’t actually be modelled, so instead it was a question of trying to come up with 118

a number of engineering solutions that were still robust, even though we were unsure of the tolerances. For me, the shear keys and the stereotomy were very important – all of the details related to making sure that every stone wasn’t going to move, even if the load path was in a completely different place than we predicted and based on things we couldn’t control – these were challenges for me. PB:  In fact, the shear keys were firstly there for registration, but they also allowed us to say that our assessment was within reasonable bounds of safety because we knew that those would keep the stones in place and prevent local sliding between them. MD:   We were looking at it from different, balancing perspectives. For me, the shear keys were there for keeping the stones in place – for stability under uncertain loading or under tolerance issues – and for you they were there for registration. JO:  From my perspective, in addition to the time involved, as well as the scale of this project (we had never built anything on this scale before. In fact, I don’t think anyone has built anything this “freeform” on this scale in stone, so we were in new territory), the fact that all of us effectively work multiple jobs – educators, engineers, etc. – was a big challenge. Carving out the time every week to make sure that we were pushing this forward was absolutely critical, because we couldn’t miss a week. The most rewarding thing for me was when it opened and when I first saw the public experiencing the room, the vault, the composition, and seeing

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their range of reactions. Some people were able to walk through and under the vault while barely looking up. It might as well have been a dropped tile ceiling that was not interesting at all, whereas for others, they really understood it. And some were truly moved by the beauty of it without necessarily understanding the tectonics that went into it. PB:   I think for most people, even if they didn’t like a particular aesthetic aspect of it, when they learned why it looked like that, that it was the result of an optimisation that was needed for fabrication or that it had a structural purpose, then this opened up another level of understanding and appreciation. Additionally, it was extremely rewarding to hear from our colleagues in engineering, who were and continue to be blown away by what we showed was possible with this structure, but also how we were able to keep that purity throughout the entire project. These are people who are often quite sceptical and difficult to impress, so their responses meant a lot to me. NP:   The beautiful vault of the chap-

el at King’s College at the University of Cambridge has served as an inspiration for much of your research, both independently and together. The vaults there have a thicknessto-span ratio proportional to an eggshell, but with the Armadillo Vault you were pushing the thinness to the order of one-half to one-third of an eggshell. How did you convince yourselves that this was possible? How did you sleep at night?

JO:   One of the very first things we

did when we were selecting the Texas Cream limestone was test it in the lab at MIT. The Escobedo Group shipped us some cubes, and we did testing of eccentric concentrated loads on the corners of the stone to study at what stress loads they would spall and crush. From the very beginning, my only concern about the extreme thinness was about a local spalling or local crushing failure of the stone at the corners. Once we had tested those and we saw that the stresses we were going to have in the vault were far lower than when this would occur in the stone, I felt confident that we could do something very thin. My second concern was about sliding, which Matt and Philippe have already referred to. The keys really helped us all sleep at night. We knew we weren’t going to get spalling at a corner because we couldn’t get stresses that high since the loads were rather low. And then we knew it would be really hard to get sliding. MD:   For me, the thing that really helped me sleep at night was the increase in the curvature on the legs. In a few of the initial designs, portions of the vault were a bit flatter, but in the end, I think we had enough structural depth and double curvature to ensure that some of the mechanisms of collapse that I was worried about were extremely unlikely to happen. The robustness of that double curvature was what helped me sleep at night. JO:   The curvature was a hugely important point, you’re right. That geometry was refined throughout the 119

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process because it’s true that early on, as we were developing compression-only, gravity-loading solutions, we had some options that were stable but maybe not as robust. The fact that Philippe’s team was able to iterate quickly through many different geometries to introduce more curvature helped us a lot. Along the way there were questions that required all three of us: Matt with the modelling, Philippe and his team with very fast turn-around revising the geometry, and my background with shells generally. PB:  That’s an aspect where one wouldn’t necessarily notice that this was one of our biggest challenges. To just have an inverted hanging form that stands nicely in compression is easy, but to be able to wrap around the columns in these thinner parts and nonetheless have a lot of local double curvature, that really demanded a lot of us on the structural form-­ finding side. MD:  There’s also the question of how you add that little bit of curvature locally while still integrating it with the stereotomy, how you divide the stones because adding local double curvature with discrete blocks isn’t a straightforward process. That is actually the bigger challenge: how you’re trying to create a dry stone vault. It was only possible with the advanced fabrication and digital techniques of your group, Philippe. JO:   Throughout the process there were several key conversations, and it would have been fascinating if we had recorded some of those. Almost every conversation was critical, every 120

small design change, everything we developed along the way. I remember a couple of really crucial conversations about curvature. It was basically a question of redundancy and making sure we not only had multiple load paths but also greater stability achieved through curvature. That was hugely important. MD:   For us, the two major loads were either people climbing on the vault or earthquakes. It’s impossible to model the actual built vault with all of the tolerance issues. The only way to deal with that was to have a more robust geometry. JO:   One other really important thing for me was, anytime in engineering when you go beyond the scope of what’s been done before geometrically, you could encounter unknown phenomena. We have to admit, what we did was risky. We had confidence from years of experience. We knew we weren’t endangering anyone’s lives, but there were high stakes to have the public walking under something so unprecedented. We never lost sight of that, and we were always being very careful, but I am grateful after the fact that the vault went up and came down again twice and no one got hurt, not even during the assembly. MD:   Honestly, another thing that helped us sleep at night was the fact that we had already decentred once successfully in Texas with the test assembly there. If we hadn’t done that, it would have all been a lot more nerve-racking.

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NP:   Did you have models that al-

lowed you to be confident about the tolerances? PB:   Because we had already focused

so much on the double curvature during the design stage, we knew that the shell was going to be quite stiff. During decentring, we had key markers at the mid-spans where we traced the vertical deflections to find out that nowhere were they more than 4 mm. That meant not only was the vault stiff but it was also assembled quite tightly, because otherwise all the accumulations of tolerances would have made the stiff geometry more flexible, resulting in more deformation. After witnessing that there was not a lot of vertical deflection, I felt confident that we were fine. MD:   I remember being concerned about the central support bearing on the soft sand infill above the rail in the middle of the room in the Arsenale. Two things helped give me confidence that it would work: first the double curvature, and second the simulations we did of different support movements and how the load redistributes – also how there are lots of other load paths that the structure could withstand and therefore take the weight. Both this project as well as the work we did for the potential shell to be built at the Martin Luther King Jr. Park in Austin, Texas, where we looked at differential support movements and how the load can redistribute in a discrete stone vault, gave me more confidence. JO:   For me, it was really the ability to carry load even through mech-

anisms, going all the way back to Jacques Heyman’s “The Stone Skeleton” article from 1966 – you have a small movement, you have some hinging – and in this case we knew that if we did get hinging, the stresses were still low enough that the stone wasn’t going to spall. At the end of the day, for such a large vault these kinds of movements of millimetres are very small. It would have been an incredible science experiment if we could have moved one of the supports outward with the scaffolding just under it to see how far it could go, but I have confidence that the supports could move much, much further than the range of possibilities without losing a stone because of all the issues discussed. PB:   Another important point, which you also alluded to, Matt, is that all of this was possible, that we could realise something so extreme in such a short amount of time, because there was mutual trust between all of the partners. This trust was built on the many, many years we’ve been collaborating. I usually thought this collaboration was most relevant for the understanding of stereotomy and construction methods from ­Escobedo or of knowing how to optimise the fabrication of the stone vaulting, but you’re right that with the MLK Jr. Park Vault we also had had a very big cut-stone project for which we had done extensive engineering and tested a lot of hypotheses. In some ways, we had already done the exercise before; we had already considered certain strategies and aspects of it. 121

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MD:   I think that design in Texas was

really important because we directly compared our methods then. It was also a full-scale project of a similar size and that gave us the confidence that we could do this even with the short time frame, since we had already done those other designs and compared our methods during those trials. JO:   That’s true. We gained a lot of experience in terms of analysis and even in terms of curvature, because I remember that we had similar conversations during the Austin project about the geometry and the curvature and redundancy. All those conversations and the engineering work that went into that project, even though we didn’t build it yet, were a training ground for the Venice project. PB:   For that project, we had done several iterations and also several large-scale, 3D-printed structural models. Initially, our first model had a dramatic global collapse triggered by a local collapse ( just a couple of stones falling out). From that, we started to look more consciously at double curvature and these local stabilities. It actually made me a little bit more nervous that in the case of the Armadillo Vault, because the absolute accuracy of both the real-scale structure and the 3D-printed model are almost the same, we never managed to assemble our 3D-printed scale model. Luckily we had sufficient confidence in the comparisons that we had done before for the other project, because that’s … JO:   Wait a minute! Are you telling us now, for the first time, that you tried 122

to assemble the 3D-printed model but it never stood up?! PB:   We printed it three times on increasingly more expensive printers to be sure, because the tolerances due to the accuracy of the 3D-printed material are the same as those expected by the Escobedo Group on the full-scale structure. It would not fit together because the tolerances did not vary linearly with size. JO:   It was more of a construction than a structural problem? PB:   Yes, but that nonetheless made the test assembly in Texas remarkably more stressful for me than it would have been had the model worked. NP:   Some might say that Italy is the

country of stone, so why did you decide to team up with the Escobedo Group from Texas? JO:   We had already had eight or more

years of direct conversation, collaboration, and learning from each other, and the Biennale project built directly on those many years of experience. We could never have done what we did with a 5 months’ timeline without a high level of trust and experience with each other. In many ways, the previous decade or more since I’ve known them, those years were basically in preparation for getting the call from Aravena inviting us to the Biennale. And it must be said, one of our very first actions after getting the invitation was to reach out to the Escobedos to say, “would you join with us on this?” Without much hesitation, they were in and put a ton of trust and faith and resources into the project to make it possible.

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PB:   If you really want to push inno-

vation and go beyond common practice, you cannot just treat the project using the typical, sequential logic of independent stages of design, engineering, fabrication and construction, you cannot design some grand thing that an engineer signs off on and then just build it. To really go to the next level, all these disciplines need to be engaged in the design process from the start. I really believe that this would not have worked in a more typical, linear process – even if we had had twice as much time. There’s engineering intuition and methods, there’s advance control of geometry, etc., but at the end of the day, the information and the direct feedback and skill of the hand and of the craft are what make it happen. That’s why we needed to work with the best! NP:   Are there things to be learned

beyond stone, beyond masonry from this project? What are the next challenges in this direction? JO:   The challenges are in the con-

struction of more efficient shell structures. They may not be in real stone; they may be in precast concrete panels or some other elements; they may have relevance to contemporary construction – something like formwork or scaffolding that gets kept in place permanently and gets a thin casting on top to reach higher. If we’re honest with ourselves, yes, we could do an exciting lobby in a particular venue on a similar scale, but if we really want to change con-

struction, the bigger message in the room at the Biennale was the floor systems, though maybe there are some longer-span possibilities where the lessons we learned from the Armadillo Vault could be applied to shell construction. PB:   That’s true. As much as we pat ourselves on the back for having achieved this engineering feat and shown something uniquely beautiful, at the end of the day it served as an eye-catcher within this large Biennale to get people to pause and hopefully listen to our story about the benefits of compression and arch action when used appropriately in the context of the developing world or our message that one could save more than 70 % of materials. If we had shown only the floor systems at the Biennale, even though they represent the key message and those research streams will have a very big impact, people would not really have understood what’s important there. We needed a bold statement to clarify that, if you understand geometry and have appropriate methods to demonstrate safety, there are extreme savings and improvements to be achieved. MD:   Even though we may not replicate this project multiple times, from an educational point of view, it’s also important that we used the same material as the master builders of the past. Everybody admires the vaults and arches of historic buildings, but they also think, “We’ve done that, we know arches. That’s not applicable anymore.” But the fact that we re-­ invented these forms using the same 123

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techniques, the same theory of compression-efficient forms, the same material, but with modern technology – that wakes up a lot of people and changes their perspectives on that type of construction. The pure-compression idea isn’t just historic. It can be reimagined in new ways. NP:  Looking back at the project, was

there anything you would have done differently? MD:   Whenever you try to do some-

thing completely new, you learn what you don’t know. That’s definitely what happened here, but that’s also what makes it worthwhile. NP:   Would you do it again? PB:   I would do it again for sure, but

thinner! [laughter] JO:   I absolutely would too. Maybe it’s because of a certain feeling of austerity in the face of climate change and pressing social problems, but I think we have to ask ourselves, how do we improve the world, how do we make it better through our work? We have a moral obligation to take the lessons of the Armadillo Vault and spread them more widely, especially in e­ ducation and construction. The ultimate message is about building better with lower environmental impact and cost. The things we demonstrated in terms of time, efficiency, digital fabrication and design processes, all of these lessons can translate into efficiencies in the world of construction, architecture, 124

and engineering, but in order to do that, we had to make a rather big statement. We had a ­special platform to be able to do that at the Biennale, but I don’t want to lose sight of the larger question of what’s at stake for the planet. How do we build better for future generations? At the heart of it, that’s what the Armadillo Vault was about. PB:   I could not agree more. The Armadillo Vault not only attracts attention and curiosity, but also demonstrates how one can bring back forgotten methods (like graphic statics) to discover elegant and efficient form or how one can convincingly show that there are other ways of doing engineering. JO:   Along those lines, there’s an absolute insistence that engineering is not a reductionist pursuit. There’s not just the one answer – the one Mies van der Rohe discovered – the steel frame. Engineering is absolutely a creative and rich activity with endless frontiers of exploration. Each of us in the project really explored our intellectual frontiers. In some ways we’re trying to push the edge of what is possible, and that’s at the very heart of engineering, whether it’s Eiffel with a 300-meter-high tower or ­Maillart with a humble concrete bridge. We’re not in the same class as those great engineers, but we are exploring intellectually in the same ways they did. We do this for many, many reasons, but at the very heart of it, we have to confess to ourselves that it’s largely an intellectual exploration. And it sure was fun and exciting too!

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NP:   You are first and foremost edu-

cators. How important is it for you to also be able to demonstrate and apply your research in practice? JO:   Our day jobs really are as edu-

cators, and this has been an exciting intellectual journey for me. Like to Philippe, when I first stood under the vault at King’s College in 1998, I had had 6 years of education in structural engineering, but I realised I didn’t have the foggiest idea how to design or calculate something like that! From a pedagogic standpoint, there are so many lessons we can learn from masonry. If it works well in masonry, then it also works well in timber, in steel, and in other materials perhaps even more so. MD:   What’s been really nice about our work with ODB is that we’ve been able to switch back and forth between allowing research to drive new solutions in practice and allowing a project like this to feed back into driving new research. I think it goes both ways. From an educator’s point of view, doing practical work keeps you grounded in doing realistic things and making sure your research is applicable, but then it also gives you new research questions to explore. Looking back at this project, it has inspired some new research ideas and new directions. JO:   I can also speak directly to the field of civil engineering and the need for professors to be engaged in practice as a way of both finding new research problems but also remaining relevant to society. After all, civil works are for society. There’s a strong

tradition in Europe of the practitioner professor who is both a leading researcher and a leader in practice as well. Sadly, this is something we have lost in the United States. In the field of civil engineering, many professors in the U.S. are developing technologies that could in theory be applied to practice, but it’s usually one or two generations in the future. That’s very different from other fields of engineering, like electrical engineering or materials science. Technologies being developed there often can be applied more quickly. They’re often dealing with very minor details, but I would argue that what we’re dealing with is at the very heart of everything an engineer should know – about geometry, about numerical models versus hand calculations, about intuition, about environmental issues. I think all three of us could say we became better engineers as a result of this project, and our students did too.

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Stereotomy and Fabrication As with all aspects of the Armadillo Vault’s design, the discretisation or tessellation was informed by constraints. These included minimising the weight of the structure on the historic floor as well as the time needed for fabrication and assembly. Because very little time was left for cutting the stones, the entire process had to be extremely efficient. To optimise fabrication, a series of measures were taken, primarily to maximise the cuts that can be processed using a circular blade and to limit the manoeuvring of blanks during the 5-axis CNC machining process. A particular challenge was to control the accumulation of tolerances as much as possible during assembly through the use of self-registering block geometries. Together, the steps undertaken to satisfy the many demanding constraints resulted in the unique appearance of the vault.

For the tesselation design, the funicular middle surface was first divided into courses using geodesic lines. These were then optimised to be as perpendicular as possible to the designed force flow.

Tessellation Design The tessellation design follows the form-finding and optimisation process defining the intrados and extrados surfaces of the vault. The resulting stone envelope was segmented into individual blocks, the voussoirs, following a tessellation pattern taking into account the fabrication and assembly constraints. To speed up the fabrication process, the stones were made as large as possible, but still light enough so that they could be handled manually using a lightweight jib crane. The size and weight of the stones were further controlled according to the curvature of their surfaces and their positions in the structure, with larger, heavier stones closer to the supports. First, the stone surface was divided into courses, which were initially formed by geodesic lines and then optimised to be as perpendicular as possible to the designed force flow towards the supports. The course lines were then split following a staggered pattern between neighbouring courses to guarantee proper 127

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interlocking of all stones in the surface of the discretised shell. Furthermore, to allow for manual lifting and positioning of the stones, their sizes were ­limited so their weights would not exceed 135 kilogrammes at the footings and 10 kilogrammes at the top.

The rough-cut pattern on the intrados, parallel to the force flow, served as an input for the generation of the final tessellation. All faces of the tessellation were designed to be convex to allow for efficient cutting of the blank stones with a circular saw.

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Voussoir Geometry Due to the limited timeframe and large number of voussoirs, the main goal for the fabrication process was to reduce the average cutting time for each stone. Additionally, since there is no mortar between the voussoirs, which could have compensated for tolerances, the interfaces between stones had to be flush and therefore precisely cut and set. To optimise the fabrication process, the voussoirs were designed to have a convex cutting geometry along the interfaces, such that they could be cut efficiently with a circular saw. To reduce machining time the bottom face of each stone blank was left untreated, thus requiring the incorporation of planar faces in the design of the doubly curved shell geometry. However, the vault has several areas with negative Gaussian curvature. Since it is geometrically impossible to discretise such a surface with a convex, planar mesh given the staggered tessellation pattern, the faces of the extrados were allowed to disconnect and to create a stepped, scale-like exterior. This visually emphasised the discrete nature of the shell and allowed the flat extrados faces to be used as a base for the machining process.

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Orientation of the disconnected, planar extrados faces was optimised to control stepping from one face to its neighbours while maintaining a minimum thickness of five centimetres for all interfaces between adjacent stones, as determined by the spalling tests. The colour plots show the step sizes between voussoirs before and after the optimisation was performed.

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Stone Cutting As a result of the stepped exterior and its planar top faces, the cubic blanks did not need to be flipped and re-referenced, significantly reducing fabrication time. The curved intrados faces were formed by side-by-side cuts with a circular blade, spaced such that thin stone fins remained. Rather than milling these away, the fins were hammered off manually to a create a rough texture for the precisely curved surface. All side surfaces of each voussoir were approximated with simple planar cuts. After this step, custom profiling tools shaved off the last millimetres in order to be able to guarantee the required 0.4 millimetre accuracy for each block. The side surfaces perpendicular to the force flow were processed with tools that create ruled surfaces with male/female registration grooves. These grooves were primarily used as a reference geometry to assist assembly, but they also prevent local sliding failure. For structural reasons, it was most important to have contacts that were as tight as possible between neighbouring stones so that, after decentring, no unpredictable settling of the assembly would occur. During the assembly process, where necessary, the interfaces were sanded off to improve the fit. The level of precision reached through manually trimming a stone depends on its initial geometry. Flat surfaces can more easily be processed further with simple templates and tools than (doubly) curved surfaces. Therefore, limiting the interfaces of the blocks to simple planar and ruled surfaces for fabrication requirements also facilitated the making of manual corrections by the expert stone masons.

Each stone had a curved intrados and planar, stepped extrados. The side surfaces were made with planar cuts, and those perpendicular to the force flow were post-processed with a custom-made tool to create ruled interfaces with male/female registration grooves.

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From top left to bottom right: Machining sequence of a typical voussoir: Placing of the blank; cutting of the planar approximation of the side faces; rough cutting of the intrados surface using a step size larger than the blade’s width; manual knocking off of the remaining stone fins; and milling of the load-bearing

interfaces with custom-developed profiling tools to add the registration grooves. As a result of capitalising on the planar extrados face, the blanks never had to be moved or flipped during the cutting process.

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Large blocks of the mild Texas Cream limestone being quarried. Part of the reason for choosing this stone was its few natural flaws, meaning that less of the stone was wasted.

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The thin stone fins, remaining from the rough cutting and with step sizes of about twice the blade’s width, are easily knocked off with a hammer.

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Some of the cut voussoirs waiting for the test assembly.

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Informing Geometry A Conversation with the Block Research Group

In this conversation, members of the Block Research Group, ETH Zürich, including Philippe Block, co-director of r­ esearch Tom Van Mele and post-doctoral researcher Matthias Ripp­ mann discuss with co-author Noelle Paulson how the design, optimisation, and fabrication of the Armadillo Vault initiated them in the practices of today’s digital master builders. Noelle Paulson:  For you personally,

what were the most rewarding aspects of the project? Philippe Block: First of all, that it came

together and in such a short time. It unified everything we have been researching and working on for the last ten years. Tom Van Mele:  Indeed, that it actually worked! Though we were certain it would stand, that was still kind of an open question until the end, but for me personally, the most rewarding moments were during the last few days before the exhibition opened to the public. Everything was up, everything was done. The quiet time in between the craziness, when we as a group were there and could have the place to ourselves, this was special. PB:   It was also rewarding that we were able to scale it up. As a group, we showed that we can not only do structural design but we also man138

aged a highly complex architectural geometry coupled with digital fabrication in the midst of extreme time constraints and, here and there, a bit of chaos. I was also surprised and glad that we managed to reach audiences outside the usual boxes we’re placed in and that triggered excitement across fields/disciplines. Matthias Rippmann:  Without doubt, it was widely appreciated. Everybody seemed to get it. They saw that using such an extreme form, we were able to go to such a thin structure. From the responses, I never got the feeling that people who had seen the vault still said, “We’ve built millions of stone structures over the millennia, what’s so special about this one?” It’s more than that. It’s the incorporation of all of our tools that allowed us to go to such extremes. PB:  I’m proud that we managed to control all of that: the geometry was one-to-one very consistent, no compromises, it just worked.

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NP:  What aspects were most chal-

NP:  What did you learn from this

lenging?

project?

TVM:   For me, it was knowing when

PB:   What I learned from this was

to stop. We were never 100 % certain, but at some point we always had to say, “Okay, this is going to be the shape, or yes, it’s going to stand” because you have to move forward on the strict timeline. None of this was based on prior experience building such structures, so we just had to say, “Okay, yes, it’s ready, let’s stop now!” MR:   We also had the added challenge of people working in completely different locations and having different local terminology. Really innovative construction projects happen all the time, also under very tight time constraints, but it should also be kept in mind that we were a relatively small but extremely diverse team mainly comprised of researchers. Before this, we had no pipeline to pull off these kinds of projects. Plus, usually in a research context we are allowed and indeed expected to do iterations and take time to validate our results. However, in architecture and in any professional environment, pragmatism is more important. Quick decisions are needed to move forward and to keep the project within budget or time constraints. The luxury of iterations was something we didn’t have with this project, which made it even more important that we could trust and rely upon our partners to know that it would all get done because there was almost no time for double-checking.

primarily the luxury of being a lean team. We worked with one vertically integrated fabricator/contractor collaborating with essentially one structural design and engineering team – that efficiency was a gift. Now having worked on other cutting-edge projects, I realise how lucky we were to work with this direct exchange and how it really enabled us to pull off such an extreme structure. TVM:   In terms of what we did, what we learned is not exactly something new because the things we thought would work did actually work, and that’s also what we learned from it: it was worth having confidence in our methods because our methods actually work. PB:  It proves that persistence pays off. We’ve dedicated many years to this in an academic, abstract, scale-model-demonstrating kind of way. We spent many years, much time in research exchange, going to stay with the Escobedos to learn how to integrate our processes with theirs and try out something new – and the same for our engineering processes. MR:   This attitude of being fully con­ vinced and drawing upon a long history of collaboration, I think that was also a driver for everybody else involved. Everybody entered into this being fully convinced that we are doing it for really good reasons. Even if it was difficult and challenging at times.

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NP:  Why did you decide to team

up with the Escobedo Group from Texas? Wouldn’t it have been easier to find a construction company in Italy? MR:   For us there was no question

we would not work with the Escobedos! Of course we would! Plus, they agreed to it almost immediately. PB:   Five minutes into the phone call with David Escobedo when I told him about the opportunity, he said, “Of course! But first I have to ask my wife.” It was Kathy who fully believed in this and went for it right away, so then David was on board too. Ours has been a long-term partnership with the Escobedo Group, which started during my PhD, but also Matthias went to work with them for a month, Cristián Calvo Barentin, a research assistant in our group, went for a couple of weeks to try out concepts on how to most efficiently send our geometry for cutting. It was always a joint commitment. TVM:   And of course simply from a pragmatic point of view, a project like this needs a financial backer, a partner who is willing to take on that aspect of the project with the same level of dedication, so it didn’t land entirely on us. It was only six months, so very quickly there was a gigantic point of no return. It’s not like a fouryear project in which there would be numerous times when one could say, “We have to put a stop to this!” MR:   David is a man of his word and was fully committed. This type of personality helped immensely. If it had been someone we didn’t know as well, 140

for example a company in Italy, even if that’s geographically more convenient to Switzerland and certainly the Biennale, the trust was so essential – and built up over such a long period of time – that it would never have worked in a different constellation. TVM:   We had even already built silly things in his backyard. PB:  The most sensational dog houses in the world! NP:  What is the future of stone as

a material? PB:   Stone has a special meaning in

the historic context of the amazing Arsenale building, and in Italy, of course. As a model, it also allows us to be as pure as possible. TVM:   People tend to discard the material as somehow not flashy enough, but there are a lot of opportunities for appropriate stone construction in the right context. PB:   Using stone was a way for us to show that one can achieve stability and strength through geometry rather than strength through material capacity. This was one of the key lessons we wanted to show. At a certain point, we were deciding between doing a full-scale, 3D-sand-printed vault or a stone vault. The difference would have been that if we had printed it, we might have had more formal freedom, but with a stone vault, we had to cut it. Not only that, but we had to think how to cut it, how to fit that cutting time within the strict time constraints, and how to deal with these processes as efficiently as possible. That all helped us to make

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our point that even by starting with such extremely hard constraints, you can nonetheless achieve something very exciting. TVM:   Stone is such an unforgiving material. That’s probably the primary reason why we chose to build it in stone. It’s not a material that people would associate with a structure that stands like this, whereas if we had 3D-printed it, people would have understood it only as a gigantic pile of glue. Stone makes a stronger statement. People ask themselves, “Wait a minute! Where is all the reinforcement?? How can stone stand like this?” NP:  It’s true. When I think of stone, I

think of big, heavy, thick blocks, not the light, thin voussoirs that I saw in the Armadillo Vault. TVM:   The thinness of the voussoirs

was also a necessity, given the limits of the historically protected building. We were really pushing to the edge of what we were comfortable with because of the need to reduce the stresses on the floor. We could have also made it five centimetres thicker, and it still would have been an incredibly impressive structure. MR:   If we had 3D printed it, it would have had a completely different character, even if we had worked with something like 3D-printed artificial sandstone, but that’s an additive and not subtractive fabrication process, which makes a big difference. Then, for instance with the intrados and extrados, we would not have ended up with the unique textures. Now, the material does the talking with the

roughly broken-off fins. How would you get the same character from a different material, but also why would you have modelled it like that? TVM: We had that in mind when we designed it. The overall design was very clear but exactly how every single stone would look was actually uncontrollable. PB:   That was also something that was extremely rewarding. Yes, we had our models; yes, we aligned the inner course lines to the force flow. We had a lot of ideas about how to distribute the splitting points over the cutting lines on the intrados to achieve a certain effect, but when we saw it, none of us could have expected how smooth the texture would be. MR:   We only really saw the effect of the intrados after it was fully decentred, something we couldn’t get to experience during the test-assembly in Texas because the falsework was never fully removed. This was unique in comparison to many other projects because we didn’t have the chance to model or visualise the specific texture of the broken-off fins during the design phase. We all had our ideas about how it would look and had done a few renders, but when it was finally fully revealed, that was a special moment. NP:   Because of these textures and

especially the fins, the vault had a very tactile quality. It seemed everyone wanted to touch it. MR:   I think some people may have

broken off a small piece, like the Berlin Wall. [laughter] 141

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PB:   Another nice aspect was the

difference between the intrados and the extrados with this shingling effect. The effect actually grew out of the necessity of not flipping the stone during the cutting process. Then, we knew mathematically, geometrically that it would have led to some awkward dovetail shapes in areas of negative curvature, which made it clear that we had to shingle and introduce a stepped extrados. From that point onwards, this was a feature that we celebrated. In the end, this was something that almost summarised the whole project – the balance between necessity and surprise and celebrating discoveries along the way. They were not just constraints but potentials that could really express other layers of reading and possibility. MR:   This really emphasised the discreteness as well. On the inside it’s surprising that it doesn’t stick out. I very much like this contrast because it underlines that the whole structure is more than the sum of its parts – both structurally and aesthetically. PB:   Yes, you don’t notice the discretisation on the inside, whereas on the outside it’s so prominent. It creates a duality between in and out. NP:  How did you deal with con-

trolling the tolerances? TVM:   The point of the structure

and its design was that it could actually stand in many different ways. We maximised the double curvature everywhere with the goal that it didn’t need to be millimetre-perfect. PB:   The registration grooves were a 142

key feature that gave us an indication of how the vault should come together. The architectural geometry, the definition of the stones with the staggering, the slight convexity, which was a necessity for efficient cutting, also helped us to find a self-registering geometry that could come together in only one way or settle very close to how it would have needed to come together. NP:   So, the concept of having reg-

istration was not planned from the beginning? PB:   It was not immediately part of

the plan but then we noticed we lost our registration on the inside because of the fabrication optimisation. We had this rough inside, so our frame of reference was gone, and we needed something to align the stones locally. TVM:   We didn’t compute it as such. In 3DEC [the Discrete Element Method used], it was modelled as if the registration grooves were not there, so we wouldn’t rely on them to provide global stability. MR:   They were basically a compensation for knowing that the actual structure (as compared to the 3DEC model) is not a perfect geometry. TVM:  That’s also why they were there for Matt [DeJong], because we already knew from previous research and papers that there is a big difference between what you build and measure and what you calculate as a perfect geometry so you can get more capacity – so, this being modelled and calculated as a perfect geometry would have been a tight call, because

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we knew it was not going to be perfect. Knowing that these registrations were not in the model but would be there in the actual built structure was what made Matt confident enough. NP:   How did you interface with the

cutting machine? MR:   It was crucial that Cristián [Cal-

vo Barentin] from our team was there in Texas to facilitate the technology transfer and also serve as a kind of local “translator”. TVM:   We talk about very specific geometric concepts and nomenclature, and the Escobedos and their team deal with these things in their own localised jargon. Of course, the physical relationship is very clear, but the way you talk about it or describe it may require some translation. Having Cristián there gave us someone we could really talk to. As one of our group, we needed fewer words to explain the same principles to him, and he already knew the geometry well, so he could immediately assess if the result was what we had been aiming for when a stone was cut. PB:   Coming from research, our instinct would be to control the machine directly using our custom software setup, but here the scale of the project and the high risk of the cutting machine actually breaking meant we had to be extra careful. Rather than directly programming G-code that would be sent straight to the machine, we really wanted to set up procedures to respect the safety protocols. This was a lesson to be learned well. Theoretically or in an

academic setting, we would probably set up a complete “digital chain” to control the machine directly from our code and do everything automatically. MR:   It would have been an academic exercise just to make a point, but it’s really not pragmatic. It took about 10 minutes per stone with some additional helper tools and then we could go through the usual process and use already existing software. It may have been a bit clumsy but it got the job done. It was one of those very pragmatic decisions you need to make during the development of an architectural project. PB:   And rather than cutting the machinist out of the loop, we instead provided him with tools to optimise his task. TVM:   It was not our job to tell them how to do their jobs. We just wanted to ensure that the translation from one setting to another happened properly and smoothly. Given the time difference between Switzerland and Texas, this would have been almost impossible if Cristián had not been there. NP:   In what ways did the theme of

“Learning from the Past” become apparent during the project? TVM:   In general, the entire approach

was based on how things were done in the past, but then we did it digitally. PB:   We’re constantly working to try to resolve hard lines of separation between the designer, architect, ­engineer, and builder. In order to really push boundaries, these categories need to be connected, not separated. 143

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With this project we proposed a model of a new “digital master builder”. It was obvious in the past that one could not build a stone cathedral by simply drawing a sketch and not knowing a thing about construction. TVM:   We did nothing like they would have done it in the past, but nevertheless the entire approach, controlling the geometry rather than doing a structural optimisation, having these few guiding principles pushed to the extreme, all of that comes from the past. We didn’t invent this. We just made it into something that was fully integrated and computationally controlled, therefore allowing us to apply the principles to make something extreme. PB:   We are proposing new ways to design using graphical techniques. The techniques themselves are not new. We’re just bringing them back and extending them through computation. This approach is so orthogonal to what much of the rest of the engineering profession believe, but the project allowed us to clarify that one should bring such methods back. NP:   Looking back at the project, is

there anything you would do differently? PB:   I personally don’t think there’s

much we should or could have done differently. Some people suggested that the tension ties were the only minor aspect of the project that we might have done differently. But I found those so important to make a statement about balancing of equilibrium rather than hiding the ties un144

der a platform. This type of approach would have been counter to our philosophy. We prefer to disseminate our research, share our tools, work in an open-source kind of manner, always be educational/pedagogic. Hiding the tension ties would have lost much of that meaning. TVM:   For me, I actually think that’s the one thing I didn’t really like, but it worked well in the end because it was so big where the metal caps on the ties were. I would have preferred to see the ties actually, but this was not possible for safety reasons. And, even though they were covered, people still stumbled over them somehow. MR:   Maybe in the very complex design and planning process we might have found better ways to collaborate earlier on. We might have underestimated the challenge of many people working together on very inter-connected problems within a very short time frame. TVM:   If we were doing this today, because everyone in our group is now more fully integrated into using our computational framework, compas, this would have been a very natural way to exchange data. But then I often had to put data back in, translating it from another process. It would be much easier now. In the end, of course we could have managed small things differently, but we were actually a very lean team of only 6 people. Everybody was so pushed down to the wire by the time constraints that, even if we had organised it differently, it would have ended up being more or less the same. There would not have been less stress.

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NP:   Would you do it again? TVM:   Never say never! PB:   I think we were all fully aware

into what kind of intensity we were launching ourselves. We did this because it was such a unique opportunity to demonstrate why it is we research what we do. Now because of it we have all these opportunities to further clarify why we have stuck to masonry for such a long time. Maybe we wouldn’t do exactly the same thing again, but there are always new things that we can demonstrate. TVM:   I agree. We probably wouldn’t do exactly the same thing again, but we will probably at least contribute to similar types of projects. I think we all agreed that a project of that magnitude is not something the research group should consistently be subjected to, but in the sense of building structures that no one has ever built before, well… we have one such large-scale structure currently under construction in our lab right now (the full-scale prototype for the roof of the NEST HiLo unit). PB:  It’s a delicate balance because we would not be in the situation we are in now as a research group if we had not had the opportunity to demonstrate our research in such a prominent way. But that opportunity meant essentially that many people had to step away from their own research for months to be able to dedicate the required resources to this effort. This then poses a conundrum, because it’s so clearly important for our research but it’s also not compatible with what we are supposed to do. But if we don’t

do those things and we can’t find the right professional partner to do it with us, how are we supposed to really push the boundaries in construction? MR:   In a way, as a research group, we have a privileged stance. We can actually take more risk. This project wouldn’t really have been feasible for a company. PB:   Also, we were extremely fortunate to have a partner willing to work 20-hour-days for 3 months virtually non-stop in order to cut the stones and assemble this. MR:   The Escobedos were fully committed to and driven by this. Otherwise, at a certain point they might have just said, “All right, this is silly!” Or, “That doesn’t make sense!” TVM:   The magnitude of this project was extreme. We could only pull this off because we’re a research group and had the freedom to decide to commit whatever it took to get this done. And the people we have working for and with us are the kind of people who are willing to work such long hours and put in such dedication.

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Construction and Assembly The Armadillo Vault has been assembled and disassembled twice by the skilled masons of the Escobedo Group under the lead of David and Matt Escobedo. A construction and assembly system was designed to accommodate their stone-setting process, while facilitating a low-tech yet precise decentring mechanism. During a first test assembly with this system at the facilities of the Escobedo Group in Buda, Texas, a reference frame was defined and the position of each stone in the assembled structures was marked and recorded with five total stations. These measurements served as a construction manual for the second assembly in Venice.

Falsework Design The falsework consisted of a discretised timber reference surface supported by eleven independent scaffolding towers, which allowed for a gradual, sequential, and circular decentring scheme. During assembly, the independent towers were connected and braced horizontally and laterally to create a rigid supporting structure. By using scaffolding towers rather than individual props, the falsework could be lowered smoothly in sections by a small crew of only eight workers. The reference surface for the stones was created with a stiff grillage of slotted wooden planks. It was designed to support the various asymmetric weight distributions of the partially assembled structure during different stages of the construction process. The top of the timber grid precisely traced the intrados of the vault, offset by two centimetres for the wooden shims. Careful control of the grid spacing allowed every stone to be supported at least by three points. The shape and size of the individual wooden elements were adapted to match the sizes of the independent towers, and further constrained to the dimensions of the shipping containers and the width of the doors in the Arsenale. 147

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Footings and Falsework Assembly Working on a hugely deformed historic floor, the first step of the entire assembly process was to recreate the reference frame for the measurement setup that was established during the test assembly in Texas, and create a level base. The prefabricated steel supports were placed with very high precision (± 0.4 mm) and levelled using hard plastic pads. The space between the pads was filled with grout to maximise contact with the ground and distribute the bearing stresses evenly over the historic floor to avoid cracking. Because the use of heavy machinery is not allowed in the Arsenale (there is a danger the equipment might crack the floor’s tiles), three custom-designed, lightweight jib cranes were used instead. The cranes were mounted on the scaffolding to reach all parts of the vault, carefully swivelling and rotating past the fragile brick columns to hoist the heavy stones, which weighed from 45 to 135 kilogrammes, to their specific locations. Stone Setting The stones were set starting from all four supports at the same pace in order to maintain a balanced equilibrium and limit the asymmetry of the loads on the falsework as much as possible. The stones were positioned using the registration grooves and the additional scratch marks made by the masons after the test assembly. The corners on the extrados of the voussoirs were measured with the total stations to define their exact positions, adjusting their height and inclination using wooden shims. After each third or fourth course was laid, the unsupported edge arches of the vault were closed to check that the pieces of the three-dimensional puzzle would still come together at the top. When misalignments were found – fractions of a millimetre in lower rows can accumulate to multiple centimetres towards the top of the vault – corrections were made or parts even entirely rebuilt. Four keystone rows were designed that needed to be assembled last. To ensure a perfect fit, the stones of these rows were generated only at the end of the test assembly in Texas based on precise measurements of the remaining space between the converging sections. The vault was slightly raised to allow the keystones to slide in and then dropped again to tightly close the surface. The interfaces at these final rows could thus not have interlocking features, such as the above-mentioned registration grooves.

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The stones were carefully positioned on the stable wooden falsework grillage by shimming the rough intrados surface from below. Registration grooves and score marks applied by the masons during the test assembly served as a local reference. The global position of each stone was carefully measured using total stations.

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The Escobedo Group’s skilled masons used their experience in traditional stone setting to manually work the stones’ interfaces until a razor-blade-tight fit was achieved.

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The falsework consisted of a rigid wooden grillage, discretised in several pieces and supported by eleven independent scaffolding towers. Although braced during assembly, the different parts were designed to be gradually lowered independently, based on a specific decentring scheme.

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After assembly, the scaffolding towers were lowered one by one, in a circular order and over several rounds. After a few turns, each of which lowered the supporting structure by

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only a fraction of a millimetre, the wooden shims started falling out, indicating that the vault was supporting itself and that the grillage pieces could be taken out safely.

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Decentring Decentring is one of the most critical moments during the construction of an unreinforced funicular vault, because any unevenly supported states are equivalent to the application of a large (asymmetric) live load. Gradual and uniform lowering of the falsework is thus essential to avoid local sliding or even global instability, which could lead to collapse. The decentring sequence and protocol were designed with this in mind. First, the lateral cross-bracing between the scaffolding towers was taken out. Then, the ties were pretensioned to 80 % of their final tensioned state. This prevents spreading of the supports immediately after decentring when the vault thrusts outwards as it starts carrying its own weight. The decentring sequence followed a circular pattern over the eleven scaffolding towers, always going from stiffer to more deformation-prone parts of the vault in increments of only 0.4 millimetre per cycle. The process involved simple, coordinated turning of the scaffold’s vertical turnbuckles. Shims falling to the ground indicated which parts of the vault were no longer supported by the falsework and thus standing on their own. It’s Alive! Once all the shims had fallen out, the scaffolding could be lowered further and the grillage pieces carried out, revealing the unique intrados pattern and texture for the first time. During the test assembly in Texas, the process was done only to the point of “structural” decentring. (To speed up disassembly there before shipment to Venice, the scaffolding was not removed). After the grillage was taken away, final cleaning could begin. Covers were placed over the tension ties so visitors would not trip while stepping over or standing on them. Measurements of the self-supporting structure revealed maximum deflections of only four millimetres at midspan. Not only was the stone surface thus very stiff due to the high degree of double curvature of the thin shell, but it had also been assembled with such impressive accuracy that only very minimal settlement occurred after decentring.

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Full test assembly and dress rehearsal at the Escobedo Group’s facilities in Buda, Texas.

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The Armadillo Vault standing by itself for the first time, ready to be taken apart, boxed up, and sent to Italy.

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A race against the clock: Crating up the stones, loading the shipping containers, trucking over 2,000 kilometres to the port in Charleston, South Carolina, navigating small barges in between the tourists on boats to the Arsenale in Venice, and squeezing through the narrow alleyways of the Arsenale.

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In less than three weeks, the Armadillo Vault was reassembled around the columns of the historic Arsenale building by the same Escobedo Group crew that assembled it the first time in Texas.

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Workers hoisting a voussoir in place using the lightweight jib cranes developed for this project.

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Multiple workers carefully positioning a voussoir by pushing and shimming from below, using the registration grooves and score marks at the side faces as reference.

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Almost ready for the Biennale opening! Some final touching up and cleaning.

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Venice Architecture Biennale 2016 director and Pritzker Prize winner, Alejandro Aravena, could not contain his enthusiasm and climbed the freshly decentred stone shell with David and Matt Escobedo.

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Balancing Craft and Machine A Conversation with the Escobedo Group

Assembling and reassembling the Armadillo Vault on both sides of the Atlantic was a rewarding and challenging experience for everyone involved. In this conversation with Philippe Block, David and Matt Escobedo of the Escobedo Group based in Buda, Texas, discuss how their deep knowledge of masonry combined with pragmatic, innovative thinking under extreme time pressure resulted in a unique structural achievement. Philippe Block:  When John [Ochsen-

DE:   I think one of the reasons we

dorf] and I contacted you about collaborating on a project for the Architecture Biennale in Venice, what was your reaction?

continued our conversation over so many years was because you, Philippe, saw our capabilities when you worked here as an intern in 2008 and kept that in the back of your mind. You knew that in us you had found someone who could actually build the craziness you and your team were imagining, so all of our years of experience plus your wild ideas came together in the way I like to work best. ME:   The years of experience also ­culminated in David continuing to build on our technology, which has been put in place over time. We ­started first doing it by hand but then gradually using different types of machinery to increase our efficiency while not losing sight of the handcrafted aspects. In this project, we were able to balance both of those things. All of that experience was ­essential to us being able to realise the vault.

David Escobedo:  My first thought was:

this is exciting! But it had already been an eight-year journey with Philippe, so it was the logical continuation of ideas and models we’ve been working on for years. Matt Escobedo:  My first feeling, when I found out about a week after the initial conversation, was cautious optimism. We’ve had opportunities in the past that fell through, so I wanted to remain reserved. I knew we could do it, but all the pieces still had to fall into place. PB:  What role did your years of ex-

perience – both individual and collaborative – play in achieving this complex construction? 170

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PB:  People always ask me why we

worked together with partners from Texas. Why do you think I chose y’all?

to employ all of that baseline knowledge we’ve gathered over the years and then be able to pour it into constructing the vault.

DE:   When we met through John, we

PB:  What were some new things you

both recognised the capabilities of the other right away. We fit well together and had the technical ability to do it. What is your answer? PB:   My answer is always that we really needed the best of the best to be able to accomplish this, and this also meant being able to trust each other and fully understand each other. We had to trust that we had the partners who could match a crazy 3D puzzle with ridiculous accuracy, and you had to trust that the engineering, the control, and the geometry would be delivered such that it would all come together and remain standing.

learned through doing this project that might be transferable or adaptable for other projects in the future?

PB:  How would you compare the Ar-

madillo Vault to other projects you are doing on a more regular basis? DE:   We have done quite a bit of ex-

traordinary stone work over the years, but that has always involved conventional engineering – lots of steel ties, concrete, and mortar – because that’s the way engineers do it these days. In contrast, the Armadillo was not at all conventional. This one was true stone. ME:   Indeed, we’ve done lots of complicated stone installations, from simple projects to very complex, large pieces (with zero joints) before, but this was on such a huge scale, which made it so different from anything we’d ever done. It did give us a chance

ME:   Probably the most important

things we learned had to do with programming the machinery and ­ultimately understanding our machine better – even things like checking the diamonds on our tooling to improve our accuracy as much as possible. In fact, we’ve already employed something that we learned from the vault on a project much simpler in scope. We realised a complex geometry by creating an asymmetrical ring out of stone blocks. It had nowhere near the same amount of surfaces as the Armadillo Vault, but there were 12 pieces, each piece weighing anywhere from 1,000 to 2,000 pounds (450 to 900 kilogrammes). We decided to leave the last piece until we got the ring closed in to the 11th piece, and then we could take exact measurements of the top, bottom, and middle, so we could get it exactly right instead of having to do it again; we basically waited for the last keystone piece similar to what we did for the Armadillo. PB:  To what extent did the con-

straints of the Biennale – for example not being able to use a crane – present an interesting or rewarding challenge? 171

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DE:  We actually encounter con-

PB:  Why was it important that you

straints all the time, with every project, but the constraints there were unique, for example the tightness of the alley, which meant we could only bring in one box of stone at a time. But once we got past the logistical nightmare of getting it there and it had arrived safely, we were all relieved. ME:   For me, I think it adds to the overall character and story of the vault that we had to work with those constraints. David figured out the use of the jib crane, and then it worked with the space. We avoided hitting the columns by mere centimetres. I enjoyed the challenge in fact. Clearly, we could have been a lot more efficient without those constraints, but it does make a better story.

could practice with the test assembly in Texas using the same crew that then went over to Venice?

pressure of the project helped drive it through to completion?

were running out of. We wanted to have the same crew together, use the jib cranes, and assemble it in Texas 100% the way we knew we were going to do it in Italy. ME:   It was obviously a question of logistics too. If we had been able to stay right in Austin, we wouldn’t necessarily have had to do a test assembly. But we knew we wouldn’t have any machinery or crew living over there, so there would be no second chances if we needed to cut a back-up. The time constraints were also extreme. We had to get it done by a certain date, so a test assembly was the only way to confirm that everything worked.

DE:   You know that’s right up my alley!

PB:  What did you have to do to

PB:   It forces you to make decisions.

achieve the re-assembly in Venice in exactly the same way as the test assembly?

PB:  Do you think the extreme time

DE: I told you four years ago, “Philippe,

I’m tired of talking about it, let’s just do it!” My other partners would have said, “This is all just talk.” I get bored easily, so I’d rather have you call and say: “This could happen!” That’s important to me because that’s how I like to do things. PB:   We also had a unique situation in which we could be our own client, our own designers, our own engineers and so on, basically all possible shortcuts in communication. To me, it was an important factor for making this happen that we didn’t have to interface with so many people. 172

DE:   It was an issue of time, which we

DE:   It was a challenge there too. I

don’t want to say that we struggled, but we did move things, make adjustments. The biggest challenge in my mind was controlling it with the total stations. We were aiming for [tolerances of ] 0.4 mm or less. If you think about how small that is, it’s crazy! PB:  How did you manage to balance

between local vs. global registration  – meaning locally seeing how the stone came together by refer-

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ring to the markings the workers made in Texas compared to the global measurements. I’m referring to the design geometry, the as-built geometry, and then finally the rebuilt geometry. DE:   We knew the design geometry

and the modelling were absolutely correct. This was verified by the computer and by your team, but how do we control the geometry during assembly? Some of the pieces have six sides. It’s sitting on the next piece, which moves by a fraction, and the whole thing starts to compound as it goes up. We did look for other measuring options, like lasers, but the technology just wasn’t there to achieve what we needed. ME:   Or at least not to control it within those constraints. Our machinery total station would not shoot well in elevation. We could shoot the points but then the elevation would be a bit different. DE:   We finally had to use two sources, one with an optical level, then do the maths here on what that point should be elevation-wise relative to the world.

he’d look at a different point than I would, therefore I was the one at the total station and would attempt to be consistent. We did try robotics, since otherwise it’s such a visually dependent thing. A company came out with their 50,000 dollars’ worth of equipment, but they couldn’t get it within the tolerances that we needed. They were a couple of thousandths off on all the points. That would be close enough if we were building a road! I mean, a quarter of an inch in a mile of road, that’s nothing, but for us in this case, it was everything. ME:   We set up a laser relatively high inside one of the windows of the Arsenale, and we magneted our laser to the top so we could shoot lines over the vault to check the elevation on the top. DE: That’s how we inverted the measurements to measure from there on down. ME:   Ultimately, it was almost an issue of feeling. We had to rely on gut feelings a lot, since part of it in the end was figuring out what just looked right. PB:  What challenges did you en-

PB:  Do you think, if you’d had more

counter in terms of transportation, logistics etc.?

time, a more comprehensive scan would have helped you?

ME:   The logistics of shipping this

DE:   We tried robotics to reduce the

chance for human error. With the total station, you’ve got a crosshair that you’re going to point to. This means that only one person can do it because each person has different eyes. If Matt would look through it,

overseas were almost more complicated than building the vault itself! It was really down to the wire. We actually had to truck all these containers cross-country to the border at Charleston, South Carolina, so that the shipment could make it in time. That gave us an additional 8 days. 173

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DE:   Charleston’s the last port, so

ME:   As a company, as a group, as a

that’s why we put it on the boat there. ME:   The trucking company thought we were crazy! They kept asking, “Why are you trucking this??!” I would tell them “You don’t understand, I have to do this, I have to make that exact ship.” DE:   We needed that extra time. Otherwise, we wouldn’t have made it. Jessica [Escobedo] and Matt coordinated it all. Matt did all the phone communication, Jessica took charge of getting it loaded. We kept calling the shipping company to ask when it would arrive. They would say, “I don’t know.” “How much will it cost?” “I don’t know.” “Okay, thank you.” ME:   It was a big challenge, but they actually ended up doing a good job, and they thought we were one of the best, most organised teams. I gave them our plan, we even had a 3D drawing by John Curry of how the boxes had to go in the containers and the puzzle for the falsework, how it all locked together. When I showed him that, he said “Wow, this is great!” and called in his boss to look at it too.

partnership, the whole process obviously was challenging, but it showed us that what we do best as a company is problem solve and then resolve. We had problems with our cutting machine, for example. The spindle decided to go out right in the middle of cutting, and we didn’t have an extra one. So we got a new one through a combination of negotiations and threats. I sat with the owner of the company and his son at a trade show in Las Vegas and negotiated with them for two hours. Finally they actually sent their technician, who was supposed to be with them in Vegas, out to Texas that night so he could fix our machine. DE:   The hardest part though was really just working too hard! [laughter] Our teams were spread out and you and your team at the Block Research Group hung in there with us through the night to exchange information and get us what we needed for the next morning.

PB:  Were there other challenging

PB:  That was an interesting aspect.

How was it to collaborate with teams all over the world?

aspects? Or rewarding ones? DE:   Everybody put in a lot of time DE:  The whole thing was a challenge!

We’ve been talking about logistics, the learning curve of controlling it, the measuring. I know I came away with a feeling that we learned more. Actually, the whole thing was a learning curve, and another feather in our cap so to speak. I mean, who else has done this?? PB:   Well, no one in the last 600 years! 174

and effort in part because of the time difference. Our guys staying later, you guys working through the night to get us the information in the morning. ME:   We’d have to be in the office at 4 a. m. to take measurements for the pieces that Matthias needed to have ready for us so we could cut them. We were in a kind of race with your team being 7 hours ahead.

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PB:   So the way to collaborate across

the Atlantic means doing all-nighters constantly. PB:  When you talk about what

you’ve done, what you’ve achieved, particularly to people who are not architects or engineers, how do you describe it? DE:   One of the first questions people

always ask is: okay, but why? This is a beautiful shape, but once you explain it to them, they say, well, why did you do it that way? I tell them about the historic building, the loads on the floor, the access points, not being able to use equipment, the weight of the stone being based on these constraints and so on. So then they start looking at the puzzle. ME:   If I had to explain it at all, people have asked me: what is it? I explain it’s not really for anything necessarily, but it represents more the many years of effort and finally having an opportunity to bring it to fruition. PB:  How do you think your peers

appreciate that you’re demonstrating the true load-bearing capacity of stone? DE:   Only a certain group of people

truly understand or appreciate it. The engineering community, they understand that it’s possible, but they say, “We would never do that because if something happens, I’ll lose my licence!” At the end of the day, people don’t want to express themselves because they’re so worried about being sued. But you know the true intellects

in town, at the university [in Austin] for example, they’re all blown away by it. PB:   On the other hand, like you said earlier, maybe it’s good that it has these multiple layers: first and foremost it’s a beautiful object, which anyone can appreciate, but then if you take the time to understand it, you can appreciate it on other levels as well. DE:   At the end of the day, everyone can see this as a beautiful shape. Yes, it has a great story too that goes deeper. Do they really want to get into the total technical part of it? It’s just ­“purity” [sic]. PB:  Many of your skilled craft work-

ers, masons, etc. come from Mexico originally. Do you also find good craft workers in the U. S. or is this becoming a lost art form? DE:   Yes, it is a dying art, the crafts-

manship of stonework or even woodwork. Yes, most if not all of our guys are Latinos. Their sons have come to work for us. Hopefully they will stay, but yes we’re losing this art. In the U. S. everybody gets out of school, whether it’s high school or college, and they only want to work with computers. We’re really lacking talented people who can actually build something, particularly with their hands. PB:  Do these computationally guid-

ed or steered machines make this worse or are they complementary? DE:   Complementary – it’s the way

you use computers. But, in a way, if 175

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those same skilled craftspeople we’re talking about weren’t here, we would have to force that machine to do even more because there wouldn’t be anyone who could finish it. And then how would you install it? There’s not a machine made now that can actually do that. Sure, you’ve got all the pieces, but you actually can’t put it together.

we drawing a lot of experience from studying throughout our careers. Instead, our knowledge is practical, gained from continuously saying, “Let’s push the boundaries and see what can be done.” To keep asking “Why can’t it be done this way? I can do it this way!” This is what David has been doing his entire career.

PB:  Are there any ways that our

PB:  Many people comment that we

theme of “Learning from the past” also applies to what you do?

were making our lives more difficult by not using mortar to take up the tolerances.

ME:   In our culture in Texas/the U. S.,

we don’t have as much practical experience with the constructions that you have in Europe, but part of our “past” is in the heritage of our workforce. I do think that part of the reason that our Latin-based workers are so skilled is that they do still build in some of those ways in Mexico, whereas we don’t here. It also gives them a passion and a deep knowledge of that type of work that we don’t have – whether it’s brick or stone or some other material. Some of the masons were not even in the trades originally. In fact, one of our best masons was a butcher, some were welders, but now they’re extremely good at their crafts and have a very deep understanding. DE:   Most of the housing down there is cementitious – it’s concrete and block walls. There’s not much wood, so if nothing else, they probably helped to build their parents’ houses, which were most likely concrete and masonry structures. ME:  As far as learning from the past, we’re not drawing from tons of knowledge about cathedrals nor are 176

DE:   Well, if we had set it in mortar

it would have been easier, but for me doing it dry was the challenge. We wanted to do it that way. I mean, anyone can fill in a little mortar, not that the brick vaults are not cool, but they’re essentially glued together. ME:   That was the challenge, but also that it had to be disassembled and reassembled. DE:   We would have set it dry, added all the shims, and then come back to add mortar later, so we would have just set up everything there. Without mortar, we couldn’t be that far off with our tolerances. ME:   In my opinion, if we had used mortar, none of this conversation would be taking place now, and there would have been no reason for a book either. It’s frankly just not that interesting. And part of our whole process of realising structures in natural materials is to create constructions that truly don’t make so much waste. So this was showing the world that stone can really do this!

CONSTR UCTION A N D A S S E M BLY

DE:   It also really illustrates the tech-

PB:  So, what’s next? Where do we go

make it happen that way, but this project was the other way around. It was about understanding the processes, the constraints, the crafts, and the knowledge that we built up together, and from that, to do something exciting.

from here? What challenges remain? Assemble it without formwork?

PB:  The hope is to find a new home

nical challenge when you see it without mortar. The geometry had to be just right for this to stand. And that’s what I see when I look at it.

ME:   What’s next is to find a home for

it. After that, I don’t know. What else can we do? Something that’s a one-off, different form finding? PB:   It’s important to understand that the Armadillo also functions as a placeholder to show what can be done with stone. We’re not necessarily proposing that anyone should have one of these in their gardens, nor are we saying that this is a new way of building. I think it’s more a way of showing that you can use the material truthfully. It’s not just a skin on the structure that has nothing to do with it. What you really see is the structure itself, when you are using these more humble, natural, traditional materials in an appropriate way. If we had put mortar in there, people would not have seen it that way. They would immediately jump to thinking that the mortar is holding it together, kind of giving it bending capacity everywhere. So, I don’t necessarily think the future is more vaults but rather the future is a more honest, truthful way of building that is respectful to materials. The only way to do that is to have real craftsmen in there. That’s the difference: if you just sketch something on the computer and then you need to realise it, you bend it and you just

for the Armadillo. How important is it to you that it remains in Texas or somewhere else in the U. S.? DE:   It’s very important to me, but

I’m being patient because I want to make sure it’s in the right place – that we’re not just going to stick it somewhere. Obviously there will be a lot of work to do at that point because it still has to be put together one last time.

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AFTERWORD

Gilles Retsin

A New Research-Driven Architectural Practice Under the title “Reporting from the Front”, the 2016 Venice Architecture Biennale interrogated a series of approaches to architecture that responded to a sense of crisis. This crisis is manifold, ranging from the rapid expansion of cities in developing countries to questions about how architects situate themselves in a volatile debate about the social responsibilities of the discipline. Curated by Alejandro Aravena, the Biennale also looked at modes of practice transforming under pressure of this frontline, blurring into other disciplines, territories and discussions. The use of the military term “front” implied the apparent urgency and danger of this crisis. If in that sense, the work presented was a series of instruments or tools used in the conflict, then one of these instruments, developed by the Block Research Group, stood out by far. Unexpectedly, it assumed the form of one of the most banal, everyday architectural elements: the floor slab. Measuring barely three square metres, these slabs are without a doubt the most effective tools in the frontline of the battle set out by Aravena. Moreover, they demonstrate some of the most fundamental shifts in architectural practice we have witnessed in recent years. An ambitious technological project, they represent the new possibilities coming out of emerging architectural research engaged with design, computation and fabrication. The Armadillo Vault, a large but thin stone shell, formed the centrepiece of Beyond Bending. Put together from a few tons of limestone to create a seemingly free-from, curved shell without using any cement, the Armadillo Vault did not fail to appeal to the public and critics visiting the Biennale. Besides the vault, a series of humble slabs produced with different materials were presented. Like much of the work displayed at the Biennale, one of the slabs was made of an earthy material – ceramic tiles. Another one, however, was made of a material no other architect in the Biennale used. In fact, it was made of a material no other architect had ever used before for a building: 3D-printed sand. The tiled ceramic slab allows for the creation of lightweight, efficient and strong floors using unskilled labour and local materials. The project, initially developed for Addis Ababa in Ethiopia, has wide implications. It cuts short an entire production chain usually required to build housing. Cement and rebar have to be imported from outside, and it requires skilled labour to build a safe 178

structure. By using a shallow, compression-only vault, cheap and abundantly available materials can create a strong and efficient slab. Moreover, the vaulted, ceramic ceiling offers a beautiful interior space for the inhabitants. It provides a sustainable solution for low-cost, accessible housing in developing countries. As a building system, this slab forms a powerful instrument in areas of rapid urban growth in the Global South. While this slab operates in the context of developing countries, which often have difficult access to materials and skills, its 3D-printed counterpart explores a powerful alternative to the normative concrete slab. At the frontline, these concrete slabs, which have defined the majority of our building stock for decades, would seem to be the most difficult subject to attack. However, the Block Research Group’s 3D-printed slab does exactly this. Again, it explores how form alone can allow an initially weak material – in fact just particles of sand – to become a strong structure. Whereas previous experiments with similar 3D-printed methods had looked at the mere aesthetic possibilities of the technology, here we see how an entire production chain and building industry can be turned upside down. The compression-only vault and series of stiffening ribs allow for the creation of a thin, shallow structure, saving both material and space. These unassuming slabs therefore have the potential to change an entire system of production and, as a result, an entire section of our built environment. As an exception in the Biennale, these prototypes unapologetically argued for an attitude that does not see technological innovation and digital tools as opposed to social change. With some exceptions, the exhibited projects did not seem too keen to involve technology in the frontline battle. This is a recurrent dialectic: technology seems to be associated with the forces at the source of the crisis – on the opposite side of the front. The systemic, technological approach represented in Beyond Bending forms a strong counterpoint to this techno-sceptic sentiment. I would argue that it is beyond any doubt that the way we engage with new information technologies is one of the main intellectual challenges for architecture today. This is both a pragmatic challenge – we don’t want Silicon Valley to replace our discipline with software – but also a fundamental cultural challenge. Before the financial crisis of 2008, architectural experimentation with digital media was enthusiastically celebrated. After the crisis, it became clear that a lot of this experimentation had solely operated in function of some form of capital: funky museums, expensive facades, big business headquarters and other eye-catching projects. Little or no research looked into housing or was engaged in larger social questions, going beyond mere formal experimentation. This realisation partially caused the seemingly accepted dialectical opposition between technology and social engagement. As 179

a result, since 2008, the “digital” has been absent from the Venice Architecture Biennales. On the world stage, however, many things have changed; since 2008 we have social networks, smartphones, the rise of accessible robots, 3D-printers and AI software. Our world has never been impacted more by technological changes. As such, by ignoring these changes, the discipline has also never been as detached from technology, and therefore from the world, as before. In this context, the Block Research Group is hugely important. It shows that progressive, technological research can be deeply applied, social and contextual. Moreover, it shows that technology in fact cannot be disconnected from the significant challenges we face today. However, it’s not just this attitude towards technology that made Beyond Bending stand out as an extremely effective and innovative exhibition. In fact, the Armadillo Vault and the series of slabs represent a much larger, more disruptive shift in the architectural discipline. Very much in response to the increased possibilities of information technologies, the research-driven practice of the Block Research Group has become a new and effective modus operandi for the discipline. Bridging between academia and practice, these new forms of practice start to enter the field at large. In many ways, the research-driven practice in itself is a response to some of the pressures architectural practice is facing. In the tradition of mavericks and innovators like Jean Prouvé and Frei Otto, this new form of practice shifts from architecture as providing services to architecture as providing products or systems. Instead of waiting for a client and a context, a research-driven practice develops products, systems and applications that can then be distributed and multiplied. The Block Research Group’s slab prototypes manifest this beautifully; they are abstract pieces of research, developed as a systemic body of knowledge, independent of a client or brief. Rather than reactive, research-driven practice is by definition pro-active and visionary. This is a fundamental shift that has deep implications for the way architects operate. The research-driven context blurs the boundaries between multiple professions: the Block Research Group acts as architects, engineers, researchers, software developers, contractors, roboticists. Beyond Bending, with its combination of technological prowess and social agency, cannot be disassociated from this emerging model of research-driven practice. Besides the criticism about technology, another discussion about the 2016 Biennale centred on a difficult political and social problem, which is central to any form of humanitarian work. Essentially, this discussion revolves around the difference between charity and development. Charity can be seen as a service-based form of humanitarian aid, where a community is given extra means, 180

but these don’t necessarily result in structural change. Structural developments on the other hand, are thought of as a systemic approach, where people are empowered with tools that can create longer-term change. Moreover, the knowledge to understand and further improve these tools is in the hands of the people themselves, not of the donors. If we extrapolate this to the Biennale, we see how traditional service-based architectural practice and research-driven practice have very different social implications. The traditional model of architectural practice offers a one-off service for free, a charitable donation. This one-off design exercise is not – to use software terminology – open source. It cannot be distributed, re-designed, re-used, and is therefore not scalable. By reducing itself to a service, some of the “do-good” work of the Biennale is difficult to scale, and it struggles to address the sense of crisis Aravena had set out. As such, it is also no wonder that we didn’t see many large-scale, structural proposals in the 2016 Biennale that addressed challenges such as the massive growth of cities or urban densification. Instead of a systemic answer, we were left with the model of the 20th century architect: the educated master who is willing to dedicate some of his time to “help” the Global South with a design. His or her expensive service gets delivered as a closed box, a finished, one-off charity, which often relies on the sponsorship of a big corporate partner. The prototypical slabs in Beyond Bending demonstrate that there is an alternative model: technologically advanced, fundamental and systemic research, resulting in smart and scalable modes of production. This is architecture beyond charity. This approach allows architects to access larger questions about some of the biggest challenges we face in the 21st century. Research-driven practice is a new and disruptive form of operation for the architect: powered by new information technologies, it produces disruptive products, rather than one-off exercises. It blurs the boundaries between academia and practice, between service and product, and between architect and engineer. The series of small, unassuming slabs exhibited at Beyond Bending therefore kick-started a new age of digital experimentation in architecture, serving as an inspiration for generations of new research-driven practices to come.

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AUTHORS

The Block Research Group (BRG), part of the Institute of Technology in Architecture at ETH Zürich, focuses its research on equilibrium analysis, computational form finding, optimisation and construction of curved surface structures, specialising in unreinforced masonry vaults and concrete shells. As part of the Swiss National Centre of Competence in Research (NCCR) Digital Fabrication, the BRG develops innovative, structurally informed bespoke prefabrication strategies and novel construction paradigms employing digital and robotic fabrication. The BRG translates its research in unique demonstrators, such as the ETH Pavilion using recycled waste for Ideas City 2015 in NYC, the unreinforced, cut-stone Armadillo Vault and the soil-pressed tile-vaulted Droneport at the Venice Architecture Biennale 2016, and the NEST HiLo research unit with its extremely thin concrete shells in Dübendorf, Switzerland. Philippe Block is professor and co-director of the BRG, and is the director of the NCCR Digital Fabrication. He studied architecture and structural engineering at the Vrije Universiteit Brussel (VUB) in Belgium and at the Massachusetts Institute of Technology (MIT) in the USA, where he earned his PhD under the guidance of Prof. John Ochsendorf in 2009, developing Thrust Network Analysis (TNA), an innovative approach for assessing the safety of historic vaulted structures with complex geometries and designing compression-only shells. With the BRG and as partner of the consultancy Ochsendorf DeJong & Block (ODB Engineering), he provides structural assessment of historic monuments and design and engineering of novel compression shell structures. Tom Van Mele is senior researcher and co-director of the BRG, where he has led research and development since 2010. In 2008, he received his PhD from the Department of Architectural Engineering at the Vrije Universiteit Brussel (VUB). His current research projects include the analysis of collapse of masonry structures, the engineering of flexible formwork systems for concrete shells, and the development of graphical design and analysis methods. He is the developer of the BRG’s web-based interactive teaching and learning platform, eQUILIBRIUM, and its open-source computational research framework for architecture, structures and fabrication, compas. Matthias Rippmann has been a member of the BRG since 2010, where he obtained his doctorate in 2016. Currently, he is a postdoctoral researcher, leading the BRG’s digital fabrication research in the NCCR Digital Fabrication. He conducts research in the field of structurally informed design and digital fabrication. He is the developer of the form-finding software RhinoVAULT, which offers TNA-based exploration of funicular shells. He studied architecture at the 184

University of Stuttgart and the University of Melbourne. He worked in Stuttgart at Behnisch Architekten, LAVA, the Institute for Lightweight Structures and Conceptual Design and Werner Sobek Engineers. In 2010, he co-founded the architecture and consultancy firm Rippmann Oesterle Knauss GmbH (ROK). Noelle Paulson completed her Master of Arts and doctoral degrees in nineteenth-century European art history at Washington University in St. Louis, Missouri, USA. Since moving to Switzerland in 2009, she has worked as a freelance art historical writer, editor and consultant as well as an executive assistant in the field of architecture and urban design. Her essays on late nineteenth-century French painting have appeared in museum exhibition catalogues for the National Gallery of Canada, Ottawa, the Phillips Collection in Washington D.C., and Kunstmuseum Winterthur, among others. A recipient of numerous travel and research fellowships, she has presented public talks in the U.S., Canada, and the U. K. She joined the direction of the Block Research Group as Administrative Coordinator in 2015.

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CONTRIBUTORS

Alejandro Aravena, a Chilean architect and executive director of Elemental S.A., curated the 15th International Architecture Exhibition – La Biennale di Venezia in 2016. He is also the recipient of the 2016 Pritzker Architecture Prize. Matthew DeJong, a structural engineer specialising in earthquake engineering and the analysis of masonry structures, is senior lecturer (associate professor) in engineering at the University of Cambridge, and a partner at Ochsendorf DeJong & Block. A former Fulbright scholar, he received his PhD from Massachusetts Institute of Technology (MIT) in 2009. David Escobedo is founding owner of the Escobedo Group where he leads a six-division, vertically-integrated general contracting firm. His primary focus is innovating the building process through digital fabrication and computation for complex and challenging structures in steel, stone and millwork. Matt Escobedo is General Manager of the Escobedo Group where he oversees the construction process for all divisions. His primary focus is providing holistic, hands-on management in the field, as well as facilities operations internally. John Ochsendorf, a structural engineer specialising in the history, preservation, and design of masonry vaulting, is the Class of 1942 Professor in the Departments of Architecture and Civil and Environmental Engineering at the Massachusetts Institute of Technology (MIT) and a partner with Ochsendorf DeJong & Block. In 2017 he was appointed the 23rd director of the American Academy in Rome. Gilles Retsin, a London-based architect, is lecturer and programme director of the M.Arch Architectural Design course at the Bartlett School of Architecture, University College London. He holds a Masters in Architecture + Urbanism (Dist) from the Architectural Association School of Architecture Design Research Laboratory (AA.DRL).

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EXHIBITION AND OBJECT CREDITS

Exhibition Concept Philippe Block, John Ochsendorf

3D-printed floor: Block Research Group, ETH Zürich – Matthias Rippmann, Ursula Frick, Andrew Liew, Tom Van Mele, Philippe Block

Authors Block Research Group, ETH Zürich Ochsendorf DeJong & Block Escobedo Group

Beyond the Dome Block Research Group, ETH Zürich – Matthias Rippmann, Robin Oval, Tomás Méndez Echenagucia, Tom Van Mele, Philippe Block

Texts Philippe Block, John Ochsendorf, Tom Van Mele, Noelle Paulson

Beyond Freeform – Armadillo Vault Structural design & Architectural geometry:  Block Research Group, ETH Zürich – Philippe Block, Tom Van Mele, Matthias Rippmann, Edyta Augustynowicz, Cristián Calvo Barentin, Tomás Méndez Echenagucia, Mariana Popescu, Andrew Liew, Anna Maragkoudaki, Ursula Frick Structural engineering: Ochsendorf DeJong & Block – Matthew DeJong, John Ochsendorf, Philippe Block, Anjali Mehrotra Fabrication & Construction: Escobedo Group – David Escobedo, Matthew Escobedo, Salvador Crisanto, John Curry, Francisco Tovar Yebra, Joyce I-Chin Chen, Adam Bath, Hector Betancourt, Luis Rivera, Antonio Rivera, Carlos Rivera, Carlos Zuniga Rivera, Samuel Rivera, Jairo Rivera, Humberto Rivera, Jesus Rosales, Dario Rivera

Design Block Research Group, ETH Zürich – Philippe Block, Edyta Augustynowicz, Matthias Rippmann Lighting Lichtkompetenz, Artemide Sponsors Kathy and David Escobedo ETH Zürich – Department of Architecture MIT – School of Architecture+Planning NCCR Digital Fabrication Artemide Swiss Arts Council – Pro Helvetia Universitat Politècnica de València Fundación José Soriano Ramos

Objects Beyond the Slab I Salvador Gomis Aviñó, Salvador Tomás Márquez, Jonathan Dessi-Olive, Camilla Mileto, Fernando Vegas López-Manzanares, Javier Gómez Patrocinio, Benjamin Ibarra Sevilla, John Ochsendorf Beyond the Slab II Concrete floor: Block Research Group, ETH Zürich – Dave Pigram, Tomás Méndez Echenagucia, Andrew Liew, Nick Krouwel, Tom Van Mele, Philippe Block

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IMAGE CREDITS

Unless otherwise noted, all drawings and diagrams are © Block Research Group, ETH Zürich Where a photographer is not given, all photographs are © Block Research Group, ETH Zürich * Images published under a Creative Commons Attribution-Share Alike 2.0 licence ** Images published under a Creative Commons Attribution 2.0 or 2.5 Generic licence Graphical concept and image editing: Naida Iljazovic Image assistance: Corentin Fivet, Ursula Frick, Alexander Kobald, Juney Lee, David López López, Hongyang Wang Foreword Pages 4–5: © J. Kurt Schmidt Reporting from the Front Page 10: © ETH Zürich / Anna Maragkoudaki Beyond the Slab I Page 16: © ETH Zürich / A. Maragkoudaki Page 18: © ETH Zürich / Nick Krouwel Building with Weak Material Page 21 (top): © Edward Allen Page 21 (bottom left): From the manuscript “Construcción de bóvedas tabicadas” (Àngel Truño i Rusiñol) at the Col•legi d’Arquitectes de Catalunya. Biblioteca. Page 21 (bottom right): © Michael Freeman / John Ochsendorf Page 23 (top): Galileo Galilei, Discourses and Mathematical Demonstrations Relating to Two New Sciences, 1638 Page 23 (bottom): Giovanni Poleni, Memorie istoriche della gran cupola del Tempio Vaticano, 1748 Page 27 (top): R. Guastavino Company, 1897. Image courtesy Avery Architectural & Fine Arts Library, Columbia University Page 28 (top): © Peter Rich Architects Page 28 (bottom) and page 29: © ETH Zürich / Lara Davis

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Pages 30–31: © Nigel Young and The Norman Foster Foundation Beyond the Slab II Pages 32, 35 and 37: © ETH Zürich / A. Maragkoudaki Page 34: © ETH Zürich / N. Krouwel Page 36: © Heiko Stachel Pages 38–39: © Marc Duerr Building with Less Material Page 46 (top): © Ezra Stoller / Esto Page 46 (bottom): © Andrea Sarti / OMA Pages 52–53: © ETH Zürich / Naida Iljazovic Beyond the Dome Page 54: © H. Stachel Pages 56–57: © ETH Zürich / A. Maragkoudaki Exploring Form and Forces Page 65: Pierre de Varignon, Nouvelle mécanique ou statique (1725), ETH-Bibliothek Zürich Page 66: Robert Maillart, graphic statics drawing (1928), ETH-Bibliothek Zürich Page 67: Robert Maillart, Salginatobel Bridge (1930), * photograph by Wikimedia Commons user Rama Pages 68–69: Robert H. Bow, Economics of Construction Related to Framed Structures (1873) Pages 76–77: © ETH Zürich and Karlsruhe Institute of Technology / Carlina Teteris Beyond Freeform Page 78: © Skender Iljazovic Pages 80–83, 85, 88–89:  © Iwan Baan Page 84 (top): © ETH Zürich / A. Maragkoudaki Page 84 (middle and bottom): © S. Iljazovic Pages 86–87: © H. Stachel Extending Stereotomy Page 91: R. Willis and T.T. Bury, On the Construction of Vaults in the Middle Ages (1910) Page 93 (top left): Stone Arches at Glendalough, ** photograph by Wikimedia Commons user psyberartist Page 93 (top middle): The Arch of Kabah, ** photograph by Robert Young Page 93 (top right): Trulli of Alberobello, ** photograph by Wikimedia Commons user Marcok

Page 93 (bottom): Sean Collier Memorial by Höweler + Yoon Architecture, photograph © Scott Newland Page 94: John Fitchen, The Construction of Gothic Cathedrals, 1981, © University of Chicago Press Page 94: Autonomous Systems Lab, Robotic Systems Lab, and Block Research Group, National Centre of Competence in Research – Digital Fabrication, ETH Zürich, 2016 Form and Structure Page 102: © H. Stachel Page 106: © MIT Civil Engineering Lab, photographs by John Ochsendorf Page 107: (c) University of Cambridge / Matthew DeJong Pages 114–115: © Escobedo Group / Lars Frazier Stereotomy and Fabrication Page 126: © Escobedo Group / L. Frazier Page 131: © Escobedo Group / L. Frazier / Aman Johnson Media Pages 132–133: © Aman Johnson Media Pages 134–137: © Escobedo Group / L. Frazier Construction and Assembly Pages 146, 152, 160 –161, 164–169: © ETH Zürich / A. Maragkoudaki Page 149: © ETH Zürich / A. Maragkoudaki and © Escobedo Group / Aman Johnson Media Pages 149 and 158–159: © Aman Johnson Media, Escobedo Group, and ETH Zürich / A. Maragkoudaki Page 150: © ETH Zürich / A. Maragkoudaki / N. Krouwel Pages 154–157: © Aman Johnson Media Pages 162–163: © ETH Zürich / N. Krouwel

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BIBLIOGRAPHY

The texts and conversations in this book draw upon the following publications: Adriaenssens, S., Block, P., Veenendaal, D., and Williams, C., eds. Shell Structures for Architecture: Form finding and optimization. London: Routledge, 2014. Allen, E. and Zalewski, W., eds. Form and Forces: Designing efficient, expressive structures. Hoboken: John Wiley and Sons, 2010. Block, P. Thrust Network Analysis: Exploring three-dimensional equilibrium. PhD diss., Massachusetts Institute of Technology, 2009. Block, P., DeJong, M., and Ochsendorf, J. “As Hangs the Flexible Line: Equilibrium of Masonry Arches.” Nexus Network Journal 8, no. 2 (2006): 13–24. Block, P. and Rippmann, M. “The Catalan Vault – A historical structural principle with a bright future.” DETAIL 5, Issue on ‘Simple and Complex’ (2013): 528–536. Block, P., Rippmann, M., and Van Mele, T. “Structural Stone Surfaces: New compression shells inspired by the past. AD Architectural Design. Special Issue: ‘Material Synthesis: Fusing the Physical and the Computational,’ edited by A. Menges 85, no. 5 (2015): 74–49. Block P., Van Mele T., Rippmann M., DeJong M., Ochsendorf J., Escobedo M. and Escobedo D. “Armadillo Vault – An extreme discrete stone shell.” DETAIL 10, Issue on ‘Roof Structures’ (2016): 940–942. Block P., Van Mele T. and Rippmann M. “Geometry of Forces: Exploring the solution space of structural design.” GAM 12, Special Issue: ‘Structural Affairs,’ edited by S. Peters and A. Trummer (2016): 28–37. Block, P., Rippmann, M., Van Mele, T., and Escobedo, D. “The Armadillo Vault: Balancing computation and traditional craft.” FABRICATE 2017. London: UCL Press, 2017, 286–293.

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Block P., Rippmann M. and Van Mele T. “Compressive Assemblies: Bottom-up performance for a new form of construction.“ AD Architectural Design. Special Issue: ‘Autonomous Assembly: Designing for a new era of collective construction,’ edited by S. Tibbits 87, no. 4 (2017): 104–109. Block P., Schlüter, A. et al. “NEST HiLo: Investigating lightweight construction and adaptive energy systems.” Journal of Building Engineering 12 (2017): 332–341. DeJong, Matthew. Seismic Assessment Strategies for Masonry Structures, Ph.D. diss., Massachusetts Institute of Technology, 2009. Heyman, J. (1966), “The Stone Skeleton”, International Journal of Solids and Structures 2, no. 2 (1966): 249–279. Ochsendorf, J. Guastavino Vaulting: The Art of Structural Tile. Princeton: Princeton University Press, 2010. Rippmann M. Funicular Shell Design: Geometric Approaches to Form Finding and Fabrication of Discrete Funicular Structures. PhD diss., ETH Zürich, 2016. Rippmann M., Van Mele T., Popescu M., Augustynowicz E., Méndez Echenagucia T., Calvo Barentin C., Frick U., and Block P. “The Armadillo Vault: Computational design and digital fabrication of a freeform stone shell.” Advances in Architectural Geometry (2016): 344–363. Van Mele T., Mehrotra A., Méndez Echenagucia T., Frick U., Augustynowicz E., Ochsendorf J., DeJong M., and Block P. “Form Finding and Structural Analysis of a Freeform Stone Vault.” Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium, Tokyo, Japan, 2016.

IMPRINT

Authors Philippe Block, Tom Van Mele Matthias Rippmann, Noelle Paulson Editor Sandra Hofmeister Project management Sandra Hofmeister, Eva Herrmann Copy editing Raymond Peat Julian Jain Design concept  Naida Iljazovic Graphic design / Cover Katja Römer Drawings Block Research Group, ETH Zürich Ralph Donhauser Production / DTP Roswitha Siegler Reproduction ludwig:media, Zell am See Printing and binding Grafisches Centrum Cuno GmbH & Co. KG, Calbe

© 2017, first edition DETAIL Business Information GmbH Munich www.detail.de isbn 978-3-95553-390-8 (Print) isbn 978-3-95553-391-5 (E-Book) isbn 978-3-95553-392-2 (Bundle) This work is subject to copyright. All rights reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in databases. For any kind of use, permission of the copyright owner must be obtained. Bibliographical information published by the German National Library. The German National Library lists this publication in the Deutsche Nationalbibliografie; detailed bibliographical data are available on the Internet at http://dnb.d-nb.de.