The secret of egg tapping boiled down: outsmart your peers on Greek Easter

Once a year, engineers can put shell theory into practice in a less conventional way: by winning their family’s egg cracking competition (also known as egg knocking or egg tapping). On Easter Sunday, it is a tradition for Greek and Armenian families to gather and play a game of egg tapping. Similar traditions exist in many different places such as in Cajun communities in Louisiana or for other occasions, like the Persian New Year Nowruz (celebrated at the beginning of spring).

“As geometric stiffness is inversely proportional to the radius of curvature, the curvier the egg, the better it will perform.”

Here’s how the game works: everyone picks one hard-boiled egg from a basket, and the battle begins. In a knock-out tournament, several players hit their eggs against each other, first bottom-to-bottom, then when bottoms are broken – top to top. When a player’s egg is cracked on both sides, he or she is eliminated. The game continues until one player remains with an intact side of their egg, and he or she is proclaimed the winner.

Egg tapping, red won [By Superbass – Own work, CC BY-SA 3.0,
Several approaches on how to outsmart your opponents in this game exist. Certain crafty rascals suggest manufacturing eggs from cement mortar or wood. Others resort to the less labor-intensive freezing of eggs. These cheats, however, will likely get you caught and we recommend you steer clear of them. Other strategists advise without any rationale, picking the largest egg or eggs from free range hens as their shells are allegedly thicker. We doubt the scientific basis for any of these suggestions and recommend you instead follow the guide below.

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Local egg shell failure due to impact load.

But first some structural mechanics. The mechanical behavior of shells is predominantly determined by the overall shell shape. When observing the failure mechanism of the egg shells, you will see a relatively small depression with some cracks (as shown on egg B above). This failure mode in shells is called local buckling, and is caused by the sudden excessive deformation of the super thin shell due to the impact of the other shell. But why did shell B break, rather than the egg used to break it?

How much a shell deflects can be predicted through what engineers call the shell’s stiffness. Stiffness depends on two factors: material properties (material stiffness) and geometry (geometric stiffness). For egg shells, geometric stiffness dominates the behavior, especially as the material of all eggs is basically identical. Thus, the secret of winning the egg challenge can be boiled down to the (local) shape of the egg. As geometric stiffness is inversely proportional to the radius of curvature, the curvier the egg, the better it will perform: geometric stiffness   ̴   1/radius.

Eggs capture
Top of the left egg shell has significantly lower radius of curvature than top of the right egg shell and so the left egg will be much stiffer (2D-simplification).


That gets us to strategy:

Step 1:  Pick the pointiest egg in the basket. The importance of this step cannot be stressed enough. Only the top part of the egg matters. Size and thickness are of very little importance. Curvature is key, but make sure the egg has no pre-existing cracks (like egg D). For example,  if  you were to consider the eggs pictured below, egg C would be the best choice.

Inked2017-04-11 15.51.08_LI.jpg
Egg C has the most curved top. It’s bottom is also less flat than for example B’s bottom. Egg D is almost as curved as C at the top (although this is less visible in the 2 D picture), but has very small cracks that have been highlighted in black.

Step 2: Polish your egg. The buckling phenomenon described above is dominated by curvature. However, local buckling can be facilitated though small imperfections (like small bumps) on your egg. Try to remove as many as possible. Also, it it is nicer to win with a clean, shiny egg.

Step 3: Start hitting. Typically, you will first use the bottom of your egg, this part of the game is relatively unimportant. Consider playing strategically: try to steer the game so you can make the first hit when you get to attack the top of the egg of your opponent (see step 4).

2017-04-11 17.40.32
Egg B breaks by hitting it with the most curvy part of egg C

Step 4: all bottoms of the eggs are broken, time to step up your game and get cracking with your pointy top. Make sure you hold your egg in a grip so that it can only be hit at the curviest spot on the top. Buttress the sides with the palm of your hand for extra support.

However, imagine someone picked egg C before you, and you ended up with the less desirable egg D. If you plotted well and are the hitter, you can still win: aim for the flatter area on egg C next to the top (see red arrow below). It does not matter how hard you hit the egg (remember Newton’s 3rd law of action-reaction), the location is much more important.

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Egg C can still be broken by hitting it on a flatter section.

Good luck in your next egg face-off.

Author: Tim Michiels

P.S.: The secret to a delicious egg salad is a splash of vinegar!

You are invited to celebrate our 1st anniversary with us!

We are delighted to be celebrating the first anniversary of the Form Finding Lab blog with you. You have been an amazing audience and we would like to thank you by sharing our highlights with you.

ENGINEERING AND ARTS: We pride ourselves at exploring the intersection of engineering and the arts. We believe that this is important for three reasons. First of all engineering works that elicit an emotional response from the public through elegance of design, increase people’s quality of life and their productivity. No better example than “The refreshing tandem: the works of the engineer Laurent Ney perceived by the visual artist Toshio Shibata”.

Esch-sur-Alzette Footbrodge, LUX(C) Toshio Shibata for Laurent Ney, Design (c) Laurent Ney

Second, innovations that will solve 21st century societal challenges, need to be firmly based on engineering principles, but also must be seamlessly interwoven with art and design. Our rammed earth wall spiral embodied the use of engineered earthen construction combined with an esthetic design intent. The engineering and design were intended to engage and enthuse the local community about zero-carbon structures.

Rammed earth spiral seating sculpture, designed and built in 2016 by the Form Finding Lab

And finally in our work we draw on approaches in art and craft to develop transformative structural designs. The physical and numerical exploration of the Costa Surface, a not well-known minimal surface, allowed us to walk that fine line between material-efficient structure and sculpture.

Numerical form finding of the Costa Surfcea, prior to its contruction

STRUCTURAL DESIGN: Infrastructure is designed to last between 100 and 200 years. Therefore, their long lifespan makes the aesthetic quality of structures also important to society. Some might doubt that aesthetic quality in structures actually exists, but its existence is proven by the number of visitors to the Brooklyn Bridge (New York City, USA, 1883) and the Eiffel Tower (Paris, France, 1887). For several iconic structures, we have interviewed their world renowned designers about how structures achieve a good degree of fit in terms of social, political and historical context, their program, technical quality, cost and context‐sensitivity. We are very proud to have a collection of exclusive interviews with many of the world leading structural, architectural and product designers including Bill Baker, Maria Blaisse, Thorsten Helbig, Marc Mimram, Mister Mourao, Eric Hines, Knut Stockhusen, Doris Kim Sung and Jane Wernick. Through these interviews we hope that our readers recognize good design and hopefully become an advocate for it.

Our visionary cohort of interviewees: Bill, Maria, Thorsten, Marc, Mourao, Eric, Knut, Doris and Jane.

FORMS and ALGORITHMS: Our research blog contributions have discussed form‐finding algorithms and design methodologies that enable unique large span bridge and building forms for a resilient and sustainable built environment. These forms are dictated by the flow of forces. Therefore, the forms can be very thin, cost‐effective, and have low carbon footprint while maintaining strength, stability, and be aesthetically pleasing and comfortable for users. You might have liked reading A structural designer’s new toolbox, Form Finding Flashback: Basento Bridge and Assessing the stability of masonry structures.

side by side
The form found shape of the Basento bridge has been compared to a nun’s headdress.

But most of all we are very grateful for you, our more than 10 000 readers who have come from all over the world to spend time with us on subjects that really matter to us. We look forward to the continuing this conversation in 2017.

The Form Finding Lab Team

PS:  and don’t forget to watch and like our videos on Our Idea Worth Spreading (Tedx talk, Prof. A.), our rammed earth installation Spiraling Dirt,  and Bamboo Structures (Senior Theses Project Lu Lu and Russell Archer) and stay updated by liking our Facebook Page.

Belgian Shell Art and Architecture : Marcel Broodthaers and Andre Paduart

This post reflects some of the storyline that Prof. Adriaenssens, invited by the Broodthaers Society of America, will be telling on Tuesday, March 28, 6:30–8pm at Hauser & Wirth Bookshop and Roth Bar, 548 West 22nd Street, New York, NY 10011.


The efficiency of shells is often exemplified by examples of nature. In particular the avarian egg shell and the sea shell come to mind.  A large chicken egg for example is about 4.5cm and has a typical shell thickness of 0.05mm ( slenderness ratio of 900) and could theoretically sustain a load of 14kN (that is the weight of about 14 American football players). The shell can be very slender and sustain high distributed loads because its form follows the flow of internal loading.  To further stiffen against impact loading, some shells in nature are equipped with corrugations like many tropical sea shells.

walking on eggs
Egg shells are amazingly strong under uniformly distributed loading.

Civil shell structures mostly originated in Germany in the beginning of the 21st century, spurred by development of analytical “shell” theory and reinforced concrete. Their evolution in that century can be marked by 3 phases.  These phases also happen to span the biological life of Belgian artist Marcel Broodthaers (1924-1976) who is , among other projects, known for his assemblies of shells of eggs and mussels.

In this post, I briefly describe the history of civil shell design and construction in Belgium in the 20th century and in particular I focus on the work of the civil engineer Andre Paduart (1914-1985), who operated in the same time and geographical space as Marcel Broodthaers.

armoire blanche
White Cabinet and White Table, Marcel Broodthaers, 1965

The early shell period 1912-1940:  utilitarian cylindrical shells in the Port of Antwerp

The initial shell designs were entirely envisaged, analyzed and built by engineers, interested in spanning large spaces without intermediate supports in the most material efficient manner.  The German contractor firm Dyckerhoff and Widmann AG first developed analytical theories to analyze shapes, related to domes (spheres) and vaults (cylinders).  Utilitarian spaces such as warehouses and aircraft hangars were roofed with these shells.  A fine example of such shells can still be found on Kaai 105, 107 and 109 at the Albert Dock in Antwerp, a port city in the North of Belgium.  The fast port reconstruction after the destruction of the Second World War demanded warehouse structures and construction techniques that were cost-effective.  The Belgian structural engineer Andre Paduart designed and built  465m of such warehouse sheds along the Docks in Antwerp. Each shed has 31 bays, covered with a reinforced concrete 8 to 12cm thin cylindrical shell. The shell had a transverse span of 15m and a rise of 3m.  To allow daylight to flood the shed, a rectangular opening (40m x 3m) ran along the crown of the cylindrical shell in the longitudinal direction. To economize, the formwork was re-used each week to build another bay.  These shells still exist today and are structurally significant because they have no edge beams and no permanent tie rods to resist the transverse shell trust.

A few international other significant shells of that period include MarketHall Leipzig (Germany, 1927 – 1930, Dyckerhoff and Widmann AG), Orly Hangar (,France, 1921, Eugene Freyssinet)

Cylindrical Shells in the Port of Anwerp designed by Andre Paduart


Second Period 50’s and 60’s: Iconic shells realized for their visual expressiveness at Expo ’58, Brussels

The increasing body of knowledge in shell theory and construction, initially led the formal language for shells. Internationally, the richness of shells from that era have widely been showcased by the ribbed spherical and cylindrical shell forms of Pier Luigi Nervi (1891-1979) and the hyperbolic paraboloid (hypar for short) thin shells of Felix Candela (1920-1997).  In 1958 Candela built his masterpiece Los Manantiales, a radially arranged assembly of expressive hypars.  In the same year the capital of Belgium, Brussels, held Expo ’58, the first major World’s Fair after World War II.  Iconic pavilions and installations, built for this grand event, included the Atomium and the Philips Pavilion, an arrangement of nine hypars designed by Le Corbusier. Lesser known are the other shells that populated the Expo’58 site including the hypar information kiosk (designed by J.P. Blondel, the vaulted United Nations Pavilion and the semi-spherical Tuilier restaurant.

In 1957,  Broodthaers was a manual laborer on the construction site of the Expo 58 “Avec l’intention de [se] rapprocher des hommes qui la construisent ” [“to get closer to the people that are physically making the Expo”]. In 1958, he published “Another World,” an essay on The Atomium published in Le Patriote illustré, vol. 74, No. 10, Brussels, 9 March 1958, p. 389.

Top Row: Atomium, Philips Pavilion, Information Kiosk, Bottom Row: United Nations Pavilion and Tuilier Restaurant
Marcel Broodthaers as a construction worker on Expo ’58 site, 1957
Marcel Broodthaers, “Another World”, an essay on the Atomium, 1958

Our attention goes out to a more sculptural shell “the Arrow” which dominated the Expo ’58 site. Andre Paduart received from the Belgian government a commission to design and construct a symbol exemplifying the “victory of civil engineering over nature”. The Arrow, a thin reinforced concrete thin folded plate cantilevered 80m and was balanced by a thin 29m span shell on three supports. The folded plate had a tickness of only 4 cm at its tip and the shell on three supports had a thickness of only 6cm.  The cantilever supported a pedestrian bridge that overlooked a scale map of Belgium.  This map showed civil engineering works!  For this incredible engineering tour de force, Andre Paduart and the architect of the project received the 1962 Construction Practice Award of the American Concrete Institute.

In 1964, Marcel Broodhaerts showcased his work “Casserole and closed mussels” and stated  ’The bursting out of the mussels from the casserole does not follow the laws of boiling, it follows the laws of artifice and results in the construction of an abstract form’

Andre Paduart (with glasses and hat) in front of architectural model of the Arrow


Postcard showing the Arrow with suspended footbridge, Andre Paduart, 1958
Casserole and Closed Mussels 1964 by Marcel Broodthaers 1924-1976
Casserole and Closed Mussels, Marcel Broodthaers, 1966


Third Phase 70’s and 80’s: Decline of shell structures and folded plates at the Groenendael Hippodrome

In the 70’s the architectural interest in the expressiveness of shells faded. At the same time, the cost of labor involved in constructing shells, became uneconomic and other long-span structural solutions were favored.  To cover the grandstand of a hippodrome near Brussels, Andre Paduart designed and constructed a 13.5m cantilevering folded plate with a thickness ranging from 7 to 12cm only.  The roof had a width of 106m and no expansion joints. The roof is reminiscent of Eduardo Torroja’s (1891-1961) Zarzuela hippodrome and Hilario Candela’s Miami Marine Stadium.  In 2012, these folded plates were demolished.

In 1976, Marcel Broodthaers is buried at the cemetery of Ixelles, Brussels at a distance of 100m to the University Libre de Bruxelles where Andre Paduart taught thin shell theory.

Folded Plate Roof at Groenendael Hippodrome, Andre Paduart, 1980
Tombstone Marcel Broodthaers, Ixelles Cemetary, 1976.

Author:  Sigrid Adriaenssens

I would like to thank Joe Scanlan for co-constructing the storyline and Paul Van Remoortere for providing valuable information.


Espion, B., Halleux, P., & Schiffmann, J. (2003). Contributions of André Paduart to the art of thin concrete shell vaulting. Proc. of the 1st Int. Congr. on Construction History, 829-838.

What I am thinking: Bill Baker at SOM

William F. Baker, also known as Bill Baker, is one of the leading structural engineers of our generation. Baker was the principal engineer of many buildings including the Burj Khalifa (Dubai, 2004)  and the Broadgate Exchange House (London, 1990) and can be considered as the exponent of the innovative structural engineering  tradition cultivated at Skidmore, Owings & Merrill.

Sigrid Adriaenssens: What is the SOM approach to design?

Bill Baker: I’m a structural engineer within an architectural engineering firm, and that makes my position at SOM a bit unusual. Many of the structural engineering firms out there are consultancy firms, whereas SOM does both. SOM is special in the emphasis on integrated design where the architects and the engineers work together from the very beginning before there is any kind of solution or scheme. This process enables us to develop things that work with SOM’s philosophy of design. The interpretation of that philosophy will keep morphing over time, but essentially what one would expect in an SOM building would be three attributes: simplicity, structural clarity, and sustainability. It’s great when a building has all three of those attributes. Those values naturally align with our philosophy as structural engineers as well. We prefer a simple solution to a complex one. We design structures that clearly express their function and have efficient structural systems that minimize the use of materials and minimize embodied carbon. Our aesthetic values and our technical values are the same. It’s not just engineering, it’s an engineering philosophy.

Bill Baker collaborating with architects and engineers on the Burj Khalifa at SOM
Bill Baker collaborating with architects and engineers on the Burj Khalifa at SOM. Photo ©SOM

How do you situate yourself in the tradition of North American Engineering?

I don’t really think of myself as a North American engineer, although I am based in North America. I look around the world for my inspiration. As far as role models, one of the greatest structural engineers that I’ve ever met is Jörg Schlaich, an engineer from Germany. I’ve had the opportunity to work under Fazlur Khan for a brief time, and I’ve studied his work in-depth. The people who I’ve found helpful in my career are both engineers and architects within SOM including Myron Goldsmith, Hal Iyengar, Stan Korista, John Zils, and Jin Kim. Jin Kim was an architect who, on my very first project, came to me and was very upset with something I had designed because I had created a stair that was very ugly. He had admonished me that my job is to design structures that architects would feel bad to cover up. He was a very important mentor to me.

SOM Colleague (Left), Fazlur Khan (middle), and Hal Iyengar (right) in the office
SOM Colleague (Left), Fazlur Khan (middle), and Hal Iyengar (right) in the office. Photo ©SOM

I’ve always had mentors from other firms. Bill LeMessurier was a great mentor to me. I spent time with him at several conferences and would call him when I needed advice on ideas related to the industry. I’ve always had a great relationship with Les Robertson, and I was fortunate enough to work with him when he was a peer reviewer on an early project of mine. We had some very interesting conversations.

However, a lot of my mentors are not necessarily designers. In the UK there is Stuart Lipton, a developer, and Peter Roger, his partner who works on the constructability of a project. They’ve been very influential on my work.

From academia, the writings and lectures of Princeton’s David Billington are very important to me.

As far as what perhaps sets me apart is that I’m a great believer in research. It is very important to me to use research to explore new structural concepts that can lead to new architecture. SOM is very active and consistent with that idea, and we have innovated new technologies and concepts that were not previously known in the profession because of our research. We’ve discovered new understandings of the way structures work, and this enables us to design in different ways. That’s something about SOM that sets us apart from other engineering firms.

Bill Baker in SOM_s Wind Tunnel
Bill Baker in SOM’s Wind Tunnel. Photo © SOM

What is your greatest professional achievement and why?

That’s a tough question. When you say “greatest”, it makes other things secondary. I have a lot of things I’m very proud of, and just like you don’t rank your children, I don’t want to rank my achievements. There are some buildings I’ve been involved in that I’m very proud of, like the General Motors entry pavilion in Detroit; the Exchange House in London that spans the tracks at the Liverpool street station; and the Burj Khalifa of course. I’m also very proud of some buildings that were never built, like 7 South Dearborn, because of the interesting concepts we used to design them.

Broadgate Exchange House
Broadgate Exchange House. Photo © Richard Waite
Burj Khalifa
Burj Khalifa. Photo © Nick Merrick | Hedrich Blessing

I greatly enjoy working with artists. They can table our technical input and use it to inform their art. Our work with Inigo Manglano-Ovalle, James Carpenter, and James Turrell was very satisfying to me.

Gravity is a Force to be Reckoned With by Inigo Manglano-Ovalle
Art Installation by Inigo Manglano-Ovalle titled “Gravity is a Force to be Reckoned With”.

That’s on the project side. On the professional side, I think I’ve been helpful in moving the profession towards a more creative way to design. By explaining what it is we do as far as research and discovering new ideas, I believe we’ve helped the profession to keep moving forward.

Within the profession, it is very important for us to promote a technology-based creative process that leads to new architecture. I’ve worked very hard at that by using the soap box here at SOM to share this knowledge in order for the profession to rise to a new level.

What is your favorite structure and why? Could it be improved and how?

The John Hancock Center in Chicago is my favorite structure because of its clarity, the simplicity, and sophistication. The way it meets the ground, the way it tells its story. How would I improve it? I’d improve it by making the floor-to-floor height a little better. The apartments are a little tight! But overall, it’s a great building. My improvements to it would be fairly secondary.

John Hancock Center
John Hancock Center. Photo © Ezra Stoller

What are Maxwell diagrams and Mitchell frames? Why are they important to you and your work?

For me, Maxwell diagrams (Graphic Statics) help the engineer visualize the forces in a way that no other methodology allows. You can visualize the forces much more clearly. Mitchell frames help you find benchmarks so you know if your solution is efficient by comparing it against a Mitchell structure. They also provide structural geometrics that one may not find using a traditional approach. They are both very important and they both lead to a creative process because they give you feedback that you can, through your intuition, create something new. I don’t think intuition comes from nothing, it is an accumulation of knowledge and experience that leads to new ideas. Having that knowledge can lead you to intuitions that you wouldn’t have otherwise.

What would you change in the education of the next generation of structural engineers?

I would put more emphasis on the theory of structures, engineering mechanics, and the behavior of materials: the true technology of our discipline. These are things that will not change unless you invent new materials. A building code has the shelf life of a banana: it’s going to change and it’s going to morph into something different. However, the underlying physics will stay the same.

What is the use of the future structural engineer? If you go back a long time, you had to understand theory because you could not calculate very much. Today, we’re in a computational age where we use a tremendous amount of brain power to manipulate the “box”.  In the future, computation will be so trivial, where it almost becomes unimportant, but the theory will be the paramount thing that the engineer will bring to design.

Bill Baker studying Burj Khalifa model
Bill Baker studying Burj Khalifa model. Photo: Courtesy of SOM

What question are you never asked and would like to be asked? What would be the answer?

If you had not become an engineer, what would you have become?

An auto-mechanic. Fixing something that’s broken is quite satisfying.


We would like to thank Bill for taking the time to answer our questions, as well as Danielle Campbell of SOM for transcribing the interview. Questions by Sigrid Adriaenssens, further editing by Tim Michiels.

What I am thinking: form making artist Maria Blaisse

Maria Blaisse is a Dutch visual artist and designer. She authored the book “The Emergence of Form”, in which she discusses her in-depth research into form in various materials and the numerous application possibilities, both autonomous and product-oriented.

Sigrid Adriaenssens: Why and how do you generate curved forms?

Maria Blaisse: discovering the curved lines .. while experimenting with incisions  in a rubber inner tube ( for a party of my children)  and while putting the forms on my head  something amazing happened. Then I realized I touched an energy field. I am still working with it.

I found the potential of the inner and outer curve of a torus. The inner curve generates energy and form, while spiraling centripetal. It was the most powerful thing to discover, the outer curve spiraling centrifugal loses form and energy. In my book the emergence of form you can see this research based on one form and one structure from here one can design any form or structure without any waste.

Variations on rubber inner tube – Copyright of Maria Blaisse

In your book “The emergence of form”, you state “form is ‘frozen’ movement”.  Please explain and illustrate that idea?

A form is always part of a movement. I found out while editing film that the stills have the most impact: the form is energized.

systematic variations in gauze structures based on one form  .png

Systematic variations in gauze structures based on one form – Copyright of Maria Blaisse

In your design approach, you emphasize beauty (wanting to ‘move’ people) but also material and energy efficiency. Why is that important to you and to society?

Continue reading “What I am thinking: form making artist Maria Blaisse”

A seismic retrofit for an adobe church in the Peruvian Andes

The Peruvian countryside is dotted with earthen buildings dating back to the Spanish conquest of the Americas. The Spanish adapted traditional European building typologies to the locally available construction material: earth.Many of these earthen buildings have stood the test of time and have become of great monumental value to local communities and visitors alike. Some of them, however, have suffered extensive damage, or even fatal collapse due to one of the threats in the new world not so critically shared by Spain: earthquakes. While buildings were soon adapted and retrofitted to resist seismic action, the combination of the low-strength adobe (mud-brick) and high regional seismicity has remained a concern for many – if not all – subsequent generations.

Remains of earth-cane barrel vault roof of a church near Ica, Peru that collapsed during the 2007 Pisco earthquake. (Image Tim Michiels, copyright The Getty Conservation Institute)

Today, relatively little attention is given within the academic community to the engineering and seismic design of earthen buildings. Despite the availability of advanced structural design codes, powerful calculation tools, and extensive material research labs, experts still struggle to characterize the behavior of masonry buildings, and especially earthen structures, during earthquakes. Thus, designing sensible and non-intrusive intervention techniques to preserve often languishing adobe monuments is a major ongoing challenge.

Front facade of the church of Kuño Tambo (Image Sara Lardinois, copyright The Getty Conservation Institute)

Continue reading “A seismic retrofit for an adobe church in the Peruvian Andes”

How to describe the esthetics of structural surfaces? (2/2)

In an earlier post, I wrote about how and why we seem at loss for words when describing the esthetics of a structural surface. I continue that discussion here and analyse what vocabulary layman use and make suggestions for where we might seek additional jargon. I  build my argument upon the results of an experiment carried out by graduate student Rebecca Napolitano in Fall 2016 on the Princeton University Campus.  In the physical experiment, a membrane was installed on a highly frequented location on a central location next to a neo-gothic medium size building.The  membrane was shown in an existing built environment, which might have caused distraction from observing the pure membrane form, but allowed for a full 3D perception of the membrane deforming in the wind.  Randomly selected 138 undergraduate students who passed by the installation, were asked to describe the membrane structure with one word.  If their response coincided with an already recorded word, they were prompted for another defining word.

This physical experiment yielded a plenitude of words which can be catalogued according to formal analysis or subjective response classes. The first category, formal analysis, is grounded in the fine arts and Vitruvian architecture tradition. This type of analysis disassociates itself from reactions such as elation, fear and awe.  These words describe emotions or subjective responses and constitute the second category.  The subcategories in both classes were pre-established before the collection of data and are based on the ones discussed by [1].

Formal Analysis

We first investigated the vocabulary pertaining to the category of formal analysis. This category holds the subcategories of form, proportion, space and visual mass.

Observing the 3D form of the membrane is not a simple process. In the past, built form has been discussed as a hierarchy of simple forms combined according to rules, into an assembly of complex forms [2].  The words in the experiments refer either to the simple or the complex form or the rule.  Simple form descriptions in Rebecca’s experiment included words such as “round”, ”bulbous”.  Complex form descriptions included  “nurbs”, ”free form” and rules included “tangent continuity”, “cambered”, “periodic”, “smooth”, “logarithmic”, “interlacing”, “weaving”, “optimized” , ”linearly disruptive” and “bendy”.

Nurbs, non-uniform rational basis spline (image credit

The subcategory proportion evaluates the geometric relationships between the different parts. Traditionally formal rules for proportioning have been defined buildings composed out of analytical forms including hemispheres and cylinders. Unfortunately, they are not that relevant for force-modeled systems such as the membranes in the experiments, because these membrane geometries are far more complex.  These geometries are generated by the laws of physics and are more difficult to proportion and steer than analytical ones.  A few words like “contrived complexity” hinting at these characteristics, showed up in the experiment.

A number of words in the experiments related to space.  The observers understood space as the Aristotelian idea that the membrane created both a positive space and a negative space or “embrace and grows space”. Words like “encompassing“ (positive space, the membrane itself) and, “limitless” and “unconstrained” (negative space, the space that co-exists separately alongside the space occupied by the membrane itself) exemplified the subcategory space.

Visual mass as opposed to actual mass can be achieved by the perceptions of light, color and texture. The untrained observer tends to make a connection between visual and gravitational mass.  Previous studies show how white surfaces, such as the one in the physical experiment, and the smoothness of the membrane in the experiment helped the structure as being perceived as lightweight [1] . These perceptions were captured in the experiments in the words “sinuous” and “slim”.

Subjective Responses

Besides the words that fall in the category of formal analysis, we closely examined the second category, called subjective responses. The results showed that the observers felt that the membrane has a certain character that spoke to them.  The words were distributed over the subcategories anthropomorphism, sensuality allusion, physical security and empathy.

Some observers saw the membrane as a living creature (eg. “sting ray”, “cocoon”) and endowed it with personality and intent. This association is called anthropomorphism.  The membranes were also perceived as “pregnant in the breeze”, “in bloom” and “about to take flight”.

Many observers found that these surfaces had a sensuous quality and captured those impressions in words like “sensual”, “voluptuous” and “calliphygian”. These words refer to the movement of the membrane as it progresses to a visual climax, followed by a relief of tension. In particular the inward and outward curving membrane surfaces have a particular sensual quality, which is missed by forms with single curvature.

Some spectators covertly or indirectly referred to an object from an external context.  The membranes evoked allusions with words such as “Rubenesque”. This word for example refers to the works of the Baroque painter Pieter-Paul Rubens (1577-1640) and means plump or rounded in an attractive way.  Other images included poetic metaphors such as “symphonic”, “motion frozen in time”, “essence of motion”, “natural choreography”.  Other allusions included scientific, artificial natural associations such as “meniscus”, “satin/silk, “hilly” and “motion of water”. These references to physical objects, although they are not grounded in the innate perception of the observer, contributed to aesthetic experiences while viewing the membrane.

Anthropomorphism, an association to a sting ray (left ), allusions to Ruben’s works (right), ,silk (bottom right) and hilly (bottom left) call the membrane in the wind to mind without mentioning it explicitly. (image courtesy Flickr the Commons)

Continue reading “How to describe the esthetics of structural surfaces? (2/2)”

How do gridshells and longspan roofs perform in earthquakes?

The 500km rupture of the 2011 M9 Great East Japan Earthquake resulted in extensive damage in over a half dozen prefectures from Tokyo to Iwate.  Several lessons can be drawn from the response of spatial structures, particularly long span roofs. While the global behavior was generally excellent, nonstructural element damage and local failure modes were widely observed. This is unfortunate, as such structures play a vital role in post-disaster recover as shelters (e.g. Shigeru Ban) and minor design changes could have prevented much of the damage. In the aftermath, the Architectural Institute of Japan [1] conducted a detailed reconnaissance of dozens of gymnasiums, sports stadia and halls and found several reoccurring damage patterns:


Miki Disaster Management Park Beans Dome, Sport Stadium and Emergency Staging Area in Hyogo Prefecture (photo credit penccil::Slowtechture)

Shear failure of baseplate anchors

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Constructing Ice Structures

Since it has been snowing in Princeton this week, there is really no better time to write about how to construct structures out of ice. The motivation of building with ice – as opposed to another construction materials such as concrete-  is that it makes experimenting much more economic and zero-carbon.  Structural ice experiments also allow for the ability to discover a new medium that could fill the demand for a building material that will not see a dramatic decrease in its strength after being subject to several extreme freeze-thaw cycles [1].  In many extreme cold environments, it would be desirable to have an inexpensive and safe way to reconstruct infrastructure or buildings out of ice to address annual need for shelters and roads rather than rebuilding or repairing these possibly concrete structures that will ultimately be damaged by the weather each year. In the following sections we provide a historic glimpse of key ice structures and how they were built.

Throughout history, ice has been used as an inexpensive and naturally available building material. The oldest known ice structures are igloos that were made from snow blocks [2]. The igloos date from prehistory and have developed a form in which the structure takes exclusively compressive stresses and experiences zero bending moment everywhere in the shell. This form, called a catenoid evolves from the revolution of a parabolic cross-section into a dome. The igloos are constructed into this form using compacted ice blocks.  The gaps between the blocks are filled with snow.  Heating in the igloo then melts the inner surface of the igloo which then refreezes as a layer of ice that contributes to the overall strength of the igloo [2].

Iglulik Snowhouse (photo by Albert Low, 1903, image credit Library and Archives Canada/C-24522).


In 1739, Russian empress Anna Ivanovna order the first ice palace to be built [2].  These impressive structures were made of blocks from rivers and lakes that were trimmed and stacked to form a masonry wall [2].  This marked the beginning of functional ice structures that did not take the traditional catenoid shape.The form was imitated in the 1980’s using cast snow in which wooden molds were used to create compact snow walls to be sculpted.

Ice palace (left) for Russian empress Anna Ivanovna (right Louis Caravaque, 1730)  (image credit wikimedia)

More practically, recent construction of ice hotels has seen the use of special wet snow being sprayed onto steel molds with heights up to 5m and spans up to 6m.  In this process the snow is allowed a two day freezing period before the molds are removed.  These structures get stronger as the snow melts and refreezes over time.  This occurs on a diurnal cycle as the top layer of snow melts slightly each day and then freezes to solid ice during the night [2].

Ice Hotel Sweden constructed of wet snow sprayed onto steel molds (image credit

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“Thinking by Modeling”- Frei Otto Exhibition

In November 2016, the ZKM – Zentrum fuer Kunst und Medien – Centre for Arts and Media – in Karlsruhe, Germany, inaugurated its exhibition on the works of Frei Otto entitled “Frei Otto – Thinking by Modeling” (November 05, 2016 – March 12, 2017): an exhibition unprecedented in terms of conception and extent, curated by Prof. Georg Vrachliotis. In the year before, Frei Otto had passed away, while in the same year he had been awarded the prestigious Pritzker Prize for architecture. As a result, the attention  of architects, engineers and designers worldwide has been refocused on the  personality, the works and the achievements of Frei Otto. The opening of the exhibition was widely picked up, attracted a lot of visitors and comes along with several “special events”, one of them being a symposium which will be held on January 26-27, 2017.

© ZKM Zentrum für Kunst und Medien, Foto: Grünschloss

The works of Frei Otto and his research teams play an active role in current design of architecture and engineering. They are often referred to when lightweight structures or bionically inspired designs are discussed. The current attention on Frei Otto,his insights and merits should be interpreted as contributions to our heritage, prospect and responsibility. His exclamation “Stop building the way you build!“, formulated during a lecture in 1977 [1], is still reverberating. This outcry can be taken as an inspiration for many disciplines, be it architecture, engineering, biology or social sciences.

Frei Otto and the Institute of Lightweight Structures in Stuttgart

The establishment of the “Institute of Lightweight Structures” at the University of Stuttgart, Germany, was a starting point to a “time line” of lightweight structures at this location. Fritz Leonhardt called Frei Otto, who was at that time living and working in Berlin, to Stuttgart University. Fritz Leonhardt (1909 – 1999) was the designer of the Stuttgart television tower which was the first of its kind being constructed in reinforced concrete, the author of books dealing with “aesthetics” of bridges, and pioneer in the field of designing structures in reinforced concrete. Leonhardt had published his thoughts about lightweight structures as a “demand of our times” in 1940 [2], a time facing material scarcity during a devastating war which had been triggered by Nazi-influenced Germany. The lack of material, or the restriction to a certain kind of material, can be taken as a source of inspiration for lightweight construction: Eladio Dieste, Felix Candela and Robert Maillart developed their unique aesthetics by this kind of limitation. Fritz Leonhardt was aware of this special quality and in that spirit he called Frei Otto to be Professor at the the Institute of Lighweight Structures IL at Stuttgart University.

During this time, Frei Otto was dealing with the detailed design of the German pavilion for the Expo Montreal in 1967, a piece of architecture which was path breaking in many ways. A test building of the Expo roof, prototype of a cable net structure, was to become the place of location of the IL.

Joerg Schlaich was the successor of Fritz Leonhardt as Professor at the University of Stuttgart. Werner Sobek assumed the chair of Frei Otto at the Institute of Lightweight Structures in 1994. In 2001, he was additionally appointed as successor to Joerg Schlaich’s Chair. The two chairs were merged to become the “Institute of Lightweight Structures and Conceptual Design” ILEK. In 2015, Werner Sobek was awarded the “Fritz Leonhardt Prize”, a distinction awarded every three years to an engineer in recognition of outstanding contributions to the area of structural engineering. In a very emotional speech, Sobek stated his view of the necessity of lightweight structures, based on very descriptive and startling numbers [3].

The circle is closing: the need for lightweight structures, be they named material-efficient or low-carbon-footprint, is even more relevant in the beginning of the 21st century. Frei Otto initiated a center of knowledge which reached out to the world.

“Thinking by Modeling” – the exhibition

The exhibition is set up in two large-scaled rooms of the “ZKM” (Zentrum fuer Kunst und Medien – Center for Arts and Media) museum in Karlsruhe. The building itself was originally built as a munition factory and is a protected monument with classical elements of industrial architecture. It hosts the ZKM since 1997.

The city of Karlsruhe is also the location of the “saai” (Suedwestdeutsches Archiv für Architektur und Ingenieurbau – Southwest German Archive of Architecture and Engineering), where Frei Otto’s works have been archived after his passing away.

Due to the initiative of Prof. Georg Vrachliotis, Professor at the KIT Karlsruhe, this impressive exhibition has been realized.

The exhibition is constituted by four elements: model landscape, open archive, cosmos, and projection.

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