Assessing the Stability of Masonry Structures (part 2): Numerical and Physical Modeling

This post is second in a series covering different assessment methods for stability of masonry structures. Part 1 covered classical and equilibrium methods; this post covers suitable numerical modeling techniques as well as different examples of physical modeling for masonry stability.

4. Numerical modeling

Several methods of numerical modeling for masonry structures exist, as demonstrated by the flowchart in Fig. 10.

Figure 10: Overview of numerical modeling methods for masonry structures, adapted from [41] with [8]
As the first level of Fig. 10 suggests, numerical modeling of masonry structures can be divided into four main categories: macro-modeling, homogenized modeling, simplified micro-modeling, and detailed micro-modeling. Asteris et al. [41] provide discussions, summarized below with some additions where noted, on the differences between these modeling approaches. Fig. 11 also depicts the different numerical modeling approaches. In this section, macro-modeling and simplified micro-modeling are the focus.

Figure 11: Illustration of different strategies for modeling true masonry sample (a): (b) one-phase macro-modeling, (c) two-phase micro-modeling, and (d) three-phase micro-modeling [41]

4.1 Macro-modeling: masonry as a one-phase material

The macro-modeling approach models both bricks and mortar (or all bricks, in the case of dry masonry) as a homogeneous continuum as in Fig. 11(b). As the subsets under macro-modeling in Fig. 10 suggest, these numerical models are typically finite element models.

Continue reading “Assessing the Stability of Masonry Structures (part 2): Numerical and Physical Modeling”

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 to see when visiting Cambridge, UK

Our Princeton alum, Anjali Mehrotra, is currently pursuing a PhD in historic masonry structures at the University of Cambridge, UK. We asked Anjali to take us on a campus tour in search of structural surfaces. This is what she showed us.

King’s College Chapel,  1446 – 1515

There is an abundance of vaulted structures in Cambridge, including the main gates of Corpus Christi College, Trinity College and St John’s College, which are also examples of fan vaults and are each adorned with the respective college’s crest.

Corpus Christi College 1353  and St John’s College 1511 gates

Other vaulted structures in St John’s include the cloisters of the neo-Gothic New Court, which were designed by Thomas Rickman and Henry Hutchinson between 1826 and 1831. Around the same time, another architect, William Wilkins, designed the Great Hall and Gatehouse of King’s College.

St John College Cloisters and detail Gatehouse King’s College

Professor Jacques Heyman, former Head of the Cambridge University Engineering Department, is widely considered to be one of the world’s leading experts in cathedral and church engineering. He revolutionized the analysis of masonry structures by translating plastic theory developed for steel design into theorems which could be used for stone as well. His book The Stone Skeleton: Structural Engineering of Masonry Architecture is the seminal work in this matter. His theories have been used for the analysis of various types of masonry structures including arches, spires and vaults, with the latter including Gothic style fan vaults, with perhaps the most famous example being the vault of King’s College Chapel in Cambridge. Built between 1512 to 1515 by John Wastell, the fan vault is 88 m long and 12 m in span, making it the world’s largest.

Professor Jacques Heyman and interior view of King’s College Chapel 1512-1515.

Author: Anjali Mehrotra

Prof. A’s Tedx Talk: Designing for strength, economy and beauty

Check out this video and like it on YouTube.

By 2050, 70% of the world’s population will live in cities. Structural engineers envision, design and construct the bridges and long‐span buildings those city dwellers depend on daily. The construction industry is one of most resource‐intensive sectors, and yet our urban infrastructure continues to be built in the massive tradition in which strength is pursued through material mass. In December 2016, Professor Adriaenssens gave aTedX talk “Designing for strength, economy, and beauty” at the GeorgeSchool, PA. Her idea is that our bridges and buildings should derive their strength and stiffness not through material mass but from their curved shape, generated by the flow of forces. As a result, these structures can be extremely thin, cost‐effective, and have a smaller carbon footprint and arguably they can have an esthetic quality to them.

Author: Prof. S. Adriaenssens