The persistence of some of the oldest structures in the world in masonry has demonstrated the high potential for masonry structures to last through various conditions over long periods of time. Masonry’s compressive strength is extraordinarily high – it is estimated that a stone pillar would have to be 2 kilometers tall in order to fail by crushing.  As a result, in contrast to materials such as concrete and steel that make up most of present-day structures, the limit state of masonry is often dictated by its geometry and not its material properties.
Research into the stability of masonry structures is valuable for two main reasons. Firstly, this research enables us to understand and preserve the structures of the past. Many structures of rich cultural heritage are made of masonry, but their stability is challenged by environmental and anthropogenic threats, such as earthquakes or terrorist attacks. [2–6] The second reason is forward-looking. In some areas of the world, masonry materials are abundant and are thus the most economic choice of building material. An understanding of stability in masonry structures can make possible design tools for materially efficient structures.
Examples of masonry structures are given below. Philadelphia City Hall (1901) is the world’s tallest masonry structure at 167 meters height. [A] The King’s College Chapel (1515) in Cambridge, UK is not even a fifth of the height of Philadelphia City Hall, but the complex geometry of its fan vaults make it a compelling study of masonry stability. [B] Finally, the Armadillo Vault (2016) is a prime example of how an understanding of masonry stability can inform efficient design today. [C]
Philadelphia City Hall (Photo: Beyond My Ken)
King’s College Chapel (Photo: SEIER+SEIER)
Armadillo Vault (Photo: Jean-Pierre Dalbéra)
Methods and theories of structural analysis for masonry structures
The structural analysis of masonry arches and structures have preoccupied countless scientists since the 17th century. In this post, studies on 1. Classical methods and 2. Limit state analysis (including equilibrium analysis and kinematic analysis) are presented. A future post will explore 3. Numerical modeling and discuss existing studies that use each method to assess masonry structures. A more comprehensive overview of studies on each analysis method can be found in [7–9].
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 – 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?
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.
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.
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 .
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 . 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”.
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  . These perceptions were captured in the experiments in the words “sinuous” and “slim”.
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, sensualityallusion, 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)
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  conducted a detailed reconnaissance of dozens of gymnasiums, sports stadia and halls and found several reoccurring damage patterns:
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 . 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 . 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 .
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 . These impressive structures were made of blocks from rivers and lakes that were trimmed and stacked to form a masonry wall . 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 .
Ice Hotel Sweden constructed of wet snow sprayed onto steel molds(image credit holidayguru.ie)
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.
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 , 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 , 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 .
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.
It has been said that the work of Frei Otto (Germany, 1912-2015) has a sculptural quality to it . Although Frei Otto’s parents were sculptors, he insisted that the shapes he produced were rigidly grounded in the laws of physics , and was very reluctant to describe their aesthetic value. This observation hints at the questions that this paper starts to address, namely how can one describe the aesthetics of a curved structural surface?
It is observed that structural aesthetic critique is a little practiced discipline. In engineering education, students generally are not encouraged to express their emotions about the built environment, and are not frequently encouraged to develop an enthusiasm for visual experiences . Beauty seems to engineers such a vague concept, hard to define accurately to others.
As the holidays are approaching and as your loved ones – yet again – run out of inspiration for your holiday gift… the Form Finding Lab comes to the rescue. We present you a list of our favorite books on engineering, architecture and anything in between.
The Form Finding Lab.
Compiled by Tim Michiels, with contributions of Sigrid Adriaenssens, Victor Charpentier, Demi Fang, Andrew Rock and Olek Niewiarowski
Marc Mimram is a celebrated French engineer and architect with projects in France and around the globe. He generously shares with us his ideas on bridge design in conversation with PhD candidate Victor Charpentier.
Victor Charpentier (VC): Marc Mimram, you are both an architect and engineer. Yet you have said that when you are given a project, the greater part of the inspiration for the initial spark comes from a third field, which is study of the landscape and geography. Can you explain why this is so important to you and how this affects your designs?
Marc Mimram (MM): Each project should be specific. It has to be depending of the situation where it take place.
To become a coherent project, it has to be related to the geography, the horizon. It should express the relation to the ground, to the sky, to the landscape considered as a geography informed by history.
In that case the structural project can take roots in the reality and forget the abstract equation of strength of materials to express gravity, the movement of forces, the movement of light; being part of the situation, part of the world, belonging to the site.
Advanced technologies have allowed structural form finding to become an integral part of many recent design projects. How do you add your personal, creative touch to a process that can become largely computational? What are your thoughts on the role of this method for the future of engineering design?
MM: The process of computational form finding is a method of optimization and as such, it follows the development of the project. It is obviously important to develop the project with frugality but the rational process of development can be plural and the choice has to be related to the specific situation, taking into account the landscape, the topography but also the economical situation, the knowledge, the development of local craftsmanship, the local materials.
In the past decade, many of your larger bridge projects have been built in Asia or in North Africa in part because of more local design freedom. In your opinion, are there too many inhibitions in the field of construction in western countries? What could be improved to bring creativity and exploration back to construction while at the same time maintaining the high standards of safety?