RuMoer 56: Form Finding| BouT | TU Delft

periodical for the Building Technologist

PRAKTIJKVERENIGING

BOUT

student association for building technology

56. Form Finding

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RUMOER 56 Oktober 2013 20th year of publication

RUMOER is a periodical from Praktijkvereniging BouT, student and practice association for Building Technology (AE+T), Faculty of Architecture, TU Delft (Delft University of Technology). This magazine is spread among members and relations.

Praktijkvereniging BouT Room 02.West.090 Faculty of Architecture, TU Delft Julianalaan 134 2628 BL Delft The Netherlands

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Text editing:

Cover design:

Muhammed Ulusoy Reinier Scholten Ate Snijder Koen Fischer Muhammed Ulusoy Reinier Scholten Koen Fischer Koen Fischer

Cover image:

LED’s, incorporated into the grid shell, emphasize the cupola’s structure and contribute the enjoyment of the spatial quality of the inner courtyard of the maritime museum Amsterdam (image courtesy J.L. Deru)

Membership Amounts per calendar year (subject to change): € 10,- Students € 20,- PhD Students and alumni € 30,- Academic Staff € 80,- Companies Single copies Available at Praktijkvereniging BouT for € 7,50.

Sponsors Praktijkvereniging BouT is still looking for (main) sponsors. Sponsors make activities possible such as study trips, symposia, lectures and much more.

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Contents

Editorial

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From the board

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Introduction of the new board members

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Challenges for complex geometry structures

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Shaping better civil structures

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An analytical solution to shell structures

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A doubly curved steel and glass dome for the historic Maritime Museum Amsterdam

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Shaping building surfaces

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Old School, New Style

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Editorial Written by: Muhammed Ulusoy, BouT Commissioner of Media “Inherently characterized by the interaction of geometry and forces, the unique nature of long span dome, shell, and membrane structures readily allows collaboration between architects and engineers in the examination of their optimal form. Through the elimination of bending and shear forces in the structure, less material and reinforcement is needed.

By minimizing the use of materials, a form that is economical, sustainable and aesthetically attractive emerges. However, this optimization must be done through form-finding methods, whereby the structure itself defines its own shape based on its figure of equilibrium under applied loads. Unlike free forms which are defined mathematically, form- finding shapes rely on the structure and loads themselves for definition.” (A.I. Fund, 2008) In this edition of Rumoer (56) we will focus on the topic of Surface Active Structures. One of the sub-topics of surface active structure is form finding. We start off our topic with a critical opinion on the subject by Andrew Borgart. In his article some relevant questions are asked and some possible directions are given on the subject of surface active structures.

By form-finding, effective structures can be built in an ergonomical, economical, durable and sustainable way.

Sigrid Adrieanssens discusses her research on this topic in her article ‘ Shaping better civil structures’.

Niels van Dijk, a graduating student at the faculty of architecture TU Delft, gives an overview on his research on form-finding in membrane shells.

The architectural firm Ney+Partners designed a roof for the inner courtyard of Het Scheepvaartmuseum in Amsterdam. In the process of designing the roof, form finding principles are intergrated in the design.

Roel Schipper, researcher and teacher at TU Delft Faculty of Civil Engineering and Geosciences, writes an article about the use of flexible moulds to shape concrete elements into curved elements. He will focus on freely formed shapes, materials used, structural models and manufacturing techniques.

The use of computer programs for calculating, designing and engineering complex geometrical structures is an challenge for future designers. Peter Eigenraam sheds a light on the subject of translating physical models into digital computer models.

This issue marks the reformation for our Publications.

The new Publications and RUMOER will consist of a committee instead of one single board member. Our goal is to publish more issues per year, increase participation from students with our practice organization and to provide our BouT members enriching topics to read. All students from the Department of Architectural Engineering and Building Technology are welcome to become a committee member or freelance writer.

(A.I. Fund, 2008, Form-finding structures, MIT Department of civil and environmental Engineering)

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film commercial trade-show report 2D and 3D visualisation

photography graphic design wedding video

OCVLVS “don’t tell — show!”

screenshot from our latest promotional film

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Oculus Film www.oculusfilm.com hans@oculusfilm.com +31 (0) 6 20025617

From the Board Written by: Dwayne van Halewijn, BouT Chairman and Educational affairs.

After 6 months of hard work and pushing BouT to a new level, our chairman Luuk Graamans changed his function at BouT for a magnificent internship in Vietnam. We thank him for all his work and wish him the best for the future.

This means that there had to be some changes within the board of BouT. Following Luuk, Dwayne van Halewijn now fulfils the seat of chairman, while keeping the educational affairs as well. Joost van de Ven (Secretary) and Freek van Zeist (Treasurer & Media) remain at their position.

BouT also welcomes two new members of the board. Tyrza Ligthart will act as Commissioner Events while Muhammed Ulusoy takes care of Publications (Rumoer). They will introduce themselves.

arrange internships and workshops as extracurricular events of which our members can benefit. With a new commission, Rumoer will be reinvented and published more often. Finally we state a long-term view, supported by documentation to ensure a healthy endurance of BouT after the current board .

We are still in 02.West.090, so come by if you have anything to ask. We can help you with almost everything. Join the innovators!

Dwayne van Halewijn BouT Chairman and Educational affairs

After a successful period of re-arranging memberships, finding new sponsors, setting up an 'Advisory Board', building a new website, bringing newsletters, publishing Rumoer, growing numbers of members, excursions, drinks, provided internships, professional networking and renewing the whole image of BouT - we will continue to seek opportunities to benefit from the fresh new start BouT has made in the past 6 months.

We are enthusiastic to continue the work we have done by providing new excursions and lectures this year.

We will keep seeking contact with professionals to

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Muhammed Ulusoy - Publications As commissioner of Publications I am concerned with publishing Rumoer magazine for BouT. My name is Muhammed Ulusoy, I am 24 years old and started studying at the faculty of Architecture in 2008. To broaden my perspective and to be an active part in the field of architecture and technology I joined BouT as commissioner Publications.

For a better magazine we formed a commission with Koen Fischer and Reinier Scholten. Together we will focus on launching three issues per year on architecturally relevant technological subjects.

As you all know Rumoer is the periodical for the building technologist, and it is our duty as Rumoer commission to keep the tradition alive and fill up all whom love Building Technology with up to date knowledge on technological innovations. This way BouT members can follow the developments in the field of architecture and technology to enrich their knowledge on varying subjects.

With this issue on Surface active structures (56), an exiting journey to discovering the fast developing technologically driven world will continue. Hereby with each issue, Rumoer offers its readers the opportunity to keep track of a varying set of technological subjects.

For any suggestions or questions concerning publications, please feel free to address me or the commission members!

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Tyrza Ligthart - Events As commissioner of Events I am concerned with the organization of excursions, trips and other events within the BouT organisation. My name is Tyrza Ligthart. I am 22 years old and I started my bachelor of Architecture in 2009. During the bachelor I found out that to me the facade is the most interesting part of a building. Mostly because of the combination of architecture and technology. Therefore I have chosen to do the Building Technology Master.

The BouT organisation enables students to get to know most recent techniques and develop contacts in the building industry, through a excursions and other interesting events. To me, this is the reason to join the BouT association and help organize these kind of events.

When you have a great idea for an event or have any questions about one, contact me!

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Challenges for complex geometry structures

Written by: Ir. Andrew Borgart, TUDelft, Netherlands

Abstract Since a decade an increasingly amount of complex geometry structures have been build. These complex structures put engineers and construction companies for sizeable problems when it comes to building an efficient and economic structure. Computational design tools and form finding / optimization methods can assist in rationalizing the engineering and construction process, but they have their limitations which should be taken into account with regards to education and for further research. New structural typologies could help to further rationalize the process, and give opportunities to design complex geometry building with coherent structures. In this article some relevant questions are asked and some possible directions are given.

The last few year’s engineers and construction companies have been struggling to keep up with these developments of designing ever-complex structures and buildings. A way for them to control the complexity is to rationalize the design, engineering and construction process. By using for example computational design tools [2] for fabrication of building parts or for the construction stage a degree of rationalization can be achieved like with the Rolex Learning Center [3]. However, using computational design tools, which can be black boxes, does not always ascertain a certain degree of understanding the complexities of such processes although being useful or even essential for their success. For designing efficient and economic complex geometry buildings in

1. Introduction Architects are increasingly designing buildings with complex geometries, which in most cases require subsequent complex structures. These can pose quite a challenge for engineers and construction companies [1].

Figure 1. Rolex Learning Center EPFL [3]

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the future, it would be desirable if not a necessity to get a better understanding of the processes involved.

This could be useful for example to rationalise further the fabrication and construction process, or to get more grip on the degree of complexities, such as managing the 3D computational model of the building, involved in the design process. The research involved to achieve this can pose new challenges for the field of structural design.

Some questions and problem statements including some possible directions concerning complex geometry structures discussed in this paper will be:

Do we need computational design tools, black boxes or a greater understanding?

Do form finding and optimization methods result in a required result and constructable design?

Do complex geometry structures need new structural typologies?

Andrew Borgart was born in 1966 and studied architecture and civil engineering at Delft University of Technology, completing his studies in 1997. Since then he has been working as an assistant professor of structural mechanics at the Faculty of Architecture of Delft University of Technology and also lectures at the Faculty of Civil Engineering. He teaches several courses in structural mechanics and special structures as part of the Master’s degree programmes for Building Technology, Architectural Engineering and Building Engineering. Borgart conducts research in the field of structural morphology of complex geometric structures, especially into the relationship between form and force of shell and membrane structures. Borgart is currently a member of the IASS Executive Council. He is chairman of IASS Working Group 15 on Structural Morphology and is also a member of the Editorial Committee of the Journal of the IASS.

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2. Do we need computational design tools, black bloxes or a greater understanding?

One of the ways of dealing with structural complexity in the design stage is to use computational tools.

These usually are tailor made and developed in a short time during the engineering stage for solving a specific problem cornering a complex part of the structure, being for example the geometry or construction method. A much-published example is the grid relaxation tool developed by Chris Williams for the roof of the inner court of the British Museum [4]. Because of the specific nature of these individual computational design tools, a generic tool that is suitable for solving all problems is virtually impossible, if it is indeed desired. Other computational tools such as finite element programmes are very useful for calculating complex geometry structures, but are in most cases black boxes which results do not always give the required insight into the structural behaviour.

Engineer and scientist Heinz Isler build many shell structures over the years. Isler exclusively used physical experiments for investigating their structural behaviour and as a form finding method [5]. One of the experiments of Isler is hanging models in which gravity forms a cloth into a near prefect funicular form for shells that are predominate in compression.

Isler also developed an efficient construction method to build his shells economically. Researchers [6] have simulated Isler’s physical experiments by using computational form finding methods based on the principle of using gravity to form a cloth into a funicular shape. It is even possible to incorporate the effect of the cloth materials texture in the computational form finding process. Isler’s shells are successful in structural behaviour, economics and beauty because the constructability fits his form finding process.

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Since the arrival of 3D computer programmes architects have been using these to explore designing irregular curved surfaces. Most of the developed classical shell theories fail to provide analytical solutions for these and thus these complex structures are calculated numerically. A disadvantage of this is that the parametric relations which are enclosed in analytical solutions are lost, making the relationship between the internal forces and stresses and the geometry of the shape less insightful. For the designer this lack of insight makes designing these irregular shaped shells even more difficult. Moreover, these irregular shaped shells are not always real shells in the sense that the loads are conveyed to the support by internal membrane forces, but act as curved structures under bending. An example of this is the Rolex Learning Center. Numeric form finding methods can be used to design these kind of structures, but in many cases this will be an academic exercise if the fabrication of the structure is not been taken into account for the simple reason that the form fined result can not be build. The result is an unusable design tool, which is the reason they are not widely used in practice at current. The possible solution would be to incorporate the fabrication aspects (production and assemblage) as variables or constraints into the form finding process (design tool). This could be achieved for example by introducing geometric mathematical descriptions of the production techniques along with the traditional form finding parameters such as loads and material in the form-finding tool.

Simple design tools such as analytical and physical models like graphical statics and hanging models can help with the conceptual design. Nevertheless, what should be understood is that the results of a hanging model or thrust line of an arch represents just one loading condition, usually only self-weight is analysed.

However, other load conditions like wind will give

different solutions. Thus by incorrect interpretation, a false sense of understanding of the true nature of the problem will lead to inadequate structures. The better a problem is understood the higher the chance of a successful design, Isler’s work is a good example of this. Analytical or semi-analytical methods (global relationship between the different parameters), such as the “rain flow analysis” [7] or graphical statics can give an approximated but quantitative insight.

Figure 2. Physical and numeric hanging cloth models [6]

Virtual models also can be used for designing or testing structures, finite element (FEM) programmes are suitable for this aim. However, finite element methods are also in most cases black boxes, and using FEM in cases for testing complex structures does not always provide the sufficient amount of insight into the structural behaviour. Using physical and virtual (FEM) models along side, each other can have a beneficiary effect the degree of understanding the structures behaviour. This way of investigating structures would also be a task for education and research.

3. Do form finding and optimization methods result in a requiered result and constructbale design?

Figure 3. (left) Thrust line of hanging model with different loads: top self-weight, bottom wind (red line) and showing difference with funicular line (self-weight) Figure 4. (right) Wall optimized with extended ESO method [8]

In the last few years a number of computational methods have been developed for structural optimization, such as methods for structural shape optimization or for topology optimization like evolutionary structural optimization methods (ESO / Extended ESO) etc [8].

Optimization in this context meaning a process, or methodology of making something (as a design, system, or decision) as fully perfect, functional, or effective as possible. This could mean for example for a load bearing structure a minimum amount 13

of material to carry its loads, such as the Michell structures.

Most current day computational methods for form finding or structural optimization in building engineering do not take into account the production and assemblage of the structure, and thus result mostly in academic solutions that are difficult to build. By developing computational methods for optimization that includes for example geometric information as a result of production constraints of structures usable results could be obtained. A way to achieve this is by describing production methods mathematically as geometric variables and constraints to be used in the numerical optimization process. The big advantage of this method would be that the optimized shape satisfies the constraints of the required production and/or assembly method and will result in cost effective structural systems for the realization of complex geometry structures but without limiting the freedom of form generation.

Evolutionary optimization tools create in most cases endless nearly similar results, which fit the optimisation criteria; they produce a design space of possible solutions to explore. An optimization process is sometimes very useful to solve complex design problems with numerous variables, for instance to optimize a complex geometry structure concerning production. A promising example of this is the production optimization by Buro Happold of the roof of the Bergen Art College designed by Snohetta Architects [9]. The aim here was to maximize the number of repetitive panels and allow for the maximum amount of quadrilateral elements.

A parametric model was used to describe the geometry of the roof in which a used tessellation technique depended on the curvature of the roof.

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First, a rectangular tessellation was used to generate the geometry of the roof and because the curvature of the roof was related to the tessellation (rectangular panels); this relation was used to check the warping angle of the rectangular panels. If this exceeded a certain specified value, a diagonal was added, thus creating two triangular panels. The different tessellation options where also tested concerning the stability of the roof.

However, evolutionary optimization tools also have their limitations. There are questions concerning the desired control a designer could have over the outcome of the process and whether it gives a sufficient amount of qualitative insight although they do provide a means of design exploration. The resulting design space of an optimization process can meet all the prerequisite requirements (including constructability) but does not always have to give a desired design solution with respect to functional use or aesthetics.

Perhaps optimization tools should give better qualitative insight of the problem to the designer for a more informed design process to be able to make adequate design decisions and should give a more holistic (globally approximate) optimization result better suited for conceptual design purposes.

A recent step and example in this direction is the newly developed holistic form-force approach Thrust Network Analysis [10], which gives the designer a clear understanding of the mechanical behaviour of compression only shells and its design possibilities.

With methods like these a greater understanding is achieved and gives the designer ways to explore for new solutions.

4 Do complex geometry structures need new structural typologies?

Figure 5. Production optimization of roof Bergen Art College [9]

Figure 6. Folded plate structure made out of timber block panels [13]

The existing typologies for building structures [11] have a long history [12] and have their basis in their own specific use of material, fabrication and assemblage method. Examples are steel trusses or concrete frames, which have proven to be successful for many structures over the years. The current questions is however, if the existing typologies are still suitable for constructing the new kind of complex geometry shapes, such as free form design?

The constructability issue of complex geometry structures concerning efficiently and economics has not been solved satisfactory yet, although existing typologies have been used to build these complex geometry structures. This has lead to structures with unsatisfactory solutions [1]. The question therefore is; do we need for building complex shapes effectively to develop new typologies? Can they help to further rationalize the building process of complex structures?

Several researchers are developing new typologies and fabrication methods by combining different technologies (technology transfer). They go beyond the traditional typologies for building structures in order to find new typologies which are better suited for the design and construction of complex geometry structures. Three different examples as proposed directions will be briefly discussed here.

A new generation of structures in wood is being developed at the EPFL in Lausanne [13]. This is done in a collaborative approach of architects, engineers, mathematicians and computer scientists. By using the different disciplines innovative typologies are being developed such as a folded plate structures which have been made out of CNC mild timber block panels.

The double curved surfaces where rationalized with 15

CAD software for production reasons. The design and fabrication method is fully automated which gives the possibility to make complicated double curved structures efficiently.

In Eindhoven [14] research is being done on developing different types of membrane moulds for the production of double curved surfaces.

One method is using air inflated membranes as temporarily scaffolding for shaping a stretched wire mesh on which concrete is sprayed, after the concrete has hardened the air inflated membranes are no longer needed and are removed. With this relatively simple method complex concrete shells can be made.

Researches of EMPA in Zurich are developing a new structural concept using an air inflated membrane and compression bars and tension cables of steel [15].

The air inflated membrane is used to give a sufficient stiff elastic foundation for the compression bar not to buckle. The result is ultra lightweight structures which can carry high loads. There are many more examples of researchers searching for new typologies and they do not all work along the same lines and principles but use a wide variety of technologies and methods. This is one of the main characteristics of current search for new principles.

5. Conclusions and forsight

[16], materials sciences, process technologies, biology etc. can provide solutions. Further examples are the study of origami from which principles can be derived for new developments of folded plate structures or studying biomimicry and extracting from natural principles sustainably solutions for production and energy use etc. Because of the extend of the nature of complex geometry structures and the possible technologies and disciplines which are available more than one solution or strategy is possible, as is being shown by the wide variety of different solutions researchers are coming up with. For complex geometry structures the future is wide open.

References [1] Borgart, A., and Kocaturk, T., Free From Design as the Digital “Zeitgeist”, Journal of the International Association for Shell And Spatial Structures: J. IASS, Vol. 48, No. 4, 2007, pp. 3-9.

[2] Coenders, J.L., and Bosia, D., Computational tools for design and engineering of complex geometrical structures: embedded design intelligence in systems for the early phases of design , The architecture co-laboratory: game, set and match II on computer games, advanced geometries and digital technologies, Oosterhuis, K., and Feireiss, L. (Eds.), Episode publishers, Rotterdam, 2006, pp. 271-279.

[3] Weilandt, A., Grohmann, M., Bollinger, K., and Wagner, M., Rolex Learning Center in Lausanne: From conceptual design to execution, Evolution and Trend is Design, Analysis and Construction of Shell and Spatial Strucutres, Domingo, A., and Lázaro, C. (Eds.), Reproval, S.L., 2009, Chapter 2.8., pp. 640-653.

In this article, issues are raised and questions are asked concerning the design, engineering and construction of complex geometry structures, which pose a challenge for the coming years for the science of structural design and engineering.

[4] Williams, C.J.K., The analytical and numerical definition of the geometry of the British Museum Great Court Roof, Mathematics & design, Burry, M., Datta, S., Dawson, A., and Rollo, A. J. (Eds.), Geelong, Victoria, Australia: Deakin University, 2001, pp. 434-440.

It is clear that to address the questions and problems concerning complex geometry structures unorthodox solutions will be needed. A transfer of technologies from a wide range of disciplines, such as mathematics

[6] Ramm, E., and Wall, W. A., Shell Structures – A Sensitive Interrelation between Physics and Numerics, International Journal for Numeric Methods in Engineering, Vol. 60, No. 1, 2004, pp. 381-427.

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[5] Chilton, J., Heinz Isler (Engineer’s Contribution to Architecture), Thomas Telford Ltd, 2000.

[7] Borgart, A., Leuw, de M., and Hoogenboom, P., The relationship of form and force in (irregular) curved surfaces, Proceedings

of the 5th International Conference on Computation of Shell and Spatial Structures: IASS/IACM 2005 Salzburg, Ramm, E., Wall, W.A., Bletzinger, K.-U., and Bischoff, M. (Eds.), 2005.

[8] Cui, C., Ohmori, H., and Sasaki, M., Computational Morphogenesis of 3D Structures by Extended ESO Methods, Journal of the International Association for Shell And Spatial Structures: J. IASS, Vol. 44, No. 1, 2003, pp. 51-61.

[9] El-Ali, J., The use of parametric design as a tool for managing complex shaped buildings, The International Colloquium of Free Form Design FFD, Delft 2006.

[10] Block, P., and Ochsendorf, J., Thrust Network Analysis: A New Methodology of Three-Dimensional Equilibrium, Journal of the International Association for Shell And Spatial Structures: J. IASS, Vol. 48, No. 3, 2007, pp. 167-173.

[11]

Engel, H., Structure Systems, Hatje Cantz, 2007.

[12] Kurrer, K.-E., The History of the Theory of Structures: From Arch Analysis to Computational Mechanics, Wiley-VCH, 2008.

[13] Weinand, Y., Innovative Timber Constructions, Journal of the International Association for Shell And Spatial Structures: J. IASS, Vol. 50, No. 2, 2009, pp. 111-120.

[14] Pronk, M., Van Rooy, I., and Schinkel, P., Double-curved surface using a membrane mould, Evolution and Trend is Design, Analysis and Construction of Shell and Spatial Strucutres, Domingo, A., and Lรกzaro, C. (Eds.), Reproval, S.L., 2009, Chapter 2.8., pp. 618-628.

[15] Luchsinger, R.H., et al., The new structural concept Tensairity: Basic principles, Proceedings of the Second International Conference on Structural Engineering, Mechanics and Computation, Zingoni, A. (Eds.), Balkema/Swets Zeitlinger, 2004.

[16] Pottmann, H., Asperl, A., and Kilian, A., Architectural Geometry, Bentley Institute Press, 2007.

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Shaping better civil structures

Written by: Prof. Sigrid Adriaenssens, Form Finding Lab, Princeton University, USA

Introduction: Improving the quality of urban life By 2050, seventy percent of the world’s population will live in cities. Fifty percent of the world’s population currently lives in an urban environment and produces more than seventy-five percent of all C02 emissions. Finding intelligent and efficient ways to provide more people with fewer resources will make cities more resilient to manmade and natural disasters and reduce their impact on the environment.

The long-term research goal of my research group, the Form Finding Lab at Princeton University, USA, is to transform the engineering design framework for a future-oriented built urban environment.

Our research addresses the following core questions: What is the relationship between form and efficiency in civil structures?; and With increasing emphasis on the preservation of natural resources, how can design theories and tools match untested sculptural ideas to the construction of feasible and materialefficient structures?

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Dialectic Form Contemporary designers of curved structures seem to be guided by only one of the following design drivers: (i) analytical geometry, (ii) sculptural aesthetics, or (iii) structural efficiency. The behavior of shape-resistant structures depends mostly on their global spatial configuration (e.g. shells), and less on the properties of their individual components (as in the case of frames). Analytical geometry is a tool that has been used since antiquity for the generation of architectural shapes. These forms, found in the Pantheon’s spherical dome (Rome, 126 AD) or Felix Candela’s hyperbolic paraboloid shells (Mexico, 1950-1997), are limited by the rules imposed by analytical geometry and the designer’s imagination. With recent geometrical modeling tools, such as Rhino and CATIA, more designers base their free- form ideas on aesthetic considerations to achieve dramatic results. This design approach expresses sculptural intentions, as experienced in Gehry’s Bilbao Guggenheim Museum (Bilbao, 1997) but is disconnected from any intent aimed at structural efficiency. This design methodology needs a good team of engineers and contractors to make the sculptural form stand up, supported on an

add-on uneconomic structure. The complex curved surface design challenge lies in determining the ‘right’ structural shape that will resist loads within its surface without the need for extra structural systems.

Our research entertains a dialogue between structural curved form and other non-structural design drivers, an approach we refer to as “dialectic” form-finding.

The word “dialectic” stems from Ancient Greek and refers to a method of argument for resolving disagreement. In the context of our research, it stands for the resolution/integration of competing (and sometimes conflicting) design drivers through a rational engineering approach. Typical design drivers for urban infrastructure are cost, technical quality (structural, environmental, and construction efficiency), urban planning (context-sensitivity) and architectural design. Our research focuses on dialectic forms driven by structure and environment, structure and construction, and structure and material. In this article we focus on forms driven by environmental and structural considerations and demonstrate how designers can create structurally efficient forms that use minimal natural resources, and maximize occupant comfort by guiding the flows of sun, wind, and light.

Sigrid Adriaenssens, PhD, is a structural engineer specializing in the form finding of structural surfaces. She is an Assistant Professor at the Department of Civil and Environmental Engineering at Princeton University, USA, where she directs the Form Finding Lab. Adriaenssens holds a PhD in lightweight structures from the University of Bath, UK, and worked as a project engineer for Jane Wernick Associates, London,UK and Ney + Partners, Brussels, Belgium . She is the first author of “Shaping Forces: Laurent Ney” (A+ Editions (CIAUD-ICASD), 2010) and “Shells for Architecture:FormFinding and Structural Optimization” (Taylor and Francis, 2014).

More information about Sigrid Adrieanssens and her work at Princeton University can be found at http://formfindinglab. princeton.edu/

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Modern Dialectic Building Forms The folded hyperbolic paraboloid (hypar) shells of the Miami Marine Stadium (Miami, 1963), shown in Figure 1, clearly showcase that structural and environmental issues can be drivers for form-generation instead of being constraints. The form of the folded hypar concrete shells imbues the grandstand roof with structural efficiency. This efficiency is exemplified by small deflections and stresses (even under hurricane wind loads, typical for the Carribean Region) (see Figure 2). Additionally the shell roof design attains environmental efficiency and maximizes spectator’s comfort in a warm and tropical climate. The hypar shapes and their orientation, parallel to the prevalent South-East ocean driven winds, provide effective shading and temperature control as shown in Figure 3.

Figure 1: The Miami Marine Shells (1963), modern reinforced concrete folded hypar shells. (Image courtesy of Friends of the Miami Marine Stadium)

In the transverse direction, the roof acts as a folded plate.

In the longitudinal direction, the roof acts as a cantilever

Figure 2: Analysis of the internal loadings and deflections hints at a structurally efficient system.

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Figure 3: The shading analysis shows that 80% of the time the grandstand is shaded, which prevents sun glare and heat gain from direct solar radiation.

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Site-specific sun shades for the prevention of skin cancer.

Annually, 1.3 million Americans are diagnosed with skin cancer, currently representing more than 50% of all cancers in the USA. Childhood exposure to the sun’s ultraviolet (UV) light increases the risk for skin cancer as an adult substantially. Starting positive sun protection early is therefore key to reducing the incidence of this disease. Natural shade provided by trees does not offer adequate UV protection. Available sun shades are mostly driven by aesthetic appeal and “one design fits all” uniformity and do not necessarily shade the intended area (see figure 4). The protective ability of a shade depends on its orientation in relation to the seasonal and hourly incidence angle of the sun. This site- and time dependency is ignored in commercially available shades. We are developing and testing the digital design to manufacturing workflow for a novel type of sun shell that efficiently shades and passively cools outdoor areas using location specificity. This grid shell of angled louver beams are environmentally and structurally optimized for each specific geographic location (Figure 5 & 6).

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Figure 4: (left) Commercially available sun shades do not necessarily shade the target area.

Figure 5: A scale model of the louvred grid shell shows the concept of shading a courtyard with an open grid shell system (left & right).

Figure 6: medium scale prototype: UV sensors below the shell validate our shading algorithms.

Design tools and theories The construction industry is one of the most resourceintensive sectors. In recent years, research in the field of the design of sustainable structures has mainly focused on quantifying the environmental impact and life cycle cost of existing structures. A life cycle assessment approach quantifies the environmental effect of a design once the design is completed.

Unfortunately, little attention has been paid to developing structural design methodologies and tools that advocate sustainable design through minimal use of materials. Traditional structural design is aimed at well-defined codes that guarantee structural strength and serviceability. These codes, however, set no specific requirements regarding the structure’s environmental impact. Due to the challenge of building more economically and sustainably, structures should be conceptualized with material and current available fabrication techniques in mind. The advent of digital modeling, optimization, form-finding and manufacturing technologies have given designers a new toolbox.

Figure 7: Structural and CO2 impact comparison for the Beijing National Stadium and the RSCA Stadium.

Form-finding of shape-resistant structures Form-finding is the process of generating shapes that are in static equilibrium for a pre-defined set of boundary conditions which include internal and external loading, support conditions, element and material properties. A comparison of two similarlooking lattice roofs, the Beijing National Stadium (Bird’s Nest, Herzog and de Meuron, 2008) and the Royal Soccer Club Anderlecht roof (for Ney and Partners, 2008) – a structure for which we performed the form-finding – reveals steel quantities and associated C02 emissions of 430kg/m2 versus 130kg/m2 and 745kgCO2/m2 versus 225kgC02/m2 respectively (shown in Figure 7). This comparison clearly shows that form-finding techniques have the potential to generate structurally stable shapes that are financially and environmentally economic.

The development of numerical form-finding algorithms and tools builds on my Ph.D. research that derived beam algorithms for a form-finding technique based on dynamic relaxation. These beam and other newly developed co-planar algorithms made the design and construction of the steel and glass grid shell over the Dutch Maritime Museum possible (Ney and Partners, Amsterdam, 2011), and it has been praised for its slenderness.

In the late 17th century, the historic stone building that now houses the Dutch Maritime Museum, was an instrument and symbol of Dutch maritime power (see Figure 8). The development of the Dutch seafaring nation was closely linked to the production of sea charts and the associated sciences (particularly geometry, topography and astronomy). This building, a former warehouse, used geometry as a basis for its design and seemed particularly suitable for a museum 23

in 1970. At the beginning of the 21st century, the building no longer met the needs of a museum. As a result, a design competition was held to cover the courtyard, as a reception area, with a translucent roof. The design brief stipulated that the new design should not damage the historic building and that any addition or change to the building’s heritage should be reversible. Laurent Ney chose the initial two-dimensional geometry for the steel/glass roof in order to tell the visitor a story about the building’s history and its close relationship to the history of the sea. At the origin of this 2D geometry lies a loxidrome map with 16 wind roses, a figure used to mark out the course for ships (see Figure 9). This geometric pattern is found on every sea chart of the 17th century, the time period the museum was built. This pattern forms the basis for the structural mesh of the proposed steel grid shell (see Figure 10). This mesh references the power of the Dutch fleet and reinstates this former admiral building as a symbolic center of the Dutch mastery of the seas. The multi-axisymmetric mesh also reinforces the monumental architecture of the 17th century building. Based on this strong contextual mesh, we used form-finding techniques and facet planarity algorithms to stir the form of the steel/glass grid shell shown in Figure 11. This realized structure has been well received and appreciated by its local community, its users and peer professionals and won the 2012 Amsterdam Architectural Prize as well as the 2012 Dutch and Belgian Steel Award. De Groene Amsterdammer writes about the joy of experiencing the cupola: “Of course, we all envy the museum’s night guard who gazes at the stars through the 1016 pieces of glass that make up the magnificent cupola designed by Laurent Ney. At least when the courtyard is not populated with adults and children, sitting on the floor eating their homemade sandwiches.”

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Hard infrastructure is intended to last generations.

As structural designers it is our professional and civil responsibility to improve the quality of life of the rapidly increasing urban population, to make cities more resilient and to reduce their impact on the natural environment.

Figure 8: The design of Dutch Maritime Museum, a 17th century gunpowder house, expresses the importance of the Dutch seafaring nation and its close link to the production of sea charts and the associated sciences (particularly geometry, topography and astronomy).

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Figure 9 : A geometric pattern, found on 17th century sea charts, lies at the base of the grid shell mesh pattern.

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Figure 10: The pattern of the steel grid shell over the courtyard of the Dutch Maritime Museum

Figure 11: Numerical form finding of the cupola starts from the two dimensional sea chart inspired mesh and develops into a structurally efficient curved shape with facet planarity (image courtesy Ney and Partners)

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Graduating Building Technology An analytical solution to shell structures

Written by: BSc Niels van Dijk, TU Delft, Netherlands

Preface Shells have geometrical and structural properties, which are closely related and together determine the structural performance. What this direct relation is, or how it influences the natural flow of forces through the material, is still unknown. For my graduation thesis I am researching this topic, with Andrew Borgart as first mentor to guide me with the calculations, and Thijs Welman as a second mentor for the computational aspects of the research. In this article I give a problem background and description and indicate the direction of the research I am conducting to solve this mystery.

History and background Throughout history people created and built the most fascinating structures. Mankind developed a good sense for how to construct certain structures, first by trial and error, later by learning how to analyse whether structures would collapse or not. With the development of computer technology more complex building shapes could be modelled, not only in design but also in structural analysis.

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Simple constructions, like beams and columns, are easily calculated. Analytically by hand, or numerically in FEM computer programs. More complex to calculate are plates and beam networks, but it is still possible to do this by hand. For shell structures, it is nearly impossible to make analytical calculations by hand, only for a small basic set of shell shapes. For these types of structures Finite Element Methods are needed to gain insight in the stresses and displacements due to certain load cases.

The most efficient way of transferring loads is trough axial (stretching and compression) forces.

A perfect shell uses this efficiency and acts mostly in compression. When architects like Gaudi started designing catenary structures, with mainly compression, an analogy with chains was used. Chains only transfer loads trough stretching forces, inverting the shape of the hanging chain, gives a structure with only compression (Block, DeJong et al. 2006). When it is not possible to build the exact inverse shape of a hanging chain, bending forces are introduced. With bending forces in a material, large deformations can be expected, and bending becomes the most important factor dimensioning your structure.

Figure 2: Gaudi, Sagrada Familia, Barcelona, Spain.

I am Niels van Dijk and started my studies at the faculty of architecture in 2007, right after high school. I started the Building Technology masters in 2011 and currently I am graduating on a combination of structural and computational research, as can be seen in the article. Besides graduating I am working as a student assistant at the chair of Structural Mechanics.

Due to the minimum presence of bending forces, compression structures can be designed with little structural height, compared to ordinary structures.

This slenderness is part of the elegance, and probably the allure, of shell structures. Famous shell builders are architect Felix Candela and engineer Heinz Isler.

Candela designed his shells trough mathematical models, using only basic shapes like hyperbolic paraboloids, making sure he could perform hand calculations on his designs. Isler was more of a mystery man, never revealing his real way of designing. What

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Figure 1: Gaudi Catenary system.

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is known is that he used a lot of physical models to test different shells and shapes to create his final design.

Until present days, there is still no way to get analytical information about freeform shells. If a designer wants to see the structural performance of a shell design, FEM calculations are almost indispensable. The output of the software is numerical, so all relation between geometry and structural performance is lost. In other words, the direct relation between geometrical en structural properties of a shell is unknown.

With the development of computer technology, a great new range of software became available. Parametric tools like Grasshopper are used by designers to make parametric relations in 3D modelling software, giving more flexibility in designing complex shapes.

In my thesis the power of this software will be used to analyse geometrical properties of shells and give

insight in the relations between geometry, flow of forces and other structural properties. Analytical relations and theories will be employed to find these mysteries of shell structures.

First analytical scheme Different professors and researchers describe analytical methods of calculating shell structures with the use of analogies to plate calculations and membrane calculations. One of them is Prof. C.R. Calladine. In his static-geometric analogy he describes a set of differential equations to calculated the forces in a shell with loading (p).

A benefit of shell structures is the fact that shells can carry loads by a combination of bending and stretching actions. The downside to this property is the analysis of the structure. The applied load is divided over the structure trough bending and stretching. To simplify

Figure 4: F. Candela, Los Manantiales, Xochimilco, Mexico.

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this problem, a split can be made in an elementary piece of shell to two distinct surfaces, one surface to take the bending actions (B-surface), and one surface to take the stretching actions (S-surface).

This theory only holds if an appropriate distribution of loads is introduced over the two surfaces, pS and pB for stretching and bending. The stretching surface can be seen as a shell analysed with the membrane hypothesis. The bending surface is closely related to a flat plate (Calladine 1977, Calladine 1983).

to make sure both surfaces still fit the original combined surface. The values of pS and gS and the values of pB and gB are related trough the before mentioned differential equations. With this relation a computational scheme is designed by Pavlovic, one of Calladines former students. The trick of this analogy is the ratio or distribution between the pS and the pB, so the ratio between the stretching and bending actions in the material.

With the split of the initial surface element, the equilibrium equations also split. In a surface with only stretching, there is only normal forces (NX, NY, NXY) and can be compared to an (inflated) membrane.

In the B-surface there is shear forces (QX, QY) and bending moments (MX, MY, MXY). This surface is harder to imagine, but it is closely related to analysing a plate structure. Plates act mainly in bending and shear actions. The resulting surfaces and forces can be seen in figure 1

Now this computational solution does not make the analysis any easier. In the past few years, different graduate students started with untangling these different steps in finding and computing these calculations with the use of more analogies and theories. Different tools are already developed in their theses that show the constructive properties of different geometries.

Continuation analytical scheme

This conceptual split is only possible if two requirements are met. In figure xxx the applied load is indicated with , and is divided over the S and B-surface. So the first requirement is p=pS+pB to ensure a valid force distribution.

(1)

The second requirement is found in the shape of the shell. Since the split is only conceptual, the two separate surfaces should still keep the same geometry. The geometry is defined by the Gaussian curvature (k) and the change in curvature (g). Both surfaces have their own equations for (g) thus giving a (gS,gB). Since these should coincide

gS = gB

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(2)

Figure 5: Split Caladine.

Figure 6: Computing Model

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D. Liang and M. Oosterhuis developed two GrassHopper tools that can perform the calculations as shown above on plate structures. One tool for the bending surface, and one tool for the stretching surface. The next step is to find the distribution of p as shown in formula (1).

One can imagine a perfect inverted chain, acting solely in stretching, and one can imagine a plate, acting mostly in bending. The ratio of stretching/bending is directly related to the geometry of the shell, the more the shell approaches a parabolic shape, the less bending occurs. The last step, and the focus of my research, is to find a quick and accurate way to determine the ratio of stretching/bending in a shell.

Figure 3: H. Isler, Deitingen Service Station, Solothurn, Switzerland

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Final analytical scheme To achieve this goal I am currently researching different theories and testing several hypotheses in software like Rhino, GrassHopper, Diana, GSA and Excel. First step is to solve this distribution in 1D structures like beams and arches with a distributed loading and next in own weight. When this is solved the step to 2D structures like plates and shells can be made. First I start with simple shapes, but the aim is to get a general solution, applicable on all shapes.

The ideal end result would be a GrassHopper script which can be used by a designer or engineer to get quick insights in the structural performances of the shell he or she is working on, just by using the surface as an input for the script. .

References Block, P., et al. (2006). “As hangs the flexible line: equilibrium of masonry arches.” Nexus network journal 8(2).

Calladine, C. R. (1977). “The static-geometric analogy in the equations of thin shell structures.” Mathematical proceedings of the Cambridge Philosophical Society 82.

Calladine, C. R. (1983). Theory of shell structures. Cambridge, Cambridge University Press.

Liang, D. (2012). A parametric structural design tool (Grasshopper interface) for plate structures. Delft.

Oosterhuis, M. (2012). A parametric structural design tool for plate structures. Delft.

Pavlovic, M. N. (1984). “A statically determinate truss model for thin shells: two-surface analysis (bending theory).” International journal for numerical methods in engineering 20.

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A doubly curved steel and glass dome for the historic Maritime Museum Amsterdam Written by: Ir. Laurent Ney, NEY+Partners, Belgium

1 The museum Het Scheepvaartmuseum in Amsterdam is known for its maritime collection, being the second largest in the world. The museum’s mission to increase and spread the knowledge of this heritage is achieved by expositions on the one hand, and academic research on the other.

Het Scheepvaartmuseum is housed in ‘s Lands Zeemagazijn (the Arsenal) in Amsterdam. In 1656, during the Golden Age, Daniel Stalpaert designed the building as a warehouse for the Admiralty of Amsterdam. At that moment Amsterdam was the largest port and market place in the world.

Today ‘s Lands Zeemagazijn is an impressive historic building that has managed to survive over 3 centuries.

It does not longer functions as a warehouse for the Port of Amsterdam, and since 1973 the building functions as a museum and archive of maritime history. [1] Although nowadays a museum, the building was never intended to be a museum. The long and rather narrow spaces around an inner courtyard, without climate control are below standards for a 21st century museum. At the end of the 20th century it was clear 34

that the building was no longer capable to host all interested visitors.

2 Design brief The specific question in the 2004 design brief to cover the inner courtyard was: “The central question is whether technique is capable to bridge the wishes of the museum as user of the building on the one hand, and the wish to preserve the historic monument’s values. In other words, is it possible to create a roof for the courtyard and limit the technical, physical and chemical effects on the historic monument such that the roof does not ‘damage’ the building? Damage needs to be considered as a degradation of the quality of the monument. Besides architectural aspects, the design is about constructive and climatological aspects of a new roof.” The re-design of the building itself was in hands of Liesbeth Van der Pol from DOK Architecten, Amsterdam.

3 Design concept - 3.1 Design philosophy One cannot design without a design philosophy, which is the invisible part to any design. Shaping forces [2] is a description that best expresses NEY & Partner’s design philosophy. An expression of the research that

is crucial to our review of engineering: finding the exact form, the precise geometry that integrates the boundary conditions and materials of a project into a single synthetic gesture.

Precisely the establishment of the fact that there is such a thing as an optimum form indicates the main conflict between engineering and architecture. We do not see the form of things as a noncommittal figure, but as a structural optimum. Not a spatial spectacular,

Laurent Ney (°1964, Thionville) is a civil structural engineer trained at the Université de Liège, Belgium, and at the Rheinisch-Westfälische Technische Hochschule in Aachen, Germany. From 1987 to 1989 he was a student and research assistant for the MSM department of professor Cescotto in Liège. He was a lecturer on Construction stability from 1995 to 2001 at the Institut Supérieur d’Architecture Lambert Lombard in Liège. Since 2005 he is a lecturer at the Université Libre de Bruxelles. From 1989 to 1996 he worked as an engineer at Bureau d’études Greisch in Liège. In 1998 he founded the engineering firm Ney & Partners in Brussels and Luxemburg.

In 2012 Ney & Partners opens a branch in Tokyo, Japan.

Figure 1: ‘s Lands Zeemagazijn, photo ca 1910-1935 (Steenbergh collection)

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but the far-reaching integration and coherence of structure and architecture in a specific context.

3.2 A glass dome The point of departure is to design a glass dome that rests lightly on a precious building. Also, the new roof should not be higher than the adjacent roofs. This is, again, a matter of respect towards the 17th century building.

The combination of both design intentions result in a dome with a maximal height of approximately 5m for a span of 47,94m (in diagonal). This proportion of L/10 is relatively flat.

Considering the shape of the building, and the intention to design with visual tranquility in mind, we set as a boundary condition that the doubly curved dome should rest on 4 straight lines, each parallel to and just above the historical gutter.

Figure 2: maritime map serves as basis for structural design

3.3 Genius loci Each site is unique. Once one realizes this simple fact, it is clear that the design process begins during a site visit. In this case the site is a building, but also an era, the past and future of a nation.

During the Admiralties the building was the center of a nation ruling the world. This building was the center of the world at one point in time. This symbolism of centrality can be found in the symmetrical architecture of the building. Its four facades refer to the four cardinal directions, and the Netherlands reign over the world.

In the 20th century the building became a depot for maritime objects. Historical nautical maps form an important aspect of the collection. The new roof 36

Figure 3: conversion of a 2D pattern to a 3D tension only structure

continues this maritime symbolism through the use of a maritime map as basis for the structure, this way the new roof becomes a guide through the rich maritime history of the Netherlands.

Compasses on maritime maps are often divided in 32 parts. As a figure, they form the basis for loxodrome maps, and were used to sail towards a destination in a ‘straight line’. The radial repetition of the compass on a Mercator map results in the line pattern as shown in figure 2.

4 Structural design Figure 5: integration of LED spots at each intersection in cylindrical hollow section

The new roof rests on the historical brick walls.

In order to arrive at a solution that requires no reinforcing of these walls, the roof rests lightly on the wall, transferring mainly vertical forces. All horizontal reaction forces are brought in equilibrium in the new roof structure itself. This is achieved by a form finding, using the method of dynamic relaxation.

4.1 Form finding A maritime map is a two-dimensional representation of a sphere. In the same sense, the loxodrome map is to be re-transformed into a dome shaped glass roof.

Traditionally form finding is based upon the hanging chain principles: “as hangs the flexible line, so but inverted will stand the rigid arch”. This principle was first noted by Robert Hooke in 1675. In order to find the optimal form for this grid shell, dynamic relaxation was used. This takes into account both elastic and bending stiffness. [3]

Figure 4: combination of 23 folding mechanisms

A priori this method renders a solution that has an optimal shape, where optimal is defined in terms of light weight. However the fact that many of the faces have more than 3 edges, this method does not take 37

planarity of these faces as a criterion for optimization.

A second method, using origami principles, was therefore applied.

4.2 Folding mechanism In 2006 Chris Williams, from Bath University UK, created a folding mechanism based on 23 independent folding mechanisms in order to obtain the loxodrome lines on a doubly curved dome consisting of planar shapes having 3 to 6 edges.

4.3 Calculation setup IThe entire roof has been 3D modeled in SAMCEFFIELD. Thus, the exact geometry (after the folding mechanism conversion) and precise dimensions of each element are taken into account for the steel code check. Also the glass panels are modeled as elastic plates to arrive at a realistic load distribution.

Figure 7: aerial view of the finished dome in 2011(image: BRS Building Systems)

Using the exact sections, mostly 40mm thick S355 steel, taking into account the varying stiffness, implies that the steel code check is an iterative process.

The steel code check itself is performed based on Eurocode steel code checks.

5 Conclusion Covering an inner courtyard is a challenge looked at for many old buildings. In the case of Het Scheepvaartmuseum it allows to drastically alter the way the building is used. By changing the inner courtyard into the central point of the building and its experience, many questions are raised. How to relate a modern, lightweight, transparent structure with the laden history and appearance of an architectural monument?

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Figure 6: finished glass dome

The steel and glass dome was conceived as a conceptual extension of the museum’s maritime archive. At the same time, these structural lines, derived from maritime maps, provided with a structurally sound concept. Although visually subordinate, the soundness of the structural concept is the foundation for the feasibility of a structure in a historic context.

The detailing of the roof is based on respect for the national monument, mainly by the reversible nature of the glass roof construction, and based on the clear view of the scenographic potential of this central object, mainly by designing an extremely slender structure based on a loxodrome map. As such, by integrating the past of the site into the future of the museum, the design has managed to satisfy the demands of two, usually opposing, parties.

5 References [1] https://www.hetscheepvaartmuseum.nl/location/monument, last accessed on November 2nd, 2012 [2] ADRIAENSSENS S., DE VOLDERE S., NEY, L., OCHSENDORF J., and STRAUWEN I, (2010).”Laurent Ney: Shaping Forces”. A+ Editions (CIAUD-ICASD) [3] ADRIAENSSENS, S., NEY, L., BODARWE, E., and WILLIAMS, C. (2012). “Finding the Form of an Irregular Meshed Steel and Glass Shell Based on Construction Constraints.” J. Archit. Eng., 18(3), 206–213.

[4] WILLIAMS, C, “Netherlands Maritime Museum – Roof Folding”, Report, September 10th 2006

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Shaping building surfaces Inspired by Renzo Piano

Written by: Roel Schipper, TU Delft, Faculty of Civil Engineering and Geosciences It was in October 1969, only one year after my first birthday, that a remarkable series of lectures took place in Delft. Structural Engineering professor Jaap Oosterhoff had invited a number of esteemed foreign guests to lecture concerning the intriguing theme “Plastics in load-bearing structures”. You should know that, at that time, plastics were the booming material, promising to solve many problems in the world1.

The lecturers were pioneers and authorities on the developments of spatial structures, such as professor Frei Otto and ir. Piet Huybers, some material experts in the field of plastics, such as professor Makowsky and Dr. Niederstadt, and a rather unknown Italian architect and researcher, dottore Renzo Piano.

Renzo Piano, having his own studio and at the same time working at the Polytechnic University of Milan, in the years between ’64 and ’69 had designed, manufactured and constructed a number of amazing light-weight spatial structures in plastic, using various innovative tech- niques that, at that time, were unseen elsewhere. The innovations concerned at least four aspects of his work: the remarkably freely formed shapes of his designs 40

the used building materials, such as fibre glass(a glass-fibre reinforced matrix of poly ester), polyethylene and polyurethane foam the structural models, using square-based pyramidal elements, barrel vaults, tensioned grid membranes and pneumatic structures the shaping and manufacturing techniques, such as vacuum pulling, casting, glueing and melting.

From the lectures described in the reader Oosterhoff [1969], one article specifically intrigued me: it is a reprint of a publication in the Italian architecture journal Casabella with the title “Experimental project of shell structures” Piano [1969]. It contains the quite detailed description of a manufacturing method for plastic 3D elements to use in free-form pavilions, such as the one shown in Fig. 1. Visible is an example of a 4 meter high, 17 meter long pavilion, consisting of three connected domes. Realizing that this shape would challenge the available manufacturing techniques, Piano also developed himself an innovative machine, which he named “stampo deformabile” or “deformable mould”, shown in Fig. 2. This machine was able to read from a scaled model of a free-form building (shown

Figure 1: Morphological study for a pavilion in glass-fibre reinforced plastic, R. Piano [1969]

Figure 2: Pavilion made out of triangular double-curved plastic panels, source: Piano [1969]

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Figure 3: Stampo Deformabile or “Deformable Mould” from Renzo Piano, source: Piano [1969]

on the left table in Fig. 2) the building height at a grid of x-y-coordinates, and translate this to full-scale panels manufactured in plastic (shown on the right table in Fig. 2), a sort of 3D-printing avant-la-lettre.

By using the manufactured plastic 3D-elements, Piano constructed a number of experimental 42

pavilions, for example the one shown in Fig. 3. The reason that the article was so intriguing, is that the manufacturing of 3D double-curved elements is the central theme of my own PhD research. Before starting with the Phd, I already found the image of Piano’s stampo deforma- bile in publications, but without the complete description and background.

Piano’s work is actually still very much up-to-date: mass-customized production of double-curved free-

Figure 4: Principle of deforming concrete after casting. Source: R. Schippers

form elements is generally regarded only possible after the realization of a flexible mould system: an adjustable formwork consisting of an elastic material that can be formed into any curved surface by the use of pistons, actuators, pin beds or the like Munro and Walczyk [2007]. On this elastic formwork the actual building element can be shaped, either by casting a hardening material such as concrete on the formwork, or by depositing a material that can be softened, such as a sheet of heated thermoplastic or glass. After the building material has taken the form of the formwork and is hardened or solidified, e.g. by hydration or cooling down, the shaped building elements is ready for use. The flexible mould can be reused for another element, possibly with a different shape.

A few years ago, researchers from the Faculty of Architecture Dr. Karel Vollers and ir. Daan Rietbergen developed and patented a flexible mould principle (Vollers and Rietbergen, 2008) Fig. 4. When I got involved in the MSc-thesis work of two students of Dr. Vollers, trying to manufacture double-curved elements in concrete, I decided that the further development of this method would be a perfect PhD-study topic. In the past year a considerable amount of time has been spent on further overthinking and improving Piano’s concept, especially for the building material concrete.

MSc students Peter Eigenraam and Marijn Kok of the Faculty of Civil Engineering and GeoSciences, MSctrack Building Engineering, have been working on the mould system respectively the material properties for this particular way of producing curved concrete elements. Resulting in a gradual improvement and practical realization of the idea in working prototypes.

Figure 5: Prototypes of Dr. Karel Vollers and ir. Daan Rietbergen (top) and Peter Eigenraam, MSc (bottom), Photo: R. Schippers

In the Stevin lab, several experiments have been conducted to find out the right concrete mixture and the accuracy of the shaping method. In Fig. 5 the principle is explained step by step: The flexible materials of 43

the mould are supported by a subsystem controlling the desired final shape (step 1). The mould is filled with self-compacting concrete (SCC) (step 2); fibres or textile can be used as reinforcement. During a short period of structural build-up, the yield strength of concrete increases (step 3). Then the mould is carefully deformed into its final shape (step 4). During this deformation, the fresh concrete has to follow the strain and stay stable under a certain slope. Concrete hardens in the deformed mould (step 5) and finally the element is demoulded (step 6). The flexible mould can be reused to produce more elements, with identical or with altered curvature and geometry.

The test setup and a number of elements are shown in Fig. 6 on the facing page. Visible is a setup of four flexible moulds, supported by flexible lathes (top image). This setup was used to do a parameter study on concrete mixture, curvature and deformation process. In the lower two images in Fig. 6 on the next page a series of (single) curved elements is visible. The process of deforming concrete after casting proved to be a feasible method, leading to accurately shaped panels with sufficient strength in a relatively simple way.

Also internationally, progress has been made in the development of the flexible mould: Adapa, a Danish firm, has built a prototype that also allows manufacturing of curved elements (Raun and Kirkegaard, 2012). The main issue, both in Adapa’s research and mine, appears to be the exact control of the shape of the mould surface. A NURBSsurface drawn in Rhino does not automatically translate to the exact and similar surface in the mould, since the weight of the concrete and the elasticity of the flexible surface lead to various effects that are difficult to understand and predict.

Making laser-scans of the elements (see Fig. 7) has demonstrated that an acceptable accuracy can be 44

reached, but that the congruent joining of the edges of elements requires more attention and thinking.

Perhaps the main reason that the flexible mould did not yet see its massive breakthrough in architecture, might be the fact that understanding and controlling the method requires a mix of various fields of expertise.

These are often not found in one person: knowledge of machine building, free-form architecture, complex geometry, computer scripting and concrete, plus the skills to sell the idea to parties that might be able to fund further research and developments. Maybe an -until now- rather unknown Dutch architecture student and researcher could fulfill this role?

References Chris Munro and Daniel Walczyk. Reconfigurable pin-type tooling: A survey of prior art and reduction to practice. Journal of Manufacturing Science and Engineering, 129(3):551–565, January 2007. ISSN 10871357. URL http://dx.doi.org/10.1115/1.2714577.

J. Oosterhoff, editor. Kunststoffen in dragende konstrukties - een verzameling tijdschriftartikelen, gebundeld ten behoeve van de leergang “kunststoffen in dragende konstrukties” op 17 en 17 oktober 1969 te delft, 1969. Stichting Post-Doktoraal Onderwijs in het Bouwen.

Renzo Piano. Progettazione sperimentale per strutture a guscio experimental project of shell structures. Casabella, 335:38–49, april 1969.

C. Raun and P.H. Kirkegaard. Reconfigurable double-curved mould. In J. Orr, M. Evernden, A. Darby, and T. Ibell, editors, Proceedings of the Second International Conference on Flex- ible Formwork, ICFF, pages 292–299. CICM and University of Bath, Dept. of Architecture and Civil Engineering, 2012.

K.J. Vollers and D. Rietbergen. A method and apparatus for forming a double-curved panel from a flat panel, 2008.

Figure 6: Test-setup and a number of precast concrete elements.

Photo: R. Schippers

Figure 7: Double-curved panel cast (top) and laser-scanned (below).

Source: R. Schippers

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Old School, New Style Form finding using hanging cloth and particle-spring method

Written by: MSc Peter Eigenraam, TUDelft, Netherlands

Preface At the first congress of the International Association for Shell Structures (IASS) Heinz Isler showed that an unlimited amount of shapes could be derived from a hanging cloth [Isler, 1960]. His method has proved to result in visually pleasing and structural efficient structures. Being introduced in a time when the computer was making its entrance, it comes as no surprise that this method takes a lot of manual work. Now, more than fifty years later, it is possible to apply this method using the modern possibilities and advantages of parametric modeling.

I have posted a short of movie this application and url-link can be found in the Bibliography. Hopefully this will inspire and challenge you to explore possibilities for the design of future projects.

shape of the cloth will change when the position of the supports is modified. When asking only little of your imagination it is easy to see that an unlimited amount of shapes can be derived from this method. However to obtain a model of this structure the shape should be fixed, for example by applying gypsum. When the gypsum is hardened the shape can be turned upside down, forming for example a roof structure or canopy like in Figure 3.

Also other materials could be used which result in different shapes. Isler also used rubber membranes.

Hanging cloth method The hanging cloth method involves a piece of cloth of any shape that is supported at a number of points.

Due to its own weight the cloth is forced to obtain a shape between the supports. A setup for this method can be found in Figure 2. The shape can be changed infuenced by changing the supports. The 46

Figure 1. Figure 1 Model of a double curved structure after using the hanging cloth form finding method introduced by Heinz Isler.

Hanging cloth analogy Using the above described method an unlimited amount of shape can be derived. However this is a very laborious job. It would be advantages if similar experiments could be simulated within a short time. Thanks to modern parametric modeling it is possible to obtain similar looking results. Here an add-on for Rhinoceros and Grasshopper was used called Kangaroo. This is a Live Physics engine that can be used for simulation and form finding [Piker, 2013]. It makes use of a particle-spring system in which particles are connected using damped springs creating a network that represent the cloth like in Figure 4. Here springs are presented as lines. At the intersection of lines the springs are connected to the particles using a hinged connection. The addon is capable of simulating the motion of this digital representation of a piece of cloth. Figure 5 shows the network of springs after the motion is damped out. It can be seen that the result is roughly similar to Figure 2. And there we have it. An old school method implemented using modern style technology.

My name is Peter Eigenraam.

After finishing my Bachelor ‘Building Technology’ in Utrecht I came to Delft to continue my studies at the faculty of Civil Engineering and recently I finished my Master on the topic of a flexible mould for the production of double curved concrete elements. During my master I became more and more interested in anything related to freeform structures, structural mechanics and parametric modeling.

This article originates from a study on shell structures designed by Heinz Isler, who inspired me through his exceptional structures. Recently I have started working for the TU Delft at the faculty of Architecture as teacher in structural mechanics.

Unfortunately it is not as easy as described. It takes a good understanding of particle-spring systems 47

and a great deal of modeling to obtain results. And it should be noted that it is not an exact simulation of a cloth, but it comes close. And once finished it provides a tool that allows to create and compare many shape within limited time. A short explanation of this system will be given, but I recommend reading more about this if you plan to use this method.

Particles are fictive objects that have mass, position, velocity, respond to forces, but have no spatial dimension. Forces can be applied to the particles.

Newton’s second law states that an object, here particle, will accelerate proportionally to the direction and magnitude of an applied force. When a force is applied to a particle it will move due to the acceleration. A new position can be calculated within a curtain time step. The particles move relative to each other and thereby the springs are stretched or compressed. Therefore the springs applies a force to the particles. This changes the sum of forces acting on a particle. In the next time step a new position can be calculated using the new direction and magnitude of the sum of forces. Damping is applied to the springs so that after many time steps the particles come to a standstill. Without damping the spring network will continue to move. Parts of what is described here and more on particle springs systems can for example be found in papers written by A. Witkin (1997) or A. Kilian and J. Ochsendorf (2005).

Modeling For a basic understanding of the model that will be presented we will go back to the hanging cloth model.

But now also a more elastic material is considered, for example rubber. Each material has its own specific properties which influence the shape. A property that influences the shape is the resistance to stretching and compression. Low resistance causes more stretching 48

than high resistance. It should be noted that a wire used in fabric cannot resist to compression, but rubber can. Another property which has influence on the shape is shear resistance. Shear can be compared to a deformation of a perfect square into a tapered shape in which one diagonal has extended and one shortened.

The same properties are of influence when you try to obtain a shape and we will see that these properties can be used when making a parametric model.

Cloth is not capable to resist compression. However, for modeling, springs (often) have a constant resistance to extension and compression. A way solve this is to divide a spring in two parts with and hinge in between as in Figure 6. When loaded in compression the hinged connection in the middle prevents the springs from being loaded in compression. Figure 7 shows a simpler situation which can be used for simulation of a rubber membrane.

More springs can be combined to form a square element which can also be recognized in Figure 4. The square element in Figure 8 can be used to simulate cloth and will therefore be called a ‘cloth element’.

The square element in Figure 9 can be used to simulate rubber and will therefore be called a ‘rubber element’.

The next step in modeling will be to apply forces to the particles and set supports. Loading should be applied only to particles at the corners of each square. The other particles serve only as connection to give the cloth element it properties. Springs will be given stiffness. When using rubber elements with a low stiffness, near zero, of the diagonal springs the network of springs will behave like a 3D catenaries as can be seen in Figure 10 and 11. A high stiffness of the diagonal springs will result in a flat shape like in Figure 12 and 13. Like properties of different types of materials the elements behavior can be influenced as desired.

Figure 2: Cloth covered with gypsum. Due to its weight the cloth obtains a shape.

Figure 4 : Network of springs that represent a piece of cloth.

Figure 3: After hardening of the gypsum the shape can be turned upside down creating a roof or canopy structure.

Figure 5: Simulated shape of hanging cloth. The shape is roughly similar to Figure 2.

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I hope to have shown you some of the possibilities of a parametric model for form finding structures by making an analogy with the work of Heinz Isler.

Parametric modeling allows application of old methods according to modern standards. If you are interested in Grasshopper-files to get started or if you have questions feel free to send me an email at P.Eigenraam@tudelft.nl. Hope you enjoy it.

Bibliography Isler, H. (1960). New Shapes for Shells. Bulletin of the IASS, No. 8.

Kilian, A. and Ochsendorf, J. (2005). “Particle-spring system for structural form finding”. Bulletin of the IASS, No. 147.

Movie “Inverted hanging model in Rhino (using Kangaroo)”, http://www. youtube.com/watch?v=29MLFvofx94 Piker, D. (2013). “Kangaroo Live Physics for Rhino and Grasshopper”.

Kangaroo manual. https://docs.google.com/document/d/1X-tW7r7tfC9d uICi7XyI9wmPkGQUPIm_8sj7bqMvTXs/preview

Figure 8: A ‘cloth element’ can resist to extension, but not to compression.

Withkin, A. (1997). “Physically Based Modeling: Principles and Practice, Particle System Dynamics”, Lecture notes. http://www.cs.cmu. edu/~baraff/sigcourse/

Figure 6: Spring that resists to extension, but not to compression.

Figure 7: Normal spring that resist to extension and compression.

Figure 9: A ‘rubber element’ can resist both extension and compression.

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Figure 10 and 11: 3D catenary shape as result of low stiffness of diagonal springs.

Figure 12 and 13: Flat shape as result of high stiffness of the diagonal springs.

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