Structural Design

A Systemic Approach

Toni Kotnik11Aalto University1toni.kotnik@aalto.fi

The paper sketches out the idea of a systemic approach to structural design.Starting with the notion of complexity as interweaving of feedback loops itintroduces a thermodynamic understanding of the problem of form-finding anddiscusses some implications for the design of building structures.

Keywords: structural design, systemic thinking, form-finding, thermodynamics,complexity

INTRODUCTIONOver the past twenty years, the introduction and in-tegration of computational methods and techniquesinto architectural design and discourse has been par-alleled by the almost ubiquitous presence of the no-tion of complexity in connection with applicationsof the digital: complex architectural geometry, com-plex fabrication, complex assembly, complex envi-ronmental performance, or complex urban analysisto name but a few. In this context, complexity is usedsynonymously as indication of an advanced level ap-plication to an otherwise well-known topic within ar-chitecture.

Such a connotation of the notion of complex-ity as advanced level application, however, stabilizesour current understanding of architecture. It veils themind-changing potential of the digital and limits theconscious recognition of computation as a paradig-matic shift within the discipline. Architecture is tak-ingpart in an "intellectual revolution [that] is happen-ing all around us, but few people are remarking onit. Computational thinking is influencing research innearly all disciplines, both in the sciences and the hu-manities. . . . It is changing thewaywe think" (Bundy,2007).

This paper is examining the notion of complexityand its relation to computation more carefully and issketchingout someof its implication for architecturalthinking, exemplifiedby changes to structural designas a sub-discipline.

WOVEN COMPLEXITYThe etymological roots of the word complex can betraced back to the Latin complecti, from com- (with,together) and plectere (to weave, to twine). In itsoriginal meaning, therefore, complexity refers to anactivity of weaving together independent threadsinto a new organized whole. This bringing together,however, is not a simple additive process as the ac-tual weaving of material illustrates: the weft and thewarp interact with each other, both threads deformand connect to one another by friction.

It is the coordinated accumulation of this activeinteraction that results in new properties of the over-all configuration that is not apparent in the threadsthemselves. Such emergent properties like a specificspatial morphology or structural rigidity are used forexample by the artist Joe Hogan in the creation ofsculptures based on traditional basket weaving tech-

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Figure 1Principle ofweaving based onembedding of weftthread intocollection of warpthreads andexamples ofpossible weavingpatterns; FromEarth And Sky,woven sculpture,2012, by Joe Hogan,Co Galway, Ireland(Photo: Rory Moore,Belfast, NorthernIreland).

niques (Figure 1). Here, especially the resulting over-all shape of the sculpture is often hard to predict asthebending stiffness of thewillowchanges along thethread as well as from thread to thread.

In general, theweaving pattern introduces an in-terdependency between neighboring threads whichcauses a feedback mechanism that influences theprecise formationof each individual thread (Figure 2).That is, weaving can be seen as the construction of anetwork of threads with a large number of overlap-ping and interacting feedback loops. It is this feed-back mechanism that guides the formation processas visible expression of the regulatory behavior anddistribution effect caused by the circular interaction.Aneffect, explored indepthfirst byNorbertWiener inhis seminal bookCybernetics or Control andCommu-nication in the Animal and the Machine published in1948 (Wiener). Together with General Systems The-ory, established by Ludwig von Bertanlanffy in the1940s, Wiener's Cybernetics provided the foundationfor the development of systemic thinking and sys-tems theory up to the present (Ståhle, 2009).

Figure 2Translation of asimple warp-weftconfiguration intothe relatedconnectivity matrixand accordingdirected graph.

With this in mind, the notion of complexity has tobe understood essentially as a systemic notion. Itrelates to pattern of interwoven simple relationshipbetween a larger set of agents that allow for feed-back loops as a form of exchange of information be-tween the agents. Complexity describes the abilityof a set of agents to organize itself into a new whole,of phase change, of re-organization into a new unity.Complexity, therefore, fundamentally is a transitionalphenomena at the transformational stage betweenhierarchies of organization. It refers to the ability in-herent in a system for organized construction, a con-struction of morphology or structural stability like inthe example of the woven sculpture by Joe Hogan.

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Figure 3Paradigmatic shiftin science fromreductionism tosystemic thinkingand relatedconcepts ofexploration thathave been taken upin digitalarchitectural designwith some temporaldelay.

SYSTEMIC BEHAVIORSystemic thinking is a holistic thinking that causeda paradigmatic shift in science by questioning theuniversality of reductionism as scientific method ofexploration. Since the 1950s, this shift has beentriggered by the availability of computational meanswhichmade is possible to handle and explore a largeset of interaction between various quantifiable enti-ties (Mussmann, 1995). The possibility to explore inmore depth the self-regulating effect of feedback hasresulted in a successivemodification or even replace-ment of reductionism as the predominant paradigmof research thinking. That is, the mechanistic under-standing of nature and the continuous top-down re-duction of the whole into parts has been exchangedfrompatterns of local interaction to the overall globalarrangement of the parts as an emergent bottom-up property of the system (Figure 3). Starting inthe late 1980s it is not surprising that architects be-came interested in these systemic models of nature

due to potentially new methods of spatial organi-zation and form-generation provided by computersand appropriate software (Weinstock, 2010). As a re-sult, over the past decade, systemic notions and con-cepts from science have diffused into architecturaldiscourse and are currently being explored for designpurposes.

One of the main applications of the self-regulating capacity of systems has been in the devel-opment of computational tools for form-finding oflong-span roof structures and lightweight structures,a classical problem in structural design, at the con-ceptual stage of the design process. Such structurestransfer their loads purely through axial or in-planeforces and the shape is determined primarily by theflow of forces in space. This distribution of forces inspace is typically not know in advance and thereforea formation process is required (Veenendaal & Block,2012).

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Figure 4Material systemwith multiple stableequilibriumpositions. Thematerial system isbased on amembrane coveredbytriangular-shapedpanels resulting in ahinged platesystem with limitedangular range.Through thelightning effect atthe interior zones ofcompression andtension can beidentified visually(Aalto University,Creative Design inEngineering,Students: IuliaRadion, JoonasJaaranen, UmarRiaz).

Before the availability of computational tools, physi-cal experiments were used to determine the shape.Probably the best-known examples are the hang-ing chain model by Antonio Gaudi for the ColòniaGüell in Barcelona or Heinz Isler's membrane modelsfor thin-walled shell buildings (Kotnik, 2011). Theseexperimental form-finding methods can be approx-imated computationally by particle-spring systems,a multibody system method (Kilian & Ochsendorf,2005). One of the first tools created to exploreparticle-spring systems as a method of form-findingwas CADenary, a simulation tool built mainly by AxelKilian in 2002. It gained popularity due to the intu-itive understandability and the interactive characterof the particle-spring system but lacked features tomake it into a versatile design tool. Someof these de-sign limitations have been overcome by Kangoroo, apopular physics engine for Rhinoceros developed byDaniel Piker that allows an interactive simulation andform-finding (Piker, 2013).

One of the big shortcomings of the particle-spring approach is that the described method ofform-finding is only valid for tension-only respec-tively compression-only structures like membranesor shells. In more general cases, the underlying dy-namic relaxation process does not converge. Thesame limitation is true for other existing methods ofform-finding in structural design like the Thrust Net-work Analysis (Block & Ochsendorf, 2007) embeddedinto Rhinovault, a form-finding software by PhilippeBlock.

The reason for this limitation is that particle-springsystems are highly ordered systems: the relation be-tween neighboring particles is very restrictive andaims for balancing out of uneven force distributionresulting in pure compression or tension within eachneighborhood of a particle and no rapid change ofthe surface geometry. This means all neighborhoodsof the surface have to be similar in their geometricquality. If, on the other hand, compression and ten-sion are available within the same neighborhood ofa particle then rapid change of the surface geometryis possible and various equilibrium solutions of thesystem can exist (Figure 4). This means, the systemicbehavior of structures in general is much more intri-cate than the existing methods of form-finding areable to capture. Compression and tension functionas pushing-and-pulling effect in the formation pro-cess of structural systems and it is well-known fromthe study of dynamic systems in physics and biol-ogy that it is the simultaneity of pushing and pullingwithin a system which is responsible for the emer-gence of new phenomena and configurations (May-field, 2013).

THERMODYNAMIC FORM-FINDINGIn order to overcome the limitations of the existingmethods of form-finding it is, therefore, suggestedthat a new systemic approach to structural design isrequired for a better understandingof formationpro-cess in structural systems.

Starting point of such a new approach is the

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Figure 5The transformedfree body diagramof static equilibriumof the hangingchain model asopen systemdiagram andalternative forceflow within systemwhich result inbending.

observation that in engineering the understandingof the system under consideration is defined by thefree body diagram, an isolated description of thepart of the structural system and all the forces act-ing upon it (Muttoni, 2006). The primary goal of thisdiagram is the detailed examination of the force dis-tribution within the structural system at static equi-librium. Hence, it describes a fixed situation, the sit-uation at the end of the formation process. Form-finding, however, is a dynamic process and is drivenby constant change of the configuration. In the caseof the particle-spring system this change is provokedby a residual force at each of the particles, a lumpedmass, that introduces some kinetic energy into thesystem (Figure 5). The process of change continuestill all the energy has dissipated and structural equi-librium is achieved. By introducing this residual forceand the initial configuration into the diagram, thefree body diagram transforms into a diagram of anopen system with the external forces as exchange ofenergy of the system with the surrounding and theresidual forces as internal energyflow. This readingofthe diagram introduces a thermodynamic perspec-tive into structural design and with it the interpreta-tion of the above mentioned form-finding methodsas near-equilibrium systems.

Such systems tend to evolve towards equilib-rium, a special state that has been the focus of multi-body research for a century. Yetmuch of the richnessof the world arises from conditions far from equilib-rium (Schneider & Sagan, 2005). Phenomena such asturbulence, earthquakes, fracture, and life itself oc-cur as phenomena far from equilibrium. Subjectingmaterials to conditions far from equilibrium leads tootherwise unattainable properties. This is also true in

structural systems.As mentioned above: one of the essential pre-

requisites for the existing form-finding methods isthe assumption of flow of forces through the sys-tem purely through axial or in-plane forces. On onehand, this enables an efficient use but on the otherhand it reduces the typology of shapes to a mini-mum. If more material is introduced into the sys-tem then other types of inner force flow get possi-ble like in the case of a beam where non-axial forceslead to the simultaneity of compression and tensionin the same material section and consequentially tobending of the beam (Figure 5). In the case of theparticle-spring system residual forces dissipate intomovement, in the case of the beam energy does notdissipateout of the systembut remainswithin, storedas elastic deformation respectively bending stress.

Thermodynamically, bending can be under-stood as dissipation of energy within the system thatis the resulting deformation is a morphological re-action of the system to the flow of energy throughspace. This interpretation seem to be farfetched.However, locally compression and tension define op-positedirectionalities. In amaterial sectionwith com-pression and tension like for example in the redirec-tion of the force flowaround a cut the resultingbend-ing can be seen as a local turbulence pattern aroundthe cut. This pattern of energy dissipation resemblesthe flow of wind around an obstacle like for examplea wall (Figure 6).

Consequently, the inner flow of forces as phe-nomenaofmechanics shares somesimilaritywith theflow of energy as phenomena of thermodynamics.An insight that forms the basis for constructal the-ory, a general theory on the formation of pattern

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Figure 6Based on plasticitytheory the flow offorces can bemanipulatedfollowing simplegeometricoperations like theredirection offorces: The directflow of inner forcesbetween twoexternal loads (a)can be redirectedwithin the materialby adding aninternal force thatpushes the flow outof its preferred lineand compensatingthe additional forceto ensureequilibrium in thesystem (b). Theresultingconfiguration offorces can beunderstood aspattern of turbulentdissipation ofenergy (c). Thediscrete turbulencepattern in forceflows resembles inan abstract way thepatterns of energydissipation - visiblein the local increaseof wind speed - thatoccur in the flow ofwind around anobstacle like a wall(d).

within flow systems (Bejan & Zane, 2012). But it alsoan insight that should motivate the interpretation ofstructural systems as distributed systems of energyin space. Such a perspective would relate the prob-lem of form-finding much closer to research in sci-ence like physics and biology and especially with re-search into pattern development in far from equi-librium open system. On the scale of urban designsuch a perspective already has been put forward al-ready (Pulselli & Tiezzi, 2009; Wilson, 2009). On thebuilding scale a thermodynamic perspective withinresearch and design is only slowly emerging (Bra-ham, 2016; Moe, 2013) but not specifically targetedtowards structural design.

CONCLUSION: DESIGN OF STRUCTUREClearly, the implied similarity of flow pattern still re-quires a lot of in depth researchbefore it canbemadeoperative and a thermodynamic approach to struc-tural design is only sketched out in a very rough way.But it already starts to point towards a possible directlinkbetweenongoing researchwithin science andar-chitectural design based on formation process. Andeven at this infant state of development some con-clusion can made regarding the implications for ourcurrent understanding of structural design.

At the moment, teaching and design of buildingstructures still is based on a reductionistic paradigmof hierarchy of structural systems governed by theidea of accumulation of forces from top to bottom

primarily along linear elements. This has fostered amove from surface to line that is the replacement ofmassive walls by linear structure and the develop-ment of building elements and fixed typologies asstructural solutions. The implied tendency towardslightness and dematerialization of structure has di-minished the potential of building structures to func-tion outside of the mono-functional purpose of pro-viding structural stability.

Within a systemic paradigm building structuresare perceived differently. Based on a thermodynamicambition building structure should be spread intospace in order to maximize the possibility for theeven distribution of loads. Animal architecture likefor examplebirdnests exemplify this verywell (Figure7): out of the interweaving of soft and flexible mate-rial structural stability emerges as complex propertylike in the initial example of the basket weaving. Atthe same time theweaving enables a flexible adapta-tion of thematerial system to the environmental con-ditions and the spatial requirements. This step-by-step construction is a formation process that resultsin a structural system that not only fulfils a mono-functional purpose but is also the generator of thespace as well as shading device and thermal regula-tion.

A system design of structural systems aims atsuch kind of polyvalent use of the building structure.Systemic structural design, therefore, has to be non-hierarchical and cannot be based on typologies but

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rather has to be based on first principles as genera-tive driver of the design. Systemic thinking in struc-tural design is themove away from the static iconog-raphyof form towards thedynamic andprocedural offormation. It is themove away from structural designtowards design of structures!

Figure 7Nest of a Baya birdin Southeast Asiaand nest constructof Social Weaver inSouth Africa.

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