Starting from the reinterpretation of the natural forms that recurs in the consolidated
shapes of historical buildings, the research proposes the umbrella vault as isolated selfsupporting
cover. The research outcome, defined with the term "structural tree", can be
considered as an extreme experimentation of the cooperation possibilities between natural
stone and steel reinforcement.
The idea arises from the observation of fan vaults in which appears an isolated support:
its static behaviour works, of course, because of the presence of an opposite structural portion.
In this case, on the contrary, there are no lateral supports but it arises as a self-referential
element, while the task of restoring the structural balance is left to the upper reinforcement
that allows a free composition of the "tree" without static constraints. The study is based on a
formal research that combines the possibility to create serial and repeatable compositions with
the achievement of an ideal static equilibrium configuration of the stone structure that
considers the collaboration between the voussoirs and the upper reinforcement.
The steel structure is not assumed as a pre-tensioned reinforcement, like in the other
prototypes, but as a passive reinforcement to recreate the compression condition of the arch,
usually generated by the opposing forces belonging to the two symmetrical halves

Bagnéris, Marine

Calabria, Claudia

Fallacara, Giuseppe

Epoka University

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.667The structural tree: new experimentation with reinforced stoneGiuseppe Fallacara1, Marine Bagnéris2 , Claudia Calabria31Researcher at the Department of Civil Engineering and Architecture, Polytechnic of Bari, Italy2Researcher at the UMR CNRS / MCC 3495 MAP-GAMSAU, Ecole Nationale Supérieure d'Architecturede Marseille, France3PhD student in Architectural and Urban Designing, Department of Civil Engineering and Architecture,Polytechnic of Bari, ItalyABSTRACTStarting from the reinterpretation of the natural forms that recurs in the consolidatedshapes of historical buildings, the research proposes the umbrella vault as isolated self-supporting cover. The research outcome, defined with the term "structural tree", can beconsidered as an extreme experimentation of the cooperation possibilities between naturalstone and steel reinforcement.The idea arises from the observation of fan vaults in which appears an isolated support:its static behaviour works, of course, because of the presence of an opposite structural portion.In this case, on the contrary, there are no lateral supports but it arises as a self-referentialelement, while the task of restoring the structural balance is left to the upper reinforcementthat allows a free composition of the "tree" without static constraints. The study is based on aformal research that combines the possibility to create serial and repeatable compositions withthe achievement of an ideal static equilibrium configuration of the stone structure thatconsiders the collaboration between the voussoirs and the upper reinforcement.The steel structure is not assumed as a pre-tensioned reinforcement, like in the otherprototypes, but as a passive reinforcement to recreate the compression condition of the arch,usually generated by the opposing forces belonging to the two symmetrical halves.INTRODUCTIONThe revival of forms derived from nature in architecture and the subsequent associationof natural structures, complex geometries and architectural forms, can be easily found inmany examples, from historic structure to contemporary applications, in which the use ofmathematical algorithms define the geometric principle that gives shape to the constructedform.In this regard should be considered the work "Fractals: Form, Chance and Dimensions"by Benoit Mandelbrot, in which there are some clear connections between the field of fractalgeometry and architecture, recognizing the affinity of the various architectural styles with thetwo opposing aspects of Euclidean geometry and fractal geometry. [1]The tree looks like a recurring element of influence of natural form in architecture,probably for the close relationship between the forces development and its shape that creates afunctional combination between support and roof.2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, EPOKA University, Tirana, ALBANIA.668In general this type of structure is shaped to respond to a compression behavior or to actlike an inverted stressed system that collect the loads up to a single anchor point.The tree structures can be divided into two types: those with a hierarchical organization, inwhich each part is geometrically similar to the whole (that can be assimilated to fractals in whichthe self-similarity is a distinctive property) and those in which the total weight is distributed tothe main support through a single point (the umbrella structures, also defined as a sub system ofthe branched constructions).Although this type of structures presents a close relationship between the load path and itsconformation, the structural behavior cannot be compared with the "tree" organism as it exists innature because the bending stresses, that in the first are systematically avoided, are a constantfeature of the second. [2]BackgroundThe formal antecedents of this type can be found in many historical examples as isolatedsupports taking part of a vaulted structure, in particular during the Gothic and late Gothic periodin which fan vaults and umbrella vaults have been a great spread.In the Jeronimos Monastery in Lisbon, the pillars that divide the nave are joined to thebarrel vault through asymmetric umbrellas with bearing radial ribs closed with thin stone slabs.The serial organization of the supports is associated with the classical static configuration ofstone vaulted structures: the umbrella is not conceivable as an isolated element but it must be partof an “arch” structure, in which the portion of the arc that originates from the support mustoppose in the same way to a second identical and symmetrical portion, bringing back the systemto an equilibrium configuration.The particular configuration of the support represents an expressive intent that does notdepart, anyway, from the traditional static configuration of the stone vaults.The same happens in all the similar examples that we can find. In the Chapter House ofWells Cathedral the central umbrella can work thanks to the presence of the eight fans thatsurround it, creating a whole structure where the various parts find their balance through theequilibrium with the opposite stresses.In the Church of the Jacobins in Toulouse, on the other hand, the idea of the iterablemodule finds its best example: there is a clear demarcation of the square spans and the repetitionof the umbrella is carried out for the entire length of the nave.But the character of isolated support can be found again only through the introduction ofother materials. The Nervi’s applications of reinforced concrete resume the idea of thejuxtaposition of modules simply joined together: the 16 elements that come in succession in theLabour Palace in Turin (1961) have a slight gap that makes even clearer the pursued concept ofiteration and seriality.The result depends, of course, from the different character of the material used. Each of thepillars presents a variable section that passes from the cruciform to the circular profile, from thebase to the top, while the umbrella is composed of a halo of steel beams with variable section.The formal expressions that exploit the potential of the steel have a great number of possiblevariations, so the tree element is materialized in many applications with different levels ofcomplexity.The Atocha station (Moneo, 1984-92) can be considered a direct consequence of the Nervi’sconception previously mentioned: once again the pillars are made of concrete but the squaremodule is divided into 4 triangles in which the beams are arranged parallel one to another. [3]2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, EPOKA University, Tirana, ALBANIA.669In the Oriente Station in Lisbon (Calatrava, 1998) the steel is, unlike the examples alreadycited, the only structural component: the branched supports bear four inclined squares made ofparallel bars, forming a light roof.The ramification of structure is carried to the extreme in the Stuttgart Airport (Gerkan, Marh &Partners, 1990), in which each support presents a triple subdivision in 48 branches to connect itwith the flat roof; in this point their diameter reaches only 16 cm [4]. As a direct derivation, in theproject "the Tote" in Mumbai (Serie Architects - 2009) the ramification fit to the roof inclinationand the two sides join one to another in the central part.In the Expo Roof of Hanover (Thomas Herzog - 2000) the mutual cooperation of wood andsteel in an umbrella structure presents another conception: the four wood shells, made of crossedbeams, define double curvature surfaces and connect to the supporting tower through a steelconnection.Here the idea of the umbrella changes and introduces the bending and deformation ofsurfaces, brought to the limit in the Shigeru Ban’s projects, as in the Nine Bridges Country Club(Korea – 2010) or in the requalification project of the Powerhouse Museum (Ultimo, Sydney,Australia - 2012).Previous experimentationsThe structural tree arises transferring to stone the idea of isolated support through thereinterpretation of natural forms; the research subject is to find conformations and methodsthrough which stone masses can find their equilibrium configuration without the typical mutualcontrast of the vaulted systems.The various aspects of the prototype proposed are, of course, a consequence of previousexperiments designed with the aim to combine the morphological research with the optimizationof the structural behavior.In the Alexandros Obelisque (Fallacara, 2006), presented at the Biennale of Venice, twodevices, that will be proposed and modified in several ways, appear for the first time: the pre-stressed steel reinforcement and the research about joints.The steel reinforcement could compensate, in terms of overall resistance, the weaknesses ofthe stone; the joints were designed imitating the knee anatomy, with the aim to allow themovement of the blocks without risking to damage the stone. Neoprene was used in the joints likecartilage, imitating the same spatial configurations between the contact surfaces of blocks.Subsequently, the structural arrangement of the pre-tensioned reinforcement will be re-applied in the construction of the Oblique Obelisque (Fallacara, 2010), in which its function iseven more important in order to contrast the horizontal thrust of the structure, due to the obliqueconformation.In this case carbon bars are applied to the structure, in order to connect the vertex of theobelisk with a point of the triangular base positioned about 2/3 from the cathetus. Each ashlar isthen fixed using a dedicated product that prevents the seeping of epoxy resin into the axial bore ofthe ashlars or into the contact surface between blocks. The carbon bars were bonded into theobelisk foundations using a direct injection of epoxy resin executed from the top.Fundamental can be considered the contribution of the prototype Foglia (Fallacara, 2009),constituted by a suspended portion of arch in order to create balconies or canopies.Here is improved the concept of the incomplete arch behaviour that needs to be balancedthrough external forces in order to find the static equilibrium: here that forces are suppliedintroducing a ‘leash’ on the extrados that blocks the keystone in the semi-arch, guaranteeing the2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, EPOKA University, Tirana, ALBANIA.670compression of the ashlars. Paradoxically, in this way, the more traction applied, the more theload bearing system is static.TheprototypeThe tree structure is designed as an isolated and iterable structure formed by a central trunkfrom which start 8 arms. Each of the stone branches is defined by a lowered curve and shows adecreasing height up to the outermost point of the structure.The possibility to create an independent element is given by the presence of a passivereinforcement that, starting from the center of the trunk, connects and compresses all the blocksof the 8 branches and ties the extremity, giving rise to a contrast force that recreates the elementscompression.The joints conformation is directly dependent from theupper reinforcement: they have a different orientation in connectionwith the strength that is expected to be exerted from the collaborationbetween the steel strip and the semi arch.Figure 2-2 Foglia prototype (Fallacara, 2009)Figure 3-4 Maquette: structural arrangement of the branches2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, EPOKA University, Tirana, ALBANIA.671The overlapping elements of the stem have been designed according to a star-shapedinterlocking joint that made them integral, very important especially for the last part that acts as acoupling for all arms.In order to experimentally verify the structural behaviour has been used a maquette made ofplastic material (ABS), created by computer numerical control machine, that replies the voussoirsshapes with the  contribution of the upper reinforcement.This construction on a small scale has allowed checking the strong points and weaknessesinherent to the considered system, constituting a first step substantially coincident with theoutcome of the structuralanalysis.Figure 8-9-10-11 Assembly stages of the maquette2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, EPOKA University, Tirana, ALBANIA.672(rapid prototyping elaboration and manufacturing by Vito Cascione, PhD Student - Department ofCivil Engineering and Architecture, Polytechnic of  Bari, Italy)The stone prototype in scale 1:1 will be built during the next July, in collaboration with theS.N.B.R. Society of Troyes and the Atelier de la Pierre d'Angle in Brignoles, with the aim toconfirm the rightness of the static research. The stone cutting will be done with CAD/CAMprocesses in Troyes, the assembly will take place in Brignoles.Numerical analysis methodologyConcerning this first prototype, the assessment of the stability is proposed using theLMGC90 open platform [5][6] dedicated for the modeling of large collections of 2D or 3Dobjects. The Non-Smooth Contact Dynamic discrete element method [8][3] is used to perform themechanical behaviour of the “structural tree”. The stone blocks are modelled as 3D rigid elementsinteracting by a Signorini-Coulomb friction law applies for contact points between blocks. Inorder to consider the tensile effect of the steel elements, an additive interaction law describing thebehaviour of an elastic wire has been introduced to connect the rigid elements on their upper-part.An initial prestress and a rigidity relying on the product of the Young modulus by the steelsection are the two parameters of this elastic law. For this preliminary study, the symmetry of thestructure leads to model only one branch loaded by its own weight. Thus, considering a givengeometry of the tree and a stone property restricted to its density (2000kg.m⁻³) due to the rigidmodelling, the friction coefficient and the initial prestress remain the variables that couldinfluence the mechanical behaviour.ResultsAn initial prestress of 10⁻³ m/m has been introduced into the elastic wires and a very smallfriction coefficient of 0.2 has initially been considered into the numerical model. This frictioncoefficient value has no relation with the dry friction between stone blocks, usually estimatedaround 0.5-0.7 but it aims at understanding the behaviour of the prototype realized in syntheticmaterial unable to undertaken any friction. The result of the numerical modelling matchesobviously well with the physical experiment. Thesame sliding mechanisms between joints areobserved leading to a global instability of the treestructure.Figure 12-13 Model shapes from the CNC machine modeler2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, EPOKA University, Tirana, ALBANIA.673DiscussionFurther simulations have been conducted on this first prototype to consider either a greaterfriction coefficient or a smaller initial prestress in order to get closer to the real structure. Indeed,the dry joints would resist with a friction coefficient closed to 0.5-0.7 as previously mentioned,while the prestress could vanish by thermal dilatation of the steel elements. The variability ofthese parameters does not imply any important changes in the mechanical behaviour; theinstability of the structure remains. Such report argues for a well-known technical requirement forstone construction, i.e. the joint orientation is a crucial parameter for the stability. Consequently,the branch subdivision must be redesigned properly according to the loading to assess therequired stability.Thus, a new design of the branch elements is proposed to be modelled. The joints areperpendicular to the neutral axis of the elements. A 0.5 friction coefficient and no initial prestressare considered for the calculation. Finally, this new arrangement of blocks conducts the flow offorces and the stability of the structure is achieved.Design applicationsThe results obtained from the serial repetition of a single support may be ideal for spacessuch as railway stations, markets, exhibitions halls and so on, that need large sizes combined withthe effect of spatial fusion. The branches may be covered with light material, such as wood orglass, and aggregate in a free manner, depending on the required function, allowing a subsequentaddition of modules without altering the overall balance of the system.Fig.14 : Numerical modelling of one branch Fig.15 : Physical modelling of one branchFig.16  Stability of the new design Fig.17  Maximal Z-displacement and tensioninto the steel elements2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, EPOKA University, Tirana, ALBANIA.674CONCLUSIONThe problem to actualize a traditional material is solved in the repetition of a shape closelyrelated to the historical inheritance but configured with the aim to disengage from the imposedcompositional limits: each tree is a self-referring structure, both in static and compositional level,and can be combined in the appropriate way in accordance to  the desired result.REFERENCES[21] Ahmeti F., (2007), Efficiency of Lightweight Structural Forms: The Case of TreelikeStructures - A comparative Structural Analysis, Master Thesis, PAGINE[22] Charleson, A., (2005), Structure as Architecture, Oxford[23] Chetouane B., Dubois F., Vinches M., Bohatier C. (2005), NSCD discrete element methodfor modelling masonry structures, International Journal for Numerical Methods inEngineering, 64, 65-94.[24] Deplazes A., (2005), Constructing Architecture: Materials, Processes, Structures, aHandbook, Basel, Switzerland, PAGINE[25] Dubois F., Jean M., Renouf M., Mozul R., Martin A., Bagnéris M. (2011), LMGC90, 10eColloque National en Calcul des Structures, Giens, France.[26] Dubois F., Jean M. (2003), LMGC90 : une plateforme de développement dédiée à lamodélisation des problèmes d’interaction, In M. Pottier-Ferry, M. Bonnet et A. Bignonnet,éditeurs : 6ème Colloque National en Calcul  des Structures, Giens, France.F gure 12 View of a possible application: railway stationFig.18  Design applications: railway station  hypothesis(Graphic rendering: Nicola Boccadoro)2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, EPOKA University, Tirana, ALBANIA.675[27] Fallacara G., (2012), Stereotomy – Stone Architecture and New Research, Paris, 94-103,132-139, 156-161.[28] Jean M.(1999), The non-smooth contact dynamic method, Computer Methods in AppliedMechanics and Engineering, 177, No 3-4, 235-257.[29] Mandelbrot, B. (1977), Fractals: Form, Chance and Dimension, San Francisco

The structural tree: new experimentation with reinforced stone

http://dspace.epoka.edu.al/bitstream/1/1236/1/465-1285-1-PB.pdf

The structural tree: new experimentation with reinforced stone

Abstract

Similar works

Full text

Available Versions

Epoka University