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Glass Tensegrity Trusses by Froli, Lani

Apr 03, 2018



  • 7/28/2019 Glass Tensegrity Trusses by Froli, Lani


    Peer-reviewed by international ex-perts and accepted for publicationby SEI Editorial Board

    Paper received: March 04, 2010Paper accepted: June 29, 2010

    Structural Engineering International 4/2010 Scientific Paper 1

    Glass Tensegrity TrussesMaurizio Froli, Prof.; Leonardo Lani, Dr-Ing.; Department of Civil Engineering, University of Pisa, Largo Lucio

    Lazzarino, Pisa, Italy. Contact: [email protected]

    On the other hand, redundancyensures at each level that, when a sin-gle component fails, the other partnercomponents are still able to bear theload although with a reduced degreeof safety.3 In laminated glass panes,the application of this principle alsoensures a pseudo-ductile behaviour:it is known indeed that if a glass sheetbreaks, the other sheets are still able tobear the load, and even if all the sheetsbreak into large fragments, (only fullythermally tempered glass breaks intomany small fragments), the redundantsandwich structure assures a post-breakage stiffness and bearing capac-ity of the component that is similar, tosome extent, to material ductility.4

    For these reasons, a suitable applicationof the two basic principles of hierarchyand redundancy can provide a struc-ture with decisive properties of globalductility and fail-safe design even ifmostly composed of glass components.Fig. 1 shows the structural organizationof the present type of glass beams.

    Additionally, if the integrity of the

    structure is enhanced by prestressing,compression stresses superimpose inglass elements to those produced bytempering, thus increasing the appar-ent tensile strength of the material.

    Structural Conceptual Designof Trabes Vitreae Tensegrity Beams

    Experiments reveal that when a tradi-tional glass beam is submitted to increas-ing flexural loads, it cracks at a certainload, developing characteristic crackpatterns. To avoid an uncontrolled pro-cess of crack initiation and propagation,

    the idea considered was to govern it byregularly pre-cutting the glass surfaceinto many equilateral triangle panesand connecting them together using asystem of prestressed steel cables.

    The principle of tensegrity permeatesthis concept, therefore it was decidedto call these beams Trabes VitreaeTensegrity or TVT, mixing Latin andEnglish words.

    Each triangular pane is composed oftwo 5 mm thick chemically tempered

    microscopic surface cracks, alwayspresent even in virgin specimens, areresponsible for the intrinsic fragilityof glass1 and for its relative low ten-sile strength. An apparent higher ten-sile strength is obtained by thermal orchemical tempering treatments, which

    induce surface compression stressesthat inhibit crack initiation and propa-gation but do not exert any influenceon fragility.2

    Prestressed CompositeGlass Beams

    Basic Concepts

    The intrinsic fragility of glass may beovercome by organizing the wholestructure in two or more hierarchiclevels, each of them composed of a

    parallel, redundant assemblage of atleast two structural components.

    The hierarchic organization of thecomponents ensures that the sequenceof progressive damage follows a pre-established order starting from thelevel where the weakest componentsare. Therefore, if we put ductile mate-rials at the lowest level, we are surethat the failure process starts hereaccompanied by large plastic defor-mations, that is, with a global ductilebehaviour.


    Ductility is usually associated withmetallic materials that are capable ofdeveloping large plastic deformations.On the other hand, fragility is tradi-tionally associated with glass materials

    or ceramics.Nevertheless, some outstanding andinnovative glass structures, like theHaus Pavilion in Rheinbach theYurakucho canopy in Tokyo, theglass stairs of the Apple Stores in SanFrancisco, have been built even in seis-mic areas where fragile failures mustbe definitely avoided.

    Indeed, although glass is fragile andweakly tension resistant, it has a veryhigh compressive strength and, if con-veniently connected with other duc-tile materials, for example, by means

    of gluing or by prestressing, it is ableto form composite structures of highmechanical performances and alsoglobal ductility.

    It is well known that stress concen-trations that occur at the apex of


    High transparency and modularity, retarded first cracking, non-brittle collapseand fail-safe design were the basic requirements that inspired and guided thedevelopment of a new kind of glass beams. The two basic conceptual designgoals were to avoid any cracking at service and to get a ductile behaviour atfailure. These objectives were reached by a preliminary subdivision of the beaminto many small triangular laminated panes and by assembling them together bymeans of prestressed steel cables. Two prototypes have been constructed at theUniversity of Pisa, tested in the elastic domain under dynamics loads and succes-sively brought to collapse under quasi-static, increasing load cycles. In order toinvestigate the decay process of residual mechanical resources, the second pro-totype has been repaired twice by substituting just the damaged triangular panesand then tested again each time up to failure. Experimental results resulted in agood agreement with non-linear numerical simulations performed by appropri-ate finite element modelling.

    Keywords: structural glass; prestressed glass structures; post-breakage behaviour;structural ductility; fail-safe design; chemical tempering; fracture mechanics.

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  • 7/28/2019 Glass Tensegrity Trusses by Froli, Lani


    2 Scientific Paper Structural Engineering International 4/2010

    Qualitative Structural Behaviour

    Phase 0: Pure Prestress

    The structural behaviour of TVTbeams is analogous to that of segmen-tal prestressed concrete beams. Duringthe shop assemblage of a beam, thetwo twin curtains are placed on ahorizontal plane and prestressed. Thedead load of the curtains is entirelysustained by the surface, thus onlyprestress forces act, inducing a quasi-isotropic distribution of compressionstresses in the glass panes (Fig. 4).

    Phase 1: Glass Decompression

    When in service, under the flexuralaction of dead loads and increasingexternal loads, tension stresses in thelower parts of the glass panels gradu-ally diminish prestress compressionsuntil a limit state of decompression is

    reached in the central part of the beam.When the external loads are furtherincreased, the decompression propa-gates from middle span towards thesupports. This stage has been denotedas Phase 1glass decompression.

    Since the steel nodes exert unilateralrestraint only at the point of contact,the decompressed vertices of the glasspanels detach and simply move a smalldistance from their supports withoutdeveloping tension stresses. The staticscheme of the beam changes thus intothat sketched in Fig. 5 where flexural

    pressure is exchanged between glassand steel nodes due to the prestressaction. In order to attenuate localcontact peaks, the vertices of the glasspanels are round, and 1 mm thick

    AW-1050A grade aluminium alloysheets have been interposed betweensteel and glass.

    The redundancy principle is applied attwo different levels: the first is that ofthe doubly laminated panes and thesecond that of the parallel arrange-ment of the two twin curtains of glasspanes and steel cables as sketched inthe scheme of Fig. 1. The relativelylarge spacing of the two curtains givesthe beam an appreciable torsionalstiffness and good lateral torsionalbuckling stability.

    glass sheets5 laminated by means ofa 1,52 mm thick PolyVinyl Butyral(PVB) interlayer.

    The beam is composed of two paral-lel twin curtains 174 mm apart, braced

    on the upper side by a horizontal trussand connected together at the loweredge nodes by means of hollow stain-less steel structures (Figs. 2 and 3).Each curtain is made of a Warren-like appearance of glass panes (Fig. 2)

    jointed at the apex by means of stain-less steel nodes (Fig. 3). Mechanicalbolting between the glass panes andsteel nodes was avoided as danger-ous local tensile peaks always occur inglass holes.

    Instead, the nodes are mutuallyconnected by means of AISI 304 stain-

    less steel cables tensioned by screwtighteners. Consequently, only contact
















    Hierarchy, increasing mechanical strength



    1st Level 2nd Level 3rd Level

    Fig. 1: Hierarchy and redundancy organization

    Fig. 2: The prototype TVTbbeam

    Fig. 3: Steel node

    Fig. 4: Phase 0 calculated compression isolines

    Fig. 5: Phase 2 Calculated compression isolines

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  • 7/28/2019 Glass Tensegrity Trusses by Froli, Lani


    Structural Engineering International 4/2010 Scientific Paper 3

    1000,00 N

    1000,00 N

    1000,00 N

    1000,00 N



    Fig. 6: Global model of TVTb

    and shear tension forces are sustainedrespectively by the lower steel barsand one order of the diagonal steelbars. Compression stresses flux withinthe glass panels following typicalboomerang-shaped patterns visiblein the same graph. Only secondarytension stresses of lower intensityaffects glass.

    Phase 2: Buckling of Upper Cables

    Compressed steel cables are graduallyde-tensioned: when the prestress load

    is fully compensated, they buckle away.This limit state has been denoted asPhase 2buckling phase.

    Phase 3: Coll

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