Glass Tensegrity Trusses by Froli, Lani

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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.

Introduction

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

Abstract

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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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

Re

dudancy,parallelassemblies

Curta

in

A

Curtain

B

Steelcable

Glasssheet

Laminatedpane

Laminated

pane

Glasssheet

Glasssheet

Glasssheet

Hierarchy, increasing mechanical strength

Steel

cable

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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1000,00 N

1000,00 N

1000,00 N

1000,00 N

Y

X

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: Collapse

After Phase 2 has been reached, a fur-ther increase in load leads to an aug-mentation of stress compressions inthe glass panes and tension stresses inthe steel rods. The dimensioning of thedifferent component parts of the beamcan be performed so that the finalPhase 3collapse takes place due tothe yielding of the steel cables and notbecause of glass rupture in compres-sion, thus resulting in a ductile collapseaccompanied by large displacements.

Depending on the slenderness of thesteel cables and on the prestress inten-sity, Phase 2 may even follow Phase 3, asindeed happened in the prototype beam,and illustrated in the following text.

Numerical Modelling

Four different finite element model(FEM) analyses have been performed

to predict the various aspects of thestructural behaviour of the beam andto better calibrate the design of theprototypes (Fig. 6):

2D non-linear geometrical analysisto evaluate the effect of prestress onthe flexural stiffness of the beam;

2D local buckling analysis to evalu-ate instability effects of prestress foreach single glass pane;

3D local geometric non-linear anal-ysis to evaluate the transversal stiff-ness of the different joints;

3D geometric non-linear analysisto evaluate the torsional stiffness ofthe beam.

The glass panels have been modelledby shell elements (4-node, 24 degreesof freedom) while the steel cableshave been reproduced by Bar ele-ments (2-node, 6 degrees of freedom)that react only to tension stresses. Theconstitutive laws for the two materialshave been deduced from EuropeanCode6, that is, glass has been schema-tized as a linear brittle elastic material

and stainless steel as linear elasticplastic material with a linear harden-ing branch.

In order to model contacts betweenglass panels and steel nodes a set of

point contactelements was introducedthat were capable of reacting justto compression stresses. Aluminiumsheets were not included in the modelbecause of their relatively small thick-ness and, for practical reasons, owing tothe coincidence of the Youngs moduliof aluminium and glass. The transversal

stiffness of the joint was preliminarilyinvestigated by a 3D local model with

solid elements (8-node, 24 degree offreedom) (Fig. 7).

Calculations have substantially con-firmed the intuitive predictions syn-thetically described in the sectionQualitative Structural Behaviour withthe only exception that the bucklingphase of upper steel cables (Phase 2)does not influence significantly theflexural response of the beam (Fig. 8).On the other hand, the decompression

phase (Phase 1) and the yielding phase(Phase 3) of the lower steel cables canbe clearly recognized.

Figure 9 shows the load factor versusdisplacement of the middle span pointfor different prestress (from 2 to 12kN) Np load in the steel cables, assum-ing P= 1 kN, the force applied to eachof the eight nodes of the beam, corre-sponds to a load factor one. The firststiffness reduction is associated withthe decompression of the lower partof the beam (Phase 1). By increasingthe prestress level, the intensity of the

external load that induces the decom-pression phase increases. The secondstep of stiffness decay is associatedwith the yielding of the lower steelcable but, of course, the ultimate limitload results independent ofNp.

Figure 10 shows the influence of Npon the axial force in the lower cable ofthe beam, and how the ultimate load isindependent of the value of prestress.

The hardening properties of stainlesssteel allowed the analysis to progress

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beyond the yield initiation of the lowerbars until the buckling of the upperbars and of the middle span glasspanels.

It can be observed that the theoreti-cal mechanical response of the beam issubstantially bilinear until yielding ofthe steel bars occurs, while the buck-

ling of the upper cables does not seemto have a relevant influence on theoverall residual stiffness.

Furthermore, the static principle,which states that prestress controlsonly serviceability limit states but notthe ultimate limit states, is confirmed.

Experimental Tests

Virgin Specimens

After the construction and testing of afirst prototype (TVTa), which sufferedsome assemblage problems concerning

prestress operation, a second proto-type beam (TVTb) was prepared hav-ing a length of 3300 mm and a heightof 572 mm. This prototype has beensubmitted to dynamic and quasi-staticcyclical laboratory tests to completelycharacterize the experimental struc-tural behaviour of the specimen and tocompare it with numerical predictions.

Dynamic Test

Dynamic tests have been performedby inducing sudden impulses both

in the horizontal and in the verticaldirection at middle span. To producethe impulses, a mass of 34 kg wasslowly applied to the beam by meansof a steel rod thus inducing a state ofinitial distortion. As the rod was sud-denly cut, the beam was submitted todamped free oscillations. Vertical andhorizontal acceleration histories wererecorded at some representative pointsof the beam, which allowed to evaluateeigen vibration periods and to controlthe attitude of the structure to dampedfree oscillations.

The assessment of the structure fre-quencies was deduced from the trendof the accelerations, appraising the dis-tance between two consecutive max-ima. Table 1 compares the theoreticaland the experimental results.

Quasi-Static Cyclic Tests

The static test of TVTb prototypehas been performed in two differentstages: during the first one, the specimenwas submitted to a progressively andcyclically increasing loading condition.

X

Y

Z

Y

XZ

(a)

(b)

Fig. 7: (a) and (b) Joint model

Plate stress 22 Mid plane (MPa)

4

8

13

1721

26

30

3435

Fig. 8: Calculated principal compression stresses

9

8

7

6

5

4Loadfactor

3

2

1

010 0 10 20 30

Displacement (mm)

40 50 60 70 80 90

Np = 2 kN

Np = 4 kN

Np = 6 kN

Np = 8 kN

Np = 10 kN

Np = 12 kN

Fig. 9: Load factor versus vertical displacement

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The comparison allows the conclu-sion that numerical and experimentalresults are rather close to each otherwith some limited discrepancies:

The first knee related to Phase 1(glass decompression) is recogniz-able although less marked as innumerical analysis;

The actual stiffness of the beambefore the first decompressionknee is lower than that obtained bynumerical analysis;

At each new load cycle, the level ofthe decompression load decreasesalthough the residual deformation isvery limited.

Each cycle ofFig. 11 encloses a finitearea showing that the beam is alsosurprisingly able to dissipate energybefore any damage occurs in the com-ponent materials. This can be attrib-uted to the friction that develops

due to relative slip movements at theinterface between the glass and steelnodes and perhaps also to viscoelasticslip movements in the PVB interlayer.

Very small transversal displacementswere measured (not shown here forthe sake of brevity) at each load cycleevidencing how good the torsionalstiffness of the beam is and how itremains constant throughout the pro-gression of the load cycles.

After the completion of the cyclicalload program, the beam was beensubmitted to a monotonic increasing

load up to collapse. In the graph inFig. 11, the load versus displacementcurve of this stage (blue line) is com-pared with the theoretical curve. Theexperimental curve has almost nodecompression knee but now the sec-ond knee is now visible, correspond-ing to yielding of the lower steel bar,which occurred at a higher load levelthan predicted. First failure symptomstherefore manifested in the ductilecomponent material of the compositestructure (Fig. 12).

In the second stage, the load wasincreased monotonically until thecollapse of the beam took place at atotal applied load of 61,84 kN (loadfactor = 7,73).

Before the application of externalloads, vertical and horizontal displace-ments induced by self weight and pre-stress were measured over a few days.Such investigations led to the conclu-sion that tension and rigidity reduc-tions that could occur with time due to

the relaxation of the cables or to otherviscosity phenomena in the PVB inter-layer could be substantially neglected.

The program of cyclic loading hasbeen performed to check precedent

Test no. Form Measured frequency (Hz) Calculated frequency (Hz)

1 In plane 19,1 76,9

2 In plane 16,9 76,9

1 Out of plane 13,4 12,1

2 Out of plane 15 12,1

Table 1: Results of the dynamics tests

Np = 2 kN

Np = 4 kN

Np = 6 kN

Np = 8 kN

Np = 10 kN

Np = 12 kN

9

8

7

6

5

4

Loadfactor

3

2

10

0 2000 4000 6000 8000 10 000 12 000

Axial force (N)

14 000 16 000 18 000 20 000

Fig. 10: Load factor versus axial force

intuitions and theoretical analyses andto evaluate the different structuralresources of the prototype, namely, theability to sustain repeated occurrenceof increasing loads without damageor significant performance decay, theresponse to the influence of unavoid-able geometrical imperfections and theeventual capacity to dissipate energywithout damage.

The results of the cyclic test program

are represented in Fig. 11 in terms oftotal applied load versus middle spanvertical displacement. The experimen-tal results are compared in the samegraph with the analytical monotonicresponse of the 2D FEM model.

9 72 kN

64 kN

56 kN

48 kN

40 kN

32 kN

24 kN

16 kN

8 kN

0 kN

8

7

6

5

4Loadfact

or

3

2

1

00 10 20 30

Displacement (mm)

40 50 60 70

Numerical model

Final pushovertest

Cyclic tests

Fig. 11: Load of middle point versus vertical displacement compared with FEM(dotted line) Fig. 12: TVT at failure

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age after buckling, they could not offer

the same degree of restraint as the vir-gin ones.

Therefore, the central panels ofTVTbbis buckled corresponding toa load factor of 4 instead of theprevious 7,5.

Next, in prototype TVTbbis, the col-lapsed central panels were substituted.The second repaired prototype wascalled TVTbtris and exhibited almostthe same ultimate load factor as theprecedent version.

Figure 13 shows the load factor ver-

sus middle span vertical displacementcycles of the virgin specimen and ofthe two repaired versions. A rathergood retention of the stiffness proper-ties of the repaired specimens can beobserved together with a progressiveincrease in the dissipated energy.

Owing to the hardening proper-

ties of stainless steel, the load can beincreased even beyond yielding: thefinal collapse of the specimen wasreached when the upper parts of mid-dle span glass panels buckled away.

Repaired Specimens

After prototype TVTb completelycollapsed as a consequence of thebreaking of middle span panels, it wasrepaired by substituting just the bro-ken panels. Prestress was restored atthe same levels of the virgin specimenTVTb.

The first repaired prototype waslabeled as TVTbbis and submittedto the same increasing load cycles ofTVTb.

Since the clam plates of the centralpanels in TVTbresulted in a little dam-

Fig. 13: Displacement origins have been shifted to the right in TVTbbis/tris

7

6

5

4

3

2

1

05 0 5 10 15 20

Displacement (mm)

25 30 35 40 45 50 55 60 650 kN

8 kN

16 kN

24 kN

32 kN

40 kN

48 kN

56 kN

Lo

adfactor

TVT

TVTbis TVTtris

Conclusion

The numerical results and the testexperiments on virgin TVTbprototypeof a prestressed composite glasssteelbeam allow the conclusion that theconstructional principle is valid andmerits further technological improve-ment and research work.

The experimental and numericalresults have underlined that TVT com-posite glasssteel beams are able todevelop a ductile break-up and that theserviceability limit state is governed bythe level of prestress in the steel cables.The cyclic load programme also evi-denced that these glass beams are ableto dissipate energy through frictionand viscoelasticity without damage.

The segmental, modular features andthe tensile integrity of these beamsallow substitutions to be limited just tothe collapsed or cracked panels, thus

reducing repair costs.

References

[1] Menc ik J. Strength and Fracture of Glass andCeramics. Elsevier: London, 1992.

[2] Sedlacek G. Ein Bemessungskonzept zur

Festigkeit thermisch vorgespannter Glser.Shaker Verlag: Aachen, 2000.

[3] Rice P, Dutton H. Structural Glass, 2nd edn.Spon Press: London, 2004.

[4] Kott A, Vogel T. Safety of laminated glassstructures after initial failure. IABSE Struct.Eng. Int. 2004; 14(2): 134138).

[5] MacrelliG. Process control methods for chem-ical strengthening of glass on industrial scale.Proc. XIX Int. Cong. Glass, Edinburgh, 2001.

[6] EN572 Glass in Building, Basic Soda LimeSilicate Glass Products, Definitions and General

Physical and Mechanical Properties, CEN/TC129 Glass in Building, 2004.

Glass Tensegrity Trusses by Froli, Lani

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