Engineering Structures 79 (2014) 276289

Contents lists available at ScienceDirect

Engineering Structures

journal homepage: www.elsevier .com/locate /engstruct

Exploratory numerical analysis of two-way straight cable-net faadessubjected to air blast loads

http://dx.doi.org/10.1016/j.engstruct.2014.08.0230141-0296/ 2014 Elsevier Ltd. All rights reserved.

Corresponding author. Tel.: +39 040 558 3842.E-mail addresses: bedon@dicar.units.it, c.bedon@libero.it (C. Bedon).

Chiara Bedon , Claudio AmadioUniversity of Trieste, Department of Engineering and Architecture, Piazzale Europa 1, 34127 Trieste, Italy

a r t i c l e i n f o

Article history:Received 13 May 2014Revised 13 August 2014Accepted 13 August 2014

Keywords:Cable-net faadeAir blast loadViscoelastic devicesFrictional devicesEnergy dissipationSDOF approachAdvanced numerical modellingDynamic nonlinear simulations

a b s t r a c t

Based on numerical and analytical results of previous literature contributions, the paper investigates thedynamic behaviour of a structural two-way straight cable-net faade subjected to medium-level blastloads. Numerical studies are dedicated, specifically, to a cable-net prototype already experimentallyinvestigated under seismic loads. Several numerical finite-element (FE) models are developed inABAQUS/Standard. A geometrically simplified, lumped-mass FE-model (M01), a detailed cable-glass model(M02) and a further simplified but computationally efficient cable-glass model (M03) are presented. Themodels are assessed and calibrated to test data of literature, as well as to simplified SDOF analytical for-mulations, in order to investigate the dynamic response of the faade under high-rate impulsive loads.Since axial forces in the cables and maximum stresses in the glass panels abruptly increase when theexplosion occurs, specific viscoelastic and frictional devices are applied at the connection between glassand cables, as well as at the end of the cables. The main advantage of the presented technological solutionis given by the partial dissipation of the incoming energy. In the first case, viscoelastic connectors addflexibility to the point-supported glass elements, hence reducing the amount of incoming blast energy.In the latter case, frictional devices dissipate through friction mechanisms the strain energy stored bythe bearing cable-net. A proper combination of these multiple devices, in conclusion, can manifest amarked increase of structural efficiency for the examined structural typology.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

The rising desire of transparency in modern buildings markedlyincreased the use of glass as a construction material able to carry-on loads in the form of innovative structural members, roofs, cur-tain walls. As a result, during the last decades traditional designconcepts rapidly evolved, in conjunction with ongoing manufac-turing developments, in order to provide appropriate technologicalsolutions to continuous advanced architectural demands [18].

Glass faades, specifically, highlighted several techniqueimprovements and optimizations, aiming to cover wide surfaceoften characterized by irregular shapes.

While the traditional unitized curtain wall or stick systems,for example, typically consists of modular units in which the glasspanels are sustained by a metallic frame composed of aluminiumtransoms and mullions rigidly connected to the structural backup(e.g. concrete slab), cable-supported faades are especially usedwhen large volumes and surfaces must be enclosed. Althoughfirstly built about 20 years ago, due to their transparency, easy

constructability and energy savings, the latter solution rapidlypropagated in worldwide as a new kind of glazing system.Compared to other steel-glass typologies (e.g. unitized curtainwalls), cable-net systems represented for several years a markedevolution of the usual design concepts, since typically associatedto high transparency and extreme minimization of the steelsupporting systems. The main advantage of cable-net faades isin fact given by the intrinsic stiffness and stability offered byappropriately pre-tensioned stainless steel cables.

In practice, single-way or two-way plane cable nets are typi-cally designed to sustain gravity loads and orthogonal distributedordinary loads (e.g. wind). In the latter case, the appropriate limi-tation of out-of-plane deflections due to in-service pressures repre-sents the most critical design goal for these flexible structuralsystems, since although subjected to often moderate pressures,large deflections could derive from their typical overall dimensionsand complex geometries (e.g. New Beijing Poly Plaza Cable-NetWall (Fig. 1a, [9]), Kempinski Hotel at Munich Airport (Fig. 1b,[10]), etc.).

In this context, numerous authors investigated through numer-ical, experimental or analytical models the static and dynamicresponse of cable-net faades in different loading conditions.

http://crossmark.crossref.org/dialog/?doi=10.1016/j.engstruct.2014.08.023&domain=pdfhttp://dx.doi.org/10.1016/j.engstruct.2014.08.023mailto:bedon@dicar.units.itmailto:c.bedon@libero.ithttp://dx.doi.org/10.1016/j.engstruct.2014.08.023http://www.sciencedirect.com/science/journal/01410296http://www.elsevier.com/locate/engstruct

Fig. 1. Examples of two-way straight cable-net faades. (a) New Beijing Poly Plaza Cable-Net Wall [9] and (b) Kempinski Hotel at Munich Airport [10].

C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289 277

Careful attention was paid especially for the study of the interac-tion between the glass panels and metal connectors [11,12]. Fenget al. [13,14] deeply investigated the behavioural trends of cable-net faades subjected to seismic events. In [15], they also high-lighted the effects of glass panels stiffness on the global dynamicresponse of steel-glass faades, providing critical discussion andcomparison of experimental and numerical predictions. Studiespresented in [16,17] have been dedicated to the nonlinear behav-iour of cable-supported faades under wind loads. Main featuresand comparative discussion of cable-truss glass faades are pro-posed in [18].

While extended rigorous investigations are available for steel-glass faades under ordinary loads, further knowledge is currentlyrequired to understand and optimize their structural behaviourunder exceptional loading conditions. The dynamic behaviour ofglazing systems under high-strain rate and impulsive loads suchas explosion, for example, still represents a research topic of greatinterests and a challenge for designers. Wide series of shock tubeexperiments, analytical investigations and FE numerical studies,in this context, have been dedicated to single laminated glasspanels subjected to air blast loads [1925]. Weggel et al. [26]investigated the dynamic behaviour of unitized curtain walls underlow-level explosions. Numerical parametric simulations have beendiscussed in [27], in order to provide pressure-impulse (PI) designcurves for the blast verification of laminated glass curtain walls.Analytical and numerical studies have been recently proposed forthe dynamic buckling verification of monolithic and laminatedglass beam-like and columns under blast loads [28].

For the specific topic of cable-supported faades, Teich et al.[29] focused on the analysis of the dynamic response of these sys-tems under explosive events, emphasizing the influence of the neg-ative phase of a blast wave pressure on their global structuralbehaviour. Wellershoff et al. [30] highlighted, through applicationto the case study of the World Trade Center building, the typicalbehaviour of a single-way straight cable supported faade underblast loads, suggesting possible mitigation techniques for the lim-itation of damages and improvement of the expected dynamicperformances.

As also highlighted in [31], the design of a blast resisting cable-supported faade strongly differs from the conventional design of aglazing system subjected to ordinary loads. When an explosionoccurs, the structural components of a cable-supported faadeare in fact affected by exceptional stresses both compressiveand tensile, due to mainly flexural deformations involved by theacting impulsive pressures and extreme deflections. While glasspresents typical high nominal compressive strength, however,maximum tensile stresses should be properly checked and limited,to preserve the faade integrity and avoid brittle failure mecha-nisms in it.

In that earlier contribution [31], appropriately designed elasto-plastic devices were proposed to be installed at the ends of the

vertical bearing cables, in order to prevent their possible brittle col-lapse under high-strain impulsive loads. The same cable-supportedfaade markedly flexible due to the presence of a single layer ofpre-stressed straight cables has been successively furtherimproved [32] by implementation of combined multiple devices,namely consisting in elastoplastic devices at the cables ends andopportune viscoelastic connectors introduced at the connectionbetween the glass panels and the cables [33]. Certainly, underexceptional loading scenarios, the structural dynamic performanceof these structural systems should be optimized in order to avoid,or at least minimize, possible injuries and structural damages, hencepreserving the activities within the building.

In this paper, based on extended numerical and analyticalresults of previous literature contributions [3133], the behav-ioural trends of a two-way straight cable-net faade subjected tomedium-level blast loads are numerically and analytically investi-gated. In particular, studies are dedicated to the dynamic behav-iour of a cable-net faade prototype already analyzed in [15]under seismic events.

Based on [3133], multiple typologies of dissipative devices areintroduced both at the connection between the glass panels andthe pretensioned cable-net, as well as at the cable ends.

Modal analyses and nonlinear dynamic incremental simulationsare performed on a lumped-mass model (M01), a geometricallydetailed cable-glass model (M02) and a further simplified but com-putationally efficient cable-glass model (M03), able to take intoaccount the bending stiffness contribution of glass panes in theform of equivalent beam elements. Parametric dynamic simula-tions are then performed, in order to highlight the efficiency andthe criticalities of each possible solution.

As shown, by means of appropriate energy dissipating compo-nents, the increase of maximum axial forces in the bearing cablesand the maximum tensile stresses in the glass panels can be mark-edly reduced, hence the structural stability of the faade systemcan be prevented.

2. Structural behaviour of cable-net faades under blast loads

2.1. Cable-net faade layout

In this paper, the cable-net faade recently analyzed underseismic events [15] is numerically investigated to demonstrate thefeasibility and potentiality of passive control systems discussed in[3133] for the mitigation of blast effects on single-way cable-supported faades to high-strain impulsive loads, by application ofthe same mitigation technique to a two-way planar cable-supported faade. The mentioned glazing system consists,specifically, in a net of pretensioned steel cables, a series of squaremonolithic glass panels and special clamping joints able to provideappropriate structural interaction between glass and steel

278 C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289

components. The faade has overall dimensions B = 11.125 m L = 11.125 m and is obtained by assembling 49 b = 1.5 m h = 1.5 mglass panels having nominal thickness t = 0.016 m. Vertical and hor-izontal / = 12 mm-diameter steel cables are subjected to an initialpretension force Hv,0 = Ho,0 = H0 = 40 kN and linked together at theirintersections. To form a bearing net, the cables are spaced at inter-vals of 1.5 m in both the x and y directions (Fig. 2). Each glass panel isthen four-point supported and connected to the cable-net by meansof stainless steel clamping joints (Fig. 3). The faade prototype isfinally sustained by means of a steel bracing frame made of squaretubes (side length 0.15 m, thickness 0.008 m) and by three furtherdiagonal square tubes (side length 0.10 m, thickness 0.005 m),hinged at the top of the steel frame to provide an appropriate out-of-plane stiffness to the composite steelglass system.

Fig. 3. Schematic view and cross-section of the typical stainless steel clamping joint[15].

2.2. Blast load definition

An explosive event typically represents an exceptional loadingcondition for structures that involves extremely rapid release ofenergy. This energy propagates, generally in thousandths of sec-onds, in the form of light, heat, sound and shock waves. From astructural point of view, the simplest way to properly simulatethe effects of far field explosive events on buildings and systemstakes the form of an air blast shock wave consisting in a pres-suretime history having specific positive and negative phases[35]. Both these positive and negative phases, properly calibratedto describe the assigned design blast load, should be generallytaken into account in simulations, as also suggested by Dharaniand Wei [21] or Teich et al. [29]. The positive phase only, in partic-ular cases, could in fact provide maximum dynamic effects mark-edly higher than those deriving from the total blast shock wave,hence resulting in improper predictions.

In practice, the positive phase, of total duration td , usually takesthe form of the exponential function proposed by Friedlander [36]:

pt p0 1t

td

ekp t

td ; 0 t td ; 1

being Eq. (1) representative of the pressure waveform p(t) in thetime interval comprised between t = 0 (e.g. maximum overpressurep0) and t td (e.g. end of the positive phase, with p(td ) = 0).

Three main parameters can affect the exponential pressurefunction given by Eq. (1), namely (i) the distance between theexplosion source and the invested building (stand-off distance,dTNT), (ii) the height of the explosion source from ground (hTNT)and (iii) the quantity of explosive (equivalent mass of TNT, MTNT).At the same time, the overpressure peak p0 is defined in accordancewith recommendations provided by the TM 5-1300 standard [37].

Fig. 2. Front and side elevations of th

The shape coefficient kp is properly estimated to take into accountthe velocity of decay of the overpressure peak p0 within the inter-val 0 6 t 6 td . Several methods and empirical equations have beenproposed in literature for a practical calculation of kp, based on theassigned blast pressure function (Eq. (1)) and its impulse ratio [35].In this work, according to [38], kp was calculated as:

kp 5:2777Z1:1975; 2

being Z = dTNT/MTNT1/3 [m/Kg1/3] the scaled distance.While the positive phase namely represents the ambient pres-

sure increase and modification due to the occurring explosion,the negative phase of an ideal blast event is characterized by apressure amount which is lower than the reference ambient pres-sure. This negative phase is typically described in the form of a tri-angular shape associated to a negative under-pressure peak pnegand a total duration ttot [36].

In this paper, a medium-level air blast load (Level C-GSA [34])was taken into account to study the behavioural trends of theinvestigated faade prototype. The main parameters of the men-tioned design blast load, based on recommendations of [34] and[37], are the impulse per unit of surface (i = 272 kPa ms), the over-pressure peak (p0 = 42.9 kPa), the duration of the positive phase(td 0:0165 s) and the total impulse duration (ttot = 0.0748 s).The resulting time-varying pressure function is proposed in Fig. 4.

2.3. Dissipative devices

A structural system subjected to an explosive load should begenerally able to be as much as possible flexible and dissipative,

e studied cable-net faade [15].

-2x10 4

0

2x10 4

4x10 4

6x10 4

Pre

ssur

e [P

a]

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Time [s]

BLAST LOADMTNT= 50KgdTNT= 30m

Fig. 4. Blast load time-varying pressure function (Level C-GSA [34]).

C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289 279

in order to decrease the incoming energy and partly dissipate it,hence avoiding the attainment of large deformations and the pos-sible failure mechanisms in its basic components. In the case ofstructural glass systems, various technological advancements havebeen proposed over the last decades to provide additional plasticflexibility after glass cracking and to ensure possible injured. Lam-inated glass, for example, still represents the typical blast resist-ing glass component, since the thermoplastic foils used to bondtogether the glass panels are able to prevent the possible detach-ment of shards after collapse, as well as to increase the dampingcapabilities of the cracked glass panels. Under extreme loadingconditions, however, the use of laminated glass alone cannot pro-vide appropriate flexibility and damping capacities to complexstructural systems such as wide glazing faades.

In this work, based on [3133], different technological solutionsare applied to the faade object of study. First, viscoleastic (VE)connectors able to partly dissipate the incoming energy by meansof viscous phenomena are applied in the point of connectionbetween the glass panels and the cable-net (Fig. 5a). In them, a vis-coelastic rubber layer of total thickness hVE can be used to provideappropriate absorption of the incoming energy. Its key parametersare in fact the elastic stiffness kd and the damping coefficient cd,being [33]:

kd G0AVEhVE

3

and

cd gkdx1

; 4

with x1 the fundamental pulsation of the faade, AVE the shearresisting area of the viscoelastic layer, G and g the shear storageand loss factor respectively of the adopted rubber compound.

Fig. 5. (a) Example of viscoelastic (VE) spider connector, cross

The main advantage of these devices is given by their highpotentiality under high-impulsive as well as moderate/lowdynamic loads. The structural efficiency of VE devices is in factstrictly related to their sliding sVE. The large the VE device slidesand the high is the term of dissipated energy. Nevertheless, com-pared to the total thickness of the viscoelastic layer hVE, this max-imum sliding should not exceed the ratio sVEmax=hVE 2 2:5.

The second typology of devices consists in frictional connectors,having a typical rigid-plastic (RP) behaviour, introduced at thecable ends (Fig. 5b). In this case, the input energy is partly dissi-pated in heat by friction mechanisms that can activate at theattainment of maximum axial forces in the cables Hmax higher thanthe sliding force Fs. As far as the axial forces Hmax in the cable-netdo not exceed Fs, the RP devices do not activate and the glazing sys-tem behaves as a traditional cable-supported faade rigidly con-nected to the structural background. The value of the slidingforce Fs, as well as the position of RP devices, should be conse-quently properly assessed in order to maximize their efficiency.

3. Preliminary analytical assessment and estimation ofmaximum blast effects

The assessment of the structural dynamic behaviour of a com-plex system such as a cable-supported faade under impulsiveloads should be generally performed by means of advanced numer-ical studies and appropriate FE simulations. From a practical pointof view, however, simple preliminary estimations could be ratio-nally obtained by means of approximate analytical formulations.

In [31], for example, an analytical model has been proposed fora first estimation of blast effects in glazing faades sustained by aseries of vertical pre-stressed straight cables. In that specific cir-cumstance, the typical multi-degree-of-freedom (MDOF), single-way cable-supported faade was approximated with an equivalentsingle-degree-of-freedom (SDOF) system subjected to an externaltotal impulse I representative of the positive phase of the assignedblast load.

The essential dynamic parameters of the equivalent SDOF wereestimated referring to Ritzs method, by using the classical energyapproach, and solving the original problem in a static way. Asshown in [31], the mentioned approach can be used for a first esti-mation of maximum deflection, velocity and pre-stressing force inthe cables for single-way planar cable-net faades under impulsiveloads. Although it does not provide information about the stressstate in the glass panels fully neglecting their bending stiffeningcontribution in the global dynamic behaviour of the whole system the approach is in fact suitable for a preliminary assessment ofthe expected dynamic effects of a design explosive load.

-section; (b) example of frictional (RP) device, rendering.

280 C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289

The same analytical approach, based on analogous energy con-siderations, is extended in this work to steel-glass faades sus-tained by a planar net of pretensioned straight cables (Fig. 6).The MDOF cable-net object of study, specifically, is described inthe form of an equivalent SDOF system whose dynamic behaviouris characterized in terms of equivalent mass m* and the equivalentstiffness k*, being rationally negligible, under high-rate impulsiveloads such as explosions, possible structural and aerolastic damp-ing contributions. Differing from [31], moreover, the presence ofa two-way cable-net rather than a single-way bracing system isproperly taken into account. As a result, the equivalent mass ofthe cable-net faade is calculated as [40]:

m M4

5

with M signifying the total mass of the glass panels.At the same time, the equivalent stiffness of the pretensioned

net is estimated as [40]:

k 4Htotlcable

2 sinp

ncables 1

26

being lcable the length of cables and ncables signifying the number ofcables arranged in each main direction of the net (or the averagenumber of vertical ncables,v and horizontal ncables,h cables, whenncables,v ncables,h). In Eq. (6), finally, Htot represents the total initialpretension applied to the bearing system and should be calculatedas:

Htot H0 ncables;v ncables;h

7

that is Htot = 2H0ncables.In these hypotheses, the fundamental period of vibration can be

estimated as:

T1 2pffiffiffiffiffiffim

k

r8

being T1 strictly related to the level of pretension force in the cable-net.

While Eq. (8) provides the fundamental period of vibration ofthe faade affected by the initial pretension force Htot H0,tot only,

Fig. 6. MDOF cable-net faade a

it should not be neglected that the design blast load involves anabrupt and marked increase of axial forces in the cables, thus a sig-nificant increase of the equivalent stiffness k* and a correspondingdecrease of the associated period of vibration T1 .

Once the equivalent dynamic parameters M* and k* are known,the maximum displacement umax and velocity vmax of the cable-netdue to the design blast load can be respectively calculated as:

umax

ffiffiffiffiffiffiffiffiffiI2

Mk

s I

ffiffiffiffiffiffiffiffiffi1

Mk

r9

and

vmax

ffiffiffiffiffiffiffiffiffiffiffiI2

Mm

s 2I

M10

being I = i Sglass the incoming impulse, with Sglass the surface offaade exposed to the assigned blast wave.

While the maximum velocity vmax can be directly estimatedfrom Eq. (10), the corresponding deflection umax should be properlypredicted by means of an iterative procedure [31]. An accurateevaluation of the equivalent stiffness k (Eq. (6)), and therefore ofthe maximum displacement umax (Eq. (9)), should in fact be devel-oped taking into account that, due to the assigned explosion, theinitial pretension force H0 affecting each cable modifies abruptly.In this context, it could be convenient to describe the final config-uration of the deformed cables constituting the cable-net in theform of a parabolic shape function [31]. Certainly, a similarassumption would be able only to approximately identify the glo-bal deformed shape of the studied cable-net. However, it is inter-esting to notice that the total increase Hblast,tot of the total initialpretension H0,tot in the cable-net could be estimated as:

Hblast;tot 83

EcableAcablel2cable

u2max 11

with Ecable the Youngs modulus of steel constituting the cables andumax the maximum deflection given by Eq. (9). As a result, the max-imum total pretension force affecting the cable-net after the explo-sion results:

Htot Hmax;tot H0;tot Hblast;tot 12

nd equivalent SDOF system.

C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289 281

In this context, an iterative process should be performed byreplacing Eq. (12) in Eq. (6), until the obtained value umax (Eq.(9)) remains constant. It is clear that once the iterative procedureis converged and umax is known, the maximum axial force occur-ring in each cable due to the design explosion can be rationallyestimated as:

Hmax H0;tot Hblast;tot

ncables;v ncables;h Hmax;tot

ncables;v ncables;h13

By replacing Hmax in Eq. (6), the corresponding increased equiv-alent stiffness kblast* can be consequently calculated and taken intoaccount in Eq. (8), hence resulting in a modified fundamental per-iod of vibration T1,blast* markedly lower than T1*.

Main results obtained by application of the discussed analyticalprocedure to the studied faade subjected to a Level C air blast loadare collected in Table 1.

The assigned design explosion involves large deflections (1/20the total span), as well as high maximum velocities (15.4 m/s)and axial forces in the cables (1.02 HR, with HR = 160 kN the char-acteristic strength of the adopted cables).

In the same table, additional analytical calculations are pro-posed for the same faade under a Level B-GSA (low-level explo-sion) and a Level D-GSA blast load (high-level explosion),respectively. As shown, independently on the intensity of theassigned explosive loads, due to their impulsive and high-rate nat-ure compared to ordinary loads extreme deformations andforces are exerted on the examined structural system. Furtheradvanced investigations are consequently required.

4. FE-modelling of the cable-net faade and preliminarynumerical investigations

Several numerical models were successively developed in ABA-QUS, in order to investigate in detail the dynamic behaviour of thestudied faade under medium-level blast loads but preserving thecomputational cost of dynamic nonlinear analyses. Dynamic simu-lations, in particular, were performed by means of the implicitABAQUS/Standard solver (Section 4.3).

Prior to the execution of parametric dynamic studies, however,the FE-models were properly assessed through linear modalanalyses to experimental results of free vibration tests presentedin [15] for the same glazing system. Detailed description ofFE-models properties is discussed in Section 4.1.

4.1. FE-model properties

4.1.1. Lumped-mass model (M01)The first geometrically simplified FE-model (M01) consisted in a

net of pretensioned cables (/ = 12 mm) and a series of lumped-masses (mi = 89.64 kg) applied at the interceptions between thecables representative of the self-weight of 49 monolithic1.5 1.5 0.016 m3 glass panels (MDOF system of Fig. 6).

Table 1Analytical estimation of maximum dynamic effects on the studied cable-net faade subjec

Parameter Description

T1 [s] Fundamental period, Eq. (8)

umax [m] Maximum displacement, Eq. (9)vmax [m/s] Maximum velocity, Eq. (10)Hmax [kN] Maximum total pretension in the cables, Eq. (13)T1,blast [s] Expected fundamental period after the explosion

has been occurred, Eq. (8) with H0 Hmax

In it, the cables were described in the form of truss elements(T3D2 elements) composed of stainless steel, being the materialcharacterized in the form of an indefinitely linear elastic mechan-ical behaviour, with Esteel = 1.03 1011 Pa the Youngs modulus,qsteel = 7300 kg/m3 the density and msteel = 0.3 the Poissons ratio.Compared to M02 and M03 FE-models (Sections 4.1.2 and 4.1.3),the main feature of M01 FE-model was given by its marked compu-tational efficiency, since consisting in 800 degrees of freedom(DOFs). Nevertheless, its main limit was represented by fullyneglecting the stiffening contribution of glass panels.

In it, specifically, the initial pretension force (H0 = 40 kN) wasapplied both to vertical and horizontal cables in the form of equiv-alent imposed displacements. In the case of the vertical cables,pinned at the lower end (Ux = Uy = Uz = 0), a vertical displacement(y-direction) was applied at their top end. Similarly, for the horizontalcables pinned at their left end (Ux = Uy = Uz = 0), an horizontal dis-placement (x-direction) was imposed at their right end.

The effect of clamping joints (Fig. 3) was then taken into accountin the form of a series of translator connectors able to link togetherthe nodes of vertical and horizontal cables at their interceptions. Inthis manner, relative rotations were prevented, so that the couplednodes of the cable-net could undergo the same out-of-plane deflec-tion when subjected to orthogonal loads, like for example externalpressures acting on the glass panels surface. A further implicitadvantage deriving from this modelling assumption, consisted inthe separate and independent application of the initial pretensionforce to vertical and horizontal cables respectively.

In accordance with the experimental measurements presented in[15] for the cable-net without glass panels (nexp 0.1%), structuraland aerolastic damping contributions were preliminary neglected.

4.1.2. Full cable-glass model (M02)In the case of the full cable-glass model (M02), the main com-

ponents of the faade were described with careful attention, inorder to appropriately simulate their structural interaction underhigh-strain impulsive loads such as explosions.

The prestressed cable-net alone, as well as the mechanicalinteraction between vertical and horizontal cables, was describedas for the model M01 (Section 4.1.1). In addition, clamped jointsand glass panels were also properly taken into account. All the con-sidered modelling assumptions typically resulted in detailed geo-metrical and mechanical description of the studied faade, butalso in marked increase of the involved DOFs (70,000), comparedto M01 FE-model. Specifically, three-dimensional four-node homo-geneous shell elements with reduced integration formulation (S4Relements available in the ABAQUS library [39]) were used todescribe the monolithic glass panels, with t = 0.016 m the totalnominal thickness. Default parameters were taken into accountfor the hourglass control. Based on preliminary studies notincluded in this paper, an almost regular and structured mesh pat-tern was used, with lmesh = 0.1 m the average size for each1.5 1.5 m glass sheet (Fig. 7). At the corners of each panel closeto the clamping joints and along the panel edges, a refined mesh

ted to air blast loads. i: impulse per unit of surface; p0: overpressure peak.

Level B (low) Level C (medium) Level D (high)i = 168 kPa ms i = 272 kPa ms i = 439 kPa msp0 = 30.4 kPa p0 = 42.9 kPa p0 = 62.6 kPa

0.578 0.578 0.5780.526 0.699 0.9129.47 15.33 24.74109 163 2490.350 0.286 0.231

Fig. 7. Detail of glass-to-cables connection and adopted mesh pattern (ABAQUS/Standard, M02 FE-model).

282 C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289

pattern and a free meshing technique were used. In this case, theminimum element size was set equal to lmesh 0.003 m (Fig. 7).

The final choice for the adopted mesh pattern globally derivedfrom an appropriate balance between mesh refinement, corre-sponding predictions in the glass panels and main purpose of thisresearch work. The investigation of possible damage mechanismsand post-cracked behavioural trends for the same faade underblast loads, hence requiring the implementation of specific damagemechanical models for glass (e.g. [2327,41]), would in fact requirean extremely refined mesh pattern, being those material models(e.g. the brittle cracking ABAQUS option [39]) generally strictlydependent on the characteristic size of elements [42].

Concerning the mechanical characterization of toughened glass,in accordance with [3133], an isotropic, linear elastic characteris-tic behaviour was in fact defined, with Eglass = 70 GPa the Youngsmodulus, qglass = 2490 kg/m3 the density and mglass = 0.23 the Pois-sons ratio. As a result, possible brittle cracking of glass paneswas fully neglected. From a numerical point of view, this assump-tion directly manifested in geometrical and mechanical simplifiedmodelling hypotheses, but anyway in reasonable FE-predictions forthe studied faade, as discussed in Sections 45. Glass is in fact amaterial characterized by typical high resistance in compressionand brittle behaviour in tension, being its nominal quasi-staticcharacteristic strength generally comprised between 45 MPa(annealed glass) and 120 MPa (fully tempered glass) often repre-sentative of the main influencing parameter for designers [43].Under high-strain loads, however, conventional quasi-static tensilestrengths are usually replaced with magnified corresponding val-ues able to take into account strain rate effects. Under explosions,having a typical duration of 0.0050.025 s, the magnified tensilestrength recommended by design manuals and standards fortoughened or thermally tempered glass as for the studied faade is 160 MPa [44]. Further references are available for glass underblast loads, but certainly the estimation of the actual tensilestrength under high-strain rates is rather difficult to exactly pre-dict. Blast design strength values for tempered glass can be in factfound comprised between 145 MPa and209 MPa [45,46], thus amagnifying dynamic coefficient at least equal to 1.2 is generallyaccepted for FT glass. Comparative discussion of technical docu-ments recommendations and assumptions is provided in [47].

Experimental studies have been performed also in [48], to investi-gate the dynamic increase of both compressive and tensilestrengths for glass under high-strain loads. Data measurementsand high-speed camera acquisitions obtained from tests performedon small cylindrical glass specimens in the range from 103 to103 s1 highlighted that the compressive strength and Young mod-ulus of glass are slightly sensitive to strain-rate effects. Conversely,the quasi-static tensile strength manifested marked dependencyon strain-rate effects and an appreciably increased dynamicresistance.

In these hypotheses, the occurring of possible failure mecha-nisms in the M02 FE-model was indirectly prevented by continu-ously monitoring the maximum tensile stresses in glass, henceensuring the exceeding of the reference magnified resistance (Sec-tions 45).

Careful consideration was then dedicated to the modelling ofthe clamping joints, since constituting the key component ofnumerical simulations. The typical metallic joint consisted of fourrigidly connected stainless steel beams (B31 elements), represen-tative of the nominal geometry of the metal fasteners. A weld con-nector, able to provide a fully bonded connection between therelative displacements (ux, uy, uz) and rotations (rx, ry, rz) of thesefour beams was used, hence ensuring the desired restraining effectbetween them. Concerning the glass panel-to-joint and joint-to-cable structural interaction, each clamping joints was attached tothe adjacent glass panels by means of appropriate join and slide-plane connectors (Fig. 8). The first typology of connectors, able toprohibit possible relative displacements (ux, uy, uz) in the interestednodes, was inserted at the top-left corner of each glass panel. Slide-plane connectors able to guarantee small relative displacements inthe plane of glass sheets were used, conversely, for the three othercorners of each panel. In this manner, the attainment of peaks ofstress at the connection points of the glass panels was prevented,especially when applying the initial pretension force in the cables.

Finally, the structural interaction between the so modelledclamped joints and the pretensioned cable-net was guaranteed bymeans of a series of two additional connectors (Fig. 8, Connector1 and Connector 2), able to provide in presence of externalpressures orthogonal to the surface the faade the same out-of-plane deflection for the glass panels and the cable-net in the inter-ested nodes.

As also discussed in [15,31,32], the mass of clamping joints wasneglected. At the same time, since characterized by a negligiblestiffness [26], the layers of structural silicone sealant interposedbetween the adjacent glass panels were not taken into account.

With reference to possible structural and aerolastic dampingeffects [15], shock excitation experiments performed on thecable-net prototype with the glass panels highlighted as expected a marked increase of dissipative capabilities for the studied sys-tem (nexp 3.4%), compared to the cable-net alone.

In this context, it should be noticed that the obtained experi-mental value is rather in agreement with simple analytical calcula-tions derived from literature. Assuming the total damping rationTOT = nstructural + naerolastic 3.4% as the sum of structural and aero-lastic damping terms, the test result can be in fact rationallyassessed, being nstructural 1% [49,50] the conventional structuralcontribution and naerolastic 2.43% the aerolastic term, with:

naerolastic cd qair Sglass vmax

2Mtotx1: 14

In Eq. (14), cd = 1 is the drag coefficient [23], qair = 1.225 kg/m3

represents the density of air, Sglass = 110.25 m2 is the faade surfaceexposed to blast, while Mtot = 4392 kg is the total mass of glasspanels. Moreover, vmax represents the velocity attained by the mov-ing faade due to the design explosion, whereas x1 is its funda-mental frequency of vibration. Based on Eqs. (10) and (8),

Fig. 8. Detail of a clamping joint (ABAQUS/Standard, M02 FE-model).

Tshell = 0.07916 s Tbeam = 0.07938 s(a) (b)

Fig. 9. Fundamental modal shape of a point-supported glass panel. (a) shell modeland (b) equivalent diagonal beam model (ABAQUS/Standard).

C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289 283

vmax = 15.33 m/s and x1 = 2p/T1 = 10.88 rad/s respectively, henceresulting in a total damping ratio nTOT 3.43% which well agreeswith shock excitation predictions [15].

The so calculated damping contribution was described in theM02 FE-model as a Rayleigh mass proportional term. Preliminarynumerical studies not included in this paper confirmed the negligi-ble effects of a similar damping term on the global dynamicresponse of the studied faade under high-rate impulsive loads.As a result, damping was successively fully neglected, as in the caseof the cable-net alone (M01 FE-model).

4.1.3. Equivalent cable-diagonal beam model (M03)In the third numerical model (M03), geometrical simplifications

were taken into account for the description of the glass panels, inorder to reduce the computational weight of model M02 but toprovide, at the same time, appropriate dynamic predictions forthe studied faade.

Specifically, the pretensioned cable-net and the clamped jointswere described as for the model M02. Conversely, in accordancewith the Grashofs method [51], the monolithic glass panels wereschematized in the form of two diagonal beam elements (B31)composed of glass, having total thickness t = 0.016 m and equiva-lent width beq.

This modelling assumption allowed to preserve the descriptionof each faade component (e.g. cables, connectors and glass panels)and the physical interaction between them, but at the same time toobtain a computationally efficient FE-model (7000 DOFs, that is1/10 than the corresponding M02 FE-model).

In doing so, the equivalent width beq was calculated to guaran-tee the same bending stiffness between each nominal glass paneland the coupled diagonal beams. By equalling the maximumdeflection of a point-supported panel under uniformly distributedload q and a simply supported beam subjected to the resultingmid-span force F = ql2/2, with l = b = h = 1.5 m the size of eachsquare panel, beq was in fact calculated as:

beq ffiffiffi2p

l3

2:4 1 m2glass

l2 1:244l 15

The t beq ffiffiffi2p

l diagonal beams were then linked together attheir mid-span node by means of a tie constraint, able to providefull coupling and interaction between them. At the same time,the self-weight of glass was described in the form of lumpedmasses mi.

Although the Grashofs method represents an approximateapproach, preliminary static, nonlinear geometry numerical analy-ses performed on a single point-supported shell glass panel and

the corresponding equivalent diagonal beam FE-model resultedin a very good agreement in terms of maximum deflections (3.8%of discrepancy), maximum tensile stresses close to the point sup-ports (4.8% of discrepancy) and maximum reaction forces (almostcoincident) transmitted to the structural background.

At the same time, further modal analyses performed on boththese FE-models manifested an almost identical fundamental per-iod of vibration (0.28% of discrepancy, Fig. 9). It was thus expected,that the FE-model M03 could provide appropriate dynamic predic-tions for the studied faade.

4.2. Assessment of FE-models and dynamic properties

Linear modal analyses were performed in ABAQUS/Standardusing the models M01, M02 and M03 respectively, in order to com-pare the obtained fundamental periods of vibrations and the corre-sponding modal shapes to experimental results obtained by Fenget al. from free vibration tests performed on their scaled prototype[15].

Compared to experiments, the obtained fundamental periods ofvibration highlighted as expected that the bending stiffness ofthe glass panels slightly affects the dynamic behaviour of the stud-ied glazing system (3% of discrepancy). First periods of vibrationresulted respectively equal to T1,M01 = 0.581 s, T1,M02 = 0.569 s and

1 2 3 4 5 6Point of measure

0.4

0.6

0.8

1.0

Mod

al a

mpl

itude

M01M02M03TEST

Fig. 11. Assessment of FE-models M01, M02 and M03 (ABAQUS/Standard) toexperimental modal amplitudes [15] (first vibration mode).

284 C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289

T1,M03 = 0.567 s, thus rather in agreement with the reference testprediction (T1,test = 0.580 s [15]), as well as with the analyticalmodel presented in Section 2 (Eq. (8) and Table 1, T1* = 0.578 s).

Concerning the fundamental modal shape of the examinedfaade, moreover, calculations performed on the amplitudes of themodal displacements recorded at 6 points of measure (Fig. 10a),compared to the corresponding free vibration measurements [15],highlighted that the simplified model M01 generally tends to over-estimate the actual flexibility of the faade (+5.8% average discrep-ancy), being not able to take into account the possible bendingstiffening contribution of the glass panels (Fig. 11). At the sametime, the model M02 more geometrically accurate provides avery good agreement with experimental measurements (+0.17%average discrepancy). The model M03, finally, although geometri-cally simplified but markedly computationally efficient, comparedto the corresponding M02 FE-model, is anyway able to rationallyreproduce the expected dynamic behaviour for the studied system(+1.07% average discrepancy). Good level of accuracy was in factfound between M03 predictions and the reference test measure-ments also for higher modes, in terms of vibration periods (e.g.T1,M03 = 0.361 s for the third vibration mode, with T3,test = 0.354 sthe corresponding experimental value [15]).

Based on this preliminary assessment, further parametricdynamic nonlinear investigations were performed on the M03FE-model, as discussed in Section 4.3.

4.3. Dynamic behaviour of the glazing system under blast loads

Incremental dynamic analyses characterized by a total durationof 32 s were performed on M01, M02 and M03 FE-models. As high-lighted in [31], an explosive event involves in cable-supportedfaades an abrupt increase of axial forces in the bearing cables.While single-way cable supported faades (e.g. [31,32]) aretypically characterized by high flexibility, however, two-waycable-net faades are generally stiffer. Their structural behaviourunder high-strain impulsive loads could consequently involveextreme damage scenarios and peaks of stress in their basiccomponents that should be properly predicted.

In this work, nonlinear dynamic simulations have been per-formed in ABAQUS/Standard. The typical simulation consisted inthree separate steps. In the two first steps, having both a totalduration of 1 s, the initial pretension force was separately assignedto horizontal and vertical cables. Once pretensioned the bearingcable-net, during the third step (duration 30 s) the glazing systemwas subjected to an explosive event described in the form of an

(a) TM01= 0.581 s (b) TM02= 0

Fig. 10. Fundamental modal shapes for FE-models (a) M01 (800 DOFs), (b

impulsive load agreeing with the pressuretime function proposedin Fig. 4. Maximum time increment was set equal to 0.005 s.

The assigned blast load, specifically, was described respectivelyin the form of nodal forces Fi applied to each lumped-mass mi(model M01), distributed pressures q acting on the surface of glasspanels (model M02) and equivalent nodal forces Fi applied to themid-span node of each diagonal glass beam (model M03).

4.3.1. Simplified M01 modelThe geometrically simplified M01 model was preliminary inves-

tigated due to extreme computational efficiency in order toassess the accuracy of the analytical procedure presented in Sec-tion 3, as well as to highlight the possible effects of the assignedblast load.

In a preliminary phase of this work, for example, it was calcu-lated that the maximum deflection of the studied faade affectedby ordinary wind loads (qwind = 0.75 kN/m2) is uM01max;wind 0:025 m(1/450 of the structural span). The obtained average velocity,for the same loading condition, is moderate (vM01max;wind 0:14 m=s),compared to maximum effects typically associated to extremeloading scenarios (e.g. Table 1). Similarly, the increase of maximumaxial forces in the bearing cables is limited, compared to the initialpretension level (HM01max;wind 45 kN; that is H

M01max;wind 1:1H0).

Conversely, explosions represent an exceptional loading condi-tion for buildings, and a prefixed level of damage should beexpected. The studied cable-net system, for example, should beable to implicitly provide an efficient support to the curtain wall.Since the ultimate strength for the used cables is HR = 160 kN, how-ever, the occurring of elevated axial forces should be avoided. Steelcables have in fact typical brittle-elastic behaviour and their

.569 s (c) TM03= 0.567 s

) M02 (70,000 DOFs) and (c) M03 (7000 DOFs). ABAQUS/Standard.

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Time [s]

-20

-16

-12

-8

-4

0

4

8

12

16

20

Vel

ocity

[m/s

]

No devicesPos.Pos. and neg.

Fig. 13. Maximum velocity in the cable-net (ABAQUS/Standard, M01 FE-model, nodevices).

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Time [s]

0

25

50

75

100

125

150

175

200

Axi

al fo

rce

[kN

]

No devicesPos.Pos. and neg.

H0

HR

Fig. 14. Maximum axial force in the cables (ABAQUS/Standard, M01 FE-model, nodevices).

C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289 285

rupture would cause the collapse of the entire suspended curtain-wall. At the same time, the possible cracking of glass panels shouldbe possibly prevented.

Main results obtained from dynamic simulations performed onthe M01 model are proposed in Figs. 1214 respectively, in theform of maximum deflections, maximum velocities and maximumaxial forces in the bearing cables.

As shown, the positive phase of blast alone involves maximumeffects that are markedly onerous for the studied system. The max-imum deflection (uM01max 0:78 m; 1/15 the total span), velocity(vM01max 16:3 m=s) and forces in the cables (H

M01max 196 kN) are

rather in agreement with the corresponding analytical predictionscollected in Table 1 (Level C blast load, Hmax = 163 kN). At the sametime, it is interesting to notice that the obtained value for the max-imum pretension force HM01max 196 kN would provide, by means ofEq. (8), a vibration period TM011;blast 0:261 s 0:45T

M011 well agreeing

with the estimated final vibration period T1;blast = 0.286 s proposedin Table 1.

Although the numerical results collected in Figs. 1214 confirmthe effectiveness of the SDOF analytical procedure for the prelimin-ary assessment of the cable-net faade dynamic response underthe positive phase of blast only, it should be anyway highlightedthat both the SDOF procedure and the M01 model do not take intoaccount the possible bending stiffening contribution of the glasspanels, as well the possible beneficial effects due to the negativephase of the assigned blast load.

The effect of the total impulsive pressure function depicted inFig. 4 can be easily noticed in the same Figs. 1214. For the studiedfaade, as expected, the negative phase of the design explosionreduces in fact up to 30% the maximum effects of the positivephase alone. As a result, the maximum deflection is uM01max 0:53 m,that is 1/20 the total span of the faade. The maximum velocityof the oscillating glazing system and the corresponding maximumaxial forces in the cables are also markedly reduced, comparedto the same faade under the positive phase only of blast,being vM01max 8:2 m=s and H

M01max 110 kN respectively (with

HM01avg 66 kN the average force after the explosion).

4.3.2. M02 and M03 modelsFinal assessment of numerical models under medium-level

blast loads was performed on M02 and M03 glazing systems sub-jected to the total design blast load defined in Fig. 4. As shown inFig. 15, an acceptable agreement was found between them. Dueto the presence of glass panels having stiffening and stabilizingeffects for the entire cable-supported system the maximumdeflection in the cable-net resulted equal to 1/28 the total span

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Time [s]

-1.2

-0.9

-0.6

-0.3

0.0

0.3

0.6

0.9

1.2

Dis

plac

emen

t [m

]

No devicesPos.Pos. and neg.

Fig. 12. Maximum deflection in the cable-net (ABAQUS/Standard, M01 FE-model,no devices).

of the faade, thus sensibly lower than the corresponding M01 pre-dictions (Fig. 15a).

In terms of maximum tensile stresses in the glass panels, simu-lations performed on M02 and M03 models confirmed that maxi-mum peaks are located near the point-supports. The typicaldistribution of maximum in-plane stresses obtained from the M02and M03 FE-models is proposed in Fig. 15b for the central panel ofthe faade (e.g. the panel subjected to maximum overall deflections,due to blast pressure), in the form of blue (min)-to-red (max) con-tour plot and vectorial representation, respectively. Despite theapproximate modelling assumptions of M03 model, acceptable cor-relations were generally found with the corresponding M02 model.In Fig. 15c, for example, tensile stresses attained close to the cornerof the same glass panel depicted in Fig. 15b are shown.

At the same time, numerical predictions obtained from boththe FE-models confirmed the assumption of an indefinitely linearelastic material for glass, being the obtained maximum tensilestresses markedly lower than the reference magnified resistance(Section 4.1.2).

Based on these statements and comparisons proposed in Fig. 15,parametric numerical simulations discussed in Section 5 were per-formed on further M03 models only.

5. FE-modelling of the faade equipped by dissipative devices

In a subsequent numerical investigation phase, different typol-ogies of dissipative devices were introduced in the cable-supported

2.00 2.25 2.50 2.75 3.00 3.25 3.50

Time [s]

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Dis

plac

emen

t [m

]

M01M02M03

2.00 2.25 2.50 2.75 3.00 3.25 3.50

Time [s]

0

10

20

30

40

50

60

Tens

ile st

ress

[MPa

]

M02M03

(a) (c)

M02 FE-model M03 FE-model(b)

Fig. 15. (a) Maximum deflections and (c) tensile stresses in the central glass panel (ABAQUS/Standard, M02 and M03 FE-models, no devices). (b) Typical distribution ofmaximum in-plane stresses due to the applied blast load (ABAQUS/Standard; M02 (blue (min)-to-red (max) contour plot) and M03 (vectorial representation) FE-models).Example for the central glass panel. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

286 C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289

faade, both at the ends of the bearing cables and at the point-supports of the glass panels, in order to analyze their effectivenessand to identify the most advantageous solution.

Studies were dedicated to faades equipped by (i) viscoelasticdevices only, (ii) frictional devices at the cable ends, (iii) combinedviscoelastic and frictional devices.

Based on previous works [3133], the reference M03 modelwas properly modified. Viscoelastic connectors, specifically, weredescribed in the form of equivalent axial springs having elasticstiffness kd and damping ratio cd, and directly connected to theglass corners. Frictional devices, indeed, were applied at the cableends in the form of rigid-plastic springs with sliding force Fs. Para-metric studies, partly discussed in Section 5, were then carried-outin order to assess the possible structural efficiency of the proposeddevices for the investigated cable-net faade.

5.1. Numerical assessment of VE and RP devices structural capabilities

5.1.1. Viscoelastic devicesIn general, comparative calculations highlighted that VE devices

can have important and efficient mitigating role in the globaldynamic behaviour of the studied faade, if properly calibrated.VE curves collected in Fig. 16, for example, are proposed for a

faade equipped by viscoelastic connectors having an elasticstiffness kd = kcable, with kcable the axial stiffness of the bearingcables. Based on a preliminary estimated stiffness kd and onEq. (4), the corresponding damping ratio cd was calculated bytaking into account the fundamental pulsation of the studiedfaade, with g = 0.6 for the rubber compound [32].

In this context, it should be noticed that the optimal ratiobetween the device stiffness and the cable stiffness was found tobe close to the unit. In the case of the single-way supported faadeinvestigated in [32], for example, the optimal kd/kcable ratio was40, due to the typically different dynamic behaviour of thatglazing system.

Certainly, VE devices add high damping capabilities in thefaade, hence resulting in markedly reduced tensile stresses in theglass panels (e.g. Fig. 16c, where the tensile stresses at the pointsupport of the central glass panel are proposed) and consequentlylower axial forces in the cables (Fig. 16b).

The damping contribution offered by the sliding mechanism ofVE layers strongly modifies the typical energy balance of the tradi-tional, conventionally restrained glazing system (Fig. 17). Since theglass panels are the first component of the faade that is exposed tothe incoming explosion, the viscous dissipation offered by VEdevices (Fig. 17a) primarily manifests in a reduced kinetic energy

2.00 2.25 2.50 2.75 3.00 3.25 3.50

Time [s]

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Dis

plac

emen

t [m

]

No devicesVEHRPVE+HRP

2.00 2.25 2.50 2.75 3.00 3.25 3.50

Time [s]

0

20

40

60

80

100

120

Axi

al fo

rce

[kN

]

No devicesVEHRPVE+HRP

H0

(a) (b)

2.00 2.25 2.50 2.75 3.00 3.25 3.50

Time [s]

0

10

20

30

40

50

Tens

ile st

ress

[MPa

]

No devicesVEHRPVE+HRP

(c)

Fig. 16. (a) Maximum deflections, (b) axial forces in the cables and (c) tensile stresses at the corner of the central glass panel (ABAQUS/Standard, M03 FE-model).

C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289 287

stored by the glass panels (Fig. 17b), and consequently in a limitedstrain energy transferred to the cables (Fig. 17c). This energy bal-ance improvement results in 50% decrease of maximum stressesin glass (Fig. 16c) and 20% reduction of maximum axial forcestransmitted to the cable-net (Fig. 16b).

5.1.2. Frictional devicesA further solution was successively numerically investigated

and frictional dissipative devices were applied at the end of thehorizontal cables only (HRP). Based on preliminary analytical esti-mations (Table 1), the sliding force of frictional connectors was setto Fs = 80 kN, that is two times the initial pretension force and halftheir characteristic tensile strength HR.

As expected, simulations highlighted that the introduction ofmono-directional (HRP) frictional devices strongly modifies theglobal dynamic response of the studied glazing system. Thecable-net is in fact partly deprived by the horizontal bearing cables,and after the activation of frictional devices the vertical cablesmust sustain the faade.

As shown in Figs. 16 and 17, however, this technical solutiondoes not provide efficient improvement in the dynamic responseof the traditional faade. Since HRP devices mainly act at the levelof the cable-net only, as expected, maximum tensile forces in theglass panels are not positively affected by the presence of the HRPmechanism (Fig. 16c; 1% decrease of maximum tensile stresses).In terms of maximum forces in the cable-net, the increase of pre-tension in the vertical cables is partly reduced. In this case, due to

activation of HRP devices, its final value is in fact almost equal tothe pre-established sliding value Fs (Fig. 16b; 23% decrease ofmaximum axial forces). At the same time, the partial release ofthe horizontal cables due to the activation of HRP devices allowsto further increase the flexibility of the glazing system, as it canbe shown from Fig. 16a and b (17% increase of fundamental per-iod of vibration). Detailed investigation of numerical predictionshighlighted that frictional devices activate almost simultaneously,when the explosion invests the faade, and their measured aver-age sliding, although moderate (0.003 m for the devices at thetop and at the base of the faade, 0.01 m for the central cablessubjected to maximum overall out-of-plane deflections), allowsto dissipate by friction up to half the total incoming energy(Fig. 17a).

5.1.3. Combined viscoelastic and frictional devicesIn conclusion, both VE and HRP were applied to the examined

glazing system. Based on previous investigations performed onthe faade equipped by VE devices or HRP devices only, the maininput parameters of both the mechanisms were set respectivelyequal to kd = kcable and Fs = 2H0.

As highlighted from Figs. 16 and 17, the efficiency of both thedevices is maximized, being part of the incoming blast energy dis-sipated both by viscous damping and friction phenomena.

The interaction of multiple devices, consequently, manifests inmarked reduction of tensile stresses in the glass panels (50%),as well as in mitigation of blast effects in the bearing cables

2.00 2.25 2.50 2.75 3.00 3.25 3.5

Time [s]

0.0x100

2.0x104

4.0x104

6.0x104

8.0x104

1.0x105

1.2x105

Dis

sipa

ted

ener

gy [J

]

Total incoming energyVE, viscous energyHRP, friction energyVE+HRP, viscous energyVE+HRP, friction energy

2.00 2.25 2.50 2.75 3.00 3.25 3.5

Time [s]

0.0x100

2.0x104

4.0x104

6.0x104

8.0x104

1.0x105

1.2x105

Kin

etic

ene

rgy

[J]

Total incoming energyNo devicesVEHRPVE+HRP

(a) (b)

2.00 2.25 2.50 2.75 3.00 3.25 3.50Time [s]

0.0x100

1.0x104

2.0x104

3.0x104

4.0x104

5.0x104

Stra

in e

nerg

y [J

]

No devicesVEHRPVE+HRP

(c)

Fig. 17. (a) Dissipated energy; (b) kinetic energy in the faade and (c) strain energy in the cable-net (ABAQUS/Standard, M03 FE-model).

288 C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289

(30%), being the faade subjected due to VE devices to areduced impulsive load.

Certainly, a proper calibration of combined VE and RP devices,as well as a correlation of their input parameters to the faademechanical and geometrical properties, is fundamental for theoptimization of their structural effectiveness. In any case, the dis-cussed results highlighted through application to a case studythe potentiality of the examined solutions. It is thus expected thatcritical discussion of comparative simulations could provide anappropriate background for further extended developments andapplications.

6. Summary and conclusions

In the paper, the structural behaviour of a glazing faade sup-ported by a two-way straight pretensioned cable-net has beeninvestigated through advanced numerical models. The faadeobject of study, experimentally analyzed under seismic loads inearlier contributions, has been in this work subjected to high-rateexplosive loads. As known, impulsive pressures due to explosionstypically involve in the invested structural systems extreme defor-mations and stresses, being these glazing faades generallydesigned to resist ordinary loads only.

Prior to development of advanced finite-element (FE) numericalmodels, simplified analytical SDOF formulations based on energyconsiderations have been proposed and discussed, in order to per-

form a preliminary estimation of maximum expected effects in thestudied system.

Dynamic nonlinear simulations have then been performed onappropriate finite-element (FE) numerical models calibrated toexperimental dynamic parameters recalled for the same faade from earlier contributions of literature.

Careful consideration has been paid, during the numerical mod-eling phase, to the assessment of possible effects due to interactionbetween glass panels and cables, when subjected to dynamicimpulsive loads. For this purpose, three different FE-models havebeen presented and compared. The first one (M01), being a geo-metrically simplified lumped-mass model, provided only approxi-mate estimations of the expected maximum effects in the cables,due to the lack of glass panes. In any case, comparison of M01 pre-dictions to SDOF analytical calculations generally manifestedrather good agreement between them, hence confirming the valid-ity of the approach. Further FE models able to include the bendingstiffening contribution of the glass panels have been successivelyimplemented. In the case of the M02 model, a geometricallydetailed description of cables, glass panels and connectors hasbeen provided. Successively, in order to reduce the computationalweight of model M02 but preserve its accuracy, a third FE-model(M03) has been developed. In this latter case, due to the approxi-mate description of glass panels in the form of well-calibrated,equivalent strips, a marked increase of computational efficiencywas obtained, as well as a rather appreciable agreement betweenM02 and M03 dynamic predictions of maximum effects of blastin the main faade components. Based on preliminary investiga-

C. Bedon, C. Amadio / Engineering Structures 79 (2014) 276289 289

tions, extended parametric dynamic analyses have been conse-quently performed on M03 FE-models.

Three typologies of devices have been introduced in the inves-tigated faade, namely at the connection between glass panelsand cables, as well as at the cable ends.

The structural efficiency under explosive loads of possible (i)viscoelastic connectors, (ii) frictional devices at the cable endsand (iii) combined multiple (i) and (ii) devices has been high-lighted by means of advanced parametric dynamic nonlinear anal-yses. Although further extended studies are required, exploratoryinvestigations emphasized the high potentiality of the proposeddissipative systems, hence suggesting possible successful applica-tions in glazing faades sustained by two-way straight cable-netsand subjected to high-strain blast pressures.

References

[1] Br L, Geiler B. MULTITERM-Fassade ein modulares Stahlfassadensystemfr kombinierte Anwendungsflle. Stahlbau 2003;72(12):8338.

[2] SCI Steel Knowledge P396. New Beijing Poly Plaza Cable-Net Wall StructuralStainless Steel Case Study 0.9; 2011 .

[3] Sobek W, Straub W, Schmid A. Horizon Serono Konstruktion des weltweitgrten zu ffnenden Glasdaches und der darunterliegenden Forumfassade.Stahlbau 2009;78(1):110.

[4] Kirchhoff J, Vaglio J, Patterson M. Double-Skin cable-net faade case study:loyola information commons. In: Proceedings of BESS2010: high performancebuilding enclosures practical sustainability symposium at cal-poly Pomona;2010.

[5] Sobek W, Weiss I. Eine Stahl-Glashalle als neuer zentraler Eingangsbereich derUniversitt Bremen. Stahlbau 2001;70(10):30913.

[6] Eekhout M, van de Rotten P. Cable stayed glass faade in the market hall Rotterdam. In: Proceedings of challenging glass 4 & COST action TU0905 finalconference, Lausanne, Switzerland; 2014.

[7] Schlaich J, Schober H, Moschner T. Prestressed cable net faades. Struct Eng Int2005;15(1):369.

[8] Schobe H, Scheider J. Developments in structural glass and glass structures.Struct Eng Int 2004;14(2):846.

[9] SOM-Skidmore Owings & Merrill (www.som.com). Rocker Faade SupportSystem, Poly Corporation Headquarters, Beijing. .

[10] Schlaich Bergermann und Partner, Screenwall Hotel Kempinski. .

[11] Vyzantiadou MA, Avdelas AV. Point fixed glazing systems: technological andmorphological aspects. J Constr Steel Res 2004;60(8):122740.

[12] Saitoh M, Okada A, Imamura R. Study on glass supporting system pinched atcorner structural characteristics and structural design method. In: Proceedingsof international symposium on theory design and realization of shell andspatial structures; 2001.

[13] Feng RQ, Wu Y, Shen SZ. Working mechanism of single-layer cable netsupported glass curtain walls. Adv Struct Eng 2007;10(2):18395.

[14] Feng RQ, Ye JH, Wu Y, Shen SZ. Nonlinear response spectra of cable net faades.Soil Dyn Earthquake Eng 2011;32:7186.

[15] Feng RQ, Zhang LL, Wu Y, Shen SZ. Dynamic performance of cable net facades. JConstr Steel Res 2009;65(12):221727.

[16] Chan SL, Liu Y, Lee A. Nonlinear analysis of pre-tensioned glass wall faade bystability function with initial imperfection. Front Arch Eng China2010;4(3):37682.

[17] Weng ZJ, Yin LF, Shan J, Tang G, Huang W. Static analytical method of single-layer plane canle net structures under bidirectional uniform load: basiccontrol equations and logarithmic solution. Eng Mech 2012;29(12):721.

[18] Mesda Y. Analytical study of the cable-truss systems on the glass curtain wallswith vertical uses. Engineering 2013;5:81926.

[19] Wedding WC, Lusk BT. Novel method to determine blast resistant glazingsystem response to explosive loading. Measurement 2012;45:14719.

[20] Zhao S, Dharani LR, Liang X. Analysis of damage in laminated architecturalglazing subjected to blast loading. Adv Struct Eng 2008;11:12934.

[21] Dharani LR, Wei J. Dynamic response of laminated glass panels subjected toblast loading. Structures under shock and impact VIII, Crete. Greece2004;15:18190.

[22] Morison C. The resistance of laminated glass to blast pressure loading and thecoefficients for single degree of freedom analysis of laminated glass. PhDThesis, Cranfield University; 2007.

[23] Larcher M, Solomos G. Laminated glass loaded by air blast waves experiments and numerical simulations. Joint Research Centre TechnicalNote, Pubsy JRC57559; 2010.

[24] Larcher M, Solomos G, Casadei F, Gebbeken N. Experimental and numericalinvestigations of laminated glass subjected to blast loading. Int J Impact Eng2012;39:4250.

[25] Hooper PA, Sukhram RAM, Blackman BRK, Dear JP. On the blast resistance oflaminated glass. Int J Solids Struct 2012;49:899918.

[26] Weggel DC, Zapata BJ. Laminated glass curtain walls and laminated glass pliessubjected to low-level blast loading. J Struct Eng 2008;134:46677.

[27] Zhang X, Hao H, Ma G. Parametric study of laminated glass window responseto blast loads. Eng Struct 2013;56:170717.

[28] Bedon C, Amadio C, Sinico A. Structural stability of compressed monolithic andlaminated glass elements under blast loads. In: Proceedings of glasscon globalconference innovation in glass technology, 710 July 2014, Philadelphia,Pennsylvania Convention Center, USA, pp. 3452 (USB Flash Drive); 2014.

[29] Teich M, Warnstedt P, Gebbeken N. The influence of negative phase loading oncable net faade response. J Arch Eng 2011. http://dx.doi.org/10.1061/(ASCE)AE.1943-5568.0000083 (in print).

[30] Wellershoff F, Lori G, Zobec M, Osterland K. Structural design of blast enhancedcable net facades. In: Proceedings of COST Action TU0905 Mid-termConference on Structural Glass, Porec, Croatia; 2013.

[31] Amadio C, Bedon C. Elastoplastic dissipative devices for the mitigation of blastresisting cable-supported faades. Eng Struct 2012;39:10315.

[32] Amadio C, Bedon C. Viscoelastic spider connectors for the mitigation of cable-supported faades subjected to air blast loads. Eng Struct 2012;42:190200.

[33] Amadio C, Bedon C. Multiple dissipative devices for blast-resisting cable-supported glazing faades. Model Simul Eng, vol. 2013, article ID 964910;2013.

[34] GSA-TSO1-2003. Standard test method for glazing and window systemssubject to dynamic overpressure loadings. U.S. General ServiceAdministration; 2003.

[35] Goel MD, Matsagar VA, Gupta AK, Marburg S. An abridged review of blast waveparameters. Defence Sci J 2012;62(5):3006.

[36] Bulson P. Explosive loading of engineering structures. A history of research anda review of recent developments. London: E&F Spon; 1997.

[37] TM 5-1300. The design of structures to resist the effects of accidentalexplosions. U.S. Dept. of the Army, the Navy and the Air Force, TechnicalManual, Washington DC; 1990.

[38] Larcher M, Hermann N, Stempniewsky L. Explosionssimulation leichterHallenhllkonstruktionen. Bauingenieur 2006;81(6):2717.

[39] Dassault Systmes Simulia Corp. ABAQUS ver. 6.9 Users Manual; Providence,RI, USA; 2009.

[40] Schleyer FK. Tensile structures analysis of cables, cable nets and cablestructures. MIT Press; 1969.

[41] Wang Z, Gong G, Zhang Y, Bai C. Simulation of the response of glass windowunder blast load. Transactions of Tianjin University, 14: 50410. TianjinUniversity and Springer-Verlag; 2008.

[42] Bedon C, Louter C. Exploratory numerical analysis of SG-laminated reinforcedglass beam experiments. Eng Struct 2014;75(9):45768.

[43] EN 572-2. Glass in buildings basic soda lime silicate glass products. CEN;2004.

[44] MoD/DE Functional Standard Design and Maintenance Guide 02. Glazingstandards for MoD buildings subject to terrorist threat, Ministry of Defence;1996.

[45] Meyers GE. BLASTOP version 1 4, US Department of Energy; 1994.[46] Mayor RP, Flanders R. Technical manual simplified computer model of air blast

effects on building walls. US Department of State, Office of DiplomaticSecurity, Washington DC; 1990.

[47] Morison C. The resistance of laminated glass to blast pressure loading and thecoefficients for single degree of freedom analysis of laminated glass. PhDDissertation, Cranfield University; 2007.

[48] Peroni M, Solomos G, Pizzinato V, Larcher M. Experimental investigation ofhigh strain-rate behaviour of glass. Appl Mech Mater 2011;82:638.

[49] Bachmann H, Ammann WJ, Florian D. Vibration problems in structures:practical guidelines. Birkhuser; 1995.

[50] Buchholdt HA. An introduction to cable roof structures. 2nd ed. ThomasTelford; 1999.

[51] Timoshenko S, Woinowsky-Krieger S. Theory of plates and shells. McGraw-HillBook Company; 1959.

http://refhub.elsevier.com/S0141-0296(14)00488-X/h0005http://refhub.elsevier.com/S0141-0296(14)00488-X/h0005http://refhub.elsevier.com/S0141-0296(14)00488-X/h0005http://www.steel-sci.orghttp://refhub.elsevier.com/S0141-0296(14)00488-X/h0015http://refhub.elsevier.com/S0141-0296(14)00488-X/h0015http://refhub.elsevier.com/S0141-0296(14)00488-X/h0015http://refhub.elsevier.com/S0141-0296(14)00488-X/h0025http://refhub.elsevier.com/S0141-0296(14)00488-X/h0025http://refhub.elsevier.com/S0141-0296(14)00488-X/h0035http://refhub.elsevier.com/S0141-0296(14)00488-X/h0035http://refhub.elsevier.com/S0141-0296(14)00488-X/h0040http://refhub.elsevier.com/S0141-0296(14)00488-X/h0040http://www.som.comhttp://www.ctbuh.org/TallBuildings/FeaturedTallBuildings/FeaturedTallBuildingArchive2013http://www.ctbuh.org/TallBuildings/FeaturedTallBuildings/FeaturedTallBuildingArchive2013http://www.sbp.de/en/build/show/9-Screenwall_Hotel_Kempinskihttp://www.sbp.de/en/build/show/9-Screenwall_Hotel_Kempinskihttp://refhub.elsevier.com/S0141-0296(14)00488-X/h0055http://refhub.elsevier.com/S0141-0296(14)00488-X/h0055http://refhub.elsevier.com/S0141-0296(14)00488-X/h0065http://refhub.elsevier.com/S0141-0296(14)00488-X/h0065http://refhub.elsevier.com/S0141-0296(14)00488-X/h0070http://refhub.elsevier.com/S0141-0296(14)00488-X/h0070http://refhub.elsevier.com/S0141-0296(14)00488-X/h0075http://refhub.elsevier.com/S0141-0296(14)00488-X/h0075http://refhub.elsevier.com/S0141-0296(14)00488-X/h0080http://refhub.elsevier.com/S0141-0296(14)00488-X/h0080http://refhub.elsevier.com/S0141-0296(14)00488-X/h0080http://refhub.elsevier.com/S0141-0296(14)00488-X/h0085http://refhub.elsevier.com/S0141-0296(14)00488-X/h0085http://refhub.elsevier.com/S0141-0296(14)00488-X/h0085http://refhub.elsevier.com/S0141-0296(14)00488-X/h0090http://refhub.elsevier.com/S0141-0296(14)00488-X/h0090http://refhub.elsevier.com/S0141-0296(14)00488-X/h0095http://refhub.elsevier.com/S0141-0296(14)00488-X/h0095http://refhub.elsevier.com/S0141-0296(14)00488-X/h0100http://refhub.elsevier.com/S0141-0296(14)00488-X/h0100http://refhub.elsevier.com/S0141-0296(14)00488-X/h0105http://refhub.elsevier.com/S0141-0296(14)00488-X/h0105http://refhub.elsevier.com/S0141-0296(14)00488-X/h0105http://refhub.elsevier.com/S0141-0296(14)00488-X/h0120http://refhub.elsevier.com/S0141-0296(14)00488-X/h0120http://refhub.elsevier.com/S0141-0296(14)00488-X/h0120http://refhub.elsevier.com/S0141-0296(14)00488-X/h0125http://refhub.elsevier.com/S0141-0296(14)00488-X/h0125http://refhub.elsevier.com/S0141-0296(14)00488-X/h0130http://refhub.elsevier.com/S0141-0296(14)00488-X/h0130http://refhub.elsevier.com/S0141-0296(14)00488-X/h0135http://refhub.elsevier.com/S0141-0296(14)00488-X/h0135http://dx.doi.org/10.1061/(ASCE)AE.1943-5568.0000083http://dx.doi.org/10.1061/(ASCE)AE.1943-5568.0000083http://refhub.elsevier.com/S0141-0296(14)00488-X/h0155http://refhub.elsevier.com/S0141-0296(14)00488-X/h0155http://refhub.elsevier.com/S0141-0296(14)00488-X/h0160http://refhub.elsevier.com/S0141-0296(14)00488-X/h0160http://refhub.elsevier.com/S0141-0296(14)00488-X/h0175http://refhub.elsevier.com/S0141-0296(14)00488-X/h0175http://refhub.elsevier.com/S0141-0296(14)00488-X/h0180http://refhub.elsevier.com/S0141-0296(14)00488-X/h0180http://refhub.elsevier.com/S0141-0296(14)00488-X/h0190http://refhub.elsevier.com/S0141-0296(14)00488-X/h0190http://refhub.elsevier.com/S0141-0296(14)00488-X/h0200http://refhub.elsevier.com/S0141-0296(14)00488-X/h0200http://refhub.elsevier.com/S0141-0296(14)00488-X/h0210http://refhub.elsevier.com/S0141-0296(14)00488-X/h0210http://refhub.elsevier.com/S0141-0296(14)00488-X/h0240http://refhub.elsevier.com/S0141-0296(14)00488-X/h0240http://refhub.elsevier.com/S0141-0296(14)00488-X/h0250http://refhub.elsevier.com/S0141-0296(14)00488-X/h0250http://refhub.elsevier.com/S0141-0296(14)00488-X/h0255http://refhub.elsevier.com/S0141-0296(14)00488-X/h0255Exploratory numerical analysis of two-way straight cable-net faades subjected to air blast loads1 Introduction2 Structural behaviour of cable-net faades under blast loads2.1 Cable-net faade layout2.2 Blast load definition2.3 Dissipative devices3 Preliminary analytical assessment and estimation of maximum blast effects4 FE-modelling of the cable-net faade and preliminary numerical investigations4.1 FE-model properties4.1.1 Lumped-mass model (M01)4.1.2 Full cable-glass model (M02)4.1.3 Equivalent cable-diagonal beam model (M03)4.2 Assessment of FE-models and dynamic properties4.3 Dynamic behaviour of the glazing system under blast loads4.3.1 Simplified M01 model4.3.2 M02 and M03 models5 FE-modelling of the faade equipped by dissipative devices5.1 Numerical assessment of VE and RP devices structural capabilities5.1.1 Viscoelastic devices5.1.2 Frictional devices5.1.3 Combined viscoelastic and frictional devices6 Summary and conclusionsReferences