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Performance of cable-supported glass façades under time-depending wind action

Performance of cable-supported glass façades under time-depending wind action Glass Struct. Eng. https://doi.org/10.1007/s40940-022-00180-2 RESEARCH PAPER Performance of cable-supported glass façades under time-depending wind action Fabio Rizzo · Chiara Bedon Received: 29 December 2021 / Accepted: 30 April 2022 © The Author(s) 2022 Abstract Cable supported glass façades are sensitive Keywords Glass façades · Building aerodynamic · to wind action because of their flexibility. Conven- Cable-supported glass façade · Wind tunnel test · tional laboratory testing to check a façade reliability Numerical modelling under the wind action is generally carried out by uni- formly air pressure tests. However, the typical wind action on a surface is known to be not uniform because 1 Introduction it varies due to building aerodynamics and wind flow turbulence, and this aspect should be properly con- The increasingly use of glass for load-bearing applica- sidered for testing protocols. This paper discusses the tions in buildings and infrastructures proved to repre- structural response of cable-supported glass façades, sent an open issue for structural designers (Bedon et al. through time history finite element (FE) analyses, under 2018). On one side, novel boundary and restraint appli- different wind action combinations that varies based on cations make the use of glass in buildings extremely the building aerodynamics (plan shapes and roof cur- versatile, compared to other constructional materials. vatures), the wind direction (0° and 90°), and the glass On the other, several safety issues are still related to panel position (up and down). Such a finding is further tensile brittleness and typical size effects for building enforced by the presence of flexible supports for the applications, under various loading conditions. constituent glass modules. The presented results show Among others, wind effects for façade systems are a strong dependence of the structural response on the responsible of stress and deflection peaks that should wind action configuration, and thus suggest the need of be properly limited, and even minimized, depending new testing protocols for similar systems. on the mechanical and geometrical features of the sys- tem object of study (Bedon et al. 2018). In most of cases, glazing windows and façades represent a highly fragile and vulnerable component for buildings, given that they are expected to act as physical barrier under F. Rizzo a multitude of design actions. For this reason, several Department of Civil Engineering, Cracow University of studies have been spent for the analysis, assessment Technology, Warszawska 24, 31-155, Krakow, Poland and even optimization of several solutions of practi- e-mail: fabio.rizzo@universityresearch.it cal interest for design, such as façades in tall buildings C. Bedon (B) (Ding and Kareem 2020) which are most sensitive to Department of Engineering and Architecture, University of Tri- wind pressures. Design criteria for façades under wind este, Via Valerio 6, 34127 Trieste, Italy e-mail: chiara.bedon@dia.units.it actions have been elaborated and discussed in Simiu 123 F. Rizzo, C. Bedon and Hendrickson (1987), Overend et al. (2007), Brewer present study, more in detail, the wind action is esti- and Sammarco (2018). The potential and feasibility of mated by wind tunnel tests on buildings covered with fragility curves in support of efficient and conserva- a hyperbolic paraboloid roof. The building prototype tive design of glass façades under wind pressure has represent a sport arena and it was supposed to have been addressed in Lima-Castillo et al. (2019). Complex very large and tall glass façades on the perimeter. The mechanical systems in which glass panels are braced pressure coefficients on the lateral surfaces are esti- by cable systems have been investigated in Yu et al. mated in wind tunnel for different wind angles and for (2017). A smart control system for cable supported different plan shapes. A special care is then given to façades under wind or even blast has been proposed the comparative investigation of wind–structure inter- in Santos et al. (2014, 2016), to prevent extreme stress action on zones close to the flow detachment edge and peaks in glass components under dynamic events. on zones that are far away from the edges. The wind induced displacements were estimated by The novelty of this paper consists of a discussion on Rizzo et al. (2021) based on a numerical model cali- the structural response of cable-supported glass façades brated towards full-scale laboratory experiments. It was under a dynamic action induced by the wind, and as far observed that the wind action estimated by wind tun- as the authors know, there are no comparable scientific nel tests affects the façade structural response closely publication on this issue. differently than laboratory air pressure tests commonly To this aim, Sect. 2 summarizes the façade geom- used to check the façade reliability. Results discussed etry and mechanical characteristics, with evidence of by Rizzo et al. (2021) proved that the wind-structure some basic preliminary considerations, while Sect. 3 interaction in the field of the glass façades should be discusses the reference wind tunnel experimental setup investigated carefully to avoid air infiltration and unde- and the wind action calculations that are used for time- sired torsion in the supporting frame members. In the dependent non-linear analyses. Numerical simulations present paper, the attention is still focused on façade are thus presented in Sect. 4, while Sect. 5 discusses glass panels under wind pressure. Compared to liter- the main results. ature studies, however, major efforts are spent on the characterization and analysis of wind effects based on original experimental pressure data. Further, the analy- 2 Structural setup of the cable-supported glass sis is focused on a special typology of cable-supported façade façade systems. More in detail, the case-study curtain wall explored in Amadio and Bedon 2012a, b, c)is 2.1 Façade system take into account and adapted to the present investiga- tion. Based on efficient but refined finite element (FE) In this paper, the analysis is focused on the cable- models developed in ABAQUS (ABAQUS computer supported glass façade originally explored in Ama- software), a set of twelve non-linear dynamic analyses dio and Bedon (2012a, b, c). The modular unit is L is carried out with the support of twelve time histo-  9 m tall and composed of B  1.55 m laminated ries of wind pressure. Typical wind effects and façade glass sheets schematized in Figs. 1 and 2 (H  3m behaviours are thus assessed from parametric analyses. their maximum height). The glass layers are fully tem- Based on simple preliminary calculations, the effects of pered, with a nominal characteristic tensile strength in boundaries for such complex mechanical systems are bending up to 120 MPa (CNR 2013; EN 16612:2019). also analysed in terms of corresponding performance As also explained in Amadio and Bedon (2012a, b, c), indicators for design. to minimize the computational cost of simulations and The purpose of this paper is to discuss the wind- simplify the analysis, the façade is assumed to be wide structure interaction for glass façades to alarm codifiers enough (B × n modules  L) to neglect the lateral and sway the scientific community on such a sensitive restraints at the vertical edges of each module. issue. The thesis supported is that the static air pressure Moreover, it is assumed that each laminated glass tests reproduced in laboratory to assess glass façade panel has a total nominal thickness t  24.52 mm, as tot against wind pressure are not reliable because the wind obtained by bonding two glass sheets (t  t  10 mm) 1 2 action is a dynamic force, and its time-depending effect and a middle PVB-interlayer (t  4.56 mm). The PVB should not be neglected (Rizzo et al. 2021). For the glass panels are braced by a system of steel vertical 123 Performance of cable-supported glass façades under time-depending wind action Fig. 1 Schematic drawing of the examined façade system, as adapted from (Amadio and Bedon 2012a, 2012b, 2012c). Figure reproduced from (Amadio and Bedon 2012c) under the terms and conditions of a Creative Commons Attribution License agreement cables with φ  36 mm diameter. To realize an effi- provide useful preliminary feedback about the expected cient bearing system for glass panels, they are spaced mechanical performance of the element. Stress and at intervals of i  1.55 m in the plane of the wall (x- deflection peaks are thus verified against the prescribed direction). At the same time, the distance between the limit values (CNR 2013; EN 16612:2019). bracing cables and laminated glass panels in z-direction In the present paper, a preliminary comparative anal- is set equal to d  65 mm. ysis for the B × L façade panel is presented in Fig. 3.At A mostly rigid restraint in z-direction is offered first, the viscous behaviour of interlayer is disregarded, by spider connectors with point-fixings (six point- and the analysis is carried out under the assumption of fixings/glass panel) according to Fig. 2. The cable sys- a “fully monolithic” glass section as in Fig. 3a, with t tot tem is finally subjected to an initial prestressing force  24.52 mm. The quasi-static wind pressure W is uni- P . formly applied to the full surface of glass. Two differ- ent boundary conditions are taken into account, namely the CS(A) configuration in Fig. 3b characterized by the presence of linear simple supports along the edges of 2.2 Glass panel under quasi-static uniform pressure glass and the “6PF(N)” configuration in Fig. 3c, where the glass panel is assumed restrained by six ideally rigid The minimization of potential stress peaks and deflec- point-fixings. The corresponding stress and deflection tions in glass panels that are characterized by high peaks are monitored with the support of non-linear cal- slenderness and flexibility for curtain wall applications culations as a function of the imposed pressure W. is—in most of cases—the primary target of design and Simple non-linear analytical calculations from CNR analysis. Besides, boundary and restraint conditions are (2013); EN 16612:2019) are preliminary taken into known to induce additional local and global behaviours account for the CS(A) configuration in Fig. 3b. This that may result in premature fracture or exceedance of means that maximum stress values and deformations reference performance limit values. are estimated (both at the centre of glass panel) as: For laminated glass panels under wind pressure, an equivalent quasi-static orthogonal pressure representa- tive of wind action peak for the location of interest can 123 F. Rizzo, C. Bedon Fig. 2 Schematic drawing of façade details: a laminated glass section, b point-fixing connection model is taken into account, due to the lack of efficient analytical formulations for such a specific restraint con- σ  k · · F (1) max 1 d dition. The typical bending behaviour can be noted in Fig. 4a. Worth to remind that the stress and deflection and peaks for the CS(A) case are expected at the centre of glass. Similar effects can be expected for the deflection A F analysis of the 6PF(N) panel with ideally rigid point- w  k · · (2) max 4 h E fixings, while stress peaks migrate from the panel cen- tre towards the region of supports. In this regard, the In Eqs. (1) and (2), A  B × L is the surface of glass, numerical stress peaks calculated in the region of point- F the design action corresponding to W, h  t the d tot fixings need to be further magnified as in CNR (2013), reference thickness, E  70 GPa the Young’s modulus that is: of glass and k , k two non-dimensional parameters 1 4 (CNR 2013; EN 16612:2019). For the 6PF(N) config- uration in Fig. 3c, the support of a simple FE numerical σ  σ · K (3) hole 123 Performance of cable-supported glass façades under time-depending wind action Fig. 3 Preliminary analysis of the glass panel under ideal boundary conditions and quasi-static wind pressure: a reference cross-section, b simple supported panel, c point-fixed panel so as to account for the stress intensification factor finally, is the trend of stress peaks towards the reference K as in Fig. 4b, with K ≈ 2.1 for the present calculation tensile resistance of glass. example. In this regard, it is important to remind that Besides, all the comparative results in Fig. 4 still the modelling strategy according to Eq. (3) represents disregard the complex behaviour of the examined glass a practical but simplified approach, because the calcu- panel as a part of the cable-supported system in Figs. 1 lation is focused on the global effect induced by load and 2 (i.e., viscous behaviour of interlayer for the lami- distribution. nated section, flexibility of bracing cables, etc.), as well Comparative results are proposed in Fig. 4c for both as the typical time variability and dependence of wind the examined conditions, as a function of a uniform actions, thus recommending a detailed time-dependent pressure W in the range of 0–30 kPa. The final effect analysis as in Sects. 3 and 4. of ideally rigid point-fixings is a stress peak increase denoted in Fig. 4c as “6PF(N) x K”, which largely exceeds the stress estimates for the CS(A) condition. 3 Wind action As far as the actual restraint configuration of glass as a part of the cable-supported façade is disregarded, The time-dependent wind action W (t) on the exam- some additional feedback about the expected perfor- ined façade was estimated according to Eq. (4), assum- mance of the examined panel can be obtained by intro- ing the mean wind velocity V equal to 24.7 m/s; it ducing in Fig. 4d the stress and deformation ratios. was calculated assuming v  31 m/s, z  0.7, b00 0 Ideal restraints, for a given panel shape, size and thick- z  12 m, k  0.23, a  500 m, k  0.32, the min r 0 a ness, result in different performance limits for ultimate air density, ρ  1.25 kg/m , A is the façades area (stress) and serviceability (deflection) states. Following (CEN (Comité Européen de Normalization) 2005). In (CNR 2013), the maximum deflection in service condi- Eq. (4) (CEN (Comité Européen de Normalization) tions is limited to H/60 (or 50 mm) for the CS(A) panel. 2005;CNR 2018), the time dependent pressure coeffi- This deflection limit reduces to L /100 (or 30 mm) min cients, cp(t ),were assumed according to results given for the 6PF(N) condition. Comparative plots exceed- by Rizzo et al. (2011) on lateral surfaces of building ing the y  1 value in Fig. 4d are thus representative covered with large span roofs. of “unsafe” deformation amplitudes to avoid for design and serviceability checks. Worth to be noted in Fig. 4d, W (t)  cp (t) · ρV · A (4) m i 123 F. Rizzo, C. Bedon (a) (b) (c) (d) Fig. 4 Preliminary analysis of the glass panel under ideal boundary conditions and quasi-static wind pressure: a numerical model for 6PF(N), with legend values in Pa (shape scale factor × 5), b stress magnification factor K for bending, c stress–deflection trends and d stress–deflection ratios as a function of the imposed pressure (ABAQUS) In total, eight different geometries of building were #7) to 98 (i.e., Geometry #6 and #8). Each test models considered to investigate the influence of the building were equipped with Teflon tubing that was calibrated aerodynamics on the façade structural response. Table such to obtain a flat frequency response up to 100 Hz; 1 and Fig. 5 summarize the reference geometries. The this was achieved by selecting the tube length and the geometrical scale of the test model was assumed equal position of a pneumatic damper. Acquisition was car- to 1:50. ried out at a sampling frequency of 252 Hz for a dura- Wind tunnel tests were carried out on four square and tion of 29.7 s. The turbulence intensity at the roof level four rectangular building pressure models, all featuring ranges between 11 and 12%. The tests were performed a hyperbolic paraboloid roof, in the CRIACIV bound- at a mean wind speed of 16.7 m/s at a height of 10 cm. ary layer wind tunnel in Prato, Italy (Rizzo et al. 2011). Sixteen wind angles were acquired in wind tunnel but The facility is an open circuit tunnel with a 2.30 m × for sake of brevity results on only 0° and 90° (Fig. 5) 1.60 m test chamber. The rigid models are made of are discussed in this paper. wood and the number of pressures taps on the lateral surface ranges from 58 (i.e., Geometry #1, #3, #5 and 123 Performance of cable-supported glass façades under time-depending wind action Table 1 Geometrical Geometry L L f f H H + f + f 1 2 1 2 1 1 1 properties of prototypes and 2 test models Model (cm) #1 80.00 80.00 2.70 5.30 13.30 21.30 #2 80.00 80.00 2.70 5.30 26.70 34.70 #3 80.00 80.00 4.40 8.90 13.30 26.70 #4 80.00 80.00 4.40 8.90 26.70 40.00 #5 40.00 80.00 2.70 5.30 13.30 21.30 #6 40.00 80.00 2.70 5.30 26.70 34.70 #7 40.00 80.00 4.40 8.90 13.30 26.70 #8 40.00 80.00 4.40 8.90 26.70 40.00 Prototype (m) #1 40.00 40.00 1.35 2.65 6.65 10.65 #2 40.00 40.00 1.35 2.65 13.35 17.35 #3 40.00 40.00 2.20 4.45 6.65 13.35 #4 40.00 40.00 2.20 4.45 13.35 20.00 #5 20.00 40.00 1.35 2.65 6.65 10.65 #6 20.00 40.00 1.35 2.65 13.35 17.35 #7 20.00 40.00 2.20 4.45 6.65 13.35 #8 20.00 40.00 2.20 4.45 13.35 20.00 Fig. 5 Building geometrical parameters and wind angles of attack during experiments: a square plan and b rectangular plan building The mean, maximum and minimum values of the were divided in subzones as it is represented in Fig. 6 pressure coefficients were calculated from the mea- from 1 to 7 for square plan building and from 1 to 5 sured time series. In particular, the maximum and min- on the side parallel to 90° and from 1 to 7 on the side imum values were calculated according to a best fit parallel to 0° (Fig. 6). Sides are named α, β, χ and γ with the Gumbel distribution, following the procedure clockwise. It was investigated because the flow field proposed by Cook and Mayne (1979) associated with around the building lateral surfaces is very different a 22% probability of being exceeded, as it is done by on zones close to the detachment edges, as for exam- Cook and Mayne (1979). ple zones #1 and #7, and on zones very distant to the Buildings were covered with a double curvature roof detachment edges as for example zone #4. However, it (i.e., hyperbolic paraboloid roof) to simulate a cable net is necessary to distinguish two parts in the same zones, tensile structure. It was made of downward cables par- the part close to the upper edge and the part close to allel to the 0° wind direction and upward cables paral- the floor. The flow field is different for these two parts lel to 90° wind direction. The building lateral surfaces of the façade and consequently it is loaded differently. 123 F. Rizzo, C. Bedon 7 5 3 6 5 2 1 4 7 7 6 6 5 5 4 4 4 5 3 3 2 3 2 2 2 1 1 0° 90° 90° y/D y/D x/B x/B 0° 45° 45° (a) (b) Fig. 6 Building lateral surface subzones: a square plan and b rectangular plan building The different flow field and consequently the differ- Table 2 Numerical analyses sets ent wind action along the same façade affects the façade Combination Analysis reliability because it can induce torsional effects on the façade beams and pillars. It can induce the detachment #1 (I) Wind action in subzone 1, geometry of the sealing gasket and consequently the air infiltra- #4 [Ref. Table 1], side β,0° tion inside the building with a negative pressure from (II) Wind action in subzone 4, geometry inside to outside. #4 [Ref. Table 1], side β,0° In order to investigate this effect, four different sets #2 (I) Wind action in subzone 1, geometry of action listed in Table 2 were considered for this study #3 [Ref. Table 1], side β,0° (in the following, Combination #1, #2, #3 and #4). Each (II) Wind action in subzone 1, geometry set consisted of two analyses for set #1, two analyses #3 [Ref. Table 1], side β, 90° for set #2, four analyses for set #3 and four analyses #3 (I) Wind action in subzone 2, geometry for set #4, that have the purpose to compare the façade #1 [Ref. Table 1], side β,0° structural response under different environmental con- (II) Wind action in subzone 2, geometry #3 [Ref. Table 1], side β,0° ditions. The exact definition of each set is discussed in the following. For sake of brevity, moreover, only (III) Wind action in subzone 2, geometry #1 [Ref. Table 1], side β, 90° selected geometries from Table 1 are discussed in this (IV) Wind action in subzone 2, geometry paper, and specifically geometries #1, #2, #3, #4 and #3 [Ref. Table 1], side β, 90° #6. Load combinations was selected to highlight the #4 (I) Wind action in subzone 1, geometry differences induced by the building geometry and the #2 [Ref. Table 1], side β,0° wind flow trend. (II) Wind action in subzone 1, geometry It is in fact important to specify that the full set of #6 [Ref. Table 1], side β,0° geometries are named geometry #1 to #8 as in Table (III) Wind action in subzone 1, geometry 1. There, the subzones are representative of the façade #2 [Ref. Table 1], side β, 90° zones illustrated in Fig. 6, where they are labelled from (IV) Wind action in subzone 1, geometry #1 to #7 for all four sides of square plan building, or #6 [Ref. Table 1], side β, 90° from #1 to #5 and from #1 to #7 for shorter and longer sides respectively of rectangular building. The first set (i.e., Combination #1) consists of two consists of two analyses with the aim to study the influ- analyses with the aim to investigate the influence of ence of the wind angle (i.e., 0° and 90°); the third com- the aerodynamic due to the flow streamlines from the bination (i.e., Combination #3) consists of four anal- detachment zone; the second set (i.e., Combination #2) yses with the aim to investigate the influence of roof 123 Performance of cable-supported glass façades under time-depending wind action curvature; finally, the fourth combination (i.e., Com- 4 Structural time history analyses bination #4) consists of four analyses with the aim to investigate the influence of the building plan geometry 4.1 Reference model (i.e., square and rectangular) for the two wind angle investigated. The parametric numerical analysis of the cable- Specifically, Combination #1 investigates, through supported glass system under wind pressure was car- two time-history analyses, the difference of the façade ried out in ABAQUS (ABAQUS computer software). response induced by the distance from the detachment To this aim, the reference numerical model was derived edge with wind angle equal to 0°. It has been done from Amadio and Bedon (2012a, b, c) and adapted to using wind tunnel experimental data elaborated for the the examined loading conditions. Composite shell ele- geometry #4 (Table 1), the wind angle (0°) on the same ments (S4R) were used to describe the glass panels, side β, for two subzones, #1, close to the detachment while beam (B31) and truss (T3D2) elements realized edge, and #4, distant from the detachment edge. the spider connectors and bracing system of cables, Combination #2 investigates, through two time- respectively. The final assembly consisted of 3900 history analyses, the difference of the façade response DOFs and around 600 elements (Fig, 7a). induced by a different wind angle. To achieve this pur- Linear elastic constitutive laws were used for mate- pose, the wind tunnel experimental data on geometry rials. For fully tempered glass, the Young’s modulus, #3 under two different wind angle, 0° and 90°, on the Poisson’ ratio and density were set in E  70GPa, same side β, for the subzones, #1, close to the detach- ν  0.23 and ρ  2500 kg/m . Furthermore, for the g g ment edge. PVB-interlayer, an equivalent elastic–plastic character- Combination #3 investigates, through four time- istic curve was taken into account, with E  8MPa PVB history analyses, for the same subzone quite close to the reference secant modulus corresponding to short- the detachment edge (i.e. subzone #2), the difference term wind actions (CNR 2013), with ν  0.49 and PVB induced by two wind angles (0° and 90°) and the dif- ρ  1100 kg/m . Finally, harmonic steel (cables) PVB ference induced by a different roof curvature, flat (i.e. and stainless steel (joints) were assumed to have a lin- geometry #1) and curved (i.e. geometry #3). ear elastic behaviour, with ρ  7800 kg/m , ν  0.3 s s Finally, Combination #4 investigates, through four and E  130 GPa, E  170 GPa respectively. s,h s,s time-history analyses, for the same subzone close to Based on the above material assumptions, especially the detachment edge (i.e. subzone #1), the difference for glass, the analysis of possible damage mechanisms induced by two wind angles (0° and 90°) and the dif- (i.e., stress peaks in the region of point-fixings) were ference induced by a different plan shape, square (i.e. based on the time-dependent analysis of maximum geometry #2) and rectangular (i.e. geometry #6). stress and deformations for the full model components. The selected combinations shall reflect any geomet- A special role was assigned to restraints, for the rical combinations available from experimental data. façade module assessment. The cables were pinned at All calculations were computed using a wind action the upper end, while the initial pretension force P for time history with a time length equal to 800 s and a the bracing system was imposed at their base in the time step equal to 0.1 s. For all analyses two-time his- form of an equivalent vertical displacement (see also tories were applied on the glass panel, the first one 1/4 Sect. 5.2). Along the elevation of the façade-module, of the glass panel height from the border down and the only z-displacements and x-rotations were allowed for second one 1/4 of the glass panel height from the border the other cables nodes, so as to account for the presence up. of adjacent façade members. Structural silicone sealant bonding glass panes was neglected, since it provides a negligible rotational stiffness (Amadio and Bedon 2012a, b, c). Each half-spider connector consisted in three rigidly connected 2-node linear beams that were linked by means of a weld connector (null relative dis- placements and rotations) and additional joins (pinned connectors with free relative rotations) to provide the 123 F. Rizzo, C. Bedon Fig. 7 Model of the façade module (ABAQUS): a general view and b schematic drawing of point-fixings. Figures reproduced from (Amadio and Bedon 2012c) under the terms and conditions of a Creative Commons Attribution License agreement mechanical interaction of glass-spider and spider-cable for nonlinear cables structures. A schematic view of nodes. A schematic drawing is proposed in Fig. 7b. reference control points and parameters is shown in Fig. 8. For the analysis of wind effects on such a structural system characterized by flexibility parameters (and 4.2 Analysis procedure and performance indicators thus stress–deflection performance indicators) highly sensitive to the features of the bracing system of cables, The typical analysis was arranged onto two steps. First, some preliminary comparative calculations were car- the façade system was subjected to self-weight and ried out for the façade module. prestress force P in the bracing cables (static step). The analysis was focused on the effects of initial pre- Secondly, the preloaded model was analysed under the stress P on the expected fundamental vibration period effects of wind pressures as in Table 2 (dynamic step). of the façade module (linear modal step), as well as This step consisted of 60,000 increments over the dura- on the maximum effects due to a quasi-static uniform tion of wind action. wind pressure (non-linear static step). To this aim, the For the post-processing stage, careful attention was characteristic axial resistance of bracing cables is also paid for the analysis of some key indicators for the per- recalled, with P  1150 kN (Amadio and Bedon Rk formance assessment of the façade module under wind 2012a, b, c), so as to express the prestressing levels actions. These included possible tensile stress peaks in of bracers as a function of the imposed force towards glass (region of point-fixings, centre of panels); max- the resistance. imum out-of-plane deflections (centre of panels); rel- As it can be seen in Fig. 9a, no marked variations ative deformation and twist of glass panels; as well as can be expected in the qualitative fundamental vibra- maximum stress peaks in the bracing cables. A dynamic tion shape of the façade module under limited prestress approach through time history analyses is considered in the present study, because of its intrinsic advantages 123 Performance of cable-supported glass façades under time-depending wind action Fig. 8 Key performance indicators for the dynamic analysis of the façade module (a) (b) Fig. 9 Analysis of pretension effects in terms of a fundamental vibration shape and b period (ABAQUS) 123 F. Rizzo, C. Bedon ratio levels. Besides, marked modifications of the corre- In Fig. 11, qualitative results are proposed for sponding vibration period are recorded in Fig. 9b from selected façade components and input pressure data. the same parametric modal analyses. As expected from the preliminary calculation steps, A more detailed analysis of results for the deflection the façade module was characterized by limited stress and stress performance of the central glass panel sub- peaks in glass, thus ensuring a mostly elastic response jected to major bending effects can be summarized as of the system under the imposed time histories. This in Fig. 10. There, the relative and absolute deflection can be noticed from the example of contour plots as in ratios are first explored, due to the high flexibility of the Fig. 11. The deformed shape of the system, even still system. Figure 10a shows the ratio of relative deflec- characterized by a cylindrical deformation in accor- tion (i.e., left-down minus middle central point of the dance with the fundamental modal shape in Fig. 9,was panel) towards the allowable limit deflection reported also found to suggest local and global effects due to in Sect. 2 (i.e., L /60  15 mm as in Fig. 4). The the non-uniform, time-dependent pressure histories for min chart data in Fig. 10a that exceed the y  1 value, wind. in this regard, represent unsafe pressure amplitudes. In this regard, Fig. 12 shows a quantitative overview Another important parameter for the dynamic perfor- of the structural response given by FE Analysis #1. mance analysis is the absolute deflection of the 9.00 m Specifically, Fig. 12a presents the left-down corner dis- tall façade. To this aim, the global deflection under ordi- placement (δ ) time history, Fig. 12b the right-up cor- nary wind pressure should be limited to a maximum of ner (δ ) displacement time history, Fig. 12c the mid- 1/100 the total span (Amadio and Bedon 2012a, b, c). In dle point displacement (δ ) time history respectively. this regard, chart data in Fig. 10b which exceed the y  Figure 12d also shows the cable displacement (δ ), 0.001 value are representative of unsafe pressure ampli- while the corresponding envelope of Von Mises cable tudes for wind. In both figures, it is wort to mention stresses (σ ) is proposed in Fig. 12e. Worth to be noted that the effect of prestress level (even under quasi-static the evolution of stress peaks in the glass panel (σ in pressure assumptions) still reflects in marked modifi- Fig. 12f. cation of the façade performance. The collected stress peaks, as shown, are relatively In this regard, Fig. 10c shows the typical distribution small to avoid any kind of damage in the façade mod- of maximum principal stresses for the central laminated ule components, or maximum deflections exceeding glass panel (10 kPa the pressure amplitude). It can be the reference limit values. Besides, the attention from notice that the expected stress peaks in glass—thanks the parametric numerical analysis outcomes is focused to the flexibility of supports—are relatively low, com- in the present study on the range of variability for the pared to the reference material resistance and to the cor- estimated performance indicators, as a major effect due responding deflection parameters. Most importantly, to the time-dependency of wind pressures. the deformed shape of the panel (and thus the corre- The statistics of output data are summarized in sponding stress distribution in glass) strongly differs Tables 3 and 4 for all Combinations (i.e., from #1 to from the idealized analysis of the plate with rigid point- #4) and corresponding FE analyses (based on Table 2). fixings as in Fig. 4, thus confirming the importance of Table 3 gives the mean, maximum, minimum and stan- refined calculations for design purposes. dard deviation value for displacements δ , δ and δ .At 1 2 3 the control points in the central glass panel. Similarly, Table 4 summarizes the variation of cable deflection 5 Discussion of time-dependent dynamic results δ and the maximum (envelope) stress parameters for cables (σ ) and glass (σ ). c g The parametric analysis with time-dependent wind For Combination #1 in Table 3, the comparison pressure was carried out for the façade module char- between subzone #1 (i.e., Analysis I) and subzone #4 acterized by a moderate prestress level in the cables, (i.e., Analysis II) shows a very large difference for the corresponding to T  0.465 s of fundamental vibra- selected control points (i.e., left-down, right-up and the tion period as in Sect. 4. The quantitative analysis of middle one) especially observing the mean value that is parametric data was again carried out based on the per- opposite. This means that subzone #1 is in suction and formance indicators and selected control points previ- subzone #4 is in pressure. This cannot be neglected ously discussed. 123 Performance of cable-supported glass façades under time-depending wind action (a) (b) (c) Fig. 10 Analysis of pretension effects in terms of a–b deflection and c stress analysis of the central glass panel under quasi-static uniform wind pressure (ABAQUS, shape scale factor × 5) 123 F. Rizzo, C. Bedon Fig. 11 Example of variation in time of: a deflection (in m), b velocity (in m/s), c maximum stress in glass (in Pa) and d Von Mises stress in cables (in Pa). ABAQUS/Standard, results from combo #3(ii) after 0.25 s of wind exposure 123 Performance of cable-supported glass façades under time-depending wind action (a) (b) (c) (d) (e) (f) Fig. 12 Glass panel response for Analysis #1: a left-down corner displacement (δ ), b right-up corner displacement (δ ), c middle point 1 2 displacement (δ ), d cable displacement (δ ), e cable Von Mises stress (σ )and e maximum principal stress in the glass panel (σ ) 3 c c g 123 F. Rizzo, C. Bedon Table 3 Maximum (M), minimum (m), mean (μ) and standard deviation (σ ) of the glass panel displacements, as measured at the left-down corner (δ ), right-up corner (δ ), or middle point (δ ) 1 2 3 Comb Analysi δ (up) δ (middle) δ (down) 1 2 3 s# μ (mm) M m σ (mm) μ (mm) M m σ (mm) μ (mm) M m σ (mm) (mm) (mm) (mm) (mm) (mm) (mm) #1 (I) 20.41 75.06 − 22.52 12.12 23.71 83.54 − 24.59 13.16 22.19 76.66 − 22.11 11.85 (II) − 19.33 4.97 − 47.55 8.60 − 20.63 3.32 − 48.99 8.41 − 18.16 0.46 − 40.78 6.55 #2 (I) 4.05 54.20 − 51.80 15.51 5.30 58.93 − 56.48 16.23 5.30 51.44 − 50.24 13.83 (II) 64.95 111.59 1.49 10.43 68.81 123.66 0.82 11.73 58.29 106.89 − 0.38 10.78 #3 (I) 12.77 64.14 − 32.57 14.60 14.21 69.49 − 36.30 15.22 12.59 58.23 − 33.18 13.00 (II) 4.05 54.20 − 51.80 15.51 5.30 58.93 − 56.48 16.23 5.30 51.44 − 50.24 13.83 (III) 67.80 113.81 1.49 10.40 71.60 114.39 0.82 11.31 60.40 98.10 − 0.38 10.18 (IV) 64.95 111.59 1.49 10.43 68.81 123.66 0.82 11.73 58.29 106.89 − 0.38 10.78 #4 (I) 38.38 57.63 1.49 5.68 40.96 69.21 0.82 7.48 35.07 67.10 − 0.38 8.08 (II) − 9.99 16.17 − 38.21 7.81 − 9.06 14.78 − 35.45 7.37 − 6.48 12.78 − 27.28 5.54 (III) 38.10 79.11 1.49 6.89 41.23 89.30 0.82 6.52 35.89 78.18 − 0.38 4.94 (IV) 74.68 103.45 1.49 5.74 74.96 113.90 0.82 6.33 59.08 97.50 − 0.38 5.88 during the design phase the façade. In Table 3, stan- wind angle equal to 90°, for the same control point. It dard deviation was assumed as a measure of the time- was also noted that the variation of the mean value of depending effect of wind pressure. It can be observed measured displacements in the middle point is smaller that for combination #1 it ranges from 6.55 (right-up, for 90° than 0° due to the building aerodynamics. subzone #4) to 13.16 (middle point, subzone #1). As it All calculations herein discussed showed alternative was expected the flow field is more instable close to the positive and negative displacements induced by pres- detachment edge (i.e., subzone #1) and that is the rea- sure and suction on the façade system, as a direct effect son because the standard deviation is bigger on this sub- of wind dynamics. zone. However, this effect should be taken into account Finally, as expected, data in Table 3 show a sig- during the design phase because it means that the façade nificant difference between square plan building and sealing gasket are more loaded by wind induced vibra- rectangular plan building for both two wind angles and tion in subzone #1 than in subzone #4. combinations object of study. For Combination #2, based on values given in Table A major sensitivity and variation of parametric FE 2, it was observed that due to the building shape and results was observed for the cable displacement (δ ), its aerodynamics, the same subzone #1 is loaded very cable stress (σ ) and glass panel stress (σ ), as it can be c g differently under wind angle 0° and 90°. seen in Table 4. The location of the glass panel around The mean value ranges from 5.30 mm to 68.81 mm the building lateral surface affects results as well as the in the middle point of the façade. It means that several building roof curvature, the wind angle and the plan wind angles should be investigated in the design the shape. Results in term of glass panel stress show that façade. the maximum peak ranges from 0.17 Pa to 4.17 MPa. Based on data given in Table 3 for Combination #3 This variation is very large and should be properly taken and for the same subzone #2, it was observed that the into account for the optimal design of glass thickness roof curvature affects the façade displacements because and point-fixing detailing. the mean value ranges from 5.30 mm (i.e., analysis Most importantly, such a stress–deflection sensitiv- (II)) to 14.21 mm (i.e., analysis (I)) with a wind angle ity to the imposed time-dependent wind pressure affects equal to 0° (middle control point). At the same time, the design of structural details, and consequently fur- the measured deflection spans from 68.81 mm (i.e., ther affects the resulting natural vibration period of analysis (IV)) to 71.60 mm (i.e., analysis (III)) with a 123 Performance of cable-supported glass façades under time-depending wind action Table 4 Maximum (M), minimum (m), mean (μ) and standard deviation (σ ) of cable displacement (δ ), cable Von Mises stress (σ ) c c and principal stress in the glass panel (σ ) Comb Analysis δ σ σ c c g μ (mm) M m σ (mm) μ M m σ (MPa) μ M m σ (MPa) (mm) (mm) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) #1 (I) 22.32 81.58 − 25.62 13.05 148.16 176.00 145.00 3.12 1.28 4.17 0.07 0.61 (II) − 21.69 2.10 − 49.81 8.35 147.39 157.00 145.00 1.82 0.88 2.22 0.09 0.39 #2 (I) 4.06 57.27 − 57.24 16.12 146.24 160.00 145.00 1.70 0.71 3.00 0.07 0.50 (II) 67.07 121.14 − 0.38 11.60 166.45 209.00 145.00 7.50 3.43 6.78 0.17 0.58 #3 (I) 12.91 67.78 − 37.24 15.11 146.77 164.00 145.00 2.38 0.91 4.13 0.07 0.61 (II) 4.06 57.27 − 57.24 16.12 146.24 160.00 145.00 1.70 0.71 3.00 0.07 0.50 (III) 69.84 112.26 − 0.38 11.19 168.22 206.00 145.00 7.52 3.56 6.08 0.17 0.55 (IV) 67.07 121.14 − 0.38 11.60 166.45 209.00 145.00 7.50 3.43 6.78 0.17 0.58 #4 (I) 39.46 67.33 − 0.38 7.40 152.37 167.00 145.00 2.74 2.09 3.64 0.17 0.37 (II) − 10.21 13.49 − 36.40 7.32 145.80 152.00 145.00 0.99 0.40 1.58 0.08 0.26 (III) 39.73 87.30 − 0.38 6.47 152.40 177.00 145.00 2.46 2.10 5.31 0.17 0.32 (IV) 73.24 111.50 − 0.38 6.27 170.74 198.00 145.00 4.23 3.71 6.34 0.17 0.31 the façade and its dynamic response, once the opti- paraboloid roof under two orthogonal wind directions mal parameters are detected. The wind induced effect (i.e. 0° and 90°). It was investigated the dependence of estimated by FE analyses suggest that the wind action the structural response on the building aerodynamics should be reproduced carefully during the preliminary given by the building plan shape and the roof curva- test of façade systems, because it is reasonable to think ture, on the wind direction and on the panel location on that the estimated variation will be closely more sig- the façade. The façade structural response was explored nificant for the case of façades on high-rise buildings for panels close to or distant from the detached zone, (Rizzo et al. 2020). and close to or distant from ground. Totally, twelve dif- ferent wind action combinations were also considered in this study and the structural response was discussed 6 Conclusions in terms of structural performance indicators. For example, as far as a global structural model is The performance of a typical cable-supported glass taken into account for glass panels, it was observed that façades under time-depending wind action estimated the structural response in term of glass displacements in wind tunnel was investigated through time history and cable stress peaks varies considerably with random Finite Element (FE) numerical analysis. A special care wind action, compared to conventional loading proto- was given to wind action description as well as to cols. In addition, it was estimated that some zones are local and global performance parameters. As known, expected in pressure and some zones in suction, for the for practical applications, the use of conventional pro- same façade components. This finding gives a torsion of tocols for loading single glass panels with ideal bound- the façade as a whole, that should be carefully analysed ary restraints is rather consolidated and generally con- during the design phase. Finally, the time history action servative approach. Besides, especially for complex shows that pressure and suction are time-depending, and wide glass facades under live loads such as wind and it means that two areas of the same panel can be actions, a balance of modelling simplicity and accuracy loaded by pressure or suction at the same time. of estimates (even on the safe side for design) should Even if the wind induced local pressures are under be properly addressed. the limits for glass panels, the wind action induced cine- The wind action was calculated from pressure matics on the façade structural system might be unsafe. coefficients estimated in wind tunnel on lateral sur- face of low-rise buildings covered with a hyperbolic 123 F. Rizzo, C. Bedon Results suggest that the pressure test on the façades Brewer TR, Sammarco EL (2018). Optimizing glass design: the role of computational wind engineering & advanced carried out in laboratory to simulate the wind action numerical analysis. In: Proceedings of Challenging Glass are not representing the real behaviour because they 6 -Conference on Architectural and Structural Applications should take into account the pressure and suction alter- of Glass. Louter, Bos, Belis, Veer, Nijsse (Eds.), Delft Uni- native given by the buildings aerodynamics and by the versity of Technology, May 2018. https://doi.org/10.7480/ cgc.6.2174. wind flow turbulence. This paper aims to recommend CEN (Comité Européen de Normalization), Eurocode 1: Actions a glass panel testing standard procedure update to sim- on structures—Part 1–4: General actions—Wind actions, ulate consistently the wind action on the glass panels EN-1991-1-4 (2005) taking into account effects due to the turbulence and to CNR (National Research Council of Italy). Istruzioni per la Pro- gettazione, l’Esecuzione ed il Controllo di Costruzioni con the aerodynamics. Elementi Strutturali di Vetro, [Guide for the Design, Con- struction and Control of Buildings with Structural Glass Funding Open access funding provided by Università degli Elements]. CNR-DT 210/2013, (2013). Free download of Studi di Trieste within the CRUI-CARE Agreement. English version at: https://www.cnr.it/en/node/3843 CNR (National Research Council of Italy) Guide for the Assess- ment of Wind Actions and Effects on Structures. CNR-DT 207/2018 (2018) Cook, N.J., Mayne, J.R.: A novel working approach to the assess- Declarations ment of wind loads for equivalent static design. J. Wind Eng. Ind. Aerodyn. 4, 149–164 (1979) Conflict of interest The authors declare that they have no con- Ding, F., Kareem, A.: Tall buildings with dynamic facade under flict of interest. winds. Engineering 6(12), 1443–1453 (2020) EN 16612:2019. Glass in building—determination of the lateral Open Access This article is licensed under a Creative Com- load resistance of glass panes by calculation. CEN, Brussels mons Attribution 4.0 International License, which permits use, Lima-Castillo, I.F., Gómez-Martínez, R., Pozos-Estrada, A.: sharing, adaptation, distribution and reproduction in any medium Methodology to develop fragility curves of glass façades or format, as long as you give appropriate credit to the original under wind-induced pressure. Int. J. Civil Eng. 17, 347–359 author(s) and the source, provide a link to the Creative Com- (2019) mons licence, and indicate if changes were made. The images Overend, M., Zammit, K., Hargreaves, D.: Applications of com- or other third party material in this article are included in the putational wind engineering in the design of glass façades. article’s Creative Commons licence, unless indicated otherwise Proc. Glass Perform. Days 2007, 444–448 (2007) in a credit line to the material. If material is not included in the Rizzo, F., D’Asdia, P., Lazzari, M., Procino, L.: Wind action article’s Creative Commons licence and your intended use is not evaluation on tension roofs of hyperbolic paraboloid shape. permitted by statutory regulation or exceeds the permitted use, Eng. Struct 33(2), 445–461 (2011) you will need to obtain permission directly from the copyright Rizzo, F., Ricciardelli, F., Maddaloni, G., Bonati, A., Occhiuzzi, holder. To view a copy of this licence, visit http://creativecomm A.: Experimental error analysis of dynamic properties for ons.org/licenses/by/4.0/. a reduced-scale high-rise building model and implications on full-scale behavior. J. Build. Eng. (2020). https://doi.org/ 10.1016/j.jobe.2019.101067 Rizzo, F., Franco, A., Bonati, A., Maddaloni, G., Caterino, N., Occhiuzzi, A.: Predictive analyses for aerodynamic inves- References tigation of curtain walls. Structures 29, 1059–1077 (2021) Santos, F., Gonçalves, P.F., Cismasiu, ¸ C., Gamboa-Marrufo, M.: ABAQUS computer software, v. 6-12-1. Simulia Smart glass facade subjected to wind loadings. Proc. Inst. Amadio, C., Bedon, C.: Elastoplastic dissipative devices for Civil En. Struct. Build. 167(12), 743–752 (2014) the mitigation of blast resisting cable-supported glazing Santos, F., Cismasiu, C., Bedon, C.: Smart glazed cable facade façades. Eng. Struct. 39, 103–115 (2012a) subjected to a blast loading. Proc. Inst. Civil En. Struct. Amadio, C., Bedon, C.: Viscoelastic spider connectors for the Build. 169(3), 223–232 (2016) mitigation of cable-supported façades subjected to air blast Simiu, E., Hendrickson, E.M.: Design criteria for glass cladding loading. Eng. Struct. 42, 190–200 (2012b) subjected to wind loads. J. Struct. Eng. (1987). https://doi. Amadio, C., Bedon, C.: Dynamic response of cable-supported org/10.1061/(ASCE)0733-9445(1987)113:3(501) façades subjected to high-level air blast loads: numerical Yu, Y., Liu, T., Zhang, Q., Yang, B.: Wind-induced response of simulations and mitigation techniques. Model. Simul. Eng. an L-shaped cable support glass curtain wall. Shock Vibr. (2012c). https://doi.org/10.1155/2012/863235 (2017). https://doi.org/10.1155/2017/4163045 Bedon, C., Zhang, X., Santos, F., Honfi, D., Kozłowski, M., Arrigoni, M., Figuli, L., Lange, D.: Performance of struc- tural glass facades under extreme loads—design methods, Publisher’s Note Springer Nature remains neutral with regard existing research, current issues and trends. Constr. Build. to jurisdictional claims in published maps and institutional affil- Mater. 163, 921–937 (2018) iations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Glass Structures & Engineering Springer Journals

Performance of cable-supported glass façades under time-depending wind action

Glass Structures & Engineering , Volume OnlineFirst – May 25, 2022

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Glass Struct. Eng. https://doi.org/10.1007/s40940-022-00180-2 RESEARCH PAPER Performance of cable-supported glass façades under time-depending wind action Fabio Rizzo · Chiara Bedon Received: 29 December 2021 / Accepted: 30 April 2022 © The Author(s) 2022 Abstract Cable supported glass façades are sensitive Keywords Glass façades · Building aerodynamic · to wind action because of their flexibility. Conven- Cable-supported glass façade · Wind tunnel test · tional laboratory testing to check a façade reliability Numerical modelling under the wind action is generally carried out by uni- formly air pressure tests. However, the typical wind action on a surface is known to be not uniform because 1 Introduction it varies due to building aerodynamics and wind flow turbulence, and this aspect should be properly con- The increasingly use of glass for load-bearing applica- sidered for testing protocols. This paper discusses the tions in buildings and infrastructures proved to repre- structural response of cable-supported glass façades, sent an open issue for structural designers (Bedon et al. through time history finite element (FE) analyses, under 2018). On one side, novel boundary and restraint appli- different wind action combinations that varies based on cations make the use of glass in buildings extremely the building aerodynamics (plan shapes and roof cur- versatile, compared to other constructional materials. vatures), the wind direction (0° and 90°), and the glass On the other, several safety issues are still related to panel position (up and down). Such a finding is further tensile brittleness and typical size effects for building enforced by the presence of flexible supports for the applications, under various loading conditions. constituent glass modules. The presented results show Among others, wind effects for façade systems are a strong dependence of the structural response on the responsible of stress and deflection peaks that should wind action configuration, and thus suggest the need of be properly limited, and even minimized, depending new testing protocols for similar systems. on the mechanical and geometrical features of the sys- tem object of study (Bedon et al. 2018). In most of cases, glazing windows and façades represent a highly fragile and vulnerable component for buildings, given that they are expected to act as physical barrier under F. Rizzo a multitude of design actions. For this reason, several Department of Civil Engineering, Cracow University of studies have been spent for the analysis, assessment Technology, Warszawska 24, 31-155, Krakow, Poland and even optimization of several solutions of practi- e-mail: fabio.rizzo@universityresearch.it cal interest for design, such as façades in tall buildings C. Bedon (B) (Ding and Kareem 2020) which are most sensitive to Department of Engineering and Architecture, University of Tri- wind pressures. Design criteria for façades under wind este, Via Valerio 6, 34127 Trieste, Italy e-mail: chiara.bedon@dia.units.it actions have been elaborated and discussed in Simiu 123 F. Rizzo, C. Bedon and Hendrickson (1987), Overend et al. (2007), Brewer present study, more in detail, the wind action is esti- and Sammarco (2018). The potential and feasibility of mated by wind tunnel tests on buildings covered with fragility curves in support of efficient and conserva- a hyperbolic paraboloid roof. The building prototype tive design of glass façades under wind pressure has represent a sport arena and it was supposed to have been addressed in Lima-Castillo et al. (2019). Complex very large and tall glass façades on the perimeter. The mechanical systems in which glass panels are braced pressure coefficients on the lateral surfaces are esti- by cable systems have been investigated in Yu et al. mated in wind tunnel for different wind angles and for (2017). A smart control system for cable supported different plan shapes. A special care is then given to façades under wind or even blast has been proposed the comparative investigation of wind–structure inter- in Santos et al. (2014, 2016), to prevent extreme stress action on zones close to the flow detachment edge and peaks in glass components under dynamic events. on zones that are far away from the edges. The wind induced displacements were estimated by The novelty of this paper consists of a discussion on Rizzo et al. (2021) based on a numerical model cali- the structural response of cable-supported glass façades brated towards full-scale laboratory experiments. It was under a dynamic action induced by the wind, and as far observed that the wind action estimated by wind tun- as the authors know, there are no comparable scientific nel tests affects the façade structural response closely publication on this issue. differently than laboratory air pressure tests commonly To this aim, Sect. 2 summarizes the façade geom- used to check the façade reliability. Results discussed etry and mechanical characteristics, with evidence of by Rizzo et al. (2021) proved that the wind-structure some basic preliminary considerations, while Sect. 3 interaction in the field of the glass façades should be discusses the reference wind tunnel experimental setup investigated carefully to avoid air infiltration and unde- and the wind action calculations that are used for time- sired torsion in the supporting frame members. In the dependent non-linear analyses. Numerical simulations present paper, the attention is still focused on façade are thus presented in Sect. 4, while Sect. 5 discusses glass panels under wind pressure. Compared to liter- the main results. ature studies, however, major efforts are spent on the characterization and analysis of wind effects based on original experimental pressure data. Further, the analy- 2 Structural setup of the cable-supported glass sis is focused on a special typology of cable-supported façade façade systems. More in detail, the case-study curtain wall explored in Amadio and Bedon 2012a, b, c)is 2.1 Façade system take into account and adapted to the present investiga- tion. Based on efficient but refined finite element (FE) In this paper, the analysis is focused on the cable- models developed in ABAQUS (ABAQUS computer supported glass façade originally explored in Ama- software), a set of twelve non-linear dynamic analyses dio and Bedon (2012a, b, c). The modular unit is L is carried out with the support of twelve time histo-  9 m tall and composed of B  1.55 m laminated ries of wind pressure. Typical wind effects and façade glass sheets schematized in Figs. 1 and 2 (H  3m behaviours are thus assessed from parametric analyses. their maximum height). The glass layers are fully tem- Based on simple preliminary calculations, the effects of pered, with a nominal characteristic tensile strength in boundaries for such complex mechanical systems are bending up to 120 MPa (CNR 2013; EN 16612:2019). also analysed in terms of corresponding performance As also explained in Amadio and Bedon (2012a, b, c), indicators for design. to minimize the computational cost of simulations and The purpose of this paper is to discuss the wind- simplify the analysis, the façade is assumed to be wide structure interaction for glass façades to alarm codifiers enough (B × n modules  L) to neglect the lateral and sway the scientific community on such a sensitive restraints at the vertical edges of each module. issue. The thesis supported is that the static air pressure Moreover, it is assumed that each laminated glass tests reproduced in laboratory to assess glass façade panel has a total nominal thickness t  24.52 mm, as tot against wind pressure are not reliable because the wind obtained by bonding two glass sheets (t  t  10 mm) 1 2 action is a dynamic force, and its time-depending effect and a middle PVB-interlayer (t  4.56 mm). The PVB should not be neglected (Rizzo et al. 2021). For the glass panels are braced by a system of steel vertical 123 Performance of cable-supported glass façades under time-depending wind action Fig. 1 Schematic drawing of the examined façade system, as adapted from (Amadio and Bedon 2012a, 2012b, 2012c). Figure reproduced from (Amadio and Bedon 2012c) under the terms and conditions of a Creative Commons Attribution License agreement cables with φ  36 mm diameter. To realize an effi- provide useful preliminary feedback about the expected cient bearing system for glass panels, they are spaced mechanical performance of the element. Stress and at intervals of i  1.55 m in the plane of the wall (x- deflection peaks are thus verified against the prescribed direction). At the same time, the distance between the limit values (CNR 2013; EN 16612:2019). bracing cables and laminated glass panels in z-direction In the present paper, a preliminary comparative anal- is set equal to d  65 mm. ysis for the B × L façade panel is presented in Fig. 3.At A mostly rigid restraint in z-direction is offered first, the viscous behaviour of interlayer is disregarded, by spider connectors with point-fixings (six point- and the analysis is carried out under the assumption of fixings/glass panel) according to Fig. 2. The cable sys- a “fully monolithic” glass section as in Fig. 3a, with t tot tem is finally subjected to an initial prestressing force  24.52 mm. The quasi-static wind pressure W is uni- P . formly applied to the full surface of glass. Two differ- ent boundary conditions are taken into account, namely the CS(A) configuration in Fig. 3b characterized by the presence of linear simple supports along the edges of 2.2 Glass panel under quasi-static uniform pressure glass and the “6PF(N)” configuration in Fig. 3c, where the glass panel is assumed restrained by six ideally rigid The minimization of potential stress peaks and deflec- point-fixings. The corresponding stress and deflection tions in glass panels that are characterized by high peaks are monitored with the support of non-linear cal- slenderness and flexibility for curtain wall applications culations as a function of the imposed pressure W. is—in most of cases—the primary target of design and Simple non-linear analytical calculations from CNR analysis. Besides, boundary and restraint conditions are (2013); EN 16612:2019) are preliminary taken into known to induce additional local and global behaviours account for the CS(A) configuration in Fig. 3b. This that may result in premature fracture or exceedance of means that maximum stress values and deformations reference performance limit values. are estimated (both at the centre of glass panel) as: For laminated glass panels under wind pressure, an equivalent quasi-static orthogonal pressure representa- tive of wind action peak for the location of interest can 123 F. Rizzo, C. Bedon Fig. 2 Schematic drawing of façade details: a laminated glass section, b point-fixing connection model is taken into account, due to the lack of efficient analytical formulations for such a specific restraint con- σ  k · · F (1) max 1 d dition. The typical bending behaviour can be noted in Fig. 4a. Worth to remind that the stress and deflection and peaks for the CS(A) case are expected at the centre of glass. Similar effects can be expected for the deflection A F analysis of the 6PF(N) panel with ideally rigid point- w  k · · (2) max 4 h E fixings, while stress peaks migrate from the panel cen- tre towards the region of supports. In this regard, the In Eqs. (1) and (2), A  B × L is the surface of glass, numerical stress peaks calculated in the region of point- F the design action corresponding to W, h  t the d tot fixings need to be further magnified as in CNR (2013), reference thickness, E  70 GPa the Young’s modulus that is: of glass and k , k two non-dimensional parameters 1 4 (CNR 2013; EN 16612:2019). For the 6PF(N) config- uration in Fig. 3c, the support of a simple FE numerical σ  σ · K (3) hole 123 Performance of cable-supported glass façades under time-depending wind action Fig. 3 Preliminary analysis of the glass panel under ideal boundary conditions and quasi-static wind pressure: a reference cross-section, b simple supported panel, c point-fixed panel so as to account for the stress intensification factor finally, is the trend of stress peaks towards the reference K as in Fig. 4b, with K ≈ 2.1 for the present calculation tensile resistance of glass. example. In this regard, it is important to remind that Besides, all the comparative results in Fig. 4 still the modelling strategy according to Eq. (3) represents disregard the complex behaviour of the examined glass a practical but simplified approach, because the calcu- panel as a part of the cable-supported system in Figs. 1 lation is focused on the global effect induced by load and 2 (i.e., viscous behaviour of interlayer for the lami- distribution. nated section, flexibility of bracing cables, etc.), as well Comparative results are proposed in Fig. 4c for both as the typical time variability and dependence of wind the examined conditions, as a function of a uniform actions, thus recommending a detailed time-dependent pressure W in the range of 0–30 kPa. The final effect analysis as in Sects. 3 and 4. of ideally rigid point-fixings is a stress peak increase denoted in Fig. 4c as “6PF(N) x K”, which largely exceeds the stress estimates for the CS(A) condition. 3 Wind action As far as the actual restraint configuration of glass as a part of the cable-supported façade is disregarded, The time-dependent wind action W (t) on the exam- some additional feedback about the expected perfor- ined façade was estimated according to Eq. (4), assum- mance of the examined panel can be obtained by intro- ing the mean wind velocity V equal to 24.7 m/s; it ducing in Fig. 4d the stress and deformation ratios. was calculated assuming v  31 m/s, z  0.7, b00 0 Ideal restraints, for a given panel shape, size and thick- z  12 m, k  0.23, a  500 m, k  0.32, the min r 0 a ness, result in different performance limits for ultimate air density, ρ  1.25 kg/m , A is the façades area (stress) and serviceability (deflection) states. Following (CEN (Comité Européen de Normalization) 2005). In (CNR 2013), the maximum deflection in service condi- Eq. (4) (CEN (Comité Européen de Normalization) tions is limited to H/60 (or 50 mm) for the CS(A) panel. 2005;CNR 2018), the time dependent pressure coeffi- This deflection limit reduces to L /100 (or 30 mm) min cients, cp(t ),were assumed according to results given for the 6PF(N) condition. Comparative plots exceed- by Rizzo et al. (2011) on lateral surfaces of building ing the y  1 value in Fig. 4d are thus representative covered with large span roofs. of “unsafe” deformation amplitudes to avoid for design and serviceability checks. Worth to be noted in Fig. 4d, W (t)  cp (t) · ρV · A (4) m i 123 F. Rizzo, C. Bedon (a) (b) (c) (d) Fig. 4 Preliminary analysis of the glass panel under ideal boundary conditions and quasi-static wind pressure: a numerical model for 6PF(N), with legend values in Pa (shape scale factor × 5), b stress magnification factor K for bending, c stress–deflection trends and d stress–deflection ratios as a function of the imposed pressure (ABAQUS) In total, eight different geometries of building were #7) to 98 (i.e., Geometry #6 and #8). Each test models considered to investigate the influence of the building were equipped with Teflon tubing that was calibrated aerodynamics on the façade structural response. Table such to obtain a flat frequency response up to 100 Hz; 1 and Fig. 5 summarize the reference geometries. The this was achieved by selecting the tube length and the geometrical scale of the test model was assumed equal position of a pneumatic damper. Acquisition was car- to 1:50. ried out at a sampling frequency of 252 Hz for a dura- Wind tunnel tests were carried out on four square and tion of 29.7 s. The turbulence intensity at the roof level four rectangular building pressure models, all featuring ranges between 11 and 12%. The tests were performed a hyperbolic paraboloid roof, in the CRIACIV bound- at a mean wind speed of 16.7 m/s at a height of 10 cm. ary layer wind tunnel in Prato, Italy (Rizzo et al. 2011). Sixteen wind angles were acquired in wind tunnel but The facility is an open circuit tunnel with a 2.30 m × for sake of brevity results on only 0° and 90° (Fig. 5) 1.60 m test chamber. The rigid models are made of are discussed in this paper. wood and the number of pressures taps on the lateral surface ranges from 58 (i.e., Geometry #1, #3, #5 and 123 Performance of cable-supported glass façades under time-depending wind action Table 1 Geometrical Geometry L L f f H H + f + f 1 2 1 2 1 1 1 properties of prototypes and 2 test models Model (cm) #1 80.00 80.00 2.70 5.30 13.30 21.30 #2 80.00 80.00 2.70 5.30 26.70 34.70 #3 80.00 80.00 4.40 8.90 13.30 26.70 #4 80.00 80.00 4.40 8.90 26.70 40.00 #5 40.00 80.00 2.70 5.30 13.30 21.30 #6 40.00 80.00 2.70 5.30 26.70 34.70 #7 40.00 80.00 4.40 8.90 13.30 26.70 #8 40.00 80.00 4.40 8.90 26.70 40.00 Prototype (m) #1 40.00 40.00 1.35 2.65 6.65 10.65 #2 40.00 40.00 1.35 2.65 13.35 17.35 #3 40.00 40.00 2.20 4.45 6.65 13.35 #4 40.00 40.00 2.20 4.45 13.35 20.00 #5 20.00 40.00 1.35 2.65 6.65 10.65 #6 20.00 40.00 1.35 2.65 13.35 17.35 #7 20.00 40.00 2.20 4.45 6.65 13.35 #8 20.00 40.00 2.20 4.45 13.35 20.00 Fig. 5 Building geometrical parameters and wind angles of attack during experiments: a square plan and b rectangular plan building The mean, maximum and minimum values of the were divided in subzones as it is represented in Fig. 6 pressure coefficients were calculated from the mea- from 1 to 7 for square plan building and from 1 to 5 sured time series. In particular, the maximum and min- on the side parallel to 90° and from 1 to 7 on the side imum values were calculated according to a best fit parallel to 0° (Fig. 6). Sides are named α, β, χ and γ with the Gumbel distribution, following the procedure clockwise. It was investigated because the flow field proposed by Cook and Mayne (1979) associated with around the building lateral surfaces is very different a 22% probability of being exceeded, as it is done by on zones close to the detachment edges, as for exam- Cook and Mayne (1979). ple zones #1 and #7, and on zones very distant to the Buildings were covered with a double curvature roof detachment edges as for example zone #4. However, it (i.e., hyperbolic paraboloid roof) to simulate a cable net is necessary to distinguish two parts in the same zones, tensile structure. It was made of downward cables par- the part close to the upper edge and the part close to allel to the 0° wind direction and upward cables paral- the floor. The flow field is different for these two parts lel to 90° wind direction. The building lateral surfaces of the façade and consequently it is loaded differently. 123 F. Rizzo, C. Bedon 7 5 3 6 5 2 1 4 7 7 6 6 5 5 4 4 4 5 3 3 2 3 2 2 2 1 1 0° 90° 90° y/D y/D x/B x/B 0° 45° 45° (a) (b) Fig. 6 Building lateral surface subzones: a square plan and b rectangular plan building The different flow field and consequently the differ- Table 2 Numerical analyses sets ent wind action along the same façade affects the façade Combination Analysis reliability because it can induce torsional effects on the façade beams and pillars. It can induce the detachment #1 (I) Wind action in subzone 1, geometry of the sealing gasket and consequently the air infiltra- #4 [Ref. Table 1], side β,0° tion inside the building with a negative pressure from (II) Wind action in subzone 4, geometry inside to outside. #4 [Ref. Table 1], side β,0° In order to investigate this effect, four different sets #2 (I) Wind action in subzone 1, geometry of action listed in Table 2 were considered for this study #3 [Ref. Table 1], side β,0° (in the following, Combination #1, #2, #3 and #4). Each (II) Wind action in subzone 1, geometry set consisted of two analyses for set #1, two analyses #3 [Ref. Table 1], side β, 90° for set #2, four analyses for set #3 and four analyses #3 (I) Wind action in subzone 2, geometry for set #4, that have the purpose to compare the façade #1 [Ref. Table 1], side β,0° structural response under different environmental con- (II) Wind action in subzone 2, geometry #3 [Ref. Table 1], side β,0° ditions. The exact definition of each set is discussed in the following. For sake of brevity, moreover, only (III) Wind action in subzone 2, geometry #1 [Ref. Table 1], side β, 90° selected geometries from Table 1 are discussed in this (IV) Wind action in subzone 2, geometry paper, and specifically geometries #1, #2, #3, #4 and #3 [Ref. Table 1], side β, 90° #6. Load combinations was selected to highlight the #4 (I) Wind action in subzone 1, geometry differences induced by the building geometry and the #2 [Ref. Table 1], side β,0° wind flow trend. (II) Wind action in subzone 1, geometry It is in fact important to specify that the full set of #6 [Ref. Table 1], side β,0° geometries are named geometry #1 to #8 as in Table (III) Wind action in subzone 1, geometry 1. There, the subzones are representative of the façade #2 [Ref. Table 1], side β, 90° zones illustrated in Fig. 6, where they are labelled from (IV) Wind action in subzone 1, geometry #1 to #7 for all four sides of square plan building, or #6 [Ref. Table 1], side β, 90° from #1 to #5 and from #1 to #7 for shorter and longer sides respectively of rectangular building. The first set (i.e., Combination #1) consists of two consists of two analyses with the aim to study the influ- analyses with the aim to investigate the influence of ence of the wind angle (i.e., 0° and 90°); the third com- the aerodynamic due to the flow streamlines from the bination (i.e., Combination #3) consists of four anal- detachment zone; the second set (i.e., Combination #2) yses with the aim to investigate the influence of roof 123 Performance of cable-supported glass façades under time-depending wind action curvature; finally, the fourth combination (i.e., Com- 4 Structural time history analyses bination #4) consists of four analyses with the aim to investigate the influence of the building plan geometry 4.1 Reference model (i.e., square and rectangular) for the two wind angle investigated. The parametric numerical analysis of the cable- Specifically, Combination #1 investigates, through supported glass system under wind pressure was car- two time-history analyses, the difference of the façade ried out in ABAQUS (ABAQUS computer software). response induced by the distance from the detachment To this aim, the reference numerical model was derived edge with wind angle equal to 0°. It has been done from Amadio and Bedon (2012a, b, c) and adapted to using wind tunnel experimental data elaborated for the the examined loading conditions. Composite shell ele- geometry #4 (Table 1), the wind angle (0°) on the same ments (S4R) were used to describe the glass panels, side β, for two subzones, #1, close to the detachment while beam (B31) and truss (T3D2) elements realized edge, and #4, distant from the detachment edge. the spider connectors and bracing system of cables, Combination #2 investigates, through two time- respectively. The final assembly consisted of 3900 history analyses, the difference of the façade response DOFs and around 600 elements (Fig, 7a). induced by a different wind angle. To achieve this pur- Linear elastic constitutive laws were used for mate- pose, the wind tunnel experimental data on geometry rials. For fully tempered glass, the Young’s modulus, #3 under two different wind angle, 0° and 90°, on the Poisson’ ratio and density were set in E  70GPa, same side β, for the subzones, #1, close to the detach- ν  0.23 and ρ  2500 kg/m . Furthermore, for the g g ment edge. PVB-interlayer, an equivalent elastic–plastic character- Combination #3 investigates, through four time- istic curve was taken into account, with E  8MPa PVB history analyses, for the same subzone quite close to the reference secant modulus corresponding to short- the detachment edge (i.e. subzone #2), the difference term wind actions (CNR 2013), with ν  0.49 and PVB induced by two wind angles (0° and 90°) and the dif- ρ  1100 kg/m . Finally, harmonic steel (cables) PVB ference induced by a different roof curvature, flat (i.e. and stainless steel (joints) were assumed to have a lin- geometry #1) and curved (i.e. geometry #3). ear elastic behaviour, with ρ  7800 kg/m , ν  0.3 s s Finally, Combination #4 investigates, through four and E  130 GPa, E  170 GPa respectively. s,h s,s time-history analyses, for the same subzone close to Based on the above material assumptions, especially the detachment edge (i.e. subzone #1), the difference for glass, the analysis of possible damage mechanisms induced by two wind angles (0° and 90°) and the dif- (i.e., stress peaks in the region of point-fixings) were ference induced by a different plan shape, square (i.e. based on the time-dependent analysis of maximum geometry #2) and rectangular (i.e. geometry #6). stress and deformations for the full model components. The selected combinations shall reflect any geomet- A special role was assigned to restraints, for the rical combinations available from experimental data. façade module assessment. The cables were pinned at All calculations were computed using a wind action the upper end, while the initial pretension force P for time history with a time length equal to 800 s and a the bracing system was imposed at their base in the time step equal to 0.1 s. For all analyses two-time his- form of an equivalent vertical displacement (see also tories were applied on the glass panel, the first one 1/4 Sect. 5.2). Along the elevation of the façade-module, of the glass panel height from the border down and the only z-displacements and x-rotations were allowed for second one 1/4 of the glass panel height from the border the other cables nodes, so as to account for the presence up. of adjacent façade members. Structural silicone sealant bonding glass panes was neglected, since it provides a negligible rotational stiffness (Amadio and Bedon 2012a, b, c). Each half-spider connector consisted in three rigidly connected 2-node linear beams that were linked by means of a weld connector (null relative dis- placements and rotations) and additional joins (pinned connectors with free relative rotations) to provide the 123 F. Rizzo, C. Bedon Fig. 7 Model of the façade module (ABAQUS): a general view and b schematic drawing of point-fixings. Figures reproduced from (Amadio and Bedon 2012c) under the terms and conditions of a Creative Commons Attribution License agreement mechanical interaction of glass-spider and spider-cable for nonlinear cables structures. A schematic view of nodes. A schematic drawing is proposed in Fig. 7b. reference control points and parameters is shown in Fig. 8. For the analysis of wind effects on such a structural system characterized by flexibility parameters (and 4.2 Analysis procedure and performance indicators thus stress–deflection performance indicators) highly sensitive to the features of the bracing system of cables, The typical analysis was arranged onto two steps. First, some preliminary comparative calculations were car- the façade system was subjected to self-weight and ried out for the façade module. prestress force P in the bracing cables (static step). The analysis was focused on the effects of initial pre- Secondly, the preloaded model was analysed under the stress P on the expected fundamental vibration period effects of wind pressures as in Table 2 (dynamic step). of the façade module (linear modal step), as well as This step consisted of 60,000 increments over the dura- on the maximum effects due to a quasi-static uniform tion of wind action. wind pressure (non-linear static step). To this aim, the For the post-processing stage, careful attention was characteristic axial resistance of bracing cables is also paid for the analysis of some key indicators for the per- recalled, with P  1150 kN (Amadio and Bedon Rk formance assessment of the façade module under wind 2012a, b, c), so as to express the prestressing levels actions. These included possible tensile stress peaks in of bracers as a function of the imposed force towards glass (region of point-fixings, centre of panels); max- the resistance. imum out-of-plane deflections (centre of panels); rel- As it can be seen in Fig. 9a, no marked variations ative deformation and twist of glass panels; as well as can be expected in the qualitative fundamental vibra- maximum stress peaks in the bracing cables. A dynamic tion shape of the façade module under limited prestress approach through time history analyses is considered in the present study, because of its intrinsic advantages 123 Performance of cable-supported glass façades under time-depending wind action Fig. 8 Key performance indicators for the dynamic analysis of the façade module (a) (b) Fig. 9 Analysis of pretension effects in terms of a fundamental vibration shape and b period (ABAQUS) 123 F. Rizzo, C. Bedon ratio levels. Besides, marked modifications of the corre- In Fig. 11, qualitative results are proposed for sponding vibration period are recorded in Fig. 9b from selected façade components and input pressure data. the same parametric modal analyses. As expected from the preliminary calculation steps, A more detailed analysis of results for the deflection the façade module was characterized by limited stress and stress performance of the central glass panel sub- peaks in glass, thus ensuring a mostly elastic response jected to major bending effects can be summarized as of the system under the imposed time histories. This in Fig. 10. There, the relative and absolute deflection can be noticed from the example of contour plots as in ratios are first explored, due to the high flexibility of the Fig. 11. The deformed shape of the system, even still system. Figure 10a shows the ratio of relative deflec- characterized by a cylindrical deformation in accor- tion (i.e., left-down minus middle central point of the dance with the fundamental modal shape in Fig. 9,was panel) towards the allowable limit deflection reported also found to suggest local and global effects due to in Sect. 2 (i.e., L /60  15 mm as in Fig. 4). The the non-uniform, time-dependent pressure histories for min chart data in Fig. 10a that exceed the y  1 value, wind. in this regard, represent unsafe pressure amplitudes. In this regard, Fig. 12 shows a quantitative overview Another important parameter for the dynamic perfor- of the structural response given by FE Analysis #1. mance analysis is the absolute deflection of the 9.00 m Specifically, Fig. 12a presents the left-down corner dis- tall façade. To this aim, the global deflection under ordi- placement (δ ) time history, Fig. 12b the right-up cor- nary wind pressure should be limited to a maximum of ner (δ ) displacement time history, Fig. 12c the mid- 1/100 the total span (Amadio and Bedon 2012a, b, c). In dle point displacement (δ ) time history respectively. this regard, chart data in Fig. 10b which exceed the y  Figure 12d also shows the cable displacement (δ ), 0.001 value are representative of unsafe pressure ampli- while the corresponding envelope of Von Mises cable tudes for wind. In both figures, it is wort to mention stresses (σ ) is proposed in Fig. 12e. Worth to be noted that the effect of prestress level (even under quasi-static the evolution of stress peaks in the glass panel (σ in pressure assumptions) still reflects in marked modifi- Fig. 12f. cation of the façade performance. The collected stress peaks, as shown, are relatively In this regard, Fig. 10c shows the typical distribution small to avoid any kind of damage in the façade mod- of maximum principal stresses for the central laminated ule components, or maximum deflections exceeding glass panel (10 kPa the pressure amplitude). It can be the reference limit values. Besides, the attention from notice that the expected stress peaks in glass—thanks the parametric numerical analysis outcomes is focused to the flexibility of supports—are relatively low, com- in the present study on the range of variability for the pared to the reference material resistance and to the cor- estimated performance indicators, as a major effect due responding deflection parameters. Most importantly, to the time-dependency of wind pressures. the deformed shape of the panel (and thus the corre- The statistics of output data are summarized in sponding stress distribution in glass) strongly differs Tables 3 and 4 for all Combinations (i.e., from #1 to from the idealized analysis of the plate with rigid point- #4) and corresponding FE analyses (based on Table 2). fixings as in Fig. 4, thus confirming the importance of Table 3 gives the mean, maximum, minimum and stan- refined calculations for design purposes. dard deviation value for displacements δ , δ and δ .At 1 2 3 the control points in the central glass panel. Similarly, Table 4 summarizes the variation of cable deflection 5 Discussion of time-dependent dynamic results δ and the maximum (envelope) stress parameters for cables (σ ) and glass (σ ). c g The parametric analysis with time-dependent wind For Combination #1 in Table 3, the comparison pressure was carried out for the façade module char- between subzone #1 (i.e., Analysis I) and subzone #4 acterized by a moderate prestress level in the cables, (i.e., Analysis II) shows a very large difference for the corresponding to T  0.465 s of fundamental vibra- selected control points (i.e., left-down, right-up and the tion period as in Sect. 4. The quantitative analysis of middle one) especially observing the mean value that is parametric data was again carried out based on the per- opposite. This means that subzone #1 is in suction and formance indicators and selected control points previ- subzone #4 is in pressure. This cannot be neglected ously discussed. 123 Performance of cable-supported glass façades under time-depending wind action (a) (b) (c) Fig. 10 Analysis of pretension effects in terms of a–b deflection and c stress analysis of the central glass panel under quasi-static uniform wind pressure (ABAQUS, shape scale factor × 5) 123 F. Rizzo, C. Bedon Fig. 11 Example of variation in time of: a deflection (in m), b velocity (in m/s), c maximum stress in glass (in Pa) and d Von Mises stress in cables (in Pa). ABAQUS/Standard, results from combo #3(ii) after 0.25 s of wind exposure 123 Performance of cable-supported glass façades under time-depending wind action (a) (b) (c) (d) (e) (f) Fig. 12 Glass panel response for Analysis #1: a left-down corner displacement (δ ), b right-up corner displacement (δ ), c middle point 1 2 displacement (δ ), d cable displacement (δ ), e cable Von Mises stress (σ )and e maximum principal stress in the glass panel (σ ) 3 c c g 123 F. Rizzo, C. Bedon Table 3 Maximum (M), minimum (m), mean (μ) and standard deviation (σ ) of the glass panel displacements, as measured at the left-down corner (δ ), right-up corner (δ ), or middle point (δ ) 1 2 3 Comb Analysi δ (up) δ (middle) δ (down) 1 2 3 s# μ (mm) M m σ (mm) μ (mm) M m σ (mm) μ (mm) M m σ (mm) (mm) (mm) (mm) (mm) (mm) (mm) #1 (I) 20.41 75.06 − 22.52 12.12 23.71 83.54 − 24.59 13.16 22.19 76.66 − 22.11 11.85 (II) − 19.33 4.97 − 47.55 8.60 − 20.63 3.32 − 48.99 8.41 − 18.16 0.46 − 40.78 6.55 #2 (I) 4.05 54.20 − 51.80 15.51 5.30 58.93 − 56.48 16.23 5.30 51.44 − 50.24 13.83 (II) 64.95 111.59 1.49 10.43 68.81 123.66 0.82 11.73 58.29 106.89 − 0.38 10.78 #3 (I) 12.77 64.14 − 32.57 14.60 14.21 69.49 − 36.30 15.22 12.59 58.23 − 33.18 13.00 (II) 4.05 54.20 − 51.80 15.51 5.30 58.93 − 56.48 16.23 5.30 51.44 − 50.24 13.83 (III) 67.80 113.81 1.49 10.40 71.60 114.39 0.82 11.31 60.40 98.10 − 0.38 10.18 (IV) 64.95 111.59 1.49 10.43 68.81 123.66 0.82 11.73 58.29 106.89 − 0.38 10.78 #4 (I) 38.38 57.63 1.49 5.68 40.96 69.21 0.82 7.48 35.07 67.10 − 0.38 8.08 (II) − 9.99 16.17 − 38.21 7.81 − 9.06 14.78 − 35.45 7.37 − 6.48 12.78 − 27.28 5.54 (III) 38.10 79.11 1.49 6.89 41.23 89.30 0.82 6.52 35.89 78.18 − 0.38 4.94 (IV) 74.68 103.45 1.49 5.74 74.96 113.90 0.82 6.33 59.08 97.50 − 0.38 5.88 during the design phase the façade. In Table 3, stan- wind angle equal to 90°, for the same control point. It dard deviation was assumed as a measure of the time- was also noted that the variation of the mean value of depending effect of wind pressure. It can be observed measured displacements in the middle point is smaller that for combination #1 it ranges from 6.55 (right-up, for 90° than 0° due to the building aerodynamics. subzone #4) to 13.16 (middle point, subzone #1). As it All calculations herein discussed showed alternative was expected the flow field is more instable close to the positive and negative displacements induced by pres- detachment edge (i.e., subzone #1) and that is the rea- sure and suction on the façade system, as a direct effect son because the standard deviation is bigger on this sub- of wind dynamics. zone. However, this effect should be taken into account Finally, as expected, data in Table 3 show a sig- during the design phase because it means that the façade nificant difference between square plan building and sealing gasket are more loaded by wind induced vibra- rectangular plan building for both two wind angles and tion in subzone #1 than in subzone #4. combinations object of study. For Combination #2, based on values given in Table A major sensitivity and variation of parametric FE 2, it was observed that due to the building shape and results was observed for the cable displacement (δ ), its aerodynamics, the same subzone #1 is loaded very cable stress (σ ) and glass panel stress (σ ), as it can be c g differently under wind angle 0° and 90°. seen in Table 4. The location of the glass panel around The mean value ranges from 5.30 mm to 68.81 mm the building lateral surface affects results as well as the in the middle point of the façade. It means that several building roof curvature, the wind angle and the plan wind angles should be investigated in the design the shape. Results in term of glass panel stress show that façade. the maximum peak ranges from 0.17 Pa to 4.17 MPa. Based on data given in Table 3 for Combination #3 This variation is very large and should be properly taken and for the same subzone #2, it was observed that the into account for the optimal design of glass thickness roof curvature affects the façade displacements because and point-fixing detailing. the mean value ranges from 5.30 mm (i.e., analysis Most importantly, such a stress–deflection sensitiv- (II)) to 14.21 mm (i.e., analysis (I)) with a wind angle ity to the imposed time-dependent wind pressure affects equal to 0° (middle control point). At the same time, the design of structural details, and consequently fur- the measured deflection spans from 68.81 mm (i.e., ther affects the resulting natural vibration period of analysis (IV)) to 71.60 mm (i.e., analysis (III)) with a 123 Performance of cable-supported glass façades under time-depending wind action Table 4 Maximum (M), minimum (m), mean (μ) and standard deviation (σ ) of cable displacement (δ ), cable Von Mises stress (σ ) c c and principal stress in the glass panel (σ ) Comb Analysis δ σ σ c c g μ (mm) M m σ (mm) μ M m σ (MPa) μ M m σ (MPa) (mm) (mm) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa) #1 (I) 22.32 81.58 − 25.62 13.05 148.16 176.00 145.00 3.12 1.28 4.17 0.07 0.61 (II) − 21.69 2.10 − 49.81 8.35 147.39 157.00 145.00 1.82 0.88 2.22 0.09 0.39 #2 (I) 4.06 57.27 − 57.24 16.12 146.24 160.00 145.00 1.70 0.71 3.00 0.07 0.50 (II) 67.07 121.14 − 0.38 11.60 166.45 209.00 145.00 7.50 3.43 6.78 0.17 0.58 #3 (I) 12.91 67.78 − 37.24 15.11 146.77 164.00 145.00 2.38 0.91 4.13 0.07 0.61 (II) 4.06 57.27 − 57.24 16.12 146.24 160.00 145.00 1.70 0.71 3.00 0.07 0.50 (III) 69.84 112.26 − 0.38 11.19 168.22 206.00 145.00 7.52 3.56 6.08 0.17 0.55 (IV) 67.07 121.14 − 0.38 11.60 166.45 209.00 145.00 7.50 3.43 6.78 0.17 0.58 #4 (I) 39.46 67.33 − 0.38 7.40 152.37 167.00 145.00 2.74 2.09 3.64 0.17 0.37 (II) − 10.21 13.49 − 36.40 7.32 145.80 152.00 145.00 0.99 0.40 1.58 0.08 0.26 (III) 39.73 87.30 − 0.38 6.47 152.40 177.00 145.00 2.46 2.10 5.31 0.17 0.32 (IV) 73.24 111.50 − 0.38 6.27 170.74 198.00 145.00 4.23 3.71 6.34 0.17 0.31 the façade and its dynamic response, once the opti- paraboloid roof under two orthogonal wind directions mal parameters are detected. The wind induced effect (i.e. 0° and 90°). It was investigated the dependence of estimated by FE analyses suggest that the wind action the structural response on the building aerodynamics should be reproduced carefully during the preliminary given by the building plan shape and the roof curva- test of façade systems, because it is reasonable to think ture, on the wind direction and on the panel location on that the estimated variation will be closely more sig- the façade. The façade structural response was explored nificant for the case of façades on high-rise buildings for panels close to or distant from the detached zone, (Rizzo et al. 2020). and close to or distant from ground. Totally, twelve dif- ferent wind action combinations were also considered in this study and the structural response was discussed 6 Conclusions in terms of structural performance indicators. For example, as far as a global structural model is The performance of a typical cable-supported glass taken into account for glass panels, it was observed that façades under time-depending wind action estimated the structural response in term of glass displacements in wind tunnel was investigated through time history and cable stress peaks varies considerably with random Finite Element (FE) numerical analysis. A special care wind action, compared to conventional loading proto- was given to wind action description as well as to cols. In addition, it was estimated that some zones are local and global performance parameters. As known, expected in pressure and some zones in suction, for the for practical applications, the use of conventional pro- same façade components. This finding gives a torsion of tocols for loading single glass panels with ideal bound- the façade as a whole, that should be carefully analysed ary restraints is rather consolidated and generally con- during the design phase. Finally, the time history action servative approach. Besides, especially for complex shows that pressure and suction are time-depending, and wide glass facades under live loads such as wind and it means that two areas of the same panel can be actions, a balance of modelling simplicity and accuracy loaded by pressure or suction at the same time. of estimates (even on the safe side for design) should Even if the wind induced local pressures are under be properly addressed. the limits for glass panels, the wind action induced cine- The wind action was calculated from pressure matics on the façade structural system might be unsafe. coefficients estimated in wind tunnel on lateral sur- face of low-rise buildings covered with a hyperbolic 123 F. Rizzo, C. Bedon Results suggest that the pressure test on the façades Brewer TR, Sammarco EL (2018). Optimizing glass design: the role of computational wind engineering & advanced carried out in laboratory to simulate the wind action numerical analysis. In: Proceedings of Challenging Glass are not representing the real behaviour because they 6 -Conference on Architectural and Structural Applications should take into account the pressure and suction alter- of Glass. Louter, Bos, Belis, Veer, Nijsse (Eds.), Delft Uni- native given by the buildings aerodynamics and by the versity of Technology, May 2018. https://doi.org/10.7480/ cgc.6.2174. wind flow turbulence. This paper aims to recommend CEN (Comité Européen de Normalization), Eurocode 1: Actions a glass panel testing standard procedure update to sim- on structures—Part 1–4: General actions—Wind actions, ulate consistently the wind action on the glass panels EN-1991-1-4 (2005) taking into account effects due to the turbulence and to CNR (National Research Council of Italy). Istruzioni per la Pro- gettazione, l’Esecuzione ed il Controllo di Costruzioni con the aerodynamics. Elementi Strutturali di Vetro, [Guide for the Design, Con- struction and Control of Buildings with Structural Glass Funding Open access funding provided by Università degli Elements]. CNR-DT 210/2013, (2013). Free download of Studi di Trieste within the CRUI-CARE Agreement. English version at: https://www.cnr.it/en/node/3843 CNR (National Research Council of Italy) Guide for the Assess- ment of Wind Actions and Effects on Structures. CNR-DT 207/2018 (2018) Cook, N.J., Mayne, J.R.: A novel working approach to the assess- Declarations ment of wind loads for equivalent static design. J. Wind Eng. Ind. Aerodyn. 4, 149–164 (1979) Conflict of interest The authors declare that they have no con- Ding, F., Kareem, A.: Tall buildings with dynamic facade under flict of interest. winds. Engineering 6(12), 1443–1453 (2020) EN 16612:2019. Glass in building—determination of the lateral Open Access This article is licensed under a Creative Com- load resistance of glass panes by calculation. CEN, Brussels mons Attribution 4.0 International License, which permits use, Lima-Castillo, I.F., Gómez-Martínez, R., Pozos-Estrada, A.: sharing, adaptation, distribution and reproduction in any medium Methodology to develop fragility curves of glass façades or format, as long as you give appropriate credit to the original under wind-induced pressure. Int. J. Civil Eng. 17, 347–359 author(s) and the source, provide a link to the Creative Com- (2019) mons licence, and indicate if changes were made. The images Overend, M., Zammit, K., Hargreaves, D.: Applications of com- or other third party material in this article are included in the putational wind engineering in the design of glass façades. article’s Creative Commons licence, unless indicated otherwise Proc. Glass Perform. Days 2007, 444–448 (2007) in a credit line to the material. If material is not included in the Rizzo, F., D’Asdia, P., Lazzari, M., Procino, L.: Wind action article’s Creative Commons licence and your intended use is not evaluation on tension roofs of hyperbolic paraboloid shape. permitted by statutory regulation or exceeds the permitted use, Eng. Struct 33(2), 445–461 (2011) you will need to obtain permission directly from the copyright Rizzo, F., Ricciardelli, F., Maddaloni, G., Bonati, A., Occhiuzzi, holder. To view a copy of this licence, visit http://creativecomm A.: Experimental error analysis of dynamic properties for ons.org/licenses/by/4.0/. a reduced-scale high-rise building model and implications on full-scale behavior. J. Build. Eng. (2020). https://doi.org/ 10.1016/j.jobe.2019.101067 Rizzo, F., Franco, A., Bonati, A., Maddaloni, G., Caterino, N., Occhiuzzi, A.: Predictive analyses for aerodynamic inves- References tigation of curtain walls. Structures 29, 1059–1077 (2021) Santos, F., Gonçalves, P.F., Cismasiu, ¸ C., Gamboa-Marrufo, M.: ABAQUS computer software, v. 6-12-1. Simulia Smart glass facade subjected to wind loadings. Proc. Inst. Amadio, C., Bedon, C.: Elastoplastic dissipative devices for Civil En. Struct. Build. 167(12), 743–752 (2014) the mitigation of blast resisting cable-supported glazing Santos, F., Cismasiu, C., Bedon, C.: Smart glazed cable facade façades. Eng. Struct. 39, 103–115 (2012a) subjected to a blast loading. Proc. Inst. Civil En. Struct. 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(2012c). https://doi.org/10.1155/2012/863235 (2017). https://doi.org/10.1155/2017/4163045 Bedon, C., Zhang, X., Santos, F., Honfi, D., Kozłowski, M., Arrigoni, M., Figuli, L., Lange, D.: Performance of struc- tural glass facades under extreme loads—design methods, Publisher’s Note Springer Nature remains neutral with regard existing research, current issues and trends. Constr. Build. to jurisdictional claims in published maps and institutional affil- Mater. 163, 921–937 (2018) iations.

Journal

Glass Structures & EngineeringSpringer Journals

Published: May 25, 2022

Keywords: Glass façades; Building aerodynamic; Cable-supported glass façade; Wind tunnel test; Numerical modelling

References