Glass facades under seismic events and explosions: a novel distributed-TMD design concept for building protection

Abstract

Glazing facades generally represent one of the most critical building components, from a structural point of view, since providing a physical separation and barrier for the building occupants. In this regard, especially under the action of extreme loads, they require specific design concepts voted to protect the building occupants. In this paper, the feasibility and potential of special mechanical connectors interposed at the interface between a given multi-storey primary building structure and the glazing facade are investigated via accurate finite-element models, under the action seismic and explosive loads. Given the case study of a 4-storey steel framed structure enclosed by a glazing curtain wall, both the global and local effects and potential benefits due to additional vibration control systems (VCSs) are preliminary assessed via numerical simulations, giving evidence of the activation—once properly designed—of a distributed-tuned-mass damper (TMD) concept involving the glass facade as a structural component of the 3D building. Differing from traditional TMD applications in civil engineering systems—namely consisting of lumped mass, damping and stiffness terms—these beneficial contributions are derived from the enclosing glass panels. Taking advantage of earlier research studies, in particular, where major efforts have been spent for the potential of visco-elastic VCSs, careful consideration is paid in this paper for the feasibility of elasto-plastic (PL) connectors, giving evidence of their response and effects under both seismic events and explosions. As shown from FE results partly discussed in the paper, the full 3D assembly can take benefit from the proposed design concept, hence suggesting the further development of the explored passive mitigation tool for the protection of the primary building structure.

1 Introduction and state-of-the-art

Glass facades are widely used in building structures, due to a series of aesthetic, thermal and lightening aspects. In most of the cases, transparent surfaces spanning from floor-to-floor are used in commercial, residential or strategic buildings. From a structural point of view, under the action of exceptional loads like impacts or accidental/natural hazards in general, glass facades represent a critical component for multi-storey buildings, due to the typically brittle behaviour and limited tensile resistance of glass panes, as well as to connection detailing etc., hence requiring specific, fail-safe design concepts (Feldmann et al. 2014; Bedon et al. 2018). In this regard, analytical, experimental and /or Finite Element (FE) numerical investigations can be found in the literature for glazing envelopes under seismic events (i.e. Behr et al. 1995; Ber et al. 2013; Stepinac et al. 2016 etc.), blast, explosions and accidental impacts (i.e. Zhang et al. 2013; Bedon et al. 2017; Lori et al. 2017; etc.), fire (i.e. Machalická et al. 2016; etc.), hurricanes and climatic loads (i.e. Masters et al. 2010; etc.), being responsible of potential severe damage scenarios and injuries, see Fig. 1. An extended state-of-the-art review on research and design standards for glass facades under extreme loads—including accidental, human induced or natural hazards—is provided in Bedon et al. (2018).

Fig. 1

Examples of glass systems under hazards: a seismic events, b hurricanes and c explosions

In this paper, based on major outcomes of an ongoing research investigation (Bedon and Amadio 2017a, 2018), careful consideration is paid for the multi-hazard performance of Unitized Glass Curtain Walls (UCGWs), and in particular for the mitigation of maximum effects due to seismic loads and blast events, being representative of emergency situations for people protection, as well as of extreme loading scenarios that buildings should properly withstand during their life-time. In doing so, the attention is focused both on the UGCW components and on the primary building, being representative of a complex 3D assembly as a whole.

The effects of special mechanical connectors interposed at the interface between a given multi-storey structure and the enclosing UGCW are hence fact investigated via efficient FE numerical models, under various extreme loading scenarios. Such a design concept and Vibration Control Systems (VCSs) are intended to act at the curtain-to-building interface, hence enabling a sort of ‘distributed-Tuned Mass Damper (TMD)’ mechanism. Compared to Bedon and Amadio (2017a, 2018), where the potential and feasibility of the distributed-TMD solution has been preliminary investigated by accounting for viscoelastic (VE) VCSs, see Fig. 2a, this paper aims to explore the efficiency of elasto-plastic (PL) VCSs, giving evidence of their global and local effects under multi-hazards. In Fig. 2b, a possible example of such a PL control systems is recalled from Bedon and Amadio (2017b), where major effects and possible benefits under blast have been explored on single modular units only. In the current paper, following earlier research investigations, it is shown that, when properly designed, PL connectors can enhance the overall dynamic performance of the UGCW they support, with marked dynamic benefits for the full 3D building they belong to.

Fig. 2

a Reference mechanical model for the analysis of buildings with dissipative glazing curtain walls, with detail of UGCW corner restraints, in accordance with Bedon and Amadio (2017a, 2018), and b possible elasto-plastic devices (Bedon and Amadio 2017b)

2 Elasto-plastic Vibration Control Systems

Since decades, both viscoelastic (VE) and elasto-plastic (PL) devices for structural engineering applications represent consolidated and efficient solutions for buildings and infrastructures mitigation, even associated to mostly different mechanical behaviours and design concepts.

First applications of VE dampers to structures was in the form of shock absorbers for military and aerospace applications, while successively—due to their intrinsic high damping ($c_{\mathrm{d}}$, in Fig. 2a) and flexibility ($K_{\mathrm{d}}$, in Fig. 2a) capacities—their engineering use has been extended to buildings and infrastructural systems under seismic, wind or impact vibrations (see for example (Chopra 2011; Kanitkar et al. 1998; Pekcan et al. 1999; Min et al. 2004; Silwal 2016; etc.). The key advantages of VE dampers—given their mechanical features—are namely represented by (A) activation at very low displacements and magnitude of the incoming impulse; (B) availability of restoring force and re-centering capacity; and (C) almost linear mechanical behaviour, hence resulting in simplified design rules and recommendations. Recent promising studies suggested the use of VE dampers in glazing systems (see Bedon and Amadio 2017a, 2018), giving evidence that VE devices introduced at the facade-to-primary structure interface can have multiple benefits on the behavioral trends of the 3D assembly, as a major effect of their additional flexibility and damping capacities. Key issues in their optimal design, on the other hand, are the sensitivity to operating frequency/temperature variations, as well as the prevention of possible failure mechanisms, i.e. delaminations or maximum shear deformations in the VE components, hence requiring fine tuning of input mechanical properties and expected structural effects.

This is not the case of elasto-plastic (PL) VCSs, like yielding metal dampers able to dissipate the incoming energy due to inelastic deformation of metals, being widely used in civil constructions (Whittaker et al. 1989; Hejazi et al. 2014; etc.), in the form ADAS (Added-Damping-And-Stiffness) dampers, etc. From a practical point of view, PL devices are mechanically described in the form of elasto-plastic bi-linear constitutive behaviour (Whittaker et al. 1989), where the key input parameter are the elastic shear stiffness $K_{\mathrm{d}}$ and the shear yielding force $F_{y,d}$. The structural efficiency of PL connectors lies in their typically high plastic dissipation. On the other hand, no re-centering capacity should be taken into account in design, since requiring their replacement after extreme loading scenarios. With respect to the distributed-TMD concept investigated in this paper, when subjected to external loads impacting on the UGCW surface, the glazing modules are expected to transfer the maximum reaction forces to the restraining PL devices. As far as these corner reaction forces do not exceed $F_{\mathrm{y,d}}$, the devices behave as linear elastic supports for the UGCW assembly. Conversely, when the incoming shear loads exceed $F_{\mathrm{y,d}}$, the PL mechanisms can activate and allow a certain sliding of VCSs, hence providing progressive plastic dissipation of the incoming energy. Taking advantage of their typical mechanical behavior, ADAS dampers have been largely used in buildings, especially for the vibration control of buildings under earthquake loads. In Bedon and Amadio (2017a), a preliminary application to UGCWs under blast has been also reported, giving evidence (at the local component level) of their potential. From a practical point of view, in accordance with Fig. 2b, the key input parameters of ADAS devices can be calculated as:

$$\begin{aligned} K_{\mathrm{d}}= & {} \frac{F_{\mathrm{y,d}} }{\Delta _{\mathrm{y,d}} }=n\cdot \frac{2}{3}\frac{E_{\mathrm{s,VCS}} t_{\mathrm{d}}^3 b_{\mathrm{d,eq}} }{l_\mathrm{d}^3 }, \end{aligned}$$

(1)

$$\begin{aligned} F_{\mathrm{y,d}}= & {} n\cdot \frac{f_{\mathrm{y,s,VCS}} t_\mathrm{d}^2 }{4}. \end{aligned}$$

(2)

In Eqs. (1)–(2), $E_{\mathrm{s,VCS}}$ and $f_{\mathrm{y,s,VCS}}$ denote the Young’s modulus and yielding stress for the steel in use for VCSs, while $t_{\mathrm{d}}$ and $l_{\mathrm{d}}$ (with $b_{\mathrm{d,eq}}=l_{\mathrm{d}}/2$) signify the nominal dimensions of ADAS yielding components, n is the number of metal plates and:

$$\begin{aligned} \Delta _{\mathrm{y}} =\frac{3}{4}\frac{f_{\mathrm{y,s,VCS}} l_\mathrm{d}^2 }{E_{\mathrm{s,VCS}} t_\mathrm{d}} \end{aligned}$$

(3)

the expected yielding displacement. In this research study, following Bedon and Amadio (2017a), ADAS devices according to Fig. 2b are implemented in a case study building under multi-hazards. In doing so, aiming to optimize the ADAS potential, a LYS (Low-Yield-Strength) steel is used for plastic VCSs (with $f_{\mathrm{y,s,VCS}}=160\,\hbox {MPa}$ for the selected LYS160 grade), being typically associated to limited yielding strength and favorable plastic dissipation and hence representing a valid solution for dampers and vibration control systems (Han et al. 2014; Zhang et al. 2016; etc.).

3 Reference building system and solving approach

3.1 Case study building

Following Bedon and Amadio (2017a, 2018), the same UGCW and case study building are taken into account, for comparative purposes. The chosen building system, being part of an academic investigation, is aimed to represent at least major features of key importance in the structural dynamics of a real building. In this context, geometrical and mechanical simplifications are included in it, compared to a full building design project. The obtained FE results, at the same time, can be intended as a useful background for the further refined development of the explored design concept.

A total dimension of $h=2.90\,\hbox {m}\times b=1.6\,\hbox {m}$ is considered for each UGCW module, spanning from floor-to-floor in the building object of analysis. There, Insulated Glass (IGU) panels are continuously supported by an aluminum frame, and rigidly connected to the main structure by means of traditional, fully rigid steel brackets. The IGU panels are composed by a monolithic, 8 mm in thickness, annealed (AN, in the following) glass ply (outside), and a laminated glass panel, obtained by assembling two 6 mm thick, heat-strengthened (HS, in the following) plies with 1.52 mm thick PVB foil (inside), see Fig. 3a. The so assembled UGCW belongs to a 4-storey, continuous steel frame building located in an earthquake-prone region of Italy, see Fig. 3b.

The primary steel building has residential destination (category of destination “A”, in accordance with the Eurocode 1 provisions (EN 1991-1-1 2004a)), base dimensions (longitudinal $\times$ transversal) of $20\,\hbox {m}\times 10\,\hbox {m}$ (3 and 2 bays in the two directions, respectively), with 12m the total height. Inter-storey floors composed of steel-concrete composite slabs ensure in-plane rigid diaphragms to the building. All the primary secondary steel members are composed of S275 steel ($f_{\mathrm{y,s}}=275\,\hbox {MPa}$ and $f_{\mathrm{u,s}}=360\,\hbox {MPa}$ the yielding and collapse stress values respectively) and designed in accordance with Eurocode 3 (EN 1993-1-1 2004b), under the effect of permanent loads and accidental loads, see Table 1.

Fig. 3

Case study building. a IGU cross-sectional detail (dimensions in mm) and b global building features

Table 1 Steel resistance classes for framing members in the 4-storey seismic resistant building

3.2 Loading protocol and analysis method

Both seismic and (external) blast events are considered in this study, so to assess the building’s structural dynamics under multi-hazards. The numerical simulations partly discussed in this paper, consequently, are carried out on two separate FE models representative of the full 3D building as well as of the single UGCW modular unit, respectively, including specific loading and boundary assumptions here summarized.

For seismic design, a set of seven natural seismic accelerograms obtained from REXEL v.3.5 software (Iervolino et al. 2010) is first taken into account (Fig. 4a). Two-component acceleration data representative of earthquake records consistent with the Eurocode 8 (EN 1998-1-1 2004c) displacement spectrum are considered, with 0.35g the corresponding Peak Ground Acceleration, ‘A’ soil type (rock), topographic category T1 and nominal life of 50 years (Ultimate Limit State). A maximum lower and upper tolerance of 10% is defined in their derivation. Through the performed non-linear dynamic analyses, such a base accelerations are imposed at the 3D building foundation, so to explore the overall structural dynamics under the s#1-to-s#7 assigned accelerograms, and to detect the corresponding global effects as the (s#1-to-s#7) mean value. Given the deformation of the 3D steel frame under the assigned set of accelerations, local phenomena in the single UGCW module are in fact successively analysed by means of FE models representative of a single UGCW module, by imposing the so derived displacement histories at the UGCW corner supports (see Fig. 4c).

Fig. 4

Examined loading scenarios: a seismic records for the input ground accelerations and b time-pressure blast wave, with c general solving numerical approach

A different solving approach is followed for explosive events, where local FE simulations on single UGCW modules are first carried out. In doing so, the reference blast design pressure is analytically derived in accordance with (GSA TS01 2003). Figure 4b shows the so obtained time-pressure loading pattern, being associated to 25Kg (medium-level explosion, denoted as ‘BL-25’ in the following sections) of explosive at 30m from the UGCW (stand-off distance, with TNT detonating at the ground level). Given the maximum reaction forces that the single UCGW module has to sustain during the explosive event, the so calculated time-force histories are then used as input loading pattern for the full 3D model. In doing so, the reflected pressure due to the incoming explosion is assumed to affect the full longitudinal side of the building (see Fig. 4c), and input time-pressure histories are properly assigned to the steel members in the points of connection of the UGCW modules, by accounting for the facade geometry. Since blast effects on the glazing facades are assessed on single UGCW modular units, by accounting for glass cracking effects, the full 3D non-linear dynamic analyses are carried out to emphasize the effects of the assigned explosion on steel members only.

3.3 Numerical modelling—3D building

The typical FE model representative of the steel building with UGCWs and different VCSs is numerically described in ABAQUS (Simulia 2017) in accordance with Bedon and Amadio (2017a, 2018), where major modelling details are provided. In presence of both the examined design loads, it is important to point out that the refined stress-strain analysis of seismic or explosion effects in the major UGCW component is separately carried out on the detailed UGCW models described in section 3.4, while the same UGCW panels are accounted—at the 3D assembly level—so to ensure an appropriate description of mass and stiffness terms for the full building, compared to the steel bare frame only, hence to estimate realistic stress scenarios for the steel members. Such a modelling strategy agrees with material and solving method assumptions that are described in the following sections.

In terms of model assembly, in particular, beam elements (B31 type) and 2D shell elements (S4R type) are used for the steel frame structure (with I-shaped beam profiles able to reproduce the nominal geometry of beams and columns) and the UGCW panels respectively (Fig. 5a). In the latter case, the nominal IGU cross-section and aluminium frame are schematically described so to account of their actual mass and stiffness contributions for the full 3D building, hence in the form of an equivalent, monolithic shell section composed of glass ($t^{*}=20\,\hbox {mm}$, with $M_{\mathrm{glass}}\approx 230\,\hbox {kg}$ for the single IGU panel). In terms of S275-type steel mechanical characterization, a Von Mises elasto-plastic constitutive law is then used for all the steel members, with $E_{\mathrm{s}}=210\,\hbox {GPa}$ the Young’s modulus, $\nu _{\mathrm{s}}=0.3$ the Poisson’s ratio and $\rho _{\mathrm{s}}=7800\,\hbox {kg/m}^{3}$ the density. The nominal yielding and collapse stress values are taken into account for the primary frame components (see section 3.1), while neglecting possible strain-rate effects due to impact loads. For the UGCW modules under seismic or explosive input, glass is finally described in the form of a linear elastic mechanical law, with $E_{\mathrm{g}}=70\,\hbox {GPa}$, $\nu _{\mathrm{g}}=0.23$ and $\rho _{\mathrm{g}}=2490\,\hbox {kg}$, hence fully disregarding their possible tensile failure. Glass cracking, in this regard, is primarily investigated at the UCGW module level (see section 3.4). The reliability of such a material modelling assumption for 3D building FE models, in addition, is properly checked in the post-processing stage (i.e. Fig. 7). In the case of seismic events, in particular, it is ensured that maximum stress peaks in glass panels do not exceed the reference resistance values. In the case of blast pressures, in accordance with Fig. 4c, the reaction forces transmitted from the UGCW modules (described in section 3.4) to the supporting steel members are considered as input load for the 3D framing system, to check the stress distribution and evolution on the bare frame only. In this manner, blast reaction forces properly accounting for glass fracture effects are assigned to steel members. At the same time, UGCW modules are considered in the 3D assembly for mass and stiffness purposes only. In both the cases, through the non-linear dynamic simulations, mass terms representative of dead and accidental loads for the so calibrated 3D building models are taken into account via equivalent lumped masses, being applied in the center of mass of each storey.

A key role is then assigned—in the 3D assembly inclusive of UGCW modules—to mechanical interactions and constraints, so to take into account the desired restraint conditions and interactions among the building components (i.e. UGCW panels-to-steel frame interaction, inter-storey floors, etc.), including the structural continuity among the UGCW facade modules (see Bedon and Amadio 2017a, 2018). Special care is spent for the mechanical connection between each UGCW panel and the adjacent steel frame, so to replace—through the FE parametric investigation—the traditional rigid brackets with PL devices. A selection of VCSs configurations discussed in this paper is reported in Table 2, with their input features.

In terms of structural damping, a $\xi _{\mathrm{s}}=2\%$ term is finally accounted for all the building components, as recommended for steel frames with welded joints. At the facade level, conversely, any kind of damping contribution due to glass and PVB dynamic effects is fully neglected. Possible dissipation is hence expected to occur due to VCSs plastic mechanisms only.

Fig. 5

Global and local FE models (ABAQUS). a 3D assembly, with evidence of rigid joints (in red) and UGCW modules hidden from view; and b single UGCW module, with evidence of P1-to-P4 control points for stress evolution in glass

3.4 Numerical modelling—UGCW module

A FE model representative of a reference UGCW modular unit is then separately described in ABAQUS. Shell, beam elements and specific mechanical joints are used, in accordance with Bedon and Amadio (2017a, 2018), to maximize the computational efficiency but preserve the accuracy of FE models, aiming to define the UCGW components and their reciprocal mechanical interactions, see Fig. 5b.

For the two AN and HS glass panels, 4-node monolithic and composite shell elements (S4R type) are used respectively, with nominal dimensions and thicknesses given in section 2.2. The aluminium frame supporting the IGU panels is indeed described via 1D beam elements (B31 type), with box cross-section well representative of a typical framing system in use for UGCWs (see also Bedon and Amadio 2017a, 2018). The thermal spacers ensuring the insulation of gas cavity are also described via rigid shell elements. In this regard, possible local effects due to spacer components flexibility and resistance are fully disregarded. Given the so assembled gas cavity, the transmission of loads from a glass panel to the other (i.e. load sharing effect) is taken into account via a mechanical “fluid cavity interaction” available in ABAQUS and able to describe—based on the equation of state of ideal gasses—the effects deriving from the presence of a given fluid (air, in this study) within the cavity. A pneumatic gas is defined for the air infill, with ideal molecular weight $M_{\mathrm{air}}= 28.97\,\hbox {kg/kmol}$, $p_{\mathrm{air}}= 1\,\hbox {atm}$ the atmospheric pressure.

In terms of materials, the brittle cracking damage model is used for glass panels, so to take into account possible tensile cracking in separate layers. Input parameters are calibrated in accordance with Bedon et al. 2014, with careful consideration for the definition of the resistance of glass, being dependent on the glass type as well as on the loading time. For AN and HS panels under seismic loads and blast events respectively, the reference values are hence set equal to 85MPa and 120MPa respectively, as also in accordance with general design assumptions for glass systems under impulsive events (see for example Meyers 1994). An elasto-plastic constitutive law is indeed then defined for the aluminium frame, with $E_{\mathrm{a}}=70\,\hbox {GPa}$, $f_{\mathrm{y,a}}=200\,\hbox {MPa}$, $f_{\mathrm{u,a}}=280\,\hbox {MPa}$ the nominal reference properties.

Also in this case, a crucial role is assigned to mechanical joints, being representative (c-i) of the actual interaction between the IGU panel and the frame (where sealant joints and gaskets are usually interposed between them), as well as (c-ii) of the structural behaviour of each VCSs. In particular, (c-i) a set of distributed “cartesian + rotation” combined joints is assigned to all the corresponding glass panel/frame nodes, hence to account for a linear connection along the IGU panel edges. Due to the presence of metal gaskets and frame members detailing, relative rotations are restrained between the so involved glass-to-frame nodes. (c-ii) To reproduce the mechanical response of VCSs, nonlinear “ cylindrical” joints are linked to the frame corner nodes and rigidly fixed to ground, see Fig. 5b. Stiffness and plastic mechanical features for each VCSs are hence properly defined, so to reproduce the effects of different connector types (see Table 2).

4 Parametric numerical investigations

4.1 Selected configurations

The full FE investigation partly summarized in this paper includes global and local FE dynamic analyses, aimed to assess the actual dynamic performance of the case study building of interest, by changing the VCSs features. Selected FE results are hence discussed with respect to the performance of the ‘M0-R’ system, being representative of the examined building with traditional rigid brackets.

The parametric study is carried out by assuming PL constitutive laws for the same VCSs, with $K_{\mathrm{d}}$ and $F_{\mathrm{y,d}}$ calculated via Eqs. (1)–(2), see Table 2 (with $f_{\mathrm{y,s,VCS}}=160\,\hbox {MPa}$, $E_{\mathrm{s,VCS}}=210\,\hbox {GPa}$ for LYS160 steel). Differing from Bedon and Amadio (2017a, 2018), due to the lack of viscous components able to provide additional damping capacities, null dissipative potential is assumed for them ($c_{\mathrm{d}}=0$). Their allowable sliding $s_{\mathrm{d,max}}$ is finally set to 50 mm, so to avoid large deformations at the UGCW level, compared to the primary building, but at the same time to offer a certain plastic dissipation to VCSs and exploit their potential.

Table 2 Input mechanical properties of VCSs for the parametric numerical study (n.a. =  not applicable)

4.2 Discussion of FE results—Global and local effects due to seismic events

The global and local effects on the building dynamics due to various VCSs input features for the examined under seismic events are first assessed. In doing so, nonlinear dynamic analyses are carried out on both the full 3D and UGCW modular FE assemblies (Fig. 4c). Actually, while it was reported in Bedon and Amadio (2017a, 2018) that additional flexibility $K_{d}$ at the UGCW corner supports can provide certain structural benefits to the building components, eigenvalue simulations can only give preliminary information on the building dynamic performance.

For the reference $K_{\mathrm{d}}$ values of Table 2, no marked qualitative variations are expected on the fundamental vibration shapes of the primary system. On the other hand, a certain effect was already noticed in terms of dynamic properties of the same 3D structure, with $T_{\mathrm{R,1}}=0.326\,\hbox {s}$ being representative of the first vibration mode of the steel structure with fully rigid brackets (M0-R) and $T_{\mathrm{PL3,1}}=0.345\,\hbox {s}$, $T_{\mathrm{PL4,1}}=0.343\,\hbox {s}$ and $T_{\mathrm{PL5,1}}=0.342\,\hbox {s}$ respectively, as obtained in presence of VCSs (i.e. $\approx$ 5% the variation for the fundamental period, compared to the M0-R system). Additional influencing parameters—not perceived by eigenvalue simulations—are then represented by the non-linear cyclic behaviour and dissipative capacity of the same VCSs under the assigned design loads, as well as by damage constitutive laws in building materials, including plastic hinges in the bare frame.

For the selected FE simulations here summarized, in particular, the use of VCSs with a certain flexibility and plastic damping capacity proved to have several effects on the overall dynamic performance of the primary steel structure under seismic events, compared to the same M0-R building. Such an outcome, being in close correlation with earlier efforts (Bedon and Amadio 2017a, 2018), further emphasizes the actual key role of UCGW connectors and restraining devices, hence the active role of the UGCW (with appropriate supports) as a structural component of the full 3D assembly leading to potential benefits for the primary members. On the other hand, the same FE simulations gave evidence of important global & local variations in the observed dynamic phenomena, due to sensitivity to VCSs input features and typology, hence requiring specific studies and fine tuning at the VCS level.

In Fig. 6a, for example, top displacements are compared as a function of time, as obtained for the M0-R, M-PL3 and M-PL5 systems under an assigned record of ground accelerations (s#5). For clarity of graphical comparisons, the intermediate M-PL4 results are omitted. As shown, given the maximum drift of $\approx$ 45 mm for the M0-R building, negligible reduction in the expected maximum displacements for the 3D frame can be perceived from the selected PL configurations, being the measured $|\hbox {u}_{\mathrm{max}}|$ values still in the order of 44 mm. Compared to the M0-R system, the PL models gave indeed evidence of a certain plastic dissipation due to VCSs progressive sliding, hence resulting in a certain reduction of lateral deformations for the 3D system. Major benefits of PL devices can be in fact noticed, from Fig. 6a, especially in the time instants following the achievement of maximum top displacements.

Fig. 6

Full 3D building under seismic events. a Top drift for the reference building under the s#5 seismic record, as obtained for the M0-R, M-PL3 and M-PL5 systems, with b plastic hinges in a transversal frame of the M0-R model ($t=3.5\,\hbox {s}$, scale factor  =  5) and c Von Mises stresses at the ‘FPL’ frame control point (ABAQUS)

Apparently, from Fig. 6a it is hence possible to conclude that maximum seismic effects on the bare steel frame are only marginally mitigated by the PL devices in use. Such a conclusion, however, can be further reconsidered as far as the plastic deformations achieved in the steel members are taken into account, see Fig. 6b. While the M0-R system gave in fact evidence of the occurrence and propagation of several plastic hinges in the framing steel beams (an example is proposed in Fig. 6b for the FT2 secondary members, $t=3.5\,\hbox {s}$), no plastic deformations were achieved in the steel structure within the M-PL3 and M-PL4 configurations. For the M-PL5 system, a limited number of plastic hinges was still noticed, even in minimum number compared to the M0-R building, hence denoting a certain mitigation of maximum seismic effects.

Fig. 7

Local effects due to seismic loads. a Maximum stresses in the frame mullion and b in glass panels, with c typical stress distribution in glass and d VCSs cyclic response (ABAQUS)

The intrinsic features of PL connectors, in this regard, can be further perceived when monitoring the stress evolution in the 3D steel members. In Fig. 6c, Von Mises stresses recorded over time at the FPL control point of Fig. 6b are proposed. There, it is possible to notice that for the M0-R building—as expected—maximum stresses arise up to the yielding resistance (275 MPa), then rapidly decay over time, as a major effect of plastic dissipation in the steel beams only. For the M-PL3 system, taking advantage of the moderate VCSs flexibility and limited resistance, it can be noticed that maximum stress peaks in the bare frame are in the order of 240MPa, as a major effect of VCSs working mechanism. This is not the case of the M-PL4 configuration, were stress peaks up to 270MPa were achieved, hence suggesting the activation of a limited number only of VCSs, as an effect of the increased $K_{\mathrm{d}}$ and $F_{\mathrm{y,d}}$ input parameters, compared to the M-PL3 solution. For the stiffer and strongest M-PL5 configuration, finally, it can be noticed in Fig. 6c that—due to the occurrence of a limited number of plastic hinges in the bare frame—maximum stresses for the FPL control point still achieve the yielding limit value of 275MPa, but rapidly decay, compared to the M0-R system, as a primary effect of the VCSs sliding and progressive plastic dissipation.

The structural efficiency of PL devices, in this sense, is strictly related to their yielding resistance $F_{\mathrm{y,d}}$, being responsible of sliding activation in the devices themselves. As far as the maximum reaction forces transferred from the UGCW panels to the structural background do not exceeds $F_{\mathrm{y,d}}$, the PL devices behave as linear elastic brackets. At the same time, however, the typically high stiffness $K_{\mathrm{d}}$ of PL connectors should be also properly taken into account. High stiffness values, in particular, could not allow to take full advantage of a certain flexibility for the activation of the distributed TMD concept, hence resulting in possible stress peaks and mostly null VCSs benefits. In this sense, a preliminary evaluation of the expected loading ratios (and in particular of the maximum reaction forces to take up at the supports) is mandatory to properly optimize the examined VCSs, so to take advantage—even within a limited set of loading configurations—of PL connectors potential. Local analysis of structural phenomena, in this sense, is also required.

As far as the local structural effects due to the assigned design loads are explored for the UGCW components, the potential of the examined VCSs can be in fact further exploited. To this aim, additional FE simulations are discussed for single UGCW modules described in section 3.4, where the input loading for seismic loads is derived from the corresponding full 3D models (relative drift at the UGCW corners, as a function of time). Since maximum deformations are achieved at the top of the steel building, time-displacement seismic input is calculated for the top inter-storey level only.

In doing so, careful consideration is spent for some key aspects in the structural performance of the UGCW, namely represented by:

• Maximum principal stresses in the AN and HS glass panels (control points according with Fig. 5b), with observation of possible tensile cracking in the separate layers;

• Maximum displacements at the IGU center (P1 control point, according with Fig. 5b);

• Von Mises stresses in the aluminium mullions (maximum envelope), with attention for yielding phenomena;

• Maximum forces and displacements in the VSCs, compared to reactions of fully rigid brackets.

Fig. 8

Full 3D building under blast loads. a plastic hinges in a transversal frame of the M0-R model ($t\,=\,0.15\,\hbox {s}$, scale factor  =  5), with b top displacement of the building, as obtained for the M0-R, M-PL3 and M-PL5 systems (ABAQUS)

For the examined case study building under seismic events, the assigned set of base accelerations proved to have limited out-of-plane effects on the UGCW components, with linear elastic response of the modular system, both in presence of fully rigid brackets and VCSs. Even in the case of the M0-R system, the UGCW modular unit gave in fact evidence of a pure elastic response, with moderate stress peaks in the supporting aluminium frame, as well as in the glass panels. To this aim, selected comparative FE results are proposed in Fig. 7a–c, with evidence of tensile stresses evolution and distribution under the s#5 ground acceleration record.

In terms of UGCW out-of-plane seismic response with PL connectors, interesting local structural effects were achieved for the M-PL3 configuration, even with limited plastic cyclic response of VCSs (Fig. 7d). Mostly similar trends were also achieved for the M-PL4 and M-PL5 configurations, as a major effect of their high elastic stiffness, with maximum stress peaks in the UGCW components still in the order of the M0-R system, but progressive dissipation of the following stress peaks. In this regard, while suggesting the potential of PL devices, the M-PL4 and M-PL5 systems highlighted the key role of optimal design for the VCS input features, being responsible of combined local & global effects on the structural dynamics. Limited mitigation effects due to seismic input, in this sense, were found to derive from a pure linear elastic behaviour of most of the VCSs (Fig. 7d). In this sense, while preliminary FE studies proved the efficiency of PL connectors for the activation of the distributed-TMD concept for the seismic mitigation of multi-storey buildings, major potential was observed for ADAS connectors with limited stiffness and resistance.

Fig. 9

Principal stress evolution in time for the a monolithic AN and b laminated HS layers for the M0-R system under BL-25 blast loads (ABAQUS), with c stress distribution in the HS panel ($t=0.0125\,\hbox {s}$, legend in [Pa])

4.3 Discussion of FE results—Global and local effects due to explosions

In parallel, the dynamic performance of the same steel building with enclosing UGCW modules was assessed with respect to the assigned BL-25 explosive load. In Figs. 8, 9, 10 and 11, a selection of global and local FE results is proposed.

Fig. 10

a Maximum displacement in the AN and HS glass panels, with b reaction force and stresses in mullions (maximum envelope) as a function of time, as obtained for the M0-R system under BL-25 blast loads (ABAQUS)

Figure 8, in particular, describes the global response of the examined 3D systems, under the effects of the assigned blast wave. For the M0-R building, major reaction forces transferred from the UGCW panels to the steel frame generally resulted in the occurrence of plastic hinges in the steel members. In Fig. 8a, a frame transversal cross-section is proposed, for comparative purposes with Fig. 6b. This is not the case of PL configurations, where a pure elastic response was observed for the steel primary structure, taking advantage of the TMD activation via VCSs. As partly observed for seismic loading scenarios, the primary building can in fact be considered as subjected to part of the total blast impulse. Such a finding is also confirmed by Fig. 8b, where the top displacements due to the incoming shock impulse are compared for the M0-R, M-PL3 and M-PL5 systems, with evidence of marked reduction of building deformations when using VCSs. For the M-PL4 system, mostly identical 3D performances were obtained, with maximum top displacements in the order of 15 mm. In this sense, the 3D frame proved to take major advantages from VCSs with higher stiffness $K_{\mathrm{d}}$ (and hence yielding resistance $F_{\mathrm{y,d}}$) since responsible of largest plastic dissipation of the incoming blast energy.

Fig. 11

UGCW module under BL-25 blast load. a Displacements and b principal stresses at the center of glass (P1), with c maximum stresses in mullions, d reaction force (ABAQUS)

As far as the local effects of blast loading and different VCSs features are taken into account, major structural outcomes can be further emphasized. In doing so, the structural response of the rigidly supported UGCW has first to be investigated, being the M0-R system representative of the traditional building configuration.

Figure 9, to this aim, shows the principal stress evolution in glass, for the AN and HS plies respectively, as observed for the M0-R system only. The assigned BL-25 impulsive pressure would result in tensile stresses exceeding the corresponding design resistances, hence leading both the glass layers (even in different time instants) to fracture. Worth of interest—as also in accordance with past experimental observations (see for example Zhang et al. 2013)—is that in the examined UGCW module with rigid corner fixings, maximum stress peaks are achieved close to the panels’ mid-span vertical edge (see ‘P4’ curves), rather than in the center of glass (‘P1’). Failure of both the AN and HS was numerically predicted for the M0-R configuration. While for the AN panel major cracks were observed, leading to collapse of the panel, minor tensile fracture was only predicted for the HS layer, hence providing—thanks to the bonding interlayer—a certain post-cracked stability and residual resistance. Such an effect can be noticed both in the residual stress distribution of Fig. 9b as well as in the evolution of out-of-plane displacements at the center of glass plates (see Fig. 9).

Due to the assigned blast pressure, even causing severe damage in glass, the aluminium frame gave evidence of a pure linear elastic response, for the M0-R system. Maximum stresses in mullions are reported in Fig. 10, where peaks can be notice to occur when the glass panels crack and the stiffness/resistance of the composite UGCW system abruptly decreases.

The maximum reaction forces transmitted by the UGCW module to the structural background were finally found to lie in maximum values in the order of $\approx$30kN/support, see Fig. 10.

This is not the case of PL systems, where maximum principal stresses in both the glass panels—as well as major structural effects in the UGCW components—were found to be highly reduced, see Fig. 11. In Fig. 11a, in particular, it can be noticed that maximum out-of-plane deflections in glass panels are in the order of $\approx$ 15 mm, with $\approx$ 45 mm the M0-R deformation, thanks to the additional flexibility of UCGW corner supports. Even the UGCW module response can still described in the form of a supported membrane under an impulsive pressure, as in the case of M0-R system, VCSs have a key role in attenuating the shock effects. In terms of maximum stresses in the glass panels, for example, pure elastic responses were achieved for the AN and HS plates, as suggested by deflection evolution over time (Fig. 11a), as well as by direct comparison of principal stresses at selected control points on the UGCW surface. In Fig. 11b, comparative results are shown for the P1 control point (HS glass), giving evidence of rather comparable maximum stresses for the selected PL configurations, being in the range of $\approx -$50% the M0-R system. Major effects—due to the examined loading and boundary condition—are expected along the UGCW edges as well as in the framing members, see Fig. 11c, hence resulting in limited reaction forces transmitted to the steel primary building (Fig. 11d). There, a certain agreement can be noticed in all the reported PL responses. Such a local effects were obtained, however, as a major effect of different cyclic behaviours for VCSs (see Fig. 12).

Fig. 12

UGCW module under BL-25 blast load. Cyclic response of VCSs (ABAQUS)

Table 3 Comparative FE results for the case study building under seismic and blast events (n.a.  =  not applicable; Y = yes; N = no)

Since plastic dissipation only can offer a certain structural benefit for the examined case study building, a key role is assigned to the optimal design of their $K_{\mathrm{d}}$ and $F_{\mathrm{y,d}}$ input features, being responsible of the actual VCSs protective contribution. As far as $K_{\mathrm{d}}$ and $F_{\mathrm{y,d}}$ is not properly calibrated, local stress peaks could be achieved in the building components, as well as the potential of PL connectors could minimize for the given design load, or even fully vanish, hence resulting in a pure linear elastic device with null damping capacity and requiring accurate fine tuning.

4.4 Preliminary design considerations

In conclusion, some preliminary design considerations are derived, based on selected FE results summarized in sections 4.2 and 4.3. In Table 3, major FE outcomes are reported.

Generally speaking, compared to VE vibration control systems assessed in Bedon and Amadio (2017a, 2018), the PL devices gave qualitative evidence of high potential for the distributed-TMD concept under investigation, both under seismic and explosive loads. At the same time, the selected FE results proved the crucial role of VCSs intrinsic features and working mechanisms, both at the local and global levels. As far as the UGCW modules are exploited in the form of passive control system for the primary building, see Table 3, the steel framed structure was observed to take benefit of PL connectors, especially with limited stiffness and resistance (M-PL3 and M-PL4 configurations), hence to suffer slightly the assigned seismic and blast loads. Major top building displacements and stress local peaks in the steel members, in addition, proved to be generally highly mitigated, compared to the M0-R system, thanks to the additional flexibility due to VCSs. Limited benefits were indeed obtained for the stiffer M-PL5 configuration, due to a mostly negligible activation of the distributed-TMD mechanism.

At the UGCW component level, further beneficial effects of the distributed-TMD activation were also noticed, see Table 3. While stress peaks in the glass panels and in the aluminium framing members were generally reduced, compared to the M0-R system, the same FE simulations gave evidence of the actual role of the PL features on their expected effects, and in particular of the high sensitivity to $K_{\mathrm{d}}$ and $F_{\mathrm{y,d}}$ reference values. On one side, higher $F_{\mathrm{y,d}}$ values suggested major structural benefits for the blast performance of the UGCW modular components (i.e., due to higher plastic dissipation), as in the case of the M-PL5 system. On the other hand, best UCGW seismic performances were found for facade modules with low-medium $K_{\mathrm{d}}$ and $F_{\mathrm{y,d}}$ input properties, due to a combination of out-of-plane relative displacements and local plastic phenomena close to the UGCW corner supports (M-PL3 and M-PL4 systems). In this regard, the M-PL3 configuration highlighted maximum VCSs slidings exceeding the reference limit value of 50 mm, while the M-PL4 system proved to do not properly exploit the VCSs capacities under seismic loads, hence suggesting major overall benefits for an intermediate M-PL3 / M-PL4 configuration.

5 Summary and conclusions

In this paper, the feasibility and potential of passive control systems consisting in glazing curtain walls with special vibration control system has been numerically investigated via extended Finite-Element numerical investigations. Careful consideration was paid—following earlier research efforts—for a reference case study building, consisting in a 4-storey continuous steel frame subjected to seismic events and explosions. The explored design concept derives from the original tuned-mass-damper (TMD) design philosophy. Compared to Bedon and Amadio (2017a, 2018), where the potential of viscoelastic vibration control systems has been preliminary assessed for the same case study building, special care has been spent for the investigation of elasto-plastic (PL) dampers, giving evidence of global and local effects for the examined building.

As shown, the use of special PL mechanical connectors able to work as dissipative supports for the same glazing modular units proved to represent an efficient tool for the mitigation of the maximum effects deriving from a seismic and blast loads, both in terms of global dynamic performance and local effects (i.e. at the level of the glazing components). Major benefits—in presence of properly designed plastic devices—can in fact be achieved in terms of reduction of:

• maximum top displacements for the steel frame,

• maximum tensile stresses in glass, and

• maximum deformations in the glazing components, with

• avoidance of plastic hinges in the steel members, and

• moderate maximum deformations achieved at the level of the dissipative connectors.

Several aspects, however, should be taken into account to properly assess and optimize the same design concept, hence requiring further investigations. Additional studies, in this regard, will be focused on several building typologies, including different number of inter-storey levels, material properties, as well as geometrical irregularities.