# Safety Issues in the Seismic Design of Secondary Frameless Glass Structures

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## Abstract

**:**

## 1. Introduction

## 2. Research in Support of Seismic Design

## 3. Seismic Design of Glass Systems Based on the CNR-DT 210 Guide

#### 3.1. Basis of Design

#### 3.2. Consequences Classes and “Secondary” Structural Components

- CC1 = glass failure has limited consequences in terms of loss of human life and small or negligible consequences in economic, social or environmental terms. CC1 includes glass structures/elements in buildings characterized by occasional presence of people. The probability of failure is P
_{f,50}= 5.83 × 10^{−4}and P_{f,1}= 1.335 × 10^{−5}(with 50 and 1 the period (in years) to which P_{f}refers); - CC2 = failure has medium consequences for human life, but considerable consequences in economic, social and environmental terms. Typical examples are glass structures/elements for residential/office buildings. In this case, P
_{f,50}= 6.2353 × 10^{−5}and P_{f,1}= 1.3 × 10^{−6}; - CC3 = failure has high consequences in terms of human life and very great consequences in economic, social terms. CC3 includes glass systems belonging to public buildings and places susceptible to overcrowding, but also stand-alone glass structures (P
_{f,50}= 8.54 × 10^{−6}, P_{f,1}= 9.96×10^{8}).

#### 3.3. Nominal Design Life and Reference Life

_{N}, as usual, defines the period over which it is assumed that a given glass system can be safely used for the intended purposes (with scheduled maintenance). Commonly, it is assumed that V

_{N}= 50 years, but other conditions may occur (Table 2).

_{N}intervals, in the range from 10 to 30 years, and a specific classification of “temporary” and “replaceable” components. Given the common applications of structural glass in buildings, such a definition fills the NTC2018 gap, where recommended V

_{N}values are (minimum) 10, 50 and 100 years for “temporary”, “common/ordinary” and “exceptional” structures respectively (Table 2).

_{N}directly reflects on the reference life V

_{R}, that is:

_{N}given in Table 2 and C

_{U}a coefficient depending on the importance class/Class of use (Table 3). With reference to the consequences of interruption of service or ultimate failure, structural glass systems must in fact satisfy specific demands, within the assembly/building they belong to.

#### 3.4. Performance Levels

_{R}(in years) of the design seismic action. The amplitude of the input design force is in fact expected to progressively magnify as far as the strategic role of the construction increases, with:

_{R}is given by Equation (1), while P

_{VR}is the probability of exceedance (in the V

_{R}interval) that defines the reference seismic action for each Limit State. Typical values in use are 81% for SLO, 63% for SLD, 10% for SLV and 5% for SLC respectively [9].

#### 3.5. Design Seismic Force and Q-Behaviour Factor

- W
_{a}is the weight of the element, - q
_{a}is the behaviour factor of the glass element/system to verify, and - S
_{a}is the peak acceleration of interest, for the element/system to verify, normalized with respect to the acceleration of gravity g.

_{a}on the surface of the panel object of analysis.

- a
_{g}the peak ground acceleration (rock soil) for the Limit State of interest; while - S accounts for soil category and topographical conditions.

_{a}modifies as a function of the features of the glass system as a part of the full building, where (see Figure 5a), where:

- Z represents the height of centre of gravity of the glass element to verify (from the foundation level);
- H is the height of the full assembly/building (from the foundation);
- T
_{a}is the fundamental period of the glass element to verify; - T
_{1}is he fundamental period of the full assembly/building, in the direction of interest.

_{a}can be directly imposed at the top of the element to verify, given that the restraints in use are properly described. The second issue is related to the local out-of-plane analysis of glass elements, and more in detail the correct evaluation of some key parameters.

_{a}can magnify up to ≈6 times the expected seismic effect of the design action given by Equation (3), depending on the Z/H and T

_{a}/T

_{1}ratios. While Z and H can be rationally estimated, and the fundamental period T

_{1}of the full building can be calculated based on approximate formulations, the reliable estimation of T

_{a}can represent a severe challenge for designers. It was shown for example in [33,34,35] that—even for simple independent glass elements with a beam behaviour—the local detailing of restraints can have marked effects on the vibration period T

_{a}(and also damping capacity). When more detailed calculations are available, the use of maximum R

_{a}values from Figure 5a could result in extremely conservative assumptions, thus in over-design of glass members.

_{a}and q

_{a}”, based on “specific technical documents”. While the peak acceleration S

_{a}is in fact properly defined in Equation (4), major uncertainties are still related to the q

_{a}estimate.

_{a}. Worth of interest, in this regard, that NTC2018 removed the earlier reference behaviour factor values for non-structural constructive elements. In the earlier edition of the NTC standard (2008), up to q

_{a}= 2 was in fact suggested for components that could be of interest for glass, that is falling in the group of “facades”. Such a lack of recommended values unavoidably turns out in verifications for glass that are generally carried out with q

_{a}= 1. On one side, wide safety levels can be preserved for glass, whose damage could certainly have relevant risk for people. On the other hand, the system itself could be over-designed, even in presence of joints and restraints with relevant dissipation capacity [1].

_{a}directly reflects on the displacement demand of glass components and related joints/restraints (§4.4.4 [9]).

## 4. Case-Study Example: Glass Partition Assembly

#### 4.1. Description of the System

#### 4.2. Reference Design Parameters, Major Requirements and Loads

_{N}≥ 50 years. From the building entrance shown in Figure 6, moreover, up to 5–10 officers can regularly access and exit the Palace (CAT. B1 destination, corresponding to offices not accessible to public [10]). The same building entrance, finally, is also recognized to act as one of the emergency exits for the Ferdinandeo Palace, thus requiring the glass walls to properly withstand the most unfavourable design combination of loads, even under exceptional service conditions. In terms of crowd, such a detail can be conventionally accounted in the form of an accidental action given by the most unfavourable among (i) a distributed pressure Q

_{k,crowd}= 2 kN/m

^{2}, (ii) a linear horizontal load (1.20 m above the walking surface, with H

_{k,crowd}= 1kN/m), or (iii) a concentrated load (P

_{k,crowd}= 2 kN, over a 50 mm × 50 mm area). In non-seismic conditions (see also Equation (6)), however, crowd effects must be combined with other relevant accidental actions. For Trieste region, the reference design wind velocity at sea level is certainly of interest, being in the order of 30 m/s. This parameter turns out in fact in a characteristic wind pressure on the glass walls up to Q

_{k,wind}= 1 kN/m

^{2}. The non-seismic combination of crowd and wind actions takes advantage—for the case-study partition—of the structural configuration of the system. In the worst condition, the glass walls are in fact expected to withstand an external wind pressure that is superimposed to an internal crowd action (emergency exit). In any case, given a series of conditions to satisfy, it is clear that the design of even simple glass walls requires a multi-stage analysis.

#### 4.3. Design Strategy

^{®}) foil.

^{®}[39]) and a soft gasket layer consisting of rigid Polyvinyl Chloride (PVC) provided by Metalglas

^{®}[40]—E

_{PVC}= 3.4 GPa its nominal modulus of elasticity—were introduced along each LG plate, to avoid direct contact between glass and metal components, while Hilti

^{®}[41] connectors (HST3-R type, M12 × 145 mm) provided a rigid link between the stone rails and the Palace foundation.

^{®}—consisted of a central M12 bolt and a steel solid section (with 42 mm the nominal diameter) for the main body and head. The total length of these devices (up to 180 mm) was properly defined for each one of them, in order to accommodate the actual distance between the partition walls and the columns of the building. A series of holes (with a diameter of 22 mm) was also realized in the resisting section of the LG panels, to facilitate the installation of the partition system but also to ensure the presence of an appropriate gap with the M12 bolts, thus preventing the occurrence of relevant stress peaks in glass due to the imposed out-of-plane or in-plane design loads.

^{®}). A similar concept was considered for the glass plates overlapping in the elevation of the system, that were connected via V-083-180N joints (Metalglas

^{®}, see Figure 10d) consisting in planar friction clamps kept together by two M10 bolts. In doing so, the installation of the overall 3D system was carried out assuming a certain gap between adjacent/overlapping/orthogonal glass plates (detail of Figure 10a, etc.). Such a choice—disregarding possible sealant joints along the LG edges—was preferred to prevent possible local interactions that could manifest in additional stress/displacement demands for the glass panels, thus ensuring a mostly independent structural response of each wall, but at the same time (thanks to the point-fixings in use) accommodating the deformations of the system as a whole 3D structural assembly.

#### 4.4. Seismic Analysis—Out-of-Plane Performance Assessment

_{a}= 1 and S = 1.2 in Equations (3) and (4), and accounting that W

_{a}≈ 250 Kg for the glass panel of Figure 8 with maximum dimensions.

_{a}was hence taken into account for the separate local analyses. Such a series of calculated F

_{a}values resulted—for out-of-plane verifications—in equivalent uniform pressures Q

_{a}according with Table 6. Within a general design process, the force and pressure values reported in the Table should be then further amplified by accounting for the R

_{a}magnifying coefficient of Equation (5), see also Figure 5a. In this study, given the small Z/H ratio of the examined system, it is reasonably assumed that R

_{a}= 1. Such an assumption is compensated by the use of q

_{a}= 1, in place of more detailed estimates that would require detailed investigations.

_{g}= 70 GPa, ν

_{g}= 0.23 and ρ

_{g}= 2500 kg/m

^{3}respectively. In the case of PVB, equivalent input parameters accounting for the viscoelastic behaviour of material were used, with a secant shear modulus G

_{PVB}given as a function of a conventional time loading (t

_{L}) and temperature (T

_{L}) for the design action of interest (see Table 7 and [3,4,9]), with ν

_{PVB}= 0.49 and ρ

_{PVB}= 1100 kg/m

^{3}.

#### 4.5. Seismic Analysis—In-Plane Performance Assessment

- (1)
- the in-plane seismic force F
_{a}that the independent glass panel must withstand, based on Equation (3), see Table 6, and - (2)
- the additional series of in-plane seismic forces R
_{Q}deriving (when present) by orthogonal LG walls, being transferred by the frictional clamps.

_{Q}that the P1 wall under out-of-plane pressure can transfer to the orthogonal P2 wall.

#### 4.6. Seismic Verification of the Glass Partition System

_{kj}), that is:

_{2j}= 0 for wind and Ψ

_{2j}= 0.3 for CAT. B1 offices. For the case-study system discussed herein, see Table 6, Equation (6) turns out in dead loads that are expected to have negligible stress and displacement effects in glass, as well as seismic forces that are sensitively lower than the combined crowd pressure (with Q = 0.3 × 2 = 0.6 kN/m

^{2}the reference design value in seismic conditions). Otherwise, the structural behaviour of the independent LG panels and the full 3D assembly must be analyzed in detail, including direct or indirect out-of-plane and in-plane loading contributions.

_{L}, conventional temperature T

_{L}), different demands are expected from each one of them. At the same time, a different mechanical contribution is expected from the PVB foils in use, thus from the assembled LG sections, given that both t

_{L}and T

_{L}can affect the shear modulus G

_{PVB}[3,4,9].

_{L}for engineering applications is expected in the range of ≈5 s [47,48,49], but can be conservatively set as for “transient” loads (§4.10 [9]), hence disregarding the enhanced stiffness of PVB layers under impact. From a practical point of view, it is in any case convenient to estimate maximum stresses and displacements in the LG elements based on separate FE analyses, and then properly combine the maximum effects.

#### 4.6.1. Resistance

_{g;d,p}> 0 for pre-stressed glass, and the resistance verification requires that the stress effects of a given design action do not exceed the capacity of the system, that is:

_{mod}, being representative of static fatigue effects and depending on the loading time t

_{L}(in hours). Given the reference values of Table 7 that must be separately taken in Equation (6), k

_{mod}can be estimated as (§2.1.1.2 [9]):

_{g;d}≈ 61.5 MPa against transient seismic loads (k

_{mod}= 0.78).

_{FE}≈ 8.6 MPa) and their concentration in a limited portion of glass (i.e., region of point-fixings), a special care is required for the stress verification close to holes and edges, where the actual limit condition to satisfy is given by:

_{t}follows Figure 15a. For LG plates as in the examined system (with a hole diameter-to-glass thickness ratio equal to d/h ≈ 1.83), Figure 15a turns out in K ≈ 2.05. Besides the availability of several literature proposals to account for the stress concentration in the region of holes (i.e., [3,4,50]), in this context, it is important to notice that the typical structural glass applications involve relatively small d/h values. At the same time, see Figure 15a, the minimum recommended value for K is in any case ≈ 1.8, thus requiring an appropriate thickness for glass members object of design. Minor variations can be expected in the reference d/h values (thus K) for LG plates, given that G

_{PVB}(or others) modifies with the loading configuration (i.e., Table 7), and thus different equivalent, monolithic glass thicknesses h should be used to account for the actual out-of-plane bending stiffness associated to each design action.

_{FE}value (see Figure 15b, with ϕ = 0°, and [51,52,53,54]). In the latter case, however, the presence of gaps (i.e., Figure 12) can strongly minimize possible stress peaks. The use of additional soft interposed layers and gaskets (i.e., aluminum or rubber, or even PVC, as in this case-study) can be further beneficial for the critical region of edges [3,4].

_{c;k}= 1000 MPa and for practical purposes—when experimental feedback is not available—could be limited to ≈350–500 MPa [55,56,57].

_{g;d}for the ith action is estimated in Equation (7) based on the corresponding k

_{mod}coefficient. Among many others [58,59,60,61], the Palmgren-Miner based, linear cumulative damage approach of Equation (11) is recommended by the CNR guide as a practical tool to account for static fatigue effects in glass, in place of theoretically exact but even complex formulations. The design issue, however, still requires extended investigations and represents an open question for the research community. With respect to the exponential model proposed by Franco & Royer in [59], that is:

_{p}= f

_{g;d,p}in Equation (7)).

_{gd}still given by Equation (7), but introducing a “weighted” k

_{mod,w}coefficient:

_{p}= f

_{g;d,p}in Equation(7))

_{mod}= 0.26 for dead loads (t

_{L}= 50 years, Table 7) and k

_{mod}= 0.78 for crowd (t

_{L}= 30 s), the corresponding f

_{g;d}values can be estimated from Equation (7) in ≈ 50 MPa and ≈ 61.5 MPa, respectively. Consequently, Equation (11) reflects in a LG structure that is able to properly withstand the imposed SLC seismic combination of Equation (6). Detailed comparative examples are proposed in Table 8 for the P1 wall under out-of-plane seismic pressure, giving evidence of the verification outcomes for all the mentioned approaches.

_{σ}is taken into account in Equation (11) for the ith design action of interest, for example, it can be seen in Figure 16a that the resistance demand due to the out-of-plane seismic pressure (E) is limited, with respect to the crowd accidental load (Q), while dead load effects (G) can be generally disregarded. Given that the stress verification is conservatively carried out with the reference t

_{L}, T

_{L}and G

_{PVB}input parameters from Table 7, a positive SLC check can be obtained (see also Figure 16b).

_{PVB}of the bonding foils (i.e., due to possible material degradation due to severe operational or ambient conditions, see also [62,63]) are expected to manifest in sensitive variations of predicted stresses, thus even in potential premature failure. As also previously discussed for Equation (6) and Table 7, careful consideration is also required for the t

_{L}characterization of seismic events (and thus G

_{PVB}assumptions), given that the dynamic response and shear stiffness of PVB foils is strongly sensitive to the vibration frequency, but also to testing procedures, thus requiring more sophisticated calculation methods (see for example [64,65,66]).

#### 4.6.2. Displacements

_{i}due to the ith action—is able to satisfy specific limit values of deformation, both out-of-plane and in-plane. For independent LG panels with point-fixing restraints in out-of-plane bending, the CNR guide recommends that Σu does not exceed the minimum value given by (§7.5 [9]):

- (a)
- u
_{lim}= L_{inf}/100, with L_{inf}the distance between two point supports (or u_{lim}= L_{inf}/50, in presence of spandrels), or - (b)
- u
_{lim}= 50 mm.

_{inf}= 2.45 m and u

_{lim}= 24.5 mm for the upper panel of the P1 wall, it can be seen that the maximum out-of-plane SLD deflection is in the order of Σu = 24.09 mm, thus able to satisfy the recommended deformation limits (i.e., with load and PVB parameters according with Table 7). As in the case of stress peaks, however, an high sensitivity of the 3D structure to operational and ambient conditions can be perceived from Figure 17b, where the total out-of-plane deformation check is proposed for the P1 wall as a function of a variable G

_{PVB}modulus.

_{max}= 0.002 × H = 9.3 mm can be taken into account for the global deformation of the LG walls. The latter represents the conventional SLD drift for masonry constructions, with H = 4.65 m the total height of the 3D partition system, thus the in-plane deformation that the LG walls should be able to accommodate without damage. As far as u

_{max}is imposed to each LG wall object of study, the hole gap for the point-fixings in use gives further evidence of intrinsic benefits, allowing to minimize the global deformation demands of the system. The global deformation of the P1 wall still qualitatively agrees with Figure 18a. A more detailed analysis of the P1 wall (and others) in-plane response, however, gives evidence of (i) an initial rigid body deformation (up to 5 mm), followed by (ii) a residual drift equal to (u

_{max}—5 mm) = 4.3 mm and activating the steel-glass contact interactions. In the latter case, compressive stress peaks in glass must be thus properly verified. Given the geometrical and mechanical details of interest in this study, see Figure 18b, compressive stresses are estimated in the order of ≈ 53 MPa, thus relatively low compared to the conventional material resistance for design (see also Section 4.6.1).

#### 4.7. Verification of Restraints and Fasteners

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Santarsiero, M.; Bedon, C.; Moupagitsoglou, K. Energy-based considerations for the seismic design of ductile and dissipative glass frames. Soil Dyn. Earthq. Eng.
**2019**, 125, 105170. [Google Scholar] [CrossRef] - Bedon, C.; Santarsiero, M. Transparency in structural glass systems via mechanical, adhesive, and laminated connections—Existing research and developments. Adv. Eng. Mater.
**2018**, 20, 1700815. [Google Scholar] [CrossRef] - Haldimann, M.; Luible, A.; Overend, M. Structural Use of Glass; IABSE: Zurich, Switzerland, 2008; ISBN 978-3-85748-119-2. (CH). [Google Scholar]
- Feldmann, M.; Kasper, R.; Abeln, B.; Cruz, P.; Belis, J.; Beyer, J.; Colvin, J.; Ensslen, F.; Eliasova, M.; Galuppi, L.; et al. Guidance for European Structural Design of Glass Components—Support to the Implementation, Harmonization and Further Development of the Eurocodes; Dimova, S., Pinto, A.V., Feldmann, M., Denton, S., Eds.; Report EUR 26439–Joint Research Centre–Institute for the Protection and Security of the Citizen: Ispra, Italy, 2014. [Google Scholar] [CrossRef]
- Bedon, C.; Zhang, X.; Santos, F.; Honfi, D.; Kozlowski, M.; Arrigoni, M.; Figuli, L.; Lange, D. Performance of structural glass facades under extreme loads—Design methods, existing research, current issues and trends. Constr. Build. Mater.
**2018**, 163, 921–937. [Google Scholar] [CrossRef] - Overend, M.; De Gaetano, S.; Haldimann, M. Diagnostic Interpretation of Glass Failure. Struct. Eng. Int.
**2007**, 17, 151–158. [Google Scholar] [CrossRef] - Honfi, D.; Reith, A.; Vigh, L.G.; Stocker, G. Why Glass Structures Fail?—Learning from Failures of Glass Structures. In Proceedings of the Challenging Glass 4 & COST Action TU0905 Final Conference, Lausanne, Switzerland, 6–7 February 2014; pp. 791–800, ISBN 978-1-138-00164-0. [Google Scholar] [CrossRef]
- European Committee for Standardization. Eurocode 8: Design of Structures for Earthquake Resistance—Part 1: General Rules, Seismic Actions and Rules for Buildings; EN 1998-1:2004; CEN: Brussels, Belgium, 2014. [Google Scholar]
- CNR-DT 210/2013. Istruzioni per la Progettazione, L’esecuzione ed il Controllo di Costruzioni con Elementi Strutturali di vetro [Guide for the Design, Construction and Control of Buildings with Structural Glass Elements]; National Research Council of Italy (CNR): Roma, Italy, 2013; (Italian version); Available online: www.cnr.it/it/node/2630 (accessed on 1 November 2019).
- NTC2018. Norme Tecniche per le Costruzioni; Design Standard for Buildings; Ministero delle Infrastrutture e dei Trasporti: Roma, Italy, 17 Gennaio 2018. (In Italian)
- Overend, M. Recent developments in design methods for glass structures. Struct. Eng.
**2010**, 88, 18–26. [Google Scholar] - Green, R. The Challenges of Writing a Structural Standard for Glass. In Proceedings of the Challenging Glass Conference, Ghent, Belgium, 16–17 June 2016; Volume 5, pp. 623–632. [Google Scholar] [CrossRef]
- Feldmann, M.; Di Biase, P. The CEN-TS “Structural Glass–Design and Construction Rules” as pre-standard for the Eurocode. In Proceedings of the Conference Engineered Transparency, Düsseldorf, Germany, 23–26 October 2018. [Google Scholar] [CrossRef]
- Sucuoglu, H.; Vallabhan, C.V.G. Behaviour of window glass panels during earthquakes. Eng. Struct.
**1997**, 19, 685–694. [Google Scholar] [CrossRef] - Wensheng, L.; Baofeng, H. Discussion on Seismic Performance Indexes of Architectural Curtain Walls. In Proceedings of the 14th WCEE Conference—World Conference on Earthquake Engineering, Beijing, China, 12–17 October 2008. [Google Scholar]
- Sivanerupan, S.; Wilson, J.L.; Gad, E.F. Structural analysis and design of glazed curtain wall systems. Aust. J. Struct. Eng.
**2011**, 12, 57–67. [Google Scholar] - Overend, M.; Nhamoinesu, S.; Watson, J. Structural Performance of Bolted Connections and Adhesively Bonded Joints in Glass Structures. J. Struct. Eng.
**2013**, 139, 04013015. [Google Scholar] [CrossRef] - Bernard, F.; Daudeville, L. Point fixings in annealed and tempered glass structures: Modeling and optimization of bolted connections. Eng. Struct.
**2009**, 31, 946–955. [Google Scholar] [CrossRef] - Nielsen, J.H.; Olesen, J.F.; Poulsen, P.N.; Stang, H. Simulation of residual stresses at holes in tempered glass: A parametric study. Mater. Struct.
**2010**, 43, 947–961. [Google Scholar] [CrossRef] - Katsivalis, I.; Thomsen, O.T.; Feih, S.; Achintha, M. Strength evaluation and failure prediction of bolted and adhesive glass/steel joints. Glass Struct. Eng.
**2018**, 3, 183–196. [Google Scholar] [CrossRef] [Green Version] - Amadio, C.; De Luca, O.; Fedrigo, C.; Fragiacomo, M.; Sandri, C. Experimental and numerical analysis of glass-to-steel joint. J. Struct. Eng.
**2008**, 134, 1389–1397. [Google Scholar] [CrossRef] - Martins, L.; Delgado, R. Seismic Behavior of Point Supported Glass Panels. In Proceedings of the Challenging Glass 3—Conference on Architectural and Structural Applications of Glass, TU Delft, Delft, The Netherlands, 28–29 June 2012. [Google Scholar]
- Sivanerupan, S.; Wilson, J.L.; Gad, E.F.; Lam, N.T.K. Drift performance of point fixed glass façade systems. Adv. Struct. Eng.
**2014**, 17, 1481–1495. [Google Scholar] [CrossRef] - Casagrande, L.; Bonati, A.; Occhiuzzi, A.; Caterino, N.; Auricchio, F. Numerical investigation on the seismic dissipation of glazed curtain wall equipped on high-rise buildings. Eng. Struct.
**2019**, 179, 225–245. [Google Scholar] [CrossRef] - Aiello, C.; Caterino, N.; Maddaloni, G.; Bonati, A.; Franco, A.; Occhiuzzi, A. Experimental and numerical investigation of cyclic response of a glass curtain wall for seismic performance assessment. Constr. Build. Mater.
**2018**, 187, 596–609. [Google Scholar] [CrossRef] - Krstevska, L.; Tashkov, L.; Rajcic, V.; Zarnic, R. Seismic behaviour of composite panel composed of laminated wood and bearing glass—Experimental investigation. Adv. Mater. Res.
**2013**, 778, 698–705. [Google Scholar] [CrossRef] - Stepinac, M.; Rajcic, V.; Zarnic, R. Timber-structural glass composite systems in earthquake environment. Gradevinar
**2016**, 68, 211–219. [Google Scholar] - Bedon, C.; Amadio, C. Numerical assessment of vibration control systems for multi-hazard design and mitigation of glass curtain walls. J. Build. Eng.
**2018**, 15, 1–13. [Google Scholar] [CrossRef] [Green Version] - Bedon, C.; Amadio, C. Enhancement of the seismic performance of multi-storey buildings by means of dissipative glazing curtain walls. Eng. Struct.
**2017**, 152, 320–334. [Google Scholar] [CrossRef] [Green Version] - Desai, P.; Golmohammadi, A.; Garlipp, R.; Gowda, B. New Point Supported Glass Seismic System. In Proceedings of the AESE 2005–First International Conference on Advances in Experimental Structural Engineering, Nagoya, Japan, 19–21 July 2005; p. 8. [Google Scholar]
- March, M. Structural glass columns in significant seismic zones. In Proceedings of the GlassCon Global 2014, Pennsylvania Convention Center, PA, USA, 7–10 July 2014; pp. 470–486. Available online: http://www.glassconglobal.com/pdfs/GlassCon-Global-2014-Proceedings-Book.pdf (accessed on 1 November 2019).
- European Committee for Standardization. Basis of Structural Design; EN 1990:2002; CEN: Brussels, Belgium, 2002. [Google Scholar]
- Bedon, C.; Fasan, M.; Amadio, C. Vibration analysis and dynamic characterization of structural glass elements with different restraints based on Operational Modal Analysis. Buildings
**2019**, 9, 13. [Google Scholar] [CrossRef] - Lenci, S.; Consolini, L.; Clementi, F. On the experimental determination of dynamical properties of laminated glass. Ann. Solid Struct. Mech.
**2015**, 7, 27–43. [Google Scholar] [CrossRef] - Zemanova, A.; Zeman, J.; Janda, T.; Schmidt, J.; Sejnoha, M. On modal analysis of laminated glass: Usability of simplified methods and Enhanced Effective Thickness. Compos. Part B Eng.
**2018**, 151, 92–105. [Google Scholar] [CrossRef] [Green Version] - Bedon, C.; Amadio, C. Buckling of flat laminated glass panels under in-plane compression or shear. Eng. Struct.
**2012**, 36, 185–197. [Google Scholar] [CrossRef] - Bedon, C.; Amadio, C. Shear glass panels with point-fixed mechanical connections: Finite-Element numerical investigation and buckling design recommendations. Eng. Struct.
**2016**, 112, 233–244. [Google Scholar] [CrossRef] - Bedon, C.; Amadio, C. A unified approach for the shear buckling design of structural glass walls with non-ideal restraints. Am. J. Eng. Appl. Sci.
**2016**, 9, 64–78. [Google Scholar] [CrossRef] - Mapei
^{®}. Technical Data Sheet and Catalogue for Silicone Sealants. Available online: www.mapei.com (accessed on 1 November 2019). - Metalglas
^{®}. Technical Data Sheet for Mapesil GP Silicone. Available online: www.metalglas.it (accessed on 1 November 2019). - Hilti
^{®}. Technical Data Sheet for HST3-R Expansion Anchor. Available online: www.hilti.it (accessed on 1 November 2019). - European Committee for Standardization. Stainless Steels—Part 1: List of Stainless Steels; EN 10088-1: 2014; CEN: Brussels, Belgium, 2014. [Google Scholar]
- Simulia. ABAQUS Computer Software; Dassault Systemes Simulia Corporation: Johnston, RI, USA, 2019. [Google Scholar]
- Calderone, I.; Davies, P.S.; Bennison, S.J.; Huang, X.; Gang, L. Effective Laminate Thickness for the Design of Laminated Glass. In Proceedings of the Glass Performance Days, Tampere, Finland, 12–15 June 2009. [Google Scholar]
- Galuppi, L.; Royer-Carfagni, G.F. Effective thickness of laminated glass beams: New expression via a variational approach. Eng. Struct.
**2012**, 38, 53–67. [Google Scholar] [CrossRef] - European Committee for Standardization. Glass in Buildings-Basic Soda Lime Silicate Glass Products; EN 572–2:2004; CEN: Brussels, Belgium, 2004. [Google Scholar]
- Bommer, J.J.; Martinez-Pereira, A. The Prediction of Strong-Motion Duration for Engineering Design. In Proceedings of the 11th WCEE-Eleventh World Conference on Earthquake Engineering, Acapulco, Mexico, 23–28 June 1996; p. 84, ISBN 0080428223. [Google Scholar]
- Kempton, J.J.; Stewart, J.P. Prediction equations for significant duration of earthquake ground motions considering site and near-source effects. Earthq. Spectra
**2006**, 22, 985–1013. [Google Scholar] [CrossRef] - Abdullah Sandikkaya, M.; Akkar, S. Cumulative absolute velocity, Arias intensity and significant duration predictive models from a pan-European strong-motion dataset. Bull. Earthq. Eng.
**2017**, 15, 1881–1898. [Google Scholar] [CrossRef] - Pilkey, W.D. Peterson’s Stress Concentration Factors, 2nd ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 1997. [Google Scholar]
- Coker, E.G.; Filon, L.N.G. Photo-Elasticity; Cambridge University Press: London, UK, 1931. [Google Scholar]
- Frocht, M.M. Photoelasticity; Wiley: New York, NY, USA, 1949; Volume 1. [Google Scholar]
- Nisida, M.; Saito, H. Stress distributions in a semi-infinite plate due to a pin determined by interferometric method. Exp. Mech.
**1966**, 6, 273–279. [Google Scholar] [CrossRef] - Hyer, M.W.; Liu, D. Stresses in pin-loaded orthotropic plates using photoelasticity. J. Compos. Mater.
**1985**, 19, 138–153. [Google Scholar] [CrossRef] - Fink, A. Ein Beitrag zum Einsatz von Floatglass als Dauerhaft Tragender Konstruktionswerkstoff im Bauwesen. Ph.D. Thesis, Institut fur Statik, Technische Universitat Darmstadt, Darmstadt, Germany, June 2000. [Google Scholar]
- Oikonomopoulou, F.; van den Broek, E.A.M.; Bristogianni, T.; Veer, F.A.; Nijsse, R. Design and experimental testing of the bundled glass column. Glass Struct. Eng.
**2017**, 2, 183–200. [Google Scholar] [CrossRef] [Green Version] - Peroni, M.; Solomos, G.; Pizzinato, V.; Larcher, M. Experimental investigation of high strain-rate behaviour of glass. Appl. Mech. Mater.
**2011**, 82, 38–63. [Google Scholar] [CrossRef] - Haldimann, M. Fracture Strength of Structural Glass Elements—Analytical and Numerical Modelling, Testing and Design. Ph.D. Thesis, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, June 2006. [Google Scholar]
- Franco, A.; Royer-Carfagni, G. Verification formulae for structural glass under combined variable loads. Eng. Struct.
**2015**, 83, 233–242. [Google Scholar] [CrossRef] - Bedon, C.; Amadio, C. Assessment of analytical formulations for the ULS resistance verification of structural glass elements accounting for the effects of different load durations. Structures
**2017**, 11, 218–228. [Google Scholar] [CrossRef] - prEN 16612; CEN/TC 250. Glass in Building—Determination of the Load Resistance of Glass Panes by Calculation and Testing; European Committee for Standardization (CEN): Brussels, Belgium, 2013. [Google Scholar]
- Bedon, C. Diagnostic analysis and dynamic identification of a glass suspension footbridge via on-site vibration experiments and FE numerical modelling. Compos. Struct.
**2019**, 216, 336–378. [Google Scholar] [CrossRef] - Ensslen, F. Influences of Laboratory and Natural Weathering on the Durability of Laminated Safety Glass. In Proceedings of the Glass Performance Days, GDP 2007, Tampere, Finland, 15–18 June 2007; p. 7. [Google Scholar]
- Hooper, P.A.; Blackman, B.R.K.; Dear, J.P. The mechanical behaviour of poly (vinyl butyral) at different strain magnitudes and strain rates. J. Mater. Sci.
**2012**, 47, 3564–3576. [Google Scholar] [CrossRef] - Andreozzi, L.; Bati, S.B.; Fagone, M.; Ranocchiai, G.; Zulli, F. Dynamic torsion tests to characterize the thermo-viscoelastic properties of polymeric interlayers for laminated glass. Constr. Build. Mater.
**2014**, 65, 1–13. [Google Scholar] [CrossRef] - Stevels, W.; D’Haene, P.; Zhang, P.; Haldeman, S. A Comparison of Different Methodologies for PVB Interlayer Modulus Characterization. In Proceedings of the Challenging Glass 5—Conference on Architectural and Structural Applications of Glass, Ghent, Belgium, 16–17 June 2016; ISBN 978-908-256-680-6. [Google Scholar]
- Trevisan, F. Experimental Tests on Steel Fasteners for a Glass Partition System; Technical Report n. 19008; Department of Engineering and Architecture, University of Trieste: Trieste, Italy, 2019; p. 8, (For internal use only). [Google Scholar]

**Figure 1.**Glass in buildings: examples of (

**a**) point-supported facade or (

**b**) glass pavilion ((

**a**,

**b**) reproduced from [1] with permission from Elsevier, license n. 4637550841997, July 2019); (

**c**,

**d**) typical point-fixings for facades (both photos reproduced from [2] with permission from WILEY-VCH Verlag GmbH, license n. 4665240805701, September 2019).

**Figure 2.**Modified spider connector with slotted holes for seismic resistant point-supported facades (adapted from [30] with permission from Sage Publishing, July 2019).

**Figure 3.**Pinned/rocking connection for glass columns in seismic regions: (

**a**) design concept; (

**b**) working mechanism and (

**c**) example of real structure (adapted from [31] under the terms and conditions of CC BY license).

**Figure 4.**Structural design of glass and reference technical documents for Italy (adapted from [4]).

**Figure 5.**Local seismic analysis of glass elements: (

**a**) variation of the R

_{a}magnification factor with T

_{a}/T

_{1}(Equation (5)) and (

**b**) reference model for the local seismic verification.

**Figure 6.**Ferdinandeo Palace (Trieste, Italy), with evidence of the intervention area: (

**a**) axonometric view and (

**b**) plan view.

**Figure 8.**Glass partition system. (

**a**) Axonometric view, with (

**b**) LG cross-section and (

**c**) detail of restraints (render by A. Danelutti, reproduced with permission).

**Figure 9.**Foundation system for the glass partition walls. (

**a**) Cross-sectional drawing (dimensions in mm) and (

**b**) detail views (photo by A. Danelutti, reproduced with permission).

**Figure 10.**Elevation restraints. (

**a**,

**b**) Glass-to-building connectors and (

**c**) glass-to-glass friction clamps for corners or (

**d**) overlying panels (photos by A. Danelutti and F. Trevisan, reproduced with permission).

**Figure 11.**Example of numerical modelling of the partition system. (

**a**) Selected P1 wall and (

**b**) corresponding FE numerical model (ABAQUS).

**Figure 12.**Schematic representation and mechanical description of the metal fasteners in use: point-fixings under (

**a**) out-of-plane or (

**b**) in-plane loads.

**Figure 13.**Numerical analysis of glass partition walls under in-place seismic loads. In evidence, the local reaction forces that the P1 wall under out-of-plane seismic pressure transfers to the P2 wall, via the metal point-fixings in use.

**Figure 14.**Seismic analysis of the P1 wall (ABAQUS): example of expected tensile stresses due to safeguard of human life and collapse (SLC) out-of-plane pressure (× 5 scale factor, legend in Pa).

**Figure 15.**Concentration factor K for the approximate estimation of stress peaks σ

_{max}in the region of glass holes (adapted from [9]), for (

**a**) plates in bending (as a function of the hole diameter (d) and glass thickness (h), see [50]), and (

**b**) under in-plane loads (as a function of the force inclination ϕ, see [51,52,53,54]).

**Figure 16.**Stress verification of the P1 wall under SLC seismic combination of loads (Equation (6), out-of-plane), as a function of G

_{PVB}: (

**a**) calculated stress peaks (near holes) and (

**b**) cumulative damage, based on different methods of literature.

**Figure 17.**Displacement verification of the P1 wall under States for Operability Damage (SLD) seismic combination of loads (out-of-plane): (

**a**) typical deformation (ABAQUS, × 10 scale factor, legend in m) and (

**b**) deformation assessment, as a function of G

_{PVB}.

**Figure 18.**Displacement verification of the P1 wall under SLD seismic combination of loads (in-plane, ABAQUS): (

**a**) typical deformation (axonometry, ×50 scale factor, legend in m) and (

**b**) detail of compressive stress peaks (front view, legend in Pa).

**Figure 19.**Example of reaction forces in the glass-to-column fasteners for the P1 wall under SLC seismic combination of loads (out-of-plane, ABAQUS, legend in N).

**Table 1.**Consequence class (CC) definition for common glass elements, based on the CNR-DT 210 guide (CC0 = secondary, non-structural elements). n.a. = no assessment is required; F = failure.

Element | CC | |
---|---|---|

pre-F (SLS, ULS) | post-F (CLS) | |

Vertical (with linear restraints) | 1 | 1/n.a. |

Vertical (with point-fixings) | 2/1 | 1/n.a. |

Roofs | 2 | 2/1 |

Fins | 2 | 2/1 |

Railings (fall danger) | 2 | 2/1 |

Floors, beams | 2 | 2 |

Pillars | 3 | 2 (with pre-F loads) |

**Table 2.**Reference design life V

_{N}for the pre-F analysis

^{1}of glass structures/elements, according to the CNR-DT 210 guide, and comparison with the NTC2018 provisions [10].

V_{N} (in years) | Example | NTC2018 |
---|---|---|

10 | Temporary structures ^{2} | Yes |

10–25 | Replaceable parts | No |

15–30 | Agricultural structures | No |

50 | Buildings, common structures | Yes |

100 | Monumental buildings, bridges, other | Yes |

^{1}The post-F V

_{N}is set equal to 10 years for CC1 and CC2, while it must be calculated from specific studies for CC3;

^{2}Excluded structures/parts that can be dismantled/reused.

Importance Class | Description | C_{U} |
---|---|---|

I | Occasional presence of people or agricultural buildings | 0.7 |

II | Normal crowd levels or factories, without essential public/social functions | 1.0 |

III | Significant crowd levels | 1.5 |

IV | Important public, or construction with strategic functions | 2.0 |

Performance Level | Description | |
---|---|---|

ND | No damage | No damage in glass; no replacement; watertightness preserved |

SD | Slight damage | Partial loss of functionality; usable building; no risk for users |

HD | Heavy damage | High degree (and cost) of functionality loss; still no risk for users |

F | Failure | Severe damage; evidence of failure; risk for users |

**Table 5.**Required performances for structural glass systems under seismic loads, according to the CNR-DT 210 guide (see also Table 4). Subscript = T

_{R}(in years, see Equation (2)).

Importance class | ||||
---|---|---|---|---|

Limit State | I | II | III | IV |

SLO | - | - | ND_{45} | ND_{60} |

SLD | SD_{35} | SD_{50} | SD_{75} | SD_{100} |

SLV | HD_{333} | HD_{475} | HD_{713} | HD_{950} |

SLC | - | - | F_{1463} | F_{1950} |

**Table 6.**Definition of the design seismic force F

_{a}and corresponding uniform pressure Q

_{a}(for out-of-plane analyses).

R_{a} = 1 (Equation (5)) | ||||
---|---|---|---|---|

Limit State | a_{g,max}[g] | S_{a}[g] | F_{a}[kN] | Q_{a}[kN/m ^{2}] |

SLO | 0.128 | 0.154 | 0.385 | 0.049 |

SLD | 0.167 | 0.201 | 0.503 | 0.064 |

SLV | 0.442 | 0.531 | 1.328 | 0.170 |

SLC | 0.546 | 0.655 | 1.638 | 0.210 |

**Table 7.**Recommended loading time t

_{L}, temperature T

_{L}and shear modulus G

_{PVB}for selected design loads (values from §4.10 [9]). * = transient load.

Design Load (Equation (6)) | t_{L}(time) | T_{L}[°C] | G_{PVB}[MPa] |
---|---|---|---|

Dead | V_{N} (50 years) | 50 | 0.052 |

Seismic | 30 s * | 30 | 0.8 |

Crowd | 30 s * | 30 | 0.8 |

**Table 8.**Calculated cumulative damage and stress verification for the P1 wall under a safeguard of human life and collapse (SLC) seismic combination of loads (out-of-plane), according to different analytical methods of literature.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bedon, C.; Amadio, C.; Noè, S.
Safety Issues in the Seismic Design of Secondary Frameless Glass Structures. *Safety* **2019**, *5*, 80.
https://doi.org/10.3390/safety5040080

**AMA Style**

Bedon C, Amadio C, Noè S.
Safety Issues in the Seismic Design of Secondary Frameless Glass Structures. *Safety*. 2019; 5(4):80.
https://doi.org/10.3390/safety5040080

**Chicago/Turabian Style**

Bedon, Chiara, Claudio Amadio, and Salvatore Noè.
2019. "Safety Issues in the Seismic Design of Secondary Frameless Glass Structures" *Safety* 5, no. 4: 80.
https://doi.org/10.3390/safety5040080