Advances in Effective Thickness

Laminated glass combines multiple plies of glass bonded with interlayers into a single lite, often for safety-glass impact performance, strength, redundancy, or to develop thicker lites for longer spans. Effective thickness is a simplified method for the structural evaluation of laminated glass section properties and is useful for the evaluation of stress, deflection, and stability with classic beam engineering equations. The effective thickness methods consist of defining the thickness of a monolithic section with equivalent flexural or torsional section properties, bounded by the non-composite layered and fully-composite monolithic limits.

The Wölfel-Bennison (W-B) effective thickness method included in the glass standard ASTM E1300 [2], developed by Wölfel [24] for concrete composite decks and advanced by Bennison et. al. [8] for laminated glass, is well known in the glazing industry. The W-B effective thickness method shows excellent correlation with finite element analysis (FEA) models (i.e., numerical models) of 2-ply simply supported laminated glass beams in flexure and has been validated with four-point bending tests [18]. Furthermore, this method will often predict near full composite behavior for short duration loads on 2-ply glass laminates with stiff interlayers (e.g., extra-stiff polyvinyl butyral (PVB) and ionoplast), preferred for structural glass applications over conventional PVB.

In accordance with the current effective thickness recommendations in ASTM E1300, we frequently observe the generic application of the W-B method for evaluation of all combinations of glass geometries, loads, and boundary conditions. Wölfel’s composite analysis method was intended for estimation of simply supported composites with out-of-plane concentric loads; however, this method lacks correlation for applications with cantilevered beam performance in flexure [15, 16] as shown in Figure 1, application (i), and glass fin stability [6], application (iii). Application of existing effective thickness models for the evaluation of stresses in cantilevered laminated glass have not been successful [16]. Very recently, the Conjugate Beam Effective Thickness method proposed by Galuppi and Nizich [12, 16] provides effective thickness formulas which more precisely correlate with cantilevered laminated glass boundary conditions.

In comparison, an alternative effective thickness method for the evaluation of flexural and torsional stiffness of 2- and 3-ply glass beams advanced by Luible [6, 19, 20], based on the sandwich beam theory presented by Stamm and Witte [23], and was recently proposed in the draft Eurocode for structural glass CEN/TS 19100 [9]. However, Luible’s method has had limited adoption for glass fin design outside of Europe. Potential reasons include continued reference to ASTM E1300 as the sole effective thickness method (as also referenced in the Australian glass standard AS-1288 [5] which includes glass fin design), as well as regional differences in engineering nomenclature, relative complexity of equations, and a contemporary preference for stiff interlayers that are widely believed to provide high coupling.

Currently, there is renewed interest in the application of softer interlayers for multi-ply (e.g., lites with 3 or more glass plies) laminated glass fins where fully-tempered glass is specified to mitigate a cohesive glass failure mode ¹ observed by Coult [10]. Specification of softer interlayers and design for post-fracture behavior have led to glass fins composed of 4 or more plies which are not readily evaluated with Luible’s method. Recently, the Enhanced Effective Thickness method [11, 13, 14] was extended to the evaluation of multi-ply beams with unlimited plies in flexure and torsion.

Here, we examine the analytical considerations for laminated glass and advances in effective thickness methods for laminated glass structural design with:

• the Conjugate Beam Effective Thickness (CBET) method recently proposed by Galuppi and Nizich [12, 16] for cantilevered laminated glass in flexure, and
• the Enhanced Effective Thickness (EET) method, widely used in Europe, proposed by Galuppi and Royer-Carfagni [13, 14] for flexure and torsion of multi-ply glass laminates with various load and boundary conditions, and extended by D’Ambrosio & Galuppi [11] to evaluate the flexural stiffness from axial loading for evaluation of critical buckling.

[1] ASTM C1048-18: Standard Specification for Heat-Strengthened and Fully Tempered Flat Glass. ASTM International. 2018. doi: 10.1520/C1048-18

[2] ASTM E1300-16: Standard practice for determining load resistance of glass in buildings. ASTM International. 2016. doi: 10.1520/E1300-16

[3] ASTM WK37764: New Guide for Structural Use of Glass in Buildings. Working Group. ASTM International. Balloted, 2021

[4] ASTM WK80563: New Guide for Effective Thickness Evaluation of Laminated Glass. Working Group. ASTM International

[5] AS 1288-R2016: Glass in buildings-Selection and installation. Standards Australia. 2016

[6] Bedon, C., Amadio, C.: Design buckling curves for glass columns and beams. Structures and Buildings Volume 168 Issue SB7. Institution of Civil Engineers. London, 2015. doi.org/10.1680/stbu.13.00113

[7] Belis, J., Mocibob, D., Luible, A., Vandebroek, M.: On the size and shape of initial out-of-plane curvatures in structural glass components. Construction and Building Materials. 25. 2011. doi.10.1016/j.conbuildmat.2010.12.021.

[8] Calderone, I., Davies, P.S., Bennison, S. J., Xiaokun, H., and Gang, L.: Effective laminate thickness for the design of laminated glass. In Proceedings of Glass Performance Days, Tampere (FI), pages 12-15, 2009

[9] CEN/TS 19100:2021: Design of glass structures. European Committee for Standardization, 2021

[10] Coult, G: Laminated glass panels; understanding a new failure mechanism. Presentation. Glass Performance Days, Finland, 2019

[11] D’Ambrosio, G., Galuppi, L., “Enhanced effective thickness model for buckling of LG beams with different boundary conditions”, Glass Structures & Engineering, v.5, pages 205–210, 2020. doi.org/10.1007/s40940-019-00116-3

[12] Galuppi, L., and Nizich, A. J., “Cantilevered laminated glass balustrades: The Conjugate Beam Effective Thickness method. part I: the analytical model,” Glass Structures & Engineering, Springer Nature, 2021. doi.org/10.1007/s40940-021-00156-8

[13] Galuppi, L., and Royer-Carfagni, G., “Enhanced Effective Thickness of multi-layered laminated glass,” Composites Part B: Engineering, Volume 64, 2014, pp. 202-213. doi.org/10.1016/j.compositesb.2013.05.025

[14] Galuppi, L., and Royer-Carfagni, G., “Enhanced Effective Thickness for laminated glass beams and plates under torsion”, Engineering Structures 206, 2020. doi.org/10.1016/j.compositesb.2013.05.025

[15] Nizich, A. J., and Galuppi, L.: Enhanced effective thickness method for cantilevered laminated glass balustrades. In Proceedings of glass Performance Days, pages 398-401, Tampere (FI), 2019

[16] Nizich, A. J., and Galuppi, L., “Cantilevered laminated glass balustrades: The Conjugate Beam Effective Thickness method. part II: comparison and application,” Glass Structures & Engineering, Springer Nature, 2022. doi.org/10.1007/s40940-021-00165-7

[17] IBC-2021 International Building Code and Commentary – Volumes 1 & 2. International Code Council, Inc. First Printing. Country Club Hills, IL. 2021

[18] Kuntsche, J., Schuster, M., and Schneider, J.: Engineering design of laminated safety glass considering the shear coupling: a review. Glass Struct Eng, v.4(2):209-228, 2019. doi.org/10.1007/s40940-019-00097-3

[19] Luible, A.: Stabilität von Tragelementen aus Glas. Thesis. Lucerne University of Applied Sciences and Arts (2004). doi.10.5075/epfl-thesis-3014

[20] Haldimann, M., Luible, A., and Overend, M.: Structural use of glass, Volume 10. International Association for Bridge and Structural Engineering. 2008. doi: 10.2749/sed010

[21] SJ Mepla: Glass Finite Element Software. Version 5.0.11. SJ Software GmbH, Aachen, Germany, 2021

[22] Strand7: Strand7 Finite Element Analysis System. Version 3.1.1. Strand7 Pty. Ltd. Sydney, 2021

[23] Stamm, K., Witte, H.: Sandwichkonstruktionen: Berechnung, Fertigung, Ausführung. Springer-Verlag; 1974

[24] Wölfel, E.: Nachgiebiger verbund - eine näherungslösung und deren anwendungsmöglichkeiten. Stahlbau, 6:173-180, 1987