Glass Structures & Engineering

, Volume 4, Issue 3, pp 421–432 | Cite as

Post-breakage in-plane stiffness of laminated glass: an engineering approach

  • Gianmaria D’Ambrosio
  • Laura GaluppiEmail author
  • Gianni Royer-Carfagni
SI: Glass Performance Paper


In the post-breakage phase, laminated glass (LG) can maintain a residual load-bearing capacity due to the tension stiffening of the polymer through the adhesion with the shards, but the determination of the overall post-breakage stiffness presents formidable difficulties. A simple model is here proposed for the in-plane response of broken thermally treated LG, characterized by a fine cracking pattern. A simple formula for the effective post-breakage stiffness under in-plane loading is provided, which depends upon interlayer modulus and amount of delamination. Comparisons with numerical experiments confirm its accuracy for interpreting the response of representative portions of broken LG, composed by a large number of glass fragments, for different shapes of the glass shards and for different amount of delamination. The proposed model may represent an useful practical tool for evaluating the post-critical response of LG under in-plane loading, in particular under shear. This may be of crucial importance in view of possible applications of LG-based elements as structural shear-resistant transparent diaphragms for the seismic retrofitting of historical monuments. Glass-based bracings shall be designed to remain sound under moderate earthquakes; they can possibly break under the most severe seismic events, but always in a ductile manner while dissipating energy, thanks to the hysteretic response of broken LG consequent to progressive delamination.


Laminated glass Post-glass-breakage response In-plane loading Effective stiffness Seismic retrofitting 



The authors acknowledge the support of the Italian Dipartimento della Protezione Civile under Project ReLUIS-DPC 2019–2021 and the support of the Italian Ministero dell’Istruzione, dell’Universita’ e della Ricerca under Grant MIUR-PRIN voce COAN code 2015JW9NJT.


This study was funded by Dipartimento della Protezione Civile, Presidenza del Consiglio dei Ministri—Italy and Ministero dell’Istruzione, dell’Universita’ e della Ricerca—Italy (MIUR-PRIN voce COAN code 2015JW9NJT).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Engineering and ArchitectureUniversity of ParmaParmaItaly
  2. 2.Construction Technologies Institute - Italian National Research Council (ITC-CNR)San Giuliano Milanese, MilanItaly

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