Probabilistic considerations about the strength of laminated annealed float glass

  • Antonio Bonati
  • Gabriele PisanoEmail author
  • Gianni Royer Carfagni
S.I.: Glass Performance Paper


Laminated structures are parallel (or redundant) systems, i.e. failure occurs when all the elements (glass plies) reach, in cascade, the ultimate limit state. Following the failure mode approach, the reliability analysis is consequent to the identification of all possible rupture modes of the glass plies, where each mode is identified by the sequence of collapse, synthetically schematized as an event-tree. The event “structural failure” is the union of all the possible failure modes. The static theorem of limit analysis guarantees that the more the structure is divided into load bearing elements acting in parallel, the safer it is, but this conclusion holds only for ideal ductile systems. For brittle glass it is often assumed that lamination gives a beneficial contribution in all cases, but glass strength is affected by a size effect in terms of area, because surface micro-cracks govern the overall capacity of the material. Taking this into account, we show through the failure mode approach, under some simplifying assumptions, that lamination can decrease the strength of a plate made of annealed glass, since the higher the number of plies is, the larger is the surface area under tensile stress. This finding focalizes the attention on the importance of an accurate characterization of the size effect in glass strength.


Laminated glass Structural safety Redundancy Strength Size effect 



GRC acknowledges 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’Università e della Ricerca under grant MIUR-PRIN voce COAN code 2015JW9NJT.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.CNR-ITC National Research CouncilInstitute for Construction TechnologiesSan Giuliano MilaneseItaly
  2. 2.Department of Engineering and ArchitectureUniversity of ParmaParmaItaly

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