Enhanced effective thickness model for buckling of LG beams with different boundary conditions


Because of their characteristic high slenderness ratios, laminated glass elements are frequently subjected to buckling phenomena. Here, simple analytical formulae for the evaluation of the effective thickness for the compressive buckling verification of laminated glass beams are proposed, based on the Enhanced Effective Thickness model, widely used for the design of laminated glass. The model applies also to multilaminates. Tables for the calculation of the relevant coefficients in the most common cases have been added for ease of reference and to facilitate the practical use. Comparison with numerical results, performed by considered paradigmatic cases, confirm the accuracy of the proposed formulae.

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  1. 1.

    As discussed in Galuppi and Royer-Carfagni (2012a), at the monolithic limit, the cross-sectional inertia equals that of the cross sections of the composing glass layers, properly spaced of the interlayer gaps.

  2. 2.

    As it is well known, the Euler’s critical load \(P_{cr}\) represents the theoretical upper limit for compressive loading in the elastic range. Indeed, a geometrically imperfect beam/column not suddenly buckle; it bends after a small axial load is applied, and the deflection grows as the load increases and tends to infinity when the load approaches the \(P_{cr}\). However, the evaluation of the Euler critical load is necessary for the buckling verification of real elements, accounting for the initial imperfection (see, for example, Amadio and Bedon 2013).

  3. 3.

    In such a quite wide element, Poisson’s effects can develop. This may be accounted for by considering the EET model for plates Galuppi and Royer-Carfagni (2012b). However, due to the considered boundary and loading condition, the out-of-plane displacement may be assumed to be dependent only on the longitudinal coordinate (as in a beam element), and this effect can be neglected.


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The authors acknowledge the support of the Italian Dipartimento della Protezione Civile under project ReLUIS-DPC 2018-2020.

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Correspondence to Laura Galuppi.

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D’Ambrosio, G., Galuppi, L. Enhanced effective thickness model for buckling of LG beams with different boundary conditions. Glass Struct Eng 5, 205–210 (2020). https://doi.org/10.1007/s40940-019-00116-3

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  • Laminated glass
  • Buckling verification
  • Effective thickness