European Journal of Wood and Wood Products

, Volume 77, Issue 3, pp 367–379 | Cite as

Equivalent stiffness of timber used in CLT: closed-form estimates and numerical validation

  • Olivier Perret
  • Arthur LebéeEmail author
  • Cyril Douthe
  • Karam Sab


In this paper, a closed-form approach is presented to estimate rapidly the equivalent stiffness of boards used in cross laminated timber (CLT) panels from local orthotropic behavior at ring scale for varying sawing patterns. It is first assumed that narrow edges are glued. In this case, closed-form Reuss and Voigt bounds are derived for the equivalent layer behavior of CLT. An application to Norway spruce boards is presented and reveals that the cross-layer (rolling) shear behavior lies between 100 and 150  MPa with a careful selection of the board sawing pattern. Then, using finite element method, upper bounds for the cross-layer shear stiffness modulus of boards with and without glued edges are calculated and theoretical predictions are compared with recommendations and experimental data from the literature. Finally, it appears that these bounds remain relevant for CLT layer with unglued narrow edges for common aspect ratios.


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Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratoire Navier UMR 8205École des Ponts ParisTech, IFSTTAR, CNRS, Université Paris-EstMarne-la-ValléeFrance

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