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

Abstract

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.

Experimental determination of the equivalent-layer shear stiffness of CLT through four-point bending of sandwich beams

“…This value is in agreement with Voigt and Reuss bounds 725 calculated in [16], assuming that the local elastic behavior of Norway spruce is the one obtained by Keunecke et al [29]. Moreover, this value is larger than the equivalent rolling shear modulus measured by Franzoni et al…”

“…[11] on the same batch of wood. This is probably because narrow 730 edges were glued in the present test whereas they were free in [11] as observed numerically by Perret et al [16]. Finally, a lower coefficient of variation (6.71%) is obtained compared to double-lap shear tests from Franzoni et al…”

“…From these observations, Ehrhart et al [23] recommend to set the effective shear modulus and strength 180 according to linear functions of the board aspect ratio revised later by Schickhofer et al [34]. In a recent study, Perret et al [16] suggest closed-form bounds of the equivalent cross-layer shear moduli of timber depending on the sawing pattern and on local mechanical characteristics at 185 ring scale. They observe particularly that, if the board is cut relatively close to the pith, the equivalent cross-layer shear modulus lies between 100 and 150 MPa.…”

“…Numerous approaches have been suggested to measure this modulus but they are not always reliable because of 40 stress concentrations or because of indirect measurement of the shear modulus. Moreover, a difference was observed between the local rolling shear modulus at ring scale, mea-sured at 50 MPa approximately for softwood species and the equivalent shear modulus at board scale which may be 45 significantly larger [14,15,16]. Indeed, at ring scale, wood elastic behavior may be modeled as orthotropic with three main directions: the longitudinal direction L corresponding to wood fibers orientation, the radial and tangential directions R and T (Figure 1).…”

A shear strength criterion for the buckling analysis of CLT walls

“…For the mean longitudinal shear modulus, CLT panels without narrow face boundings are considered, so that according to [22,23], = 450 MPa. The three configurations are hence summarized in Figure 2 and their characteristics are recalled in Table 1.…”