# Sustainable Cross-Laminated Timber Structures in a Seismic Area: Overview and Future Trends
## 4 Modeling Strategies of the Components
### Material Modeling
#### 4.1.2 Out-of-Plane Modeling  
The out-of-plane flexural behaviour of CLT panels is significantly influenced by the shear deformations of the transverse layers. This phenomenon, indicated as \"rolling shear\", is due to the tangential stresses (\(\tau\)) acting in the orthogonal to grain direction within transverse layers of the panels. Due to the low value of the shear or tangential modulus in the orthogonal to grain direction of timber boards (named rolling shear modulus \(-\)G\({}_{\text{R}}\)), grains rolling off one from each other occur in transverse layers (Figure 8). As a consequence, increases of deflections and vibrations of the panel and modification of its internal stresses arise [51; 52]. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Load Direction** & **[PERSON] and Fellmoser**[48] & **[PERSON] et al. [50] \\ \hline  & & & \(E_{L}=k_{3}E_{0}\) & \(E_{L}=\frac{n_{L}}{n_{\text{tot}}}E_{0}\) \\  & & where: & & where: \\  & & \(k_{3}=\frac{k_{3}}{n_{\text{I}}}\) & n\({}_{\text{I}}\) = numb. of layers in the \\  & & & \(\left(1-\frac{E_{0}}{E_{0}}\right)\frac{d_{\text{R}-2}+d_{\text{R}-4}+...+d_{ 1}}{d_{n}}\) & longitudinal direction \\  & & & \(n_{\text{tot}}\) = total numb. of layers \\ \hline \hline \end{tabular} \(a_{\text{m}}=\text{panel total thickness, }a_{\text{I}}=\text{thickness of the middle layer, }a_{\text{m}-2}=\text{distance between two transverse layers}\) (measured between the center of gravity of each layer), E\({}_{0}=\text{[PERSON]'s modulus of raw material}\).  
\end{table} 
Table 2: Coefficients for effective stiffness for cross-lam panels loaded in-plane. The rolling shear phenomenon was first raised by [PERSON] and [PERSON] [51], who highlighted its effect on the flexural behaviour of CLT floors having different length-to-depth aspect ratios. Experimental studies aimed at investigating different aspects have been conducted [53; 54; 55; 56], as well as numerical investigations. A multi-scale finite element model accounting for the rolling shear failure by means of an homogenization and cohesive zone model of the panel has been proposed by [PERSON] et al. [57]; such a model is able to capture the interlaminar and inter-fibre cracking and to solve the macroscopic equilibrium using computations. [PERSON] et al. [58] investigated the structural design and modelling by advanced plates theory which combines accuracy of the description of deformations and stresses in the plate with computational efficiency, and compared the results with analytical solutions. Consequently, practical tools for engineering applications aimed at evaluating deflections affected by the rolling shear have been proposed in literature, and part of them has been included in manuals or guidelines [2; 11]. These models are based on the beam theory, but take into account shear deformations in transverse layers. For instance the \"\(\gamma\)-method\" (also included in Eurocode 5) allows consideration for composite beams joined by metal fasteners, where the transverse cross-layers in CLT are considered as equivalent shear fasteners uniformly distributed over the length of the panel. In Table 3 are reported the formula for evaluating the effective flexural stiffness (EI)\({}_{\text{eff}}\) of the panels through the coefficient \(\gamma\) which takes into account the shear deformations in the transverse layers. Another method is the \"shear analogy method\" introduced by [PERSON] [59]. Therein, the effective flexural stiffness (EI)\({}_{\text{eff}}\) and the shear stiffness (GA) are assigned to two displacement-coupled beams: Beam A is given by the sum of the inherent flexural and shear stiffness of the individual layer along its own centres, while beam B is given by the Huygens-Stainer points, or an increased moment of inertia because of the distance from the neutral axis of the flexural and shear stiffness of the panel.