## 3 Numerical Model
### Material Properties  
For the composite materials, an elastic-perfectly plastic material model has been adopted--Table 1 shows selected sheet material properties taken from the manufacturer's data. The yield strength was assumed to be the tensile strength of the composite. The sections were created by taking into account the thickness of the material. A Poisson ratio of 0.3 was assumed for each composite. In the case of laminated veneer lumber, two types of material models were verified: a linear elastic one and a linearly elastic-perfectly plastic one considering [PERSON]'s yield criterion. Tables 2 and 3 show the mechanical and orthotropic properties of the material. These were determined based on our experimental studies [16], the manufacturers' data [17], and the findings of other researchers [25]. The yield stress was used as the bending strength value determined experimentally on unreinforced members. Figure 2: Selected assumptions for numerical analysis. The \"Engineering constant\" option was used to enter the orthotropic properties of the veneer. The Hill function was entered via the \"Potential\" sub-option and calculated using Formula (1):  
\[f(\sigma)=\sqrt{F(\sigma_{22}-\sigma_{33})^{2}+G(\sigma_{33}-\sigma_{11})^{2}+H( \sigma_{11}-\sigma_{22})^{2}+2N\tau_{12}^{2}+2M\tau_{13}^{2}+2L\tau_{23}^{2}} \tag{1}\]  
In which \(\sigma_{ij}\) and \(\tau_{ij}\) correspond to the stress tensors \(\sigma\) and the six constants estimated according to Formulae (2) and (3):  
\[F=\frac{1}{2}\left(\frac{1}{R_{22}^{2}}+\frac{1}{R_{33}^{2}}-\frac{1}{R_{11}^{ 2}}\right),\ G=\frac{1}{2}\left(\frac{1}{R_{33}^{2}}+\frac{1}{R_{11}^{2}}- \frac{1}{R_{22}^{2}}\right),H=\frac{1}{2}\left(\frac{1}{R_{11}^{2}}+\frac{1}{ R_{22}^{2}}-\frac{1}{R_{33}^{2}}\right), \tag{2}\]  
\[N=\frac{3}{2R_{12}^{2}},M=\frac{3}{2R_{13}^{2}},L=\frac{3}{2R_{23}^{2}} \tag{3}\]  
In which \(R_{ij}\) constants were estimated from [26] according to Equation (4):  
\[R_{11}=\frac{\overline{\sigma}_{11}}{\sigma^{0}},R_{22}=R_{33}=\frac{ \overline{\sigma}_{22}}{\sigma^{0}}=\frac{\overline{\sigma}_{33}}{\sigma^{0}},R_{12}=R_{13}=\frac{\overline{\sigma}_{12}}{\tau^{0}}=\frac{\overline{\sigma }_{13}}{\tau^{0}},R_{23}=\frac{\overline{\sigma}_{23}}{\tau^{0}} \tag{4}\]  
in which \(\tau^{0}=\sigma^{0}/\surd 3\). Estimated constants for the analysis are shown in Table 4.  
As mentioned above, the analyses neglected the effect of the adhesive on the static behavior of the beams. In the following section, a distinction has been made between the numerical models according to the material model used for the laminated veneer. The letters EL indicate elastic models, and the letters EL-PL indicate the elastic-plastic model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **S\&P** & **S\&P** & **S\&P** & **S\&P** \\  & **A-Sheet** & **G-Sheet** & **C-Sheet** & **C-Sheet** & **C-Sheet** \\  & **120** & **E90/10** & **240** & **640** \\ \hline Tensile strength\(f_{\text{f}}\) [N/mm\({}^{2}\)] & 2900 & 3400 & 5100 & 2600 \\ Mouduls of elasticity \(E_{FRP}\) [N/mm\({}^{2}\)] & 120,000 & 73,000 & 265,000 & 640,000 \\ Thickness \(t_{FRP}\) [mm] & 0.200 & 0.289 & 0.333 & 0.189 \\ Poisson’s Ratio [-] & 0.3 & 0.3 & 0.3 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Selected mechanical and physical properties of composite sheets [18; 19; 20; 21]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{5}{c}{**Parameter**} & **Value** \\ \hline Compressive strength, parallel to the grain \(f_{\text{c,0}}\) [MPa] & 58.5 \\ Compressive strength perpendicular to the grain \(f_{\text{c,90,alge}}\) [MPa] & 9.5 \\ Bending strength (in edgewise condition) \(f_{\text{m,0,alge}}\) [MPa] & 65 \\ Shear strength parallel to the grain in edgewise condition \(f_{\text{c,0,alge}}\) [MPa] & 4.6 \\ Shear strength parallel to the grain in flatwise condition \(f_{\text{c,0,flat}}\) [MPa] & 2.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical properties of laminated veneer lumber [16; 17].