## 3 FE Analysis
### Material Properties  
The top, bottom, and web plates in the TG200 decks are composed of several layers of matrix and angled fibers, and the amount of angled fibers critically determines the orthotropic material properties of these plates. The weight of angled fibers per unit area for the top plate in the prototype and modified-type TG200 are shown in Table 7. The modified type has more fibers in the longitudinal direction and chopped strand mat (CSM) material but significantly less fibers in other directions. For the prototype, coupon tests to determine \(E_{x}\), \(E_{y}\), \(G_{xy}\) and \(v_{xy}\) were performed [1,3], and the measured values are shown in Table 8. Coupon tests for the modified type were not performed. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Descriptions**} & \multicolumn{3}{c}{**Fiber Weight with Angle per Unit Area (g/m\({}^{2}\))**} & \multicolumn{1}{c}{**Total Fiber**} \\ \cline{2-7}  & 0° (L) & 45° & 90° & \(-\)45° & **CSM** & **Weight (g/m\({}^{2}\))** \\ \hline Prototype & 1500 + Rov. * & 1560 & 7775 & 1560 & 900 & 13,295 \\ \hline Modified & 2550 + Rov. * & 891 & 4722 & 891 & 1800 & 10,929 \\ \hline \hline \end{tabular}  
* The weight of glass fiber roving is ignored.  
\end{table} 
Table 7: Weight of angled fibers per unit area in the TG200 top plate. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Description (\({}^{\text{\tiny{(1)}}}\))**} & \multicolumn{3}{c}{**Top Plate**} & \multicolumn{2}{c}{**Bottom Plate**} & \multicolumn{2}{c}{**Web**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Tested Value**} & \multicolumn{2}{c}{**Assumed Value**} & \multicolumn{1}{c}{**Tested Value**} & \multicolumn{1}{c}{**Assumed Value**} & \multicolumn{1}{c}{**Tested Value**} & \multicolumn{1}{c}{**Assumed Value**} \\ \hline Elastic modulus & \(E_{x}\) (\({}^{\text{\tiny{(2)}}}\)) & 16.8 & 11.2 & 20.8 & 13.9 & 18.6 & 12.4 \\ (GPa) & \(E_{y}\) (\({}^{\text{\tiny{(3)}}}\)) & 19.8 & 13.2 & 14.3 & 9.5 & 15.3 & 10.2 \\  & \(E_{z}\) (\({}^{\text{\tiny{(3)}}}\)) & 4.1 & 4.1 & 4.1 & 4.1 & 4.1 & 4.1 \\ \hline Shear modulus & \(G_{xy}\) (\({}^{\text{\tiny{(1)}}}\)) & 5.8 & 3.9 & 4.7 & 3.1 & 4.6 & 3.1 \\ (GPa) & \(G_{xz}\) (\({}^{\text{\tiny{(1)}}}\)) & 3.6 & 2.9 & 4.1 & 3.3 & 3.8 & 3.1 \\  & \(G_{yz}\) (\({}^{\text{\tiny{(5)}}}\)) & 4.0 & 3.2 & 3.3 & 2.6 & 3.4 & 2.7 \\ \hline Poisson’s ratio & \(v_{xy}\) (\({}^{\text{\tiny{(2)}}}\)) & 0.182 & 0.182 & 0.182 & 0.182 & 0.174 & 0.174 \\  & \(v_{yx}\) (\({}^{\text{\tiny{(4)}}}\)) & 0.215 & 0.215 & 0.153 & 0.125 & 0.210 & 0.144 \\ Poisson’s ratio & \(v_{xx}\) (\({}^{\text{\tiny{(4)}}}\)) & 0.303 & 0.300 & 0.304 & 0.298 & 0.304 & 0.299 \\  & \(v_{xx}\) (\({}^{\text{\tiny{(4)}}}\)) & 0.074 & 0.110 & 0.060 & 0.088 & 0.067 & 0.099 \\  & \(v_{yz}\) (\({}^{\text{\tiny{(4)}}}\)) & 0.304 & 0.299 & 0.303 & 0.299 & 0.302 & 0.301 \\  & \(v_{xy}\) (\({}^{\text{\tiny{(4)}}}\)) & 0.063 & 0.093 & 0.087 & 0.129 & 0.081 & 0.121 \\ \hline \hline \end{tabular}  
* Notes: \({}^{\text{\tiny{(1)}}}\)\(x\), \(y\), and \(z\) represent the longitudinal, transverse, and through-thickness directions \(w.r.t\) and the pultrusion direction, respectively. \({}^{\text{\tiny{(2)}}}\) Test values for TG200 [1,3]. \({}^{\text{\tiny{(3)}}}\) Test values for Duraspan deck [19]. \({}^{\text{\tiny{(4)}}}\) Estimate values using \(\frac{v_{yz}}{k_{z}}=\frac{v_{yz}}{k_{z}}\)[20]. \({}^{\text{\tiny{(5)}}}\) Approximate values using \(G_{ij}=\frac{\sqrt{k_{z}k_{z}}}{2\left(1+\sqrt{k_{z}^{\text{\tiny{(5)}}}+v_{yz}^ {\text{\tiny{(5)}}}}\right)}\)[21].  
\end{table} 
Table 8: Material properties of TG200 deck substrate. Figure 7: Partial section view of the discretized FE model.