## 2 Limit State Design for a Pultruded GFRP Bridge Deck
### Partial Safety Factors  
A partial safety factor for the design strengths of material should be applied in the design of a pultruded GFRP bridge deck. As given by Equation (2), the partial safety factor (\(\gamma_{ms}\)) for the deck substrate is obtained by multiplying three partial safety coefficients (\(\gamma_{ms,i}\)). These consider the effect of deviations from the tested values (\(\gamma_{ms,1}\)), the material and production processes (\(\gamma_{ms,2}\)), and the environment and loading duration (\(\gamma_{ms,3}\)), with respect to the material properties [17]. \[\gamma_{ms}=\gamma_{ms,1}\times\gamma_{ms,2}\times\gamma_{ms,3} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Description** & **Load Type** & **Force Effect** & **Load Modifier** & **Load Factor** & **Factored Load** \\  & **(Q\({}_{i}\))** & **(\(\gamma_{i}\))** & **(\(\gamma_{i}\))** & **(Q)** \\ \hline Dead load & Uniformly distributed load & 2.685 kN/m\({}^{2}\) & 1.0 & 1.25 & 3.356 kN/m\({}^{2}\) \\ \hline \multirow{3}{*}{Live load} & LC1 & \multirow{2}{*}{120.0 kN/wheel} & \multirow{2}{*}{1.0} & \multirow{2}{*}{1.80} & \multirow{2}{*}{216.0 kN/wheel} \\  & (rear wheel load) & & & & \\ \cline{1-1} \cline{3-5}  & LC2 & \multirow{2}{*}{84.4 kN/wheel} & \multirow{2}{*}{1.0} & \multirow{2}{*}{152.0 kN/wheel} \\  & (mid. wheel load) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Factored dead and live loads in ULS. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Design Standard** & **Deflection Limits** & **Design Load** \\ \hline \multirow{3}{*}{AASHTO LRFD [13]} & Vehicular: L/800 & \multirow{3}{*}{HS-93} \\  & Vehicular and pedestrian: & & \\ \cline{1-1} \cline{3-5}  & & \(\mathrm{L/1000}\) & \\ \cline{1-1} \cline{3-5}  & & & \\ \cline{1-1} \cline{3-5}  & & & \\ \cline{1-1} \cline{3-5}  & & & \\ \cline{1-1} \cline{3-5}  & & & \\ \cline{1-1} \cline{3-5}  & & & \\ \cline{1-1} \cline{3-5}  & & & \\ \cline{1-1} \cline{3-5}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Deflection criteria in various design standards. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Description** & **Self-Weight** & **Remarks** \\ \hline GFRP Deck & 90 kgf/m\({}^{2}\) & - \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Asphalt pavement \\ (\(t\) = 8 cm) \\ \end{tabular} } & \multirow{2}{*}{184 kgf/m\({}^{2}\)} & \multirow{2}{*}{2300 kgf/m\({}^{3}\)\(\times\) 0.08 m} \\  & & & \\ \hline Total & 274 kgf/m\({}^{2}\) & 2.685 kN/m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Self-weight of the deck and pavement. The partial safety coefficients for the strength of the deck substrate are shown in Table 5. A partial safety factor (\(\gamma_{ms}=3.16\)), calculated from Equation (2), is multiplied by the tested strength of the deck substrate to obtain its design strength. As given by Equation (3), the partial safety factors for the adhesive in joints can be obtained by considering the adhesive properties (\(\gamma_{ma,1}\)), the method of adhesive application (\(\gamma_{ma,2}\)), the type of loading (\(\gamma_{ma,3}\)), and environmental conditions (\(\gamma_{ma,4}\)) [17]. The partial safety coefficients applied to the adhesive strengths are shown in Table 6. The partial safety factor (\(\gamma_{ma}=2.34\)), calculated using Equation (3), is multiplied with the test strength of the adhesive to obtain its design strength. The calculated design strengths of the deck substrate and adhesive are compared with the corresponding maximum stresses from the FE analysis to check the failure modes in Sections 4.3-4.6. \[\gamma_{m}=\gamma_{m,1}\times\gamma_{m,2}\times\gamma_{m,3}\times\gamma_{m,4} \tag{3}\]