## 3 Results: Single-Lap Joint Validation by Applying FEA
### Results  
The following Figures 8-10 present the comparison of stresses obtained from 2D, 3D FEA models and the general formulas of Bigwood and Crocombe [24] presented in Appendix C. The stress curves of formulas [24] show similar behaviors to the results obtained with the numerical analysis (FEA), however, the normal stress generated by the \(T\) force (Figure 8a) is zero.  
The distribution of the maximum shear stresses of the \(T\) force, from the 3D model, at the first interface stress distribution between layers 1 and 2 of adherent 1 is presented in Figure 11.  
The distribution of normal and shear stresses on adhesive and adherent 1 interfaces resulting from the \(V\) force, 2D model, are presented in Figure 12.  
The results obtained in the adhesive at the endpoints A and B (Figure 3) with the proposed normal and shear stress formulas, and stresses calculate with FEA are presented in Tables 2 and 3 corresponding to the forces \(P\), \(V\), and \(T\). Only results are presented in points A and B because they have greater values than points C and D. These tables present the application of the failure criterion (Equation (19b)), showing that the criterion is met.  
Figure 7: (a) 3D model: fiber-reinforced plastic (FRP) panel 210 \(\times\) 600 mm, with 2\({}^{\prime\prime}\) pipe laminate, (b) 2D model: FRP Panel 210 mm by unitary width, with 2\({}^{\prime\prime}\) pipe laminate.  
Figure 11: Force T, \(x\)-direction, from the 3D model: first interface stress distribution between layers 1 and 2 of adherent 1.  
Figure 8: Force \(T,x\)-direction: stress curve, (**a**) normal, (**b**) shear.  
Figure 10: Force V, \(z\)-direction: stress curve, (**a**) normal, (**b**) shear.  
Figure 9: Force \(P,y\)-direction: stress curve, (**a**) normal, (**b**) shear.  
Figure 12: Force V, \(z\)-direction, from the 2D model: stress distribution, (**a**) normal, (**b**) shear.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Variable**} & \multirow{3}{*}{**Value**} & \multicolumn{6}{c}{**Bigwood and Crocombe Formulas**} \\ \cline{3-8}  & & \multicolumn{3}{c}{**A (0,0,0) mm**} & \multicolumn{3}{c}{**B (0,75,0) mm**} \\ \cline{3-8}  & & \(\sigma\) & \(\tau\) & \(\sigma\) & \(\tau\) & \(\tau\) \\  & & **(MPa)** & **(MPa)** & **(MPa)** & **(MPa)** & **(MPa)** \\ \cline{3-8}  & & **z** & **yz** & **xz** & **z** & **yz** & **xz** \\ \hline \(T\) (N/mm) & 4899 & 0.000 & - & 7.858 & 0.000 & - & 7.858 \\ \(V\) (N/mm) & 5127 & 2.148 & 1.031 & - & \(-\)0.652 & 3.076 & - \\ \(P\) (N/mm) & 134 & 0.509 & \(-\)0.287 & - & \(-\)0.003 & 0.016 & - \\ \hline \(\sigma_{z}\) (MPa) & 2.657 & - & - & \(-\)0.655 & - & - \\ \(\tau_{yz}\) (MPa) & - & 0.744 & - & - & 3.092 & - \\ \(\tau_{xz}\) (MPa) & - & - & 7.858 & - & - & 7.858 \\ \hline \(Z_{t}\) (MPa) & & 9.500 & & & 9.500 & \\ \(S_{t}\) (MPa) & & 17.950 & & & 17.950 & \\ \hline Interlaminar Stress & & 0.650 & & & 0.650 & \\ Fraction, \(F_{rc-i}\) & & & & & & \\ \hline Failure Criteria & & 0.500 & & & 0.510 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Failure criteria the tubular hybrid joint: Bigwood and Crocombe formulas.  
Using the formulas of the failure criterion it is possible to obtain the limit values of the safety factor \(S_{f}\) and the design pressure \(p\) that the adhesive joint can withstand. Table 4 presents the limit design pressure p, keeping constant interlaminar stress fraction at 0.650. Similarly, Table 5 presents as an alternative to the maximum safety factor \(S_{f}\) to which this FRP panel can be subjected, maintaining a constant design pressure of 5.160 kN/m\({}^{2}\). These indicated limit values of \(p\) and \(S_{f}\) application are subject to compliance of the critical layer analysis of FRP panel proposed by SSC-Lloyd's Register, [39].  
The safety factor \(S_{f}\) is defined as:  
\[S_{f}=\frac{1}{F_{rc-i}} \tag{22}\]