## 3 Results and Analysis
### Effect of Welding Residual Stress on Ultimate Strength  
Based on the results presented Appendix B, Figures 8a,b, 8a,b and 10a,b show the ultimate strength ratio versus the column slenderness ratio with and without accounting for the welding residual stress for the flat-bar stiffener, angle-bar stiffener and the tee-bar stiffener respectively. It can be seen that, for all the stiffened plates, the ultimate strength ratio falls into the range [0.9, 1.0] for column slenderness ratios smaller than 0.4, and as the column slenderness ratio increases, the ultimate strength ratio decreases. The trend lines are obtained by fitting the numerical results for the ultimate strength. For the three types of stiffened plates, the trend lines obtained with and without accounting for the welding residual stress are compared in Figures 8c, 9c and 10c respectively. It can be seen that, for each type of stiffened plate, the trend line obtained with accounting for the welding residual stress is the very similar to that without. However, the results obtained without accounting for the welding residual strength is in general larger than with, which indicates that welding residual stress has a negative influence on the ultimate strength. When the column slenderness ratio reaches a certain value, the difference between the two trend lines diminishes. For the flat-bar stiffened plates, the influence of the welding residual stress on the ultimate strength disappears when \(\lambda>0.8\), as shown in Figure 8c, where the two trend lines merge into one. For the angle-bar stiffened plates and the tee-bar stiffened plates, the welding residual stress does not have any differences when \(\lambda>1\). To better show the differences between the ultimate strengths of the stiffened plates made of different steels with and without accounting for the welding residual stress. The relative differences in the ultimate strength are calculated with the results obtained the welding residual stress accounted for being the reference. These relative differences are plotted in Figures 8d, 9d and 10d, respectively. It can be seen that, for large column slenderness ratios, the numerical results for the ultimate strength accounting for the welding residual stress are slightly larger (approximately 1%) than those without. This particular observation may have probably resulted from the simplified model for the welding residual stress distribution. However, under these circumstances (i.e., large slenderness ratios), linear elastic buckling is often present and the ultimate strength of the stiffened plate is small, and the influence of the welding residual stress can be neglected. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Steel Grades**} & **Yield Strength** & **Young’s Modulus** & **Poisson Ratio** & \multirow{2}{*}{**Steel Types**} \\  & & \(\sigma_{Y}\) **(Mpa)** & \(E\) **(Gpa)** & \(\mu\) & \\ \hline
1 & S235 & 235 & & & medium strength steel \\
2 & S315 & 313.6 & & high strength steel \\
3 & S355 & 355 & & high strength steel \\
4 & S390 & 390 & & high strength steel \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Employed shipbuilding steels and their basic mechanical properties. Figure 8: Ultimate strength of flat-bar stiffened plates versus column slenderness ratio. Figure 9: Ultimate strength of angle-bar stiffened plates versus column slenderness ratio. The average difference between the strength with and without accounting for the welding residual stress are calculated based on the 240 samples of each type of stiffened plates, as shown in Appendix B. For the flat-bar stiffened plates, the average difference between the strengths with and without accounting for the welding residual stress is about 2.6%, and the maximum difference is 8.9%, which is the case of F3513 built in S315. For angle-bar stiffened plates, the average difference in ultimate strength between with and without accounting for the welding residual stress is 3.5%, and the maximum difference is 8.6% (A3513 built in S390).