## 2 Finite Element Model to Determine SCF
### Hot-Spot Stress  
The SCF is calculated as the ratio between the hot-spot stress at the weld toe and the nominal brace stress. The surface stress extrapolation method is used to determine hot-spot stress. However, for the grooving corrosion, the surface stress of the chord near  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Range** \\ \hline End preparation angle, \(\omega\) & From \(10^{\circ}\) (or \(45^{\circ}\) for \(\psi>105^{\circ}\)) to \(90^{\circ}\) \\ Root opening, R & From 2 mm to 6 mm \\ Root face, c & From 0 to 2 mm \\ Joint included angle, \(\varphi\) & From \(37.5^{\circ}\) to \(60^{\circ}\) for \(\psi\leq 105^{\circ}\) \\ \
\begin{tabular}{c} Weld leg size, F \\ Weld thickness, t\({}_{\mathrm{w}}\) \\ \end{tabular} & From 0 to t/2 as \(\psi\) varies from \(135^{\circ}\) to \(90^{\circ}\) \\
\begin{tabular}{c} Weld thickness, t\({}_{\mathrm{w}}\) \\ \end{tabular} & Not less than t \\ \hline \hline \end{tabular}
\end{table}
Table 1: Prequalified joint dimensions and groove angle for the T-shaped tubular joint with \(90^{\circ}\leq\psi\leq 143^{\circ}\).  
Figure 3: Mesh distribution of the tubular joint: (**a**) global view; (**b**) around the intersection; (**c**) around the weld toe.  
the weld toe is not monotonic when approaching the weld toe. There is a decrease and subsequent increase in the stress component perpendicular to the weld toe, so the use of the surface extrapolation method may be questionable [25]. Additionally, for the non-uniform corrosion degradation condition, because the stress concentration is more localized, the stress at the reference points of the surface stress extrapolation method cannot reflect the stress at the weld toe. Therefore, in the present study, the through-thickness linearization method is used to determine the hot-spot stress.  
The stress distribution along the weld toe section can be separated into three components, namely the membrane stress, bending stress and nonlinear stress [26]. The peak stress \(\sigma_{peak}\) at the weld toe is the summation of the three components. The hot-spot stress is the summation of the membrane stress \(\sigma_{ls}^{m}\) and the bending stress \(\sigma_{ls}^{b}\), as shown in Figure 4.  
The stress linearization at the weld toe section can be carried out by ANSYS. The path along the thickness direction is defined in the section. By defining the local coordinate system, the stress component perpendicular to the weld toe section is obtained for all the nodes on the path. The membrane stress and bending stress are calculated automatically.  
To validate the FE analysis method, the obtained SCF results are compared with the experimental results provided by [PERSON] et al. [27] and [PERSON] [28] and the results of Efthymiou equations [8], as shown in Figure 5. Although the experimental method is based on the surface stress extrapolation method, the results obtained by FE analyses using the through-thickness linearization method are consistent with the experimental results. The shape of the SCF distribution from the experimental measurement is well captured. In the case of axial loading and IPB, there are some differences at the crown, which is reasonable, because the strain gauge failed to provide accurate information about the position of the weld toe and weld geometry in the experiment, and some measurement inaccuracies have been reported [27]. Compared with Efthymiou equations, the SCF calculated by the FE method at the saddle is underestimated under axial loading and IPB, while the SCF of the crown is slightly overestimated. This error may be due to the modelling of the weld geometry in the FE method, which is not considered in the development of the Efthymiou equations.  
Figure 4: The stress field in the critical section of the welded toe.