## 5 Results and Discussion
### Spectral Fatigue Analysis  
Spectral fatigue analysis aims to evaluate the stresses induced by repeated or cyclic loads acting on the connections of tubular elements comprising the structure. These loads arise due to gravitational and environmental forces experienced throughout the service life of the structure. The primary objective is to determine the design fatigue life of each joint and member, ensuring that it is not less than the expected service life of the structure multiplied by an appropriate safety factor. The analysis is based on [PERSON]'s fatigue damage accumulation theory, which states that fatigue damage (D) is determined by the ratio of the number of cycles n(s) at a specific stress range acting on the structure to the corresponding number of cycles to failure N(s) for the same stress range. When the cumulative damage across all stress ranges reaches or exceeds unity, fatigue failure occurs. The spectral fatigue method incorporates wave incidence probability to define stress intervals and their corresponding cycle counts affecting the welds of the tubular joints. Once the number of cycles within each stress interval is established, the resulting fatigue damage can be assessed by comparing these values with the allowable cycles defined in S-N curves (stress range vs. number of cycles). Fatigue life estimations were derived from the S-N curves specified in API RP 2A-WSD, 22 nd edition [35]. Specifically, the WJT curve was used for tubular connections fabricated from steel with a yield strength below 72 ksi (Figure 12). For welded joints, improvement factors related to fatigue performance can be achieved through several methods, including controlled burr grinding of the weld toe (WJ1), hammer peening (WJ2), or as-welded profile control to generate a smooth concave profile that transitions seamlessly into the parent metal (WJ3). Table 9 presents the improvement factors that can be applied [35]. Figure 12: API S–N curves. Note: The symbol “E” denotes scientific notation, representing multiplication by 10 raised to the indicated power. For example, 1.5E3 indicates \(1.5\times 10^{3}\). The results of the spectral fatigue analysis are illustrated in Figure 13. By utilizing the S-N curve from API (2014) [35] (see Figure 12), it is observed that node 370 exhibits a service life of 9.22 years, which is below the minimum design life of 20 years. Consequently, the following solutions are proposed: increasing the tube thickness or diameter, enhancing the yield strength, or applying a weld profile control technique, as detailed in Table 9. The application of the WJ1 technique extends the joint's life to 13.23 years; however, this remains below the required threshold. Further analysis was conducted using the weld toe burr grinding technique (WJ2), which significantly increased the service life to 27.10 years, thereby meeting the minimum requirement of 20 years. These findings demonstrate that implementing weld profile control techniques can enhance the service life of tubular joints without altering their geometric profiles (thickness or diameter). However, proper cathodic protection is necessary for the effective application of these techniques. A summary of the analyses is presented below, highlighting the differences in structural behavior under various scenarios that the platform may encounter throughout its service life, as detailed in Table 10.  
Figure 13: Summary of estimated life (in years) using API S-N curves. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Weld Improvement Technique** & \
\begin{tabular}{c} **Improvement Factors** \\ **for “S”** \\ \end{tabular} &
\begin{tabular}{c} **Improvement Factors** \\ **for “N”** \\ \end{tabular} & **Type** \\ \hline Profile (see 14.1.3.4) * & \(\tau^{-0.1\;a}\) & varies & WJ1 \\ Weld toe burr grinding & 1.25 & 2 & WJ2 \\ Hammer peening & 1.56 & 4 & WJ3 \\ \hline \hline \multicolumn{4}{c}{Chord side only} \\ \hline \hline \end{tabular}  
* Values taken from “API RP 2A WSD 22 ed” [35].  
\end{table}