# Influence of Linear Springing on the Fatigue Damage of Ultra Large Ore Carriers
## 6 Conclusions  
This paper presents the hull structure fatigue damage calculation of the springing response of ultra large ore carriers. A three-dimensional linear frequency domain hydroelasticity analysis method is applied to calculate the load response of the hull girder, and a spectral analysis method is adopted to calculate the fatigue damage to the deck and bottom longitudinals. The rain flow correction and narrow band approximation are used to account for the effect of springing response on structural fatigue damage. Analyses have been conducted for the influence of a wide variety of parameters on the fatigue damage of the vessels, including hull length, sea state, vessel speed, heading angle, and also the loading condition. The following conclusions are drawn:  
Figure 14: Fatigue damages at different headings.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **250,000 DWT OC** & **300,000 DWT OC** & **388,000 DWT OC** & **400,000 DWT OC** \\ \hline Full loading condition & 1.192 & 1.143 & 1.153 & 1.159 \\ Ballast condition & 1.196 & 1.161 & 1.157 & 1.167 \\ Combined loading condition & 1.193 & 1.150 & 1.155 & 1.163 \\ \hline \end{tabular}
\end{table}
Table 5: The damage ratio of deck longitudinally at midship of the OCs under different loading conditions.  
1. Based on a 3D linear frequency domain hydroelasticity analysis method, and when combined with a spectral analysis method for strength assessment of ship hull structure, a method is established for evaluating the structure fatigue damage of ultra large ore carriers.
2. The springing response may make significant contribution to the structure fatigue damage of ultra large ore carrier. Vessels of a larger length usually have larger fatigue damage ratio. In particular, the damage ratio is 1.184 for the smallest ship investigated, while 1.784 for the largest.
3. The structural damping has a large influence on the peak value of the springing response, and thus significantly affects the fatigue damage of ultra large ore carriers. For the 400,000 DWT ore carrier, the peak value of the springing response decreases rapidly when the structural damping coefficient increases from 0.01 to 0.03. However, the rate of decrease slows down after the structural damping coefficient exceeds 0.05.
4. The springing effect on the structural fatigue damage is pronounced in moderate sea states. The results that were obtained for the fatigue damage of the four ultra large ore carriers show that, when the range of zero-cross period is 4.5-12.5 s and with wave height of 3.5-10.5 m, the fatigue damage due to springing significantly increases. However, the significant effect is observed in other sea states.
5. According the results, navigation at a relatively high speed in moderate mild seas results in larger fatigue damage than that at a reduced speed in high seas.
6. Another observation is that the fatigue damage is significant when the when the wave heading ranges from \(-60^{\circ}\) to \(+60^{\circ}\).
7. As for the loading condition, no distinct difference is observed in the effect of linear springing on the fatigue damage between the full loading and the ballast condition.  
All the authors contributed equally to bringing this paper to its present form. The study design was done by the first author, [PERSON], who also made significant contribution to the data analysis and data interpretation. The second author, [PERSON], performed a major part of the data analysis, and part of the writing. The third author, [PERSON], made an important contribution with data collection and data analysis. The forth and the fifth authors, [PERSON]-Q.Z. & [PERSON], made important contributions to the study design, composition, and revision.  
The project was supported by the National Natural Science Foundation of China (51679049, 51761135013).  
The authors declare no conflict of interest.