## 4 Discussion  
As the size of a wind turbine rotor blade is increases, the SCF at the bolt threads sensitive to fatigue becomes a more important parameter for the bolted joint connection to endure the designed fatigue life and to avoid the loosening of a bolt joint connection or even consecutive blade failure. In this work, the SCFs at the bolt threads of the bolted joint connection such as bolt-insert joint and bolt-nut joint were thoroughly computed by two-dimensional and three-dimensional linear finite  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case (2D Model)** & **1a** & **1b** & **1c** & **1d** & **1e (w/cone)** & **1f (w/cone)** \\ \hline SCF & 3.94 & 3.87 & 2.32 & 2.30 & 2.30 & 2.01 \\ Norm stress (MPa) & 393 & 393 & 650 & 650 & 650 & 650 \\ Max. stress (MPa) & 1548 & 1520 & 1504 & 1495 & 1497 & 1305 \\ Reduction (\%) & 0 & 2 & 41 & 42 & 41 & 49 \\ \hline \hline \end{tabular}
\end{table}
Table 10: SCF with varying parameters (straight/shank and with/without a relief cone).  
Figure 14: 2D bolt joint models with varying parameters (straight/shank and with/without a relief cone).  
Figure 15: 3D Bolt joint models with varying parameters (straight/shank and with/without a relief cone).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case (2D Model)** & **2a** & **2b** & **2c** & **2d** & **2e (w/cone)** & **2f (w/cone)** \\ \hline SCF & 3.47 & 3.41 & 2.10 & 2.06 & 2.18 & 1.84 \\ Norm stress (MPa) & 393 & 393 & 650 & 650 & 650 & 650 \\ Max. stress (MPa) & 1365 & 1340 & 1362 & 1339 & 1416 & 1196 \\ Reduction (\%) & 0 & 2 & 40 & 41 & 37 & 47 \\ \hline \hline \end{tabular}
\end{table}
Table 11: SCF with varying parameters (straight/shank and with/without a relief cone).  
element analysis methods with contact elements in detail, and the effect of various design parameters on the SCF were investigated as well. From this work, it is shown that a round nut is better than a standard nut at reducing stress concentration factor by 18.5% on average. Two-dimensional and three-dimensional FE analysis resulted in remarkably close SCFs, from 3.04 to 2.41 and from 2.98 to 2.51, respectively, from standard nut type to round nut type. However, the different nut heights of 40 mm, 44.5 mm, and 49 mm, or different number of engaged threads of 7, 8, and 9, showed little effect on SCFs. That is, the nut height or the number of the engaged threads was not a critical parameter in reducing the SCFs. Among other design parameters, the reduced shank diameter of the neck-down bolt was a dominant player in reducing SCF by 41% irrespective of nut type. In addition to the reduced shank diameter effect, the SCF was reduced further by 13% from 2.32 to 2.01 with the application of the relief cone angle at the bolt threads. Therefore, it was recommended to use the bolted joint model consisting of a neck-down bolt (reduced shank bolt) with a relief cone and a root insert with a large shank diameter to reduce the SCF by 50%, and it is also recommended to use the round nut type for additional reduction. Besides, based on the excellent agreement between two-dimensional and three-dimensional finite element analysis results, 2D finite element analysis is preferred due to the easy FE modeling, high-quality mesh construction, and high computational efficiency. During the current work, the pretension load was only considered for the comprehensive investigation of SCF at the bolt threads. Therefore, for further reliable and fatigue-safe bolted connection at the blade root joint, multiple loading conditions and fatigue analysis methodologies need to be considered in the future.  
This work was supported by Brain Pool Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (grant number: 2019H1D3A2A02102093).  
**Acknowledgments:** I acknowledge the administrative and technical support of the Offshore Floating Wind Energy System Engineering Department of University of Ulsan.  
**Conflicts of Interest:** The author declares no conflict of interest.