## 4 Design Load Analysis
### Sources of Loads
An assumption that the total force due to waves acting on a structure can be computed by the linear superimposition of the drag and inertia forces is made in [PERSON]'s equation. For [PERSON]'s equation \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Lowest astronomical tide, LAT (m) & \(-\)1.06 \\ Tidal range, \(\Delta z_{tike}\) (m) & 2.22 \\ Storm surge, \(\Delta z_{surge}\) (m) & 2.13 \\ Air gap, \(\Delta z_{air}\) (m) & 1.5 \\ Significant wave height, \(H_{s}\) (m) & 9.4 \\ Maximum 50-year wave height, \(H_{S0,max}\) (m) & 17.48 \\ Maximum wave period range, \(7_{50}\) (s) & 10.8–14 \\ Maximum wave height above still water for deck height calculation, \(\xi_{w}\) (m) & 11.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Water levels and wave data of interest for the K-13 deep-water site. Figure 2: Representation of the loads on the support structure of the offshore wind turbine (OWT) and jacket geometry embedded in layered soil. to be applied to determine the wave loads acting on the structure, the member diameter, \(D\), has to be less than one-fifth of the wavelength, \(\lambda\), i.e.,  
\[D\leq 0.2\lambda. \tag{13}\]  
For slender members such as jacket members submerged in water, both current and wave loads can be determined using Morison's equation [71]. \[F=F_{d}+F_{m}=\frac{1}{2}\rho_{w}C_{d}D|u_{x}|u_{x}+\rho_{w}C_{m}\frac{\pi D^{ 2}}{4}a_{x}, \tag{14}\]  
where the drag force is the first term while the inertia force is the second term; \(\rho_{w}\) is the density of water; \(C_{d}\) and \(C_{m}\) are the drag and inertia coefficients of the pile, respectively, and their corresponding values are 1.25 and 2.0, respectively [5]; \(D\) is the cylinder diameter; \(a_{x}\) and \(u_{x}\) are the horizontal wave-induced or current-induced acceleration and velocity of water, respectively, which were derived from the [PERSON] third-order theory. Current loads are dynamic loads which are produced by the flow of water from external sources, apart from surface waves. Current can cause drag loads on the support structure. The current velocity \(u_{c}(z)\) is described by a sub-surface current exponential profile from the mean sea level (MSL) to the seabed, \(d\). The total current velocity of a submerged, stationary, tubular member, in the absence of vortex shedding, can be calculated as follows:  
\[u_{c}(z)=u_{c,MSL}\left(\frac{d+z}{d}\right)^{1/7}, \tag{15}\]  
where \(u_{c,MSL}\) is the current velocity at MSL, and \(d\) is the depth of water from MSL to the seabed. The wave particle velocity and the current velocity are summed up in Morison's drag term in Equation (14), assuming that the wave and current are aligned. The wind loads on the tower structure are a result of the drag and a function of the average wind velocity \(\overline{V}(z)\). The wind shear is generally represented by a power law profile, defined by the following equation:  
\[\overline{V}(z)=\overline{V}_{r}\left(\frac{Z}{Z_{r}}\right)^{\alpha}, \tag{16}\]  
where \(\overline{V}_{r}\) denotes the reference wind speed at the elevation of nacelle altitude \(Z_{r}\), and \(\alpha\) is the roughness coefficient with a value of 0.115 for the offshore site [24]. Wind loads acting along the tower can be calculated as follows:  
\[F_{lower}(z)=\frac{1}{2}\rho_{a}C_{D,T}D(z)\overline{V}_{r}^{2}(z), \tag{17}\]  
where \(C_{D,T}\) is the coefficient of drag of the tower, with a typical value of 1.0 [24], and \(D(z)\) represents the external diameter of tapered tower at height \(z\). Having determined the wind loads, the moments due to the action of the wind loads can then be calculated. Hydrostatic pressure, which acts on the submerged sections of the jacket support structure, is a constant normal load and varies with the depth of water. The hydrostatic force can be expressed as  
\[F_{h}=\rho_{w}gh, \tag{18}\]  
where \(F_{h}\) is the hydrostatic force, \(g\) is the acceleration due to gravity, and \(h\) is the depth of the water.