## 2 Existing Procedures for Hull Girder Load Adjustment
### Vertical and Horizontal Bending Moment Adjustment Procedure  
To meet the VBM and HBM targets, we can apply opposite directional moments to both ends of the hold model. As you can see in Figure 16, the opposing moments generate bending moments only, and the shear force remains unchanged. The FE analysis results show the bending deformation and the longitudinal stress by color.  
The amount of VBM to be applied at both ends for VBM adjustment is calculated from the difference between the target value and the peak value obtained from the loads applied so far, as shown in Equations (27)-(29) presented in DNV-CG-0127 [25]. The peak VBM is calculated by adding the VBM caused by the local load and the VBM caused by the load applied during VSF adjustment.  
\[M_{v-end}=M_{v-targ}-M_{v-peak} \tag{27}\]  
\[M_{v-peak}=\left\{M_{v-FEM}(x)+M_{lineload}+M_{Y\_aft}\left(2\frac{x-x_{aft} }{x_{fore}-x_{aft}}-1\right)\right\} \tag{28}\]  
\[M_{lineload}=\left(x-x_{aft}\right)F-\sum_{i}(x-x_{i})\delta w_{i} \tag{29}\]  
where  
\(M_{v-end}=\) additional vertical bending moment to be applied to both ends of the model;  
\(M_{v-targ}=\) target hogging or sagging vertical bending moment;  
\(M_{v-peak}=\) maximum or minimum bending moment within the length of the mid-hold due to applied loads;  
\(M_{v-FEM}(x)=\) vertical bending moment at position x, due to the local loads;  
\(M_{lineload}=\) vertical bending moment at position x, due to the application of vertical line loads at the frame according to method 2 for vertical shear force adjustment.  
The process of adjusting the local VBM to the target VBM after adjusting the VSF is shown in Figure 17. The red colour of the local VBM is shifted to cyan colour by the additional moments \(M_{lineload}\), \(M_{Y\_aft}\), and \(M_{Y\_fwd}\) applied when adjusting the VSF. Notice that the value of the VSF being adjusted is small, so it has a minimal effect on the local VBM. We can then apply \(M_{v-end}\) to move the cyan colour to the adjusted VBM of the magenta colour to match the target VBM.  
Figure 16: Opposite directional moment effect under simply supported boundary condition.  
The amount of HBM to be applied at both ends for HBM adjustment is calculated from the difference between the target value and the peak value obtained from the load applied so far, as shown in Equation (30) presented in DNV-CG-0127 [25]. The peak HBM is calculated from the HBM caused by the local load.  
\[M_{h-end}=M_{h-targ}-M_{h-peak} \tag{30}\]  
where  
\(M_{h-end}\) = additional horizontal bending moment to be applied to both ends of the model;  
\(M_{h-targ}\) = target horizontal bending moment;  
\(M_{h-peak}\) = maximum or minimum bending moment within the length of the mid-hold due to the local loads.  
The process of matching the local HBM to the target HBM is shown in Figure 18. Since there is no HSF adjustment process, there is no need to consider the effect of HSF, and the difference between the local HBM's peak and the target HBM's value, \(M_{h-end}\), is applied. It can be seen that the local HBM of red colour shifts to the HBM of magenta colour and becomes consistent with the target value.