# Safety Assessment for Upper Part of Floating Crane Considering Minimum Luffing Angle
## 4 Consideration and Discussion of Structure Analysis Result
### Allowable Stress Setting and Stress Assessment  
The allowable stress for members that compose the upper part of a 250 ton floating crane has been applied according to the KR rules, which is shown in the Table 10. In this table, the combined stress means the von-Mises stress. The yield stress of materials has been applied according to the standard of the Table 9.2.19 among Chapter 2 Cargo Handling Appliances in Additional Installations from the 9 th edition of the KR rules. As tensile, compressive, and bending stresses are applied simultaneously on the members in the upper structure of the crane, the allowable stress has been applied to the combined stress to evaluate the safety of the structural members.  
Figure 11: Displacement of Z-axis for boom (CLC1).  
Figure 12: Displacement of X-axis for back tower.  
From the analysis result, the stress value in the stowage condition is shown to be higher in the boom at the maximum compression of 212.9 MPa and the maximum tension of 182.0 MPa. The position was near the bottom part of the boom and the connection part of the diagonal member (Brace). It is judged that the moment has been enlarged by the effect from load through the inclination of a ship and wind load.  
For the structures of the back tower and attached support under the service condition (Max. tension 126.0 MPa, Max. compression 162.8 MPa) and the luffing condition (Max. tension 127.3 MPa, Max. compression 172.9 MPa), they have shown higher stress values. The members (Hinge hole at front bottom) that support according to the movement of the boom have shown higher stress. The result implemented by the assessment method for allowable stress has been arranged in Table 11 with the maximum values of combined stress. As all stresses have not exceeded the allowable stress, it is judged that they retain structural safety.  
ABS [29] defines an allowable stress coefficient (as safety factor of material), 0.85, by von-Mises stress using the FEM of fine mesh analysis about all loads. The computed tensile, bending, and shear stress components and, as applicable, combinations of such stresses, for primary structural members are not to exceed the allowable stress, F, as obtained from the following equation:  
\[\text{F}=F_{y}\times S_{c}. \tag{3}\]  
Here, \(F_{y}\) is the specified minimum yield point of the material, and \(S_{c}\) is the allowable stress coefficient. Allowable stresses for AH32 and AH36 of ABS are 268 and 302 MPa, respectively, and the combined stress results of the boom and the back tower satisfy the ABS allowable stress design criteria for all the load cases in Table 11.  
Meanwhile, DNVGL [30] regulates the safety factors of yielding about three load cases, respectively. For the purpose of making the nominal safety dependent upon the probability of occurrence of the loading, three general cases of loading are defined, for which the required safety factors are different:  
- Safety factor 1.5 for crane working without wind (Case I)  
- Safety factor 1.33 for crane working with wind (Case II)  
- Safety factor 1.10 for crane subjected to exceptional loadings (Case III).  
Therefore, allowable stresses (unit: MPa) of AH32 are Case I: 210, Case II: 237, Case III: 286, and AH36 has Case I: 237, Case II: 267, and Case III: 323. The combined stress results of the boom and the back tower satisfy the DNVGL allowable stress design criteria for all the load cases shown in Table 11.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Load** & \multirow{2}{*}{**Mat.**} & \multicolumn{4}{c}{**Kind of Stress**} \\ \cline{3-6}
**Condition** & & **Tension** & **Shear** & **Compression** & **Combined** \\ \hline \multirow{2}{*}{CLC 1-4} & AH32 & 242.6 & 141.8 & 211.1 & 280.4 \\ \multirow{2}{*}{CLC 7} & AH36 & 273.6 & 159.8 & 237.9 & 316.0 \\ \multirow{2}{*}{CLC 5-6} & AH32 & 274.1 & 157.5 & 239.4 & 315.0 \\ \multirow{2}{*}{CLC 5-6} & AH36 & 308.9 & 177.5 & 269.8 & 355.0 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Allowable stress for AH32 and AH36 (unit: MPa).