# Safety Assessment for Upper Part of Floating Crane Considering Minimum Luffing Angle
## 4 Consideration and Discussion of Structure Analysis Result
### Assessment Result of Buckling Stress  
Relatively, buckling is a kind of unstable elastic phenomenon that occurs easily at a relatively long structure to the cross-section such as the boom. The damage on the structure by buckling is important to the safety assessment of the crane. In the present study, the luffing angle has been minimized to conduct the buckling assessment on the part that receives the compression. The calculation equation of KR has been used to implement the assessment. The structures of boom and back tower have been designed for a panel. Using the composition information of the panel, the stress of each direction, which occurs in three different positions, has been calculated to obtain the buckling coefficient for the panel element. The following Equation (4) has been used for the calculation. \[\sigma_{c}=\sigma_{E}:\] (when \[\sigma_{E}\ \leq 0.5\sigma_{y}\] ) \[\sigma_{c}=\sigma_{y}\Big{(}1-\frac{\sigma_{y}}{\sigma_{E}}\Big{)} \ : \tag{4}\] \[\lambda=\sigma_{c}/\sigma_{act}\]  
Here, \(\sigma_{c}\) is the critical buckling stress and \(\sigma_{E}\) is the elastic critical buckling stress. \(\sigma_{y}\) is the yield stress of material on which the high tensile steel (AH32, AH36) regulated in KR has been reflected. \(\sigma_{act}\) is the calculated stress of a structure. \(\lambda\) is the buckling coefficient. If this coefficient is less than 1.0, it is evaluated for the occurrence of buckling. Figure 13 shows the assessment positions for the buckling stress of the boom and Figure 14 shows the assessment positions of buckling stress of the back tower. For such assessment positions of buckling stress, the assessment has been conducted mainly on the parts that receive the compression through the screening process based on the result of stress analysis. As a result, shown as the arrangement in Table 12, as the buckling coefficient of a structural member exceeds 1.0, it has been found out that the buckling did not occur. In this table, a and b mean the measurements of panel members (long width a, short width b) and t means the thickness of the panel. \(f_{mat}\) means the material constant defined in the KR rules, while 0.72 and 0.78 are the constants for HT36 steel and HT32 steel, respectively. \(\sigma_{eq}\) is the component of equivalent stress that represents the von-Mises stress. Figure 13: Positions for buckling calculation of the boom. ABS specifies a buckling state limit in which members subjected to axial compression or combined loads, such as axial compression and bending moment, are to be assessed in accordance with their requirements [31]. Assessment performed in accordance with other applicable standards will be subject to special consideration. For the buckling state limit of plates subjected to in-plane and lateral pressure loads, the following strength criterion is to be satisfied:  
\[\left(\frac{\sigma_{xmax}}{\eta\sigma_{Cx}}\right)^{2}+\left(\frac{\sigma_{ ymax}}{\eta\sigma_{Cy}}\right)^{2}+\left(\frac{\tau}{\eta\tau_{C}}\right)^{2}\ \leq 1. \tag{5}\]  
Here, \(\sigma_{Cx}\) is the critical buckling stress for uniaxial compression in the longitudinal direction. \(\sigma_{Cy}\) is the critical buckling stress for uniaxial compression in the transverse direction. \(\tau_{C}\) is the critical buckling stress for edge shear. \(\eta\) is the maximum allowable strength utilization factor, as defined in Subsection 1/11 and 3/1.7 of the rule [31]. \(\sigma_{xmax}\) is the maximum compressive stress in the longitudinal direction. \(\sigma_{ymax}\) is the maximum compressive stress in the transverse direction, and \(\tau\) is the edge shear stress. The maximum allowable strength utilization factor is defined based on load conditions representing various operation modes of offshore structures. [PERSON] and [PERSON] [32] summarized the utilization factor in relation to local plate buckling as 0.6 for normal operations  
Figure 14: Positions for buckling calculation of the back tower.