## 5 Discussion
### An Approximate Method to Estimate the Dominant Behavior during the Impact  
The effectiveness of the expanded criterion was verified for RP6, which featured large web heights. However, it is crucial to establish clear conditions for determining suitable criteria for specific prototype structures based on their dominant behaviors. A straightforward method based on elastic-plastic theory was proposed to identify the dominant behavior of a prototype under impact loading. The static concentrated force that induces the plastic hinge formation for an integrated stiffener within a stiffened plate, as shown in Figure 24, can be estimated as follows:  
\[M_{0}=\sigma_{0}S_{S}=\frac{P_{1}l_{S}}{8}\to P_{1}=\frac{8\sigma_{0}S_{S}}{l_ {S}}, \tag{25}\]  
where \(l_{S}\) is the stiffener span length, and stress \(\sigma_{0}\) is taken as the average value of the yield stress \(\sigma_{Y}\) and ultimate stress \(\sigma_{u}\). In addition, considerable research has been conducted on the buckling characteristics of web plates subjected to concentrated in-plane forces. [PERSON] [31] derived a formula for determining the critical buckling force (\(P_{cr}\)) of a rectangular plate with four simply  
Figure 23: Comparison between distorted model and reference model. (**a**) Acceleration; (**b**) displacement. Figure 24: Schematic of static concentrated force \(P_{1}\). supported edges subjected to a pair of concentrated compressive forces on opposite sides, as shown in Figure 25. The formula for a web plate during impact is expressed as follows:  
\[P_{\sigma}=\frac{4\pi D}{h_{w}}=\frac{\pi Et_{w}^{3}}{3h_{w}(1-v^{2})}, \tag{26}\]  
where \(h_{w}\) is the web girder depth and \(t_{w}\) is the web girder thickness. Given the specific boundary conditions and load case inherent in the analysis of the investigated stiffened plate, where a concentrated load was applied only from one side, it was imperative to modify the critical buckling force calculated from Equation (26). To achieve this, a coefficient derived from finite element (FE) results was introduced. By leveraging these numerical findings, a coefficient denoted as \(C=1.324\) is proposed to adaptively estimate the critical buckling force (\(P_{cr-e}\)) for the web plate in this study, as defined in Equation (27). \[P_{cr-e}=CP_{cr}=1.324P_{cr}, \tag{27}\]  
Therefore, the ratio \(P_{1}/P_{cr-e}\), where \(P_{1}\) denotes the force that causes plastic hinge formation, is calculated to determine the threshold between the static moment-dominant and web thickness-dominant intervals Table 16 lists the relevant geometric parameters and analytical results for the static concentrated force \(P_{1}\), \(P_{cr-e}\) and ratio \(P_{1}/P_{cr-e}\). Based on the results of the finite element analysis, it is evident that when the ratio \(P_{1}/P_{cr-e}\) of the reference model is less than 1.55 (\(RP\)-\(1\)-\(RP\)-5), the stiffener exhibits a more dominant behavior characterized by bending and membrane actions. In such cases, Criterion 1 was deemed more appropriate. Conversely, when the ratio \(P_{1}/P_{cr-e}\) of the reference model exceeds 3.21 (\(RP\)-6), both the reference and distorted models exhibit a heavy buckle, functioning as a web girder. In these scenarios, Criterion 2 was more suitable, as shown in Table 16.