PSI - Issue 48

Nemanja Ilić et al. / Procedia Structural Integrity 48 (2023) 318 – 325 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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curvature of the hull for both conditions: sagging and hogging. In sagging, the deck segments start to collapse due to buckling at 0.3 1/km curvature. Then, the collapse is transferred to other vertical segments below the deck zone until the bending moment gets the tipping point, which is 242.2 MNm. After that, the structure is assumed to be collapsed and unable to carry loads. During the collapse of the upper segments, as they are no longer participating in cross section moment of inertia and the position of the neutral axis is lowering towards the bottom zone. In hogging condition, the sequences are similar, but vice versa. The collapse of the segments (bottom) begins a bit later - at around 0.4 1/km curvature of the hull. Consequently, the neutral axis rises as the collapse is transferred to the vertical segments above the bottom. Finally, the ultimate bending moment of 265.2 MNm is reached. This bending moment – curvature dependency is typical for hull sections. On the other hand, a more simplified, Paik – Mansour method gives lower ultimate bending moments than PCA: 3% for sagging and 20% for hogging. Paik – Mansour method is sensitive to segment division and position of the neutral axis so the results can vary. Nevertheless, for the quick estimation of ultimate bending moment, this method appears to be sufficient. The traditional and elastic-based methods showed different ultimate bending moments. The first-collapse method, as expected, gave the ultimate bending moment significantly smaller (more than two times in both sagging and hogging) than one obtained from methods that include buckling of the cross-section segments along the vertical axis. This means that, the hull will firstly experience the bottom or deck segment buckling than the overall collapse, which is expected. However, when it comes to other one, the first- yield method, ultimate bending moment is far larger, even exceeding the PCA and Paik – Mansour value in case of hogging. This is unexpected since in case of most sea-going ships, as the maximum first-yield bending moment is generally larger than maximum first-collapse bending moment, but lesser than ultimate bending moment calculated according to PCA and Paik – Mansour methods. However, the IWV hull considered here has transverse framing of the side structure, which is not the case for sea-going large ships. Therefore, IWV has more segments exhibiting lower buckling stresses that collapses earlier than it would be the case in longitudinally framed side structure. The vessel ultimate capacity is overwhelmingly governed by buckling rather than yielding. 5. Conclusions The paper shows the results of the progressive collapse analysis (PCA) performed on a typical inland waterway tanker that operates on the Danube and the Rhine. Results displayed a collapse sequence illustrated through the dependency between the vertical bending moment and imposed curvature of the hull. PCA allows identification of the collapse start and moreover, the determination of the ultimate bending moment or hull capacity. This is important since the ultimate bending moment shows the capacity of the hull to resist the extreme events such as excessive and unpredicted loadings (grounding, overloading, etc.). The paper goal was to provide a benchmark calculation for inland tankers. This is not the case for sea-going ships, where even the corresponding regulations are developed. Nonetheless, the calculation procedures used here are transferred from the rules of the classification societies for sea-going ships to one inland cargo vessel. Most dominant phenomenon governing the ultimate strength of the IWV hull is buckling. In case of sagging and hogging scenarios, the PCA obtained ultimate bending moments showed similar results to ones derived from Paik – Mansour method. The difference was 3% for sagging and 20% for hogging. Moreover, the first-collapse bending moment, based on the collapse of just bottom and deck segment, showed more than two times lower values of ultimate hull capacity. This is expected and consistent to the results often seen for sea-going ship. However, the first-yielding moments are relatively large, suggesting that overall collapse (PCA and Paik – Mansour) is dominantly governed by the buckling of segments, not yielding, especially considering transverse framed side structure. The analysis here shows that the progressive collapse analysis can be employed in strength assessment practice for IWV. This is important in order to establish the structure’s limit , understand and predict the structural behavior in case of extreme loadings. Consequently, an incorporation within the technical standards should follow. Acknowledgements This work was supported by Ministry of Education, Science and Technological Development of Serbia (Project no. 451-03-47/2023-01/ 200105 from 3 February 2023).