PSI - Issue 48

Nikola Momčilović et al. / Procedia Structural Integrity 48 (2023) 12 – 18 N. Mom č ilovi ć et al / Structural Integrity Procedia 00 (2023) 000 – 000

13

2

1. Introduction Over the past decade, ultimate strength assessments of ships have emerged as an important tool in ship structural design process. They provide an evaluation of structural safety level with respect to hull girder collapse, as emphasized by Paik (2018) and Yao and Fujikubo (2016). Traditionally, ship structural integrity is assessed using classification societies’ prescribed rule -based procedures and additionally, direct calculations; for instance, ones from BV (2020) or LR (2020). The outcomes of these assessments are then compared to the rule-prescribed stress in order to prove the strength of the structure. Such stress, i.e., a criterion, is provided as a share of the yield stress which keeps the evaluation always within the elastic behavior of the structure. The difference between the criterion and yield stress is considered as a safety margin. Moreover, these analyses generally use service loadings, as well as scantlings obtained for a new built ship, see Motok et al. (2022). This approach can deliver a sense of safety of the structure. In contrast to the traditional approach, extreme loadings (large bow waves, overloading events, grounding, etc.) produce nonlinear effects and might lead to the collapse of the hull girder, i.e., ultimate strength, and the loss of the ship. These loadings are still not in widespread use during the design phase, although classification societies introduced the procedures for the estimation of ultimate bending moment, see IACS (2022). Coupled with ship’s ageing and corresponding degradation of structural elements (for instance, a corrosion), the ultimate strength of ship can be significantly diminished. Therefore, in addition to being designed according to their as - built scantlings (upon delivery of the ship from the shipyard), ships can be also designed considering their ultimate strength with regards to desired age (longevity) of structure, that includes reduced scantlings. Ultimate strength calculation procedures are systematically presented in ISSC (2018). Olmez and Bayraktarkatal (2016) performed a comprehensive ultimate strength analysis using incremental-iterative progressive collapse analysis (PCA). PCA and nonlinear finite element method (NLFEM) is applied Tekgoz et al. (2018) for intact and damaged container ship subjected to asymmetrical bending loadings. Corrosion wastage in ultimate strength calculations is modeled by Vu Van and Yang (2017) and Nouri and Khedmati (2020). Findings showed that corrosion has an influence on ship ultimate bending moment. Specifically, pitting effects are studied by Piscopo and Scamardella (2021). Tekgoz et al. (2020) delivered a review of ultimate strength assessments of ageing and damaged ship structures. To conclude, although literature consists of studies on ultimate strength of ships, a very small portion considers ageing effect due to corrosion. Hence, this paper delivers the ultimate strength calculation performed on a case study of a 180 m long bulk carrier using its:  as-built scantlings, Bulk carrier is selected as it represents one of the largest ship types in merchant fleet. The particulars of the most significant bulk carriers built in the past decades can be found in work done by Kalajd žić et al. (2022), while data on their ageing, by means of corrosion wastage, are published in Ivošević et al. (2021) and Ivošević et al. (2022). As -built bulk carrier, which is analyzed here, is subjected to the ultimate strength evaluations using incremental-iterative PCA method given in IACS (2022). Random pitting corrosion is analyzed taking into account pitting intensity degree (DOP) and corrosion intensity degree (DOC) of affected zones, as proposed by Piscopo and Scamardella (2021). Furthermore, ageing effects due to uniform corrosion are modeled by reducing the thicknesses of the structural elements. 2. Methodology There are several methods available for the calculation of ultimate strength of ships. Paik and Mansour (1995) and Paik et al. (2013) developed two of the presumed methods. In the first one, it is assumed that cross section experiences buckling along the height of the upper or lower part of the section (depending which one is subjected to compression) and on other side, just most distanced elements experience yielding. The other method adds the assumption that yielding has occurred also along the height of the tensioned part of the cross section. Nevertheless, the sum forces along the height of the cross section must remain zero, to achieve equilibrium for both methods included. More sophisticated procedures are NLFEM and PCA. NLFEM can be time consuming, but unlike PCA, considers the interaction between elements.  scantlings diminished by pitting corrosion,  scantlings diminished by uniform corrosion.