Uncertainty of ship hull girder ultimate strength in global bending predicted by Smith-type collapse analysis

S Li, D K Kim, J W Ringsberg , B Liu, S D Benson

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The engineering modelling of ship hull girder strength consists of global and local levels. The Smith-type progressive collapse analysis is a typical example of this, in which the global model requires input from the local model to describe the underlying local structural behaviour, i.e., load-shortening curve (LSC). However, the modelling is prone to uncertainty due to the statistical variability of the basic variables (aleatoric uncertainty) and the inadequacy of engineering models in both global and local levels (epistemic uncertainty). The former can be well tackled by a probabilistic sampling, whereas dealing with the latter for ship hull girder strength lacks an established approach. There can be different sources of epistemic uncertainty. In the modelling of ship hull girder strength, this may be partially manifested as that caused by different choices of local engineering models for predicting the LSC. In light of this, a novel probabilistic method is applied in this research to quantify the uncertainty related to the local models, i.e., the combined computational uncertainty of ultimate compressive strength and post-collapse strength of structural elements. The adopted approach is a hybrid method incorporating the Smith-type progressive collapse method with Monte-Carlo Simulation and an adaptable LSC algorithm. Case studies are performed for the first time on four merchant ships under both uni-axial and bi-axial bending load cases. It is shown that the ultimate strength in sagging is subjected to the most significant computational uncertainty as compared with those in hogging and horizontal bending. In a bi-axial load case, the computational uncertainty estimated for vertical bending will be counteracted as the horizontal bending increases. Nevertheless, this change is not directly proportional to the bi-axial load component ratio and appreciably varies between different ship types. The insights and data provided by this study may eventually resolve the epistemic uncertainty in ship hull girder strength estimation so that improving the ultimate limit state-based reliability analysis.
Original languageEnglish
Pages (from-to)A185-A206
Number of pages22
JournalTransactions of the Royal Institution of Naval Architects Part A: International Journal of Maritime Engineering
Issue numberA2
Publication statusPublished - 30 Nov 2022


  • girder strength
  • ship hull bending
  • structural behaviour


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