Stochastic Model of the Still Water Bending Moment of Oil Tankers

In this paper a predictive model is adopted for quantifying the stochastic variability of the global static bending load acting on a tanker ship in sagging. The purpose of the investigation is to provide quantitative information on the uncertainties affecting the prediction of still water load effect to be possibly utilised in a reliability evaluation of the hull girder strength. The various sources of variability in bending loads are reviewed, then the attention is focussed on the influence of the uncertainties affecting the cargo weight distribution on board. Loading modes corresponding to uniform filling levels are analysed in particular, based on the note that such conditions are both the most frequent and those inducing the highest sagging moments. The loading process is simulated by a stochastic variation of the filling levels in the various tanks around the nominal values. The characteristics of the probability distributions for filling levels are derived from a specific analysis carried out on the detailed reports of two sister ships, compiled at the end of the loading process. These data reflect also geometrical and operational constraints of the specific ships. The fluctuation of filling levels represents a disturbance in input to the loading process that is partially controlled by means of a feed-back based on trim checks. The corresponding variations in the still water bending moment (SWBM) are identified, with retro-actions triggered by different levels of deviation from the predicted trim conditions. The advantages of the predictive procedure are seen in a direct modelling of physical quantities subjected to uncertainties and of the control process put in place by the crew, allowing a better understanding of the reasons for the variability of the bending loads. Further, the model allows to focus on a specific loading condition that can be adopted as reference situation for the structural checks. The results in terms of mean values and coefficients of variation are compared with those provided by other procedures proposed in literature and considerations are made on a possible improvement in the stochastic model of SWBM in reliability evaluations.