A probabilistic approach to assess the computational uncertainty of ultimate strength of hull girders

The simplified progressive collapse method is codified in the IACS Common Structural Rules (CSR) to calculate the ultimate strength of ship hull girders in longitudinal bending. Several benchmark studies have demonstrated the uncertainty of this method, which is primarily attributed to the variation in the load-shortening curve (LSC) of local structural components adopted by different participants. Quantifying this computational uncertainty will allow the model error factor applied for the ultimate strength of hull girder in a reliability-based ship structural design to be determined. A probabilistic approach is proposed in this paper to evaluate the prediction uncertainty of ultimate strength of the hull girder caused by the critical characteristics within the LSCs. The probability distributions of critical load-shortening characteristics of stiffened panels are developed based on a dataset generated by empirical formulae and the nonlinear finite element method. An adaptable LSC formulation, with the ability to cater for specific response features of local components, is utilised in conjunction with the Monte-Carlo simulation procedure and the simplified progressive collapse method to calculate the ultimate strength of a hull girder at each sampling. The proposed method is applied to four merchant ships and four naval vessels. The computational uncertainties of the ultimate strength of the case study vessels are discussed in association with their mean values and standard deviations. The study shows that the ultimate strength of ship hull girders is subjected to different uncertainties in sagging and hogging. Whist the strength of merchant ships are primarily governed by the ultimate compressive strength of critical stiffened panels, the strength of naval vessels are also sensitive to the post-collapse response of critical members.