For many years, ship structural researchers have been working towards the goal of reliability-based limit state design of ship structures. However, reliability-based design requires calculation of the ultimate limit state, not only of the hull girder, but also of all the structural panels and other members. Also, these calculations must be performed a large number of times. Therefore, it is not practical to use iterative finite element analyses for these calculations. For efficient computations, ultimate strength formulations must be developed as closedform expressions, both for structural components and for the complete hull girder.
A number of studies on the ultimate collapse strength of ships’ hulls have been undertaken theoretically, numerically and experimentally. Some of the results have been reviewed by the ISSC Technical Committee III.1 on ‘Ultimate Strength’. The ultimate strength reliability of ships’ hulls, considering existing local damage related to corrosion, fatigue and collision/grounding, has also been studied.
Previous studies on the development of a formulation for ultimate hull strength prediction may be classified into three groups. The 1st is a linear approach, where the behaviour of the hull up to failure of the compression flange is assumed to be linear elastic, i.e. ignoring buckling, and the ultimate moment capacity of the hull is basically expressed as the ultimate strength of the compression flange multiplied by the elastic section modulus, with a simple correction for buckling and yielding. The 2nd is an empirical approach, where an expression is derived on the basis of experimental or numerical data from scaled or real hull models.
The 3rd is an analytical approach, based on a presumed stress distribution over the hull section (plane sections remain plane) from which the moment of resistance of the hull is theoretically calculated, taking into account buckling in the compression flange and yielding in the tension flange.
The 1st approach is quite simple, but its accuracy is usually wanting because, after buckling of the compression flange, the behaviour of the hull is no longer linear, and the neutral axis changes position. Empirical formulations (the 2nd approach) may provide reasonable solutions for conventional hulls, but one has to be careful in using empirical formulations for new and general-type hulls, since they are usually derived on the basis of limited data, or for a particular hull form, using an empirical formulation. On the other hand, analytical formulations (the 3rd approach) can be applied to new or general hulls because they include section effects more precisely.

The ship hull ultimate strength formula is eventually expressed as a function of design parameters related to geometric and material properties including plate thickness, yield strength and Young’s modulus. When time-variant structural degradation (e.g. corrosion) is considered, the value of member thickness at any particular time is a function of such damage. In probability-based design methods, all the design parameters are treated as the random variables. The hull ultimate strength formula for hogging normally differs from that for sagging.

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