In the design of a vessel’s ultimate strength the extreme hogging condition is of great concern. Due to special properties of container ship structures, such as large bow flare and overhanging stern, wave-induced slamming makes the ship responses more skewed to sagging conditions. In particular in large sea states, the ratio between maximum sagging and hogging can be quite high. Hence, the sagging condition might be very crucial with respect to a ship’s ultimate strength. In this study, the extreme response caused by hogging and sagging is derived from upcrossing spectrums of ship responses. The Weibull fitting method and Rice’s formula for the computation of the upcrossing spectrum are discussed using full-scale measurements from a container vessel on the North Atlantic trade. The extreme ship responses are therefore predicted using the long-term upcrossing spectrum. In the case where the ship response can be approximately treated as a series of stationary Gaussian processes, the corresponding upcrossings are computed by the explicit Rice’s formula. For the non-Gaussian ship response, it is shown that the 4-moment Hermite transformation is an efficient approach to compute the corresponding upcrossing spectrums. The parameters in the transformation mainly depend on the wave environments and operation profiles. The relations between these parameters and the wave environments are needed if no measurement is available. However, according to the full-scale measurements, it is not possible to find general formulas to estimate the parameters in terms of wave environments or operation profiles for the practical applications.

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