The seaway loadings upon ships are inherently random in nature and can best be described by probabilistic methods. The primary loadings are those that cause a response of the overall hull girder and consist of vertical bending moments, lateral bending moments, and torsional moments. Since it is highly probable that these loads can be severe, it is important to predict the maximum lifetime or extreme values. Of equal concern is the cumulative effect of all of the waves upon the fatigue life of the ship. This paper presents a probabilistic method for predicting both the extreme and fatigue loadings in a unified and consistent manner.

The first part of the seaway loading is the low frequency, wave buoyancy contribution. This loading distribution is obtained by dividing the lifetime of the ship into two thousand stochastic cells defined by operability (probabilities of ship heading and speed) and sea conditions (wave height probabilities and spectral parameters). The ship response in the frequency domain (Response Amplitude Operators, RAO’s) for each operability condition is multiplied by the ocean spectrum for each wave height and spectral shape. The resulting response spectra produce the probability distributions for determining extreme and cumulative wave buoyancy loadings. This paper presents unique algorithms for the bending and torsional RAO’s based upon extensive model test and sea trial data, as well as data validating the probability distributions.

The second part of the seaway loading is the dynamic (high frequency) contribution from slam-induced whip-ping. The probability distributions for the filtered, high frequency responses were determined from model tests and sea trials. Algorithms for predicting the dynamic contributions to vertical and lateral bending are developed as functions of ship geometry, operability, and sea parameters. The whipping distributions are then combined with the wave distributions to form distributions for the total primary load for each cell. The method of combination accounts for the phasing of the slam event with the wave buoyancy cycle and includes algorithms for the hydrodynamic damping. A cumulative lifetime load distribution is then formed from the summation of all of the wave events in all of the cells. The cumulative exceedance load distribution is used for predicting both extreme events and fatigue lives.

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