We present a method for the estimation of the distribution of the quasi-static hogging-bending moment for a floating body. Starting points of this study are temporal characteristics of the sea state. The approximation is deduced from the estimation of the joint distribution of crest amplitude and crest length. The quality of the model is investigated by comparing computed distributions with empirical ones, originating from real measurements on which a Fourier snapshot-method has been applied. The question on how precise the representation of the sea state (the entire wave spectrum or only reduced parameters) needs to be in order to obtain proper densities for crest amplitude and crest length is also addressed.
Irregular waves are commonly defined from spectra or time histories at a single location. Nevertheless, estimation of the actual wavelength is required in a number of engineering applications. For example, when a ship or a FPSO experiences high waves at sea, the maximum quasi-static hogging bending-moment in the wave is determined by the spatial shape of the water surface at the instant of the crest near the mid-point of the floating body. The model for the joint distribution of crest amplitude and crest length in this paper is derived as a so-called exact distribution. For a proper calculation of these integrals, algorithms have been developed which need the covariance structure of the problem as input (Rychlik 1992). Spectral densities, frequently used in engineering applications, are easily transformed to covariances by the FFT algorithm. This joint distribution is used to find an approximation of the distribution of the quasi-static hogging bending-moment of a floating body. The quality of the model is assessed by comparing the computed intensity distribution with an empirical distribution, originating from real measurements on which the Fourier snapshotmethod has been applied.