A statistical estimate of the extreme wave force per unit length acting on a section of a fixed cylindrical pile in a random sea-state is derived. The random motion of the sea is described by a spectrum of wave heights in conjunction with linear wave theory. The wave force is assumed to depend linearly on the water particle acceleration and non-linearly on the water velocity according to the Morison formula. The interaction of the velocity and acceleration contributions and the contribution of a small steady current are accounted for by an asymptotic approximation valid for large forces. The expected rate of occurrences of extremes based on a simple peak definition agrees satisfactorily with a more elaborate result based on a true maximum definition. The formulas derived here provide a basis for a design-force procedure which could provide an improvement over the design-wave procedure commonly used for the analysis of offshore structures.

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