Application of Morison's Equation to Fixed Offshore Platforms
Authors: Wade B.G. , Dwyer M. 
Published: December 2007

Four methods for calculating wave forces acting on tubular members affixed offshore platforms are presented and compared under identical design conditions to demonstrate their significant differences. Many wave-crest locations and wave-approach directions are considered. Variation of base shears and overturning moments among these methods is found to exceed 21 percent. percent. Introduction
Numerous technical papers, texts, and offshore design codes have used Morison's equation to determine hydrodynamic forces on small, tubular, structural elements. The Morison equation includes terms for both drag and inertial forces. The drag term includes a drag coefficient, CD, and water-particle velocity, while the inertia term includes an inertial coefficient, C1, and water-particle acceleration. This equation applies to small objects (compared with wave length) where wave kinematics do not change appreciably over a distance equal to the width of the structural element. Morison's equation was developed to determine the hydrodynamic force on a small cylindrical body that is at right angles to the water-particle velocity and acceleration vectors. However, when a cylinder is oriented randomly with respect to the mud line, there is considerable question about the application of Morison's equation.
Borgman, Ippen, Bursnall et al., Chakrabarti et al., and Morgan et al. have shown how for a vertical cylinder Morison's equation may be applied to a cylindrical member oriented randomly with respect to the mud line. A review of the references reveals that there are many methods for calculating wave forces acting on tubular members of fixed offshore platforms. Four different methods are presented in this study, each within procedures generally used by the industry for computing procedures generally used by the industry for computing wave forces on a randomly oriented cylindrical member. Formulation of the methods considered is based on various interpretations of the application of Morison's equation. The wave-force calculation methods presented here are in the literature. This study compares these various methods with identical design conditions and demonstrates significant differences among the methods.
The wave-force equation introduced by Morison et al. is
-&gt; -&gt; -&gt; -&gt; F = 1/2 CDpdv x v x + 1/4 Clp d2 a x
-&gt; -&gt; F p = ----,...................................(1) d -&gt; -&gt; where vx and ax are the horizontal water-particle velocity and acceleration vectors, respectively, acting on a vertical cylinder of a diameter, d, in water of mass density, p. Both water-particle kinematic vectors are normal to the cylinder and, consequently, the force vector, will be acting in a direction parallel to the mud line. Wave-induced motion, however, includes both horizontal and vertical kinematic components. Furthermore, except for conductors, offshore platforms rarely have cylindrical members that are perfectly vertical. In each wave-force calculation method presented, the total water-particle velocity vector is assumed to be
-&gt; -&gt; -&gt; v = v x + v y,...........................(2)
and the total acceleration vector is
-&gt; -&gt; -&gt; a = a x + a y,...........................(3)
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