Simplified analysis of force-deflection characteristics of tangent and uplift catenary moorings

This paper describes a new method and a set of equations for calculating the force-deflection characteristics of the catenary anchor leg. The traditional catenary equations reference horizontal deflection of the catenary top to the catenary generation point which is used to mathematically ?generate” the catenary curve shape. The catenary generation point is not stationary; its horizontal and vertical positions change as the catenary deflects. Thus several cumbersome calculations are required to relate deflection to its original position in the no-load case. The simplified catenary equations, discussed in this paper, directly reference the horizontal catenary top deflection to a stationary point corresponding to the no-load or undeflected position of the catenary. They avoid the complexities of calculating the scope of the catenary and the position of the catenary generation point. This greatly simplifies the analysis of catenary anchor leg moorings. The simplified catenary equations are presented for two cases. In the first case, the lowest point of the catenary, called the base point, is tangent to the ground plane, so that no uplift is applied. In the second case, the catenary applies an uplift force to an anchor on the ground plane, and the base point is below the ground plane. This paper will be of interest to the designers of catenary mooring systems, suspension bridges and other catenary structures and systems.