Determination of Total Base Shear and Bending Moment Power Spectra for an Offshore Structure at Sea
Authors: Kaplan Paul , Jiang Chen-Wen , Dello Stritto Frank J. 
Published: October 2008

Abstract
An analytical approach via frequency domain techniques is applied to determine the power spectra of total base shear and bending moment acting on an offshore structure. The particular structure considered was the Ocean Test Structure (OTS) located in the Gulf of Mexico. Measurements of these power spectra for a number of different wave records were established by analysis of the measured force data in the OTS project. The present paper provides a theoretical analysis applied to this data in order to determine the power spectra from first principles based upon knowledge of the geometry of the structure and the power spectrum of the incident wave system.
The basic force model used is the Morison equation representation applied to a structure made of a number of vertical legs, horizontal bracing elements, and inclined members. The methods and approximations used in the analysis are described, with the final results compared with the measured spectra. Good agreement between theory and experiment is exhibited. There by providing a useful tool for applications involving studies of fatigue other dynamic response aspects of offshore platforms.

Introduction
Among the various forces acting on an offshore structure, which should be properly predicted for design use, are the total base shear and the bending moment. In the present study, an analytical approach via frequency domain techniques is applied to determine the power spectra of total base shear and bending moment acting on an offshore structure. The particular structure considered is the Ocean Test Structure (OTS) which was located in the Gulf of Mexico and used for an extensive series of tests and analyses by a consortium of organizations engaged in off- shore engineering. Computer analysis of measured test data in order to obtain the various spectra and related quantities for the structure was carried out by Richman and Bendat [1]. The results giving these spectra are available on a magnetic tape associated with that study.
There has not been any theoretical analysis which was directly applied to the measured OTS data in order to determine these power spectra, based upon knowledge of the geometry of the structure and the power spectrum of the incident wave system. Directional wave analysis procedures were utilized by Borgman and Yfantis [2] in the analysis of force relationships, where the procedure used in that analysis increased the effective vertical leg volume to account for all of the other structural members. The effects of phase due to different spatial locations and orientations of such members cannot be accurately represented by such a projected area approximation.
In establishing the analysis of the power spectra for the total shear and bending moment on the structure, the basic local force model used is the Morrison equation representation. The method of statistical linearization is applied to the quadratic form of the drag force term in order to allow ease of analysis using such a model. The mean square were velocities are assumed to be independent of the orientation of the member and equal to the horizontal mean square velocity.