A Deterministic Fatigue Analysis for Offshore Platforms
Authors: Maddox N.R. 
Published: December 2007

As platforms are placed in deeper water, their natural periods will increase, making them more susceptible to dynamic response and fatigue. An algorithm is developed for addressing these problems, using a multidegree-of-freedom, lumped-mass mathematical model to represent the structure and finite-length synthetic-wave profiles to represent sea states comprising the environment.

Introduction
Most offshore oil platforms are in less than 400 ft of water and are subjected only occasionally to severe storms. Deck weights have been relatively light because these platforms are close to shore and can he readily resupplied platforms are close to shore and can he readily resupplied at almost any time of the year. As a result of these circumstances, static wave force calculation procedures have been used to design platforms subjected to predicted extreme storm waves. Fatigue traditionally has not been a problem because the design storms or near-design storms problem because the design storms or near-design storms occur so infrequently that there are very few high-stress cycles. More frequent winter storms are at such a low stress level that there is very little cumulative fatigue damage.
As the offshore oil industry moves into deeper water and more hostile environments, platform design problems change. It is no longer sufficient to design for a static wave since deepwater platforms are subject to appreciable dynamic excitation by wave profiles with dominant periods of about 12 to 15 seconds. Nor is it sufficient to design only for a severe storm; material around the brace and leg joints must be analyzed for fatigue and results must be incorporated into the designs of the joints.
The fatigue model described in this paper is based on the well known Palmgren-Miner rule:
(1)
which says that the ratio of the number of cycles at a given stress level to the number of cycles to failure at that stress level, summed over the various stress levels experienced during the life of the structure, should be less than or equal to 1 to avoid rapidly propagating cracks.
The denominator of these ratios on the left-hand side of the equation is obtained from an S-N curve taken from Ref. 3. This paper concerns the numerators of the ratios, which are essentially the points of the stress-history curve for a particular location in the joint of a platform. This curve is obtained from a hindcast of the operational and severe seas at the platform location and the resulting response of the platform to such sea states. Most wave-induced dynamic-response analyses available in the literature are based on power spectral density or frequency domain techniques. These methods require that the analysis be linear or linearized; when used with a fatigue model, the methods require additional assumptions concerning the numbers and magnitudes of the stress cycles. This paper uses a time-domain approach similar to that used by Burke and Tighe. A finite-length wave profile is passed by the platform and no simplifying assumptions passed by the platform and no simplifying assumptions are necessary in determining the response or counting stress cycles.

Mathematical Model
Platforms are essentially composed of continuous Platforms are essentially composed of continuous beam-columns, each of which can vibrate lateral to its own longitudinal axis. Additional modes of vibration include over-all platform bending; these modes are the ones of interest here.
JPT
P. 901