As the offshore oil industry moves into deeper water, fixed-bottom platforms will be found to exhibit dynamic amplification of wave induced response. The resulting dynamic loads will have a significant effect on the cyclic stresses used in a fatigue analysis. State-of the- art fatigue analyses require some sort of stress-history curve, which is extracted from the dynamic response indicated by a mathematical model of a platform.
Equations of motion are expressed in matrix algebra and are formulated for' a-lumped- mass model where the masses of the legs, bracing, conductors, and affected water-are concentrated at the horizontal framing levels. Viscous damping is included and is assumed to bad linear combination of mass and stiffness matrices. The forcing function is based on the static accumulation of wave-induced force vectors at the various nodal points as described by a generalized version of Morison's equation. Water particle velocities and accelerations are calculated using a modified Airy wave theory for a multiple celerity wave profile. The mathematical model of the platform is subjected-to finite length synthetic wave profiles representing operational and severe sea states for a given location.
The response of the platform is monitored for each transient record and is linearly transformed into stress as a function of time. An algorithm for counting cycles is proposed, and a resulting stress-history curve is developed for a given location on a platform. This curve is in turn used in a fatigue analysis based on the Palmyra-Miner rule.
The response of the platform for a finite length record is also determined for a severe sea state and an extrapolation procedure is developed for acquiring platform design loads.
An example platform for 850 feet of water is analyzed.
The majority of offshore oil platforms have been placed in less than 400 feet 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 be readily are supplied 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 occur so infrequently (if ever) 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 ail-industry moves into deeper water and more hostile environments, platform design problems change and so do the resulting designs. It is no longer sufficient to design for a static wave since geed water platforms are subject to Appreciable dynamic excitation by wave profiles with dominant periods in the neighborhood of 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.