The Effect of Dynamic Rebound on the Design of Fixed Offshore Structures Using Directional Wave Criteria
Authors: Bangs A.S. , Morrison D.G. , Dorgant P.L. 
Published: October 2008

Abstract
The API RP 2A 20ttt Edition allows for directionally in wave loading, with the wave height in the minimum direction as low as 70% of the wave height in the maximum direction. The resulting statically applied loads may differ by as much as 50% from the maximum to the minimum wave directions. This paper describes the finding that dynamic directional wave loading design according to API IV 2A can result in much larger than expected loads along the "reverse" direction to thatof the major wave heading, Rigorous random wave analyses on jackets in 600 to 900 ft water depths using RP 2A and accounting for dynamic structural behavior, revealed significant "rebound" (opposite to major wave heading) inertial Loading. These rebound loads were target than the applied loads from the minimum wave specified by RP 2A directional criteria. Results quantify and explain the components of the rebound load. This paper develops a practical recipe, using RP 2A, that accounts for dynamic structural response. The design procedure is verified with rigorous random wave analysis results

Introduction
Prior to 1994, most fixed offshore structures designed for installation in the Gulf of Mexico were analyzed using wave loads based on a single, unidirectional wave height. In other words, the maximum wave (typically close to 72 ft in height in deep water) was assumed to approach the structure from all directions. The same assumption was made for the current profile. Depending on the geometry of the structure, this generally resulted in static base shears and overturning moments of similar magnitudes in all directions.
For the design of dynamically active (high natural period) structures, the static wave and current loads are typically combined with inertia loads to account for dynamic loading. A common design approach is to calculate a Dynamic Amplification Factor (DAF), based on the ratio of dynamic load to static bad, determined from a random wave dynamic analysis. (As with static wave and current loading, random wave dynamic analyses have typically used an unidirectional procedure, in which the maximum sea state is assumed to approach the platform from all directions). The static wave and current load. multiplied by (DAF-1.0) gives the required magnitude of the inertial loading. Using DAFs calculated for base shear and overturning moments, an inertia load set may be calculated from the combination of two modes (Kint and Morrison, 1990).
With the adoption of API Recommended Practice 2A, 20th Edition. the wave load criteria for the Gulf of Mexico was changed to a multi-directional formulation. The multi-directorial criteria, judged by the API Task Group on Wave Force Commentary to be a more accurate representation of reality, allows the use of reduced wave heights in several directions. The direction wave heights for a structure in 900 ft water depth (WD), based on RP 2A 20th Ed., are illustrated in Figure 1. In this case, the maximum wave height is 70.3 ft. for a wave traveling in the 290° compass direction.