Design Force Envelopes for Compliant Towers
Authors: Chen C.Y. , Suhendra R. 
Published: October 2008

ABSTRACT
This paper discusses an approach for constructing design force envelopes for compliant towers. The approach is based on expected extreme story forces derived from a Weibull distribution fitted to the time-history peak story forces obtained from random seas. A compliant tower for 2040 foot water depth was used to represent the model for this investigation. The expected extreme story forces envelopes were compared with those obtained from the envelopes of snapshots at maximum applied loads and dynamic responses due to waves with large wave height. The comparison results indicate that the story forces envelopes do not necessarily occur at the times of maximum dynamic base shear and dynamic overturning moment. Furthermore, the maximum dynamic responses from one particular extreme wave record do not guarantee that the maxima have been captured.

INTRODUCTION
The compliant tower concept has been shown to be one of the alternative structural configurations suitable for deeper water prospects. Its feasibility and cost benefits were addressed by Maus et al (Ref I) and Willet al (Ref2). While compliant towers have been under development for many years, most publications on this subject emphasized discussions of global responses (e.g. Steele et al, ReO, and Morrison et al, Ref 4) and very few on constructing sufficient and reliable design load cases for code check purposes.
In the conventional fixed jacket designs, a snapshot at the time of maximum dynamic base shear (which generally coincides with the tinkle of maximum dynamic overturning moment, jacket bending moment, and deck displacement) is commonly used as the design load case. However, for compliant towers, the time of maximum dynamic base shear does not necessarily coincide with the time of maximum dynamic over turning moment or the time of maximum design force envelopes (story shear and bendingmoment). Therefore, the conventional design procedure for fixed platforms may not be sufficient for compliant towers.
For compliant towers, one common approach (snapshot approach) to build the design force envelopes would be to use the story shears and bending moments at the times of maximum applied loads and dynamic global responses (base shear, overturning moment, deck displacement, ..., etc.) from one or several random wave records with large wave heights. However, this approach may not yield the desirable maximum design force envelopes for a given probability of accidence. The chances to overlook the extreme story shears and bending moments envelopes are even greater when only one extreme wave record is used.
To offset the above described deficiency and complement the snapshot approach, this paper discusses an approach to generate design force envelopes of compliant towers based on the expected extreme story forces. A Weibull distribution fitted to the time history peak story forces in random seas was used to predict the expected extreme story forces for a given probability of accidence. A 2040 ft compliant tower was adopted to illustrate this approach. The design force envelopes obtained using this approach were presented and compared with those from the snapshot approach.