1. Fatigue of Offshore Structures: Applications and Research Issues Steve Winterstein stevewinterstein@alum.mit.edu

2. Fatigue Under Random Loads Mean Damage Rate: where S = stress range; c and m material properties Welded steels: m = 2 - 4; Composites: m = 6 - 12

3. Fatigue Under Random Loads Mean Damage Rate: where S = stress range; c and m material properties Welded steels: m = 2 - 4; Composites: m = 6 - 12

4. Fatigue Under Random Loads Mean Damage Rate: where S = stress range; c and m material properties Welded steels: m = 2 - 4; Composites: m = 6 - 12 Assumes: Stresses Gaussian, narrow-band

5. Fatigue Under Random Loads Mean Damage Rate: where S = stress range; c and m material properties Welded steels: m = 2 - 4; Composites: m = 6 - 12 Assumes: Stresses Gaussian, narrow-band Common errors: Assume Gaussian, narrow-band

6. Bandwidth & Non-Gaussian Effects Damage Rate: E[D T ] = C BW * C NG * E[D T | Rayleigh] C BW, C NG = corrections for bandwidth, non-Gaussian effects

7. Bandwidth & Non-Gaussian Effects Damage Rate: E[D T ] = C BW * C NG * E[D T | Rayleigh] C BW, C NG = corrections for bandwidth, non-Gaussian effects Bandwidth Corrections: Unimodal spectra: Wirsching (1980s) Bimodal spectra: Jiao and Moan (1990s) Arbitrary spectra: Simulation (2000s: becoming cheaper)

8. Bandwidth & Non-Gaussian Effects Damage Rate: E[D T ] = C BW * C NG * E[D T | Rayleigh] C BW, C NG = corrections for bandwidth, non-Gaussian effects Bandwidth Corrections: Unimodal spectra: Wirsching (1980s) Bimodal spectra: Jiao and Moan (1990s) Arbitrary spectra: Simulation (2000s: becoming cheaper) Typically: C BW < 1

9. Bandwidth & Non-Gaussian Effects Damage Rate: E[D T ] = C BW * C NG * E[D T | Rayleigh] C BW, C NG = corrections for bandwidth, non-Gaussian effects Bandwidth Corrections: Unimodal spectra: Wirsching (1980s) Bimodal spectra: Jiao and Moan (1990s) Arbitrary spectra: Simulation (2000s: becoming cheaper) Typically: C BW < 1 Non-Gaussian Corrections: Nonlinear transfer functions from hydrodynamics Moment-based models (Hermite) & simulation or closed-form estimates of C NG

10. Bandwidth & Non-Gaussian Effects Damage Rate: E[D T ] = C BW * C NG * E[D T | Rayleigh] C BW, C NG = corrections for bandwidth, non-Gaussian effects Bandwidth Corrections: Unimodal spectra: Wirsching (1980s) Bimodal spectra: Jiao and Moan (1990s) Arbitrary spectra: Simulation (2000s: becoming cheaper) Typically: C BW < 1 Non-Gaussian Corrections: Nonlinear transfer functions from hydrodynamics Moment-based models (Hermite) & simulation or closed-form estimates of C NG Typically: C NG > 1

11. Can We Even Predict RMS stresses? Container Ships: Yes (Without Springing)

12. Can We Even Predict RMS stresses? Container Ships: Yes (Without Springing) TLP Tendons: Yes (With Springing)

13. Can We Even Predict RMS stresses? Container Ships: Yes (Without Springing) TLP Tendons: Yes (With Springing) VIV of Risers: No

14. Can We Even Predict RMS stresses? Container Ships: Yes (Without Springing) TLP Tendons: Yes (With Springing) VIV of Risers: No FPSOs: ??

15. Ship Fatigue: Theory vs Data Observed Damage (horizontal scale): predicted from measured strains by inferring stresses, fatigue damage. Predicted Damage (vertical scale): linear model based on observed H S Ref: W. Mao et al, “The Effect of Whipping/Springing on Fatigue Damage and Extreme Response of Ship Structures,” Paper 20124, OMAE 2010, Shanghai.

16. TLP Tendon Fatigue: 1 st -order vs Combined Loads Water Depth: 300m One of earliest TLPs (installed 1992) Ref: “Volterra Models of Ocean Structures: Extremes and Fatigue Reliability,” J.Eng.Mech.,1994

17. TLP Tendon Fatigue: 1 st -order vs Combined Loads Damage contribution of various Tp Large damage at Tp = 7s due to frequency of seastates Large damage at Tp = 12s due to geometry of platform Larger non-Gauss effects if T PITCH = 3.5s (resonance when Tp = 7s) Ref: “Volterra Models of Ocean Structures: Extremes and Fatigue Reliability,” J.Eng.Mech.,1994

18. VIV: Theory (Shear7) vs Data Ref: M. Tognarelli et al, “Reliability-Based Factors of Safety for VIV Fatigue Using Field Measurements,” Paper 21001, OMAE 2010, Shanghai.

19. VIV Factor: m=3.3, s=1.4 Median:  50 =27

20. LRFD Fatigue Design

24. Finally: Combined Damage on an FPSO High-cycle (low amplitude) loads due to waves… D FAST Low-cycle (high amplitude) loads due to other source (e.g., FPSO loading/unloading) --> D SLOW How to combine D FAST and D SLOW ?

25. SRSS: Largest safe region; least conservative

26. Proposed Combination “Rules” D TOT = [ D SLOW K + D FAST K ] 1/K K = 1/m Lotsberg (2005): Effectively adds stress amplitudes K= 2/m: Random vibration approach; adds variances K = 1: “Linear” damage accumulation K = 2: SRSS applied to damage (not rms levels) Notes: Less conservative rule as K increases; m = S-N slope: Damage = c S m ; D 1/m = c’ S

27. Combined Fatigue: DNV Approach

28. Merci beaucoup! Extra background slides follow…

29. The Snorre Tension-Leg Platform Water depth: 300m One of earliest TLPs (installed 1992)

34. How important are T N =2.5s cycles? Important when T WAVE = 2.5s … but this condition has small wave heights Important when T WAVE = 5.0s … due to second-order nonlinearity (springing) Non-Gaussian effects when T WAVE = 5.0s:

35. Answer: The Fatiguing Bookkeeping Likelihood of various (Hs,Tp)

36. Answer: The Fatiguing Bookkeeping Likelihood of various (Hs,Tp) Damage contribution of various (Hs,Tp)

37. Answer: The Fatiguing Bookkeeping Likelihood of various (Hs,Tp) Damage contribution of various Tp

38. Results: Damage contribution of various Tp Large damage at Tp = 7s due to frequency of seastates Large damage at Tp = 12s due to geometry of platform Larger non-Gauss effects if T PITCH = 3.5s (resonance when Tp = 7s)