Report

Fatigue of Offshore Structures: Applications and Research Issues Steve Winterstein [email protected] 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 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 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 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 Bandwidth & Non-Gaussian Effects Damage Rate: E[DT] = CBW * CNG * E[DT | Rayleigh] CBW, CNG = corrections for bandwidth, non-Gaussian effects Bandwidth & Non-Gaussian Effects Damage Rate: E[DT] = CBW * CNG * E[DT | Rayleigh] CBW, CNG = corrections for bandwidth, non-Gaussian effects Bandwidth Corrections: • Unimodal spectra: Wirsching (1980s) • Bimodal spectra: Jiao and Moan (1990s) • Arbitrary spectra: Simulation (2000s: becoming cheaper) Bandwidth & Non-Gaussian Effects Damage Rate: E[DT] = CBW * CNG * E[DT | Rayleigh] CBW, CNG = 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: CBW < 1 Bandwidth & Non-Gaussian Effects Damage Rate: E[DT] = CBW * CNG * E[DT | Rayleigh] CBW, CNG = 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: CBW < 1 Non-Gaussian Corrections: • Nonlinear transfer functions from hydrodynamics • Moment-based models (Hermite) & simulation or closed-form estimates of CNG Bandwidth & Non-Gaussian Effects Damage Rate: E[DT] = CBW * CNG * E[DT | Rayleigh] CBW, CNG = 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: CBW < 1 Non-Gaussian Corrections: • Nonlinear transfer functions from hydrodynamics • Moment-based models (Hermite) & simulation or closed-form estimates of CNG • Typically: CNG > 1 Can We Even Predict RMS stresses? Container Ships: Yes (Without Springing) Can We Even Predict RMS stresses? Container Ships: Yes (Without Springing) TLP Tendons: Yes (With Springing) Can We Even Predict RMS stresses? Container Ships: Yes (Without Springing) TLP Tendons: Yes (With Springing) VIV of Risers: No Can We Even Predict RMS stresses? Container Ships: Yes (Without Springing) TLP Tendons: Yes (With Springing) VIV of Risers: No FPSOs: ?? 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 HS Ref: W. Mao et al, “The Effect of Whipping/Springing on Fatigue Damage and Extreme Response of Ship Structures,” Paper 20124, OMAE 2010, Shanghai. TLP Tendon Fatigue: 1st-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 TLP Tendon Fatigue: 1st-order vs Combined Loads 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 TPITCH = 3.5s (resonance when Tp = 7s) Damage contribution of various Tp Ref: “Volterra Models of Ocean Structures: Extremes and Fatigue Reliability,” J.Eng.Mech.,1994 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. VIV Factor: m=3.3, s=1.4 Median: a50=27 LRFD Fatigue Design LRFD Fatigue Design LRFD Fatigue Design LRFD Fatigue Design Finally: Combined Damage on an FPSO •High-cycle (low amplitude) loads due to waves… DFAST •Low-cycle (high amplitude) loads due to other source (e.g., FPSO loading/unloading) --> DSLOW •How to combine DFAST and DSLOW? SRSS: Largest safe region; least conservative Proposed Combination “Rules” DTOT = [ DSLOW K + DFAST 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 Sm; D1/m = c’ S Combined Fatigue: DNV Approach Merci beaucoup! Extra background slides follow… The Snorre Tension-Leg Platform Water depth: 300m One of earliest TLPs (installed 1992) How important are TN=2.5s cycles? • Important when TWAVE = 2.5s … but this condition has small wave heights • Important when TWAVE = 5.0s … due to second-order nonlinearity (springing) • Non-Gaussian effects when TWAVE = 5.0s: Answer: The Fatiguing Bookkeeping Likelihood of various (Hs,Tp) Answer: The Fatiguing Bookkeeping Likelihood of various (Hs,Tp) Damage contribution of various (Hs,Tp) Answer: The Fatiguing Bookkeeping Likelihood of various (Hs,Tp) Damage contribution of various Tp Results: 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 TPITCH = 3.5s (resonance when Tp = 7s) Damage contribution of various Tp