ssc-367 - Ship Structure Committee

SSC-367 - 

FATIGUE TECHNOLOGY 

ASSESSMENT AND STRATEGIES 

FOR FATIGUE AVOIDANCE IN 

MARINE STRUCTURES 

This document has been approved 

for public release and sale; its 

distribution is urdimited 

SHIP STRUCTURE 

1993 

COMMITTEE 

—.—— 

.——--———- 

__—————

SSC-367 ‘ 





This document has been approved 

for public release and srilq its 

distribution is unlimited 


1993 

COMMITTEE

SHIP STRUCTURF COMMllTFF 

The SHIP STRLfCTURE COMMllTEE is constituted to prosecute a research program to improve the hull structures of ships and other 

marine structures by an extension of knowledge pertaining to design, materials, and methods of construction. 

RADM A. E. Henn, USCG (Chairman) 

Chief, Office of Marine Safety, Security 

and Environmental Protection 

U. S. Coast Guard 

Mr. Thomas 1-1,Peirce Mr. H. T, Hailer Dr. Donald Liu 

Marine Research and Development Associate Administrator for Ship- Seniqr Vice President 

Coordinator building and Ship Operations American Bureau of Shipping 

Transportation Development Center Maritime Administration 

Transport Canada 

Mr. Alexander Malakhoff Mr. Thomas W. Allen 

CDR Stephen E. Sharpe, USCG 

Director, Structural Integrity 

Engineering Offmer (N7) Executtie Dkector 

Subgroup (SW 05P) Military Sealift Command 

Shi Structure Committee 

Naval Sea Systems Command 

U. i . Coast Guard 

CONTRACTING OFFICER TEC HNICAL REPRESENTATIVE 

Mr. WNiam J. Slekierka 

SEA05P4 


~Hl P STRUCTURF 

SUBCOMMIITFF 

The SHIP STRUCTURE SUBCOMMllTEE acts for the Ship Structure Committee on technical matters by providing technical 

coordination for determinating the goals and objectives of the program and by evaluating and interpreting the results in terms of 

structural design, construction, and operation. 

AMERICAN BUREAU OF SHIPPING NAVALSEA SYSTEMS COM MAND TRANSPORT CANADA 

Mr. Stephen G. Amtson (Chairman) Dr. Robert A Sielski 

Mr. John Grinstead 

Mr. John F. ConIon 

Mr. Charles L Null Mr. Ian Bayly 

Dr. John S. Spenmr Mr. W. Thomas Packard Mr. David L. Stocks 

Mr. Glenn M. M.he Mr. Allen H. Engle Mr. Peter Timonin 

MILITARY SFAI IFT COMMAN~ 

E ADMINISTRATION U. S, COAST GUARD 

Mr. Rolwt E. Van Jones Mr. Frederick Seibold CAPT T. E. Thompson 

Mr. Rickard A. Anderson Mr. Norman O. Hammer 

CAPT W. E. Colburn, Jr. 

Mr. Michael W. Touma 

Mr. Chao H. Lin Mr. Rubin Scheinberg 

Mr. Jeffrey E. Beach Dr. Walter M, Maclean Mr. Il. Paul Cojeen 

SHIP STRUCTURE SUBCOMMlmEE LIAISON MEMBERS 

U. S. COAST GUARD ACADEMY 

NATI ONAL ACAD~Y OF SCIENCES - 

LCDR Bruce FL Mustain 

Mr. Alexander 

B. Stavovy 

U.S. MFRCHAN T MARINF ACADFMY 

Dr. C. B. Kim 

u. S, NAVAL ACADEMY 

Dr. Rarrrswar Bhattacharyya 

STATE UNIVERSITY OF NEW YORK 

~ 

Dr. W. R. Porter 

SOCIETY OF NAVAL ARCHITECTS AND 

MARINE ENGINEERS 

~TION#.&AEC~~EMY OF SCIENCES - 


Mr. Peter M. Palermo 

WFI IIING RFSFARCHCOUNC II 

Dr. Ma_tin Prager 

~ L INSTITUTE 

Mr. Alexander 

D. Wilson 

DEPARTMENTOF NATIONAL DEFENCE - CANADA 

Dr. William 

Sandberg 

Dr. Neil G. Pegg 

OFFICE OF NAVAI RFSEARG H 

Dr. Yapa D. S. Rajapaske

MemberAgencies: 

United States Coast Guard 


Maritime Administration 

American Bureau of Shipping 

Miiitaty Sealift Command 


~ 

c 

Ship 

Structure 

Committee 

An Interagency AdvisoryCommittee 

May 17, 1993 

AddressCorrespondence to: 

Executive Director 

ShipStructure Committee 

U.S.CoastGuard(G-Ml/R) 

2100SecondStreet, S.W. 

Washington, D.C.20593-0001 

PH:(202)267-0003 

FAX:(202)267-4677 

SSC-367 

SR-1324 

FATIGUE TECHNOLOGY ASSESSMENT AND STRATEGIES FOR FATIGUE 

AVOIDANCE IN MARINE STRUCTURES 

This report synthesizes the state-of-the–art in fatigue 

technology as it relates to the marine field. Over the years 

more sophisticated methods have been developed to anticipate the 

life cycle loads on structures and more accurately predict the 

failure modes. As new design methods have been developed and 

more intricate and less robust structures have been built it has 

become more critical than ever that the design tools used be the 

most effective for the task. This report categorizes fatigue 

failure parameters, identifies strengths and weaknesses of the 

available design methods, and recommends fatigue avoidance 

strategies based upon variables that contribute to the 

uncertainties of fatigue life. The report concludes with 

recommendations for further research in this field. 

Gmdvwm 

A. E. HENN 

Rear Admiral, U.S. Coast Guard 

Chairman, Ship Structure Committee

—.--— 

1. Report No. 

2. Gowotnmrnt AcenszIon Na. 

T*chnical 

3. Rompiqnt’s Cataiog No. 

I?cport Documentation Fagc 

4. T,tle and $ubti~i= 

I 

FATIGUEDESIGNPROCEDURES 

5. ROport Dot. 

June1992 

6. Perfoming Organl*at~en coda 

7. Authds) 8. Porfeming Orgonitatien Report No. 

CuneytC.Capanoglu 

s.performing Or~mizotion Nemo rnd Addro~c 

SR-1324 

12. Spontsrinq A90ncy Namo and Addr**s 

Is,suppi~mentary 

Not*~ 

EARLAND WRIGHT 

180HowardStreet 

SanFrancisco, CA 94105 

10. Work Unit No. (TRAIS) 

11.co~timet or Grant No. 

DTCG23-88-C-2~29 

1s.TYP- et Rwport ad Period Covormd 

ShipStructure Committee 

U.S.CoastGuard(G-M) 

2100 SecondStreet, SW 

Washington,DC 20593 1d.Sponsoring A9cnty Cod. 

SponsoredbytheShipStructure Committeeanditsmembersagencies. 

FiialRepo~ 

G-M 

16. Abstract 

Thisreponprovidesanup-todateassessmentoffatigue technology, directed specifically toward 

themarineindustry. A comprehensive overviewoffatigue analysis anddesign,aglobalreviewof 

fatioueincluding rulesandregulations andcurrentpractices, anda fatigueanalysis anddesign 

criteria, areprovidedasa generalguideline tofatigue assessment.A detailed discussion ofall 

fatigueparametersisgroupedunderthreeanalysis blocks: 

● 

● 

● 

Fatiguestressmodel,covering environmental forces, structuresponseandloading, 

stress 

responseamplitudeoperations (RAOS)andhot-spot stresses 

Fatiguestresshistory modelcoveringlong-term distribution ofenvironmental loading 

Fatigueresistance ofstructures anddamageassessmentmathodolo@es 

Theanalysesanddesignparametersthataffectfatigue assessmentarediscussedtogetherwith 

uncertainties andresearchgaps,toprovideabasisfordeveloping strategies forfatigue avoidance. 

Additional in-depthdiscussions ofwave environmt,stressconcentration factors,etc.are 

presentedintheappendixes. 

17. Key Word, 

Assessmentoffatigue technology, 

fatioue stressmdels,fatigue 

stresshistory models,$atigue 

resistance, fatioueparamatefs 

andfatigue avoidancestrategies 

19. S* Curity ciassil. (of this toport) 

FormDOT F 1700.7(8G721 

UnCJSssifiarj 

.+ 

I 

~. SOcutity CII 

lB. Distribution $tot~~t 

Available from: 

National TechnicalInformation Serv. 

U.S.DepartmentofCommerce 

Springfield, VA 22151 

1.(*f thi c p~o) 21.No. of Pegms 

Unclassified 

R=ptoductian O{ compktad 

page authorized 

194 EXCI. 

Appendixes 

22. Pri =~

-. —---- —-...–. . 

COMVEflSION 

FACTORS 

Apprmimat, Conversions toMeiricMmsures 

m 

— C4 

Approxinmta Conversionsfrom Mstric Mcasutes 

WlwnVW Mnow Multiply b~ 

—- 

C4 

Symbol 

Wlmt Yom Know 

Muhirlf by 

la Find 

LENGTH 

,,,,,’ 

in 

h 

Vd 

mi 

in2 

~2 

d 

mi 2 

02 

lb 

tap 

rkap 

N a= 

c 

P1 

qt 

LENGTH 

“2.5 

30 

0.9 

I .e 

AREA 

squwc inches 6.6 

square feet 0.0s 

cquam yards OJJ 

mqusmmiles 2.6 

■clmm 0.4 

Oumcea 26 

-~ 0,45 

Cflai tam 0.9 

12000 lb} 

cenlimslera 

centimwmc 

mmers 

kitmneters 

mquwe Centilrwws 

Wplwa 

matO1!J 

cqume inmrs 

aqunre kilcmetems 

hectwea 

cm 

cm 

m 

km 

*2 

~2 

~2 

km2 

hm 

MASS {wtight] —- = 

VOLUME 

t*mspnns 5 

Iab!eapwms 15 

lfukt Cslnces 30 

cups 0.24 

pints 0.4? 

qumta 0.95 

gallons 3.6 

cubic hat 0.03 

cubic yards 0,16 

grcnls 

kil~ann 

tmmes 

milliliters 

milliliters 

milliliters 

!itels 

liters 

Iilers 

liters 

cubic mews 

cubic rnmers 

n 

kg 

t 

ml 

ml 

ml 

1 

I 

) 

I 

~3 

~? 

—: 

- 

— 

— 

—- 

—. 

—. 

m 

. 

a 

c- 

m 

m 

— . 

—- 

—- 

— 

—- 

— 

— 

— 

— 

m 

C4 

0 

Oi 

m 

c- 

w 

mm 

cm 

km 

m 

km 

9 

kg 

t 

n-d 

I 

t 

I 

m’ 

~3 

miIlinw[ws 0.04 

canlimmlera 0,4 

maters 3.3 

Mstara 1.1 

hikmwters 0.6 

AREA 

sqtmr.s intimaters 0.t6 

equmrs matam 1.2 

squsre kilowlem 0.4 

hactamt ~10,OCSIn?) 2.6 

MASS ~waight] 

gram3 0.033 

wagramm 2.2 

tmlms{loal kg) 1.1 

VOLUME 

millilitcms 0.03 

liters 2.1 

Iilars 1.06 

Iiwm 0.26 

cubic maters 35 

cubic nwlers 1.3 

TEMPERATURE [mwet] 

inches 

inclces 

fear 

yank 

miles 

in 

in 

rt 

yd 

mi 

sqcme inches in2 

equw. ymcls 

& 

squw* milas 

mi2 

mxas 

amca 

pOLsur, 

dmrt 

m 

Icmm 

fluid ounces 

piwCc 

quacta 

02 

lb 

fl Oz 

m 

qt 

gctkma 

gsl 

cubic led fta 

cubic yalds 

vd3 

TEMPERATWIE 

‘F Fehmnheit 5/9 (atCar 

tempamture scdmacling 

321 

{exmtj 

Celsius 

ten-mma twe 

.1 in : 2.54 lEIIacllyl. Fw olher ● xacl converswm and more #i?4a#Id tables. see NBS hl,sc. P, b!J1.286, 

Unts d We,ghts ❑wltdeasures, PTece$2.25, SD Catatog No. C13.102O6. 

“c 

Celsius 9/6 (then 

tampefmclra add 32) 

Mwanhail *F 

tsmpmatum 

‘F 

‘f 32 9e.6 2r2 

-40 0 40 80 I20 160 zm 

l,, ,,, ;.:l’ll,l{ 

l’; 

I 4 # I * I 1 * 

1 1 1 1 I 

-:: -20 0 20 40 60 “ eo ion 

3-r @c

FATIGUE TECHNOLOGY Assessment AND DEVELOPMENT OF 

STRATEGIES FOR FATIGUE AVOIDANCE IN MARINE STRUCTURES 

FINAL REPORT 

CONTENTS 

Abstract 

Contents 

List of Figures 

Common Terms 

i 

ii 

ix 

xi 

1. INTRODUCTION 

1.1 Background 

1.2 Objectives 

1.3 scope 

1-1 

1-2 

1“3 

2* OVERVIEW OF FATIGUE 

2.1 Fatigue Phenomena 

2.2 Fatigue Analysis 

2.2.1 Analysis Sequence 

2.2.2 Analysis Methods 

2.3 Significance of Fatigue Failure 

2.4 Fatigue Failure Avoidance 

2-1 . 

2-3 

2-7 

2-8 

3. FATIGUE DESIGN AND ANALYSES PARAMETERS 

3.1 Review of Fatigue Design Parameters 

3.1.1 Design Parameters 

3.1.2 Fabrication and Post Fabrication Parameters 

3.1.3 In-Service Parameters 

3.2 Review Of Fatigue Analysis Parameters 

3.2.1 Fatigue Analysis Criteria 

3.2.2 InteractingParameters 

3.2.3 Stress Model Parameters 

3.2.4 Stress History Model Parameters 

3.2.5 Fatigue Damage Computation Parameters 

3-1 

3-7 

ii

4. GLOBAL REVIEW OF FATIGUE 

4.1 Applicable Analysis Methods 

4.1.1 Background 

4.1.2 Simplified Analysis and Design Methods 

4.1.3 Detailed Analyses and Design Methods 

4.1.4 Other Methods 

4-1 

4.2 Fatigue Rules and Regulations 4-16 

4.2.1 Applicable Methods 

4.2.2 SCFS, S-N Curves and Cumulative Damage 

4.2.3 Fatigue Analysis Based on Fracture Mechanics 

4.3 Current Industry Practices 4-23 

4.3.1 Ordinary Designs 

4.3.2 Specialized Designs 

4.4 Sensitivity of Fatigue Parameters 4-25 

4.5 Fatigue Design and Analysis Criteria 4-26 

4.5.1 Basis for the Preparationof Criteria 

4.5.2 Applicable Software 

4.5.3 Fatigue Versus Other Design and Scheduling Requirements 

5. FATIGUE STRESS MODELS 

5.1 Review of Applicable Modeling Strategies 5-1 

5.1.1 Modeling Strategies 

5.1.2 Comparison of Structures 

. 

5.2 Floating Marine Structures 5-4 

5.2.1 Ship Structures 

5.2.2 Stationary Marine Structures 

5.2.3 Overview and Recommendations 

5.3 Bottom-SupportedMarine Structures 5-16 

5.3.1 Load or HydrodynamicsModel 

5.3.2 Mass Model 

5.3.3 Motions Model and Analyses Techniques 

5.3.4 Stiffness Model 


5.4 Development of Hot Spot Stresses 5-25 

5.4.1 Nominal Stresses and Stress RAOS 

5.4.2 Stress Concentration Factors and Hot Spot Stresses 

5.4.3 Empirical Equations 

5.4.4 Illustrationof a T-Joint SCFS 


. . . 

111 

( .-. ,)

6. FATIGUE STRESS HISTORY MODELS 

6,1 Determination of Fatigue Environments 

6.1.1 Data Sources 

6.1.2 Wave and Wind Spectra 

6.1.3 Scatter Diagram 

6.1.4 Directionalityand Spreading 

6-1 

6.2 Stress Spectrum 6-10 

6.2.1 Stress RAOS 

6.2.2 Response Analysis 

6.2,3 Uncertainties and Gaps in Stress Spectrum Development 

6.2.4 Decompose into Stress Record 

6.3 Time-Domain Analyses 6-14 

6.3.1 Stress Statistics 

6.3.2 70 PercentileSpectra 

6.4 Overview and Recommendations 6-15 

7. FATIGUE DAMAGE ASSESSMENT 

7.1 Basic Principles of Fatigue Damage Assessment 

7.2 S-N Curves 

7.2.1 Design Parameters 

7.2.2 Fabrication and Post-FabricationParameters 

7.2.3 EnvironmentalParameters 

7.3 Fatigue Damage Computation 

7.3.1 Miner’s Rule 

7.3.2 Alternative Rules 

7.4 Stress History and Upgraded Miner’s Rule 


7.4.2 Miner’s Rule IncorporatingRainflow Correction 

7.4.3 Other Alternatives 

7.5 Overview and Recommendations 

7.5.1 Application of S-N Curves 

7.5.2 Fatigue Damage Computation 

7-1 

7-2 

7-11 

7-14 

7-19 

iv 

-7

8. FATIGUE DUE TO VORTEX SHEDDING 

8.1 Vortex Shedding Phenomenon 


8.1.2 Vortex Induced Vibrations (VIV) 

8.2 Analyses and Design For Vortex Shedding 

8.2.1 Susceptibilityto Vortex Shedding 

8.2.2 VIV Response and Stresses 

8.3 Fatigue Damage Assessment 

8.4 Methods of Minimizing Vortex Shedding Oscillations 

8.5 Recommendations 

8-1 

8-3 

8-5 

8-6 

8-6 

9. FATIGUE AVOIDANCE STRATEGY 

9.1 Review of Factors Contributing to Failure 

9.2 Basic Fatigue Avoidance Strategies 

9.2,1 Basic Premises 

9.2.2 Fatigue Avoidance Strategies 

9.3 Fatigue Strength ImprovementStrategies 

9.3.1 Fabrication Effects 

9.3.2 Post-FabricationStrength Improvement 

9.3,3 Comparison of Strength ImprovementStrategies 

9.4 Fatigue Analysis Strategies 

9.4.1 Review of Uncertainties,Gaps and Research Needs 

9.4.2 Recent Research Activities 

9.4.3 Cost-EffectiveAnalysis Strategies 

9.5 Recommendations 

9.5.1 Research Priorities 

9.5.2 Rules and Regulations 

10. REFERENCES 

9-1 

9-2 

9-7 

9-14 

9-22 

1o-1 

v

APPENDICES 

A. REVIEW OF OCEAN ENVIRONMENT 

A.1 

A.2 

A.3 

IRREGULARWAVES 

PROBABILITYCHARACTERISTICSOF WAVE SPECTRA 

A.2.1 CharacteristicFrequencies and Periods 

A.2.2 CharacteristicWave Heights 

WAVE SPECTRA FORMULAS 

A.3.1 Bretschneiderand ISSC Spectrum 

A.3.2 Pierson-MoskowitzSpectrum 

A.3.3 JONSWAP and Related Spectra 

A.3.4 Scott and Scott-WiegelSpectra 

A-1 

A-5 

A-n 

A.4 

SELECTING A WAVE SPECTRUM A-16 

A.4.1 Wave Hindcasting 

A.4.2 Direct Wave Measurements 

A.5 

A.6 

A.7 

A.8 

WAVE SCATTER DIAGRAM 

WAVE EXCEEDANCE CURVE 

WAVE HISTOGRAM AND THE 

EXTREME VALUES AND THE 

A-19 

A-21 

RAYLEIGH DISTRIBUTION A-22 . 

WEIBULL DISTRIBUTION A-22 

A.9 

A.1O 

WIND ENVIRONMENT 

A-23 

A.9.1 Air Turbulence, Surface Rouqhness and Wind Profile 

A.9.2 Applied, Mean and Cyclic Velocities 

A.9.3 Gust Spectra “ 

REFERENCES A-28 

vi 

(-’ 

7

B. REVIEW OF LINEAR SYSTEM RESPONSE TO RANDOM EXCITATION 

B.1 GENERAL 

B.1.l Introduction 

6.1.2 Abstract 

B.1.3 Purpose 

B.2 RESPONSE TO RANDOM WAVES 

B.2.1 Spectrum Analysis Procedure 

B.2.2 Transfer Function 

6.2.3 Wave Spectra 

B.2.4 Force Spectrum 

B.2.5 White Noise Spectrum 

6.3 EXTREME RESPONSE 

6.3.1 Maximum Wave Height Method 

B.3.2 Wave Spectrum Method 

B.4 OPERATIONAL RESPONSE 

B.4.1 Special Family Method 


B-1 

B-2 

B-15 

B-17 

c. STRESS CONCENTRATION FACTORS 

C*1 OVERVIEW 

C*2 STRESS CONCENTRATION FACTOR EQUATIONS 

C.2.1 Kuang with Marshall Reduction 

C.2.2 Smedley-Wordsworth 

C.3 PARAMETRIC STUDY RESULTS 

C.3.1 Figures 

C.3.2 Tables 

C*4 FINITE ELEMENT ANALYSES RESULTS 

C.3.1 Column-GirderConnection 

C*5 REFERENCES 

c-1 

c-4 

C-6 

C-15 

C-17 

vii

D. VORTEX SHEDDING AVOIDANCE AND FATIGUE DAMAGE COMPUTATION 

NOMENCLATURE 

i 

D.1 

D.2 

D.3 

D.4 

D.5 

D*6 

D.7 

D*8 

0.9 

INTRODUCTION D-1 

VORTEX SHEDDING PARAMETERS D-2 

SUSCEPTIBILITYTO VORTEX SHEDDING D-7 

D.3.1 In-Line Vortex Shedding 

D.3.2 Cross-Flow Vortex Shedding 

D.3.3 Critical Flow Velocities 

AMPLITUDES OF VIBRATION D-9 

D.4.1 In-Line Vortex Shedding Amplitudes 

D.4.2 Cross-Flow Vortex Shedding Amplitudes 

STRESSES DUE TO VORTEX SHEDDING D-13 

FATIGUE LIFE EVALUATION D-14 

EXAMPLE PROBLEMS D-17 

D.7.1 Avoidance of Wind-Induced Cross-Flow Vortex Shedding 

D.7.2 Analysis for Wind-Induced Cross-Flow Vortex Shedding 

METHODS OF MINIMIZING VORTEX SHEDDING OSCILLATIONS D-23 —. 

D.8.1 Control of Structural Design 

D.8.2 Mass and Damping 

D.8.3 Devices and Spoilers 

REFERENCES D-27 

. . . 

Vlll

LIST OF FIGURES 

LIST OF FIGURES 

(cent.) 

FIGURE 

TITLE 

9-1 Typical Methods to Improve Fatigue Strength 

9-2 Typical Weld Toe Defects and Corrective Measures 

9-3 Fatigue Life ImprovementDue to Weld Toe Abrasive 

Water Jet Erosion 

9-4 Comparison of Fatigue Strength ImprovementTechniques 

9-5 Summary of Relevant Research Activities 

.—. . . . ...—

COMMON TERMS 

USED 

IN FATIGUE AND IN THIS REPORT 

BTM 

: Bottom turret mooring system for a tanker. Can 

be permanent or disconnectable. 

CAPEX 

: Capital expenditures incurred prior to 

structure commissioning and beginning 

operation. 

CATHODIC PROTECTION 

: An approachto reduce material corrosive action 

by making it the cathode of an electrolytic 

cell. This is done by utilizing sacrificial 

anodes (i.e. couplingwith more electropositive 

metal) or impressed current. 

COMPLEX JOINT 

: An intersection of several members, having a 

subassemblageof componentmembers. Applicable 

to a column-to-pontoon joint of a 

semisubmersible or a large leg joint of a 

platform containing stiffened bulkheads, 

diaphragms and other tubulars. 

CRUCIFORM JOINT 

: A transverse load carrying joint made up two 

plates welded on to either side of a 

perpendicularplate utilizing full penetration 

welds. 

DYNAMIC AMPLIFICATION FACTOR : The maximum dynamic and static load ratios, 

(DAF) 

such as the DAF applicable to base shear or 

overturningmoment. 

HEAT AFFECTED ZONE (HAZ) 

: The area of parent plate material susceptible 

to material degradationdue to welding process.

HOT-SPOT STRESS 

. 

The hot-spot stress is the peak stress in the 

immediate vicinity of a structural 

discontinuity,such as the stiffener edge or a 

cutout. On a tubular joint, the hot-spot 

stress usually occurs at the weld toe of the 

incoming tubular (brace) or the main tubular 

(chord). 

FATIGUE LIFE 

. 

● 

The number of stress cycles that occur before 

failure, typically corresponding to either 

first discernible surface cracking (Nl) or the 

first occurrence of through thickness 

cracking. 

FATIGUE STRENGTH 

● 

✎ 

The stress range corresponding 

to 

a number of 

cycles at which failure occurs. 

FPSO 

. 

Floating production, storage 

and offloading 

tanker. 

IRREGULARITYFACTOR 

● 

✎ 

The ratio of mean crossings with positive 

slopes to the number of peaks or valleys in the 

stress history. 

KEULEGAN-CARPENTERNUMBER, Kc : 

A parameter used to define the flow properties 

around a cylinder. Equal to the product of the 

amplitude of velocity and oscillation period, 

divided by the cylinder diameter. 

MEAN ZERO-CROSSING PERIOD : 

The mean zero-crossing period is the average 

time between successive wave crossings with a 

positive slope (up-crossing) of the zero axis 

in a time history. 

xii

MODELING ERROR (Xme) 

: Typically defined as the ratio of actual 

behavior of the structure to the one predicted 

by the model. It is often used to assess the 

accuracy of excitational loads, motions, and 

stresses. 

MODELING UNCERTAINTY 

NARROW-BAND LOADING 

: The random component of the modeling error, 

x, and defined by its coefficient of 

v%iation, (C.O.V.)X . 

me 

: The stress cycles are readily identifiable, 

making the choice of counting method of stress 

cycles immaterial. 

NOMINAL STRESS 

: The nominal stress is the stress obtained by 

dividing the member generalized forces (forces 

and moments) by member section properties 

(cross-sectionalarea and section modulus). 

OPEX 

: Operating expenditures due to maintenance, 

inspection, repairs as well as cost of fuel, 

variables,personnel,etc. during the life of a 

structure. 

PLASMA DRESSING 

: Application of plasma arc welding technique to 

remelt the weld toe (similarto TIG dressing) 

POST WELD HEAT TREATMENT 

(PWHT) 

: A procedure of heating a welded joint to 

relieve residual fabrication stresses. 

Typically, the joint is heated to 1076 1150°F 

(580-620”C), held at that temperaturefor about 

an hour for each one inch (2.5 rein/mm) 

thickness, and cooled in air. 

xiii

QA/Qc 

: Quality Assurance/QualityControl 

Quality assurance generally refers to the 

procedures and methods put into effect to 

ensure quality a priori, while quality control 

generally refers to reviews and checks afterthe-fact 

to implement corrective measures, as 

necessary. 

: The term random waves is used to characterize 

the irregular sea surface and associatedwater 

particle kinematics that occur in the ocean. 

Analytically random waves are represented as a 

summation of sinusoidal waves of different 

heights, periods, phases and directions. 

REGULAR WAVES 

: Regularwaves are unidirectionaland associated 

water particle kinematics and sea surface 

elevations are periodic. 

S-N CURVE 

: The S-N curves define the fatigue strength of a 

detail/joint by representing test data in an 

empirical form to establish a relationship 

between stress ranges and the number of cycles 

of stress range for fatigue failure. 

SEA STATE 

: An oceanographicenvironmentwith a wave height 

range characterized as a stationary random 

process for a specific duration. 

SIGNIFICANT WAVE HEIGHT 

: A statistic typically used to characterize the 

wave heights in a sea state. It is defined as 

the average height of the heighestone-third of 

all the individual waves present in a sea 

state. 

xiv

SIMPLE JOINT 

: An intersection of two or more structural 

members. Also applicableto an intersectionof 

unstiffenedor ring-stiffenedcylinders. 

STEADY STATE 

: Generally refers to the periodic response of a 

dynamic system after initial starting 

transients have decayed to negligible 

amplitude. 

STRESS CONCENTRATION FACTOR : The ratio of hot-spot stress to the nominal 

(SCF) 

stress (in neighborhoodof hot-spot) and often 

max. mized at geometric discontinueties. 

STRIP THEORY 

: App” ied to various strip methods to determine 

the 

bod 

hydrodynamic loadings on “ ong slender 

es and can account for the effect of 

diffracted and radiated waves. 

TIG DRESSING 

: Tungsten-inert-gas dressing is applied to 

remelt the weld toe material to reduce both the 

SCF by minimizingdiscontinuitiesand to remove 

defects such as slag inclusions. 

TRANSFER FUNCTION 

: A transfer function defines the unitized 

structural response as a function of frequency 

(eg ratio of structural response to the wave 

amplitude applicable for each frequency). 

WELD TOE 

: The point of intersection of the weld profile 

and parent plate. 

WIDE-BAND LOADING 

: The smaller stress cycles are interspersed 

among larger stress cycles, making the 

definitionof stress cycle more difficult. The 

use of different counting methods will result 

in different fatigue damage predictions. 

xv

1. 

INTRODUCTION 

1.1 

BACKGROUND 

The detailed design of a structure focuses largely on sizing the 

structurescomponentmembers and on developingthe details to resist 

extreme functionaland environmentalloads. The analysisand design 

to resist extreme loading conditions is intended primarily to 

prevent material yield and buckling failures; the details are also 

chosen to help prevent fatigue failures due to cyclic loading. 

,-. 

The use of proven details and selection of steel with material 

properties resistingpropagationof defects are longstandingdesign 

practices. Analysis and design to ensure that fatigue life is 

substantiallyin excessof the design life becamegenerally accepted 

in the late 1960s. Initial simplistic analysis methods have 

gradually become more sophisticated. Oceanographic data collected 

over the last twenty years now allow better definition of wind and 

wave data over many parts of the world. Several test programs have 

allowed comparison of actual and analytically computed loads on 

marine structures. Laboratorytest data anddata from structures in 

servicenow allowbetterdefinitionof defect (crack)propagation in 

an ocean environment. 

Although engineers have progressed beyond simplified deterministic 

analyses, occasionallyventuring into full probabilistic analysis, 

substantialuncertaintiesstill are associatedwith fatigue analysis 

and design. Fatigue life may change dramatically with a small 

change in any of many variables,requiringthat the fatigue analysis 

and design of a marine structure be conducted as a series of 

parametric studies. The results of these studies, used to upgrade 

fatigue-sensitiveareas/details of the structure, allow development 

of a design that will provide a satisfactory level of confidence 

against fatigue failure. 

Review of past fatigue failures shows that it is often difficult to 

determine whether a failure was due to poor design, material 

1-1

imperfections, fabrication defects, improper inspection or 

maintenance, unpredicted loads or, more likely, a combination of 

these interactingvariables. As the complexityof marinestructures 

increases,betterunderstandingof the variablescontributingto the 

integrity of structure components and the global response of the 

structure becomes very important. Although several excellent 

documents on fatigue are available, most address fatigue design of 

either ship or offshore platform structures (References1.1 through 

1.8). Thus the engineer may have difficulty in assessing the 

significance of fatigue within the context of overall design of 

marine structures. It is also difficult to evaluatethe sensitivity 

and interactionof variables affecting fatigue life or the relative 

uncertaintiesthat are built in. The UEGReconnnendations(Reference 

1.8), although applicable to only tubular joints, provides a 

detailed discussion of various design requirements and code 

recommendations. 

Fatigue analysis and design must be carried out while the structure 

is being designed and revised to satisfy numerous other pre-service 

and in-service loading conditions. Thus, to achieve an effective 

design the overall design strategy should incorporatefatigue as an 

integral part of design, with primary impact on design details, 

redundancy, material and fabrication specifications, operational 

performance, inspection program and cost. Because structures’ 

susceptibility to fatigue and the severity of fatigue environment 

varies, the chosen fatigue design and analysis methodology, the 

sequence, and the extent of the fatigue design effort should be 

compatible with the overall design program and should be carefully 

planned and monitored to prevent construction delays or costly 

modifications during construction. 

1.2 

OBJECTIVES 

This document was prepared to provide the engineer with an up-todate 

assessment of fatigue analysis and design. It may be used 

either as a comprehensive guideline or a quick reference source. 

The first four sections of the report provide an overview and 

1-2

general assessmentof fatiguewhile the Iatterfive sectionsprovide 

in-depth discussion. The objectives of the document are: 

● 

Review, assess anddocument all fatigue parametersthat maybe 

grouped into a set of parameters (i.e., strength models, 

stress history models, analysis methods, etc.) 

● 

Review, assess and document strengths and weaknesses of 

current fatigue analysis and design procedures in conjunction 

with existing codes and standards. 

● 

Documentresearchgaps andrecomnend additionalresearchbased 

innumerous analyticalandexperimentalwork resultspublished 

every year. 

● 

Recommend a guideline on fatigue avoidance strategy based on 

numerous variablescontributingto the uncertainty of fatigue 

life, on recent research results and on current practices. 

9 

Assess and discussthe accuracyof fatigue life estimationand 

the complexity of computation based on the implication of 

uncertainties associatedwith the fatigue parameters and the 

time and effort necessary to carry out fatigue analysis and 

design to various levels of complexity. 

1.3 

SCOPE 

The following tasks were key elements in preparation of this 

document. 

● 

Review and assess global fatigue analysis, including fatigue 

as an integral part of design effort, current industry 

practices, codes and standards, and the implications of 

fatigue damage. 

● 

Review and assess all parameters within the stress model 

umbrella for their relative accuracy as well as application, 

1“3

including environmental conditions, structural response, 

generationofloa&, developmentof stress response amplitude 

operators (RAOS) and hot-spot stresses. 

● 

Review and assess all parameters within the stress history 

model umbrella, including scatter diagram, hindcasting, wave 

spectra and application ranges. 

Review fatiguedamage assessmentmethodologies, includingthe 

effects of numerous analysis and design uncertainties, and 

prepare a guideline to both improve fatigue performance of 

marine structures and simplify fatigue analysis. 

● 

Report the findingsin aclearand concise document, including 

directly applicable unpublished and published data. 

1-4

2. 

OVERVIEW OF FATIGUE 

2.1 

FATIGUE PHENOMENA 

Metal structures subjected to variable or repeated loads can fail 

without ever reachingtheir staticstrengthdesign loads. This type 

of failure,which consistsof the formationand growth of a crack or 

cracks, has come to be known as “fatigue”. 

Failures observed due to the growth of defects subjected to cyclic 

loadings is due to a very complex phenomena, affected by many 

parameters. Any environment or condition that results in cyclic 

Ioading and reversalof componentstressesmay cause fatiguedamage. 

Cyclic stresses are typically caused by machinery vibrations, 

temperature changes and wind and wave actions. But although 

vibrations and temperaturechanges may be important to fatigue in a 

local component, these loadings are not a major concern in the 

global behavior of typical marine structures. Thus, the overview 

presented in this section addresses wave and wind environments, 

excitation forces on mobile and stationary structures and the 

response of these structures to excitation forces. 

A defect subjected to a large number of cyclic stresses undergoes 

three phases of stable crack growth: 

● 

● 

● 

Crack initiation, or development of a defect into a 

macroscopic crack. 

Crack propagation, or development of a crack into a critical 

size. 

Cracked weldment residual strength exceedence. 

The relative durations of these three phases depend on many 

variables,includingmaterialproperties,defectgeometry, structure 

stiffness, stress cycle magnitudes, distribution and sequence, 

operating environment and maintenance. The objective is to prevent 

fatigue failure by designing to ensure that the time required to 

2-1

complete the three-phasestable crack growth is always greater than 

the design fatigue life. 

The basic characteristicsof defects and the fatigue phenomena may 

be summarized as: 

Eventhe most thorough inspectionsat the fabricationfacility 

will not reveal very small defects (less than 0.5 mm). 

These defects will grow when subjectedto cyclic stresses due 

to environmentalloads, structure dynamics (vortex shedding, 

machinery vibrations, etc.), temperature changes, etc. 

Repeated cyclic stresses and defect growth are additive, 

making the fatigue damage cumulative. 

In most cases, fatigue is insensitive to the presence of 

constant loads. Consequently, stress ranges (i.e., peak-topeak 

values) are used to characterize fatigue stresses. 

Although a small number of extreme stress ranges may 

contribute to fatigue damage, most fatigue damage is due to 

the occurance of a large number of small stress ranges. 

Poor structuraldesign details will amplify peak stresses. 

Distortions and residual stresses introduced during original 

fabrication (as well as extensive repair efforts) often 

adversely affect material resistance to crack growth. 

Corrosion and ocean environment adversely affect material 

resistance to crack growth. 

Asimplifiecl summary of fatigue phenomena is presented on Figure 2- 

. 

1. 

2-2

2.2 FATIGUE ANALYSIS 

2.2.1 Anal.vsisSequence 

The basic fatigue analysis sequence is shown as a block diagram on 

Figure 2-2 and further discussed in this overview and in Sections 3 

through 7. 

Fatique Environment 

Wave and wind environments are both site- and time-dependent.A 

brief observationofwind and the waves it generates shows that they 

are random phenomena,where wind speed, direction and duration and 

wave height, period and breadth continually change. 

Although the real sea is random, the wave environment can be 

described by two methods. In the deterministic method, the sea is 

described as composed of identical, regular, individualwaves. In 

the spectral method, the sea is described as a function of sea 

surface elevation due to regular waves combining to form an 

irregular sea. 

The service life of a vessel/structure may be 20 to 40 years. 

During the service life more than 500 millionwaves arelikely to be 

applied on the vessel/structure. The fatigue environment is often 

defined basedon a series of 15020 minues records taken every3 or 

4 hours. The environment is summarizd in a wave scatter diagram. 

The wave scatter diagram is a grid of boxes with rows of equal Hs 

(significant wave height) and columns for characteristic period, 

often Tz (zero up-crossing period) or Ts (significantperiod). 

For example: Wave records taken by a weather buoy can be sampled 

every four hours. The sample records are reduced by Fast Fourier 

Transform (FFT) and integratedto derive the statistical parameters 

of Hs and Tz. The whole of the sample parameters are sorted by Hs 

and Tz. The number of samples of each Hs-Tz combination are placed 

in the correspondingbox in the scatter diagram. Often the scatter 

2-3 

-J .;– 

., --,

diagram boxes are normalized so that the sum of all of the numbers 

is 1000. The shapes of the reduced spectra can be compared and a 

representative spectrum formula can be fit to the typical shape. 

The JONSWAP spectrum is often used to fit sampled spectra shapes, 

because of the flexibility offered by the Gamma and Sigma 

parameters; see AppendixA, Section3.3. Similar seastates are then 

combined into a scatter diagram. 

The wind loading on a structure is composed of mean and cyclic 

components. To carry out a fatigue analysis of a structure 

subjected to cyclic wind loading the magnitude of loading and 

associated frequencies must be quantified. Individual component 

members of a structuresubjectedto continuousmean wind loadingmay 

be susceptible to vortex shedding vibrations. A comprehensive 

coverage of wind-inducedfatigue phenomena is presented in Appendix 

D. 

Acomprehensive reviewof ocean environment,covering both waves and 

wind, is presented in Appendices A and B. 

FatictueStress Model 

The term fatigue stressmodel is often used to define a combination 

of analysis steps, covering: 

● 

● 

● 

Generation of loads 

Structural analysis to determine nominal stresses 

Estimation of hot spot stresses 

These analysis steps are identified as fatigue analysis blocks and 

combined into a single stress model block on Figure 2-2. 

The analysis steps undertaken to determine the local hot spot 

stresses are sequentialand an inaccuracyat any step contributesto 

compounding of the overall inaccuracy. Although many variables 

directly influencethe accuracyof estimatedhot spot stresses, some 

of the more importantvariables are listed below: 

2-4

● 

Loads generated as affected by the definition of environment, 

selection of wave theories, response characteristics of the 

vessel/structuresubjectedtoexcitationalenvironmentalloads 

and computer modeling. 

● 

Structural analysis as affected by the computer model, 

software package and engineering decision/selection of 

locations for determinatingof nominal stress. 

● ✍ 

Hot spot stresses as affected by determination of stress 

concentrationfactors (SCFsdeterminedfromempiricalformulas 

based on databasesof numericaland experimentalwork) and the 

engineering decision on multiple recomputation of SCFS to 

account for variations in stress distribution (i.e., 

reclassificationofdetail/joint for each transfer function). 

Another vary importantvariable,fatigue analysismethod, is briefly 

discussed in Section 2.2.2. 

Fatique Stress Historv Model 

The stresses computed may be either stress states (defined by wave 

height and wave period and representing a single cycle of loading) 

or peak values associatedwith discretewaves. A generalized stress 

history model combines this data with long-term wind and wave 

distributions (scatter diagram, spectra, directionality, etc.) to 

develop a long-term distribution of stresses. 

Material Resistance to Fatique Failure (StrenqthModel) 

The material resistance to fatigue failure will primarily depend on 

the characteristics of detail/joint geometry, material chemical 

compositionand mechanical properties,and the service environment. 

The material resistance is typically determined in a laboratory 

environmentby the applicationof constantamplitude stress cycle on 

various detail/joint geometries until fatigue failure occurs. By 

2-5

carrying out similar tests for different stress amplitudes a 

relationship between the stress amplitude (S) and the number of 

cycles (N) is established. The S-N curves developed for simple 

details (i.e., stiffener, cutout, etc., applicable for most ship 

details) account for the peak (hot spot) stresses and can be 

directly used with the member nominal stresses. 

The tubular joint details (i.e., T, K, Y, etc., joints applicable 

for an offshore platform) exhibit a wide variety of joint 

configurations and details. The S-N curves for tubular joint 

details do not account for hot spot stresses, requiring the 

application of stress concentration factors (SCFS) on computed 

nominal stresses. 

Cumulative Fatique Damaqe 

A relatively simple approach used to obtain fatigue damage requires 

dividingof stressrangedistributionintoconstant amplitudestress 

range blocks, assumingthat the damage per load cycle is the same at 

a given stress range. The damage for each constant stress block is 

defined as a ratio of the number of cycles of the stress block 

required to reach failure. The most often used Palmgren-Miner 

linear damage rule defines the cumulative damage as the sum of 

fatigue damage incurred at every stress block. 

2.2.2 

Analysis Methods 

A suitable fatigue analysis method depends on many parameters, 

includingstructureconfiguration,fatigueenvironment,operational 

characteristics and the design requirements. A fatigue analysis 

method may be deterministicor probabilistic. A fully probabilistic 

method accounting for uncertainties in defining stresses due to 

random loads, scatter in S-N data and randomness of failure is 

suited to marine structures. However, less complex deterministic 

methods are primarily used to analyze the fatigue lives of marine 

structures. 

2-6

A deterministic method is sometimes identified as probabilistic 

analysis as the randomnessof the ocean environment is accounted for 

by incorporatingthe wave spectra. Thus, dependingon how the loads 

are generated, the fatigue analyses method may be identified as: 

● 

Deterministic - Single Wave 

● Spectral - Regular Waves in Time-Domain 

● Spectral - Regular Waves in Frequency-Domain 

● Spectral - IrregularWaves in Time-Domain 

● Spectral - Wind Gust 

Further discussion on fatigue analyses parameters and analysis 

sequence is presented in Sections 3 and 4, respectively. 

2.3 

SIGNIFICANCE OF FATIGUE FAILURE 

An improperdesign may lead to an unacceptablecatastrophic fatigue 

failure, resulting in loss of life and damage to the environment. 

Non-catastrophic fatigue failures are also unacceptable due to 

difficulty and cost of repairs as well as the need to increase 

costly inspection and maintenance intervals. 

Numerous marine structures of different configurations are in 

operation. As illustrated on Figure 2-3, these structures may be 

grouped as “mobile”or “stationary”,depending on their functional 

requirement. Although mobile vessels/structurecan be moved to a 

shipyard for repairs, the total cost of the repair includes 

downtime. Stationary offshore vessel/structure inspections and 

repairs are extremely costly due to on-location work and their 

operating environment, yet the effectiveness of repairs is often 

uncertain. Thus, for bothmobile and stationarymarine structures, 

it is essential to consider avoidance of fatigue failure at every 

phase of design and fabrication. 

2-7

2.4 FATIGUE FAILURE AVOIDANCE 

Fatigue failure avoidance is not just a motto, but a goal that can 

be achieved with relativeease if the fatigue design is an integral 

part of the original design program. 

Despite their diversity,most marine structuresare designed tomeet 

established functional requirements, environmental criteria and 

rules and regulations. The design process is executed through 

several stages to optimize structure configuration and operational 

performance. Since the objectives identified to achieve 

optimization are not necessarily compatible, various trade-offs 

become necessary. To ensurethat fatigue failureavoidancestrategy 

is compatible with the overall design objectives an interactive 

design sequence is essential. 

2-8

1 

APPLICATION OF NUMEROUS 

CYCLIC STRESSES 

MATERIAL 

RESISTANCE 

AFFECTED BY 

FABRICATION 

EFFECTS 

MATERIAL 

RESISTANCE 

‘AFFECTED BY 

IN-SERVICE 

EFFECTS 

9STABLE 

CRACK GROWTH 

I FATIGUE FAILURE I 

Figure 2-1 Fatigue Phenomena Block Diagram Summary 

--l 

/:, J 

-.

ENVIRONMENTAL CRITERIA 

(DEFINITIONOF ENVIRONMENT 

HIND, WAVE ETC.) 

.—. —.— - 

r 

GENERATION OF LOADS “1 

I 

I 

I 

I STRUCTURAL ANALYSIS TO LI FATIGUE STRESS 

MODEL 

1’ OBTAIN NOMINAL STRESSES I 

1 I 

ESTIMATION OF HOT SPOT STRESSES 

EACH STRUCTURAL DETAIL 

L- -—- —. -— -—. .1 

rI -—-—--—.—. 

TIME HISTORY OF STRESSES + 

‘ 

L-’ 

-—-— . .—. —. 

J 

FATIGUE STRESS 

HISTORY MODEL 

RESISTANCE TO FATIGUE FAILURE 

~ 

I 

ESTIMATION OF CUMULATIVE 

FATIGUE DAMAGE 

I 

Figure 2-2 Fatigue Analysis Block Diagram Summary

I 

MOBiLEANDSTATIONARY 

MARWE STRUCTURES I 

& 

Ifltil 

Rm4Mmm5 

n—— 

Q ?LOAIWO 

MAW 

L 

Hmm 

. m Jails 

El 

●xa5 m 

-imr 

El 11- 

m-. 

WM!zs 

mm 

flwimm 

m@ 

Figure2-3 

MOBILE AND STATIONARY 


121 

-mm 

● —m 

8-wn 

El 

JAtm-v? 

u R41S1 

la 

mwm/ 

Wur Vm2s

-. 

(THIS PAGE INTENTIONALLY LEFT BLANK)

3. 

FATIGUE DESIGN AND ANALYSIS PARAMETERS 

One approach to assess the variables,parameters and assumptionson 

fatigue is to separate the design from analysis. Fatigue design 

parametersdo affectthe fatigueperformanceand they can be revised 

during the design process to optimize the structure. 

Fatigue analysis parameters and assumptions affect the computed 

fatigue life of the structure. The analyses approach selected 

should be compatible with the structure configuration and its 

fatigue sensitivity. Both fatigue design and analyses parameters 

are summarized on Figure 3-1 and discussed in the following 

sections. 

3.1 

REVIEW OF FATIGUE DESIGN PARAMETERS 

All of the parameters affecting fatigue performance of a marine 

structure and its components can be grouped into three categories 

based on both function and chronological order. The three groups 

are: 

● 

● 

● 

Design parameters 

Fabrication and post-fabricationparameters 

In-Serviceparameters 

The parameters in these three groups actually dictate crack 

initiation,crack propagation to a critical size and exceedance of 

cracked weldment residual strength. While these parameters are 

assessed and incorporated into a design program to qualitatively 

enhance fatigue performance,quantitativeanalyses are necessaryto 

verify that the structure’s components have satisfactory fatigue 

lives. Fatigue analysis parameters and analysis sequence are 

discussed in Sections 3.2 and 3.3, respectively. 

3-1 

.,

3*1*1 Desiqn Parameters 

There are numerousparametersthat can be incorporatedinto a design 

to enhance fatigue performance, These parameters are grouped into 

four general categories: 

● 

● 

● 

● 

Global configuration 

Component characteristicsand structural details 

Material selection 

Fabrication procedures and specifications 

The effect of these parameters 

discussed as follows. 

are summarized on Figure 3-2 and 

Global Configuration 

The overall configuration of every marine structure, mobile or 

stationary, should be reviewed to ensure that the applied 

environmental forces will be minimized. Trade-offs are often 

necessary to ensure that the extreme environment and operating 

environmentloadingsare both as low as possible (althoughit may be 

that neither is minimized) to ensure overall optimum performance. 

Planned redundancy is extremely beneficial to fatigue performance 

because alternativeload paths are providedto accommodatea fatigue 

failure. Such redundanciesprevent catastrophicfailures, and also 

provide ample time for repair of local failures. 

Component Characteristicand Structural Details 

Wherever possible,acomponent’s arrangementand stiffnessshouldbe 

similar to that of adjacent components to ensure a relatively 

uniform load distribution. Nominal stresses at a given detail will 

be amplified because of the geometry of the detail. The ratio of 

the peak or hot spot stress to the nominal stress, known as the 

stress concentration factor (SCF), is affected by many variables, 

including component member load paths, interface plate thicknesses 

3-2

and in-plane/out-of-planeangles,and stub-to-chorddiameter ratios 

(for tubular members). 

The arrangement of structural details is very important from a 

standpoint of their configuration (affecting SCFS) and access 

(affectingqualityof work). Shiphullstiffenersare often arranged 

with these considerationsinmind. Similarly,tubular interfacesof 

less than 30 degrees are not desirable in order to ensure reasonable 

access for assembly and inspection. 

Material Selection 

Steel material is selected not only for strength but also for its 

other characteristics,includingweldabilityand durability. Thus, 

the material selected should have both the chemical composition and 

the mechanical properties to optimize its performance. The use of 

higher strength steel requires specification of higher material 

toughness requirements to meet the limits on fabrication flaws. 

Since the material with higher toughness can tolerate larger loads 

for a given flaw without brittle fracture during its service life, 

such a material is preferred. 

Impuritiesinsteel (includingCarbon,Nitrogen,Phosphorus,Sulphur 

and Silicon) can cause temper embrittlement, thereby decreasing 

notch toughness during the cooling of quenched and tempered steel. 

Desirable notch toughness (Charpy) and Crack Tip Opening 

Displacement (CTOD) test results are not always achieved at the 

fabrication yard. Inspection of the welded joint root, weld 

material and the heat-affected zone (HAZ) may show degradation of 

root toughness, sometimesextending into the parent material beyond 

the HAZ. 

Studies carried out by Soyak et al (Reference 3.1) to assess 

fracture behavior in alowtoughness HAZ indicatedthat a small lowtoughness 

area in the HAZcan be masked by the higher-toughnessarea 

surrounding it. Thus, Soyak et al recommend requiring testing of 

3-3 

..— .——.

not three but five Charpy specimens from the low-toughness HAZ 

region to more accurately predict brittle fracture. 

On the other hand, crack-toughness levels implied in the impact 

tests required in design guidelines may be overly conservative. 

Pense’s work (Reference 3.2) indicates that the ship hull strain 

rates during crack initiation,propagationand arrest are lower than 

those estimated, confirming higher levels of crack-toughness. 

Fabrication Specificationsand Procedures 

Degradation of root toughness extending into the parent material 

beyond the HAZ can be caused by procedures used in the fabrication 

yard. Loosely specified fabrication tolerances often result in 

fabrication and assembly distortions and may cause strain aging 

embrittlement. Unnecessarily tight tolerances could result in 

repair work that might contribute to degradation of material. 

Fabrication procedures contribute to the pattern of local weldment 

defect distribution, residual stress pattern in the HAZ, and 

material properties. Since these factors in turn directly affect 

crack growth, fabrication procedures should be carefully developed 

for each design. 

3.1.2 

Fabrication and Post-FabricationParameters 

Activities in the shipyard or fabricationyard directly impact the 

fabricatedmarine structure. These activitiescan be categorizedas 

either fabrication or post-fabricationparameters (Figure3-3). 

Fabrication Parameters 

The primary fabrication parameters can be defined by the questions 

who, what, when and how. Each of these parameters affects the 

fabricationquality, in terms of residualstresses,defects,repairs 

and post fabrication processes. These variables, which determine 

3-4

the general quality of fabrication, also affect specifics such as 

the rate of crack growth and corrosion. 

The four primary fabrication parameters are: 

● 

Who is Doinq the Work? (i.e. personnel qualificat 

on) 

● 

What are the Work Requirements? (i.e.,defining th( 

program 

● 

When is the Work Done? (i.e., sequence/timingof activity) 

● 

How is the Work Done? (i.e., following the specifications) 

Post-FabricationParameters 

Both the design parameters and fabrication parameters directly 

affect fatigue performance of a fabricated component, thereby 

influencing the post-fabrication processes. The post-fabrication 

processes discussed here are activities that enhance the fatigue 

performance of the structure component. 

The toe of the weld and the weld root often contain geometric 

imperfections and high localized stresses and therefore they are 

often the site of fatigue crack propagation. To enhance fatigue 

performance,modificationof both the weld geometry and the residual 

stress is recommended. The weld geometry can be improved by weld 

toe grinding,which is often specifiedto obtain a smooth transition 

from weld to the parent material. This process should improve 

fatigue life locally both by removing small defects left at the toe 

during welding and by reducing the stress concentrationat the weld 

toe due to elimination of any notches. Weld toe remelting (by TIG 

or plasma dressing) and the use of special electrodes for the final 

pass at the toe can also improve fatigue performance. 

Post-weld heat treatment (PWHT) is recommended to relieve residual 

stresses introducedin welding thick sections,typically defined as 

having a wall thickness in excess of 2.5 in (63 mm) in U.S. (less 

3-5

elsewhere). Both thermal stress relief and weld material straining 

to set up desirable compressive stresses at the weld toe are used. 

Typically, a node subjected to PWHT experiences both stress and 

strain relief and should exhibit improved fatigue performance. 

However, the efficiency of PWHT needs further verification. Some 

experts in the field consider it difficult to justify any 

improvement of fatigue performance as a result of stress relief. 

Corrosionprotection is necessaryto ensure as-designedperformance 

of the structure, including achieving the desired fatigue life. 

Post fabrication work on corrosion protection systems varies from 

installation of anodes for cathodic protection to coating and 

painting. 

3.1.3 In-Service Parameters 

The environment in which fatigue cracks initiate and grow 

substantially affects fatigue life. The environment affects 

corrosionand crack growth due to both the nature of the environment 

(i.e., sea water properties, including conductivity, salinity, 

dissolved oxygen, pH and temperature) and the magnitude and 

frequency of the applied loading (i.e., wind, wave and current 

characteristics). 

Environmental loads that cause reversal of stress on a marine 

structure component are primarily caused by wave and wind 

action. While the loading directionality and distribution is often 

carefully accounted for, the sequence of loading usually is not. 

The other in-serviceparametersreflect inspection,maintenance and 

repair philosophy and have a major influence on corrosion and the 

rate of crack growth. The in-serviceparameters are summarized on 

Figure 3-4. 

3-6

3.2 REVIEW OF FATIGUE ANALYSIS PARAMETERS 

3.2.1 Fatique Analysis Criteria 

Fatigue analysis criteria for marine structures are developed in 

conjunctionwith the overall design criteria. The structure type, 

environmentalconditionsand the scope of the overall design effort 

all affect the fatigue analysis criteria. A fatigue life that is 

twice as long as the structure’sdesign life is routinely specified 

to ensure satisfactory fatigue performance. Larger safety factors 

are often used for critical components where inspection and/or 

repairs are difficult. 

For many marine structures the use of a probabilistic fatigue 

analysis, based on a probabilistic simulation of applied forces, 

residual stresses, defects and imperfections, crack growth and 

failure, appears to be desirable. This true probabilistic method 

may be considered an emerging technology and the time and cost 

constraints often require alternative methods to develop a design 

that meets the fatigue criteria. 

Although the following sections refer to both “deterministic”and 

“probabilistic”fatigue methods, essentially the discussions cover 

deterministicmethods. The probabilisticmethodsdefined only refer 

to probabilistictreatment of the ocean environment. 

3.2.2 Interacting Parameters 

Fatiguedesign and analysis is carriedout in conjunctionwith other 

activities that ensure proper design of the structure to meet all 

pre-service and in-service loading conditions. The structure and 

its component members must have sufficient strength to resist the 

extreme loads for a range of conditions, and these conditions are 

often interdependent. 

The design is an iterative process in which the general 

configuration gradually evolves. Thus, the fatigue design and 

3-7

-- 

analysis process is often initiated after the initial structure 

configuration has been defined, but while its components are still 

being designed and modified. 

3.2.3 

Stress Model Parameters 

A generalized stress model representsall of the steps necessary to 

define the local stress ranges throughout the structure due to the 

structure’s global response to excitation loads. These parameters 

are as follows: 

Motions [Hydrodynamics)Model 

Amotions (hydrodynamics)model includesvariousmodels necessaryto 

determine the applied excitation forces, response of the structure 

to these forces, and the resultant loads on the system. The choice 

of a model primarilydepends on the structureconfiguration. While 

a continuous finite element model may be used for ship-shaped 

structuresor semisubmersibleswith orthotropicallystiffenedplate 

system (i.e. continuoussystems),a discrete space frame consisting 

of strut members are typically used for the analyses of an offshore 

platform. 

Floating structures,whether ship-shaped,twin-hulledor of another 

configuration,may requirethe use of diffractionanalysesto define 

the hydrodynamiccoefficients. Diffractionpressuresgenerated are 

transformed intomember wave loadswhile the radiationpressuresare 

transformedintoaddedmass and dampingcoefficients. This approach 

is valid to obtain hydrodynamic coefficients for non-conventional 

geometries,the motion analysisutilizinghydrodynamiccoefficients 

does account for the effects of member interaction and radiation 

damping components. 

Bottom-supportedstructuresare generallymade up of small-diameter 

tubulars, and their drag and inertia coefficients can be defined 

based on previous analytical and model basin work on tubulars. 

However, some componentsare frequency-dependentfor arange ofwave 

3-8

frequencies of interest, requiring definition of frequency 

dependency. 

Thus, some of the more importantparameters to be considered in the 

development of a hydrodynamicsmodel are: 

● 

Structureconfiguration(continuousversus discrete systems). 

● 

Structure size and irregularityof shape. 

● 

Structure component member dimensions (with respect to both 

the structure and the wave length). 

● 

Component member arrangement (distancefrom each other). 

● 

Component 

coefficients. 

member shape, affecting its hydrodynamic 

Analysis Techniques 

Analysis techniques, or the approaches used to generate and apply 

environmental loads, fall into two categories: deterministic 

analysis and spectral analysis. Deterministicanalysis is based on 

the use of wave exceedance curves to define the wave occurrences. 

Spectral analysis (alsoreferredtoas probabilisticanalysis of the 

ocean environment only) is based on the use of wave spectra to 

properly account for the actual distribution of energy over the 

entire frequency range. 

The five approaches can be defined in these two categories: 

● 

Selected Wave[s) - Determinist-it 

Aclosed-form deterministicanalysisprocedure recommendedby 

Williams and Rinne (Reference 3.3) is often used as a 

screening process. This approach may be considered a 

marginally acceptable first step in carrying out a fatigue 

3-9

analysis of a fixed platform. As discussed in Section 3.2.4 

under Stress History Parameters, wave scatter diagrams are 

used to develop wave height exceedance curves in each wave 

direction and used to obtain the stress exceedance curves. 

Consideringboth the effort needed and the questionablelevel 

of accuracy of selecting wave heights to represent a wide 

range of wave heights and periods, it may be better to 

initiate a spectral fatigue analysis directly. 

● 

Reqular Waves in Time Domain - Spectral 

Because a spectralfatigueanalysis is carriedout to properly 

account for the actual distribution of wave energy over the 

entire frequency range, a sufficient number of time domain 

solutions is required to define the stress ranges for 

sufficientpairs of wave heightsand frequencies. A resultof 

this procedure is development of another characteristic 

element of spectral fatigue analysis, namely, the stress 

transfer functions, or response amplitude operators (RAOS). 

For each wave period in the transfer function, a sinusoidal 

wave is propagated past the structure and a wave load time 

history is generated. The equations of motion (structure 

response) are solved to obtain a steady state response. A 

point on the transfer functionat the wave period is the ratio 

of the responseamplitudeto the wave ampl” tude. A sufficient 

number of frequencies is required to incorporate the 

characteristicpeaks and valleys. 

● 

Random Waves in Time Domain - Spectral 

The use of randomwaves avoidsthe necessityof selectingwave 

heights and frequencies associated with the regular wave 

analysis. 

3-1o

● 

Reqular Waves in FrecjuencvDomain - Spectral 

This method, based on the use of regular waves in the 

frequency domain, requires linearization of wave loading. 

Approximatingthe wave loadingby sinusoidallyvaryingforces, 

and assuming a constant sea surface elevationdoes contribute 

to some inaccuracies. However, these approximations also 

allow equationsof motion to be solvedwithout having to carry 

out direct time integration, thereby greatly facilitating 

fatigue analysis work. 

The approach chosen should depend on the structure type and 

the environment. For most “rigid body” inertially driven 

floating structures, frequency-domain spectral fatigue 

analysis is recommended. However, for tethered structures 

such as a TLP, and for structures in areas where large waves 

contribute substantially to cumulative fatigue damage, the 

effects of linearizationand inundation are substantial. In 

these cases the preferredapproachmaybe time-domainspectral 

fatigue analysis. Even time-domain solutions at several 

frequencies may be sufficient to compare the RAOS obtained 

from a frequency-domain solution and to calibrate them as 

necessary. 

● 

Wind Gust - Spectral 

Most marine structures are designed to resist extreme wind 

loadings,but they are rarely susceptibletocyclic wind gusts 

that cause fatigue damage. Some structures, such as flare 

towers or radio towers, support negligible equipment and 

weights; as a result, they are often made up of light and 

slender members, making them susceptible to wind-caused 

fatigue damage. 

As with analysisof the wave environment,structuressubjected 

to wind turbulencecan be analyzed by quantifyingcyclic wind 

forces and their associated frequencies. The total applied 

3-11

wind loading on a structure is due to mean and cyclic 

components. The loads are computed and statically applied on 

the structureand then convertedto harmonicloads for dynamic 

analysis. 

The stresses obtained at each frequency are unitized by 

dividing them by the corresponding cyclic wind speeds. 

Application of wind spectra to define the occurrence of wind 

speeds and gust spectra to define the energy content of the 

gust on unitized stress ranges yields the stress spectrum. 

Further discussionwind loading is provided in Sections 6 and 

Appendix D. 

Structural Analysis Model 

A floating structure is by definition in equilibrium. The applied 

loads and inertial response from the motions analysis provide a 

balance of forces and moments for the six degree of freedom system. 

To obtain a stiffness solution,the structuremodel may be provided 

with hypothetical supports. A typical solution should yield close 

to zero loads at those hypothetical supports. The deformations 

obtained from stiffness analysis at member joints are transformed 

into stresses. 

A single- or a dual-hulled structure is a continuous system with 

large stiffenedmembers/components. Applied loads on the structure 

necessitatedeterminationof hullgirder bendingmoments in vertical 

and horizontal axes and local internal and external pressure 

effects. The use of beam elements may be appropriate when local 

pressureeffects are small and stressdistributionpatterns arewell 

understood. Since the local pressure effects are substantial for 

ship structuresand the local stressdistributionsrapidlychange as 

a function of several parameters, a finite element analysis is the 

generally recommended approach to determine the local stress 

distributions. 

3-12

The finite element models of increasing mesh refinement are often 

used to obtain accurate stress range data locally in fatigue 

sensitive areas. Thus, an overall coarse mesh model of the 

structure used in the first stage of analyses is modified by 

increasingmesh refinement in various fatigue sensitive areas. The 

finite element models are typically built from membrane plate 

elements,bendingplate elements,bar elementsand beam elementsand 

further discussed in Section 5. 

Because the individual joints and members define the global 

structure, the boundary conditions should also reflect the true 

response of the structure when subjected to the excitation 

loads. For a bottom-supported structure, individual piles can be 

simulated by individual springs. Whatever the support 

characteristics,a foundationmatrix can be developed to represent 

the foundation-structureinterface at the seafloor. It should be 

noted that the foundation matrix developed for an extreme 

environmentwould be too flexible for a milder fatigue environment. 

Thus, the foundationmatrix developed should be compatiblewith the 

applicable load range. 

Stress Response Amplitude Operators (RAOS) 

The stress RAOS or stress transfer functions are obtained by 

unitizing the stress ranges. If the wave height specified is other 

than the unit wave height (doubleamplitude of 2 feet or 2 meters), 

stress ranges at each frequency are divided by the wave heights 

input to generate the loads. Similarly, wind loads computed based 

on cyclic wind velocities at each frequency are divided by the 

respective velocities to obtain the unitized stress ranges. 

Stress Concentration Factors [SCF] and Hot Spot Stresses 

The stresses obtained from a stiffness analysis, and the RAOS 

generated,representnominalor averagestresses. However,the load 

path and the detailing of orthotropically stiffened plate or an 

intersection of tubular members will exhibit hot-spot or peak 

3’13 

/ Ii7 

-/

stresses several times greater than the nominal stresses. The 

fatigue test results for a wide variety of shiphull stiffener 

geometries can be used directly with the nominal stresses. 

At an intersectionof a tubular brace and chord, depending on the 

interfacegeometry,the maximum hot-spotstressesoften occur either 

on the weld toe of the incoming brace member or on the main chord. 

The ratio of the hot-spot stress to the nominal stress is defined as 

the stress concentrationfactor (SCF). 

SCF =U.aX/Un 

The SCF value is probably the most important single variable that 

affects the fatigue life of a detail/joint,necessitating accurate 

determination of SCFS. 

There are several practical approaches for determining SCF values. 

The first approach is to develop an analytical model of the 

detail/joint and carry out a finite element analysis (FEA). When 

modeled correctly, determination of SCFS by FEA is a very reliable 

approach. The second approach is to test a physical model and 

obtain the hot-spot stresses from measurements. Whether a straingauged 

acrylicmodel or other alternativesare used, the accuracyof 

hot-spotstresseslargelydependson the abilityto predict hot-spot 

stress locations and obtain measurements in those areas. 

Although reliable and recommended for obtaining SCFS, these two 

methods are time consuming and expensive. Thus, a third approach, 

based on applying empirical formulations to determine SCFS, has 

been extensively accepted for fatigue analysis of marine 

structures. A set of empirical formulae developed by Kuang 

(Reference 3.4) were derived by evaluating extensive thin-shell 

finite element analyses results. The formulae proposed by Smedley 

(Reference 3.5) and Wordsworth (Reference3.6) of Lloyds Register 

were derived from evaluating the results of strain-gauged acrylic 

models. 

3-14

The stressmodel parametersdiscussedabove are summarizedon Figure 

3-5. A summary of empirical equations, parametric study results 

obtained by using applicable empirical equations for T, K and X 

joints, and an illustrative finite element analyses results for a 

complex joint are presented in Appendix C. 

3.2.4 Stress History Model Parameters 

The wave scatterdiagram and wave directionalitydata are necessary 

whether a deterministic or a spectral analysis technique is used. 

In a deterministicanalysiswave exceedance curves are generated in 

each wave direction and used with the hot-spot stresses to obtain 

the stress exceedance curves. 

For a spectral fatigue analysis, a scatter diagram and the 

directional probability is used with wave or wind spectrato obtain 

the stress spectrum from hot-spot stresses. These parameters are 

summarized on Figure 3-6. Stress History Models are discussed 

further in Section 6. 

3.2.5 FaticiueDamaqe Comtmtation Parameters 

Many parameters affect the fatigue life computation. Some, such as 

stress sequence, maintenance and repairs, lapses in corrosion 

protection, etc., are not accounted for in fatigue damage 

computation. Fatiguedamage is characterizedby an accumulationof 

damage due to cyclic loading, with fatigue failure occurring when 

the accumulateddamage reaches the critical level. To evaluate the 

damage, the stress-time history is broken into cycles from which a 

distribution of stress ranges is obtained. The variable-amplitude 

stress range distribution is divided into constant-amplitudestress 

range blocks, Sri, to allow the use of constant-amplitude S-N 

curves. 

3-15

Selection of S-N Curve 

The S-N curve defines the relationship between a constant-stress 

amplitude block and the number of cycles necessary to cause the 

failure of a given detail/joint. Such S-N curves are largely 

derived by testingmodels ofsimplifieddetail/joint componentswith 

subjecting constant amplitude stress reversals in a laboratory 

environment. The laboratoryenvironmentis substantiallydifferent 

from the typical marine environment.Similarly, the laboratory 

models are idealized while actual marine structure details/joints 

incorporate fabrication residual stresses and substantial welding 

defects. 

The S-N curve defining a particular type of detail/joint and 

material properties is derived by obtaining the mean of the test 

data and then defining the mean minus two standarddeviations. S-N 

curveswere firstdevelopedfor fillet-weldedplate details and some 

small scale-tests on tubular joints. Later tests provided data on 

more complexdetails and thickerplate sections. The S-N curves for 

continuous system details (i.e., ship hull stiffening) are 

typically reduced by the ratio of hot spot-to-nominalstresses and 

can be used directly with shiphull nominal stresses to determine 

fatiguedamage. The S-N curves for discrete systemjoints represent 

the failure stresses and necessitate multiplication of nominal 

stresses by SCFS to obtain hot spot stresses. 

The choice of an applicable S-N curve depends not only on the 

material, configuration of the detail/joint and the fabrication 

effects (residualstresses,weld profile,defects,etc.) but also on 

the service condition of the structure. The original 

U.K. Departmentof Energy (DEn)recommendedQ-curve, based on simple 

thin plate details, has been replaced by a T-curve (Reference1.6). 

The American Petroleum Institute (API) recommended X-curve 

(Reference 1.5) is applicable to a welded profile that merges with 

the adjoining base material smoothly. If the weld profile is not 

smooth, then a lower X’-curve is applicable. 

3-16

While API S-N curves are applicableto stationarymarine structures, 

other S-N curves by DEn and Det norske Veritas (DnV - Ref. 1.7) may 

be equally applicableto stationaryand mobile vessels with tubular 

and orthogonally stiffened plate construction. The preferred S-N 

curve should be defined in the design criteria. Typical S-N curves 

applicableformarine structuresare illustratedon Figure3-7. S-N 

curves are discussed further in Section 5. 

Cumulative Damacle 

The calculation of cumulative damage is typically performed using 

the Palmgren-Minerdamage rule. In this approach fatigue damage is 

calculated by dividing stress range distribution into constant 

amplitude stress range blocks, assuming that the damage per load 

cycle is constant at a given stress range and equal to: 

Dti = l/N 

where, 

Dtiis the damage, and 

N is the constant-amplitudenumber of cycles to 

given stress range. 

failure at a 

Another key assumption of the Palmgren-Miner damage rule is that 

damage is independent of order in which loads are applied. 

Accordingly, for the case of a stress history with multiple stress 

blocks, Sti,each block having n cycles, the cumulative damage is 

defined by: 

This is the Miner-Palmgren formula, where: 

3-17

D is the cumulative damage, 

k is the number of stress blocks, 

n is the number of stress cycles in stress block i with 

constant stress range, and 

N is the number of cycles to failure at constant stress range. 

Although the linear Palmgren-Minerdamage rule is extensively used, 

the significance of constant-amplitudeloading and the sequence of 

loading (i.e.,large stress blocks during the beginning rather than 

toward the end of design life) may be important to correct 

assessmentof fatigue damage. This subject is discussed further in 

Section 7. 

Fatique Life Evaluation 

Fatiguedamage and fatigue life should redetermined at all critical 

hot-spot stress areas. While one or two areas may be targeted on a 

plate and stiffenerinterface,at least eight points are recommended 

on a tubularmember. If eight points, spaced at45 degree intervals 

around the circumference, are chosen, relatively accurate hot-spot 

stresses and fatigue damage data will be obtained. Typically, 

fatigue damage (D) is calculated on an annual basis. The fatigue 

life (L) is then determinedby taking the inverseof the accumulated 

damage ratio (D). 

3-18

DESIGN 

Osn40H rAnNsirsR8 FAMcA~ M POST-F~ATW MRA~ 

PRIMARY AFFECT 

SHsRusX 

PRIMARY AFFECT uA-FuRtA PRIMAR7 EFFECT 

AFFECT 

PARA~ 

~=~t~v:.Y 

-==’’” 

WEICSR cwuncmm 

ROBWOI 

Stroamca 

ENMRWMENT 

● * 

FAEIRiCATtW TCUfSANIXS 

7 

. Wa$h Z.me 

DActn 

FAMHXSW4 I%roarm ● k WOtw 

and 

FABRICAllON SEWENCE WALIN Repski Mate of 

AND TIME {1.mpwaturo) 

&OcA Growth 

ENMRWA4ENT#L LWCW3 

PaJt- 

RATE ff HEAT iNPtJl # T**, A7$Otudo CrJrc.dm 

Fobrkatlm — 

AND CK!JJNG Moon LOW+ of Str.as and 

PrOc*u*m 

● OkOcUmd F7c4cbtnty Ratad 

and Oll$rktkm 

CmKA Growth 

● Str+uhg Squa~ 

===J-E=i=2:a* 

lNsPEcnot4 

MAINIIk+ANCE 

-:=%s: - 

WO 

REPA!R 

WALYSIS 

Os’tsss PAmMiTsRo 

~–––––______T ‘ 

I 

I 

t 

/ 

![ 

I 

I 

I 

I 

I 

FAllWE AN#lYSAS 

~lERIA 

IN-SSRMCE 

SPREADING 

STRSNGIH FtEOUIREWNIS 

~ _ _ ‘__“?_!! ‘_- WRSMldSTW4Y MWSL P~ FAT@3LR OAMMM C0WUTA7SON ?~ 

; ~.––. –_____T ~_––____7 

MOnWS -l 

II ----- 

[LOAb uwn] II I 

I 

--—._ 

[ P:=-’=E] 

SIRUS’SURA 1[ 

I I 

ANMWAS 

It 

Mwm 

I I ANAll?4S lEC%tNICUES tJ_- SCASIER 

● Oefrxma!kma 

WAGRAM 

I [ ●sh~&.3wa:i 

● Str-scc I i 

lNllAl 

● 

I I 

Rqutor ~, h 

I I FAAK 

smucnmAL lim*-Oanah, +=cIroI 

OIRECTIONAUTY . 

● Rqulor Wwn h 

i 

I 

cm FlaJRAnm rmqum@lw161,~d 1 -r WND 

I “:::%% ‘&m, 

SI?3ESS HOT SPOT 

I 

.Mnd 13Joi, %cclrd 

WAVE 

RAOm 

STRESSES 

II 

I 

IT 

J 

II 

I 

11 

I 

II 

~ I EMP=~ 

IJ 

Smss 

cmcwmmwm 

ANAL71tCAL F.E,A. r~ 

(w,) 

II 

II 

II 

II 

II 

EKaEIANCE 

II 

II 

‘1 I 

II 

CURWE 

II 

{Oyrmruc 

I 

FAllOUE 

STRESS II S-H 

I 

OWA~ 

WAW m WC MsTmr 

Cunuz 

I 

CC#APUTATtSW 

SPECTffA 11— I 

(Spmtrd 

Wl@a) II I 

II 

TrPIC#lLY 

LINACCCAINTEOPARAMETERS 

I I ;!$i%!l!ii%pr.t=llm I 

II II I 

~___________J &:-:=________J L___________I l_–___–. __J 

II 

II 

I 

I 

I 

I 

I 

I 

Figure 

3-1 FATIGUE DESIGN AND ANALYSIS PARAMETERS

Primarily Affect ---------+ 

r 

I 

GLOBAL 

CONFIGURATION 

,[ 

● Applied Forces 

* Structure Response 

● Structure Redundancy 

# 

* $tre$s Levels 

COMPONENT CHARACTERISTIC . * Stress Concentration 

AND STRUCTURAL DETAILS 

● Access, Workmanship and and Details 

MATERIAL SELECTION 

J 

* Chemical Composition 

and Weldability 

* Mechanical Properties 

and HAZ 

1* Corrosion Fatigue Behavior 

r 

4 

* Local Deformations and 

FABRICATION PROCEDURE 4 Residual Stress Pattern 

AND SPECIFICATIONS 

* Defect Distribution and 

< < 

Initial Rate of Growth 

Figure 3-2 Design Parameters

Primarily Affect .--------+’ & In-turn Affect --------~ 

WELDER QUALIFICATION 

t 

IFABRICATION TOLERANCES~ 

IFABRICATION SEQUENCE ~ 

AND TIME (Temperature) 

FABRICATION 

QUALITY 

Residual Stresse: 

Defects 

Repairs 

t 4 

Post-Fabrication 

IRATE OF HEAT INPUT ~ 

Processes 

IAND COOLING I b 1 

c 

o 

R 

R 

o 

s 

I 

o 

N 

& 

c 

R 

A 

c 

K 

G 

R 

o 

w 

T 

H 

WELD TOE GRINDING 

POST- 

,.., 

IPWHT FOR STRESS RELIEF 

FABRICATION 

4 

CORROSION PROTECTION 

PROCESSES 

Figure 3-3 Fabricationand Post-FabricationParameters

Primarily Affect .~:--------+. 

ENVIRONMENT 

* Air 

* Splash Zone 

* Sea Water 

ENVIRONMENTAL LOADING 

* Type, Amplitude and 

Mean Level of Stress 

* Directional Probability 

and Distribution 

* Stressing Sequence 

i 

Corrosion 

and 

Rate of 

Crack Growth 

INSPECTION 

MAINTENANCE 

— 

REPAIR 

Figure 3-4 In-Service Parameters

MOTIONS MODEL 

— .—. ● ;LOADS MODEL ~ 

I 

iMASS MODEL~ 

ANALYSIS TECHNIQUES 

● 

Single Wave-Deterministic 

* Regular Waves In Time-Domain 

Spectral 

I 

* 

* 

STRUCTURAL 

ANALYSIS 

MODEL 

Deformations 

Stresses 

* Random Waves In Time-Domain 

Spectral 

● 

Regular Waves In Frequency-Oomairn 

Spectral 

* Wind Gust-Spectral 

I 

STRESS 

RAos 

I * Finite Element Analysis (FEA)I STRESS 

t I I 

* Testing-Strain Gauge I 

m 

i 

HOT 

SPOT 

STRESSES 

t 

CONCENTRATION 1 

.— 

* Empirical Formulations FACTORS 

(SCF) 

Figure 3-5 

Stress Model Parameters 

5’-7 

- ,“

SCAITER 

DIAGRAM 

Y 

WAVE 

DIRECTIONALIIV 

EXCEEOANCE 

- - 

CURVE 

(Oetenninistic 

Analysis) 

STRESS 

HISTORY 

J 

WIND 

WAVE OR WIND 

WAVE 4 SPECTRA 

(Spectral 

SPREADING 

4 

Analysis) 

Figure 3-6 Time History Model Parameters

loa 

1 

10 

-— 

— 

— 

-t-i-nT 

1[ 

-t 

_~ _ 

—_ 

t 

— .- . J . . . -,- 

. . — — . . . 

— 

4 

1 j~l I@ 

Endurume(cycles) 

Figure 3-7 Typical S-N Curves

,,- ... , . . . . . . . . . . . :.:- .-, .....==— 

.: 

(THIS PAGE INTENTIONALLY LEFT BLANK)

4. GLOBAL REVIEW OF FATIGUE 

4.1 APPLICABLE ANALYSIS METHODS 


Analysis and design of marine structures in the past often did not 

include explicit treatment of fatigue. With the installation of 

offshore platforms in deeper water increasedemphasis was placed in 

fatigue design. An experience-based allowable stress methods 

developed were soon complementedwith detailed analyses methods. 

Ship structure design often did not incorporate explicit treatment 

of fatigue through analysis. However, with the increasing use of 

higher strength steels, the cyclic stress ranges also increased, 

necessitating fatigue analysis of more structures. Although the 

allowable stress methods developed are used in the design of 

majority of ship structures, more and more of the new designs 

incorporatedetailed analysis methods. 

Several methods may be applicable and acceptable for the fatigue 

analysis and design of a marine structure. The most suitablemethod 

depends on many parameters, including structure configuration 

(shape, redundancy, details/joints, etc.), fatigue envir[ nment, 

operational characteristics/constraints, and the design 

requirements. The complexity and cost of this analysis and design 

effort should be compatible with available design informat” on and 

the desired degree of accuracy of the analysis and design. 

The design and analysisparametersdiscussed in Sections 3.1 and3.2 

are summarizedon Figure3-1. The four dotted-line boxes around the 

analysis parameters illustrate a typical analysis sequence. 

Although the methods used in obtaining the hot-spot stress (stress 

model), stress spectrum (stresshistorymodel), and the fatigue life 

may differ, the general sequence shown is usually followed. A 

different sequence is applicable for a simplified analysis and 

design method. An allowable stress approach is one such example. 

4-1

The different methods and their applicationsequences are discussed 

in the following sections. 

4.1.2 

Simplified Analysis and DesictnMethods 

The simplified analysis and design methods applicable to ship 

structures and offshore structures are based largely on both 

theoretical knowledge and past experience and account for the 

environmentlikely to be encountered. Typically, ship hull girders 

are designed to resist maximum bending moments due to still water 

plus awave-induced conditionderivedfrom harsh North Atlanticwave 

data (Reference 4.1). The basic hull girder, designed for the 

extreme environment loading, is intended to have ample crosssectional 

area and moment of inertiato keep the magnitude of stress 

reversalslow and exhibit low susceptibilityto fatiguedamage. The 

minimum plate and scantling sizes specified and the detailing 

developed are intended to keep the nominal and peak stress ranges 

low to prevent fatigue failures in the secondary members. In 

addition,steel is specifiedto ensurethat its chemical composition 

and mechanical propertieswill make it less susceptible to fatigue 

failure. 

Similarly, offshore platform joints are designed to resist maximum 

punching shear and crushing stresses. The joint details are 

developed to minimize the SCFS and cyclic stress ranges to make them 

less susceptible to fatigue failure. Such an indirect approach to 

fatiguedesign shouldbe supplementedby an empirical approach based 

on constant stress range cycle fatigue life test data. 

ShitIStructures 

An allowable stress method for ship structuredesign should be used 

to assess applied stresses against allowable stresses. The 

objective of applying the method is to identify those conditions 

that requireno furtherfatigue assessmentand those conditionsthat 

require more comprehensive fatigue analyses. 

4-2

An allowable stress method, also considered a screening process, 

relies on both theory and experience. The procedure developed 

should be calibrated against available fatigue failure data and 

typically incorporatesthe following steps: 

1. Computation of wave-induced loads 

2. Determinationof applied stress levels 

3. Determinationof allowable stress levels 

4. Adjustment of allowable stress levels 

5. Assessmentofvariouscomponents/detailsforsusceptibi lityto 

fatigue failure. 

The wave-inducedloads are computedusing simplifiedformulae,where 

the long-storm distribution of fatigue loading is represented by a 

single characteristic value. The vertical bending moment is 

computed as a function of the vessel length, breadth and block 

coefficient along the longitudinal axis. The applied (nominal) 

cyclic stress amplitude is determined by using beam theory and 

dividing the vertical bending moment at any point along the 

longitudinal axis with hull girder section modulus. 

The allowable stresses depend on many variables. For a simplified 

method an allowablestress may be defined as a function of location 

(deck, side shell, etc.) and detai1 geometry (1ocal stress factor). 

Typically, such a method is based on a 20-year service life, 

standard corrosioneffects and a nominal geographic area. Thus if 

specific service life or routing information is available, the 

allowable stress levels are adjusted. Two of the of the simplified 

analysis methods are: 

1. ABS’ Al1owable Stress Method 

This allowablestressmethod by Thayamballi (Reference4.2) is 

primarily intended for use in fatigue screening of tankers. 

The simplifiedformulae presentedallow calculationof several 

types of loadingon atanker due to wave-inducedmotions. The 

loading types and their relevancy are: 

4“3

● 

Vertical bending moment - needed to determine stresses 

along the longitudinal axis 

● 

Internal tank load - needed to determile stresses at 

tank boundaries 

● 

Externalpressureload- needed todeterm” ne stressesat 

outer hull 

Each of these component loads are applied to the structure 

independentof one another. The method implementsbeam theory 

to obtain nominalstresses,except for special caseswhere ABS 

Steel Vessel Rules require special consideration. ABS Rules 

requiring structural analysis also provide substantial 

flexibilityfor engineeringjudgement. The fatigue sensitive 

areas of the deck, tanks and the hull shell, where the 

stresses are to be determined, are illustratedon Figure 4-1. 

Although the method is intended to provide allowable stress 

levels for normal operating routes, the allowable stress 

levels can be adjusted. Thus, a vessel operating in harsh 

geographic regions can still be screened for fatigue by 

reducing the allowable stress levels as function of the 

severity of the environment. The structural components of a 

vessel having stress levels meeting the reduced allowable 

stress levels may not require a detailed fatigue analysis. 

2. Munse’s Method 

This allowable stress method for determining ship hull 

performance by Munse et al (Reference 4.3) is a practical 

method of designing ship hull structural details for fatigue 

loading. 

The method is considered reliable, as it is based on a study 

of measured fatigue failure (S-N curves) data for 69 

structuraldetails. The design method also incorporatesthe 

4-4

esults of work covering assessment of 634 structural 

configurations (fromReferences4.4 and 4.5). It establishes 

the basis for selecting and evaluating ship details and 

developing a ship details design procedure. This method 

accounts for three of the most important parameters that 

affect fatigue life of a ship detail: 

● 

Mean fatigue resistance of local fatigue details (S-N 

curve) 

● 

Applicationof a ’’reliability”factorto accountforS-N 

data scatter and slope 

● 

Applicationofa “randomload” factorto account for the 

projected stress history 

Munse’s design method can also be used to estimate fatigue 

life based on actual or assumed stress history and a 

reliability factor. A study carried out at the American 

Bureau of Shipping (ABS) (Reference4.6) to evaluate fatigue 

life predictionsutilizedseveralmethods, includingMunse’s. 

The study, based on stress histories derived from strain 

measurements of containership hatch-corners, provided good 

comparative results. Although Munse’s method neglects the 

effect of mean stress, the fatigue lives computed compared 

well with lives that are computed using other methods. 

Munse’s design method is an acceptable fatigue design 

procedure for all vessels. This design method allows proper 

selectionof design details and providesfor design of a costeffective 

vessel appropriate for the long term environmental 

loadings. Vessels that are considered non-standard due to 

their configuration and/or function (such as a tanker with 

internal turret mooring or a drillship) should be further 

analyzed, including a thorough spectral fatigue analysis. 

Munse’s design procedureis suimnarizedin the block diagramon 

Figure 4-2. 

4-5

Offshore structures such as a semisubmersibledrilling vessel is a 

continuous system,typicallyhaving orthogonallystiffenedmembers. 

While a simplified method, such as Munse’s, may be an applicable 

screening method, such structures have very specialized 

configurations, response characteristics and structural details. 

Thus, each structure should be considered unique, requiring a 

detailed fatigue analyses. 

An offshore platform is made up discrete members and joints. Since 

each structure is unique, a detailed fatigue analysis is 

recommended. However, asimplified method may beappl icable if such 

a method can be developed based on a large number of similar 

structures in a given geographic region. Such a method was 

developed for the Gulf of Mexico by American Petroleum Institute 

(Reference 1.5) and discussed further. 

The simplifiedAPI method (Section5.1.1 of Reference 1.5) is based 

on defining the allowable peak stresses as a function of water 

depth, design fatigue life, member location and the applicable S-N 

curve. Although the approach can be modified to apply to other 

geographic areas, it was developed by calibrating previously 

completed fatigue analyses of fixed offshore platforms. The 

maximum allowable stress method is applicable to typical Gulf of 

Mexico platforms with structural redundancy, natural periods less 

than three seconds, and the water depths of 400 feet or less. 

ThisAPI allowablestressmethod i$ intendedfor use as a simplified 

fatigue assessmentprocedurefor Gulf of Mexico platforms subjected 

to long-term cyclic stresses considered small relative to the 

extreme environment stresses. The method attempts to predict 

fatigue behavior as a function of the design wave event for a 

generalized platform. It should be noted that the applied force 

levels can vary substantiallywith platform geometry. The relative 

importanceof extremedesignwaves and operatingenvironment fatigue 

waves changes with both the water depth and the actual member/joint 

4-6

location. Thus, the method should be used with caution. Detailed 

discussionon this method and thecal ibrationeffort is presentedby 

Luyties and Geyer (Reference4.7). 

4.1.3 

Detailed Analyses and Desicm Methods 

The detailed analyses and design methods applicable to ship 

structures and offshoremarine structuresgenerally follow the same 

analyses sequence and incorporate the variables associated with 

strength model, time history model and damage computation. The 

differencesamongthe various types of detailed analyses are largely 

in the methodology implemented to obtain hot-spot stresses, to 

develop the stress spectrum and to compute the fatigue life. 

Adetailed fatigueanalysis is reconmnendedfor all marine structures 

susceptibleto fatiguefailure. While simplifieddesignmethods are 

valid in determining the viability of structural details/joints of 

typical ships/tankersbuilt from mild steelor offshore platforms in 

shallow waters of Gulf of Mexico, a detailed fatigue analysis is 

often necessary for other structures. Projected fatigue lives of 

a marine structure subjected to cyclic stresses should then be 

determined at all critical areas. The uncertainties in fatigue 

design and analysisparameters require that more emphasis be placed 

on the relative fatigue lives computed than on the absolute lives 

obtained. As a result, fatigue analysis is considered to be a 

systematic process to identify details/joints susceptible to 

failure, and to modify those susceptible areas to yield fatigue 

lives substantiallyin excess of the design life. The following are 

some detailed analysesoptions that apply to ship structures and to 

fixed and mobile marine structures. 

Ship Structures 

A ship that fails to meet simplified fatigue analysis requirements 

will not necessarilyhave fatigue failures. It only implies that a 

more detailed fatigue analysis is required. Typically, detailed 

4-7

analysis is likely to be requiredwhen one or more 

are applicable: 

of the following 

● 

The ship structure configuration has unique 

characteristics. 

● 

The structure is built from high strength steel. 

● 

The use of high strength steel allowed reduction of scantling 

sizes basedon strengthrequirementsand due considerationfor 

fatigue phenomenawas not given. 

● 

The operational routes for the vessel are more severe than 

typical,making the structuralcomponentsmore susceptibleto 


The detailed fatigue analysis sequence for ship structures is 

similar to fatigue analysesof other marine structures and includes 

all of the analyses parameters shown on Figure 3-1. However, the 

ship geometry,appreciableforwardspeed and the varying operational 

routes require a special effort to determine the ship motions, 

applied loads, stress distribution of loads and the long term 

distribution of fatigue stresses. Typically, a detailed fatigue 

analysis is a spectralfatigue,requiringdeterminationof long term 

fatigue stress distribution for each case, accounting for each 

seastate and the applicableduration for that seastate. 

Although very different from simplified fatigue analyses described 

in Section 4.1.2, when the spectral fatigue analysis approach is 

modified to representthe long term fatiguestress distributionwith 

a shape factor (i.e.Weibull approach), it is sometimes identified 

as a simplified fatigue analyses. 

Some of the characteristicsof a spectral fatigue analysis and an 

alternate Weibull approach are as follows: 

4-8

1. SDectral FaticlueAnalvsis 

Although spectral fatigue analyses for ship structures and 

other often stationary.offshore structures are similar, the 

methods used to determine loads and stresses are different. 

Ashipstructure requiresdeterminationof hull girder bending 

moments in vertical ,and horizontal axes along the entire 

longitudinal axis (i.e., hull length). In addition, local 

internaland external pressure effects need to be determined. 

Most often the appliedwave loads are computed with the useof 

linear ship motion theory for wave crestline positions at 90 

degree phase angle separation (i.e. in-phase and out-of-phase 

componentsof wave). Since the fatigue damage occurs largely 

due to normal operating sea states the use of linear ship 

motion theory is considered appropriatefor large majority of 

spectral fatigue analyses. However, some vessels may have 

unique configurations,move at high speeds or be susceptible 

to extreme loading fatigue damage. For such vessels the 

ability to predict wave nonlinearities and vessel hogging, 

sagging and racking effects accuratelymay become important. 

In such instances a non-linear ship motion theory may be 

preferred over linear ship motion theory. Further discussion 

on the specifics of global and local load determination is 

presented in Section 5. 

The structural analyses needed to convert the in-phase and 

out-of-phasecomponents of the load transfer function varies 

1argely with the character sties of the structure 

configuration. The beam elements used in the structural 

stiffness analyses of a discrete system, such as an offshore 

platform, may be appropriate for standard ship structures 

where other detailed analyses and experience allow reasonably 

accurate estimation of local stress distribution. This 

approachmay be appropriate if loading is largely due to hull 

girder bending moments in vertical and horizontal axis. 

However, secondary girder bending moments due to external 

4-9

dynamic loads on vessel bottom may be appreciable. In 

addition,vesselscontainingcargo such as oilt iron ore etc., 

will have inertial loads on internal tank walls/transverse 

bulkheads. 

The secondary bending, when appreciable, does affect the 

magnitude of local stress distribution. The geometric 

complexities also contribute to the difficulty in estimating 

local stressdistribution. Since the fatigue life estimate is 

function of stress range cubed, the accuracy of fatigue life 

estimate is very much a function of the accuracy of local 

stress distribution. Thus, a finite element analysis is the 

generally reconmnendedapproach to determine the local stress 

distributionsfor continuoussystemsuch as ships and tankers. 

The stress range transfer functions are obtained to define 

response of the ship structure for all sea states covering a 

range of frequencies. Thus, in-phase and out-of-phase loads 

at each frequency and for each wave direction must be 

determined to define the stress range transfer function. In 

practice, the effort can be curtailed. A careful review of 

load transfer functions should allow selection of several 

importantfrequenciesand determinationof stresses for those 

frequencies. 

The number of constant amplitude stress range cycles to reach 

failure is empiricallydefinedas an S-N curve that mayor may 

not includethe effect of localizedstress peaking. Thus, in 

addition to selecting an S-N curve appropriate for the 

structuraldetail and operatingenvironment,the S-N curve and 

the structural analyses should be consistent. The stress 

range histogram developed and the S-N curve selected for the 

location allows determination of fatigue damage per year and 

fatigue life by using Miner’s linear cumulative damage rule. 

4-1o

2. Weibull AtIDroach 

The Weibull shape factor is a stress range distribution 

parameter. The Weibull shape factor used with the 

characteristicstress range allows carrying out of a fatigue 

analyses with a relatively 

Since the Weibull approach 

few structural analysis cases. 

differs from detailed spectral 

fatigueanalysisonly in how the stressrange is obtained,the 

accuracyof fatigue lives obtainedwith this approach largely 

depends on the validity of Weibull shape factor. 

The Weibull shape factor may vary between 0.8 and 1.2. If 

information on structure and route characteristics are not 

available, a shape factor of 1.0 may be used. Shape factors 

obtained by calibrating the characteristic stress range 

against a spectral fatigue approach indicate that single most 

important variable affecting the shape factor is the 

environment. In severe North Atlantic and Pacific wave 

loadings,the shape factoris higher;the shape factoris also 

generally lower for those ship structures with longer hulls. 

Although the shape factor may be somewhat different for 

differentparts of the structure (i.e. bulkheads, bottom) and 

itmay also depend on the number of cycles to failure, further 

work is necessary to document those effects. 

Fixed and Mobile Marine Structures 

The structures referred to in this section are both floating and 

bottom-supported steel structures. Most organizations that issue 

recommendations, rules, regulations and codes distinguish between 

floating and fixed structures because of the differences in their 

configurations and the resulting differences in applied loads, 

structureresponse,redundancyand accessibilityfor inspectionand 

repairs. The requirements vary substantially in scope and detail 

from one document to another, but efforts to provide consistent yet 

flexible fatigue analysis requirements have been successful. 

4-11

In general, the minimumrequirement for fatigue analysis is defined 

as the need to ensure the integrityof the structure against cyclic 

loading for aperiod greater than the design life. Some documents, 

such as the ABS MODU rules (Reference4.8) state that the type and 

extent of the fatigueanalysisshould depend on the intendedmode of 

operation and the operating environments. Thus, the designer,with 

the Owner’s input and concurrence is responsible for developingthe 

design criteria, methodology and analysis documentation for 

certification of a design that meets the fatigue requirements. 

Further discussion on fatigue rules and standards is presented in 

Section 4.2 

Fixed Structures 

As illustrated on Figure 3-5, there are several alternative 

approaches to determining the hot-spot stress, stress history and 

fatigue life. A flowchart shown on Figure 4-3 illustrates a 

deterministicanalysisapplicablefor a fixed platform in amoderate 

water depth site subjectedto relativelymild fatigue environment. 

The method relies on obtaining hot-spot stresses for one or two 

selectedregularwaves and generationof wave exceedancecurves from 

the scatter diagram to obtain the stress history. Although this 

method requires substantialcomputer use and is considered to be a 

detailed analysis, it is also considered to be a screening method 

and useful in initial sizing of the structure components. 

Amoredesirable alternativeapproachto a deterministicanalysis is 

to carry out a spectralfatigue analysis. The appliedwave loads on 

a structurecan be generated in the time domain and in the frequency 

domain. A structure,such as a flare boom,maybe subjectedto wind 

loading only. For such structureswind gust loads can be similarly 

generated to evaluate wind-induced fatigue loading. The stress 

spectrum is then generated from hot spot stresses, scatter diagram 

and specific wave or wind spectra. 

One variable in defining the stress spectrum is whether or not to 

account for wave spreading. The purpose for distributing the wave 

4-12

energy about the central direction by using a ‘spreading function” 

is to represent the nature more realistically. Considering the 

uncertainties and complexity of implementation,wave spreading is 

not generally incorporated into design. While it is a valid 

parameter that can be used to more accuratelydetermine the fatigue 

lives ofan as-designedor as-builtstructure (seeSection 6.1.4 for 

definition of spreading function), it is often unconservative to 

neglect it when dynamics are significant. 

It is also necessary to assess the significance of short-term 

density functionsdevelopedfrom statisticalparameters. The joint 

probability of significant wave height and characteristic period 

(i.e., each sea state) is used to develop short-term probability 

density function of the stress range. This function is often 

idealized by a Rayleigh distribution and can be further improved. 

This improvement,incorporationof a rainflow correction factor, is 

discussed by Wirsching (Reference 4.9). Fatigue damage is then 

typically computed for each sea state by using the S-N curve and the 

Miner-Palmgren cumulative damage formulation. An alternative to 

this approach is based on weighting and sunrningthe probability 

density functions to obtain a long-term probability density 

function. Total damage can then be computed based on either 

numerical integrationor the use of Weibull shape parameter and a 

closed form solution. Chen (Reference 4.10) offers a short-term 

closed form method that facilitates spectral fatigue analysis. 

Spectral fatigue analysis is discussed further in Sections 5, 6 and 

7. 

Mobile and Stationary Vessels 

Both conventional single-hull and twin-hull mobile and stationary 

vessels differ from fixed structures in the characteristics of 

applied environmental forces and the response of the structure to 

these forces. Thus, fatigue analysisof these vessels differs from 

that of fixed structures primarily in generation of applied forces 

and determination of stresses. Those vessels going from port-to- 

4-13 

-7 ‘-) 

‘> 

I .-/,

port are also subjectedto differentenvironments,necessitatingthe 

use of scatter diagrams applicable for each route. 

While a diffraction analysis method may be used to develop the 

excitationalforcesdirectly, it is often usedto compute equivalent 

hydrodynamic coefficients. These coefficients are then used in 

Morison’s formulationto generate wave forces. A typical spectral 

fatigue analysis sequence,includinggeneration of dynamic inertial 

response loads compatiblewith excitational forces, is illustrated 

on Figure 4-4. 

Inthe past conventionalsingle-hullvesselswere generallydesigned 

conservatively to meet both strength and fatigue requirements. 

Following initiationof monitoring programs to obtain wave loading 

and stress histories of selected cargo ships and tankers, fatigue 

design criteria were further improved. One reason for the 

preference of this design approach over the analysis approach is 

that most vessels are mobile and subjectedto multitude of site and 

time specific environment over their design lives, necessitating 

certain conservatism in their design. The use of vessels for 

specializedfunctions,such as bow-mooredstoragetanker or a drillship 

with a large opening (moonpool) to facilitate drilling, 

necessitateddetailedfatigueanalysesto evaluate the other fatigue 

sensitive areas throughout the structure. 

The detailed fatigue analysis, carried out on increasing number of 

floating structures, follow the basic steps shown on Figure 4-4. 

While both space frame models with beam elements and finite element 

models are used to analyze twin-hull structures, finite element 

models are almost exclusively used for single-hull vessels. 

4.1.4 Other Methods 

Complete ProbabilisticMethods 

A reliability-basedfatigue analysis is ideally suited to account 

for various uncertainties associated with fatigue parameters. 

4-14

Although considered to be an emerging technology and necessitate 

time consuming effort, probabilisticmethods have been effectively 

utilized in some fatigue analyses. Typically, such a method 

accounts for: 

● . 

Inaccuraciesin defining stresses due to random loadings 

● 

Uncertainties and observed scatter in S-N data 

● 

Randomness of failure in the use of simplified models 

A probabilistic method recommended by Wirsching (Reference 4.11) 

utilizesa fulldistributionalprocedureand the variablesdiscussed 

above are assumed to have a log-normal distribution. 

Adetailed analysis and design method, based on the use of a finite 

element model, to determine environmental loading, vessel response 

and load and stress distribution does not need to be a complete 

probabilisticmethod. Daidola and Basar(Reference 4.12) d“ scussing 

lack of statistical data on ship strengths and stresses recommend 

development of a semiprobabilisticanalysis method which does not 

require a distribution shape. 

Fracture Mechanics Methods 

A fracture mechanics method addresses the relationship between 

defect geometry, material, and the stress history. The defect 

geometry can be accurately modeled with finite elements. Stress 

intensityfactorscharacterizingthe defect behavior and the fatigue 

crack growth laws allow determination of defect growth 

characteristics. Thus, a hypothetical or an actual defect is used 

as the basis for determining the fatigue life and identifying the 

necessary corrective measure. 

The initial defect size and location and the stress intensity are 

very important parameters in determining crack growth period to 

failure. The fracturemechanics approach is a useful tool to assess 

4-15

the sensitivity of fabricationdefects in determining the fitnessfor-purpose 

of the component. This concept, first described by 

Wells (Reference 4.13), allows engineering assessment of weld 

defects to determine those defects that require repair as well as 

those that are considered fit-for-purposewithout a repair. 

4.2 

FATIGUE RULES AND REGULATIONS 

The primary objective of the various recommendations, rules, 

regulations and codes applicable to marine structures is to ensure 

that the design and analysis process results in construction of 

marine structures.that can resist both extreme loads and cyclic 

operating loads and have adequate fatigue lives. 

Rules and recommendations issued by classification societies and 

certifying agenciesmay representthe minimum requirements based on 

research and development. The hull girder design criteria given by 

each of the four leading classificationsocieties (American Bureau 

of Shipping, Lloyd’s Register of Shipping, Bureau Veritas and Det 

Norske Veritas) is very similar and differs only in some of the 

details. While the design basis primarily addresses stillwater and 

wave-induced bending moments, some discussion on dynamic stress 

increments and fatigue file assessment is often provided. Recent 

research and development efforts have produced several recommended 

fatigue design guidelines. Rules and reconunendationson offshore 

structures are very specific on fatigue design. Guidelines are 

provided to carry out both simplified and detailed analyses. 

Commentary to 

development of 

such guidelines also provide background for the 

fatigue design methods. 

Fatigue design methods chosen vary depending on several factors, 

including the owner’s design philosophy. Most fatigue design 

methods are variations of a method based on application of S-N 

curves representingthe fatigue strengthof similardetails/joints. 

A basic S-N curve applicablefor a given detail/joint also requires 

adjustments to incorporate the influence of variables. Although 

4-16

many design rules implement this approach, the recommended S-N 

curves are often different from each other. 

Assessment of defects detected during fabrication, or cracks 

discovered while the structure is in service, is best accomplished 

using fracturemechanicsand crackgrowth laws. Fitness-for-purpose 

considerations will then directly affect repair programs and 

inspection schedule. 

The reconunendations,rules, regulations and codes that apply to 

fatiguedesign have evolvedover the past 20 years, and severalhave 

been revised or reissued in the last five years. These documents 

are discussed briefly below as they apply to vessels and other 

marine structures. 

The American Welding Society (AWS) and American Institutefor Steel 

Construction (AISC) fatigue design specifications (Reference4.15) 

provide the basis for approximate fatigue design based on S-N 

curves. However, unless the method developed accounts for the most 

likely loads and other uncertainties, various critical and noncritical 

fatigue cracks are.likely to occur. 

Most documents on fatigue provide substantial flexibility in 

carrying out comprehensivefatigue design and analysis, while also 

incorporating extensive guidelines. Various DnV documents on 

specific types of structures such as Steel Ships (Reference4.16), 

Tension Leg Platforms (Reference4.17, Part 3, Chapter 6) and Fixed 

Steel Platforms (Reference4.17, Part3, Chapter 4) provide general 

guidelines and referto acomprehensive documenton fatigue’analysis 

(Reference 1.7). The UEG Recommendations (Reference 1.8) are 

similar to U.K. DEn Guidance Notes (Reference 1.6), differences 

largely limited to the revisions introduced in the latest (fourth) 

edition of Guidance Notes. 

4-17 

-7 “7

4.2.1 Applicable Methods 

Simplified Analvsis Methods: 

ABS provides a simplified allowable stress method, suitable for 

fatigue screening of tankers. As discussed in Section 4.1.2, the 

method allows substantial flexibility for engineering judgement. 

Both DnV (Reference 1.7) and API (Reference 1.5) provide for 

simplified fatigue assessmentof fixed offshore platforms. The API 

approach requires that the peak hot-spot stresses for the fatigue 

design wave do not exceed the allowable peak hot-spot stresses. 

This simplifiedapproach is based on detailed fatigue evaluation of 

typical Gulf of Mexico jackets in less than 400 feet water depth, 

with natural periods less than 3 seconds. Variations in structure 

geometry, and in the approximationsintroduced,make the simplified 

analysis best suited for screening of similar structures for 

sensitivity to fatigue loadings. 

The simplified DnV fatigue analysis is useful if the long-term 

stress distribution for a given area is not known. This simplified 

method provides an empirical relationshipto determine the maximum 

allowable stress range during a 20-year life as a function of S-N 

curve parameters, long-term stress distribution as function of a 

Weibull parameter and the complete ganunafunction. This method is 

quite useful as a design parametric tool because it allows 

assessment of joint configurations for weld type and plate 

thicknesses and facilitates selection of details least susceptible 

to fatigue failure. However, since it is difficult to define 

accurately and/or conservativelythe long-term stress distribution 

as a function of a Weibull parameter, the computed fatigue lives 

should be used cautiously. 

4-18

Detailed Anal.vsisMethods 

The detailed fatigue analysis sequence for ship structures is 

similar to fatigue analyses of other marine structures. While 

appreciableforward speed and ship motions complicate determination 

of cyclic stress distributions, finite element based spectral 

fatigue analyses approachesrecormnendedby classification societies 

are similar to those recotmnendationsapplicable to offshore 

structures. 

The recommendationsand rules applicableto fixed offshore platforms 

are generally quite flexible in the use of applicable analysis 

methods. To ensurestructural integrity,al1 cyclic 1oads that wil1 

cause appreciablefatiguedamage must be considered, includingthose 

due to transportation and all in-service loading for stationary 

structures. Several methods of determining the applied loads are 

acceptable to DnV (Reference 1.7), API (Reference 1.5) and the DEn 

(Reference 1.6). For fixed platforms, both deterministic and 

spectral methods can be used to generate the applied loads and 

determine the hot-spot stresses. However, a spectral analysis 

approach is often recommended to properly account for the wave 

energy distribution over the entire frequency range. 

Comparative studies carried out on a benchmark API platform, 

utilizing four separate approaches (one deterministic and three 

spectral), yielded large scatter of fatigue lives due to inherent 

differences from one analysis approach to another. Such results 

justify the philosophy conveyed in most recommendations and rules, 

including API (Reference 1.5) and DEn Guidance Notes (Reference 

1.6), that the fatigue analysis be treated as a systematic 

parametric analysis, requiring determination of the sensitivity of 

various parameters that affect fatigue lives. 

. 

4-19

4.2.2 SCFS, S-N Curves and Cumulative Damaqe 

Stress Concentration Factors (SCFsl 

It is desirable that the discontinuitiesthat result in high stress 

concentrationsbe evaluated by laboratorytesting or finite element 

analysis. But because these methods of obtaining stress 

concentration factors (SCFS) are often not practical, empirical 

formulations are widely used to determine the SCFS. Most 

reconunendationsand rules provide general guidelines on the use of 

SCFS and refer other reference documents. Lloyd’s Register was 

responsible for carrying out extensive strain-gaged acrylic model 

tests and developing SCF formulas. These empirical formulas are 

incorporated into Lloyd’s Register Rules (Reference 4.18). 

Assessment of various SCF formulas is discussed further in Section 

5.4 and Appendix C. 

S-N Curves 

For the purposes of defining fatigue strength as a function of 

constant amplitudestress and the number of cycles to reach failure, 

welded joints are divided into several classes. DnV (Reference1.7) 

provides an S-N curve identifiedas “T-curve”for all tubular joints 

and eight other classes to define other joints, depending upon: 

● 

● 

● 

The geometrical arrangement of the detail 

The directionof the fluctuatingstressrelative to the detail 

The method of fabrication and inspection of the detail 

API provides two S-N curves to define the tubular joints. The X- 

curve presumes welds that merge with the adjoining base metal 

smoothly (i.e., profile control), while the X’-curve is applicable 

for welds that do not exhibit a profile control. The API X-curve 

was originallybased on the 1972 AWS test data and has been upgraded 

based on later editions ofAWS D1.1 (Reference4.14). 

4-20

The DnV X-curve and the DEn Guidance Note Q-curve of 1977 were also 

based on the original AWS test data and the recommended S-N curve. 

Recent experimental work carried out in Europe has provided 

additional data on fatigue strengthof tubular joints. Statistical 

evaluation of these test results provided the basis for revision of 

both the DnV (Reference 4.17) X-curve and the DEn Guidance Notes 

(Reference1.6) Q-curve. As illustratedon Figure 4-5, the slopeof 

the new T-curve is steeper and typically results in lower lives, 

often necessitatingan increaseinwall thickness. The DEn Guidance 

Notes reconunendedT-curve is identical to the DnV T-curve up to 10 

million cycles for catholicallyprotected areas. 

The basis for the revision of the S-N curves by both DnV and DEn is 

primarily due to evaluation and assessmentof test data. While the 

AWS data are based on some plate and some small-diameter thin-wall 

sections,the Europeandata are obtainedmostly from largerdiameter 

tubulars with 5/8 inch and 1-1/4 inch (16 mm and 32 mm) wall 

thicknesses. It appears that an inverse log-log slope of 3.0 

(versus4.38 for the API X-curve)was chosen for the T-curve because 

of the scatter of data and to ensure consistency with the British 

Standards BS5400. Basedon statisticalevaluationoftest data and 

Gurney’s (Reference4.19) analyticalstudieson plate thickness,the 

T-curve is adjusted due to changes in plate thickness. 

Although the DnV (Reference4.17) document states that all tubular 

joints are assumed to be of Class T, an X-curve is also considered 

acceptable,providedweld profiling is carried out. The comparison 

of the API X-curve and the T-curve (Figure 4-5) shows that the two 

curves intersect at about 500,000 cycles and would yield similar 

1ives for a plate thickness of 1-1/4 inch (32 mm). However, for 

plate thicknesses greater than 1-1/4 inches the use of a T-curve in 

the computation of fatigue lives will result in shorter lives. 

4-21

Cumulative Damaae 

The use of the Palmgren-Miner 1inear damage rule is considered 

appropriate by all of the recommendations, regulations and rules. 

A cumulative sum of the number of cycles at each constant stress 

divided by the number of cycles to failure should always be less 

than l.Oforthe desired service (design)life. While this value is 

directly tied to the S-N curve selected,the desirable ratio (i.e., 

safety factor) of fatigue to service life is not always specified. 

The API reconunendedfatigue life is at least twice the service 

life. For criticalmembers that may affect structure redundancy and 

integrity,API recotmnendsthe use of higher fatigue to design life 

ratios. 

The DEn Guidance Notes reconunendadditional safety factors to 

account for structural redundancy and the implications of fatigue 

failure on the structure. However, no specific safety factor is 

recommended. 

4.2.3 Fatiaue Analvsis Based on Fracture Mechanics 

The fatigue crack propagation analysis is typically used to assess 

crack growth and fitness-for-purposeof defects discovered at the 

fabrication yard. Test data on crack growth can also be used to 

determine fatigue lives. The DnV CN 30.2 document (Reference 1.7) 

provides a crack growth rate data and fracture mechanics-based 

procedure for fatigue analysis and design. 

Whether the welded joint details have surface or root defects, the 

growth of such defects into fatigue cracks depends on several 

factors, including joint connection geometry, cyclic stress range 

history, weld profile and defect size. The equations provided to 

solve for the number of cycles to reach fatigue failure containmany 

parameters and allow evaluation of various joint and defect 

geometries. As an example, butt weld toe defects in a connecting 

plate whether in air or seawater, can be assessed with and without 

4-22

ending restrictions. Cruciform and tubular joint defects can be 

similarly assessed. The DnV CN 30.2 document provides standard 

crack growth parameters to facilitate a fatigue analysis based on 

fracturemechanics. LotsbergandAndersson (Reference4.20) further 

discuss fracturemechanics-basedfatigueanalysis and i11ustratethe 

approach with several examples of crack growth calculation. 

4*3 

CURRENT INDUSTRY PRACTICES 

Current industry design practices for marine structures are 

significantly more advanced than the design practices of only 20 

years ago. The extensive use of ever more powerful computers and 

the deve~opmentofa wide range of softwarepackages has facilitated 

the design and analysis of marine structures. Research work on 

long-term ocean environment, model basin studies on structure 

motions, structurecomponentmember testingfor stressdistribution, 

buckling,yielding and fatigue failureall have been instrumentalin 

developing better and more effective means of designing marine 

structures. Structural reliability research has also provided the 

means to incorporate the large number of uncertainties into the 

analysis and design effort. 

Fatigue analysis and design is perhaps the part of the overall 

analysis and design effort that benefits the most from these 

developments. Since the hot spot stress is a primary variable 

influencingfatigue life, analyticaland experimentalprograms have 

been carried out to helpdevelopdetails/jointswith lower hot spot 

stresses. Good design detailingwithout fabricationquality is not 

adequate. Thus, parameters affecting fabrication quality are 

incorporated into current design practices and fabrication 

specifications. It is feasible to analyze each joint of a discrete 

system such as a fixed platform. However, a continuous system, such 

as a ship, has thousands of details/joints and lends itself to a 

selective analysis. Current industry practice is to select number 

of cross-sections along the hull and analyze a dozen or more 

details/joints at each cross-section. 

4-23

Although additionalresearch is needed to expandthe availabledata, 

the industry has the ability to incorporate most sophisticated 

analysis procedures into fatigue design. The degree of 

sophisticationneeded to design a marine structure that has fatigue 

life in excess of its design life depends both on the structure and 

its operating environment. Thus, the effort necessary may be 

grouped into ordinary and special designs. 

4.3.1 Ordinarv Desiqns 

All marine structurescan be designed effectivelyby ordinary means 

if those structuresare not going to be subjectedto any appreciable 

fatigue environment. For example, offshore platforms in relatively 

shallow waters may be susceptibleto typhoon/hurricaneloading but 

less susceptibleto cyclic loadings that cause fatigue, eliminating 

the need for comprehensivefatigue analyses. Such structures can be 

designed for other loadingconditionsand checked against fatigueby 

approximate allowable stress procedures. 

The design of ships still is largely based on design rules (such as 

ABS, Reference4.1)developed by combiningtheoreticalknowledgeand 

design experience. Most ships in-serviceare designed to meet these 

rules and other fatigue design procedures (References 1.2 and 4.3) 

to ensure that the component details meet fatigue requirements. 

This approach has been quite satisfactoryfor most ships. Recently 

built vessels, especially large tankers built in the last several 

years have exhibited substantial fatigue problems. These problems 

may be largely attributed to the use of high strength steel, 

resulting in the use of lower plate thicknesses and yielding higher 

stress levels. As a result, detailed fatigue analysis and design 

procedures are implementedon more and more vessels. 

4.3.2 Sr)ecializedDesicms 

Those vessels with specialized functions and/or configurations, or 

which are likely to be moored in a specific area for an extended 

4-24

period, are also designed tomeet the rules and other fatigue design 

procedures. However, such vessels also require spectral fatigue 

analysisto define the loadings,response and stress distributions. 

Often, model basin tests are also carried out to validate the 

applied loadings and motions. 

Stationary marine structures are generally unique and have 

specialized functions. Since the design criteria and functional 

requirements dictate the general configuration of such structures, 

each structuremust be analyzedthoroughlyto generate the loads,to 

determine the response to these loads, and to determine its 

susceptibility to.fatigue. Most specialized structures require 

spectral fatigue analysis. 

4.4 

SENSITIVITY OF FATIGUE PARAMETERS 

Fatiguedesign and analysis parametersdiscussed in Sections 3.1 and 

3.2 i11ustrate the general interaction of these parameters. The 

specific interactions and the actual sensitivities of these 

parameters depend largely on the structure’s global configuration, 

joint configuration and details, material characteristics, 

fabrication quality and the design requirements other than fatigue. 

Therefore, fatigue analysis and design efforts often incorporate 

flexibilityto carry out parallel studies to assess the sensitivity 

of major parameters that affect fatigue life. 

Although the parametersillustratedon Figure3-l are all important, 

some of the more important parameters for fatigue life improvement 

are: 

● 

Enhance fabrication quality and minimize defects 

● 

Minimize applied loads and motions to minimize nominal cyclic 

stress ranges 

● 

Optimize the design for uniform load distributions 

4-25

● 

Optimize the design details to minimize SCFS 

Another parameter that is not important to the actual fatigue life 

but very important to the computed fatigue life is the analysis 

method and the assumptionsused in the analysis. Although there is 

no substitute for experience, comparative studies carried out by 

others should be utilized and the analysis method selected and the 

assumptionsmade should be applicableto the marine structure being 

designed. 

4.5 

FATIGUE DESIGN AND ANALYSIS CRITERIA 

Fatigue design and analysis criteria are generally covered in one 

chapter of the structural design basis document. Fatigue criteria 

may also be jointly prepared by the engineer and the owner as a 

separate design brief to document the fatigue design and analysis 

basis. 

4.5.1 Basis for the Preparation of Criteria 

The design and analysis criteria serve the purpose of clearly 

defining the work to be undertaken. Three primary variables that 

affect the fatigue design and analysis criteria are: 

● 

The owner’s requirements for work scope 

and schedule 

● 

The engineer’s assessment of the 

sensitivity to fatigue and the required 

marine structure’s 

level of analysis 

● 

The role of classification societies 

The owner, engineer and classification society all agree that the 

design and analysis should lead to quality fabrication and ensure 

the structural and operational integrity of the marine structure 

throughout its design life. To accomplish these goals, a design 

should provide a balance between efficiency and redundancy and also 

4-26

incorporates inspection-strategy(References4.21, 4.22 and 4.23). 

As a result, the design effort must incorporate consideration of 

global response, alternate load paths, local stress distributions, 

structural detailing, material selection, fabrication procedures, 

etc., to ensure that the structure’s fatigue sensitivity is 

minimized. However, the extent of the fatigue analysis is a 

function of cost as well as technical considerations. A marine 

structure costing $1 million and another costing $50 million will 

not be analyzed to the same extent. In lieu of extensive analysis, 

approximate analysis combined with greater safety factors is 

appropriate for less costly structures. 

A fatigue criteriadocument maybe very general, stating the design 

and analysis objectivesand the classificationand/or certification 

requirements. It can also list every method to be implemented and 

every assumption to be made in the execution of fatigue analysis. 

Most often the document will specify the scope of work, define 

overall methodology, and provide the data necessary for fatigue 

analysis. 

A typical fatigue design and analysis criteria table of contents 

contains the following elements: 

1. INTRODUCTION 

1.1 Objectives 

1.2 Scope 

1.3 Third Party Inputs 

2. MODELLING 

2.1 Loads Model 

2.2 Mass Model 

2.3 Stiffness Model 

3. OCEAN ENVIRONMENT 

3.1 Applicable Sea States 

3.2 RecommendedWave Theories 

3.3 Wave Directionality and Distribution 

3.4 Wave Scatter Diagrams and Recorded Data 

3.5 Wave Spectra 

4. PRELIMINARYANALYSIS 

4.1 Applicable Method 

4.2 Accuracy of Results 

4-27

5. 

6. 

7. 

8. 

DETAILED ANALYSIS 

5.1 Structure Motions and Loading 

5.2 Calibration of Loading 

5.3 Nominal Stresses 

5.4 Applicable-SCF Formulations 

5.5 S-N Curve and Fatigue Damage Calculation 

FATIGUE SENSITIVITY STUDIES 

6.1 Study Parameters 

6.2 Areas Selected and Extent of Study 

REFERENCES 

APPENDIXES 

4.5.2 Almlicable Software 

The analysis method chosen has to be compatible with the computer 

softwares available. Since a wide range of computer software is 

available, the analyses method and the software should be chosen 

based on structure configuration, applicable environmental loads, 

structuralresponseto appliedloading,stressdistributionpatterns 

and susceptibilityto fatigue failure. 

,.-. 

The softwarepackagesnecessaryto carry out the analysis and design 

functions should facilitate determination of: 

● 

● 

● 

● 

Ocean environment loads 

Structure motions 

Structural analyses and stress distributions 

Stress history and fatigue damage evaluation 

While there are special-purpose software programs such as SEALOAD 

(Reference 4.24) to generate wave loads and SHIPMOTION (Reference 

4.25) to determine motions, these and other software programs are 

often a component of larger generalized systems. A large system 

will facilitateexecutionof all functionsfromwave load generation 

to fatigueclamageassessmentwithin the system,eliminatingthe need 

for external data transfers. 

4-28

‘Thereare numerous finite element programswell-suited for detailed 

analyses and design of continuous structures such as ships, 

semisubmersibles and TLPs. The best known of these programs in 

public-domain are ANSYS, NASTRAN, SAPIV, DAISY and SESAM. Mansour 

and Thayamballi (Reference 4.26) provide a survey of computer 

software and they discuss programs specifically developed for the 

marine industry. 

4.5.3 

Fatique Versus Other Desiqn and Scheduling Requirements 

Fatigue analysis and design is only one of many aspects of the 

overall analysis and design effort. Because the final as-designed 

structure must meet many varied pre-service and in-service 

requirements, the fatigue design effort reflects the necessary 

interactions among various activities. The design criteria 

typically includespecific assumptionsand procedures to coordinate 

such activities. As an example, some of these interactions for a 

fixed offshore platform design project are as follows: 

● 

A computermodel used to generateextreme environment loads is 

also used for fatigue analysis,with changes in hydrodynamics 

coefficients and foundationmatrix as necessary. 

● 

A computer analysis model used for stiffness analysis should 

not account for the effect of thickened brace stubs, but the 

stress ranges used for fatigueanalysis should account for the 

increased thickness. 

The overall design schedule often dictates that fatigue design and 

analysis be carried out inunediatelyafter the structure’s general 

configurationis finalized. But the fatiguedesign must incorporate 

flexibility,to allowfor significantconfigurationrevisionsduring 

the detailed design, which will affect both the applied loads and 

the stress ranges. The desired flexibility is often obtained by 

carrying out parametric studies to identifythe effects of changes, 

4-29

and by providing sufficientmargin when determining the desirable 

fatigue lives. 

4-30

LOCATIONs oF FATIGUE CMCKS 

Figure 4-1 Typical Fatigue Sensitive Ship Structure Details 

DesignProcedure 

‘“m 

Choose a loadingshape paratmter k, 

‘ftheweibull ‘distribution 

2. 

* 

Ship Detail Identify the number designation of 

Catalog the critical details. (Fi s. A.1 

through A.12 of Appendix A 7 

3“v ‘ind 

4“w’ 

‘“v 

‘“- oflo-,. 

: I) 5-N curve slope, m, of detail 

2)‘:z’’’:’tressrange 

(See Table B.1 and Fig. B.1 of Appendix B) 

Find random load factor,

ICOMPUTER MODEL I MASS MODEL I 

I 

I 

WAVE LOADING 

SPECIFICATIONOF WAVE GRID 

WAVE THEORY, MARINE GROWIH, DRAG 

& INERTIACOEFFS,WAVE DIRECTION, 

WAVE PERIOD AND WAVE HEIGHT 

TRANSFER OF WAVE LOADS 

FROM NON-STRUCTURAL TO 

STRUCTURAL MEMBERS 

t 

DEFINITIONOF ENVIRONMENTAL DATA 

EXCEEDANCE CURVE, DIRECTIONAL 

PROBABILITIES,ANNUAL ANO 

FAIGUE WAVES 

L===l 

DEFINllIONOF FATIGUEPARAMETERS 

FATIGUE LIFE 

EVALUATION 

Figure 

4-3 A Typical Detenai.nistic Fatigue Analysis Flow Chati

TW=’T 

——— ———___ __ 

r 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

MOTIONS MODEL 

● W/ m W/O DiffmcUrn Andpls 

● LOd -muon 

STRUCTURES MODEL 

1 

I 

I 

I 

I 

I 

I 

I 

———— ———— 

I r 1 

TESllNG 

I I STRAIN GAUGE j 

I L ——— ——— —— 

1 I 

L ———— —.—— ———— .J 

I 

I 

I 

I 

EMPIRICAL 

ANALYTICAL I 

A 

STRESS RAO’S 

u FORMULATIONS F.E.A. 

n 

I 

: I I 

% ———— ———— ———— ——— J 

~ 

4 

——— ——— —.. ——_ ___ __ 

I 

HOT SPOT 

STRESSES 

I 

___ 

__ 

... 

I 

/ 

> DEFINE DEFINE DEFINE 

u 

p WAVE SPECTRUM SCATTER DIAGRAM DIRECTIONALPROB. 

~J 

Xgo 

%2 

& 

VI 

STRESS SPECTRUM 

——— ———— ———— ———— _. —— _ 

+ \ 

I DEFINE I 

1 S-N CURVE 1 

FATIGUEDAMAGE 

ANALYSIS 

Figure 4-4 A ~lcal 

Spectral Fatigue Analysis Flow Chart

tl 

MASSMODEL 

1 I r 

* 

RIGID 600Y 

MASS MATRIX 

HYTIR&D#MtC 

+ E m 

OYNAtilC 

WSSEL ACCELERATIONS MOTION ANALYSIS 

LOADINGS: 

AND 

ANO WAkE LOAD 

lNERTtA + WAVE WAX LOAOINGS - GElN&R~TlC&4S 

t 

I 

nSTIFFNESS 

ANALYSIS 

FOR ALL LOADINGS 

I 

WAVE HEl&T 

I 

t 

GENERATESTRESS RESPONSE 

AMPLITUDEOPERATORS(I?AO’S) 

ANO SELECTCRIICAL MEMBERS 

FOR FATIGUE ANALYSIS 

v 

DEFINE ENMRONMENTALOATA 

SCATTER DIAGRAM. YfAW 

SPECIRLIM AND 

DIRECTIONAL PROBABiU~ES ‘ 

t 

I 

DEflNE S-N CURVE ANO 

STRESS CONCENTRATIONFACTORS 

I 

PERFORMSPECTRAL 

FATIWE ANALYSIS 

I 

F@re 4-4 A Typical Spectral Fatigue Analysis Flow Chart 

( 

.–k.) 

---F’

1 

—. 

— 

— 

— 

— 

-.. - 

.. - 

. - 

I 

— 

7- + 

x 

— 

\ 

— 

-- 

— 

+ 

— 

— 

.. 

. 

——— - - 

— 

—— —. 

—- . —. 

—. 

.——+.. 

... . —- 

— 

— 

— 

-. 

,.. 

-. . 

— . 

. — 

—- 

. —— 

. —.. .— - 

—, ., 

..-. - 

. . ,——. . — — . 

.-—. . . —.— -— .— -- 

... . . -. --- - 

,.. 

“Iok 105 

6 

Enduran#(cycles) 

UuxK, 

-dtism~ 

K, s- 

m ~ 

log,, Io& *,@ IQ& 

B 2343x101S 15.3697 35.3~ 4.o 0.1S21 0.414M l.olxlo~ 102 

C L012x1014 14.0342 32.3153 3.5 0.2Ml 0.47m 

D 3.9::x10U IZ.6M7 29.0144 3.0 02095 0.4824 

E 3_23Wx10U 12.3169 2S.S216 3.o 0.250J 0.5~ 

F 1.2s9x101z 1223X3 2g.1~0 3.o 0.2133 0.5~ 

K* 

Nlmmi 

4.23X1(+3 78 

1.5M012 53 

l.wxlo~ 47 

M3X1012 

F21231z10U 12.~ 27.S38? 3.o 0.22~ 0.52U 0.43x101Z 35 

G 0.56&c10i1 11.732S 27.0S14 3.0 0.1793 0.4129 0.23x101J 29 

WO~lOU 11JS42 26.6324 3.o 0.1346 0.42S1 0.16x101z 25 

T 4=s1012 12.- 29.1520 3.0 0.- OS’20 1.46xl@ 53* 

w 

● 

l~ti~w 

Fm~*eTc~~k_ti&lok 

IwAN) - t 2.MM . 0.Z43M . 31~1@~ 

Figure 4-5 me 

DnV X- and the New T-Cumes

“k- N 

++’ 

b. 

-- 

0 

N 

0 

NOTE - 

PERMISSIBLE CYCLES OF LOAD N 

These curves may be represented mathemahcall y as 

N= 2x109 30 -m 

() JZ 

where N is the permmslble number of cycles for apphed cyclic stress range Jd. with A aref and m as listed below. 

1 IIref m 

sTRESS RANGE AT 

INvERSE 

ENDURANCE LIMIT AT 

CURVE 

2 MILLION CYCLES LOG-LOG SLOPE 2W MILL1ON CYCLES 

x 14.5 ksi [100 MPa) 4.3s 5.o7 ksi (35 MPa) 

x’ 11.4 ksi (79 MPa) 3.74 3.33 kai (23 MPa) 

Figure 4-6 API X- and X ~-roes and DnV T-Cume

TOP[C 

U.K.DEPARTMENTOF ENERGY(OEn) 

AMERICANPETROLEUMINSTITUTE 

GENERALCONSIDERATIONS 

o Fatiguelife Life*~Servlce Life Life> 2x Serv~ceLife 

o FatigueLoading 

o FatigueAnalyslsjDes~gn 

All cyclicloads(Ref.21.2.1OC) (Ref.5.2.5) 

- SimplifiedMethod No Yes,allowablestressmethod 

appl~cableto Gulfof~exlco (GOM) 

(Ref.5.1.1) 

- DetailedAnalysis Recommended Recommendedfor: 

waterdepth~400 ~t (122m),or 

* lifeshouldnotbe 620years - platformperiod> 3 see,or 

andan additionalfactoron - environmentharsherthanGOM 

Ilfeis recommendedwhen (Ref.5.1.2) 

structuralredundancyis 

ln~dequate(Ref.21.2.10f) 

DETERMINATIONOF STRESSES 

o Ob.ject~ve To determinecycl~cstressranges To determineCYCIICstresses 

(j.e.,meanstressesare neglected- properlyaccountingactualj 

Ref.21.2.11) 

distributionof waveenergyover 

entirefrequencyrange,spectral 

analysistechniquesare recommended. 

o Modeling No spectficreference Spaceframeanalysistoobtaln 

structuralresponseandstress 

distribution(Includlngdynnmlc 

effects) 

o Analysis A detailedfatigueanalyslsallowln9 Typically,spectralanalysisto 

eachcrltlcalareato be considered. determinestressresponsefor each 

sea state. 

J 

Page1 of 5 

. 

Figure4-7 Comparisonof Recommendations 

U.K.GuidanceNotesandAPI RP 2A

~ AMERICAN ETPOLEUMlNSTITUTE 

)tiotSpotStress RangeIs theproductof the nom~na~ RangeIsohtalnedby multiplyingthe 

stressrangeIn the braceandthe nominalstressrangeat’tubular 

SCF. ItIncorporatesthe effectsof jointby SCF. 

overalljointgeometrybut.omitsthe 

stressconcentratingInfluenceof 

theweld itself. 

iTRESSCONCENTRATION 

‘ACTORS(SCFs~ 

} Scf ho referencesgiven SCFSdefinedarebaseduponmodl~led 

Kelloggformulas forchord and 

Marshallformula[ forbrace 1 (Ref. 

C5.1,Table5.1.1-1) 

ISimpleJoints- Nodal 

JEmpiricalEquations 

OtherJoints 

iTRESSHISTORY 

Nonedefined 

Noned~flned 

SCFSdefinehot spotstresses 

Immediatelyadjacentto the olnt 

intersection(0.25”toO.1d from 

weldtoe,Ref.C 5.4) 

K, T, Y andX jointsdefinedfor 

axial,In-planeandout~ofplane 

loading 

Recommendsa braceSCF~6 (Ref.5.5) 

)WaveClimate 

Page2 of 5 

i 


U.K.GuidanceNotesandAP1fW 2A 

Waveclimatesmay be derivedfrom 

bothrecordeddataandhlndcasts. 

Aggregateof allsea statesto be 

expectedoverthe longterm 

condensedIntorepresentativesea 

states. 

A sea state,characterized by wave 

energyspectrumandprobabilityof 

occurrence,may be definedby: 

o Twoparameterscatterdiagrams 

o Directionalscatterdiagrams 

o i)lrectlonalscatterdiagramswith 

spreading

:1 

U.K.DEPARTMENTOF ENERGY(DEn) 


The long-termwaveheight 

distributionmay be representedby 

the sumof twoWelbulldlstrlbutlons 

one fornormalandanotherfor 

hurricaneconditions(Ref.Ftg. 

C5.2.1) 

FATIGUESTRENGTH 

o Definedby S-ticurvesbasedon Mean-minus-two-standard devlatlon X curveIs suffclentlydevaluedto 

experimentaldata curves[Ref.21.2.10.f) accountforthickness/sfzeffect. 

log(tq= log (K1]-do -m.log(S8) 

A slopeof m=-3adoptedbasedon 

data 

o TubularJoints 

- Recommended Fullpenetrationwelds- T curve Smoothweldmetalmergingwith 

(Ref.21.2- 12a) 

parentmetal- X curve,otherwiseX’ 

curve(Ref.C5,4) 

- Alternate Partialpenetrationwelds- W curve NotCovered 

o OtherJojnts Oneof 8 classes: 0, C, D, f, ~2,G 

& W,dependingon geometry,stress 

ReferstoAWS 01.1 

directionandmethodof manufacture 

and InspectIon 

Q OtherParametersAffectingS-N 

Curves 

- Environment CatholicallyprotectedjointsInSea S-N curves(X’andX) presume 

waterequivalentto jointsIn air. effectivecathodicprotection. 

Unprotectedjointsin seawater Fatigueprovisionsof AWS D1.1apply 

requireS-Ncurveto be reducedby a to membersand jotntsIn atmospheric 

factorof 2 on llfe(Ref.A21.2.13a) service. 

P 

. , 


U.K.GuidanceNotesandAPIRP 2A 

\ 

f

TOPIC 

U.K.DEPARTH~NT(lFENERGY(lJEn) 


- PlateThickness 

Ooesnotrecommendfurtherreduction 

of S-ll%rve for freecorrosion(fC) 

basedon testdataon bothFC and 

cathodicprotection(CP).(Ref.C 

5.5) 

nodaljoints BasicS-N curvefortB=32mn (T Not covered 

curve) 

CorrectIonS = s~ (32/t)$ 

non-nodaljoints BasicS-NcurvefortBf22nsm (B-G ~ot covered 

curve) 

CorrectionS = S It./t]* 

(Ref.FigureA.2!.2.!f3b) 

- Weld Improvement 30% in strength(2.2factoron life) Profilingallowstheuse of X-curve 

by controlledmachiningorgrlnding ratherthanXi-curve 

of weldtoe (Ref.FigureA,21.8) 

‘ATIGUEDAMAGECOMPUTATION 

Note: Requireda smoothconcave 

profileat weld toewlthmln. 0.5~ 

penetrationIntotheplate. 

ieconmnended Method 

Cunrnulative damageby ~fner’sRule 

(Ref.21.2.14) 

Cwnulativedamage byt41ner’srule 

wherestressresponses’foreachsea 

statearecombinedtntothe long 

termstresscflstrlbution, which 

shouldthenbe usedtocalculatethe 

cumulativedamageratio. Alter-‘ 

natively,thedamageratiomaybe 

computedfor eachseastateand 

combinedto obtainthecumulative 

damageratio,(Ref.5.2.4) 

Page4 of 5 


---- U.K.GuidanceNotesandAP1 RF 2A 

(:;;

TOPIC 

U.K.DEPARTMENJOFEIWRGV(oEn) 

OTtiERCOMPONENTS 

Castor ForgedSteel 

Covered(Ref.21.2.15) 

flotcovered 

OTHERCONSIDERATICINS 

Fatiguesertsitlvlty and 

of failurestudies. 

WI 

consequence 

RecommendsIdentlflcationof 

crltlcaljolntslmembersand 

developinga selectlveinspection 

programcompatiblewithbothfatigue 

sensitivityand failureconsequence 

(Ref.21.2.10e) 

Beneficialreduction~p toe ~eve~of 

tensileresidualstress.”However, 

no benefitsassumedon fatfguellfe. 

(Ref.21.2.11) 

Conslc&eredbeneflc~a]as ~esldua” 

stressesinfluehtiecrack 

Inltlatlon.However,no benefits 

assumedon fatiguellfe. 

Treatmentof low stress 

cycles 

Non-propagatingstressat Y= 107 

(Ref.A21.2.13c) 

Non-propagatingstressa? 1!= 200 x 106 

Treatmentof highstresscycles 

T curveextrapolatedbackto stress 

rangeSB = 292~ (Ref.A! 21.2.13d) 

Endurancellmlts= 

5.07ksl (35?4Pa forX-curve 

3.33kst (23MPa1 

forX’-curve 

Page5 of 5 


U.K.GuidanceNotesandAP1 RP 2A

(THIS PAGE INTENTIONALLY LEFT BLANK) 

-,-.

5. 

FATIGUE STRESS MODELS 

5.1 

REVIEW OF APPLICABLE MODELING STRATEGIES 

The structure configuration essentially dictates the modeling 

strategies and the analysis methodologies. Various strip methods 

are used to determinethe wave loadingson long, slender bodies such 

as ships. The strip theory can account for the effect of diffracted 

and radiatedwaves. The hydrodynamicloadings on ships, aswell as 

semisubmersibles,can beobtainedfromthree-dimensionaldiffraction 

analysis. 

Discrete systems, such as bottom-supported fixed platforms, are 

substantiallydifferent from continuous systems, such as ships and 

semisubmersibles, in the characteristicsof the applied loadings, 

their response to these loads, and the resulting stress 

distribution. Although the components of the strength model are 

similar for both systems, the specifics and the related 

uncertainties are different. Thus, fatigue stress models for 

bottom-supported and floating marine structures are discussed 

separately in Sections 5.2 and 5.3, respectively. 

5.1.1 Modelinq Strategies 

Analytical models are developed to determine excitational loads, 

motions/response,anddeformations/stresses. The levelofdesirable 

model complexity depends on many variables, including: 

● 

The desired level of accuracy of results. 

● 

Theaccuracyofvariables/assumptions input intothe analysis. 

● 

The effect of modeling complex 

the interpretationof results. 

ty on modeling errors and on 

5-1

● 

The effect of modeling complexity on analysis schedule and 

cost. 

The current state-of-knowledgeprovides us with the tools necessary 

to develop and analyze models. The desirable level of modeling 

sophistication, different for each structure, is thus determined 

based on tradeoffs among some of the variables given above. 

The goal of a modeling strategy should always be to achieve 

realistically accurate results consistently and without excessive 

complexity. The analysis assumptions and the modeling strategy is 

very important in minimizing modeling accuracy/error. Most 

engineers rely on previouswork and engineeringjudgement to reduce 

the level of modeling errors, typically defined as the ratio of 

actual-to-predicted results. Such a subjective approach can be 

supplemented by statistical methods to define the modeling 

uncertainty. The mean value of the modeling error, Xme, is defined 

as the “bias.”While the modeling uncertainty is referred to as the 

random component of the modeling error. The modeling uncertainty, 

given by its coefficient of variation, (C.o.v.)x is meaningful 

me 

only if sufficient data is available. 

5.1.2 

Comparison of Structures 

A discrete system composed of numerous members and joints (such as 

an offshore platform) is modeled as a 3-D space frame. Individual 

members of the system are modeled as stick elements, with correct 

dimensions (diameter, net length) and hydrodynamic coefficients. 

The two basic premises affectingthe accuracy of wave loadings are: 

● 

The hydrodynamicforces are typically computed based on water 

particle kinematics along each member centerline. When the 

wave length-to-cylinderdiameter ratio is less than about 10, 

the wave force computed based on a stick model centerline is 

too conservative. 

5-2

● 

The water particle kinematicsare assumedto be unaffectedly 

the presence of such members. When the cylinders are spaced 

so that they are at least 3 or 4 diameters apart, the wave 

inertia forces on one cylinder are relatively unaffected by 

the presence of the other cylinders as the radiation effects 

are small. 

Since platform member diameters are typica” ly less than 3 feet 

(2.Om) for braces and less than 6 feet (2.0 m) for legs, the two 

basic premises are valid. Even if a 10 foot (3.Om) diameter leg is 

utilized, for a wave period of 6 seconds the wave length-to-leg 

diameter ratio is in excess of 18. Thus, diffraction effects are 

smal1. 

However, a45 foot (14m) diameter column of a tension leg platform 

will have a wave length-to-columndiameter ratio of only about 4 for 

a wave period of 6 seconds. The columns are likely to be only3 to 

4 diameters apart. The column spacing is even less for a 

semisubmersiblehavingthree columns on each pontoon. Thus, the two 

premises are not applicable for structures made up of large 

members. The water particlekinematicsat member centerlinesareno 

longer valid for smallwave periods and the presence of such members 

in the proximity of others affects the water particle kinematics. 

Although the stickmodel ofa platformcan be modeled from one joint 

node to another, the applied loads could be in error by 2% to 3% 

because the loadings on member ends within the chord are computed 

more than once due to member overlaps, Most software packages 

include an option to define the member ends within the chord, 

preventing multiple computation of the applied loads, buoyancy and 

weight at each joint. 

Accurate definitionofa ship’sdeck strength is importantto define 

the box-girder-likeresponse of the entire hull. If a strip method 

is not used, the plate elements of the model used in a diffraction 

analysis (for loads) and the finite element analysis (for stresses) 

5-3

shall have sufficiently fine mesh and member properties to ensure 

accuracy of the results. On other floating structures,such as the 

TLP and a semisubmersible,the diaphragm action of the deck plating 

can be represented either by shear plates or by equivalent beams. 

5.2 

FLOATING MARINE STRUCTURES 

Both mobile and stationarymarine structures are discussed in this 

section. The overall discussion is applicable to configurations 

ranging from ships and barges to semisubmersiblesand tension leg 

platforms (TLPs). 

The floating marine structure configuration and the mode of 

operation (mobile versus stationary) are the primary variables 

affecting the development of an appropriate “loads” or 

“hydrodynamics”model. The problems encountered and the technique 

applied to determine the wave loads are different for ships and 

other stationary marine structures for several reasons: 

● 

While ships are treated as slender bodies, most offshore 

structures other than FPSOS, FOSS and drillships can not be 

treated as slender bodies. 

● 

The three-dimensional flow calculation technique can be 

appliedto typicalstationarystructuresbut cannot be applied 

to ships that have a constant forward speed. 

● 

Steady-state response of a stationary structure to 

excitationalwave loads allowsdeterminationof relativewater 

particle velocities and accelerations and assessment of 

structurecompliancy (netloading). These excitationalloads 

have less influence on ships in-motion (i.e., near-complete 

compliancy). 

● 

Stationaryfloatingmarine structuresaremoored/tethered and 

are subjectedto low-frequencydrift forces,which, due to the 

5-4

“radiation pressure” of waves, significantly affect the 

mooring/tetheringsystem design. 

5.2.1 shillStructures 

Determination of Loads 

Seakeeping and wave loads on ship structuresare determined largely 

based on two-dimensional solutions of flow problems for plane 

sections. Combinationsof various plane section solutions provide 

an approximate loading for the entire hull. Approaches based on 

utilizing the plane sections of slender hulls are identified as 

“strip methods.” Typically, a strip method utilizes a linear 

relationship between wave amplitude and response in a frequencydomain 

solution. However,non-linearresponses in a time domain can 

be also solved. 

A two-dimensional flow problem is often analyzed for a range of 

variables. Typically,solutionsareobtainedfor one wave direction 

and a number of frequencies. Then other wave directions, defining 

an angle of encounter between the wave and the ship, are chosen and 

solutionsobtained. The studyresults are interpolated to determine 

the ship responseamplitudes. Althougheightwave directionsshould 

be considered for stress analysis (head and following seas, beam 

seas, bow quartering and stern quartering), several directions can 

be disregarded (globaleffectsof port and starboardquarteringseas 

are similar) for motions analysis. 

Typically, strip methods disregard the longitudinal forces due to 

surge motions of the ship. Longitudinal forces are small and the 

use of Froude-Krilof forces and hydrostatic head appears to be 

satisfactoryto determinethe hull longitudinalstresses. However, 

work carried out by Fukusawa et al (Reference 5.1) indicates that 

the deck longitudinal stresses of a fully loaded tanker may be 

increased appreciablydue to longitudinalwave forces. 

5-5

The ship motion and wave action result in truly complicated 

interaction of variables affecting the loading on the hull 

structure. Theloads dueto incident,diffractedand radiatedwaves 

and due to ship forward motions may be approximated for various 

sections of the hull by the use of strip theory. Loads due to 

diffraction and radiation can be also directly obtained from a 

three-dimensional flow solution. Work carried out by Liapis and 

Beck (Reference5.2) provides a very good comparison of various 3-D 

flow solutions, strip theorysolutionand experimentalresults. The 

added mass and damping coefficients plotted against frequency on 

Figure 5-1 indqcate that the coefficients obtained by Liapis and 

Beck are quite close to those obtained based on both strip theory 

and experimental work. Actually, over the range of applicable 

frequencies,the three sets of coefficients based on 3-D solutions 

show larger scatter. 

Considering the difficulties of applying 3-D solutions and the 

proven reliability of good strip methods, a strip method is 1ikely 

to remain the preferred approach to determine the applied loads in 

most ships. Ships with special characteristicCS, including 

supertankers, navy vessels, drillships, etc., are the likely 

candidates for application of 3-D flow solutions. It should be 

emphasized that whichever solution method is chosen, substantially 

greater inaccuraciesare introduced into the hull loading due to: 

● 

Uncertaintieson wave height and period (wave statistics) 

● 

Uncertaintiesregarding ship routing and the correlationwith 

wave environment 

● 

● 

The variable nature of ship cargo and ballasting 

Inaccuraciesin hull response to applied loads 

The precedingdiscussioncoverswave loadingon ships susceptibleto 

cumulative fatigue damage. A linear theory is applicable to 

determine the applied loading for fatigue analyses and design. In 

an extremelyharshenvironment,wave nonlinearitieshave substantial 

5-6

influence on the applied loading. However, a linear theory can 

still be used in a harsh environmentto produce approximateloadings 

as harsh environment generally contributes very little to the 

cumulative fatigue damage. 

If an appreciable portion of fatigue damage is due to harsh 

environment loading, some of the important variables not accounted 

for in linear theory should be evaluated: 

● 

● 

● 

● 

● 

Wave steepness 

Wave slamming 

Viscous effects 

Hydrostatic effects (due to flaring ship sections) 

Hydrodynamic effects (due to flaring ship sections) 

These primary and other secondary nonlinearity effects on ship 

loading can be accounted for by perturbation and simulation 

methods. Second-order perturbation methods are relatively simple 

and they are used to solve the wave action/ship motion problem in 

the frequency domain. A detailed discussion of second order 

perturbationmethods is presented in References 5.3 and 5.4. 

Another approach to determine the non-linear effects is the 

integration over time of the applied forces on the structure. A 

detaileddiscussionofsuchsimul ationmethods, includingprinciples 

of effective computer simulations, is presentedby Hooft (Reference 

5.5). 

Motions Model and Anal.vsisTechniques 

Since the linear ship motion theory is considered appropriate for 

large majority of spectral fatigue analyses, the modeling and 

analysis technique is further discussed. 

Typically, a standard ship or a tanker has two distinct drafts, one 

for laden and another for ballast condition. The pre-analyses 

effort usually covers the following: 

5-7

● 

Preparationof a table of offsets for the vessel,defining the 

geometry with stations (20 or more)along the longitudinal 

axis and points (15 or more) at each station (i.e. describing 

the transverse section). 

● 

Preparationof weightdistributionto define structure (steel) 

and variables (ballast,cargo, fuel, etc.). 

● 

Utilization of table of offsets and weight distribution to 

compute bending moments and shear forces at each station. 

The 

shear force and bending moment diagrams developed along the 

length of the vessel facilitate equilibrium checks. 

The vessel motion anlalysis requires definition of vessel 

hydrodynamic properties: For a linear strip theory based ship 

motion computerprogram,the hydrodynamicpropertiesdefiningvessel 

added mass and damping coefficientsmay be input based on available 

data onsimilarvessels. Conforrnalmapping approach is also used to 

define the added mass and damping coefficients. However, if the 

vessel configuration is unique, a 2D or 3D diffraction analysis is 

recommended to define the hydrodynamicproperties. 

The 1inear strip theory based ship motion program, uti1izing the 

hydrodynamiccoefficients,is usedto generateequilibriumsolutions 

for vessel motions in six degrees of freedom. Then, the transfer 

functionscan be defined for verticaland lateral bending,torsional 

moments, vessel accelerations and hydrodynamic pressures at each 

station along the vessel longitudinal axis. 

Finite Element Stiffness Model 

The load transfer function, both in-phase and out-of-phase 

components, are used in the stress analyses to obtain corresponding 

stress range transfer functions. The computer model and the 

structural analysis used is very important to define local stress 

ranges. Fatigue is a local phenomena.and it isimportant to define 

5-8

their function, selecting appropriate element aspect ratios (less 

than 1:2) will contribute both to better accuracy and a better 

model. 

5.2.2 

Stationary Marine Structures 

Determination of Loads 

Stationarymarine structureshavevariousconfigurationsand exhibit 

a wide range of compliancy. A substantial effort is desirable to 

minimize the fatigue loadings on stationary structures. For a 

moored tanker FPSO the smallestfunctionalsize exhibitinga minimum 

silhouette is desirable. For structures composed of columns and 

pontoons, the column spacing,column water plane area, displacement 

of pontoons affecting overall center of buoyancy and the total 

displacement are some of the interactingparameters that affect not 

only the magnitude and characterof the applied loading but also the 

response of the structureto applied loading (see Reference 5.6 for 

structure configurationoptimization). 

While the hydrodynamic forces on a slender stationary body can be 

determined based on strip method or diffraction theory, a structure 

made up of columns and pontoons can be determined either by 

Morison’s equation or by diffraction theory. As discussed in 

Section 5.1, large diameters disturb the flow, leading to 

diffraction which is highly frequency dependent. There are two 

benefits of using diffraction theory: 

● 

Diffraction usually causes a reduction in the wave loads, 

● 

Viscosity can be ignored and thus, treating the flow as 

irrotational,potential flow theory may be used. 

The hydrodynamicloads actingon astructure are typically generated 

using a combination of three-dimensionaldiffraction theory, i.e., 

a source-sink distributed potential theory (Reference 5.7) and a 

conventional Morison’s equation. Although a two-dimensional 

5-1o 

/ 1A

analysis program can be used, a three-dimensional program 

facilitates overall analysis effectiveness. 

To analyze, the structure surface is divided into panels, much like 

a finite elementmodel and the potentialflow problem is solved over 

each panel and yields diffraction and radiation pressures on these 

panels. While the diffractionpressuresare transformedintomember 

wave loads, the radiation pressures are transformed into added mass 

coefficients. Hydrodynamic drag forces on these members and both 

the drag and potentialforces on smallermembers (simulatedby stick 

elements) are generated using Morison’s equation. Diffraction 

effects are strongly dependent on frequency, so a range of 

frequenciesmust be addressed. 

Mass Model 

Typically the deck structural members are modeled by using 

equivalent members to represent the deck structure mass and 

stiffness. All other members subjectedto hydrodynamicloading are 

modeled, with appropriate mass distribution. The accuracy of 

structuremass and its distributiondirectly affect the accuracy of 

structure motions. 

Motions Model and Analysis Techniques 

The mass model discussedabove allowsdeterminationofa structure’s 

inertialresponseto the appliedexcitationalenvironmentalloadsby 

obtaining solutions to the six-degree-of-freedom equilibrium 

equations. Considering the rigid-body motions, the dynamic force 

equilibrium on a structure can be expressed using the following 

system of six simultaneousequations: 

[ [W+[Mal1 {x}+[ [CRI+[CV] J {x}+[IfJ {X} = {FO}+{FI}+{FD,} 5-1 

This equation differs from that in Section 5.3.3 in that (1) primary 

damping is due to wave radiation and viscous effects, (2) 

5-11

hydrostatic stiffness is introduced and (3) the make-up of applied 

forces differs. 

The terms given represent: 

[M] = 6x6 structuremass matrix 

[Ma] = 6x6 added mass matrix 

[CR] = 6x6wave radiation damping matrix 

[Cv] = 6x6 linearized viscous damping matrix 

[KH] = 6x6 hydrostatic stiffness matrix 

(FD) = 6x1 linearizedwave drag force vector 

(F,) = 6x1 wave inertia force vector 

(F~~) = 6x1 diffracted wave inertia force vector 

{x}, {x}, {x} = 6x1 structure displacement, velocity and 

acceleration 

If a structure such as a TLP is tethered to the seafloor, the 

stiffness matrix is modified from: 

[&J {x} to [[&-J + [K~l1 {x} 

where, the [KT]represents 6x6 tether stiffness matrix. 

As discussed in previous sections,the structureconfigurationsand 

the motion characteristics (i.e., steady state harmonic motion) 

facilitate the 6 x 6 motions equations solution over the frequency 

domain. 

It is recommended that the significant wave height in the wave 

scatter diagram that is likely to contribute most to the fatigue 

damage be chosen to linearize the drag forces for all wave 

frequencies. 

The basic approach discussed here has been utilized frequently in 

recent years, and is discussed herein as it was implementedon the 

design and analysis of a TLP by $ircar et al (Reference5.8). The

approach, also called “consistent method” differs from the 

conventionalanalysesmethod only in the generation of hydrodynamic 

loads. The hydrodynamic loads for a conventional analysis are 

typicallygenerated based on a method by Hooft (Reference5.5) with 

a modified form of Morison’s equation. Although the conventional 

method also yields reliable results in most cases, it should be 

noted that the hydrodynamic interactionamong component members of 

the structure is neglected. Figure5-2 shows that the appliedheave 

and pitch loadingsbased on both consistentand conventionalmethods 

are very similar for wave periods (4 to 8 sec.) that contribute 

largely to fatigue damage. For larger wave periods (9 to 15 sec.) 

representing less frequent larger waves, the consistent method 

provides more reliable results. 

Stiffness Model 

Typicallythe hydrodynamicmodel,mass model and stiffnessmodel are 

all developed from the same structuralmodel. The stiffness model 

incorporates correct member cross-sectional areas and stiffness 

properties,joint releases and boundary conditionsto allow correct 

distribution of structuralmember loadings and stresses. 

The stiffness analysis is performed for each wave period and 

direction to obtain in-phase and out-of-phasemember stresses. It 

is necessarythat nominal stressescomputed are realistic. Thus, if 

stick members are used to represent large members with internal 

chords and bulkheads,additionalfinite element study of such areas 

may be necessary. By using the loads from stick model analyses as 

the applied loads on a detailed finite element model of a joint, 

accurate stress distribution can be obtained to define the nominal 

stresses in each sub-componentof such complex joints. 

5.2.3 

Overview and Recommendations 

Although allowable stressmethods may be used to size the component 

members of marine structures and to develop better details, a 

detailed fatigue analysis is recommended for each structure. Each 

5-13

structure is unique and an allowable stressmethod based on typical 

structures and a typical environmentwill only provide information 

on relative susceptibility of various joints/details to fatigue 

failure. In addition,newer vesselsare often constructedfrom high 

strength steel, allowingthe use of thinner plates. Ship structure 

scantlingsizes are basedon strengthrequirementsand any reduction 

in scantling sizes without due consideration for fatigue phenomena 

is likely to make the allowable stress method unconservative. 

Therefore, allowable stress methods can be used as a “screening 

process” and a detailed fatigue analysis is recommended to ensure 

integrity of the design. 

Ship Structures 

The use of a linear ship motion theory is appropr”ate for fatigue 

analysis of most vessels. For most vessels structural dynamic 

amplifications,wave nonlinearities,and effects such as springing 

due to high forward speeds have negligibleeffect on overall fatigue 

lives. However, some vesselsoperating in harsh environmentsmaybe 

subjected to appreciable fatigue damage due to harsh environment 

loading. For such vessels the ability to predict wave 

nonlinearities and vessel hogging, sagging and racking effects 

accurately may become important. In such instances, a non-linear 

ship motion theory may be preferred over a linear ship motion 

theory. 

Fatigue is a local stress phenomena and it necessitates accurate 

definition of stresses for very complex geometries. In addition to 

primary hull girder bending in horizontal and vertical axis, 

substantial secondary girder bending moments will occur due to 

external dynamic loads on vessel bottom and internal inertialloads 

due to vessel contents. Thus, a beam theory based nominal stresses 

due to primary hul1 bending are inaccurateboth due to complexityof 

geometry and the local load effects. A finite element model should 

be developed to represent the behavior of the vessel and to 

determine the local stress distributions accurately. 

5-14 

HL

For each load component (in-phase and out-of-phase) at each 

frequencyof agiven wave directionthe finite elementmodel is used 

to generate local stress distributions. The stress range transfer 

functions are then generated for each wave direction. Although 

current computers are well suited to compute large problems, the 

number of frequenciesnecessary to define the transfer function may 

be small. Using the predominantload transfer function as guide a 

limited number of frequencies (say4 to 6) maybe adequateto define 

the other transfer functions. The use of a stress range 

distribution parameter allows carrying out of a fatigue analysis 

with relatively few structural analyses cases. The accuracy of 

fatigue lives obtained largely depends on the validity of the 

Weibull shape factor used. 

The shape factors obtained by calibratingthe characteristicstress 

range against spectral fatigue approach indicate that the single 

most important variable affecting the shape factor is the 

environment. While the shape factor may vary from 0.8 to 1.2, 

depending on the route characteristicsand on structuregeometry, a 

factor of 1.0 may be used when such information is not available. 

Stationary Marine Structures 

The accuracy of stress transfer function for a joint/detail of a 

stationarymarine structuredependson many variables, includingthe 

accuracy of applied loads, motion response characteristics and the 

stress distribution. Hydrodynamic forces may be determined by 

either Morison’s equation or by diffractiontheory. Since the wave 

length-to-member sizes are small for most floating (i.e. 

semisubmersibles,TLPs) structures, diffraction effects should be 

accounted for. 

A 2D or 3D diffraction analysis can be used to generate the 

hydrodynamic coefficients. Then, utilizing these coefficients, 

Morison’s equation can be used to generate theappliedl oads. As an 

alternative,diffraction analysis can be used to generate the wave 

5-15

loads directly. Since the diffraction effects are strongly 

dependent on frequency, a wide range of frequenciesmust be used. 

The response of the floating structure to applied wave loadings 

depends on its own geometry, stiffness and mass properties. Water 

plane area and its distribution (i.e., hydrostatic-stiffness)and 

mass properties directly affect the natural periods and the heave, 

pitch and roll response amplitudes. For a tethered structure,such 

as a TLP, tether stiffnesswill predominate hydrostatic stiffness. 

Tether pretensionswill control surge and sway natural periods and 

response amplitudes. The primary damping is due to wave radiation 

and viscous effects. 

It is recommended that the “consistent approach” discussed in 

Section 5.2.2 is used to accuratelygenerate hydrodynamicloads. A 

finite element model of the structure can be used to obtain the 

solution to the motions analysis and determine the stress 

distributions. As an alternate,a stickmodel maybe used to obtain 

solutions to the equations of motion and to define global 

deformations and forces. Then, additionalfinite element models of 

various interfaces will be necessary to determine local stress 

distributions accurately. The boundary conditions for the finite 

element models will be the stick model deformations. 

5.3 

BOTTOM-SUPPORTEDMARINE STRUCTURES 

This section discusses bottom-supportedmarine structures that are 

represented by three-dimensional space frames and composed of 

cylindrical shells. The dynamics of a large gravity-type bottom 

supported structure dynamics are somewhat similar to those of a 

fixed platform. However, the characteristicsof excitationalloads 

on gravity structureshave more in common with floating structures. 

5.3.1 Load or HydrodynamicsModel 

A wave force acting on a single stationary element is due to both 

the accelerationof water particles (inertialforce) and the kinetic 

5-16

energy of the water particle (drag force). These forces are given 

by Morison’s equation as: 

5-2 

where: 

F = 

hydrodynamicforce vector per unit length acting normal 

to the axis of the member 

F,&FD= 

inertia and drag components of F 

P 

= 

density of water 

cm ‘ 

inertia force coefficient 

cd = 

drag force coefficient 

D= 

diameter of a tubular 

u“ = 

duw 

component of the velocity vector of the water normal to 

the axis of the member 

= component of the accelerationvector of the water 

normal to the axis of the member 

liw=— dt 

II 

= denotes absolute value 

An appropriateapproachto estimatethe wave forces with reasonable 

accuracy is to assess the load model in its entirety, and for its 

component elements. 

The element diameter should reflect any geometric variations, 

including marine growth. The Cd and Cm values applied may range 

5-17

typically from 0.6 to 0.8 and 1.5 to 2.0, respectively. Very 

comprehensive experimental data obtained from full-scale 

measurements of the second Christchurch Bay Tower (References5.9, 

5.10 and 5.11) validate the coefficients in use today. As 

illustrated on Figure 5-3, the Cd and the Cm values applicable for 

most cylindrical members near the water surface (Level 3) are 0.66 

and 1.8, respectively. Although these values are applicable for 

Keulegan-Carpenter (Ke) number in excess of 30, even when Ke is 

reduced to 5, the inertiacoefficient,Cm, value reaches 2.0, while 

the drag coefficient, Cd, gradually increases to unity at Ke equal 

to 10. 

These coefficients also decrease with the distance from the water 

surface. However,becausethe uncertaintiesinmarine growth (which 

directly affects the surface roughness and therefore the drag 

coefficient)and the additionaleffortnecessaryto input,check and 

justify different coefficients,it is advisableto use one set ofC~ 

and Cm values. 

The use of conventionalMorison’s equation and the wave kinematics 

for regular two-dimensionalwaves has proven to be valid for jacket 

structures in moderate water depths. Assessment of measureclwave 

forcedata (Reference5.12) for extremewave loading associatedwith 

directionally spread seas in a hurricaneenvironment in the Gulfof 

Mexico compares quite well with those analytically computed. 

Morison’s equation is 

cylindrical members by 

also valid to compute forces on nonapplying 

appropriate Cd and Cm values and 

equivalent diameters. Suitable values of Cd and Cm for different 

cross-sections may be obtained from a Det norske Veritas (DnV) 

document (Reference4.16.) 

If the extreme loadings are to be computed, an applicable wave 

theory, compatiblewith the wave steepness,water depth, etc., must 

be used. The applied total load on a structure composed of many 

members is then the cumulative sum of loads computed on each member 

5-18

for a pre-definedwave height, wave period and crestline position. 

This conventionalregularwave method produces applied hydrodynamic 

loads that has been validated by an extensive performancerecord of 

structures in shallow-to-moderatewater depths. However, such a 

method is not advisable for structures in deeper water and 

exhibiting dynamic response. More rigorous approach to represent 

the true response characteristicsis necessary (References5.13 and 

5.14). 

5.3.2 Mass Model 

For a bottom-supportedstructurein relativelyshallowwater, amass 

model may or may not be necessary. Such a rigid structure has 

natural periods that are less than about 3 seconds and exhibits 

little dynamic response when subjected to long-period waves 

associated with a harsh environment. For such an environment the 

static forces obtained due to water particle kinematics can be 

increased slightly to account for the dynamic response predicted 

(i.e., computation based on estimated natural periods). However, 

most of the fatigue damage is likely to occur due to short-period 

waves, necessitatingdeterminationof platform dynamic response to 

a wide range of wave periods. 

Whether platform dynamic response is to be determined or not, the 

dynamic amplificationfactors (DAF)used in a deterministicfatigue 

analysisrequire an accurateestimateof naturalperiods and the use 

of a mass model is recommended to obtain an eigenvalue solution. 

For a spectralfatigue analysis,only the use of amass model allows 

determinationof platform dynamic response and direct generation of 

structure inertia loads that are compatible with the excitation 

loads due to waves. 

A mass model of a three-dimensionalspace frame should incorporate 

all structuralmembers. The mass will be accuratelydefined if the 

weight of all structuraland non-structuralmembers,deck equipment, 

ballast,hydrodynamicmass, etc., are accountedfor correctly and in 

their respective locations. Ideally, all member weights should 

5-19

therefore be defined uniformly along the member lengths. However, 

considering the cost of modal analysis, most structural member 

weights are input as lumped masses at member ends that attach to 

applicable joints. 

5.3.3 Motions Model and Analyses Techniques 

The mass model discussedabove allowsdeterminationofa structure’s 

initial responseto applied excitationalenvironmentalloads by the 

use of equilibrium equation solutions. The dynamic force 

equilibrium on a structure can be expressed using the following 

system of six simultaneousequations: 

[ [M + [Ma]} {x} + [cl {X} + [K] {x} = {FD}+ {F,} 5-3 

where: 

[M] = 

[Ma] = 

[c] = 

[K] = 

(FD) = 

(Fl) = 

{x},{x},{x} = 

6 x 6 structuremass matrix 

6 x 6 added mass matrix 

6 x 6 structure damping matrix 

6 x 6 structure stiffness matrix 

6x1 wave drag force vector 

6x1 wave inertia force vector 

6x1 structure displacement, velocity and 

acceleration 

The terms on the right hand side of the dynamic equilibrium 

equations represent external forces applied to the structure. 

Following solution of the equilibrium equations, the structure 

dynamic response can be moved to the right hand side of the equation 

to define the resultant loading. 

Thus, the net loading using Morison’s equation given in Section 

Eqn. 5-2 can be rewritten as: 

F net = : PD2[Cm~- 

(Cm-l) UJ + ~f)C~Dulul 

5-20

where: 

u 

= defined as the net velocity vector component s 

UW-UG 

Uw 

u= 

= the componentof the velocity vector of the water 

= the structure velocity 

Uw 

= the component 

water 

of the acceleration vector of the 

U* 

cm 

= the structure acceleration 

= added mass coefficient is often taken to be a 

variable ranging from 1.5 to 2.0. It is 

recommended that Cm be taken as 2.0, which is 

consistent with the potential flow solution for 

added mass. 

It is necessary to choose an appropriate method or analysis 

technique that is compatiblewith fatigue design parameters such as 

the structure configuration and its susceptibility to fatigue and 

the environment. If the structure dynamics are negligible, and a 

deterministicanalysis,based on the use of wave exceedence curves, 

may be appropriate for initial sizing of platform components. 

However, for most structures, the dynamic response should be 

incorporated into the fatigue analyses as illustrated in the above 

given equilibrium equations. 

A rigorous analysis using a time integration method to determine 

platform global and local dynamic responses at each wave height and 

period is time consuming and costly. Therefore, it is desirable to 

have an alternative analysis procedure. One such alternative 

proposed by Serrahn (Reference5.15) consists of a hybrid time and 

frequencydomain analysismethod. The analysisflow charton Figure 

5-4 summarizes this analysis methodology. 

Global spectral static and dynamic responses (e.g. base shear and 

overturningmoment) aredeterminedat selecteddiscretewave heights 

and periods. The static response is determined based on an applied 

5-21

load analysisof adetailed three-dimensionalmodel of the platform. 

An eigenvalue (modal) analysis is also performed on the same model 

to determine platformnaturalperiods and mode shapes. The platform 

global dynamic responses are determined by separating each applied 

static wave loading into its Fourier series components and solving 

directly for the dynamic response (This method of solution is 

detailed in Appendix E of Ref. 5.15). Spectral analyses for both 

the static and dynamic responsesare then performedand the spectral 

inertial load calculated. Inertial load sets are then developed 

from the modal results of the previous eigenvalue analysis which 

produce the calculated global spectral inertial response (This 

method of inertial load development is detailed in Appendix F of 

Ref. 5.15). 

Such analyses can be repeated for various wave spectra, structural 

damping, platform peri?d, etc. at a relatively nominal increase in 

analysis time and computer cost. Therefore,this method facilitate 

parametric studies to assess fatigue sensitivity of the platform. 

Of the three spectral analysisoptions availableto define the wave 

loading, the frequency-domainsolution, providing member and joint 

in-and out-of-phase wave loads is most frequently used due to its 

simplicity. For an iterativedesign process, an analysis approach 

utilizing random waves or regular waves in time domain is 

appropriate but not frequently used due to both time and cost 

constraints. Thus, a hybrid time and frequency domain method is 

well suited for spectral fatigue analysis of a bottom-supported 

structure. Figure 5-5 illustratesthe scatter of fatigue lives as 

a function of the analysis method chosen. 

Another appropriate procedureto define hydrodynamicsandwave-force 

model, proposed by Kint and Morrison (Reference5.16), is based on 

a short extract from a random simulation substituted for a design 

wave. The proposedprocedureoffers a valid and a relativelysimple 

alternative to the conventional regular wave analysis. Inertial 

loads due to structure response can be obtained and dynamic 

amplification factors (DAFs) determined by performing a number of 

5-22

simulations of random waves. The basic DAF approach, allowing 

combination of inertial loads compatible with static loads, is 

further discussed by Digre et al (Reference 5.17). Typically, 

simulation of the response is performed, the ratio of dynamic-tostatic 

loads determined (i.e. DAF) 

until the DAF stabilizes. Larrabee 

and the process is repeated 

(Reference5.18) also provides 

further discussion on the logic beh” nd DAF approach. 

5.3.4 Stiffness Model 

The load and the stiffness models are essentially the same. 

Typically, a three-dimensionalspace framemodel of the structureis 

made up of individual joints and members, each defining the joint 

and member incidence, coordinates, hydrodynamic coefficients, 

etc. that are necessary for generationof environmentalloads. The 

loads model, providedwith member cross-sectionareas and stiffness 

properties,joint releases,and boundaryconditions,transformsinto 

a stiffness model. The structure mass model incorporates the 

correctmember sizes,joint coordinatesand boundaryconditions,and 

can be considered a stiffness model. Static stiffness analysis 

solution follows standard structural analysis technique. Dynamic 

analysis is typically based on a modal (eigenvalue) analysis 

solution; two modal analysis solution techniques may be used: 

● 

The subspace iteration technique is a Ritz-type iteration 

model used on a lumped mass system that produces eigenvectors 

and eigenvalues for a reduced set of equations. This is the 

method of choice for most fixed offshorestructuressinceonly 

a relativelysmall number of modes are required to adequately 

model the total structure response. 

● The Householder tridiagonalization technique first 

tridiagonalized the dynamic matrix, then computes all 

eigenvectors and eigenvalues by inverse iteration. This 

technique is most appropriate for structures with a small 

number of degrees of freedom, for structureswhere all modal 

5-23

esponsesare required , or where consistentmass modeling has 

been used. 

Once eigenvectors and eigenvalues have been determined, specific 

dynamic analysesunder load (suchas wave loading)maybe performed. 

As previously mentioned, rigorous time integration analyses may be 

undertaken, evaluating the dynamic response of the platform over 

many cycles of wave loading until steady state response is achieved. 

However, the previously recommended approach of expressing the 

applied loading as a Fourier series and solving and superimposing 

the response of each platform mode to each Fourier sinusoidal 

component allows direct determinationof platform dynamic response 

without time consuming and costly time integrationanalyses. 

The global analysis carried out is often intended to analyze the 

three-dimensionalspace frame lateral deformations and ensure that 

all components of the structure meet fatigue requirements. An 

emphasis should also be placed on plan-level components near the 

water surfaceand subjectedto vertical (out-of-plane)deformations. 


Small structures in shallow-to-moderate water depths and in 

relatively mild environments are typically not analyzed for 

fatigue. Often, stress levels are evaluated and API’s simplified 

allowable stress method is used to verify the integrity of design. 

Other structures are designed for a wide range of pre-service and 

in-service design conditions, including fatigue. Since a fatigue 

analysis is carried out to ensure that the design has adequate 

safety against damage due to fatigue during the planned life of the 

structure, it should address the variables affecting fatigue 

appropriately. Modeling and analysisvariables (stiffnessand mass 

models, loading coefficients, stress RAOS, SCFS, etc.), affecting 

the strength model, and the wave climate (scatter diagram, 

directionalprobability,wave spectrum),affectingthe time history 

model, incorporatesubstantial uncertainties. 

5-24

The analysis effort must be kept comparatively flexible and 

manageable and the level of effort should be compatiblewith design 

objectives and available information. 

It is recommended that a simplified allowable stress approach or a 

deterministic fatigue analyses be limited to initial sizing of 

members, if considered desirable. A thorough spectral fatigue 

analysis is recommended to identify fatigue sensitive 

components/detailsof a structure and to take corrective measures. 

Considering its relative ease of application a spectral frequencydomain 

method is well suited for design. A time-domain method is 

better suited to determine the response of a bottom-supported 

structure. Since it is time consuming and costly to determine 

global and local dynamic response of the platform for each wave 

height and period, an alternate less time consuming method is 

desirable. Several methods (References 5.15 and 5.16) are 

appropriate. A hybrid time- and frequency-domain analysis method 

(Reference 5.9), also facilitates carrying out of extensive 

parametric studies to assess fatigue sensitivity of structure 

components for a wide range of variables and is recommended for 

fatigue analyses and design. 

5.4 

DEVELOPMENT OF HOT-SPOT STRESSES 

5.4.1 

Nominal Stresses and Stress RAOS 

The stresses obtained from a stiffness analysis, and the response 

amplitude operators (RAOS)generated, represent nominal or average 

stresses. Ingeneral,correct inputof member cross-sectionalareas 

and sectionpropertiesallowdeterminationof nominal stressesquite 

accurately. 

More complex joints, incorporating bulkhead and diaphragm sub 

assemblies, require careful evaluation to determine the realistic 

load paths. To determine the nominal stresses at complex joints, 

5-25

either multiple stick elements (for each load path) or a finite 

element model should be utilized. 

5.4.2 Stress Concentration Factors and Hot-SPot Stresses 

Background 

The locations at which maximum stresses occur are called hot spots. 

Hot spots usually occur at discontinuities such as the stiffener 

edge or a cutout. On tubular member intersections, they usual1y 

occur on either the weld toe of the incoming tubular (brace) or of 

the main tubular (chord), depending on the geometry of the joint. 

The stress concentration factor (SCF) is evaluated by taking the 

ratio of the hot-spot principal stress to the nominal principal 

stress. The hot-spot stress used in fatigue life assessment is 

raised to a power of the inverse of the slope of the S-N curve 

used. Since the inverse of the slope of S-N curve is usually 

between 2.5 and 4.0, the choice of SCF can have approximately a 

cubic effect on damage. Thus the SCF value is probably the most 

important variable affecting the applicable stress ranges through 

the life of a structure and thus the fatigue life of joints. 

There are several practical approaches for determining SCF values: 

● 

Develop an analyticalmodel ofthedetail/joint and carry out 

a finite element analysis (FEA). 

● 

Test a physical model and obtain hot-spot stresses from 

measurements. 

● 

Use empirical formulations. 

The use of FEA is the most reliable and reasonably cost-effective 

approach for complex joints. When modeled correctly, the SCFS 

obtained by FEA are very reliable and depend largely on the mesh 

sizes used in the analysis. Whether the physical model used to 

determine the hot-spot stresses is an acrylic model or another 

5-26

alternative, the accuracy of hot-spot stresses depends largely on 

the ability to predict hot-spot stress locations in advance and 

obtain measurements in those areas. 

Since the use of both FEA and the physical model requires 

substantial investmentof time and cost, they can be used only on a 

selective basis. Thus, most structure hot-spot stresses must be 

defined based on the applicationof empirical formulations. 

Joint Geometry 

The primary variables affecting the magnitude of stress 

concentrationare weld profile and joint geometry. The weld profile 

is accounted for in the S-N curve. The joint geometric 

characteristics determine the magnitude of stress concentration. 

For most simple structuraldetails, typically awide range of plate 

and stiffener joints, the nominal stresses can be used directly to 

compute fatigue lives as the effect of SCFS are incorporatedin the 

S-N curves. 

The joint geometriesof tubularmembers are quite complex andthe S- 

N curves are used with the hot spot stresses, requiring definition 

of SCFS for each joint geometry and loading. The SCFS are 

determined for axial load, in-planemoment and out-of-planemoment. 

Typically, a peak SCF is determined and conservatively applied to 

eight points around the intersection. For the crown and saddle 

points shown on Figure 5-7 separate SCFS can be determined. At 

other locations, the SCFS are then interpolated between the crown 

and saddle positions. 

Joint Definition 

When tubular members frame into one another, they form a tubular 

joint, with the largest diameter or thickest member being the 

through member or chord and all other members being braces. 

5-27

Braces may have stubs or cones, which are the part of the brace 

member welded to the chord. Typically,both the stubs and the cones 

are thicker than the brace members. 

To facilitatethe developmentand use of empiricalequationsseveral 

parametersare used in definingthe characteristicsof a joint. The 

chord diameter and thickness are referred to as D and T 

respectively. The brace or stub diameterand thicknessare referred 

to as d andt. The angle from the chord to the brace is defined as 

theta 0. The ratio of the brace diameter to chord diameter is 

defined as beta, B. The ratio of chord radius to chord thickness is 

defined as gamma, y. The ratio of brace thickness to chord 

thickness is defined as tau, ~. The empirical equations used to 

determine SCFS utilize the parameters . The (3,~, y, T. The 

terminologyused in defining a simple joint is shown in Figure 5-7. 

Joint Type and Classification 

Joints are classified intotypes based on geometry and loading. The 

joint type usually looks like the letter formed from the brace and 

chord intersection. Four basic joint types exist in offshore 

structures: 

1) T or Y joint 

2) K joint 

3) KT joint 

4) X joint 

Figure 5-8 shows the four common joint types. 

Although the joint type usually looks like the letter formed from 

the brace and chord intersection,the joint is actually classified 

according to load distribution. If the axial load is transferred 

between the brace and chord by shear, then the joint is classified 

as a T or Y joint. If the load is transferredbetween the braces at 

a joint, without traveling through the joint, then the joint is 

5-28

classified as a K joint. If the load is transferred by some 

combinationof shear through the joint and brace-to-brace,then the 

joint is classified as a KT joint. 

If the load is transferredthrough one side of the chord to another, 

then the joint is classified as an Xjoint. Figure 5-9 shows joint 

classification by load distribution. 

5.4.3 

Empirical Eauations 

Prior to the discussion of empirical equations it is beneficial to 

briefly discuss the available data on SCFS. Review of various 

publisheddata (References1.8, 5.19, 5.20, 5.21 and 5.22) indicate 

that substantial scatter of SCFS is observed. Variations in SCFS 

occur in both nominally identical joints and in symmetrical 

locations of joints where one would expect little variations in 

SCFS. Material and fabrication imperfectionscontribute to the SCF 

variations. Lalani et al (Reference 5.23) point out that the 

parameterscontributingto these variationscan be grouped intotwo: 

● 

Experimental error, including modeling, gauge position and 

measurements and the loading. 

● 

Expected variations due to material and fabrication 

imperfections,includingvariations in weld profile, size and 

imperfections. 

The use of empirical formulationshas been extensively accepted for 

fatigue analysisof marine structures. A set of empirical formulae 

developed by Kuang (Reference 3.2) were derived by evaluating 

extensive thin-shellFEA results. The formulae proposed by Smedley 

(Reference3.3) and Wordsworth (Reference3.4) of Lloyd’s Registry 

were derived from evaluating the results of strain-gauged acrylic 

models. Other empirical equations published include those by 

Gibstein (References 5.21, 5.24), Efthymiou (5.19) and Wordsworth 

(5.25). 

5-29

Whatever the basis for an empirical formula, the formula has an 

applicable range of parametersand the level of conservatismvaries 

not only with the formulation but also within the applicable range 

of parameters. The use ofSCFs also requires judgement not only on 

the applicabilityof an empirical formula but also on assessment of 

implicationsof in-plane and out-of-plane loadings/stresses. 

The parametricequationsdevelopedby Kuang,Smedley-Wordsworth,and 

$medley consist of different relationships defined by the joint 

variables D, T, d, t, L, g, and 9. 

Different equations are applicable for d fferent joint types. 

Presently, the joint types and the applicable equations most often 

used are listed below: 

Joint T.YPe 

TorY 

K 

KT 

x 

Applicable Equations 

Kuang, Smedley-Wordsworth,& Efthymiou 

Kuang, & Smedley-Wordsworth 

Smedley-Wordsworth 

Smedley-Wordsworth,& $medley 

The empiricalequationsgiven byUEG (Reference1.8) are based on an 

extensive database and relate to Woodworth equations. Modification 

of Woodworth equations and the extension of the validity ranges 

allow the application of UEG equations to joints with extreme 

geometries. Comparisonof variousempiricalequationsshow thatUEG 

equations yield generally conservative values of SCFS and are 

considered to be most reliable. On the otherhand none of the 

equations appear to allow accurate determination of K-joint SCFS 

subjected to axial loading. 

An excellent overview and reliability assessment of SCF empirical 

equations are providedby Ma et al (Reference5.20),Tolloczko et al 

(Reference 5.22) and Lalani et al (Reference 5.23). Further 

discussion on SCFS and the predicted chord SCF for the different 

equations for T and K joints are presented in Appendix C. 

5-30

Details of Equations 

The details of some of the equations are given in Appendix C. The 

equations are given in simple terms of joint geometry: D, T, d, t, 

L, g, and r. The Kuang brace SCFS have been modified for the 

Marshall reduction. The Smedley-Wordsworth chord SCFS have been 

modified for the recommendedd/D limitation. 

The parametric equations should not be used outside of their 

assigned limits without justification. Near the assigned limits, 

the SCFS rapid decrease should be noted to determine if the 

calculated SCF is unconservative. The Smedley-Wordsworth effects 

revised for d/D limitation can dramatically increase SCFS for d/D 

ratios near 1.0. 

Minimum Stress Concentration Factor 

The minimum stress concentration factor for all modes of loading 

should be 2.0. This is generally accepted as an industry lower 

bound. However, acrylicmodel tests from the Tern project in United 

Kingdom showed a SCF of 1.6 could be used as a lower bound. 

5.4.4 Illustrationof a T-Joint SCFS 

A typical T-joint with an assumed applied axial load is used to 

illustrate the application of empirical equations. 

The joint shown on Figure 5-10 is classified by load path and the 

joint variablesare specifiedin orderto determine an SCF according 

to Kuang and Smedley-Wordsworth criteria. The Kuang brace SCF 

includes a Marshall reduction factor, Qr. The Smedley-Wordsworth 

chord SCF calculation uses the d/D limitation. 


Uncertainties 

5-31

The SCF equations currently in use for simple tubular joint design 

are based on results of acrylicmodel tests and finite element (FE) 

analysis. Lloyd’s Register has recently studied these empirical 

questionsand assessedtheirreliabilitywhen comparedagainststeel 

specimentest data. Althoughthe empiricalequationsare considered 

reasonably reliable, substantial uncertainties exist as the SCF 

equations: 

● 

● 

● 

Sometimes do not properly account for relative braceloads 

Sometimes do not properly represent the stress at the brace 

and chord connection of interest 

Axial SCF value for crown and saddle is not constant 

The FE analysis of SCFS yield substantially different values 

depending on both the modeling techniques and the computer program 

used. The use of a thin or a thick element, modeling of the weld 

and the definition of chord length substantially influence the 

computed SCFS. 

SCF equations for a T or a Y joint typically contain a term for 

chord length. Since the appropriate length for a chord is not 

defined, most designers use the chord can length. While this is 

conservative,the use of the half of the bay length to representthe 

chord could be very unconservative. 

Substantial work carried out in Europe need further assessment and 

analyses. An API Task Group will be formed in 1991 to review the 

SCF equations in detail, to identifytheir validity and limitations 

and to recommend preferred SCF equations for specific joint types 

and load components. 

An API initiated joint industry project (JIP) is proposed to 

summarize the computer programs used and modeling strategies 

implemented to investigate variables affecting the SCF (including 

chord length) and to developguidelineson obtainingSCFS by the use 

of FE analysis. 

5-32

Screeninq Process 

For a preliminarydesign ofa structure it is common practice to use 

a blanket SCF of 5.0 or 6.0 for all joints, depending upon dynamic 

effects. If the structure is susceptible to dynamic amplification 

the higher blanket SCF should be used. Once the fatigue sensitive 

joints are identified during this screening process, the SCFS for 

these joints should be determined. 

In the determinationofSCFs a parametricstudyofvariablesd/Dand 

t/T should be considered. The joint fatigue life is a function of 

nominal brace stress and SCF. To increase joint fatigue life, the 

nominal brace stress or the SCF should be reduced. An increase in 

brace diameter can dramaticallyreduce nominal brace stress without 

a significant increase in SCF. This is particularlytrue for brace 

members intersecting large diameter legs. However, where members 

are more similar in size, an increase in brace diameter also 

requires an increase in chord diameter. 

By increasing the brace diameter rather than increasing the brace 

thickness, a more effective section can be used and prohibitively 

low diameter to thickness ratios can be avoided. Increasing the 

brace diametermay be the easiestwayto increasejoint fatiguelife 

during preliminary design. The chord diameter may also have to be 

increased to offset the SCF increasesif the brace area and section 

modulus are increased. 

Comprehensive Desiqn 

Once the member diameters are finalized a comprehensive fatigue 

analysis and design may be carried out. The parameter most easily 

modified during this stage is the member thickness. An increase in 

brace thickness increases brace axial and bending section 

properties, which will reduce brace nominal stress. However, as 

stated above, the chord thickness should be increased accordingly. 

Otherwise the brace nominal stress reduction will be offset by the 

joint SCF increase, resulting in marginal difference in fatigue 

5-33

life. During the comprehensive design the best parameter to 

increase is brace thickness while keeping t/T constant. 

Further improvementsin fatiguelivesmaybe obtained by determining 

the SCF through the use of finite elements analysis or models 

tests. Another alternative to lower the SCF is to stiffen the 

joints with rings and thus reduce the SCFS to the lower bound 

values. However, considering the increased fabrication costs of 

stiffened joints, the use of rings should be considered the least 

desirable option to lower the SCFS and improve the fatigue lives. 

The validity of SCF equations and their sensitivities to various 

geometric parameters are illustrated in Appendix C. It is 

recommended that the tables and figures provided are studied to 

determine an acceptable approach compatible with the specific 

problem on hand. A finite element study results are also included 

in Appendix C to illustratethe range of SCFS for a typical complex 

joint. Since empirical equations are applicable for only simple 

joints, a FEA is recommended for determination of complex joint 

SCFS. 

5-34

-“ 

30 Calculation l.iaoas 6 Beck (1905) 

Exserlment, Gerritsma & Beukelman 11964) 

\ $trln Theory 

1 30 Calculation Inglis and Price (79B21 

I 

-, , 

-, * JO calculation Chang [lg77] 

=zl=~ 

\ 

\ 

“$ ‘\ 

---- -. - . . - . .- 

‘-”-””” 

Figure 5-1 Comparison of Heave Added Mass and Oamping 

coefficients Based on Different Methods 

(From Reference 5.2) 

Im 

lm- 

140- 

120- 

lM - 

w- 

m- 

40- 

20- 

1 

0 

2 

18 a2 2s 

Figure 5-2 Comparison of Wave Loading Based Conventional 

and Consistent Methods 

(From Reference 5.8)

?.s 

I 

z - 

]LEvE~ ~ 

1,5 

\ 

i i+ 

11 Is 

1CM 

I 

0.5 

5 

Icd 

0 L 

I 23 57\o 20 3Q 50 70 

Keuleqon - Carpenter- No. 

Figure 5-3 Comparison of Mean Cd and Cm Values for Christchurch Bay Tower 


/“7; “< , ._.

PlatlOrmDetailed 

3-D ModW 

1 

I Generate -C 1 

I WsMebads I 

Sekted H@%ioci I 

I 

s- AmJyses 

and DAFs 

I 

StaficForms I I Ineftial Forcss [ 

Msmber Erid 

Total I=Orms 

Figure 5-4 Dynamic Wave mad Analysis Methodology

-. 

Figure 5-5 Comparison of Detailed Fatigue Analyses Techniques

I ‘-l 

!1r.“N%%’, 

QN 

SECTION 

A-A 

I ‘STUDOF HEA~ WALL OR 

SPECIAL STEEL IN BRACg 

[OPTIONAL) 

\ 

THROUGH J ,\ 

i 

BRACE 

‘A L‘\ 

p 

DETAIL OF SIMPLE JOINT 

DETAIL OF OVERLAPPING 

JOINT 

Figure 5-6 Jo~t GeOIW~ (From -f ereme 1-5) 

Crown point “ 

Figure 5-7 Stiple Joint Terminolo~ (From Reference 1.6)

( -t ) 

( 

T–JOINT 

Y–JOINT 

( \ I / 

K–JOINT K–T JOINT X–JOINT 

Figure 5-8 Common Joint Types

JOINT IN=PLANE OUT–OF–PLANE 

CLASSIFICATION AXIAL BENDING BENDING 

T 

I 

+, (Q) ~+= 

P/2 P/2 M/2 M/2 

\ 

/’ 

P 

M 

M 

L 

\ 

P 

x.P 

\ 

x J 

“’ M 

M 

(“ 

M 

/“ 

x“ /’ M 

K 

‘c 

P sin Q 

-% 

‘o < 

P sin 9 

\ 

P 

T 

Figure 5-9 Joint Classification by Mading

SMEDLEY-WORDSWORTH 

0 

d =— = 

D 

600 

m 

VALIDITY CHECK 

= 0.500 0.13 s a =0.500 s 10 / 

Y“ 

D 

T= 

1200 

2(40) 

= 15.0 lzsy= 15.0 s 32 / 

T = += 

20 

-m- 

= 0.500 0.25 s T = 0.500 s 1.0 / 

e = 90° 30° s e =90° s 90° 4 

AXIAL SCF CHORD 

SADDLE SCF = Y T 6 (6.78 - 6.42 0°”5) Sin(1”7~.7B3)e = 8.40 

CROWN SCF = [0.7i-l.37Y005~(l-d)][2Sin0*5@ - Sin30] 

.— 

KUANG 

a 

T(2Y6-T)(3-6 Sino)$ino 

+[ 

l=S(l.2-B)(COS40+ 1.5)1 = z 16 

][1.05+ 309 

2Y-3 

. 

=— d = 600 

= 0.500 0.30 s B 

D 

= 0.500 s 80 / 

Tm 

Y 

Y- 

T 

.. 

--D- ‘+% 

= 0.0333 0.015 s y = 0.0333 s 0.060 J 

t 20 

7 =_ T = 

40 

a =— = 

II 1200 

L m 

= 0.500 0.20 s T = 0.500 s 0.80 / 

= 0.0571 0.05 S a = 0.0571 s 0.30 / 

Q = 90° 30° so = 90° s 90° / 

AXIAL SCF CHORD 

SCF = 1.177y-0”808e-i ”283~l”333d-0.057sin1.6g40 = 7.40 

Figure 5-10 Sample Evaluationof a T-Joint

6. FATIGUE STRESS HISTORY MODELS 

Creation of the fatigue stress historymodel requires determination 

of the fatigueenvironmentand applicationof the environmentto the 

structure to produce stresses. The environment can be applied to 

the structure by either a spectral analysis or by a time-domain 

analysis. The spectral analysis derives the stress range and an 

average N number of cycles from the statistical properties of the 

stress response spectrum. A true time-domain analysis sorts the 

stress ranges and accumulatesthe stress range counts as the stress 

time history is being generated. For practical reasons a hybrid 

time-domain method is often used to generate stress history. 

6.1 

DETERMINATIONOF FATIGUE ENVIRONMENTS 

To evaluate the fatigue life of a fixed structure or a floating 

vessel a representativefatigue environmentmust be modeled. For a 

fixed structurethe fatigueenvironmentwill be the typicalwave and 

wind conditions for the surrounding area. For a ship the fatigue 

environment will be the typical environmental conditions along 

various routes. 

6.1.1 Data Sources 

The types of environmentaldata range from actual wave and/or wind 

records to recreated (hindcast)data. The wave and wind recordsmay 

be raw recordings (not generally available) or condensed summary 

reports produced by government agencies or environmental 

consultants. Hindcastdata are generatedby various computermodels 

using environmental information available for the area or nearby 

areas. 

6-1

Wave Records 

Older wave and wind informationhas come from voluntaryobservations 

by ship personneland frommeasurementsby weather ships and coastal 

weather stations. The most likely source of current wave records 

are from government agencies such as the National Oceanographic and 

Atmospheric Administration (NOAA),obtained through various means, 

including weather platforms and weather buoys. Newer techniques 

using measurements from satellites provide more comprehensivewave 

records. Hoffman and Walden (Reference6.1) discuss environmental 

wave data gathering in detail. 

While majority of the published wave data is from the North 

Atlantic, much of the data applicableto the Pacificwere published 

in Japanese and Chinese. Several recent publications (References 

6.2, 6.3 and 6.4) in English provide additionaldescription of wave 

environment in Asia - Pacific. 

The older wave and wind data has the advantage that it covers many 

years (decades), but the disadvantages are that the wave heights 

were visually estimated, the wave periods were crudely timed, and 

the wind measurements were likely biased by the vessel speed. 

Various data analysts have devised formulas to correct the 

“observed” data. For example, Hogben and Lumb (Reference 6.5) 

developed the equations to correlate the significant wave height 

(Hs) and the mean zero uncrossing period (Tz) with the observed 

data: 

Hs = ( 1.23 + 0.44*HOWS) 

(meters) 

Tz = ( 4.7 +0.32*Tows ) 

(seconds) 

HOws is the wave height and Tows is the period reported by observers 

on weather ships. 

6-2

Actual recordedwave elevationdata is the most accurate information 

available. However, wave records are only available for a few 

locations, and typically the time spans of available recorded wave 

data are less than 10 years. Even recorded data may not be 

complete. The most serious fault in recorded data is that 

measurement techniques cannot detect the higher frequency waves. 

Wave rider buoys measure wave slope and wave heights are derived 

from the slope records. The resolution of these slope measurements 

are limited by the dimensions and motion properties of the buoy. 

The recorded data does not readily allow detection of the very long 

period waves and subsequent data analyses “filter” out the long 

period information. Filteringis used to separate “sea” and “swell” 

wave spectra. The sea/swell filtering technique is often a simple 

truncation of the measured spectrum above and below a selected 

frequency. Thus, the higher frequency “sea” part of the spectrum 

loses its longer period wave information. 

Wind Data 

The sources of wind data are the same as for wave data. Older data 

tends to be voluntary observations from ships and newer data comes 

from measurements on platforms or from weather buoys. Satellites 

may provide informationon high altitudewinds by tracking clouds or 

from lower level winds by tracking weather balloons. 

The older observations are logged anemometer readings and are 

typicallyonly the mean wind speed. The height abovewater at which 

the wind speed was measured may be unknown. Various analysts have 

devised methods to correlate observed wind data to actual measured 

data. 

Existingoil platforms allowedgathering of extensivewind records, 

including gust readings which can be analyzed to derive wind 

spectrum information. The presence of the platform has some effect 

upon the measured wind velocity, and the location of the anemometer 

is very important to the accuracy of the measurements. 

6-3

In many cases wind informationmay be available from transmitting 

ships or nearby coastal weather stations for areas where wave data 

is either skimpy or questionable. For these cases various equations 

have been developed to estimate or verify the wave information. 

Example equations to relate wind speed to wave height can be as 

simple as the “25% Rule”, 

H~ = 0.25 * U 

where Hs is the significant wave height in feet and U is the 

observed wind speed in feet/see. More involved equations include 

the wind “fetch” and the wind duration. The wind fetch is the 

distance over water that the wind acts. Appendix B presents the 

equations developed by Bretschneider to calculate wave height and 

period based on wind speed, duration and fetch. 

Hindcast Data 

Elaborate computer models have been developed to “hindcast” or 

recreate weather (wind and wave) records. The hindcast models may 

be for a region (such as the North Sea), or the models may be 

oceanic or even global. One important consideration in the 

developmentof hindcastmodels is the sensitivityof these modelsto 

interaction of various parameters. Using available wind and wave 

data to correlate the hindcast results can improve the accuracy of 

hindcast models. 

The hindcast models derive wind information from pressure and 

temperatureinformation. Pressuremeasurementsare fairlyaccurate, 

and the techniques of combining the pressure readings from many 

measurementstationsto produceisobarplots allowsdeterminationof 

the pressures over a large region without making measurements at 

each grid point. The temperatures measured at coastal weather 

stations surrounding the area of interest along with whatever 

temperature measurements available from the area can be used to 

identify temperature gradients, fronts, etc. 

6-4

Wave informationis calculatedfrom wind, accountingfor direction, 

duration and fetch. By integrating the weather conditions over 

small time steps, a wind and wave history can be built. The 

resulting records can be analyzed in a manner similar to that used 

with actual wind and wave records to produce wave scatter diagrams 

and wave exceedence curves. 

6.1.2 Wave and Wind SDectra 

Wave and wind spectra define the energy that is being applied to a 

structure or vessel. There are many wave spectra formulations and 

some of these are discussed in Appendix A. The most general and 

therefore most useful wave spectrum formulation is the General 

JONSWAP. The General JONSWAP spectra include the Bretschneider 

spectra which in turn include the Pierson-Moskowitz spectra. 

Reference 6.6 presents a summary of the various wind spectra. The 

spectrum recommended in Reference 6,6 is defined as follows: 

JONSWAP Wave SDectrum 

The JONSWAP (JointNorth Sea Wave Project)spectrumwas derived from 

wave measurements in the southern North Sea and is based on older 

spectraformulations,Pierson-Moskowitz/Bretschneider/ISSCModified 

P-M. The Mean JONSWAP spectrum has fixed parameters and represents 

the waves measured during the project. The General JONSWAP 

parameters can be varied so that the spectrum can represent either 

fully developed seas or developing seas. 

The formula for the JONSWAP spectrum is as follows: 

s(f) = a (g2/f5)EXP[-1.25(f/fm)-4]qa 

where 

a = EXP[-.5 (f-fm)2/(sfm)2] 

The Mean JONSWAP is defined with the following parameters. 

6-5 

l-u /J

q = 3.3 

s = 0.07, for f< fm 

s = 0.09, for f > fm 

The Bretschneider spectrum is a subset of the General JONSWAP; 

setting the gamma parameter to 1.0 converts the JONSWAP spectrum 

into the Bretschneideror ISSCModified P-M spectrum. Also setting 

the alpha parameterto 0.0081 convertsthe JONSWAP spectrum intothe 

Pierson-Moskowitzspectrum. 

As a guideline, the JONSWAP spectrum with gamma = 2 would be an 

applicablespectrum for confined regional areas. The Bretschneider 

spectrum (JONSWAPwith gamma = 1) would be applicablefor open ocean 

(Pacific or Atlantic) areas. 

Ochi-Shin Wind Spectra 

Ochi and Shin reviewed six wind spectra formulations currently in 

use and have created an average wind spectrum to represent the 

variation (gusts) of the wind about the mean value. The wind 

spectrum represents the average of measured spectra and was 

deliberately devised to accurately represent the low frequency 

portion of the wind spectrum. The equation has three forms 

depending upon the frequency range. 

s(f*) = 

{ 

583 f* 

420 f*0”70/(l+f*O-3’) ”-5 

838 f*/(l+f*0.3s)ll.s 

with 

f* = f z/uz, 

where 

f = frequency in Hz, 

z = height above sea level in meters, and 

Uz= mean wind speed at height z in meters/see. 

6“6

6.1.3 Scatter Diaqram 

Wave scatter diagrams show the occurrences of combinations of 

significantwave heightand averagezero-uncrossingperiod overmany 

years. 

$iqnificant Heiqht vs Zero-crossinq Period 

Irregular waves do not have any consistent pattern of height or 

period, but exhibitcompleterandomness. Irregularwave heightsand 

periods are usually defined by the statistical properties of the 

wave record or by the properties of the energy spectrum which 

represents the random sea. The significantwave height is taken to 

be four times the standard deviation of the recorded water surface 

elevations,or if the sea is representedby a half-amplitudeenergy 

spectrum, the significantwave height is four times the square-root 

of the area under the spectrum. The average zero-uncrossingperiod 

is the average of the time intervals between negative to positive 

sign changes in the recorded water surface elevations, or is the 

square-root of the area under the spectrum divided by the squareroot 

of second moment of the spectrum (frequency in Hz). 

The wave height and period distributionovertime can be obtained by 

actual wave measurements. The heights and periods of all waves in 

a given direction are observed for short periods of time at regular 

intervals. A short time intervalof severalhours maybe considered 

constant. For this sea state, defined as “stationary”, the mean 

zero- uncrossing period, Tz, and the significant wave height, Hs, 

are calculated. The Hs and Tz pairs are ordered, and their 

probabilitiesof occurrencewritten in a matrix form, called a wave 

scatter diagram. A typical wave scatter diagram, presenting 

statistical data on the occurrence of significant wave height and 

zero-uncrossingperiod for one direction is shown on Figure 6-1 and 

further discussed in Appendix B. 

6-7

Seasonal Variation 

The annual wave scatter diagram is often separated out into monthly 

or seasonal (spring, summer, fall and winter) scatter diagrams. 

Because a fatigue environment covers many years, the seasonal or 

monthly scatter diagram cell values may be added to produce the 

annual diagram. 

Directional Variation 

Sometimes the wave scatter diagram is separated out by direction. 

This may be important for fixed structures, because waves from one 

directionmay cause a different stress distributionthan waves from 

another direction. 

Sea and Swell 

Sometimes the wave scatter diagrams are separated into “sea” and 

“swell”. The sea scatterdiagram shows the significantwave heights 

and zero-uncrossingperiodsdefiningsea spectra. The swell scatter 

diagram usually shows the heightsand periodsof long period regular 

waves. This separated informationcan be helpful in analyzing the 

structure, because the swell may be present a large percentage of 

the time, and the swell is likely to be from a different direction 

than the higher frequency waves producing unique stress 

distributions. 

6.1.4 Directionality and Spreadinq 

The directions that have been referred to up to now have been the 

“central”directionof the sea. Irregularwaves are often idealized 

as two-dimensionalwith wave crests parallel in the third dimension 

and all waves moving forward. Such an irregularsea is called long 

crested. In reality, storms occur over a finite area and the wave 

heightsdiminishdue to lateral spreading. If such waves meet other 

waves from different directions, a more typical “confused” sea is 

observed. A confused sea is referredto as a short-crestedsea. The 

6-8

waves in a short crested sea approach from a range of directions 

centered about the central direction. 

Directionality 

For a fixed structure the direction of the sea will affect the 

stressdistributionwithin the structure. Most fatigueanalysesare 

performed for four or eight wave directions. When directional wave 

scatter diagrams are available the sea direction can be matched to 

the analysisdirection, and the fatiguedamage accumulated. If the 

data availabledo not includewave directionality,directionscan be 

estimated on the basis of wind roses or hindcasting. 

Spreading 

In order to model a short crested sea a “spreadingfunction” is used 

to distribute the wave energy about the central direction. In 

typical analyses the short crested sea is represented by a set of 

long crested spectra coming from directions spread over -90 deg to 

+90 deg from the central direction 

to the specified short-crestedsea 

and having a total energy equal 

spectrum. 

The directional spreadingfunction as defined by Kinra and Marshall 

(Reference6.7) is often used in the following form. 

D (8) = Cn COSn (1?) 

where n is a positive integer and is measured from the central 

direction. The coefficient C. should satisfy the following: 

A typical n value for wind-driven seas would be 2, while an 

appropriatevalue for a limited fetch (restrictedspreading)may be 

6-9

4. ~arpkaya 

spreading. 

(Reference 6.8) provides further 

discussion on 

A significant effect of short crested seas is that they can cause 

response in a direction orthogonalto the central direction, i.e. a 

ship may develop considerableroll motion even though the vessel is 

headed into the waves. 

In the design and analysis of typical offshore platforms (i.e., 

conventional structures in shallow or moderate waterdepths) 

spreading is generally neglected. However, for both typical and 

nonconventional structures such as the tripod or an extended base 

platform (see Figure 6-2) spreadingmay be significant. A platform 

with very differentresponsecharacteristicsin two orthogonalaxes, 

such as the extended-base platform, may be susceptible to larger 

dynamic response in one axis. Even a typical platform, with a 

natural period coinciding with the wave force cancellation 

frequency, will be subjected to higher wave loading at the 

cancellation frequency and neglecting of spreading may not be 

conservative. 

6.2 

STRESS SPECTRUM 

A stress spectrum is the stress energy distribution resulting from 

loading the structurewith a particular sea spectrum. 

6.2.1 Stress RAOs 

In order to derive the stress statisticsa stress response spectrum 

is developed. The stress response spectrum is the product of the 

wave spectrum ordinates times the stress response amplitude 

operators squared. The stress response amplitude operators (RAOS) 

are the stresses representing a “unit amplitude” regular wave, 

obtained by normalizing the input wave heights. 

The stress responsesto a set of regularwaves coveringthe complete 

frequency (or period) range and the complete direction range are 

6-10 

[,>—~q

evaluated as explained in Section 5. For a vessel global effects 

of port and starboard quartering seas are identical, allowing 

reduction of applied loading cases. Similarly, for a platform with 

two planes of symmetry several of the eight loading cases (45 

deg. intervals)may be combined. 

6.2.2 

Res~onse Analysis 

The response analysis squares the stress RAOS; multiplies them by 

the spectrum ordinate; multiplies that product by the spreading 

function;andsums/integratesoverdirections the resultsto produce 

the stress spectrum. 

The stress range spectra is integrated to allow determination of 

various statistical parameters, including the zero-uncrossing 

frequency, the mean squared value, etc., from which the short-term 

probabilitystatistics preconstructed. The ’’Rayleigh’’ distribution 

can be used to idealize the stress range associated with a 

particular cell (Hs and T) in the scatter diagram. Then, the 

fatigue damage associated with each block can be computed, the 

cumulative damage thus incorporating the weighting effect of the 

joint probability of wave scatter diagram. Since the damage for 

each cell is computed numerically, this approach is generally 

defined as the “short-termnumerical method.” 

The typical loading response exhibits smaller stress cycles 

interspersed among larger stress cycles, making it difficult to 

identify the number of cycles contributing to fatigue damage. 

Rainflow counting is the name of a large class of stress cycle 

counting methods often applied to upgrade the short-term 

statistics. The rainflow parameter, introduced by Wirsching 

(Reference 6.9) is frequently used in upgrading stress spectra 

statistics. 

The stress range associated with a particular block of the wave 

scatter diagram is random in nature and governed by a probability 

density function. Such a density function, covering the fatigue 

6-11

~. \“ 

life of a structure,cannot be defined bya closed-formmathematical 

function. Most often a numerical long-termdensity function of the 

stress range is used to determine the fatigue damage and the method 

is identifiedas the “long-termnumerical method”. If the long-term 

stress range density function is idealized, an approximate density 

function can be used. “Weibull” distribution is one commonly 

accepted shape parameter used to describe the long-term stress 

density function. The fatigue damage computed is closed 

form. Incorporating the Weibull shape parameter is generally 

referred to as the “Long-TermClosed-FormMethod”. 

6.2.3 Uncertainties and Gaps in Stress SDectrum Develo~ment 

There are several important variables contribut 

uncertainties in the development of the spectrum. 

ng to the 

Analysis assumptions substantially influence the calculated 

results. The most important of these is the selection of scatter 

diagram blocks. While atypical scatterdiagram has40t060 blocks 

(each representingthe joint probabilityof Hs and T), these blocks 

are often arbitrarily grouped into 10 to 15 super blocks to 

facilitate analyses. In addition to the uncertainties introduced 

dueto lumpingof these blocks,validityof Rayleighdistributionis 

also jeopardizeddue to limitednumber of blocksdefining the entire 

environment. 

Other analyses uncertainties result from the use or omission of 

various parameters (rainflow counting, Weibull d stribution) and 

their validity for the problem at hand. 

Work carried out by various investigatorshave he” ped enhance the 

reliability of spectral fatigue analysis. Chen and Maurakis 

(Reference6.10) offer a close form spectralfatigue analysesmethod 

that eliminates some of the uncertainties due to analyses 

assumptions and computational procedures. The computer program 

developed, incorporating the self-contained algorithm, appears to 

minimize the uncertainties due to analytical assumptions (i.e., 

6-12

judgement errors) and facilities carrying out of a cost-effective 

spectral fatigue analysis. 

Some studies show that full-scale service stress data match the 

predicted design stresses reasonablywell. However, it should also 

be noted that full-scale service stress data may substantially 

differ from those predicted during design. This may be especially 

true for ships and both the short-term and the long-term service 

stress data require a careful scrutiny. Evaluation of full-scale 

service stress data on three different ship types (a high-speed 

containership, a bulk carrier and a VLCC) by Dalzell et al 

(Reference6.11) shows that short-termwave-induced bending moment 

do not reasonably fit the Rayleigh distribution. The combined 

dynamic stress distributionsfor two of the three ship types did not 

fit the Rayleigh or the exponential distributions. Dalzell et al 

recommend that additionalresponse calculationsare carried out for 

different ship types utilizing Rayleigh and broad-band 

distributions. Comparison of response calculations with 

experimentaland/orfull-scaleresultsshould indicatethe magnitude 

of error and advisabilityof corrective measures. 

6.2.4 Decompose into Stress Record 

To obtain a stress histogram from the response statistics, the 

stress response spectrum for each wave spectrum in the scatter 

diagram can be decomposed into a finite Fourierseries. In orderto 

produce a realistic stress record, the number of frequencies 

required will be on the order of 100. Each component will have an 

amplitude defined by the differential stress energy in the 

neighborhood of the frequency. Each component will be given a 

random phase. By summingthe componentsateach time step, a stress 

value is obtained. The stress value is then accumulated into the 

stress histogram, accordingto the probabilityof occurrenceof the 

particularwave spectrum. The stress histogram can then be used to 

evaluate the fatigue life at the hot spot. 

6-13

6.3 TIME-DOMAIN ANALYSES 

Nonlinear effects, such as submersion/ immersion, velocity squared 

drag, mean drift offset, etc., may have a noticeable influence upon 

the stresses of a structure. When the nonlinear effects are 

substantial, the stresses may be directly calculated from a timedomain 

analysis. For a time-domain analysis a discrete set of 

regular waves are selected to represent the typical sea spectrum. 

The structure response and the stress responses are evaluated by 

stepping the waves past the structure in small time increments. At 

each time step the Newtonian laws are satisfied. 

The regular waves may be selected at equal frequency increments. 

Each wave will be the same frequency difference away from its 

neighbors, but each wave will have a different height corresponding 

to the energy within its frequency increment. Typically, wave 

period incrementsshould not be greater than 2 seconds to correctly 

define the effects of wave period variability. Wave heights in3 ft 

(lm) increments are considered acceptable. 

Alternatively, the regular waves may be selected so that they each 

have the same energy (height). The area under the sea spectrum is 

decided into bands of equal area. Either the centroid frequency 

(first frequency moment divialedby area) or the zero-uncrossing 

frequency (square-root of the second frequency moment divided by 

area) of the frequency band is used as the regular wave frequency. 

Regardlessof the selectiontechnique,each regularwave is assigned 

a phase using some randomizing method. A number of waves, on the 

order of 100, should be selected to insure that the random wave 

record does not repeat itself during the “sampling”time. 

Since any “bin” in the scatter diagram is characterized by a 

characteristic wave height and a characteristic period, another 

alternativetechniquemay be used to facilitatethe work. “Bins”of 

unequal period (frequency) may also be used to help prevent 

repetition of the random wave record. 

6-14

6.3.1 Stress Statistics 

The resulting stress records are then processed to find the stress 

statistics. The significantstress can redetermined as four times 

the standarddeviation of the stress values. Stress histogramscan 

also be derived from the records. 

6.3.2 70 Percentile Spectra 

Time-domain analyses tend to be computation intensive, and they 

often require costly computer runs. Therefore, the number and 

extent of time-domain analyses must be kept within reason by 

selecting one or a few representative sea spectra for evaluation. 

Selecting the representativesea spectrum and the regular waves to 

model it will have an effect upon the resulting fatigue life. 

Because the fatigue damage is an accumulation over many years of 

exposure to mostly mundane sea conditions, the selected 

(representative)sea state must be an average or mean condition, 

with a slight hedge toward conservatism. A recommendedselectionis 

a spectrumalong 70 percentilewave height line, i.e. from a cell in 

the scatter diagram below which lie 70% of the scatter diagram 

probabilities. Thezero-uncrossing period would be near the median 

on the 70 percentile line with a slight offset to the side that is 

expected to produce the greater stresses. 

6.4 OVERVIEW AND RECOMMENDATIONS 

The long term wave environment, as defined by a wave scatter 

diagram, is usually based on measurements and hindcasting. 

Measurements should be reviewed as to the extent of area covered, 

the time lengthof coverage,and the measurementsystem. Typically, 

measurements are made for limited time spans. Accelerometers of a 

measurement system may have limitations, preventing accurate 

description of wave energy content in all frequency ranges and in 

all directions. 

6-15

The wave environmentdefinitionsbased on hindcast models are quite 

reliable. However,modelingparametersshouldbe carefullyreviewed 

to ensure accuracy of the data. The environment is defined by 

multiple “bins” in the scatter diagram, each “bin” representing a 

significantwave height and a zero uncrossingperiod. Each “bin” is 

used to generate a specific wave spectra, defining that seastate. 

Since wind fetch and geographic parameters differ from one area to 

another,mathematical formulationsdeveloped to define wave spectra 

in one area may not be applicable to another area. Thus, as 

discussed in Section 6.1 and in Appendix B, P-M, Bretschneider, 

ISSC, JONSWAP, etc. wave spectra should be carefully reviewed as to 

their applicabilityto a given geographic area. 

6-16

Ss@e WaveScatt@rDiagram 

s 

i 

9 

n 

: 

i 

c 

a 

n 

t 

u 

a 

v 

e 

H 

e 

i 

: 

t 

(m) 

12 . . . . . . . . . . . . . ...+-+-.. . .+ . . . . ...++ . . . ...++.+- . . .+-- ..-..+. . . . ...+-... . . .+ . . . . ...+- -. ..-.+ 

I I I 

1 I 1 I I I 

I I 1 1 I 1 I ! i 

I 

11 :. . . . ...+... . . .-+..-... .+- . . . ...+- -. ..-.+-... -..+...-.-.+. . . . ...+.--- --.+-----..+. . ...--+ 

I I 

I I I 

I I I I 0.s : 1.0 ~ 

: 

I 

i 

I 

10 ; . . . . ...+....- . .+ . . . . ...+.-+ . . . .+. -.....+. . . . - . .+. ------+. . . . ---+------ .+-- .--..+... . ...+ 

I 

I 

I 

I 

i 

i I I 

I 

I 

I 

I 1.0 ~ 2.0 ~ 1.5 : 

I I 

9 . . . . . . . . . . . . . ...+.......+-. . . . . .+--- . ...+--- . - . .+ . . ...--+. . . . ...+-..++. . . . . . . . . . . . . . . ..-+ 

I 1 I I I I 0.5~ 1.5 ~ 2.5 ~ 3.0 ~ 0.5 [ i I 

8 . . . . . . . . . . . . . -.-+..... . .+.-.....+-- . -- ..+----- . .+--- . ...+. - . .-..+-... . . -+---- ...+. -. . ...+ 

I 1.0 \ 

I I I 

1 I 

5.0 ~ 5.5 ~ 2.5 ~ 0.5 ~ 1 I I 

7 . . . . . . . .. . . . . . . . . . . . . . . .. . - . . . -.+------ +.- ...-.+... . - . .+ . ...-..+. . . . . ..*..-... .. . . . . . . .. 

I 

I I I I 1 5.0 ~ 13.0 ~ 11.0~ 2.0 f 

I 1 I I 

6 . . . . . . . . . . . . . .-.+.-... . .+ . . . . ...+- - . --.-+---- . . .+ . . ...-.+. . . . ...+.-.. . . -+. -.....+- -. ...-+ 

I I I 0.5 ~ 6.0 ~ 18.0 : 23.0 ~ 8.5 : 1.0 { 

1 1 1 

I 

I 

I 

5 +. . . . ...+-. . . +-.+..... . .+ . . . . ...+- - . ...++---- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...+ 

1 

I I I 4.0 ~ 26.5 ~ 4&5 ~ 26.5 ~ 7.0 ; 2.5 ~ 0.5 ~ 0.5 ~ I 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . ...+.-.. . . .+. -.....+. . . . ...+.... . . .++- .-...+. -. . ...+ 

I I 1.5 ~ 39.5 : 79.5 : 63.5 ~ 20.0 ~ 6.o ~ 3.0 ~ 1.5 ~ 0.5 ~ 0.5 : 

3; . . . . ...+..++. . .+++-....++. . . . . .+- . . . ...+. . . . . . . . . . . . . . . . . . . . . ..+.-..-. .+-= -s---+--- . ..-+ 

I 0.5 : 50.0 : 105.0 ~ 95.5 ~ 35.0 [ 11.5 { 5.5 ~ 2.0 ~ 1.5 ~ I I 

I 1 

2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . ...++... . . . . . . . . . . . . . . . . ...+-... . . .+- . . . ...+. . . ...-+ 

I 1-5 ~ 59-5 \ 89*O ~ 34.5 : 12-O { 7.0 ~ 4.0 ~ 1.5 ~ 0.5 ~ I 

I 

1 . . . . . . . . . . . . . ...+..... . . . . . . . . . . . . . . . ...+..... . . . . . . . . . . . . . . . . ...++... . . . . . . . . . . . . . . . . ...+ 

I 

2.5 ~ l&O ~ 8.0 ~ 2.5 ~ 2.5 ~ 1.5 ~ 0.5 : I I I I 

04 . . . . ...+... . . ..+...... . . . . . . . . . . . . . . ...+.... . . .+. -.....+. . . . ...+.... . . . . . . . . . . . . . . . . ...+ 

2 3 4 5 6 7 8 9 10 11 12 13 

Zero Up-crossing Perid, Tz (SSC) 

W of Occurances*.5 

,.-. 

Figure 6-1 Typical Wave Scatter Oiagram 

?+’ ?4 

. ,., 

I 

Figure 

6-2 

Platfo= with Different Dynamic Response 

Characteristics in Two orthogonal -is

.,..,, 

....- ., ;., .. 

.... 

.- 

.. 

..- .. 

( 

THIS PAGE INTENTI 

ALLY LEFT BLANK 

.,.

7. 

7.1 BASIC PRINCIPLES OF FATIGUE DAMAGE ASSESSMENT 

Fatiguedamage of marine structuresis typicallydetermined usingS- 

N curves and the linear cumulative damage rule known as Miner’s 

rule. The S-N curves are usually provided in design standards, 

where each curve is applicableto specific joint configurations. 

The S-N curves applicable to details with complex stress patterns, 

such as tubular joint interfaces, require amplification of the 

nominal stresses by stress concentration factors (SCFS). The S-N 

curves applicable to details with simple stress patterns, such as 

hull scantlings, often include geometric effects and therefore can 

be used directly with nominal stresses. 

Application of Miner’s rule typically implies that the long-term 

distribution of stress range is replaced by a stress histogram 

consisting of a number of constant amplitude stress range blocks. 

Thus, for a stress history covering many stress ranges, each with a 

number of cycles (N), damage for each stress block is added to 

produce cumulative fatiguedamage. An alternativeto this approach 

is based on weighting and summing the probabilitydensity functions 

to obtain a long-term probability density function. Total damage 

can then be computed based on either numerical integration or the 

use of Weibull shape parameter and a closed form solution. Chen 

(Reference 4.10) offers a short-term closed form method that 

facilitates spectral fatigue analysis. Further discussion on this 

subject is presented in Section 6.2. 

As discussed in Section 4.1, various recommendations, rules and 

standards differ in defining desirable fatigue lives and the 

specifics and applications of S-N curves. However, these 

recommendations,rules and standards (References 1.5, 1.6, 1.7 and 

4.14) generally adhere to the following basic principles of fatigue 

damage determination: 

7-1

● 

Fatiguetest data should be carefullyevaluated andS-N curves 

should be generated by statisticalmeans to allow estimation 

of failure probabilityand incorporationof conservatism into 

the design. Separate S-N curves should be applicable to 

different weld details and in some applications to different 

profiles. 

● 

S-N 

not 

curves include a level of fabricationeffects that should 

be exceeded. 

● 

The cumulative fatigue damage computation should be based on 

Miner’s rule, and should consider the damaging effects of all 

loadings (both global and local). 

Fatigue damage assessment technology has benefitted from the 

application of fatigue crack growth data and fracture mechanics 

analysis of defects. In addition to predicting fatigue life, 

fracture mechanics analysis allows better understanding of various 

parameters that affect the behavior of welded joints. In turn, 

experimental data and fracture mechanics analysis have allowed 

upgrading of recommendedS-N curves (References1.5, 1.7) including 

Gurney’s work on the influence of plate thickness (Reference 7.1). 

7.2 

S-N CURVES 

The S-N curves recommended by various rules, recommendations and 

codes are based on the application of constant amplitude stress 

cycle on various detail/joint geometries in the laboratory until 

fatigue failure. Most S-N curves for simple details (stiffener, 

cutout, etc.) account for the local notch stress and can be used 

with the member nominal stresses. Tubular joints of offshore 

structures exhibit a wide variety of joint configurations and 

details. Therefore, while the S-N curves account for several 

parameters (platethickness,weld profile), theydo not account for 

peak stresses, requiring the application of SCF’S on computed 

nominal stresses to obtain peak (hot-spot)stresses. 

7-2

The S-N curves that can be used directly with the nominal stresses 

most often apply to ship structuredetails. Munse’s SSC-318 report 

(Reference 1.3) documents the S-N curves for 69 ship structure 

details and refers to earlierwork by Jordan and Cochran (Reference 

7.2) on in-service performance of ship structure details. 

Tubular offshore components have more complex geometries and are 

subjected to corrosive ocean environment, requiring careful 

assessment of all parameters contributing to fatigue failure and 

selection of appropriateS-N curves. 

Many design, fabrication and in-service factors affect the fatigue 

lives of details/joints. Fatigue cracks in welded joints often 

initiate at weld discontinuities introduced during fabrication. 

Weld quality problems that contributeto the degradation of fatigue 

strength include: 

● 

● 

● 

● 

● 

Planar defects in the body of the weld 

Incompletepenetration 

Imperfectweld root quality 

Imperfectweld toe profile 

Development of an embrittled heat affected zone (HAZ) 

Fatigue assessment requires definition of the number of applied 

stress cycles (N). Welded details/joints subjected to repeated 

cyclic stresseswill go through several stages of crack growth. For 

each hot-spot stress range (s), failure is assumed to go through 

three stages: 

● 

● 

● 

First discernible surface cracking (Nl) 

First through-wall cracking (N2) 

Extensive cracking and end of testing (N3) 

Ideally, cracks should be large enough to detect, yet not large 

enough to cause failure and alterationof load path. To ensure that 

cracks are repairable, the number of cycles to failure in fatigue 

7-3

assessmentis typically identifiedas the number requiredto produce 

through-wallcracking (N2),which can often be visually detected in 

a laboratory environment. To ensure accuracy of results tubular 

joints being tested in a laboratory are sometimes pressurized and 

the 

number of cycles to N2 is tied to the first drop in pressure. 

Tests are carried out for numerous stress range blocks to determine 

the number of stress cycles needed to reach failure, allowing 

development of an S-N curve. An S-N curve is also based on 

idealized laboratory conditions that may not fully represent the 

actual fatigue life in a marine environment. As discussed in 

Section 4.2.2, the S-N data for offshore components are based on 

testing of fillet-weldedplates and small-scaletubularjoints. The 

test data on Figure 7-1 indicate substantial scatter and allow 

development of S-N curves for a 99% confidence 1evel or a 95% 

confidence level (representingthe characteristic strength at two 

standard deviations). 

The use ofan S-N curve based on strictly small specimen data is not 

advisable. Smal1 test specimens usual1y do not depict welded 

offshore component details accurately as full-scale component 

fabricationresidual stresses are substantiallydifferent from test 

specimen residual stresses. Further discussion on size effect of 

welded joints is presented by Marshall (Reference 7.3). 

It is also necessary to consider definition of hot spot stress 

1evels. API reconnnendedX and X’-curves (with and without smooth 

transition of weld profile at weld toe) are derived from hot spot 

stresses obtained from strain gages placed within 0.25 inch (6 mm) 

to O.lRt of the weld toe. The hot spot stresses as obtained are 

less severe than the local stress concentrations at the weld toe, 

but the S-N curve developed accounts for this difference. DEn 

Guidance Notes (Reference1.6) defines the hot spot stress as “that 

which is as near the weld as possible without being influenced by 

the weld profile”. 

7-4

The primary factors that influence the fatigue life assessment are 

discussed as follows: 

7.2.1 Desicm Parameters 

The design is optimized to ensure effective resistance of marine 

structures to both extreme and operating fatigue loads. Typically 

thestructureandjoint/detail configurationsshould redeveloped to 

minimize stress concentrations and stress levels, and arranged to 

provide easy access to help maintain welding quality. The material 

should be selected to have an acceptable chemical composition to 

ensure weldability and satisfactorymechanical properties to ensure 

notch toughness. 

Fabrication specifications should permit only minimized mismatch 

tolerances, thereby reducing SCF’S and residual stresses. They 

should also controlthe quantity and quality of repair work, thereby 

ensuring allowabledefects in weldments comply with specifications. 

These design parametersare discussed in Section3. and described in 

more detail below. 

Material Strenctth 

Fatigue strengths of marine structure components are sometimes 

assumed to be affected by material strength. Cast steel node or 

forged components of a structure have significant fatigue crack 

initiation periods and material strength may have an effect on 

fatigue lives. However, material strength does not affect the 

fatigue life of welded components of marine structures. As-welded 

joints of marine structures contain inherent flaws and Maddox 

(Reference 7.4) has shown that the fatigue 1ife of such joints is 

largely expended in crack propagation. While increased material 

strength retardscrack initiation,the rate of crack growth has been 

shown to be insensitive to material strength. Experimental work 

carried out by Hartt et al (Reference 7.5) on high strength steel 

(HSS) specimens in a corrosive ocean environment indicated fatigue 

7-5

damage accumulation similar to that of structural steel. Gurney 

(Reference 7.6) indicatesthat increased material tensile strength 

does not increase fatigue resistance and implies that a fatigue 

design approach incorporatingmaterial tensi1e strength is not valid 

for welded marine structures. 

The effect of initial flaw size on 

affecting crack propagation should 

size estimatingprocedureby Grover 

in assessing fatigue crack growth. 

fatigue life and the parameters 

be understood. An initial flow 

(Reference7.7) is quite helpful 

Plate Thickness 

Current S-N curves reconunended by DnV (Reference 1.7), DEn 

(Reference 1.6) and AWS (Reference 4.13) incorporate a thickness 

correction factor. DnV and DEn recommendations largely reflect 

early work by Gurney (Reference 7.1) and many test programs 

corroborating plate thickness effect corrections proposed by 

Gurney. Class B, C, D, E, F, F2, G and N curves are applicable to 

non-tubular (including tube-to-plate) joints based on detail 

geometry, stressing pattern and method of fabrication/inspection. 

While these eight classes are applicablewithout correctionto plate 

thicknessupto7/8inch (22MM), class Tcurve (for tubular joints) 

is applicable to 1-1/4 inch (32 mm) plate. 

The UK DEn Guidance Notes recoimnendspecific size effect (i.e., 

plate thickness) correction factors in the following form: 

S = Sb (32/t)l/4 

7“1 

where 

s = 

fatigue strength of a joint under consideration 

(N/nun2) 

7-6

‘b = 

fatigue strength of a joint applicable to T curve 

for 32 & wall thickness (N/mm2) 

t = wall thickness of a joint under consideration (nnn) 

Although the tubular joint test data available may be insufficient 

to document the size effect throughout the range of plate 

thicknesses in use, the data available has been grouped, analyzed 

and relative fatiguestrengthdata documented. Tolloczko and Lalani 

(Reference7.8) report that sizeeffect is adequatelyrepresentedin 

the Guidance Notes (Reference 1.6) and that none of the more than 

300 datapoints fall below the applicableS-N curves. 

Test results show that plate thickness or scale increases can 

adversely affect fatigue strength, perhaps due to increase in weld 

toe stresses with an increase in plate thickness. S-N curves 

modified to account for thickness-effect of thick plates often 

substantially affect the fatigue lives computed. Some experts 

consider the applicable plate thickness correction to be mild for 

typical nodes. However, additionalwork by Maddox (Reference 7.9) 

indicates that thickness correction may be too severe if only the 

primary plate thickness is increased. His work on cruciform-type 

joints (Figure7-2) indicatesthat the joint proportions ratio (L/B) 

has greater effect on fatigue strength than does the primary plate 

thickness. 

.- 

While Maddox’s encouraging results are applicable to joints 

subjected to axial tension, increased primary plate thickness 

subjected to bending stresses still adversely affects the fatigue 

life. A typical joint in most marine structures is likely to be 

subjected to substantial bending stresses. Thus, before any 

relaxation of plate thickness effect on the S-N curves is attempted 

further data are necessary for a range of geometries and combined 

loading conditions. 

7-7

“FabricationRestrictions 

Fabrication specifications and drawings often attempt to minimize 

the conditions that may adversely affect fatigue strength of a 

detail/joint. Fatigue tests performed on various types of joints, 

and fracture mechanics analysis carried out by Maddox (Reference 

7.10), indicate that the fatigue life of a joint does not change 

appreciablydue to attachmentof a backing bar on a plate. Fatigue 

strength also”hasbeen shown to be unaffectedby poor fit-up between 

the backing bar andthe plateor by the configurationof the backing 

bar. However, it should be emphasized that fatigue strength not 

changing appreciably due to attachment of a backing bar or a poor 

fit-up may have more to do with the root condition without backing 

bar. 

7.2.2 

Fabrication and Post-FabricationParameters 

Fabricationparameterscoverall of the fabrication activities that 

affect the quality of welded details/joints. These parameters, 

ranging from welder qualificationto heat input and cooling rates, 

were identifiedon Figure 3-3 and discussed in Section 3.1.2. 

Misalignments 

Misalignments adversely affect the fatigue strength of a 

detail/joint. When a misalignment between two elements is large, 

both elementsmay haveto be improperlydeformedto align them prior 

to welding. Such joints incorporatesubstantialresidual stresses. 

If the misalignment between two elements is small, they may be 

welded as-is, but the misalignmentcauses a stress concentrationdue 

to the resulting secondary bending. 

Because misalignment increasesthe stress at the weld toe of joints 

loaded axially, the stress magnification factor (Kc) can be 

correlated to fatigue damage. Fatigue test results for different 

levels of misalignment in plate joints and tubulars carried out by

Maddox (Reference 7.11) provide the basis for assessment of 

misalignments. 

Weld Quality 

A significant scatter of fatigue life test data is expected and 

appropriatelyaccountedfor. Acharacteristic strengthrepresenting 

a 95% confidence level in test data may be used to assess data 

points falling substantiallybelow the S-N curve. Such data points 

are likely to be due to a problem with the welding procedure or the 

welder qualification. Weld quality degradation (and therefore 

fatigue life degradation) due to incomplete penetration and poor 

weld root quality can be minimized by developing a welding 

specification applicable to the specific configuration and closely 

adhering to it during fabrication. Weld quality degradation due to 

undercut at the weld toe can be similarly minimized. 

Weld Toe Profile 

The significance of weld profiles on joints subjected to fatigue 

loading is controversial. Substantial time and expenditures are 

necessary to prepare a favorable weld profile, and weld profiling 

may increasewelding costs by as much as 20%. Thus, weld profi1ing 

is limited to specific tubular joints of discrete marine systems. 

While API RP2A does “not recognize and quantify plate thickness 

effects, theAPI S-N curves recognize and quantifyweld profile. As 

illustrated on Figure 4-3 in Section 4.1.2, API (Reference 1.5) 

recommends the use of an X-curve for welds with a favorable profile 

while the X’-curve is reconnnendedfor welds without such a profile. 

As il1ustrated on Figure 7-3, substantial preparation, weld bead 

shape, applicationof extra weld beads and grinding may be necessary 

to allow the use of an X-curve. 

7-9 

! “-7 / 

[/

Fatigue strength of a tubular joint is shown to improvedue to weld 

profiling (References 7.12 and 7.13). Weld profiling (including 

grinding of weld toe) has two primary benefits: 

● It can minimize the potential for crack propagation by 

removing inherent crack-like flaws. 

● It can reduce stress concentrations by improving local weld 

profile. 

However, grindingto remove flaws and to provide a smooth transition 

between the weld and parent material is not universally accepted as 

quantifiable benefit unless the weld toe undercut is sufficient. 

Both AWSand API do not require a correctivemeasure if the undercut 

of weld toe is less than 0.01 in. (See Figure C 10.7.5, Reference 

4.14). DnV (Section3.3.1 , Reference 1.7) states, “the effect of 

weld profiling giving the weld a smooth concave profile compared 

with the typical triangular or convex shape~ improve the fatigue 

properties.”Although DnV accepts the use of an X-curve (in lieu of 

a T-curve) provided weld profiling is carried out, it also 

stipulates that the effect of profiling on the S-N curves will be 

considered for each case separately. 

The weld profiles applicabletoAPI XandX’ S-N curves are shown on 

Figure 7-3. However, to ensure that the flaws at weld toe are 

removed, grinding or AWJ process should result in sufficient 

undercut at the weld toe. The minimum undercut recommended by the 

DEn Guidance Notes (Reference 1.6) is shown on Figure 7-4. 

Further discussion and an excellentoverview of the effects of weld 

improvementtechniques is provided by Bignonnet (Reference7.14). 

7.2.3 

Environmental Parameters 

The environment in which fatigue cracks initiate and propagate 

substantiallyaffectsfatiguelife. The amplitude,distributionand 

7-1o

frequency of loading identify severity of the fatigue environment. 

Although a structure’sconfigurationcan be optimizedto reduce the 

stress range, the site-specificenvironmental loading controls the 

choice of fatigue design and analyses method. 

An environmental parameter that affects fatigue is either air or 

seawater. Because of the adverse effects of seawater corrosion on 

fatigue strength, adesign factor is often applied for fatigue life 

in a seawater environment. However, an effective cathodic 

protection systemwill reduce or prevent seawater corrosion, and if 

such a system is used, the design factor may be deemed unnecessary. 

This approach (and its inclusion in various rules, recommendations 

and standards) is based on corrosion fatigue test data on welded 

plate specimenswith and without cathodic protection. 

Environmentaleffects on welded flat plates have been assumed to be 

the same as those on tubular joints. However, Wylde et al 

(Reference 7.15) have indicated that the corrosive effect of 

seawater on tubular joints may be greater than the effect on flat 

plate specimens. Althoughdifficultto document, tubular jointsmay 

be more susceptibleto environmentaleffects than small welded flat 

plates due to scale effects, including initial flaws. Flat plates 

may have longer fatigue lives as substantial time will be expended 

in initiation of flaws. 

7.3 

FATIGUE DAMAGE COMPUTATION 

State-of-the-art methodology for determining fatigue lives and 

designing structures with fatigue lives in excess of the design 

lives is primarily based on S-N curves and the cumulative damage 

rule. The cumulative damage rule is an approach used to obtain 

fatigue damage by dividing the stress range distribution into 

constant amplitude stress blocks, assuming that the damage per load 

cycle is the same at a given stress range. 

7“11

Current recommendations,rules and standardsuniformlyallowthe use 

of Miner’s rule to compute the cumulative damage. Applicable 

cumulative damage rules are discussed in this section, followed in 

Section 7.4 by a discussion of stress spectrum in the context of 

fatigue damage computation. 

7.3.1 

Miner’s Rule 

The damage for each constant stress block is defined as a ratio of 

the number of cycles of the stress block required to reach failure. 

Thus, the Palmgren-Minerlinear damage rule defines the cumulative 

damage (D) for multiple stress blocks as equal to: 

‘i 

D=:T < 1.0 

i=l i 

As briefly discussed in Section 3.2.5, Miner’s rule can either 

overpredict or underpredict the cumulative damage. 

One source of inaccuracy regarding cumulative damage is the 

applicationof constantamplitudestressblocks; itmay be important 

to be able to predict the fatigue damage due to variable amplitude 

loading. Another source of inaccuracy is the sequence of loading; 

while Miner’s rule cannot account for the loading sequence, 

occurrence of large amplitude loads early in fatigue life can 

accelerate the rate of crack growth. Another source of inaccuracy 

for wide band processes is the choice of cycle counting method, 

which is further discussed in Section 7.4. 

Despite these sources of potential inaccuracy,Miner’s rule is used 

to compute fatigue damage because of its simplicity as well as its 

ability to predict fatigue damage conservativelymost of the time. 

Other uncertainties in determining wave environment, wave loading 

and hot-spot stresses contribute far more to the inaccuracy of 

7-12 

[7 ‘cd 

1/

fatigue damage predictions. Fatigue analysis assumptions also 

contribute to the inaccuracyof fatigue damage predictions. As an 

example, 10 to 15 stress blocks, each representing a significant 

wave height and a zero-crossing point, may be used in the fatigue 

analyses. Theuseof40to 50 stress blocks is desirable, but often 

considered impracticalfor most analyses. 

7.3.2 

Alternative Rules 

The ability to use servohydraulic testing machines and to apply 

computer-controlled loads has allowed testing of a substantial 

number of specimens subjected to variable amplitude loading 

(References 7.16, 7.17, 7.18 and 7.19). Gerald et al (Reference 

7.20) provide an excellent overview on variable amplitude loading. 

Some analytical work carried out and many of the test results show 

that Miner’s rule is realistic and conservative. However, some of 

the test results also show that Miner’s rule may lead to 

underpredictionof fatigue damage. 

One source of discrepancymay be crack growth fluctuations. Stress 

block procedures used in tests result in the application of high 

tensile stresses, which can retard crack growth. Test specimens 

subjected to random loadings are less likely to have similar high 

tensile stresses. Another source of discrepancy is the counting of 

stress cycles. Gurney (Reference 7.17) and Trufiakov (Reference 

7.21) conclude that small fluctuations superimposed on each stress 

cycle add substantiallyto fatigue damage. 

Miner’s rule is the acceptedmethod for fatigue damage computation. 

However, since alternativesto Miner’s rule have been proposed it is 

beneficial to review one such rule. 

Gurney proposes a damage rule by expressing the applied stress 

spectrum in terms of the maximum stress range (Smax),the number of 

cycles (ni) applied at proportions (pi) of smax, and its length 

(1 ni)defined as the block 1ength. Gurney’s rule states: 

7-13

n 

NB=T 

1 

[p=+pi 

Ei 

. 

‘c 

where: 

NB. = predicted life in blocks 

NC = constant amplitude life at SmaX 

NEI = 

i = 

number of cycles per block 2 ‘i ‘max 

lton 

This product rule can be compared to Miner’s 

NB=~ 

‘c 

x Pi ni 

1 

where m is the slope of the S-N curve expressed as SmN - constant K 

It should be noted that Gurney’s rule may also result in 

underprediction of fatigue damage. Study of spectrum shape and 

block length (Reference7.22) indicatesthat for long block lengths 

Gurney’s rule may be unsafe. 

7.4 STRESS HISTORY AND UPGRADED MINER’S RULE 


Miner’s linear cumulativedamage rule can be used safely, provided 

some of the wave environment uncertainties (including counting of 

cycles and evaluatingthe stress ranges compatible with cycles) are 

properly accounted for. 

7“14

Typically, the sea state represented by joint probabilities of 

significant wave heights and characteristic periods (scatter 

diagram) is applied to the transfer function to produce the stress 

range spectrum. Integration of the spectra provides a number of 

statistical parameters, such as the bandwidth, the zero-uncrossing 

frequency, etc., allowing development of short-term probability 

density functions. 

The short-term probabilitydensity function of the stress range for 

each significant wave height and its characteristic period is 

generally defined by using a Rayleigh distribution. For this 

assumption to be valid, (1) a large number of sea states must be 

used, and (2) the stress cycles can be considered narrow-banded. 

Individualstress cycles are considerednarrow-bandedwhen they are 

readily identifiable and there is no ambiguity in counting the 

stress cycles. The wide-banded loadings exhibit smaller stress 

cycles interspersed among larger stress cycles. Because it is 

difficult to define the stress cycles, different cycle counting 

methods result in different fatigue damage predictions. 

Rainflow counting is the name of a large class of stress cycle 

counting methods, including the original rainflow method, Hayes 

method, range-pair counting, range-pair-range counting, ordered 

overall range counting, racetrack counting and hysteresis loop 

counting. 

Rainflow counting and other alternatives are briefly discussed in 

Sections 7.4.2 and 7.4.3, respectively, to illustrate the options 

availableto upgradeMiner’s rule. However, it should be noted that 

two very important variables affecting fatigue life computation 

should be addressed in any attempt to upgrade Miner’s rule: 

(1) S-N curves are based on constant amplitude stress blocks and 

should be compared against variable amplitude results. 

7-15

(2) Damage computation does not account for stress sequence and 

may overpredict fatigue lives ofjoints/details subjected to 

large stress amplitude ranges early on, accelerating crack 

propagation. 

7.4.2 Miner’s Rule IncorDoratinqRainflow Correction 

The rainflowcountingprocedure ismore accuratethan other counting 

methods because the rainflow procedure is based on counting the 

reversals in accordancewith the material stress-strain response. 

Modified Miner’s rule uses the rainflowcycle counting procedure but 

does not require the stress process to be simulated. 

D =#E (Sm) 

where: 

n = 

K= 

E(Sm) = 

s = 

total number of cycles 

constant, equal to SmN 

the mean value of S 

a random variable denoting fatigue stress cycles 

If the process 

D can be shown 

is stationary, Gaussian and narrow band, the damage 

that: 

where: 

u = 

ro = 

RMS of the process 

gamma function 

7-16

When the structure response yields narrow-banded stress cycles, the 

choice of counting method is imaterial. Even for moderately wide 

band stress cycle histories, the various cycle counting methods 

produce similar fatigue damage predictions. The choice of counting 

method becomes significant only for wide band stress histories with 

an irregularityfactor equal to or less than 0.5. The irregularity 

factor is a measure of the band width, defined as the ratio of mean 

crossings with positive slopes to the number of peaks or valleys in 

the stress history. 

7.4.3 

Other Alternatives 

An alternativeapproachto predicting fatigue damage under wide-band 

stresses is to use the narrow-band stress approach and apply an 

adjustment factor. Assuming a narrow band fatigue stress with the 

same RMS, and the same expected rate of zero crossings, fo, as the 

wide band stress, a damage estimate can readily be carried out. 

Given the spectral density of the stress w(f), the kth moment of of 

spectral density function mK is equal to: 

f= fK w(f) df , while the 

‘K= 0 

RMS (Std dev.) = ~= i%, 

and the expected rate of zero crossings 

with slope 

f. = d~/mo 

With this equivalent narrow band process, the fatigue damage can be 

predicted by the following closed form solution: 

7-17

DNB = (f. T/K) (2/2 U)m r (f+ 1) 

where 

n = f. T 

T= design life 

Wirsching (Reference 7.23) proposes that the fatigue damage be 

expressed as: 

o = a ‘NB 

where A is the adjustmentfactorto fatiguedamage predicted based on 

a narrow-band stress. Thus, the rainflow counting effect to fatigue 

damage can be incorporated directly if J is known. An empirical 

formula proposed by Wirsching is as follows: 

A (E, m) = a(m) + [1-a(m)] (LE)b(m) 

where 

a(m) = 0.926 - 0.033 m 

b(m) = 1.587m - 2.323 

Thus the fatigue damage obtained by incorporating the narrow-band 

adjustment factor, A provides a closed-form formulation. The 

empirical formula allows fatigue damage predictions quite close to 

those obtained by incorporatingthe direct rainflow method. 

The A parameter introduced by Wirsching is an equivalent rainflow 

adjustment factor intendedto correct the slight conservatism of the 

Rayleigh distribution. Whether a closed-form or a numerical 

integrationis carriedout, short-termstatisticsand the probability 

density function allow obtaining of partial damage, weighting and 

summing of all damages. 

7-18

Following the weighting of the short-term density functions, the 

long-term density functions for the structure’s design life are 

obtained. While the cumulative damage may be computed through 

numerical integration, an approximation is introduced to allow 

application of a closed-form solution. Typically, a Weibull shape 

parameter (Weibull distribution) is used in predicting cumulative 

fatigue damage based on the 1ong-term, closed-form method. This 

subject is discussed further in Section 6 and in a comprehensive 

paper by Chen and Mavrakis (Reference7.24). 

7.5 

OVERVIEW AND RECOMMENDATIONS 

7.5.1 

Application of S-N Curves 

The S-N curves used indeterminingfatiguedamage computations should 

be compatible with structural details investigated. The S-N curve 

including the effect of peak stresses should be used together with 

nominal stresses at the detail, while the S-N curve uninfluenced by 

the weld profile should be used with nominal stresses increased“by 

appropriate SCFS. 

Scatter in fatigue test data should also be appropriately accounted 

for. One primary parameter affecting scatter of S-N data may be 

plate thickness. As plate thickness increases higher localized 

stresses will occur near plate surface, accelerating propagation of 

fatigue cracks. Consideringthat small specimen S-Ndata needto be 

adjusted for scale effects and a reasonable confidence level should 

be achieved, S-N curves may be obtained assuming 95% to 97.5% 

confidence level and a log normal distribution. 

There are other parameters that are difficult to assess yet they 

affect the crack growth and fatigue failure, causing substantial 

scatter of S-N data points. One importantconsideration is the size 

of initialflaw (crack)and another is the number of flaws. Although 

further work is necessary, Morgan’s (Reference 7.25) findings on 

7-19

interactionof multiple fatigue cracks provide valuable insight into 

scatter of S-N data points. 

Additional parameterscontributingto the fatigue life uncertainties 

are the effects of corrosive sea water environment and the 

implications of long-life regime. Although catholically protected 

offshore structure components in sea water are assumed to have the 

same fatigue resistance as those components in air, the basis for 

this assumption is the test data for simple plate specimens. Some 

large scale tubular joint tests indicate (Reference 7.15) that the 

corrosive effects of seawater on tubular joints may be greater than 

the effect on small flat specimens. More test data is necessary to 

quantify corrosive effects. 

There are limited number of test data in long-life regime. As a 

result, some codes do not provide endurance limit, some have a 

changing slope and some have a definite plateau at different number 

of cycles. These and other uncertainties require further research 

work to upgrade current S-N curves. Current research efforts on 

fatigue resistance are summarized in Section 9. 

The S-N curves recommended byAPI, DEn and DnV (References 1.5, 1.6 

and 1.7) may be used in the computation of fatigue damage. While 

most early S-N curves were based on AWS data, current DEn curves are 

largely based on work at the Welding Institute (primarilyGurney and 

Maddox). DEn Guidance Notes also provide tables, allowing the 

selection of S-N curves for specific details. For ship structure 

details, appropriate DEn S-N curves can be selected based on 

judgement in assessing the details and tables. Earlier works by 

Munse (Reference 1.3) and Jordan and Cochran (Reference 4.4) can be 

used directly or in comparison of component test data for ship 

structure details. 

The S-N curves given in DEn Guidance Notes are applicable to a base 

case plate thickness of 7/8 inch (22 mm), requiring an adjustment of 

the S-N curves for thicker plates. Consideringfurther validationof 

7-20

thickness effect is necessary and the ship structure plate 

thicknesses are not excessive, the correction factor may be 

neglected. 

The S-N curves reconanendedbyAPI for offshore platforms may be used 

in the computation of tubular component fatigue damage. The API X- 

curve and the DEn T-curve (identicalto DnV T-curve up to 10 million 

cycles for catholically protected areas - see Section 4.2.2) 

intersect at about 500,000 cycles and would yield similar lives for 

a plate thicknessof 1-1/4 inch (32nmI). Most tubular chord and stub 

thicknesses are likely to be greater than 1-1/4 inches and the 

applicationof correctedDEn or DnV T-curves to compute fatigue lives 

will result in shorter lives and considered to be appropriate. 

Consideringthe effectsof plate thickness,weld profile and undercut 

on fatigue strength and the S-N curves it may be prudent to reassess 

the hot spot stress range concept. Tolloczko et al (Reference 7.8) 

recommend modifying the definition of hot spot stress range to 

reflect weld toe defects. Then, the S-N curves will reflect only the 

size effects. 

7.5.2 Fatiaue DamacteComputation 

Fatigue lives determined based on S-N curves and Miner’s cumulative 

damage rule are uniformlyacceptableto certifyingand classification 

agencies. The national and internationalstandards allow the use of 

simple cumulative damage rule for the computation of damage. Large 

number of test results as well as the in-serviceperformance records 

of marine structures indicate adequacy of this approach. 

Alternative rules to compute fatigue damage and methods to upgrade 

Miner’s rule have been proposed. Although necessary to evaluate 

possible benefitsof such alternatives,additionalcomplexity and the 

cost should also be considered. Since the S-N curves are developed 

based on constant amplitude stress ranges, the effect of variable 

7-21

amplitude loading and loading sequence on fatigue life is a valid 

concern. 

The results obtainedfrom a substantialnumber of specimenssubjected 

to variable amplitude loading show that Miner’s rule is appropriate 

and generally conservative. Dobson et al (Reference 7.26) studied 

loading histories of containershipsbased on recorded service data. 

When the stress intensity ranges were expressed as the root-meansquare, 

the crack growth of laboratory specimens subjected to 

constant-amplitude loading history compared quite well with those 

specimens subjected to constant amplitude loading. 

Fatigue damage computation is based on stress ranges and number of 

cycles and does not account for stress sequence. Since welded 

structure fatigue lives are largely expended in crack propagation, 

applicationof sufficientnumber of large stress amplitudes early in 

fatigue life is likely to accelerate crack propagation and 

overpredictingof fatigue life. The uncertainty of stress sequence, 

aside, the use of rainflowcounting procedure, based on counting the 

reversals in accordancewith the material stress-strainresponse,may 

enhance accuracy of damage computation. However, improvement in 

accuracy is significantonly for wide band stress histories with an 

irregularity factor equal to or less than 0.5. When the structure 

response yields narrow-banded stress cycles, the choice of counting 

method is innnaterial. Even for moderately wide band stress cycle 

histories,the variouscycle countingmethods produce similar fatigue 

damage predictions. Although further research is necessary, 

especially on the effect of stress sequence, the use of S-N curves 

and Miner’s cumulative fatigue damage rule is appropriate. 

7-22

:Ilo 

I Cn 

80 

to 

40 

. 

20 

T- 

m 10 

m -k 

8 

u 

A. 

c 

* 

.-i- 

4, 

1“ 

,. 

z ȯnaxxs 

HLL SICKI S 

“ $lReSs nrwct 

I 

oa— 

x + 

Figure 7-I S-N Curve for a Transverse Butt Weld and Test Data 

#’+’7, 

— 

I 

13 20 30 Lo 50 

ThiCkn@SS. s mm 

Figure 7-2 Theoretical Thickness Effect for a Cruciform Joint 


.,

n“ 

CAP PASSES 

ROOT = * 

{ 

A A 4 I 

u 

A) WITH PROFILE CONTROL 

1 

J 4. AI 

B) WITHOUT pROFILE CONTROL 

1 

Figure 7-3 Weld Profiles for API X and X’ S-N Curves 


Bmce — 

Defect - 

Dcpthof grinding 

should be 0.5mm 

below bottom of 

ony visible 

und~rcut 

B..- 

m 

Depth 

.+ 

of grinding 

should be 0-5 mm 

below bottom of 

any vlslbie 

undercut 

Chord 

Chord 

Defect 

in Brace 

Defect 

in Chord 

Gridne mMd lac mngenudly m the plsu mrha 8s m A. WIII ~ 

Iiuk mpmwm!m m strm@. Grindingmm atcd kku k ptuc 

3urhcGssmB.inoIdcrlOrcInOvclm*- 

Figure 7-4 DEn Guidence Notes Recommended Weld Profiling and Undercut 

(From Reference 1.6)

8. 

FATIGUE DUETO VORTEX SHEDDING 

This section specificallyaddresses fatigue due to vortex shedding. 

Fatigue due to vortex-induced vibrations is different from other 

forms of fatigue discussed in previous sections only in its loading 

characteristics. Generally, relatively small number of slender 

members are susceptible to vortex-induced fatigue. However, 

response to vortex shedding cannot be predicted using conventional 

dynamic analyses techniques because the problem is non-linear. In 

compliancewith project objectives, a brief discussion is presented 

on vortex sheddingphenomena,analysisand design, damage assessment 

and avoidance. A comprehensive discussion, including example 

problems, is presented in Appendix D. 

VORTEX SHEDDING PHENOMENON 

8.1.1 

Background 

Amember exposedto fluid flow may be subjectedto unsteadydrag and 

lift forces caused by sheddingof vortices. While the vortices shed 

are most often due to steadywind or current flow, the phenomena can 

occur due to combined wave and current action. Depending on the 

member’s natural frequency and the velocity of fluid flow, the 

member may experience sustained vibrations. 

Many structure members may be susceptible to vortex induced 

vibrations (VIV). Relatively large diameter cylindrical brace 

members of a fixed offshore platform can be designed to avoid VIV. 

Component members of a cargo boom on a ship or the flare structure 

on production units (FPSO, platform, etc.) are relatively slender 

and can not be readily designed to avoid VIV. Then, they need to be 

either designed to have adequate fatigue strength to resist the VIV 

over the design life of the structure or provided with devices or 

spoilers to modify the vortex shedding and/or member natural 

frequencies. 

8-1

It should be pointed out that the effect of wind-induced vibration 

is often not adequatelyaddressedduring design. The basis for the 

issuing of an offshore Safety Notice 7/87 by the U.K. DEn to all 

North Sea Operators for reassessment of platform flare boom 

structuraladequacywas the discoveryof fatigue cracks in the flare 

boom struts. Bell and Morgan (Reference 8.1) report that the 

original design documents revealed relatively low fatigue stresses 

and high fatigue lives. Reanalyses of the flare boom joints 

indicated that the extensive cracking observed may be due to the 

combined effect of poor weld quality in the joints and the largerthan-expected 

stress cycles due to vortex-induced vibrations. 

8.1.2 

Vortex Induced Vibration (VIV) 

At low fluid velocities (expressed as Reynold’s numbers) the flow 

acrossthe cylindricalmember remains stable. As the fluid velocity 

increases (i.e.,higherReynold’snumbers)the innermostpart of the 

shear layer adjacent to the cylinder moves more slowly than the 

outer part of the layer. As a result, the shear layers “roll-up” 

into discrete swirling vortices. These vortices are shed 

periodically,either in pairs (in-lineflow) or sequentially (crossflow) 

from two sides of the cylinder, generating unsteady and very 

complex pressure distribution. As illustrated on Figure 8-1 (from 

Reference 8.2), the laminar boundary layer goes through several 

stages of vortex turbulence with increasing Reynold’s numbers. A 

detailed discussion on vortices and pressure distribution is 

presented by Marris (Reference8.3). 

If the cylindrical member natural frequency (fn) is close to the 

vortex sheddingfrequency,vibrationsof the cylinder may affect the 

vortices shed. The vortex sheddingfrequency (fv)will no longerbe 

dependent onthe Strouhalnumber (St),and is likely to become equal 

to the natural frequency of vibration. If this “lock-in” effect 

materializes, further increases in the vibration amplitudes will be 

observed. To prevent the occurrence of critical velocity (fc), 

where the member natural frequency is equal to the vortex shedding 

8-2

frequency (i.e. fc = fn = fv), member stiffness and mass may be 

modified. The maximum amplitude of oscil1ation for the critical 

velocity is an important variable, directly affecting the stress 

amplitudes. The maximum amplitude of oscillation of a member 

depends on member support conditions and the Ks value, reaching a 

value approximately equal to member diameter for simply supported 

boundary conditiens. To prevent the lock-in effect, it is desirable 

to keep the member natural frequenciesto less than 70%or more than 

130% of the vortex shedding frequency, whenever practical. 

8.2 

ANALYSES AND DESIGN FOR VORTEX SHEDDING 

The interactivenature of the vortices shed and the vibration of the 

cylinder makes analytical prediction of response to vortex induced 

vibration (VIV) extremely difficult. Empirical formulations 

(References 8.5, 8.6 and 8.7) have been developed to reflect the 

state-of-the-artwith respect to VIV technology. These empirical 

approaches incorporate various parameters and are based on the 

comparison of specificparametricvalues with experimental results. 

Empirical formulations can be effective y used to avoid VIV, but 

they are less reliable at predicting the occurrence of VIV and 

determining the response amplitudes. 

8.2.1 

Suscelltibilityto Vortex Sheddinq 

Cylindrical members may experience either in-line or cross flow 

oscillations for a range of flow velocity and member response 

characteristicratios. To define susceptibilityof a member to VIV, 

a reduced velocity (Vr) term is introduced: 

v 

vr=— 

fnd 

where:

v= flow velocity normal to the cylinder axis 

fn = fundamental frequency of the member (H) 

d= diameter of the member 

Susceptibilityof a member to VIV in air is different than in water 

due to the density of air flowing around the member being different 

than the density of water. Susceptibility of a member is defined 

for in-line and cross-flow oscillations in both environments. 

In-line VIVmay occur when: 

l*2svr

8.2.2 

VIV Response and Stresses 

A strategy based on avoidance of VIV is quite feasible for most 

marine structures. Primarystructuralmembers are usually designed 

to be sturdy enough that they are not susceptible toVIV. However, 

some secondary or non-structuralmembers may be susceptible to VIV 

in water and in air. An empirical approach proposed by DnV 

(Reference 8.7) does not account for the nonlinear relationship 

betweenresponseanddamping,therebyyielding conservativeresponse 

amplitudes and stresses. To predict response amplitudes more 

reliably an approach based on Hallam et at (Reference 8.9) is 

recommended. 

Cross-flow oscillations due to wind action may not always be 

preventable, requiring the members to have sufficient resistance. 

An empirical formulation based on a procedure by Engineering 

Sciences Data’ Unit ESDU (Reference 8.6) that accounts for 

interaction between vortices shed and forces induced is 

recommended. This procedure and the basis for estimating maximum 

bending stresses for different boundaryconditions are discussed in 

Sections D.4 andD.5 of Appendix D. 

8.3 

FATIGUE DAMAGE ASSESSMENT 

All members susceptible to VIV should be assessed for fatigue 

damage. First, the fatigue damage due to VIV is calculated. Then 

a global fatigue analyses is performed and fatigue determined for 

all critical members. The total fatigue damage is equal to the sum 

of local (VIV) and global fatigue damage on each member. 

Step-by-step determination of both local and global fatigue damage 

is discussed further in Section D.6 of Appendix D. Application of 

the procedurecould indicatethat the fatigue life is expended after 

relatively small number of oscillations, requiring corrective 

measures to be taken either in the design process or during 

fabrication (devices,spoilers, etc.). 

8-5

8.4 METHODS OF MINIMIZING VORTEX SHEDDING OSCILLATIONS 

Because the environmental factors that cause vortex-induced 

oscillations (wave, current and wind) cannot be controlled, 

minimizing the oscillations depends primarily on the physical 

characteristicsof the structure. 

There are several ways to solve the problem of vortex-induced 

oscillations: 

● 

Controlof structuraldesign (length,diameter, end fixity)to 

obtainmember naturalperiodsto avoid the critical velocity. 

● 

Control of structuraldesign to have sufficiently high values 

of effective mass and inherent damping to avoid the critical 

velocity. 

● 

Altering the pattern of the approachingflowto modify vortex 

shedding frequency. 

Further discussion on this subject is presented in Section D.8 of 

Appendix D. 

8.5 

RECOMMENDATIONS 

Fatigue damage due to vortex shedding is best prevented during the 

design of the structure by sizing the members (length-to-length 

ratio, rigidity, damping, etc.) to ensure that critical velocity 

values are avoided. If geometric, design schedule or-economic 

constraints preclude resizing of members susceptible to VIV, the 

total fatigue damage due to local (VIV) and global response should 

be computed and the integrity of those members verified. If a 

limited number of members are found to be susceptible to fatigue 

failure, the flow around such members may be modified through the 

use of devices and spoilers. 

8-6

Verification of a member’s structural integrity due to VIV fatigue 

is difficult due to the-interactivenature of the vortices shed and 

the vibration of the member. State-of-the-artprocedures developed 

to determine the responseamplitudesof amember incorporateseveral 

approximations. It is reconunendedthat some of the more important 

of these approximationsare carefully considered before starting a 

VIV analyses: 

● 

Experimental data used to correlate parameters in the 

development of empirical procedures are limited. Published 

data is not available for in-line VIV in uniform oscillatory 

flOw. 

● 

Accuratedeterminationof structuraldamping ratios in air and 

inwater isdifficult. Thedamping ratios directly affect the 

stability parameter and may contribute to either 

underestimationor overestimationof the vibration amplitudes 

and stresses. 

● 

Tubulars extendingover multiple supportsneed to reevaluated 

by considering support sleeve tolerances and spanwise 

correlation of varying lengths and fixity prior to the 

determinationof natural frequencies. 

8-7 

/ y_.

Ra < S REGIME OF UNSE?ARATE~ FLOW 

5 TO 15 c Ro 

VOfiTICES IN WAKE 

4G

9. 

FATIGUE AVOIDANCE STRATEGY 

Most marine structures are designed and analyzed to resist extreme 

loadings. Some structures,includingoffshore structures and ships 

with special features,are also checked for fatigue. This approach 

may be valid for structures in environments not susceptible to 

fatigue loadings. A good overall design of marine structures 

susceptible to fatigue loading (largeships and tankers, stationary 

fixed and floatingstructures,etc.) can be achievedwhen fatigue is 

given an equal emphasis to stability, strength and other 

considerations during design, long before steel is ordered. 

Fatigue design should be both an integral part of an overall design 

effort and a part of a strategy covering the entire design life of 

the structure. Thus the design, fabrication, inspection and 

operationalmaintenanceshould be treated as interactiveparameters 

that affect fatigue avoidance strategy. 

While most offshore structuressusceptibleto fatigue were properly 

analyzed and designed to prevent fatigue failures, ship-shaped 

vessels were seldom analyzed and designed for fatigue. The use of 

high strength steel in recently constructed vessels proved that an 

indirect fatigue design (i.e. member sizing, detailing) is not 

sufficient to prevent fatigue failures. As a result, large number 

of vessels constructed by reputable firms now incorporate detailed 

finite element analysis and design to prevent fatigue failures. 

9*1 

REVIEW OF FACTORS CONTRIBUTINGTO FAILURE 

Mobile vessels and stationary structures differ not only in their 

general configuration but also in the nature of applied 

environmental loading. A stationary structure’s site-specific 

environment usually determines the stress ranges and the number of 

stress cycles, and is a major variable affecting fatigue life. The 

next most importantvariables are the parameters affecting design 

and fabrication quality. While maintenance may not be important 

early in design life, it assumes a major role as the structure 

9-1 

j:) >~

ages. The designer has no control over the environment, but other 

factors can be addressed to enhance fatigue quality. 

The factors that affect fatigue quality can be reviewed in four 

groups. It appears reasonable to assume that each of these four 

groups contributes equally to fatigue failure: 

● 

● 

● 

● 

Design 

Fabrication 

Maintenance 

Operational Loads 

The fatigue life of a vessel is similarly affected by the activities 

undertakenduringdesign,fabrication,maintenancework and severity 

of operational loads. Skaar (Reference9.1) reports that a survey 

to assess the approximate importance of design, fabrication, 

maintenance and operations indicated that each contributes about 

equally to overall quality. 

9.2 

BASIC FATIGUE AVOIDANCE STRATEGIES 

9.2.1 Basic Premises 

Review of fatigue failures shows that while relatively few failures 

threaten structural integrity, repairs are costly and the cost of 

continuous inspection and maintenance is appreciable. A survey of 

design configurations and structural details shows that designers 

who have access to operational feedback on inspection, repair and 

maintenance, generally develop more reliable designs. To ensure a 

functional,high-qualitystructure(i.e.,with structural integrity) 

that is cost-effective, both capital expenditures (CAPEX) and 

operating expenditures (OPEX) should be addressed simultaneously. 

The review of marine structures indicate several design 

philosophies: 

9-2

● 

An indirect fatigue design where the design for extreme 

Ioadingandexperience-based detailingare intendedto provide 

ample fatigue resistance. This approach may be valid for 

structures subjected to negligible cyclic loadings. 

● ✍ 

Simplified allowable stress methods based on in-servicedata 

and valid theoreticaldevelopments. This approach isvalid as 

a design tool to size structure components. 

● 

Comprehensive fatigue analyses and design methods with 

appropriatefatigue strength and stress history models. This 

approach, including finite element analyses to accurately 

determine the stress distributions, should be used in the 

design of all structures susceptible to fatigue failure. 

● 

Comprehensivefatigue analyses and design methods, taking the 

lifetime inspection and maintenance strategies into account. 

This is the valid approach to implement a cost-effective 

fatigue avoidance strategy. 

Design, inspection and maintenance are thus logically treated as 

interdependent parts of an overall process contributing to the 

quality of a structure. 

The other basic premises affecting fatigue avoidance strategies can 

be summarized as follows: 

● 

The fatigue life is usually taken as twice the design life. 

The target fatigue lives can be chosen tobe about fiveto ten 

times the design life with very little increase in steel. 

The additional expenditures caused by the slight increase in 

steel cost can be offset many times over by savings in 

operating expendituresassociatedwith inspection,repair and 

maintenance. 

● 

Service experience is of utmost importance in the design of 

marine structures. The designer should have an access to 

9-3

failure data on various structures, including continuous 

system stiffening details (i.e., orthotropically stiffened 

hul1plate). 

● 

Typically, stiffening detail failures cause serviceability 

problems, affecting the extent of a structure’s repair work 

and cost. Unrepaired, they may cause buckling, flooding and 

progressive collapse, thereby, resulting in the pollution of 

the environment and the loss of structural integrity. 

● 

Typical tubular interface failures of stationary structures 

can cause substantial degradation in structural integrity. 

Repairs on location, especially underwater, are extremely 

costly and are not always entirely successful. 

9.2.2 FatictueAvoidance Strategies 

Fatigue avoidancestrategiesfor ships and tankers are both similar 

and dissimilar to those for fixed and floating stationary 

structures. The primary components of continuous systems (ship 

longitudinal girder, semisubmersiblecolumn, etc.) are designed to 

provide ample strength, and the redundant load paths provided by 

multiple stiffenersmake fatigue more a serviceability problem. A 

discrete system such as a fixed platform may have redundancy to 

prevent major degradation of the structure, yet redistribution of 

load paths will accelerate crack growth in adjacent areas and can 

cause failures in these areas. To prevent additional failures, 

repair work should not be postponed beyond a reasonable period. 

The basic fatigue avoidance strategies are best addressed as the 

factors that affect design and maintenance: 

9-4

“!M91! 

● 

Global Configurations 

A design strategy that provides a global configuration with 

redundancy and minimizes both the applied loads and the 

response will enhance structure fatigue life and reduce 

maintenance costs. 

Both continuous system and discrete system global 

configurationscan be optimizedto various degrees to minimize 

the effect of applied loads and the response of the structure 

to these appliedloads. The dynamic response of the structure 

can contributeto substantialcyclic stress (i.e. both global 

and local dynamics, including vortex induced vibrations) and 

should be minimized. 

•~ 

Joint/Weld Details 

The structuraljoint/welddetails should be developed basedon 

operatingexperience,analyticalstudiesand assessmentof the 

impact of actual fabricationyard work to minimize the stress 

concentrations,adversefabricationeffects and stresslevels. 

The joint/weld details should be designed to prevent large 

stress concentrations. Review of typical joint/detail 

failures and analytical parametric studies should be used to 

identify both “desirable” and “undesirable”details. Review 

of some of the published data on structural detail’failures 

(References9.2, 9.3, 4.2 and 4.3) also illustrate that such 

fatigue failures can be significantly decreased by avoiding 

magnification of stress patterns on a structure detail. 

Jordan and Cochran (Reference9.2) surveyed 3,307 failures in 

over 50 ships and presented their findings by grouping the 

structural details into 12 families The review of details 

within each family (twelvefamilies: beam brackets, tripping 

brackets, non-tight collars, t. ght collars, gunwale 

9-5

connections, knife edge crossings, miscellaneous cutouts, 

clearance cuts, deck cutouts, stanchionends, stiffenerends, 

and panel stiffener ends) should provide an invaluable 

operationalfeedbackto the designer in understandingrelative 

susceptibilityof different details to fatigue failure. 

● 

Material and Fabrication 

The material selected, procedures specified and fabrication 

specificationsissuedshouldbe compatiblewith each other and 

meet the requirements of the intended function of the 

structure. 

The design effort should ensure selection of material with 

chemical composition and material properties applicable for 

the structure’s intended function. Welding material and 

procedures should be compatible with the structural material 

selected. Overall fabrication specifications, covering 

fabrication tolerances, repair procedures, etc., should be 

developed to meet the target objectives. Specifications 

should reflect a balance between cost and fit-for-purpose 

approach to quality. 

Maintenance 

Stationary structures may require a higher degree of design 

conservatism than mobile structures to minimize the cost of 

maintenance, inspection and repair. Maintenance and inspection 

programs should be developed during design to reflect both design 

conservatism and functionalityof the structure and its components. 

Maintenance, 

parameters. 

differs from 

inspection and repair are interactive in-service 

The maintenance and inspection of continuous systems 

discrete systems largely in degree of accessibility. 

Most continuous systems (such as interiors of hulls, columns and 

pontoons)can be routinely inspectedandmaintained. Such units can 

be brought to shipyards for scheduled or unscheduled repairs. 

9-6

Fatigue avoidance strategy for mobile vessels should consider both 

the consequence of limited degradation due to fatigue failure and 

the relative ease of routine maintenance and scheduled repairs. 

Most discrete systems, such as offshore platforms, are stationary 

and their components are generally not accessible for internal 

inspection. Thus, inspectionis carried out externally, both above 

and below water. Any repair work undertaken is costly and may be 

only partially successful. Were regulations impose comprehensive 

inspection and maintenance programs, such as in the North Sea, a 

fatigue design philosophyaddressingthe inspection and maintenance 

issues also facilitates certification of design. Typically, 

redundancy and consequence of failure dictate the inspection 

intervals. Those areas known to be susceptible to fatigue failure 

will require more frequent inspection intervals. Similarly, 

inspectionresults should be the basis for altering the recommended 

inspection schedule as necessary. 

Analysis 

Analytical assumptions and the methodology implemented for fatigue 

life computations have dramatic effects. The choice of fatigue 

analyses appropriate for a specific project depends on the 

information available, research gaps, and sensitivity of structure 

to fatigue failure. Because fatigue analysis approach is not truly 

an avoidance strategy, it is discussed separately in Section 9.4. 

9.3 

FATIGUE STRENGTH IMPROVEMENTSTRATEGIES 

Fatigue strength improvement and fatigue avoidance strategies 

benefit from application of an appropriate design philosophy that 

allows development of structure and component integrity, and that 

facilitatesqualityof construction. The specificmethods discussed 

in the section are remedial measures for fatigue strength 

improvement. 

9-7

9.3.1 Fabrication Effects 

The fatigue strength of welded joints/details is lower than the 

parent material due a wide range of fabrication effects. Some of 

the primary causes for the degradation of fatigue strength are due 

to: 

● 

Increase in peak stresses due to geometrical effects and 

discontinuities(stressamplification)andmismatchtolerances 

(bending stress) introduced. 

● 

Residual stresses introduced 

excessive heat input, etc. 

due to welding, forced fit, 

● 

Defects introduced in the weld 

edge of welds. 

material, and undercut at the 

Adverse fabrication effects are minimized by addressing 

during design and specification writing. 

Both 

the issues 

experience 

(operationaland design)and parametricstudiesal1ow developmentof 

“desirable” details to minimize the local increase of stresses. 

Fabrication specifications are prepared to optimize fabrication 

quality without excessive expenditures. 

9.3.2 Post-FabricationStrenqth Improvement 

Numerouspost-fabricationprocessescan partiallyor totally counter 

the fabrication effects that contribute to degradation of fatigue 

strength. However, post-fabrication processes may be costly and 

should not be incorporated in the design process routinely. 

The developmentof fatigue cracks depends largelyon the geometryof 

the joint detail and often developat the weld toe. Any mismatchof 

parent plates will facilitate propagation of the crack through the 

weld until a failure across the throat is observed. Deposition of 

extra weld metal in the throat area to decrease the shear stress can 

9-8

improve the fatigue strength. The methods available to improve 

fatigue strength can be-grouped into two: 

● 

● 

Modification of weld toe profile 

Modification of residual stress distribution 

Some of the methods in each category are identified on Figure 9-1 

and discussed in this section. 

Modification of Weld Profile 

Both contour grinding of the weld profile and the local grinding of 

the weld toe area are recommendedto improve fatigue strength. The 

two key objectives in the modification of weld toe profile are: 

● 

● 

Remove defects at the weld toe. 

Develop a smooth transition between weld material and parent 

plate. 

By applying either local grinding or remelting techniques to remove 

defects and discontinuities, the fatigue life is increased as a 

function of time required for crack initiation. Some applicable 

methods are as follows: 

● ✍ 

Grindinq 

Full-profile burr grinding, toe burr grinding or localized 

disc grinding can be carried out. Considering the time 

required for grinding, local-weldtoe grinding has become one 

of the most frequently used grinding methods. Careful and 

controlledlocal grindingof the weld toe improvesthe fatigue 

strength of a specimen in air by at least 30%, equivalent to 

an increase in fatigue life by a factor greater than 2. 

However, to obtain such a benefit the grinding must extend 

about 0.04 inch (1 nun)beneath the plate surface. Typical 

defects and correctivemeasures are shown on Figure 9-2. 

9-9

● 

Controlled Erosion 

An alternate weld toe modification technique uses a highcontaining 

grit. Under carefully 

pressure water jet 

controlled conditions the weld toe area can be eroded as 

though itwere beingground. Work carried outon filletwelds 

with abrasive water jetting (AWJ) by Maddox and Padilla 

(Reference9.4) andKing (Reference9.5) indicatethat fatigue 

life improvement due to AWJ erosion and toe grinding are 

comparable. The S-N curve improvements obtained due to weld 

toe abrasivewater jet erosion are illustratedon Figure 9-3. 

This approach does not require heat input and can be carried 

out quickly, offering an advantage over alternative methods. 

● 

Remeltinq Techniques 

Remeltingweld material to a shallow depth along the weld toe 

results in removal of inclusions and helps achieve a smooth 

transitionbetweentheweld and the platematerial. Tungsteninert-gas 

(TIG) and plasma welding are not practical 

techniquesfor routine use, but TIGandplasma dressing can be 

used to improve the fatigue strength of selective areas. 

TIG welding is based on astringer bead process 

is performed on welds made by other processes 

region is melted to a shallow depth without 

TIG dressing 

where the toe 

the use of a 

filler material. Slag particles in the remelted zone are 

brought to the surface, 1caving the weld toe area practical1y 

defect free. Ahigh heat inputshould be maintainedto obtain 

a good profile and a low hardness. A low hardness in the 

heat-affectedzone (HAZ)may be also achieved by a second TIG 

pass. 

Plasma dressing requires remelting the weld toe using the 

plasma arc welding technique. It is very similar to TIG 

dressing, but plasma dressing uses a wider weld pool and 

higher heat input. This technique is relatively insensitive 

9-1o

to the electrode position, so the strength improvements are 

better than the improvementsobtained from TIG dressing. 

Although overall weld profiling is considered desirable for 

tubular intersections, rules and recommendations other than 

API do not allow improvement in fatigue strength of a joint 

unless weld profiling is accompanied by weld toe grinding. 

Tliefatigue strength increaseof welded joints dueto weld toe 

grinding in air is considered equally applicable to 

catholicallyprotectedwelded joints in seawater. However, in 

the absence of cathodic protection, a corrosive environment 

helps to initiate fatigue cracks. Thus, without cathodic 

protection, fatigue strength improvement due to weld toe 

grinding cannot be justified. 

The fatigue strength increaseinwelded joints dueto weld toe 

grinding is basedon simple plate specimenstested in air and 

in seawater (with and without cathodicprotection). However, 

extensionof welded plate specimentest data to tubular joints 

may not be correct. Hork carried out by Wylde et al 

(Reference 9.6) indicates that additional research is 

necessary because: 

1) The corrosive effect of seawater appears to be greater 

on tubular joints than on flat plates. 

2) Cathodic protection appears to be less effective on 

tubular joints than on flat plates. 

Modification of Residual Stress Distribution 

A wide range of residual stress techniques are available to 

redistribute the fabrication stresses at a welded joint. If large 

residual tensile stresses are present at a welded joint, the applied 

stress cycle near the weld toe can remain wholly tensile. Thus, 

9-11

after 

a given number of stress cycles, the stress range to cause 

failure is practicallyconstant for a wide range of mean stresses. 

The undesirable tensile residual stresses at the weld can be 

modified by the following methods to set up desirable compressive 

stresses at the weld toe: 

● 

Stress Relief 

Various fatigue tests on simpleplate specimens indicate that 

an improvedfatigue strength can be obtained by stress relief 

due to post-weld heat treatment (PWHT). However, PIate and 

stiffening elements of continuous systems rarely require 

stressrelief. Thick tubularjointswith residual stressesas 

a result of fabrication work can often benefit from stress 

relief. Yet, it is not clear that a complex joint with builtin 

constraints can be effectively stress relieved. It is 

1ikely that substantial residual strains and stresses wil1 

remain at a joint assembly after PWHT. 

Localized stress relief may be very beneficial in an 

embrittled heat-affected zone (HAZ). Typically, high 

localized heat input in a HAZ alters the material properties 

and causes reduced fatigue life due to unstable fracture. A 

PWHT carriedout to improvetoughnessof the HAZmay partially 

restorethe fatiguestrengthof welded joints, as the residual 

stresses have an influence in the development of fatigue 

cracks. Previous investigations on this subject (Reference 

1.8) document influence of PWHT on fatigue. 

● 

Compressive Overstressinq 

Compressiveoverstressingis a technique in which compressive 

residual stresses are introduced at the weld toe. 

Experimental results and analytical work demonstrate 

effectivenessof prior overstressing,but the procedure to be 

implementeddoes not appear to be practical for most marine 

9-12

structures. A comprehensive discussion of strength 

improvementtechniquesby Booth (Reference9.7) is recotmnended 

for further review of compressive overstressing. 

Peening is a cold working process intended to produce surface 

deformations to develop residual compressive stresses. When 

impact loading on the material surface would otherwise cause 

the surface layer to expand laterally, the layer underneath 

prevents such surface layer expansion, creating the 

compressiveresidualstressesat the surface. Typical peening 

methods are hamer peening, shot peening and needle peening. 

Further discussion on peening techniques and their relative 

benefits is provided by Maddox (Reference 9.8). 

9.3.3 

Comt)arisonof StrenctthImrirovementStratecties 

Strength improvement techniques are time consuming and costly and 

they should be applied selectively. Comparison of different 

techniques allows assessment of their effectiveness and cost. The 

recommended strength improvement strategy depends on the 

characteristics of the structure (global and local) and the 

preference for one technique over others based on effectiveness, 

cost and fabricationyard characteristics. 

Some of the more important comparisons of various approaches 

available to improve fatigue strength of weld details subjected to 

a wide range of stresses are as follows: 

● 

Full profile burr grinding is preferable to toe burr grinding 

only, or disc-grinding only, because it results in higher 

fatigue strength even at a substantial cost penalty. 

Disc grinding requires the least time and cost. However, it 

produces score marks perpendicular to the principal stress 

direction, making this technique less effective than others. 

9-13

A second pass with polishingdisc is considered advisable. A 

complete chapter on weld toe grinding by Woodley (Reference 

9.9) provides a detailed discussion on grinding techniques. 

● 

Using a high-pressure abrasive water jet (AWJ) process for 

controllederosion of the weld toe area can be as effectiveas 

grinding. Its simplicity, speed and non-utilization of heat 

make controlled erosion very promising. Work carried out by 

King (Reference9.5) indicatethat AWJ process is suitable for 

a range of material removal applications, includingweld toe 

dressing, gouging and weld edge preparation. 

● 

A wider weld pool makes plasma dressing less sensitive to the 

positioning of the electrode relative to the weld toe, 

compared with TIG dressing. Therefore, the fatigue strength 

improvementobtained from plasma dressing is generally better 

than that obtained from TIG dressing. 

Both methods are suitable for automation and cost-effective 

application. 

● 

Review of grinding, remeltingand peening techniques indicate 

substantial scatter of fatigue strength improvements. 

Typically the best fatigue strength improvementsare achieved 

byTIG dressing and hannnerpeening. Toe disc grinding is the 

least effective technique. Figure 9-4, obtained from 

Reference 9.7, provides a good comparison of various fatigue 

strength improvementtechniques. 

9.4 FATIGUE ANALYSIS STRATEGIES 

9.4.1 Review of Uncertainties.Gaps and Research Needs 

There are many uncertainties in a fatigue analysis, carried out to 

determine the fatigue lives of marine structure components. To 

ensure validity of analysis the first objective is to accurately 

predict the stress-historyfor the lifetime of the structure. The 

9-14

second objective is to accurately evaluate the fatigue strength of 

the structure components and to calculate the cumulative fatigue 

damage basedon stress-historyand fatigue strength. While some of 

the uncertaintiesoccur in nature,others are caused by shortcomings 

in simulating the actual behavior. 

Uncertainties in Predicting Stress Histor.v 

It is necessaryto model the actual structure as closely as possible 

to determine the applied loads and the response of the structure to 

these applied loads. Since marine structures are typically 

indeterminate structures, stresses are strongly dependent on the 

structuralconfiguration,necessitatingcareful simulationof actual 

member and joint behavior. 

a) Hydrodynamic Loads Model 

The ship structureloads model allows the use of strip methods 

or 3-D flw solutions to determine the wave loads. The 

accuracyof the wave loaddeterminationdepends on the ability 

to accurately define the wave force coefficients, marine 

growth, wave steepness, hydrostatic effects and hydrodynamic 

effects. 

The loads on a stationary semisubmersible or fixed platform 

are typically determined from Morison’s equation. Fixed 

platform loads are largely affected by the accuracy of wave 

inertia and drag force coefficients, wave steepness, marine 

growth and the shieldingeffectof componentmembers.’ The use 

of a stick model is valid for a fixed platform, the use of a 

stick model for a structure made up of large members will 

result in inaccurate loads. 

Becauselargememberswill disturb the flow, leading to highly 

frequency dependent diffraction, a three-dimensional 

diffraction theory is often used to determine the wave force 

componentsto directly accountfor the effect of one member on 

9-15

others. Extensive analytical and experimental work provides 

validation of techniques used to generate the loads. 

Fcrstandard vesselswith aforward speed, stripmethods often 

provide the desirable accuracy. Although the diffraction 

methods are still considered largely a research tool by many, 

they are now used as an analyses and design tool by others. 

Limited amount of available data on wave-induced and dynamic 

impact (i.e. slawaning)loading on vessels and the vessel 

responsedo not facilitatecalibrationof analysesmodels. It 

is necessary to obtain sufficient data for various vessel 

types for an extended period. Boylston and Stambaugh 

(Reference 9.10) recommended program to obtain loading 

computer records, based on vessel strains for at least three 

vessel types over a five-year period, should provide 

sufficient data on probabilistic loadings and the vessel 

response. 

b) 

Mass. Motions and Stiffness Models 

There are few uncertainties in developing an accurate mass 

model. The motionsmodel, however, is largely affected by the 

assumptions made to define the motions and stiffness models 

and the analyses techniques chosen. The uncertainties built 

into these models that allow the definition of nominal 

stresses are: 

linearizationof drag term 

definitionof joint releases,complexityof joint, joint 

flexibility etc. 

definition of strongbacks and global versus local 

distribution of loads 

added mass 

appurtenancesmodelling 

structuraldamping (for bottom-supported structures) 

foundationmatrix (for bottom-supportedstructures) 

9-16

elative slippage--betweenjacket legs and piles. 

Additionaluncertaintiesintroduceddue to assumptionsmadeon 

analyses techniques, are: 

applicationof regular or random waves 

applicationoftime-domainor frequencydomain solutions 

use of deterministic versus spectral analyses 

While some of the uncertainties relate to analytical 

simulation of actual conditions, others reflect the 

uncertainties in both the nature and in simulation. Most 

analysis and modeling uncertaintiescan be minimized, and the 

current state-of-knowledge and tools available facilitate 

obtaining accurate nominal stress distributions. 

Since the structuredynamic responses (bothglobal and local, 

including vortex induced vibrations) contribute substantial 

cyclic stresses, it is extremely important to minimize the 

uncertainties in simulating structure responses. 

c) 

Hot Snot Stresses 

Peak stresses can be reasonably well defined by the use of 

physical models and finite element analyses. However, for 

most analysis and design work the time and cost constraints 

necessitate the use of empirical formulations to obtain the 

SCFS and define the hot-spot stresses. 

Al1 empirical formulations have application 1imits and the 

accuracy of the SCFS computed depend on several variables. 

More finiteelementwork is requiredto define the interaction 

of parameters for a wide range of joint geometries to upgrade 

existing empirical formulations. 

9-17

d) Stress SDectrum 

Hot-spot stresses combined with the long-term effects of the 

environment allow development of the stress spectrum. 

Randomnessof ocean environmentmakes both the short and longterm 

prediction of sea states quite difficult. The 

uncertainties of nature that influence the life-time stress 

history of a stationary structure are: 

- Use of full scatter diagram ofHs andT 

- Variations ofT 

- Percentage of occurrence estimates 

- Wave directionality 

- Interactionof wave and current 

For some site-specific stationary structures, a good existing 

databasemay allow comprehensivehindcastingstudies to predict both 

short- and long-term environment with a reasonable certainty. A 

reliability-based full probabilistic fatigue analysis al1ows 

selection of the degree of reliability that affects the fatigue 

life, such as the environmental loading, size and distribution of 

defects, fatigue strength, etc. However, even commonly used 

spectralfatigueanalyses,which isdeterministic, (i.e. application 

of only probabilisticenvironmentalconditions),the desirablelevel 

of uncertainty for the environment can be chosen to be compatible 

with the other factors that affect the computed fatigue life. 

For oceangoing ships which move through various site-specific 

environmentsin a singleroute, the stress history is very difficult 

to define. A full probabilisticreliabilityanalysis, orthe useof 

conservativeupper bound conditions,is necessary to account for the 

many different routes over the the uncertainties regarding the use 

of very different routes over the life of the vessel as well as 

route changes due to extreme environmental conditions. 

9-18

h!!!u 

Fatiguestrength is not analyzedbut determinedfrom laboratorytest 

specimens. The experimental work that allows the definition of 

fatigue strength and the S-N curves require substantial further 

work. Some of the basic variables contributing to the uncertainty 

fatigue strength include the effects of: 

Geometry (weld profile, toe discontinuity, etc.) 

Defect type, size and location 

Definition of fatigue failure (Nl, N2) in S-N data 

Size on S-N data 

Assumption of a linear model and log normal distribution for 

N 

Environment (corrosion,cathodic protection, etc.) 

Load amplitude and sequence 

Fabrication residual stresses 

Post-fabricationprocedures to increase fatigue strength 

-. 

Due to large uncertainties in each of the items listed, the fatigue 

strength data show a very large scatter, requiring the use of 

somewhat conservative S-N curves. The available test data on high 

stress range-low cycle fatigue failure is limited. Thus, the S-N 

curves for the 1000 to 10,000 cycle range are less reliable than the 

high cycle ranges. 

While additional work is necessary to better define geometric 

variations, the recent research has shown that there are also some 

uncertainties regarding the: 

● 

● 

● 

Beneficialeffect of weld profilewithout weld toe grindingor 

remelting 

Assumption of catholically protected joints in sea water 

having the same fatigue strength in air 

Classification of joints based on geometry rather than load 

pattern 

9“19

Cumulativefatiguedamagecomputationshave been and still are based 

on Miner’s linear cumulativedamage rule. Alternative stress cycle 

(rainflow)countingmethods have allowed reduction of uncertainties 

for wide-band loading. Gurney’s rule provides an alternative to 

Miner’s rule. However, the most important research gap in the 

computation of fatigue damage is the sequence of loading. The wave 

1oading, which is of stochastic nature, have been simulated by 

Markow matrix (Reference9.11) to carry out fatigue test of plates 

under stochastic and constant amplitude loading (Reference 9.12). 

These initial tests indicate fatigue strength properties for 

constant amplitude and spectrum loading may be different. Unti1 

more research is carried out on loading sequence it should be 

presumed that a certain number of large amplitude stress cycles 

during the beginning of a structure’s life would be likely to 

accelerate the fatigue crack growth of most defects. A series of 

tests being carried out at Technical University of Denmark 

(Reference 9.13) should provide more definitive conclusions on 

fatigue life of welded joints subjected to spectrum loading under 

various corrosive conditions. 

9.4.2 

Recent Research Activities 

Extensive fatigue research activities were carried out in the 

1980s. A large percentage of these activitieswere carried out in 

Europe, addressing the parameters affecting fatigue life of 

joints/detailsin the extremeNorth Sea environment. Other research 

activities carried out in the United States and elsewhere indicate 

that the research activities are often complementary and generally 

avoid duplication of effort. 

The fatigue research activities are generally carried out in two or 

three phases over multiple years. While some research activities 

were completed, others will continue into early 1990s. These 

research activities may be grouped into following areas and the 

relevant activities are sunanarizedon Figure 9-5. 

9-20

● 

Stress concentrationfactors; includingcollating of existing 

data, calibration of SCF equations and development of 

parametric equations. 

● 

Fatigue analysis and design methods; includingfinite element 

analysis procedures and application of fatigue design rules. 

● 

Fatigue resistance; including simple plate S-N curves and 

complex details, S-N curves for stiffened joints and S-N 

curves for different materials. 

● 

Effect of various parameters on fatigue life; including the 

effect of cathodicprotectionin seawater,plate thicknessand 

weld profile effects. 

● 

Fatigue 

life improvementtechniques. 

●- Fatigue 

damage, 

life determination; including review of cumulative 

assessment of random loading and low cycle fatigue. 

9.4.3 Cost-EffectiveAnalysis Strategies 

Acost-effective analysesstrategy is relativelyeasy to develop for 

any marine structure. First, the structure configuration and the 

likely marine environment should be assessed to determine 

susceptibility of the structure to fatigue. Second, structure 

configuration and operational response characteristics should be 

assessed to determinethe desirable analyses techniques to generate 

the loads and to determine the response of the structure.” 

Although computer cost is an important variable in developing an 

analysis strategy, computer cost should be assessed in conjunction 

with engineering time and effort as well as the time available to 

completethe fatigueanalysisand design. Most important,design is 

an iterative process and structural changes will invariably occur 

during fatigue analysis. Thus, fatigue analysis should be treated 

9-21

as a parametric study intended to identify the fatigue-susceptible 

areas for improvement. 

Considering that small increases in steel used can appreciably 

increase fatigue lives, it is recommended that the target fatigue 

lives (at least for a screening effort) be taken as five to ten 

times the design life while most rules and reconunendationsspecify 

a factor of two between fatigue and design life. Then, changes 

introduced during design that has an impact on applied loads and 

stress distributions can be readily accommodated. 

9.5 

RECOMMENDATIONS 

Fatigue avoidance strategiesadopted and the design tools used have 

served as well. However, further efforts are necessary in carrying 

out more research, in developing further improvements in analyses 

and design, and in upgrading the rules and regulations to 

incorporate the research results. 

Recommendationspresented in Section 5 through8 provided the basis 

for further in-depth discussions in Section 9. Applicable 

references in each section are listed in Section 10. Some of the 

primary recommendations are listed as follows: 

● 

Although “allowable stress” methods may be used as a 

“screening process,” a detailed fatigue analysis is often 

necessary. 

● 

Assessment of various empirical equations indicate that the 

UEGequations yield conservativepredictionofSCFs for awide 

range of geometry. However, empirical equations provided by 

UEG, Efthymiou,Kuang and others should be reviewed for joint 

geometry and loading condition to allow selection of most 

appropriate equation. 

● 

The long-term wave 

models are quite 

environment definitions based on hindcast 

reliable. However, modeling parameters 

9-22

should be carefully reviewed and the model calibrated to 

ensure the reliability of data. 

● ✍ 

The S-N curvesused indetennining fatiguedamage computations 

should be compatiblewith structural details investigated. 

● 

Considering the effect of size, weld profile and undercut on 

fatigue strengthand S-N curves, it may be prudent to reassess 

the hot spot stress range concept. The definition of hot spot 

stressrange can be modified to reflect the weld toe defects. 

● 

The use of Miner’s cumulativefatiguedamage rule with the S-N 

curves is appropriate. Further research, especial1y on the 

effects of stress sequence and counting of stress reversals, 

is considered necessary. 

9.5.1 Research Priorities 

Whether designinga supertankeror an offshoreplatform, significant 

fai1ure modes can be identified, environmental 1oads generated, 

structure response characteristics determined, and stress 

superpositionscompatiblewith the environmentand the failuremodes 

computed. Although strength statistics for these structures can be 

expressed in terms of means and variance, lack of sufficient 

statistical data on loads, stresses and strength prevent full 

probabilistic fatigue analyses. A development of a semiprobabilisticanalysisapproachapplicableto 

various structuresand 

that does not require a distribution shape is desirable. 

While a typical fatigue damage assessment is based on fatigue 

strength data yielding S-N curves, such an assessment can also be 

made based on fracture mechanics and crack growth laws. While the 

damage assessment is based on propagationof individual crack, work 

carried out by Morgan (Reference 9.14) has indicated possible 

interactionof multiple cracks. Thus, further work is necessary to 

obtain data on interaction of cracks as well as interaction of 

parameters affecting development of S-N curves. 

9-23 

..2I‘7

Additional areas requiring further research are sununarizedas 

follows: 

Parallel study of weld profile and weld toe defects. 

Analytical study of existing data for weld toe defect stress 

levels and through-thicknessstress levels. 

Identification of the type and magnitude of the errors 

introduced in laboratory work and development of appropriate 

means to normalize test data. 

Further assessment of empirical equations. Available test 

data should be further evaluated, incorporating necessary 

correction of data, and reliability and limitation of 

equations revised, as necessary. 

Carrying out of additional tests in both air and in ocean 

environment to fill the gaps in existing research. 

Development of NDE methods to quantify residual stresses 

introducedduring fabrication. 

Further study of long-term wave environment. 

Further assessment of stress sequence on fatigue life. 

9.5.2 

Rules and Regulations 

Existing rules, regulations and codes are adequate and generally 

conservative. However, differences exist between various rules, 

regulations and codes, including omissions and inconsistencies. 

Research data obtained in the 1980s was the basis for revisions 

introduced into the 4th Edition of Guidance Notes (1990). Similar 

effort has been initiated to revise API RP 2A. Some of the recent 

studies published (References 7.8 and 5.20) follow a deliberate 

format to facilitate extraction of data to upgrade existing rules 

9-24 

-m’ 

..7 ,

and regulations. These and other study results should prove 

valuable in revision and upgrading of rules and regulations. 

9-25

GROUP 

Modification of 

Weld Profile 

Modification of Residual 

Stress Distribution 

METHOD 

a. Local and Contour 

Grinding 

a. Stress Relief 

b. Controlled Erosion 

c. Remelting Techniques 

- TIG Dressing 

- Plasma Dressing 

b. Compressive 

Overstressing 

- Local Compression 

- Spot Heating 

c. Peening 

- Shot Peening 

- Hammer Peening 

- Needle I%ening 

Figure 9-1 Typical Methods to Improve Fatigue Strength

UNDERCUT 

CWCK-LIKE 

DEFECT & .’i ~HyDROGEN 

,:- ,. 

-. ,?, 

i-,. . 

HAz 

clUCK 

~SION 

LINE 

~LL 

PROFIU 

TOE GRINDING 

IACK 

OF _ETm,,ON FUSION 

i 

! 

-t- 

O. S-l. Omm 

Figure g-2 Typical Weld Toe Defects and CorrectiveMeasures 

\ 

● m weld toes erad 

by abrasve.wter 

jet 

x’ 

● 

A$-welded 

“+% 

/ 8’- 

Figure 9-3 Fatigue Life ImprovementDue to Weld Toe Abrasive 

Water Jet Erosion 

(FroITIReference 9.4)

400 ‘,, . . 

350 - I I 

300r 

[ ~ 

,05- I 

104 105 

\ 

\\ 

106 

Endurance, cycie$ 

\ < 

\ 

d 445 

“ - Siaot heated 

FuIIv bttfr ground 

S~Ot Deened 

OWflOaded at 

232N/mm2 

-“ i 

=A$+elded 

1Q7 

I 

... 

400 

I 

300 – TIG dressed (high tensile steel) 

m 

: 200 . 

2 

g 150– 

5 

L TOOdiw ground : 

! 100– 

Overlaadcdat 232N/mm2 

50 

5 

350- 

wEl- 

Id 1135 

2 345 

\ 

\ \ ASw,~~ 

I 

I 

234j 

106. 107 

Endurance, 

cycies 

Figure g-q Comparison of Fatigue 

(From 

Ref erer-tce 

Strength Improvement Techniques 

9.7)

SOMEOF THERELEVANT FATIGUERESEARCHPROJECTS 

TOPIC 

SUBJECT 

INVESTIGATOR 

COMPLETION & 

COMMENTS 

I 

STRESS CONCENTRATION 

Calibration of various SCF equations 

with Sillpletubularjoint test data 

Lloyd’s Registry 

1988 


Development of SCF equations for 

Internally stiffened complex 

tubular joints 

Lloyd’s Registry 

1990 


Development of SCF equations for 

multiplanar joint CHS and RHS”sections 

Univ. of Delft 

1992 


Assessment of S-N curve for lnternallystlffened 

tubular joints 

TMI/tiEL 

& Lloyd’s 

1990 


Development of S-N curve for slngleslded 

closure welds on tuhulars 

TW1/Glasgow 

I.lrtiversity 

1989 


Extend the range of hot spot stress 

approach to low cycle fatigue 

Unlverlty 

of Delft 

1989 

PARAMETERS AFFECTING 

FATIGUE LIFE 

Study of the chord plate thickness 

and other geometric parameters 

TWI 

1992 


FATIGUE LIFE 

Study of the plate thickness and weld 

profile effects on fatigue llfe 

Florida Atlantlc 

University 

1990 


FATIGUE LIFE 

Study of the weld profile effects and 

assessment of AtiS/APIrequirements 

TWI/EWI 

1989 


FATIGUE LIFE 

Study of cathodic protection effect 

on tubular joint fatigue 

TWI/SSNTEF 

1991 

Figure 9-5 Summary of Relevant 

Page 1 of 2 

Research Activities 

(.jd

TOPIC 

SUBJECT 

INVESTIGATOR 

COMPLETION & 

COMMENTS 

PARAMETERSAFFECTING 

FATIGUE LIFE 

Study of the effect of seawater on 

thick welded long-llfe joints 

TWI 

1992 


FATIGUE LIFE 

Application of fatigue life improvement 

1. 

techniques 

TWI 

FATIGLJEANALYSIS 

Correlation of simple p]ate S-y curves for 

complex details and F.E. analyses procedure! 

EW1/TWI 

Non-tubular details 

“only;through 1992 

FATIGUE ANALYSIS 

Development of SCF, S-N curves and 

materials data for cast steel pocles 

Wimpey 

1988 


Reviewof cumulative damage of welded joints 

TWI 

? 


Fa~igue of welded joints under random 

loading and Imp?lcatlonson the accuracy 

of Miner’s Rule 

TMI 

1990 


Effect of loading sequence on 

fatigue life 

Technical Univ. 

of Denmark 

1991 ‘ 

Figure 9-5 Summary of Relevant Research Activities 

Page’2of 2 

---c-

10. REFERENCES 

1.1 Fatigue Handbook - Offshore Steel Structures, Edited by 

A. Almar-Naess, Tabin Publishers, Trondheim, Norway, 1985. 

1.2 Fatigue Analyses of Tankers, Technical Report No. RD-89020F, 

Research and Development Department, American Bureau of 

Shipping, December 1989. 

1.3 Munse, W.H., Wilbur, T.W., Tellaliar, M.L., Nicoll, K., and 

Wilson, K., Fatigue Characterization of Fabricated Ship 

Details for Design, Ship Structure ConnnitteeReport SSC-318, 

1983. 

1.4 Wirsching, P.H., “Probability Based Fatigue Design Criteria 

for OffshoreStructures,”Final ProjectReport onAPI PRAC81- 

15, University of Arizona, Tucsonj 1983. 

1.5 RecommendedPracticefor Planning,Designing and Constructing 

Fixed Offshore P1atform,API ReconmnendedPractice 2A (RP 2A), 

EighteenthEdition,American Petroleum Institute,Sept. 1989. 

1.6 Offshore Installations: Guidance on Design, Constructionand 

Certification, U.K. Department of Energy (UK DEn) Guidance 

Notes, Fourth Edition, June 1990. 

1.7 Fatigue Strength Analysis for Mobile Offshore Units, 

Classification Notes, Note No. 30.2, Det Norske Veritas, 

August 1984. 

1.8 Design of Tubular Joints for Offshore Structures, Underwater 

EngineeringGroup, UEG Publication UR33, 1985. 

1o-1

3.1 Soyak, J. F., Caldwell, J. W., and Shoemaker,A.K., “Fatigueand 

FractureToughness Characterizationof SAW and SMAA537 Class 

I Ship Steel Weldments,”Ship Structure ConunitteeReportSSC- 

303, 1981. 

3.2 Pense, A.W., “Evaluationof FractureCriteria for Ship Steels 

and Weldments,”ShipStructureCommitteeReportSSC-307, 1981. 

3.3 Williams, A.K., and Rinne, J.E., “FatigueAnalysis procedure 

of Steel Offshore Structures”, Proceedings of Institute of 

Civil Engineers, Part 1, November 1976. 

3.4 Kuang, J.G., Potvin, A.B., Leick, R.D., and Kahrlich, J.L, 

“Stress Concentration in Tubular Joints,” Journal of Society 

of Petroleum Engineers,August 1977. 

3.5 Smedley, G.P., and Wordsworth, A.C., ‘Stress Concentration 

.- 

Factors of Unstiffened Tubular Joints,” European Offshore 

Steels Research Seminar, The Welding Institute, Cambridge, 

England, 1978. 

3.6 Worsworth, A.C., “Stress Concentration Factors at K and KT 

Tubular Joints,” Fatigue in Offshore Structural Steel, ICE, 

London, 1981. 

4.1 Rules for Buildingand ClassingSteel Vessels,American Bureau 

of Shipping, 1988. 

4.2 Thayamballi,A.K., “FatigueScreening for Tankers,” Report RD 

90005, American Bureau of Shipping, Research and Development 

Division, May 1990. 

10-2

4*3 

Munse, W.H., Wilbur, T.U., Tellalian, M.L., Nicoll, K., and 

Wilson, K., Fatigue Characterization of Fabricated Ship 

Details for Design, Ship Structure ConanitteeReport SSC-318, 

1984. 

4.4 

Jordan, C.R., and Cochran, C.S., ‘In-Service Performance of 

StructuralDetails,”Ship StructureConunittee Report SSC-272, 

1978. 

4.5 

Jordan,C.R., andCochran,C.S., “FurtherSurvey of In-Service 

Performance ofStructural Details,” Ship Structure Committee 

Report SSC-294, 1980. 

4.6 

Chen, Y-K., Chiou, J-W, and Thayamballi, A.K, “Validation of 

Fatigue Life Prediction Using Containership Hatch-Corner 

Strain Measurements,” SNAME Transactions, Volume 94, 1986, 

pp. 255-282. 

4.7 

Luyties,W.H., and Geyer, J.F., “TheDevelopment of Allowable 

Fatigue Stresses in API RP 2A,” Nineteenth Annual Offshore 

TechnologyConference,OTC Paper No. 5555, Houston, TX, 1987. 

4.8 

Rules for Building and Classing Mobile Offshore Drilling 

Units, American Bureau of Shipping, 1980. 

4*9 

Wirsching, P.H., “Digital Simulation of Fatigue Damage in 

Offshore Structures,” Computational Method for Offshore 

Structures, Editors: H. Armen and S.G. Stiansen, ASME, 1980. 

4.10 

Chen, Y.N., and Mavrakis, S.A.,“Closed-FormSpectral Fatigue 

Analysis for Compliant Offshore Structures,” Journal of Ship 

Research. 

4.11 

Wirsching, P.H., “Probability Based Fatigue Design Criteria 

15, University of Arizona, Tuscon, 1983. 

10-3 

for OffshoreStructures,nFinal ProjectReport onAPI PRAC81- 

-+?-

4.12 Daidola, J.C., and Basar, N.S., ‘probabilistic Structural 

Analysis of Ship Hull Longitudinal Stresses,” Ship Structure 

ConunitteeReport SSC-301, 1981. 

4.13 Wells, A.A., “The Waning of Fitness-for-Purpose and the 

Concept of Defect Tolerance,” International Conference on 

Fitness for Purpose Validation of bleldedConstructions, The 

Welding Institute,Volume 1, Paper No. 33, London, 1981. 

4.14 Structural Welding Code, American Welding Society, AWS D1.1, 

1988. 

4.15 Specifications for the Design, Fabrication and Erection of 

Structural Steel for Buildings, American Institute of Steel 

Construction, 1989. 

4.16 Rules for Steel Ships, Oil Productionand Storage Vessels,Det 

norske Veritas, Part 5, Chapter 9, 1986. 

4.17 Rules for Classificationof Fixed Offshore Installations,Det 

norske Veritas, January 1989. 

4.18 Rules and Regulationsfor the Classificationof Fixed Ofshore 

Installations, Lloyd’s Register, Part 4, Steel Structures, 

July 1988. 

4.19 Gurney, T.R., “The Influence of Thickness of the Fatigue 

Strength of Welded Joints,” BOSS Conference, London, August 

1979, Paper No. 41. 

4.20 Lotsberg, I., and Anderssson, H., “Fatigue in Building Codes 

Background and Applications,H Chapter 11, Fatigue Handbook - 

Offshore Steel Structures, Edited by A. Almar-Naess, Tapir, 

1985. 

10-4

4.21 

Weidler, J.B., and Karsan, D.I., ‘Design, Inspection and 

Redundancy Invest~nt Versus Risk for Pile-Founded Offshore 

Structures,”ProceedingsOf The InternationalSymposiumOn The 

Role Of Design, Inspectionand RedundancyinMarine Structural 

Reliabi” ity, Williamsburg,VA, November 1983. 

4.22 

Capanog” u, C. “Design of Floating Offshore Platforms,” 

Proceed ngs Of The International Symposium On The Role Of 

Design, Inspection and Redundancy in Marine Structural 

Reliability, Paper No. 19, Williamsburg, VA, November 1983. 

4.23 

ISSC Design PhilosophyCommittee (1983),Design Philosophy of 

MarineStructuresReport,InternationalShipbuildingProgress, 

Volume 30, No. 346, June 1984. 

4.24 

4.25 

SEALOAD,A Programfor Wave, Wind and Current Load Generation, 

Earl and Wright Developed SEADYN System Component, 1990. 

SHIPMOTION, A Program for Ship Motion Analysis, An American 

BureauofShippingDevelopedABS/DAISY System Component, 1989. 

— 

4.26 

Mansour,A.E. andThayamballi,A., “Computer-AidedPreliminary 

Ship StructuralDesign,” Ship StructureCommittee ReportSSC- 

302, 1981. 

5.1 

Fukusawa, T., Fujino, M., Koyanagi, M. and Kawamura, T., 

“Effectsof Axial Forceson Deck Stress in Case of Slammingof 

Large Bulk Carrier,” JSNAJ, Vol. 155, 1984. 

5.2 

Liapis, S. and Beck, R.F., “Seakeeping Computations Using 

Time-Domain Analysis,” 4th International Conference on 

Numerical Ship Hydrodynamics,Washington, 1985. 

5*3 

Papanikolaou, A., Zaraphonitis, G. and Perras, P., “On 

Computer-AidedSimulationsof Large Amplitude Roll Motions of 

Ships in Waves and of Dynamic Stability,” IMAEM ’87, Varna, 

1987. 

10-5 

.-,—, :, 

/’ .,< 7’ 

>—

5.4 Papanikolaou,A. and Zaraphonitis, G., “On An Improved Near 

Field Method For the Evaluationof Second-Order ForcesActing 

on 3D Bodies in Waves,” IMAEM ’87, Varna, 1987. 

5.5 Hooft, J.P., “Hydrodynamic Aspects of Semisubmersibles,” 

Doctoral Thesis From Delft Technical University, The 

Netherlands, 1972. 

5.6 Capanoglu,C.C., “Designof a CompliantTension LegPlatform- 

Naval Architectural and Structural Design Considerations,” 

Marine Technology, Vol. 16N0. 4, October 1979, pp. 343-353. 

5.7 Garrison,C.J., ‘Hydrodynamicsof LargeDisplacementFixedand 

Floating Structures in Waves,” Report No. 80-102, December 

1980, C.J. Garrison Associates. 

5.8 Sircar, S., Rager, B.L., Praught, M.W. and Adams, C.J., ‘A 

Consistent Method for Motions, Strength and Fatigue Analysis 

of TLPs,” Proceedings of Seventh International Offshore 

Mechanics and Arctic Engineering Conference, OMAE, Houston, 

February 1988. 

5.9 Bishop, J.R., “Wave Force Investigations at the Second 

Christchurch Bay Tower,” NMIReport R177, 1984. 

5.10 Bishop, J.R., “Wave Force Data From the Second Christchurch 

BayTower,” Proceedingsof OffshoreTechnologyConference,OTC 

Paper No. 4953, Houston, 1985. 

5.11 Tickell, R.S. and Bishop, J.R., “Analyses of Wave and Wave 

Forces at the Second ChristchurchBay Tower,” Proceedingsof 

OffshoreMechanicsandArctic Engineering,OMAE, Dallas, 1985. 

5.12 Bea, R.G., Pawsey, S.F. and Litton, R.W., “Measured and 

Predicted Wave Forces on Offsfhore Platforms,” Twentieth 

Offshore Technology Conference, OTC 5787, Houston, TX, 1988.

5.13 Rodenbush, G., “Random Directional Wave Forces on Template 

Offshore Platforms,” Proceedings of the Eighteenth Offshore 

Technology Conference, OTC 5098, Houston, TX, 1986. 

5.14 Rodenbush, G. and Forristall, G.Z., “An Empirical Model for 

Random Directional Wave Kinematics Near the Free Surface,” 

Proceedings of the Eighteenth Offshore Technology Conference 

OTC 5097, Houston, TX, 1986. 

5.15 API PRAC PROJECT 83-22 Report, ‘Implementation of a 

Reliability-Based API RP 2A Format,” American Petroleum 

InstituteJanuary 1985. 

5.16 Kint, T.E., and Morrison, D.G., “Dynamic Design and Analysis 

Methodology for Deepwater Bottom-Founded Structure,” 

Proceedings of the Twenty-Second Offshore Technology 

Conference, OTC 6342, Houston, TX, 1990. 

5.17 Digre, K.A. Brasted, L.K., and Marshall, P.W., “TheDesignof 

the Bullwinkle Platform.” Proceedings of the Twenty-First 

Offshore Technology Conference, OTC 6050, Houston, TX, 1989. 

5.18 Larrabee, R.D., “Dynamics Analysis,” ASCE Continuing 

Education, Structural Reliability of Offshore Platorms, 

Houston, TX, 1989. 

5.19 Efthymiou, M. et al, “Stress Concentrations in T/Y and 

Gap/Overlap K-Joint,” The Forth International Conference on 

Behavior of Offshore Structures, Amsterdam, The Netherlands, 

1985. 

5.20 Ma, S.Y.A. and Tebbet, I.E., “New Data on the Ultimate 

Strength of Tubular Welded K-Joints Under Moment Loads,” 

TwentiethAnnual OffshoreTechnologyConference,OTC PaperNo. 

5831, Houston, TX, May 1988. 

10-7

5.21 -”’ ” ”---”---” ‘“--”------”- 

tilDsZeln,M.B., “StressConcentrationin TubularK-Jointswith 

Diameter Ratio Equal to One, “PaperTS 10, Proceedingsof the 

Third International ECSC Offshore Conference on Steel in 

Marine Structures (SIMS 87), Delft, the Netherlands, 1987. 

5.22 

Tolloczko, J.A., and Lalani,M., “The Implicationsof New Data 

in the Fatigue Life Assessment of Tubular Joints,” Twentieth 

Annual Offshore Technology Conference, OTC Paper No. 5662, 

Houston, TX, May 1988. 

5.23 

Lalani,M. etal, “ImprovedFatigue Life Estimationof Tubular 

Joints, “EighteenthAnnualOffshoreTechnologyConference,OTC 

Paper No. 5306, Houston, TX, 1986. 

5.24 

Gibstein, M.B., “Parametric Stress Analysis of T-Joints,” 

Paper No. 26, European Offshore Steels Research Seminar, 

Cambridge, November 1978. 

5.25 

Wordsworth,A.C., “Aspectsof Stress Concentration Factors at 

Tubular Joints,” Paper TS8, Third InternationalECSC Offshore 

Conferenceon Steel in Marine Structures (SIMS87), Delft, The 


6.1 

Hoffman, D., and Walden, D.A., “EnvironmentalWave Data for 

Determining Hull Structural Loadings, A Report to Ship 

Structures Cotmnittee,SSC-268, 1977. 

6.2 

Bian Jiaxi and Yuan Yeli, “Meteo-OceanographicStudy of JHN 

Blocks 16/06 in South China Sea”, China Ocean Technology 

Company (COTC), Ltd., July 1988. 

6.3 

Meteo-Oceanographic Study of ACT Blocks 16/04-16/08 and 

PhillipsArea 15/11 in South China Sea. A Report Prepared by 

Snamprogetti for ACT Operators Group, March 1988. 

10-8

6.4 Study of Environmental Design Criteria For JHN’s Offshore 

China Lufeng Project, A Report to Earl and Wright, Shezhen 

China Ocan Technology Company (COTC), January 1991. 

6.5 N. Hogben and F.E. Lumb, “OceanWave Statistics,”Hjnistryof 

Technology, National Physical Laboratory, London: Her 

Majesty’s Stationary Office, 1967. 

6.6 M.K. Ochi and Y.S. Chin, “Wind Turbulent Spectra for Design 

Consideration of Offshore Structures,” Offshore Technology 

Conference 1988, OTC 5736. 

6.7 Kinra, R., and Marshall, P., “Fatigue Analyses of Cognac 

Platform,’’Journalof PetroleumEnergy,SPE 8600, March 1980. 

6.8 Sarpkaya, T. and Isaacson, M., “Mechanics of Wave Forces on 

Offshore Structures,”Van Nostrand Reinhold Co., 1981. 

6.9 Wirsching, P.H., “Digital Simulation of Fatigue Damage in 


Structures,H. Armenand S.G. Stiansen,Editors,ASMB, 1980. 

6.10 Chen, Y.N., and Maurakis, S.A., “Close Form Spectral Fatigue 

Analysis of Compliant Offshore Structures, “Journal of Ship 

Research. 

6.11 Dalzell, J.F., Maniar, N.M., and Hsu, M.W., “Examination of 

Service and Stress Data of Three Ships for Developmentof Hull 

Girder Load Criteria,” Ship Structure Committee Report SSC- 

287, 1979. 

7.1 Gurney, T.R., “The Influence of Thickness of the Fatigue 

Strength of Welded Joints,” Proceedings of 2nd International 

Conference on Behavior of Offshore Structures (BOSS ‘79), 

London, 1979. 

10-9

“7.2 

Jordan, C.R., and Cochran, C.S., “In-Service Performance of 

Ship StructureDetails,” ShipStructureConnnitteeReport,SSC- 

272, 1978. 

7*3 

Marshall, P.W., “Size Effect in Tubular Welded Joints,” ASCE 

Annual Structures Congress, Houston, TX, October 17, 1983. 

7.4 

Maddox, S.J., “Assessingthe Significanceof Welds Subject to 

Fatigue,” Welding Journal, 1070, 53 (9) 401. 

7.5 

Hartt, W.H., Rengan,K. and Sablok,A.K., “FatigueProperties 

of Exemplary High-Strength Steels in Seawater,” Twentieth 

Annual Offshore Technology Conerence, OTC 5663, Houston, TX, 

May 1988. 

7.6 

Gurney, T.R., “Fatigue of Welded Structures,” Cambridge 

University Press, 2nd. Edition, 1978. 

7.7 

Grover, J.L., “Initial Flaw Size Estimating Procedures for 

Fatigue Crack Growth Calculations,” InternationalConference 

on Fatigue of Welded Constructions, Paper No. 15, Brighton, 

England, April 1987. 

7.8 

Tolloczko, J.A. and Lalani, M., “The Implication of New Data 

on the Fatigue Life Assessment of Tubular Joints,” Twentieth 

Annual Offshore TechnologyConference,OTC 5662, Houston, TX, 

May 1988. 

7.9 

Maddox, S.J., “The Effect of Plate Thickness on the Fatigue 

Strength of Fillet Welded Joints,” Welding Institute Report 

1987, 7814.01. 

7.10 

Maddox, S.J., “A Study of the Fatigue Behavior of Butt Welds 

Made on Backing Bars,” Proceedings5th European Conference on 

Fracture Life Assessment of Dynamically Loaded Materials and 

Structures,” Lisbon, 1984, 197-215. 

1o-1o

7.11 

Maddox, S.J., “Fitnessfor PurposeAssessment of Misalignment 

in Transverse Butt Welds Subject to Fatigue Loading,”Welding 

InstituteMembers Report 279/1985. 

7.12 

Marshall, P.W., “Stateof the Artinthe U.S.A.,“ Paper PSIof 

Proceedings of the Third International ECSC Offshore 

Conferenceon Steel in Marine Structures (SIMS87), Delft,The 


7.13 

Dijkstra, O.D. et al, “The Effect of 

Weld Profile on the Fatigue Behavior 

Joints,” Seventeenth Annual Offshore 

OTC 4866, Houston, TX, May 1985. 

Grinding and a Special 

of Large Scale Tubular 

Technology Conference, 

7.14 

Bignonnet, A., “Improving the Fatigue Strength 

Structures,” Paper PS4 of the Proceedings of 

International ECSC Offshore Conference on Steel 

Structures (SIMS87), Delft, netherlands, 1987. 

of Welded 

the Third 

in Marine 

7.15 

Wylde, J.G., Booth, G.S., and Iwasaki, T., Fatigue Tests on 

Welded TubularJoints in Air and in Sea Water,” Proceedingsof 

International Conference on Fatigue and Crack Growth in 

Offshore Structures, I Mech E, 1986. 

7.16 

Gurney, T.R., “Further Fatigue Tests on Fillet Welded Joints 

Under Simple VariableAmplitude Loading,”Appendix A, Welding 

InstituteMembers Report 182/1982. 

7.17 

Gurney, T.R., “Fatigue Tests on Fillet Welded Joints Under 

VariableAmplitude Loading,”Welding InstituteMembers Report 

293/1985. 

7.18 

Gurney,T.R., “SomeVariableAmplitudeFatigue Testson Fillet 

Welded Joints,” Paper No. 65, International Conference on 

Fatigueof Welded Constructions,Brighton, England, 7-9 April 

1987. 

10-11 / 

.7,3 

~ --’

7.19 Niemi, E.J., “FatigueTests on Butt and Fillet Welded Joints 

Under VariableAmplitude Loading,” Paper No. 8, International 

Conference on Fatigue of Welded Constructions, Brighton, 

England, 7-9 April 1987. 

7.20 Gerald, J. et al, “Comparison of European Data on Fatigue 

Under Variable Amplitude Loading,” Paper TS48 of the Third 

International ECSC Offshore Conference on Steel Marine 

Structures (SIMS 87), Delft, Netherlands, 1987. 

7.21 Trufiakov, V.I., and Kovalchuk, V.S., “The Estimation of the 

Fatigue Crack Propagation Rate Under Bicyclic Loading,U IIW 

Document X111-1139-84, 1984. 

7.22 Gurney, T.R., “The Influence of Spectrum Shape on Cumulative 

Damage of Plateswith FilletWelded EdgeAttachments,‘Welding 

InstituteReports7816.03/86/495.2, 1987 and 7920.01/87/555.1 

7.23 Wirsching, P.H., “Digital Simulation of Fatigue Damage in 


Structures, H. Armen and S.G. Stiansen, Editors, ASME, 1980. 

7.24 Chen, Y.N. and Mavrakis, S.A., ‘Close Form Spectral Fatigue 

Analysis for Compliant Offshore Structures,” Journal of Ship 

Research. 

7.25 Morgan, H.G., “Interaction of Multiple Fatigue Cracks”, 

InternationalConference on Fatigue of Welded Constructions, 

Paper No. 35, Brighton, England, April 1987. 

7.26 Dobson, W.G., Broderick, R.F., Wheaton, J.W., Giannotti, 

J. and Stambaugh, K.A., “Fatigue Considerations in View of 

Measured Spectra,” Ship Structures ConnnitteeReport SSC-315, 

1983. 

10-12

8.1 Bel1, E.R.G. and Morgan, D.G., “Repair and Analysis of 

Cracking in the-hiurchisonFlare Boom,” Twentieth Annual 

Offshore Technology Conference, OTC 5814, Houston, TX, May 

1988. 

8.2 Strouhal, V., Uber Eine Besondere Art der Tonerregung, 

Ann. Physik, Leipzig, 1878. 

8.3 Marris, A.W., “AReview of Vortex Streets, Periodic Waves and 

Induced Vibration Phenomena,” Journal of Basic Eng., V. 86, 

1964, pp 185-194. 

8.4 Sarpkaya, T., and Isaacson, M., Mechanics of Wave Forces on 

Offshore Structures,Van Nostrand Reinhold, New York, 1981. 

8.5 Hunt, R.J., “Practice For Establishing If A Structure Will 

Undergo Vortex-InducedVibrations,”CONFIDENTIALSIPM Report, 

EPD/112, June 1987. 

8.6 Engineering Sciences Data Unit, “Across Flow Response Due to 

Vortex Shedding”, Publication No. 78006, London, England, 

October, 1978. 

8.7 Det Norske Veritas, “Rules for Submarine Pipeline Systems”, 

Oslo, Norway, 1981. 

8.8 Zedan, M.F., Yeung, J.Y., Ratios, H.J., and Fischer, F.J., 

“Dynamic Response of a Cantilever Pile to Vortex Shedding in 

RegularWaves,”Proceedingsof OffshoreTechnology Conference, 

OTC Paper No. 3799, Houston, May 1980. 

8.9 Hallam, H.G., Heaf, N.J., and Wootton, F.R., “Dynamics of 

Marine Structures,”CIRIA Underwater EngineeringGroup Report 

UR8 (2nd Edition), 1977. 

10-13 -, 

“7 ----1, 

,, d 

,>

9.1 Skaar, K.T., “ContributingFactorstoShipQual ity”,Reportof 

ConnnitteeV.3-Service experience - Ships, Proceedings of the 

Tenth International Ship and Offshore Structures Congress, 

Volume 2, Lyngby, Denmark, August 1988. 

9.2 Jordan, G.P. and Cochran, C.S., “In-Service Performance of 

StructuralDetails,”Ship StructureConnnitteeReport SSC-272, 

1978. 

9.3 Notes on Structural Failure in Ships, Report NO. 19, Lloyd’s 

Register of Shipping, 1962. 

9.4 Maddox, S.J., and Padilla, J.A., “Fatigue Life Improvementby 

Water Jet Erosion”,Welding InstituteMembers Report 280/1985. 

9.5 King, C.G, “Abrasive Water Jetting: A New Aid to Welded 

Fabrications,” OTC Paper No. 5817, 20th Annual Offshore 

Technology Conference, Houston TX, May 1988. 

.. 

9.6 Wylde, J.G., Booth, G,S., and Iwasaki, T., “Fatigue Tests 

Welded Tubular Joints in Air and Sea Water”, Proceedings 

International Conference on Fatigue and Crack Growth 

Offshore Structures, I Mach E, 1986, pp. 155-170. 

on 

of 

in 

9*7 Booth, G.S., “Chapter 2 - A Review of Fatigue Strength 

Improvement Techniques”, Improving the Fatigue Strength of 

Welded Joints, The Welding Institute, 1983. 

9.8 Maddox, S.J., “Improvingthe FatigueStrength of Welded Joints 

by Peening”, Metal Construction, 1985, 17(4) pp 220-224. 

9.9 Woodley, C.C., “Chapter 4 PracticalApplications of Weld Toe 

Grinding”, Improving the Fatigue Strength of Welded Joints, 

The Welding Institute, 1983. 

9.10 Boylston, J.W., and Stambaugh,K.A., “Developmentofa Plan to 

Obtain In-ServiceStill Water Bending Moment Information for 

10-14 

~ Zy 

f-‘ 

,-+

StatisticalCharacterization,”ShipStructureConnnitteeReport 

SSC-319, 1984. - 

9.11 

Krenk, S. and Gluver, H., “A Markow Matrix for Fatigue Load 

Simulation and Rainflow Range Evaluation,” Symposium on 

Stochastic Structural Dynamics, Urbana, Illinois, 1988. 

9.12 

Krenk, S. and Thorup, E., “Stochasticand Constant Amplitude 

Fatigue Test of Plate Specimens with a Central Hole,” Report 

No. R 242, Department of Structural Engineering, Technical 

University of Denmark, 1989. 

9.13 

Agerskov, H. and Aarkrog, P., “Fatigue Investigation on 

Offshore Steel Structures Under Spectrum Loading,” 

InternationalSyposiumon Offshore Brazil ’89,Riode Janeiro, 

Bvazil, August 1989. 

,. 

9.14 

Morgan, G.G., “Interaction of Multiple Fatigue Cracks,” 

InternationalConference on Fatigue of Welded Constructions, 

Brighton, England, 7-9 April 1987. 

*IJ.S. G.P.0:1993-343-273:80107 10-15 

,.— .-

COMMllTEE 

ON MARINE STRUCTURES 

Commission on Engineering and Technical Systems 

National Academy of Sciences - National Research Council 

The COMMITTEE ON MARINE STRUCTURES has technical cognizance over the interagency 

Structure Committee’s research program. 

Peter M. Palermo Chairmanj Alexandria, VA 

Mark Y. Berman, Amoco Production Company, Tulsa, OK 

Subrata K. Chakrabarti, Chicago Bridge and Iron, Plainfield, IL 

Rolf D. Glasfeld, General Dynamics Corporation, Groton, CT 

William H. Harttl Florida Atlantic University, Boca Raton, FL 

Alexander B. Stavovy, National Research Council, Washington, DC 

Stephen E. Sharpe, Ship Structure Committee, Washington, DC 

LOADS WORK 

GROUP 

Subrata K. Chakrabarti Chairman, Chicago Bridge and Iron Company, Plainfield, IL 

Howard M. Bunch, University of Michigan, Ann Arbor, Ml 

Peter A. Gale, John J. McMullen Associates, Arlington, VA 

Hsien Yun Jan, Martech Incorporated, Neshanic Station, NJ 

Naresh Maniar, M. Rosenblatt & Son, Incorporated, New York, NY 

Solomon C. S. Yim, Oregon State University, Corvallis, OR 

MATERIALS WORK GROUP 

William H. Hartt Chairman, Florida Atlantic University, Boca Raton, FL 

Santiago Ibarra, Jr., Amoco Corporation, Naperville, IL 

John Landes, University of Tennessee, Knoxville, TN 

Barbara A. Shaw, Pennsylvania State University, University Park, PA 

James M. Sawhill, Jr., Newport News Shipbuilding, Newport News, VA 

Bruce R. Somers, Lehigh University, Bethlehem, PA 

Jerry G. Williams, Conoco, Inc., Ponca City, OK 

c-3 $olo7&

SHIP STRUCTURE COMMITTEE PUBLICATIONS 

SSC-351 An Introduction to Structural Reliability Theorv by Alaa E. Mansour 

1990 

SSC-352 Marine Structural Steel Touahness Data Bank by J. G. Kaufman and 

M. Prager 1990 

SSC-353 Analvsis of Wave Characteristics inExtreme Seas by WilliamH.Buckley 

1989 

SSC-354 Structural Redundance forDiscreteand Continuous Systems by P.K. 

Das and J.F.Garside 1990 

SSC-355 Relation of Inspection Findinqs to Fatique Reliability by M. Shinozuka 

1989 

SSC-356 Fatique Performance Under Multiaxial Lod by Karl A. Stambaugh, 

Paul R. Van Mater, Jr.,and WilliamH.Munse 1990 

SSC-357 Carbon Equivalence and Weldability of Microalloyed Steels by C. D. 

Lundin, T. P. S. Gill, C. Y. P, Qiao, Y. Wang, and K. K. Kang 1990 

SSC-358 Structural Behavior After Fatique by Brian N. Leis 1987 

SSC-359 Hydrodynamic Hull Dampinq (Phase 1) by V. Ankudinov 1987 

SSC-360 Use of Fiber Reinforced Plastic inMarine Structuresby EricGreene 

1990 

SSC-361 Hull Stra~pinq of Ship= by Nedret S. Basar and Roderick B. Hulls 1990 

SSC-362 Shipboard Wave Heiqht Sensor by R. Atwater 1990 

SSC-363 Uncertainties in Stress Analysis on Marine Structures by E. Nikolaidis 

and P. Kaplan 1991 

SSC-364 Inelastic Deformation of Plate Panels by Eric Jennings, Kim Grubbs, 

Charles Zanis, and Louis Raymond 1991 

SSC-365 Marine Structural Inteqrity Proqrams (MSIP) by Robert G. Bea 1992 

SSC-366 Threshold Corrosion Fatique of Welded Shipbuilding Steels by G. H. 

Reynolds and J. A. Todd 1992 

None Ship Structure Committee Publications - A Special Bibliography 

c-q 

f@lo7-s9

U.S.Department 

of Transportation 

United States 

CoastGuard 

/47 

● 

● 

,*c%,, 

# 

~ 

@ 

%,J 






APPENDICES 

his dmumcnt has been approvsd 

for public rdsaseandsalwits 

distribution is unlimited 


COMMITTEE 

1993 C-,1 %r@llz’”” 

.,-Q#q 

/ ‘$’”

~HIP STRUCTURF CO MMllTEF 

The SHIP STRUCTURE COMMllTEE is constituted to prosecute a research program to improve the hull structures of ships and other 

marine structures by an extension of knowledge pertaining to design, materials, and methods of construction. 

RADM A. E. Henn, USCG (Chairman) 

Chief, Office of Marine Safety, Security 

and Environmental Protection 

U, S, Coast Guard 

Mr. Thomas H. Peirce Mr. tit T, Hailer Dr. Donald Mu 

Marine Research and Development Associate Administrator for Ship- Senior Vrce President 

Coordinator building and Ship Operations 

Ameri=n Bureau of Shipping 

Transportation Development Center Maritime Administration 


Mr. Alexander Malakhoff Mr. Thomas W. Allen CDR Stephen E. Sharpe, USCG 

Director, Structural Integrity Engineering Officer (N7) Executive Director 

Subgroup (SEA 05P) Military Sealift Command 

Naval Sea Systems Command :Y1.%%;s?m’”ee 

CONTRACTING OFFICER TECHNICAL REPRESENTATIVE 

Mr. William J. Siekierka 

SEA05P4 


SHIP ST 

RUCTLJRFSUR~OMMllTFF 

The SHIP STRUCTURE SLIBCOMMllTEE acts for the Ship Structure Committee on technical matters by providing technical 

coordination for determinating the goals atrd objectives of the program and by evaluating and interpreting the results in terms of 

structural design, construction, and operation. 

AMERICAN BUREAU OF SHIPPING NAVAL S EA SYSTEMS COM MAND TRANSPORT CANADA 

Mr. Stephen G. Arntson (Chairman) Dr. Robert A. Sielski 

Mr. John Grinstead 

Mr. John F, ConIon 

Mr. Charles L Null Mr. Ian Bayly 

Dr. John S, Spencer Mr. W. Thomas Packard Mr. David L, Stocks 

Mr, Glenn M, Ashe Mr. Allen H. Engle Mr. Peter Timonin 

&llLITARY SEAI IFT COM MAND jYIARITIME ADMINI STRA TIO~ U, S, COAST GU ARD 

Mr, Robert E. Van Jones Mr. Frederick Seibold CAPT T. E. Thompson 

Mr. Rickard A Anderson Mr. Norman 0, Hammer 

CAPT W. E, Colburn, Jr. 

Mr. Michael W. Touma 

Mr. Chao H. Lin 

Mr. Rubin Scheinberg 

Mr, Jeffrey E. Beach Dr. Walter M. Maclean Mr. H. Paul Cojeen 

SHIP STRUCTURE SUBCOMMITTEE LIAISON MEMBERS 

~Y 

LCDR 

Bruce R. Mustain 

~s - 

~n 

Mr. Alexander 

B. Stavovy 

U. S. M FRCHANT MARINE ACAO EMY 

Dr. C. B, Kim 

~Y 

NATIONAL ACADEMY OF SCIENCES - 

COMMllTEE ON MARINE STRUCTURES 

Mr. Peter M. Palermo 

Dr. Ramswar 

Bhattacharyya 

~SEARCHCOUNCll 

STATE UMNIV~~SITY OF NEW YORK 

Dr. Martin 

Prager 

Dr. W. R. Porter 

SOCIETY OF NAVAL ARC HITECTS AND 

MARINE ENGINEERS 

AMERICAN IRON AND STEEL INSTITUTE 

Mr, Alexander D. Wilson 

DEPARTMENTOF NATIONAL DEFENCE - CANADA 

Dr. William 

Sandberg 

Dr, Neil G. Pegg 

OFFI CE OF NAVAL RESEARCH 

Dr. 

Yapa D, S. Rajapaske

Member Agencies: 

United States Coast Guard 


Maritime Administration 

American Bureau of Sh@ping 

Military Sealifi Command 

Transpmt Canada 

Ship 

Structure 

Committee 

An Interagency AdvisoryCommittee 

May 17, 1993 

Address Correspondence to: 

Executive Director 

Ship Structure Committee 

U.S. Coast Guard (G-Ml/R) 

2100 Second Street, S.W. 

Washington, D.C. 20593-0001 

PH: (202) 267-0003 

FAX: (202) 267-4677 


SR-1324 

FATIGUE TECHNOLOGY ASSESSMENT AND STRATEGIES FOR FATIGUE 

AVOIDANCE IN MARINE STRUCTURES 

.—.. 

This report synthesizes the state-of–the-art in fatigue 

technology as it relates to the marine field. Over the years 

more sophisticated methods have been developed to anticipate the 

life cycle loads on structures and more accurately predict the 

failure modes. As new design methods have been developed and 

more intricate and less robust structures have been built it has 

become more critical than ever that the design tools used be the 

most effective for the task. This report categorizes fatigue 

failure parameters, identifies strengths and weaknesses of the 

available design methods, and recommends fatigue avoidance 

strategies based upon variables that contribute to the 

uncertainties of fatigue life. 

This set of Appendices includes more in-depth presentations of 

the methods used in modeling the loads from wind and waves, 

linear system response to random excitation, stress concentration 

factors, vortex shedding and fatigue damage calculation. 

G.P.Y&n 

.. 

A. E. HENN 

Rear Admiral, U.S. coast Guard 

Chairman, Ship Structure Committee 

.-.

T*chnical 

Report Documentation Poge 

1. Report No. 2. Governmtmt Acc*ssioti No. 3. Rocip,~ntrs Catalog Ne. 

4. Title and subtitle 5. Rcportiko 

June1992 

FATIGUEDESIGNPROCEDURES 6.Performing Organization Cod= 

7. AuthorIs) 

8. PorfaminQ 0r9anizatisn R9part No. 

CuneytC.Capanoglu 

SR-1324 

9. Prrfnrmin9 Or~anization Namm rnd AdAmss 10. Work Unit No. (TRAIs) 

EARL AND WRIGHT 11. Controctar Gr~nt N*. 

180 Howard Street 

DTCG23-88-C-20029 

San Francisco, CA 94105 

13. TYP. of R-part ondPried C-word 

~2. 5POm~Or~mQ Aq~n=yNa~~ ~mdAddr*~~ 

Ship Structure Committee 

Final Repoti 

U.S. Coast Guard (G-M) 

2100 Second Street, SW 

IS. supplementary Notes 

Washington, DC 20593 

I 

14. Sponsoring Agency Cod. 

SponsoredbytheShipStructure Committeeanditsmembersagencies. 

G-M 

ABSTRACT 

This report provides an up-to-date assessment of fatigue technology, directed specifically toward 

the marineindustry, A comprehensive overview of fatigue analysis and design, a global review of 

fatigue including rules and regulations and current practices, and a fatigue analysis and design 

criteria, are provided as a general guideline to fatigue assessment. A detailed discussion of all 

fatigue parameters is grouped under three analysis blocks: 

● Fatigue stress model, covering environmental forces, structure response and loading, stress 

response amplitude operations (RAOS] and hot-spot stresses 

● Fatigue stress history model covering long-term distribution of environmental loading 

● Fatigue resistance of structures and damage assessment methodologies 

The analyses and design parameters that affect fatigue assessment are discussed together with 

uncertainties and research gaps,to provide a basis for developing strategies for fatigue avoidance. 

Additional in-depth discussions of wave environment, stress concentration factors, etc. are 

presented in the appendixes. 

17. Key Words 

18. Distribution Statwn.nt 

Assessment of fatigue technology, 

fatigue stress models, fatigue Available from: 

stress history models, fatigue National Technical information Serv. 

resistance, fatigue parameters U. S, Department of Commerce 

and fatigue avoidance strategies Springfield, VA 22151 

19. .lecunty Cl=$sif. (~f this r-pert) 

Unclassified 

I 

I 

20. s~curity Classif. (of this POW) 

Unclassified 

Form DOT F 1700.7 (8-72) Reproduction Oi completed page authorized 

I 

21. No. O{ PU9*S I 

22. Pri CC 

194 EXCI, 

Appendixas

‘ METRIC CONVERSION FACTORS 

ApproMimMcCofrvmsiortsto M-ttie 

Measures 

Approximate Convwsions from Mstric Measures 

Svmbol Whoa Yss Know Multiply br 1. Find Srmbd 

LEUGTH 

To Find 

{n 

rt 

d 

mi 

LENGTH 

iriches “2.5 

Ieet 30 

V*lds 0.9 

mi!0s 1.6 

AflEA 

cent imtsm 

Csnl imtercl 

mslers 

kilcamsters 

cm 

cm 

m 

km 

\m m 

h 

m 

cm 

mil!inwm.m 0.04 

cen!imstem 0.4 

MStelm 3.3 

mstms 1.1 

hilcrrmtsm 0.6 

AREA 

inchea 

inchea 

feet 

#s 

miles 

in 

in 

{1 

yd 

mi 

square inche9 6.5 

qu~mfeet 0,03 

squareyard- 0.0 

wrtmm miles 2.8 

WI*S 0.4 

MASS 

{wci~ht) 

square 

centimeters 

square Iwlem 

SqUam ms!em 

sqtmm 

hectares 

kilwnalms 

cm2 

# 

~2 

kmz 

ha 

3quH0centkmtms 0.16 

equem rmdem 1.2 

!#rIIDmkihmwmem 0.4 

tmctmY4 {10,000 m2) 2.6 

MASS 

[woighl] 

squme inches 

square yamrs $ 

squsm miles 

mi2 

■cms 

or 

lb 

ounces 

2B 

pumds 0.45 

ad Imm 0.9 

@UI lb} 

grsms 

kibgmms 

Iwnms 

Q 

kg 

I 

o 

kg 

t 

grwm 0.035 

kifmm 2.2 

tmlnes [1OOOho) 1.1 

csmces 

Smmds 

Oz 

14 

VOLUME 

VOLUME 

TrwP 

tee9pms 5 

tnbte~poons 15 

fluid ounces 30 

cups 0.24 

pints 0.4? 

quarts 0.95 

galtmil 3,8 

cubic !Set 0.03 

cubtc yerds 0.76 

mill ili!em 

mitli litem 

mit Iilitem 

liters 

liters 

Iilers 

liters 

cubic meters 

cubic melevs 

ml 

ml 

ml 

I 

1 

I 

I 

~3 

~3 

ml 

! 

1 

I 

~3 

~3 

rni m tiwm 0.03 

Iitsrs 2.1 

Iitem 1.m 

Iiims 0.26 

cubic mstem 35 

cubic memrs 1.3 

TEMPERATURE 

[S12SCi~ 

Ituid unCOS 1103 

pints 

m 

qualm 

qt 

gallons 

gsl 

chic reet i? 

cubic yalds vd3 

TEMPERATUFIE 

‘F Fahrenheit 5/9 Iaflm 

tempemtum subtrmct ing 

32} 

{exsci) 

.1 m = 2.54 P2xacllvl. F#wother enad co.versdws and more Nrtanicd tables, see MM Mqsc. PIIM. 2W 

Unts of We, ghW md.Mea5uIe5. P. Ice 3-2.25,SD Cal-log !h. Ct3.102!36. 

“c 

Celsius 

9/5 [then 

Fahranhefit ‘F 

tsmpemlum mkl32) 

Wwerstum 

Celsius 

“c 

temmmaaure ‘F 

‘F 32 98.6 212 

-40 0 40 00 t20 160 Zcm 

1 I I 4 I # 1 I 1 # l,t+; i:l,ll, t~ 

l’; 1 1 1 I 

-$: -20 0 20 40 60 “ 60 IOD 

37 

Oc





APPENDICES 

CONTENTS 

APPEN131X A Review oftheOcean Environment 

APPENDIX B Review ofLinearSystem Response toRandom Excitation 

,— 

APPENDIX C StressConcentrationFactors 

APPENDIX D VortexShedding Avoidance and FatigueDamage Computation

APPENDIX A 

REVIEW OF OCEAN ENVIRONMENT 

CONTENTS 

A. 

REVIEW OF OCEAN ENVIRONMENT 

A.1 

A.2 

IRREGULAR WAVES 

PROBABILITY CHARACTERISTICS OF WAVE SPECTRA 

A.2.1 

A.2.2 

Characteristic Frequencies and Periods 

Characteristic Wave Heights 

A.3 


A.3.1 

A.3.2 

A.3.3 

A.3.4 

Bretschneider and ISSC Spectrum 

Pierson-MoskowitzSpectrum 

JONSWAP and Related Spectra 

Scott and Scott-Wiegel Spectra 

A.4 

SELECTING A WAVE SPECTRUM 

A.4.1 

A.4.2 

Wave Hindcasting 

Direct Wave Measurements 

A.5 

A.6 

A.7 

A.8 

A.9 

WAVE SCAITER DIAGRAM 

WAVE EXCEEDANCE CURVE 

WAVE HISTOGRAM AND THE RAYLEIGH DISTRIBUTION 

EXTREME VALUES AND THE WEIBULL DISTRIBUTION 


A.9.1 

A.9.2 

A.9.3 

Air Turbulence, Surface Roughness and Wind Profile 

Applied, Mean and Cyclic Velocities 

Gust Spectra 

A.1O 

REFERENCES

A. REVIEH OF OCEANENVIRONMENT 

The ocean environment is characterized by waves, wind and current. 

The waves are typically irregular (confused or random seas). Some 

waves are generated locally by the wind, and some waves are generated 

great distances away. The wind is unsteady, with gusts. The wind 

varies with height above water. The current is caused by the wind, 

by waves, by the tide, and by global temperature differences. The 

current varies with depth. All of these characteristics vary with 

time. 

A.1 IRREGULARWAVES 

Irregular waves (a random sea) can be described as the sum of an 

infinite number of individual regular (sinusoidal)waves of different 

amplitude, frequency, and phase (Figure A-l). Therefore, the 

randomly varying sea surface elevation can be represented by a 

Fourier series. 

N 

n(t) = z 

i=l 

a*cos(wi*t+Oi) i 

— 

where n(t) is the water surface elevation measured from 

still water level, 

ai 

is the amplitude of each component regular wave, 

w. is the frequency of each component regular wave, 

1 

$j is the phase ang’ e of each component regular 

wave, and 

t 

is time. 

A-1 

,/-—, 

w!

The most distinctive feature-of a random sea is that it never repeats 

its pattern and it is impossible to predict.its shape. -Therefore, 

total energy is used to define a particular sea. The energy (E) in 

an individual regular wave per unit surface area is, 

E = +*p*g*a2 

and the total energy of the sea is the sum of the energies of the 

constituent regular waves. 

N 

E = $*P*g* z a: 

i=l 

The total energy of the sea is distributed according to the 

frequencies of the various wave components. The amount of energy per 

unit surface area within the small frequency band (tii,wi+dm) is, 

E{wi) = +*D*g*ai2*d~ 

The total energy of the sea is then the sum of the energies within 

the individualwave components. If the sea is made up of an infinite 

number of waves, the energies of the waves form a smooth curve, and 

the above summationmay be replaced by an integral. 

The smooth distribution of the wave energy is called the energy 

spectrum or wave spectrum of the random sea, and is often designated 

as S(W). 

A wave spectrum is normally depicted as a curve with an 

ordinate of energy and an abscissa of frequency. A typical wave 

spectrum has a central peak with a tapered energy distribution either 

side of the peak. 

A-2

The recommended form of displaying a wave spectrum is with an 

ordinate of %*a2 and an abscissa of M, radial frequency. However, 

since the engineer will encounter wave spectra equations in a number 

of forms, using various bases and units, the applicable conversion 

factors are provided in the following sections. 

Suectrum Basis 

The recommended spectrum basis is half amplitude squared or energy. 

Often spectrum equations having a different basis are encountered. 

Before any statistical calculations are performed with a spectrum 

equation, the equation should be converted to the recommended basis. 

For a “half amplitude” or “energy” spectrum, the basis is one-half 

times the amplitude squared. 

S(M) = **n* 

S(m)dm = E / (pg) 

where, 

s 

is the spectral ordinate, 

(IJ 

is the radial frequency, 

is the wave amplitude of the constituent wave of 

frequency, 

E 

is the energy content of the constituent wave of 

frequency, M. 

For an “amplitude” spectrum, the basis is amplitude squared. 

A-3

s(w) = 2*(4*112) - 

For a “height” spectrum, the basis is height squared. 

S(u) = h2 

s(u) = 8*(+*n2) 

where, 

h 

is the height of the constituent wave of 

frequency, M. 

For a “height double” spectrum, the basis is two times the height 

squared. 

s(w) = s*h2 

,. , 

S(u) = 16*(%*r12) 

The basis of the spectrum must be determined before the spectrum 

used in an analysis, because the ordinate of one representation 

the spectrum may be as much as 16 times as great as the ordinate 

another representation. 

is 

of 

of 

Units 

The spectrum equation may be expressed in terms of radial frequency, 

circular frequency, or period. Conversion between circular frequency 

and radial frequency is accomplished by multiplying by the 

constant, 27T. 

u . 2T*f 

s(w) = s(f) / (21r) 

A-4

where, 

f is the circular frequency. 

The conversion between period and radial frequency is more 

complicated. 

111 = 2T/T 

S(f) = T2*S(T) 

s(w) = T2*S(T) / (2Ir) 

where, 

T is the period. 

When converting between period and frequency, the abscissa axis is 

reversed. Zero period becomes infinite frequency, and infinite 

period becomes zero frequency. 

Wave spectrum equations may be used with any length units by 

remembering that the spectrum ordinate is proportional to amplitude 

squared or height squared. 

— 

‘(m)meter = (0.3048)2*S(~)feet 

The mathematical formulation for the wave spectrum equation will 

often include the significant height squared or the gravitational 

constant squared, which when entered in the appropriate units will 

convert the equation to the desired length units. 

A.2 PROBABILITY CHARACTERISTICSOF WAVE SPECTRA 

The characteristics of ocean waves are determined by assuming that 

the randomness of the surface of the sea can be described by two 

A-5

common probability distributions, the Gaussian (or normal) 

distribution and-the Rayleigh distribution. These probability 

distributions are used to define the distribution of wave elevations, n, 

and of wave heights, H, respectively. 

A.2.1 

CharacteristicFrequencies and Periods 

For design purposes sea spectra equations are selected to represent 

middle aged seas that would exist some time after a storm, yet which 

are still young enough to have a good dispersion of wave 

frequencies. The primary assumption about the design seas is that 

the wave elevations follow a Gaussian or normal distribution. 

Samples of wave records tend to support this assumption. In 

conjunction with the Gaussian distribution assumption, the wave 

elevations are assumed to have a zero mean. Digitized wave records 

tend to have a slight drift of the mean away from zero, usually 

attributed to tide or instrument drift. The Gaussian distribution 

assumption is equivalent to assuming that the phase angles of the 

constituentwaves within a wave spectrum, are uniformly distributed. 

The Gaussian distribution allows one to calculate statistical 

parameters which are used to describe the random sea. The mean 

elevation of the water surface is the first moment of the Gaussian 

probability density function. The mean-square is the second moment 

taken about zero, and the root-mean-square is the positive square 

root of the mean-square. The variance is the second moment taken 

about the mean value. The standard deviation is the positive square 

root of the variance. Since the wave elevations are assumed to have 

a zero mean value, the variance is equal to the mean-square, and the 

standard deviation is equal to the root-mean-square. In present 

practice, the area under a random wave energy spectrum is equated to 

the variance. 

In a similar way, the characteristic frequencies and periods of a 

wave spectrum are defined in terms of the shape, the area, and/or the 

area moments of the ~*a2 wave spectrum. Depending upon the 

A-6 

i 

ij 

-,,

particular wave spectrum formula, these characteristic periods may or 

may not-reflect any real period. The area and area moments are 

calculated as follows. 

Area: 

Nth Area Moment: 

mn=f~w 

‘*S(m)dw 

The characteristic frequencies and periods are defined as follows. 

mm: 

Peak frequency 

The peak 

5(w) 

is 

frequency is 

a maximum. 

the frequency at which the spectral ordinate, 

‘P: 

Peak period 

The peak 

period is the 

S(M) is a maximum. 

period corresponding to the frequency at which 

T = 2il/um 

P 

Tm: 

Modal period 

The modal period is the period at which S(T) is a maximum. Since the 

spectrum equations in terms of frequency and in terms of period 

differ by the period squared factor, the modal period is shifted away 

from the peak period. 

A-7 

/‘f

T: v. 

Visually Observed Period, or Mean Period, or Apparent 

Period 

The visually observed period is the centroid of the S(u) spectrum. 

The International Ship Structures Congress (ISSC) and some 

environmental reporting agencies have adopted Tv as the period 

visually estimated by observers. 

Tv = 2~*(mo/m2) 4 

Tz : 

Average Zero-uncrossing period or Average Period 

The average zero-uncrossing period is the average period between 

successive zero up-crossings. The average period may be obtained 

from a wave record with reasonable accuracy. 

Tz 

= 2n*(mo/mz) 4 

Tc : 

Crest Period 

The crest period is the average period between successive crests. 

The crest period may be taken from a wave record, but its accuracy is 

dependent upon the resolution of the wave measurement and recording 

equipment and the sampling rate. 

Tc 

= 2~*(mz/mq) % 

T5: 

Significant 

Period 

The significantperiod is the average period of the highest one-third 

of the waves. Some environmental reporting agencies give the sea 

characteristicsusing Ts and Hs, the significant wave height. There 

are two equations relating Ts to Tp. 

Ts = 0.8568*TP, Old 

A-8

T~ = 0.9457*T P’ 

New 

The first equation applies to original Bretschneider wave spectrum, 

and the second is the result of recent wave studies (See Reference 

A.I). 

The peak period, Tp, is an unambiguous property of all common wave 

spectra, and is therefore the preferred period to use in describing a 

random sea. 

A.2.2 

CharacteristicWave Heiqhts 

From the assumption that the wave elevations tend to follow a 

Gaussian distribution, it is possible to show that the wave heights 

follow a Rayleigh distribution. Since wave heights are measured from 

a through to succeeding crest, wave heights are always positive which 

agrees with the non-zero property of the Rayleigh probability 

density. From the associated property that the wave heights follow a 

Rayleigh distribution, the expected wave height, the significantwave 

height, and extreme wave heights may be calculated. The equation for 

the average height of the one-over-nth of the highest waves is as 

follows. 

— 

where: 

H,,n/ (mo) + = 2* [2*ln(n)]%+ 

n*(2~)%*{l-erf[(ln(n)}%l} 

m 

o 

is the variance or the area under the energy 

spectrum, 

In 

is the natural logrithm, 

erf 

is the error function, (the error function is 

explained and tables of error function values are 

available in mathematics table books.) 

A-9

The characteristic wave heights of a spectrum are related to the 

total energy in the spectrum. The energy is proportional to the area 

under the +*a2 spectrum. 

Ha: 

Average Wave Height 

The average or mean height of all of the waves is found by setting 

n=l. 

Ha= 2.51*(mO)% 

H~: Significant Height 

The significant height is the average height of the highest one-third 

of all the waves, often denoted as H 1/3” 

Hs = 4.00*(mO)* 

H max: 

Maximum Height 

The maximum height is the 1-gest wave height expected 

number of waves, (n on the order of 1000), or over a 

period, (t on the order of hours). 

among a large 

long sampling 

The maximum wave height is often taken to be the average of the 

l/1000th highest waves. 

H = 7.94*(m )% = 1.985*Hs 

1/1000 o 

Using the one-over-nth equation and neglecting the second term gives 

the following equation. 

or 

H 

1/n 

= 2*[ln(n)]+*(mO)% 

A-10

H = 2*[2*ln(n) ]+*Hs 

1/n 

For n = 1000, this gives, 

H 

1/1000 

= 7.43*(mO)+ = 1.86*Hs 

For a given observation time, t, in hours, the most probable extreme 

wave height is given by the following equation. 

H max = 

2*[2*mO*ln(3600*t/Tz)]% 

The 3600*t/Tz is the average number of zero up-crossings in time, t. 

-> 

A.3 


The Bretschneider and Pierson-Moskowitz spectra are the best known of 

,... 

the one-dimensional frequency spectra that have been used to describe 

ocean waves. The JONSWAP spectrum is a recent extension of the 

Bretschneider spectrum and has an additional term which may be used 

to give a spectrum with a sharper peak. 

A.3.1 

Bretschneider and ISSC Spectrum 

The Bretschneider (ReferenceA.2) spectrum and the spectrum proposed 

as a modified Pierson-Moskowitz spectrum by the Second 

International 

Ship Structures Congress (Reference A.4) are identical. 

The 

Bretschneider equation in terms of radial frequency is as follows. 

S(U) = (5/16)*(Hs)2*(um”/w5)*exp [-1.25*(U/Mm)-’ ] 

where: 

A-n 

H~ is the significantwave height, and 

‘m 

is the 

frequency of maximum spectral energy. 

The Bretschneider equation 

may be written in terms of the peak period 

instead of the peak frequency, by substituting urn=2iT/T. 

P 

S(u) = (5/16)*(ti)2* [(21r)4/(u5*(T)4)]* 

exp[-l~25*(2~q/(~*T )4] p 

A.3.2 

Pierson-Moskowitz Spectrum 

The Pierson-Moskowitz (Reference A.4) spectrum was created to fit 

North Atlantic weather data. The P-M spectrum is the same as the 

Bretschneider spectrum, but with the H* and Mm dependence merged 

into a single parameter. The frequency used in the exponential has - 

also been made a function of reported wind speed. The equation for 

the Pierson-Moskowitz spectrum is as follows. 

S(u) = a*g2/~S)*exp[-~*(~0/~)4] 

where: 

a 

: 0.0081 

B 

= 0.74 

&l 

o 

= g/u 

and, U 

is the wind speed reported by the weather ships. 

The Pierson-Moskowitz spectrum equation may be obtained from the 

Bretschneider equation by using one of the following relations 

between H~ and Wm. 

A-12 

--;”, 

:“,< L.

H~ = 0.1610*g/(um)2 

‘m = o.4o125*g/(H# 

An interesting point that may be noted is that if B 

were set equal 

to 0.75 instead of 0.74, the w would be the frequency 

o 

corresponding to the modal period, Tm. 

A.3.3 

JONSWAP and Related Spectra 

The JONSWAP wave spectrum equation resulted from the Joint North Sea 

Wave Project (Reference A.5). The JONSWAP equation is the original 

Bretschneider wave spectrum equation with an extra term added. The 

extra term may be used to produce a sharply peaked spectrum with more 

energy near the peak frequency. The JONSWAP spectrum can be used to 

represent the Bretschneider wave spectrum, the original Pierson- 

Moskowitz wave spectrum, and the ISSC modified P-M spectrum. The 

full JONSWAP equation is as follows. 

s(w) = (aj*g2u5 ) *exp[-1.25*W/um-’)*ya 

where: 

a = exp [-**(M-Wm)2 / (U*WM)2] 

‘m 

is the frequency of maximum spectral energy. 

The Joint 

North Sea Wave Project recommended the following mean 

values to represent the North Sea wave spectra. 

Y = 3.3 

0 = 0.07, for W

a 

= 0.09, for UJ>wm 

The 

U 

value of Q is found by integrating the spectrum and adjusting 

to give the desired area. 

The 

Bretschneider equation and the ISSC equation can be obtained by 

setting the following parameter values. 

Y = 1.0 

a = (5/16 )*( Hs)2*(#/g2 

The Pierson-Moskowitz equation is obtained from the further 

restriction that Hs and Urn are related. 

H~ = 0.1610*g/(wm)2 

or 

‘m = 

0.140125* (g/H5)+ 

or 

a = 0.0081 

When Y is set to one the JONSWAP term is effectively turned off. 

Without the JONSklAP term, the wave spectrum equation can be 

mathematically integrated to give the following relationships among 

the characteristicwave periods. 

Tp = 1.1362 *TM 

‘P 

= 1.2957 *TV 

‘P = 1.4077 *TZ A-14

‘P = 1.1671*TS . 

For Y = 1, the fourth area moment is infinite. The crest period, 

T~, is therefore zero. 

For values of y other than one, the JONSWAP equation cannot be 

mathematically integrated. The period relationships as a function 

of Ycan be calculated by numerical integration of the wave spectrum 

equation over the range from three-tenths of the peak frequency to 

ten times the peak frequency. 

The shape of the JONSWAP spectrum can be further adjusted by changing 

the values of e. The e values are sometimes varied when the JONSWAP 

spectrum is used to fit measured wave spectra. 

.- 

A.3.4 

Scott and Scott-Wieqel Spectra 

The Scott (Reference A.6) spectrum was also formulated to fit North 

Atlantic weather data. The Scott spectrum is the Derbyshire 

(Reference A.7) spectrum with S1ight modifications to the constants 

in the equation. The spectrum equation is as follows. 

s(w) 

= 0.214*(Hs)2*exp[-(~-wm)/ {0.065*(U-Mm+0.26)}4] 

for -0.26 < OJ-Wm < 1.65 

= o, elsewhere. 

where 

A-15 

2.3

H~ is the significant height, 

‘m = 3.15*T-l+&Wl*T-2, 

T 

is the characteristic period of the waves. 

The timis the frequency of the peak 

unfortunately, the period, T, used in the 

correspond to any of the mathematical 

spectrum. The equation for ~mwas derived 

data. 

spectral energy, but 

equation for ~mdoes not 

characteristics of the 

as a curve fit to real 

The Scott-Wiegel spectrum is a Scott spectrum modification that was 

proposed by Wiegel (Reference A.8). The constants are adjusted to 

match the equation to a “100-year storm” wave condition. The new 

equation is as follows. 

S(UJ) = 0.300* (H~)*exp[-(w-wm)4/ 

{0.0.353* (M-WM+0.26) } ] 

The umin 

equation. 

this equation is 1.125 times that specified for the Scott 

A.4 SELECTING A WAVE SPECTRUM 

Information about the random sea characteristics in a particular area 

is derived by either ‘wave hindcasting’ or by direct wave 

measurement. For many areas of the world’s oceans, the only data 

available is measured wind speeds and visually estimated wave 

heights. Sometimes the estimated wave heights are supplemented by 

estimated wave periods. For afew areas of intense oil development, 

such as the North Sea, direct wave measurement projects have produced 

detailed wave spectra information. 

A-16

A.4.1 

Wave Hindcastinq 

Wave hindcasting is a term used to describe the process of estimating 

the random sea characteristics of an area based upon meteorological 

or wind data. Various researchers (ReferencesA.2, A.4, A.6, A.7 and 

A.8) have attempted to derive a relationship between the wind speed 

over a recent period of time and the spectrum of the random sea 

generated by the particular wind. The wind speed data is usually 

qualified by two additional parameters, the duration that the wind 

has been blowing at that speed and the fetch or distance over open 

ocean that the wind has been blowing. 

A set of equations as derived by Bretschneider (ReferenceA.2), which 

relate wind speed, duration and fetch are as follows. 

g*H# 

= 0.283*tanh[0..125*(g*F/Uz)””42] 

g*Ts / (2r*U) = 1.2*tanh[0.077*(gF/U2)””42 

... 

g*t minl” = 

6.5882*exp{[0.161*A2-0.3692*h+2.024]% 

+ O.8798*A} 

where 

u 

is the wind speed, 

F 

is the fetch, 

A 

= ln[g*F/U2], 

t min 

is the minimum duration for which the fetch will 

determine the significant height and period, and 

tanh 

is the hyperbolic tangent. 

A-17 

-) s“

If the wind duration is less than tmin, then the third equation is 

used to find the fetch which would correspond to tmin = t. 

For a fully arisen sea, the above equations simplify to the 

following. 

g*Hs/U2 = 0.283 

g*Ts/(2T*U) = 1.2 

Other relationships have been developed in the references. Often 

specialized weather/wave research companies have developed elaborate 

wave hindcasting models to derive the wave spectra characteristics 

for particular areas. However, the assumptions incorporated into 

these models have very profound impact on the outcome. 

A.4.2 

Direct Wave Measurements 

By installing a wave probe or a wave buoy in the ocean area of 

interest, wave elevation histories may be directly measured. The 

elevation of the sea at a particular point is either recorded by 

analog means or is sampled at short time intervals (typically one 

second) and recorded digitally. The wave elevations are usually 

recorded intermittently, ie. the recorder is turned on for say 30 min 

every four hours. 

The wave records are then reduced by computer, and the wave 

characteristics are summarized in various ways. Two common ways of 

summarizing the data are as a wave scatter diagram and/or as a wave 

height exceedance diagram. 

The wave scatter diagram is a grid with each cell containing the 

number or occurances of a particular significant wave height range 

and wave period range. The wave period range may be defined in terms 

of either peak period or zero-uncrossingperiod. 

A-la 

w

The wave height exceedance diagram is a curve showing the percentage 

of the wave records for which the significant wave height was greater 

that the particular height. 

M 

WAVE SCATTER DIAGRAM 

Wave scatter diagrams show the occurances of combinations of 

significant wave height and average zero-uncrossing period over an 

extended time period such as many years. 

Wave height distribution over time can be obtained by actual wave 

measurements. The heights and periods of all waves in a given 

direction are observed for short periods of time at regular 

intervals. A short time interval of several hours may be considered 

constant. For this sea state, defined as “stationary”,the mean zero 

up-crossing period, Tz, and the significant wave height, Hs, are 

calculated. The Hs and Tz pairs are ordered and their probabilities 

of occurance written in a matrix form, called a wave scatter diagram. 

Sometimes wave scatter diagrams are available for the sea and for the 

swell. The sea scatter diagram includes the sea spectra generated 

locally. The swell scatter diagram contains the swell spectra (or 

regular waves) generated far from the area, days before. Due to 

greater energy losses in high frequency waves and the continual phase 

shifting caused by viscosity, the energy in irregular seas tends to 

shift toward longer periods, and the spectra becomes more peaked as 

time passes. The energy in the swell is concentrated about a single 

long period/low frequency, and often the swell is treated as a single 

regular wave. 

A typical wave scatter diagram, presenting statistical data on the 

occurance of significant wave height and zero up-crossing period per 

wave direction is shown on Figure A-2. 

A-19

Sample Wave scatter Diagram 

s 

12 +..-..+---.-+-----+-w---+-----+-_---+-----+-----+-.---+.----+-.-_-+ 

i 1111111 11111 

9 11 +---..+----.+-----+-..--+----.+-----+----.+-----+-.---+-.---+-----+ 

n 111111 10.511.01 I I I 

i 10 +-----+-----+-..--+----.+.----+-..--+-----+-.---+-----+---..+----.+ 

f 111[11 11.012.011.51 I I 

i 9 +----.+.----+...--+--...+-----+-.-.-+-----+..---+--..-+---.-+---..+ 

c 1111 10.511.512.513.010.51 I I 

a 8 +-----+-----+-----+-----+-----+-----+-----+-----+-----+--.--+---.-+ 

n 1111 11.015.015.512.510.51 I I 

t 7 +-----+-----+-----+-----+-----+-----+-----+-----+-----+---.-+-----+ 

1111 I 5.0 113.0 111.0I 2.0 I I I I 

w 6 +-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-.---+ 

a II I 0.5 I 6.0 118.0 123.0 I 8.5 I 1.0 I I I I 

v 5 +-----+-----+-----+-----+-----+-----+-----+-----+---.-+-----+-----+ 

e II I 4.0 126.5 148.5 126.5 I 7.0 I 2.5 I 0.5 I 0.5 I I 

4 +-----+-----+-----+-----+-----+-----+-----+-----+-..--+-----+-----+ 

H I 1 1.5 139.5 179.5 163.5 120.0 I 6.0 I 3.0 I 1.5 I 0.5 I 0.5 I 

e 3 +-----+-----+-----+-----+-----+-----+-----+-----+-----+---.-+-----+ 

i I 0.5 150.0 I105.OI95.5 135.0 111.5 I 5.5 I 2.0 I 1.5 I I I 

— 

9 ,2+-----+-----+-----+.----+-----+-----+-----+-----+-----+.----+---..+ 

h I 1.5 159.5 189.0 134.5 112.0 I 7.0 I 4,0 I 1.5 I 0.5 I I I 

t 1 +-----+-----+-----+-----+-----+-----+-----+-----+-.----+-----+-----+ 

12.5118 .018.012.512.511.510.5 I I i I I 

(m) O +-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ 

2 3 4 5 6 7 8 9 10 11 12 13 

Zero Up-crossing Period, Tz (see) 

Sum of Occurances 999.5 

Figure A-2 A Typical Wave Scatter Diagram for the Central North Sea 

A-20

Using the significant wave height and zero up-crossing period from 

the wave scatter diagram and selecting a representative sea spectrum 

formulation, the energy of each sea state can be reconstructed. 

A*6 WAVE EXCEEDANCE CURVE 

A wave exceedance curve shows the number (percentage)of waves that 

are greater than a given wave height ‘for consistent wave height 

intervals. Table A-1 shows the type of data contained on a wave 

exceedance curve. 

Wave Height (ft) 

Cl 

5 

10 

15 

20 

25 

30 

35 

40 

Number of Waves 

35,351,396 

3,723,300 

393,887 

41,874 

4,471 

480 

51 

5 

1 

(N) 

Table A-1 Wave Exceedance Data for Campos Basin 

(Number of Waves from Northeast) 

This data can be plotted on semi-log paper and closely approximated 

by a straight line plot. Typically, a wave exceedance H-N curve can 

be defined with the following equation. 

H 

= Hm+mz * 109 f!h 

where 

Hm 

is the maximum wave height for the design life, 

‘z 

is the slope of the H-log N curve, -Hm/log Nh, 

MIC:500400CC-A 

A-21

Nm is the total number of waves in the design life, and 

Nh is the 

H. 

number of occurances of waves with height exceeding 

A.7 WAVE HISTOGRAM AND THE RAYLEIGH DISTRIBUTION 

Actual wave height measurements can be plotted to show the number of 

waves of a given height at equal wave height intervals. The 

histogram obtained can be defined by a simple curve. 

A simple curve that fits most wave histograms is the Rayleigh 

distribution. Past work have shown that the Rayleigh distribution 

often allows accurate description of observed wave height 

distributions over a short term. 

The Rayleigh distribution is typically given as, 

,..., 

p(Hi) = 2*Hi *EXP(-H12/~2) * (1/~2) 

where 

P(Hi) 

is the wave height percentage of occurances, 

Hi 

is the wave heights at constant increments, 

~ 2 is the average of all wave heights squared. 

A.8 EXTREMEVALUESAND THE WEIBULL DISTRIBUTION 

For design purposes an estimate of the maximum wave height (extreme 

value) is required. The Rayleigh distribution provides such an 

estimate over a short duration. However, in order to estimate the 

extreme wave that may occur in say 100 years, the Weibull 

distribution is often used. 

A-22

The equation for the Weibulldistribution is as follows. 

P(H) = 1 - EXP[ -( (H-E)/e )= ] 

where 

P(H) 

is the cumulative probability, 

H 

is the extreme height, 

E 

is the location parameter that locates one end of 

the density function, 

e 

is the scale parameter, and 

a 

is the shape parameter. 

By plotting the wave exceedance data on Weibull graph paper, the 

distribution can be fit with a straight line and the extreme value 

for any cumulative probability can be found by extrapolation. 

A.9 


The wind environment, source of most ocean waves, is random in 

nature. The wind speed, its profile and its directionality are 

therefore best described by probabilistic methods. 

A.9.1 

Air Turbulence, Surface Roughness and Wind Profile 

Air turbulence and wind speed characteristics are primarily 

influenced by the stability of the air layer and terrain. For 

extreme wind gusts the influence of stability is small, making 

A-23

turbulence largely a function of terrain roughness. In an ocean 

environment, the wave profi1e makes prediction of wind 

characteristics more difficult. As the wind speed increases, the 

wave height also increases, thereby increasing the surface 

roughness. A surface roughness parameter is used as a measure of the 

retarding effect of water surface on the wind speed. 

A simple relationship developed by Charnock (ReferenceA.9) is often 

used to define the surface roughness parameter and the frictional 

velocity in terms of mean wind speed. Further discussion on surface 

roughness parameter and drag factor is presented in an ESDU document 

(Reference A.10). 

Full scale experiments carried out by Bell and Shears (Reference 

All) may indicate that although turbulence will decay with the 

distance above sea surface, it may be reasonably constant to heights 

that are applicable for offshore structures. 

Considering that wind flow characteristics are primarily influenced 

by energy loss due to surface friction, the mean wind profile for an 

ocean environment may be assumed to be similar to that on land and to 

follow this power law: 

v mz 

= Vmzl (z/zL) u 

where: 

v mz 

= mean wind velocity at height z above LAT 

v mzl 

= mean wind velocity of reference height above 

LAT 

= height at point under consideration above 

IAT 

A-24

Z1 = reference height, 30 ft (10 M), above LAT 

(typical) 

u 

= 

height exponent, typically 0.13 to 0.15. 

A.9.2 

Applied, Mean and Cyclic Velocities 

The random wind velocity at height z can be thought of as a 

combination of time-averaged mean velocity, Vmz, and a time varying 

cyclic component, vz (t). 

Vz (t) = Vmz + v~ (t) 

A range of mean and associated cyclic wind speeds can be extracted 

from an anemogram and divided into one- to four-hour groups over 

which the cyclic component of the wind speed is approximately 

equal. By describing cyclic wind speeds associated with an average 

value of the mean component of the wind speed over a particular 

period of time, a number of pairs of mean and associated cyclic 

speeds can be obtained. In addition to the applied, mean and cyclic 

wind speeds shown on Table A-2, their probability of occurrence is 

necessary to generate a scatter diagram. If sufficient data are not 

available, the number of occurrences can be extrapolated based on 

similar data. Table A-2 is given only to illustrate the wind make-up 

and the uncertainties associated with wind data. 

A-25

Applied Wind 

Speed Vz(t) 

ft/s (m/s) 

Mean Wind 

Speed Vmz 

ft/s (m/s) 

.---------_ 

Cyclic Wind Probability 

Speed vz(t) of 

ft/s (m/s) Occurrence % 

4.26 (13) 

78.7 (24) 

101.7 (31) 

134.5 (41) 

154.0 (50) 

180.4 (55) 

29.5 (9) 

62.3 (19) 

78.7 (24) 

101.7 (31) 

124.6 (38) 

131.2 (40) 

13.1 (4) 16.7 

16.4 (5) 45.8 

23.0 (7) 12.5 

32.8 (10) 16.7 

39.4 (12) 4.2 

49.2 (15) 4.2 

Table A-2 Applied, Mean 

Extreme Gust Environment 

and Cyclic Wind Speed Distribution for an 

A.9.3 

Gust Spectra 

The power spectral density function provides information on the 

energy content of fluctuating wind flow at each frequency 

component. A study of 90 strong winds over terrains of different 

roughness in the United States, Canada, Great Britain, and Australia 

at heights ranging from 25 feet (8m) to 500 feet (150m) allowed 

Davenport (Reference A.12) to propose a power density spectrum of 

along-wind gust (the longitudinal component of gust velocity). 

A modified version of the Davenport spectrum, due to Harris 

(Reference ??), is given by: 

m=qf 

kV; 

(2 + f’)$i’ 

where: 

A-26

n 

= fluctuating frequency 2 

S(n) 

= power density [(m/see )/Hz] 

k 

= surface roughness drag factor corresponding 

to the mean velocity at 30 ft (lOm) (i.e. 

0.0015) 

v 

= 

mean hourly wind speed at 30 ft (lOm) m 

f 

= 

non-dimensionalfrequency (nL/V ) m 

L 

= 

length scale of turbulence ( 1200 to 1800m, 

typical) 

-, 

The Harris spectra may be used to develop the wind spectra for each 

one of the mean wind speeds associated with the scatter diagram. 

... 

A-27

A.1O 

REFERENCES 

A*I 

Mechanics of Wave Forces on Offshore Structures, Sarpkaya, 

T. and Isaacson,M., Van Nostrand Reinhold Company, 1981. 

A.2 

Bretschneider, C.L., “Wave Variability and Wave Spectra for 

Wind-Generated Gravity Waves,” Beach Erosion Board, Corps 

of Engineers, Technical Memo No. 118, 1959, pp. 146- 180. 

A.3 

Report of Committee 1, “Environmental Conditions,” 

Proceedings Second International Ship Structures Congress, 

Delft, Netherlands, July 1964, Vol. 1, pp. 1:5-1:13. 

A.4 

Pierson, W.J. and Moskowitz, L., “A Proposed Spectral Form 

for Fully Developed Wind Seas Based on the Similarity 

Theory of S.A. Kitaigordsky,” Journal of Geophysical 

Research, Vol. 69, No. 24, Dec 1964. 

A.5 

Rye, H., Byrd, R., and Torum, A., “Sharply Peaked Wave 

Energy Spectra in the North Sea,” Offshore Technology 

Conference, 1974, No. OTC 2107, pp. 739-744. 

A*6 

Scott, J.R., “A Sea Spectrum for Model Tests and Long-Term 

Ship Prediction,” Journal of Ship Research, Vol. 9, No. 3, 

Dec. 1965, pp. 145-152. 

A.7 

Derbyshire, J., “The One-Dimensional Wave Spectrum in the 

Atlantic Ocean and in Coastal Waters,” Proceedings of 

Conference on Ocean Wave Spectra, 1961, pp. 27-39. 

A.8 

Wiegel, R.L., “Design of Offshore Structures Using Wave 

Spectra,” Proceedings Oceanology International, Brighton, 

England, 1975, pp. 233-243. 

A-28

‘GiiQH1 

REGULAR 

WAVES 

TI T2 T3 

I 

T4 

T5 

..-. 

SWL 

HI 

H3 

n / 

t 

IRREGULAR 

WAVES 

Figure A-I Regular and Irregular Waves

APPENDIX B 

REVIEW OF LINEAR SYSTEM RESPONSE 

TO RANDOM EXCITATION 

CONTENTS 


B.1 GENERAL 

B.1.l 

B.1.2 

B.1.3 

Introduction 

Abstract 

Purpose 


B.2.1 Spectrum Analysis Procedure 

8.2.2 Transfer Function 

6.2.2.1 Equations of Motions 

6.2.2.2 Response Amplitude Operator 


6.2.3.1 Wave Slope Spectra 

6.2.3.2 Wave Spectra for Moving Vessels 

B.2.3.3 Short-Crested Seas 

B.2.4 Force Spectrum 

B.2.5 White Noise Spectrum 

B.3 EXTREME RESPONSE 

B.3.1 

B.3.2 

Maximum Wave Height Method 

Wave Spectrum Method 


B.4.1 

B.4.2 

Special Family Method 

Wave Spectrum Method


B.1 GENERAL 

B.1.l 

Introduction 

Spectral analysis is used to determine the response of linear systems 

to random excitation. In the case of offshore structures, the random 

excitation comes from either irregular waves or winds. Typical 

offshore systems subjected to spectral analysis include ships, 

semisubmersibles, jack-ups, tension-leg platforms and bottomsupported 

fixed platforms. Responses of interest include motions, 

accelerations, and member internal forces, moments, and stresses. 

Floating units are evaluated by spectral analysis for motions in 

random seas. The strength and structural fatigue integrity are often 

assessed with spectral analysis. 

B.1.2 

Abstract 

A spectral analysis combines a set of regular wave response amplitude 

operators, RAOS, with a sea spectrum to produce a response 

spectrum. Characteristics of the response may be calculated from the 

response spectrum, and a random sea transfer function can be derived. 

For certain spectral analyses, the sea spectrum-must be modified to 

produce a wave slope spectrum or to adjust the sea spectrum for 

vessel speed. A spreading function can be applied to the sea 

spectrum to model a short-crested random sea. 

A wave force spectrum can be created directly from force RAOS and the 

sea spectrum. 

A regular wave transfer function is found as the solution to the 

equations of motion. The regular wave transfer function can be. 

expressed in terms of RAO and a phase angle. 

B-1

Awhite noise function-may be used to represent a very broad banded 

input spectrum, if the response spectrum is narrow banded. 

The extreme response can be calculated from a given extreme wave, or 

the extreme response may be statistically derived from a set of 

spectral analyses. 

The sea spectra used in the computation of random sea response can be 

reduced in number by selecting a smaller family of representative 

spectra, or by creating a set of mean spectra. 

0.1.3 m 

The purpose of this appendix is to provide a background of the 

spectral analysis method and to clarify the concept of a response 

spectrum and how its properties are derived. 

P, 


The spectral analysis method is a means of taking the known response 

of an offshore structure to regular waves and determining the 

structure’s response to a random sea. The input to the spectral 

analysis method is the response amplitude per unit wave amplitude (or 

equally, the response double amplitude per unit wave height) for a 

range of periods or frequencies of regular waves. These ratios of 

response amplitude to wave amplitude are known as “Response Amplitude 

Operators” or just “RAOS.” The response of the offshore structure is 

first obtained for a set of unit amplitude, regular, sinusiodal 

waves. The regular wave response may be obtained either from model 

tests or from empirical or theoretical analyses. 

A wave energy spectrum is selected to represent the random sea. Wave 

spectra are described in Appendix A. The wave spectrum represents 

the distribution of the random sea’s energy among an infinite set of 

regular waves that when added together create the random character of 

B-2 /l-l-

the sea. By assuming thatthe response is linear, the response of 

the offshore structure to a regular wave is equal to the RAO times 

the regular wave amplitude. By assuming that the response to one 

wave does not affect the response to another wave, the response of 

the offshore structure to a random sea is the sum of its responses to 

each of the constituent regular waves in the random sea. The 

response is therefore a collection of responses each with a different 

amplitude, frequency, and phase. 

The energy of each constituent wave is proportional to the wave 

amplitude squared. The energy of the response to a constituentwave 

of the random sea is proportional to the response squared, or is 

proportional to the RAO squared times the wave amplitude squared. 

The response energy may also be represented by a spectrum from which 

characteristics of the response may be derived. From the response 

spectrum characteristics and the wave spectrum characteristics, a 

“transfer function” can be obtained which relates the response and 

wave characteristics. 

B.2.1 

Spectrum Analysis Procedure 

The spectral analysis procedure involves four steps: 1) obtaining 

the response amplitude operators, 2) multiplying the wave spectrum 

ordinates by the RAOS squared to get the response spectrum, 3) 

calculating the response spectrum characteristics, and 4) using the 

response spectrum characteristics to compute the random sea response 

transfer function. 

The RAOS are usually calculated for a discrete set of wave 

frequencies, and the discrete RAOS are then fit with a curve to 

produce a continuous function. The singular term “RAt)” is used both 

to signify a single response amplitude to wave amplitude ratio and to 

signify the continuous function through all of the RAOS. Any 

response that is linearly related (proportional) to wave amplitude 

may be reduced to an RAO function. Typical responses are motions, 

accelerations, bending moments, shears, stresses, etc. 

B-3

Multiplication of the wave spectrum ordinates by the RAO squared is 

simple. The two underlying assumptions are that the response varies 

linearly with wave amplitude and the assumption that the response to 

a wave of one frequency is independent of the response to waves of 

other frequencies. 

Response spectrum characteristics are taken from the shape of the 

spectrum or are calculated from the area under the response spectrum 

and the area moments of the response spectrum. Typical 

characteristics are significant response amplitude, maximum response 

amplitude, mean period of the response, and peak period of the 

response spectrum. 

The random sea transfer function is the ratio of a response spectrum 

characteristic to a wave spectrum characteristic. A random sea 

transfer function is usually presented as a function of the random 

sea characteristic period. A typical transfer function might be the 

ratio of maximum bending moment amplitude per unit significant wave 

height. The transfer function is useful for estimating the response 

to another wave spectrum with similar form but different amplitude. 

. 

B.2.2 

Transfer Function 

A transfer function converts input to output for linear systems. A 

transfer function is graphically represented in Figure B-1. A 

transfer function can relate motion response to the height of 

incident waves directly, or a transfer function can relate motion 

response to wave force, or a transfer function can relate member 

stresses to wave or wind force. 

For typical applications to the design of offshore structures, the 

input energy forms are waves, current and wind. The desired output 

forms are static displacements, dynamic displacements, and member 

stresses. 

B-4

B.2.2.1 Equation of Motions 

By assuming that the motions are small enough that the inertial, 

damping and spring forces can be summed linearly, the equation of 

motion can be formulated. 

M*X + D*X + K*X = F(x,t) 

where M is the mass matrix which includes the structure mass 

properties plus the hydrodynamic added mass effects, 

D 

is the linearized damping matrix which includes the 

viscous damping, the wave damping, and the structural 

damping effects, 

-.> 

K 

is the stiffness matrix which includes the waterplane 

spring properties, 

moorings or tendons, 

the structure and any 

the restoring properties of 

and the stiffness properties of 

foundation, 

x 

is the system displacement vector, 

i 

is the system velocity vector = (dx/dt), 

— 

x 

is the system acceleration vector, = (d2x/dt2), and 

F 

is the force vector which may be calculated from 

empirical methods such as Morrison’s equation or from 

diffraction theory methods. 

The equations of motion can be solved with frequency domain or time 

domain techniques. The frequency domain solution involves the 

methods of harmonic analysis or the methods of Laplace and Fourier 

transforms. The time domain solution involves the numerical solution 

by a time step simulation of the motion. 

B-5

B.2.2.2 Response Amplitude Operator 

The solution of the equations of motion result in a transfer 

function. The motion transfer function has an in-phase component and 

an out-of-phase component. The transfer function is usually 

represented in complex form, 

x(u) 

= A*[XI(UJ) + i*XO(U)] 

or in angular form, 

x(u)= A*[XI*cos(Ut) +XO*sin(mt)] 

where 

x 

is the total response, 

A 

is the wave height, 

XI 

is the in-phase component of the response for unit 

wave height, and 

Xo 

is the out-of-phase component of the response for unit 

wave height. 

From this equation, the response amplitude operator (amplitude per 

unit wave height), is found to be, 

RAO = SQRT (X12 +X02), 

and the phase of the harmonic response relative to the wave is, 

o = ATAN (XO/XI). 

The response can be written in terms of the RAO and phase as, 

B-6 

,. I

X(w) = A*RAO(w)*cos(wt+ O(W)). 

When a spectral analysis is applied to the transfer function the 

wave amplitudes, A, become a function of wave frequency, u, and 

the X(U) is replaced by the differential slice of the response 

power density spectrum. 

SR(m)*dm = [A(W)*RAO(U)]2 

or 

SR(w)*dw = A2(u)*RA02(w) 

or 

SR(~)*dw = S(w)*du*RA02(w) 

Thus, Sf(w) = S(U)*RA02(W) 

The 

the 

response spectrum S(W) 

RAO squared. 

is therefore just the sea spectrum times 

For multiple-degree-of-freedom systems, there is coupling between 

some of the motions, such as pitch and heave. For example, to obtain 

the motion or motion RAO for heave of a point distant from the center 

of pitch rotation, the pitch times rotation arm must be added to the 

structure heave. This addition must be added with proper 

consideration of the relative phase angles of the pitch and heave 

motions, and therefore, such addition must be performed at the 

regular wave analysis stage. The combined heave (w/pitch) RAO can 

then be used in a spectral analysis to obtain the heave spectrum and 

heave response characteristicsat the point. 

6-7


The wave spectrum used in the spectral analysis may be an idealized 

mathematical spectrum or a set of data points derived from the 

measurement of real waves. When a set of data points are used, a 

linear or higher order curve fit is employed to create a continuous 

function. Custom wave spectra for specific regions are often 

provided as one of the conventional idealized spectra with parameter 

values selected to match a set of measured wave data. For areas 

where there is little wave data, wave height characteristics are 

estimated from wind speed records from the general area. 

B.2.3.1 Wave Slope Spectra 

For certain responses, particularly the angular motions of pitch and 

roll, the RAO is often presented as response angle per unit wave 

slope angle. For these cases the wave spectrum in amplitude squared 

must be converted to a wave slope spectrum. The maximum slope of any 

constituent wave of the spectrum is assumed to be small enough that 

the wave slope angle in radians is approximately equal to the tangent 

of the wave slope. The water depth is assumed to be deep enough (at 

least one-half the longest wave length) that the wave length is 

approximately equal to: 

(g/2~)*T2 or 2~g/~2. 

By using the Fourier series representation of the wave spectrum, 

selecting one constituent wave, and expressing the wave equation in 

spatial terms instead of temporal terms, the wave slope is derived as 

follows. 

rI=a*cos(2rx/L) = a*cos(x~2/g) 

dq/dx = -(a~2/g)*sin(x~2/g) 

B-8 

LJt Y

[dn/dx]max= aW2/g . 

Squaring the equation to 

get the slope squared, 

[dn/dx]2 = a2*(~4/g2) 

Therefore, the wave spectrum equation must be multiplied by (~4/g2) 

to obtain the slope spectrum. The wave slope angle spectrum is the 

wave slope spectrum converted to degrees squared, i.e., multiplied by 

(180/r)2. 

B.2.3.2 Wave Spectra for Moving Vessels 

For self-propelled vessels or structures under tow, the forward speed 

of the vessel or structure will have an effect upon the apparent 

frequency of the waves. The apparent frequency of the waves is 

usually referred to as the encounter frequency. For a vessel heading 

into the waves the encounter frequency is higher than the wave 

frequency seen by a stationary structure. For a vessel moving in the 

same direction as the waves, the encounter frequency is less than the 

wave frequency seen by a fixed structure, and if the vessel’s speed 

is great enough it may be overrunning some of the shorter waves which 

will give the appearance that these shorter waves are coming from 

ahead instead of from behind. 

The encounter frequency for a regular wave is given by the following 

relationship. 

‘e = u + VuZ/g 

where u is the wave frequen~y in radians per second as seen 

from a stationary observer, 

v is the 

velocity component parallel to and opposite in 

direction to the wave direction, and 

%-9

9 is the acceleration of gravity in units compatible 

with .thevelocity units. .’ 

The energy of, or area under the curve of the sea spectrum must 

remain constant. 

f$e(@*dwe = fS(w)*du 

Taking the derivative of the encounter frequency equation gives the 

following. 

dwe = [1 + 2Vw/g]*dw 

Substituting the derivative 

following. 

nto the area ntegral gives the 

f$e(ue)*[l +2Vw/g]*dw = ~S(w)*dw 

Therefore, equating the integrands gives the relationship between the 

encounter spectrum and the stationary sea spectrum. 

Se(we) = s(l.u)/[l+2vw/gl 

This equation is required to transform a stationary sea spectrum to 

an encounter spectrum for the purpose of intergrating the responses. 

However, if only the response statistics are desired, and not the 

actual response spectrum, then the same substitutions as above can be 

made. 

se = s/[1 +2vw/g] 

dwe = [1+2VU /g]*du 

B-10 

@

Jr 2*$ *dti= Jr 2*S*du 

eeee. 

Therefore, the encounter frequency need only be used to select the 

response amplitude operator and the integration is still over the 

stationary frequency, u. 

i.e., 

re = r(we) = r(w + 

2 

VU/g) 

B.2.3.3 Short-Crested Seas 

The usual mathematical representation of a sea spectrum is onedimensional 

with the random waves traveling in a single direction 

with the crests and troughs of the waves extending to infinity on 

either side of the direction of wave travel. A one-dimensional 

irregular sea is also referred to as a long-crested irregular sea. 

In the real ocean the waves tend to be short-crested due to the 

interactionof waves from different directions. 

A two-dimensional spectrum (short-crested sea) is created from a 

standard one-dimensional mathematical spectrum by multiplying the 

spectrum by a “spreading function.” The most commonly used spreading 

function is the “cosine-squared”function. 

f(lp)= (2/Tr)*cos2$ 

where * is the angle away from the general wave heading, 

(-lT/2q%/2) 

The cosine-squared spreading function spreads the sea spectrum over 

an angle +/- 90 degrees from the general wave heading. 

To incorporatemulti-directional or short-crested irregular seas into 

a spectral analysis, the RAOS for a range of wave headings must be 

obtained. A spectral analysis is performed for each heading using 

the one-dimensional sea spectrum. The results of the one-dimensional 

analyses are then multiplied by integration factors and summed. 

B-n

The following is..a. sample...of..a“.set. of...heading angles 

integration factors for a cosine squared spreading function. 

and the 

$ Factor 

~o 

0.2200 

*2O0 0.1945 

*4O0 0.1300 

~600 0.0567 

3800 0 ● 0088 

6.2.4 Force Spectrum 

For simple single-degree-of-freedomsystems, 

generated directly from the calculated or 

forces. 

a force spectrum can be 

measured regular wave 

The force on the structure is calculated by empirical or theoretical 

methods, or is derived by analyzing measured strain records from 

tests on the structure or on a model of the structure. This force is 

the right hand side of the equation of motion as described in Section 

B.2.2.1. 

The force itself has an in-phase and an out-of-phase component 

relative to the regular wave which generates the force. The force 

can be written in complex form, 

F(u) = A*[FI(u) + i*FO(m)] 

or in force RAO and phase form, 

F(w) 

= A*RAOf(w)*cos(wt+$(w)) 

where 

RAOf = SQRT (F12 

+ F02), and 

@ ‘ATAN (FO/FI). 

B–12

The force..spectrum can be created by multiplying a selected wave 

spectrum times the force RAO squared. 

Sf(M) = S(W)*RAOf2(U) 

B.2.5 

White Noise Spectrum 

Most sea spectra have a well defined peak of energy and the energy 

trails off to near zero away from the peak. Other environmental 

inputs that are described by spectra, such as wind force, may not 

have a definite peak and may even appear constant over a wide range 

(broad band) of frequencies. 

Often the response RAO is narrow banded, that is, the structure tends 

to respond at a narrow range of frequencies, centered about a 

resonant frequency. When the combination of a broad banded 

excitation spectrum and a narrow banded RAO exist, the spectral 

analysis can be greatly simplified. 

A broad banded spectrum can be approximated by a “white noise 

spectrum” which has constant energy over the whole frequency range of 

the spectrum. 

— 

For a single degree of freedom system, the response can be defined in 

terms of a “dynamic amplification function” times an expected static 

displacement. The dynamic amplification function is as follows, 

where 

IH(w)I= l/[(l-w/un)2)2 + (2gu/un)2]% 

u) is radial frequency, 

u 

is the undamped “natural frequency”, 

% = (k/m)%, B-13

is the damping ratio,..the ratio of.the actual damping to 

the critical damping. g = c/(4km)$, 

k 

is the spring constant, 

m 

is the mass that is in motion, and 

c 

is the actual damping. 

The expected static displacement is simply force divided by the 

spring constant, or the expected static displacement spectrum is as 

follows, 

Sd(d ‘Sf(u)/k2 

From 

these equations, the response 

spectrum is found to be, 

R(u) = (1/k2)*lH(w)12*Sf(~), 

and the mean squared response 

is, 

y2(t) =O~m(l/k)2*lH(w)12*Sf(m)*dw. 

The (l/k)z is constant, and by approximating the force spectrum by a 

white noise spectrum with magnitude Sf(wn),the mean squared response 

is simplified to, 

Y2(t) = (Sf(u)n/k2)*O~m lH(w)12*dm. 

For lightly damped systems, (&

0.3 EXTREME RESPONSE 

The extreme response of an offshore structure may be determined in 

two ways. An extreme environmental event may be selected, and the 

responses to the extreme event then calculated. A set of 

environmental spectra can be selected; the response spectra to each 

environmental spectra calculated; and the extreme responses derived 

by statistical analysis of the response spectra. The first method is 

often called a “deterministic” method, and the second method is 

referred to as a “probabilistic”method. In actual design practice 

the two methods are often intermixed or combined in order to confirm 

that the extreme response has been found. 

B.3.1 

Maximum Wave Height Method 

In deterministic design, a set of extreme conditions is supplied by 

oceanographers or meteorologists. The extreme conditions are of 

course derived from statistical analyses of wave and weather records, 

but the design engineer is usually not involved in that stage of the 

calculations. 

,..,, 

The given extreme conditions are applied to the offshore structure to 

determine the various responses. Unfortunately, the given extreme 

conditions may not always produce the extreme responses. For 

example, the prying and racking loads governing the design of many 

structural members of semisubmersibles are typically maximized in 

waves with lower heights and shorter lengths then the maximum height 

wave. Tendon loads on tension leg platforms (TLPs) are also often 

maximized in waves that are lower and shorter than the maximum wave. 

Since the oceanographer or meteorologistwho produced the set of 

extreme conditions does not have information about the 

characteristics of the offshore structure, he/she is unable to select 

an extreme or near extreme condition that will produce the greatest 

response. Conversely, the design engineer usually has little or no 

information about the wave and weather data that was used to derive 

B-15

the set of extreme conditions, and thus, he/she is unable to create 

alternate conditions to.check for greater response. 

The design engineer may request a range of extreme conditions, such 

as: the maximum height wave with a period of 9 see, the maximum 

height wave with a period of 10 see, etc. The increased number of 

conditions increases the number of analyses required, but allows the 

design engineer to confirm which conditions produce the extreme 

responses. 

The maximum wave height method is best used when 

highly nonlinear and the spectral analysis method 

appropriate. 

the response is 

is therefore not 


A full probabilistic analysis involves calculating responses to the 

entire suite of possible environmental conditions. Statistical 

analysis of these responses is then performed In order to predict a 

suitable extreme for each response. This requires far fewer 

assumptions on the part of those who supply environmental criteria, 

but a much more extensive set of environmental data. 

/ -. 

With the wave spectrum method, a set of wave spectra are provided by 

oceanographers or meteorologists. The RAOS for the response of 

interest are squared and multiplied by the wave spectrum. A wave 

spectrum is assumed to represent a Gaussian random distribution. 

Since the response spectrum is created by a linear multiplication, 

the response spectrum also represents a Gaussian random 

distribution. 

be calculated 

maximum, etc. wave heights. 

The significant response, maximum response, etc. can 

using the equations for calculating the significant, 

The equations 

response: 

for maximum wave height are summarized here in terms of 

B-16

Significant response, (DA): 

R5 = 4.00*(mO)~ 

Maximum response in 1000 cycles, (DA): 

R1/looo = 

7.43*(mO)~ = 1.86*Rs 

Maximum response is t hours, (DA): 

R max 

= 2*[2*mo*ln(3600*t/Tz)]$ 

where m. is the area under the response 

spectrum, 

Tz is the zero-up-crossing period of 

from the equation, 

the response as found 

Tz = 2~*(mo/m2)4, and 

m2 

is the second radial frequency moment of 

the response spectrum. 


In order to determine the normal day-to-day motions and stresses to 

assess motion related downtime and fatigue damage, the distribution 

of wave heights versus wave periods are considered. A wave scatter 

diagram condenses and summarizes wave height and wave period 

statistics. It is a two-parameter probability density function. 

Typically a wave scatter diagram is presented as a grid of boxes, 

with one axis of the grid being average zero-up-crossing periods and 

the other axis being significant wave heights. Within the boxes of 

the wave scatter diagram are numbers which represent the percentage 

of the sea records having the corresponding characteristics of Hs and 

Tz see Figure A-2. 

B-17

A response scatter diagram could be generated by taking the wave 

spectrum.for each sample used to.create the.wave scatter diagram and 

performing a spectral analysis for the response. The computed 

characteristics are then used to assign the percentage of occurrence 

to the appropriate box in the response scatter diagram. This entails 

considerablework and can be simplified by reducing the number of sea 

spectra considered, as described below. 

B.4.1 

Special Family Method 

All of the original sea spectra used to define the wave scatter 

diagram must be available, in order to select a special family of sea 

spectra to represent the whole population. 

The sea spectra are first grouped by wave height bands, such as O to 

2 ft significant wave height, 2 ft to 4 ft H~, etc. The average 

properties of the spectra within a group are computed. Within each 

group, which may contain thousands of sample sea spectra, a small set 

of sea spectra are selected to represent all of the spectra in the 

group. The small set will typically contain 4 to 10 spectra. 

The spectra of a representative set are selected by a Monte Carlo 

(Shotgun) process which randomly picks, say 8, spectra from the 

group. The mean spectrum and the standard deviation of the spectral 

ordinates about the mean spectrum are computed for the 8 spectra. A 

weighted sum of differences in properties between the 8 spectra and 

the total population of the group represent the “goodness of fit” of 

that set of 8 spectra. 

A second representative set of 8 spectra is then selected from the 

group, and the “goodness of fit” of the second set is computed. The 

better set (first or second) is retained and compared to a third 

sample of 8, etc. The process is repeated many times, say 1000, 

within each wave group. 

R-18

From this process, the original number of sea spectra, which may have 

been thousands, is reduced to the number of wave height bands times 

the number of spectra in each representative set. 

B.4.2 

Wave Spectrum Method 

A reduced set of sea spectra can be generated to represent the 

variation of Hs and Tz as given in a wave scatter diagram. 

If the original sea spectra are not available, a set of sea spectra 

can be created directly from the wave scatter diagram. In this case 

the shape of the spectrum must be assumed. For various areas of the 

world’s oceans, preferred mathematical spectrum equations exist. For 

the,North Sea, the mean JONSWAP spectrum is preferred. For open 

ocean, the Bretschneider (ISSC) spectrum is preferred. For the Gulf 

of Mexico, the Scott spectrum has been recommended. 

Using the Hs and Tz for each populated box in the wave scatter 

diagram, and the selected sea spectrum equation, a set of wave 

spectra are defined. With this method the number of sea spectra is 

reduced to the number of populated boxes in the wave scatter diagram, 

but no more than the number of wave height bands times the number of 

wave period band. 

B–19

2.4 

2.2 

2 

1 

‘Sen &-”Swull$p~ctru 

1.8 

SEA 

1.6 

1,4 M’ 

1- 

SWELL 

1.2- 

0.8- 

0.6- 

I 

/ 

0.4- #---- 

0,2- 

0 I 1 # i 1 I i 1 

0.2 0,8 1 1.4 1.8 2,2 2.5 3 3.4 

RodialFrequency(md~see) 

z 

I 

E 

1.2 

I 

1.1 - 

1- 

0.9- 

1 

Iicspmse A-nplitudcOpcrotur 

0.8- 

0.7- 

0.6- 

0,5- 

0.4- 

0.3- 

0.2- 

0.1 - 

0 

0.2 0.8 1 1.4 1.8 2.2 2,8 3 3.4 

Radial Frcqurwmy 

(md/see) 

0.9 

I 

Rtspcmse 

Spectrum 

k 

0.8- 

0.7- 

0.6- 

0.5- 

0.4- 

0.3- 

0.2- 

0.1 - 

0 # 1 1 # 1 1 [ 1 I 1 i ! 

0.2 0.8 1 1.4 1,8 2.2 2.s 3 3.4 

Figure 

Rsdbl Frsqusney (rod/%w) 

B-1 Sea Spectra, Response Amplitude 

and Response Spectrum 

Operator (RAO) 

&

APPENDIX C 

STRESS CONCENTRATIONFACTORS 

CONTENTS 

c. STRESS CONCENTRATION FACTORS 

C*1 OVERVIEW 

C.1.l Objectives and Scope 

C*l.2 Current Technology 

C.2 STRESS CONCENTRATION FACTOR EQUATIONS 

C*2.1 

C.2.2 

Kuang with Marshall Reduction 


C.3 PARAMETRIC STUDY RESULTS 

C.3.1 

C.3.2 

Ffigures 

Tables 

C.4 FINITE ELEMENT ANALYSES RESULTS 

C.4.1 

Column-GirderConnection 

C.5 REFERENCES

L ‘2

c. STRESSCONCENTRATIONFACTORS. 

C.1 OVERVIEW 

C.1.l 

Objectives and Scope 

A comprehensive document on stress Concentration factors (SCF) would 

include assessment of test results, detailed review of empirical 

equations, evaluation of finite element studies, and presentation of 

parametric studies showing the sensitivities of parameters affecting 

SCFS. 

The objective of this appendix is limited. Following a brief 

discussion of empirical equations, parametric study results are 

presented to assist the engineer in avoiding undesirable joint 

details. The sensitivity and interaction of variables shown in 

tables and figures also allow quick assessment of steps necessary to 

improve other geometries. 

Empirical formulations are applicable to a limited range of simple 

joint geometries. A complex joint often requires carrying out of a 

finite element analyses (FEA) to determine the SCFS. The results of 

a FEA is also presented to illustratethe applicable SCFS for a given 

geometry. 

— 

C1.2 Current Technology 

The SCF values can be computed through the use of a number of 

alternative equations. These equations have been mostly based on 

analytical (finite element) and small-scale experimental (acrylic 

model test) work. The tests carried out on joints that reflect those 

in-service (i.e. both in size and fabrication methods) are few and 

limited to several simple joint configurations. Thus, the equations 

available should be reviewed carefully to ascertain their range of 

validity and overall reliability prior to their use in design. 

Considering the simple joint configurations of T, Y, DT, K and X, the 

equations available for use in design are: 

c-l

o Kuang (ReferenceCl) “ 

o Wordsworth (ReferencesC.2, C.3) 

o Gibstein (ReferencesC.4, C.5) 

o Efthymiou (ReferenceC.6) 

o Marshall (ReferenceC.7) 

o UEG (ReferenceC.8) 

There are significant differences in the validity ranges of these 

equations. The SCFS computed based on different equations also often 

vary considerably. The Kuang equations are applicable to T, Y, and K 

joints for various load types. Wordsworth and Wordsworth/Smedley 

equations are applicable to all simple joints. Gibstein equations 

are applicable to T joints while the Efthymiou equations cover T/Y 

joints and simple/overlappingK/YT joints. The equations proposed by 

Marshall are applicable to simple joints, based on those equations by 

Kellogg (Reference C.9), and were incorporatedinto API RP 2A. 

Substantial work has been carried out to validate the applicability 

of various SCF equations. Although some of the work carried out by 

major oil companies are unpublished, such work still influence ongoing 

analytical and experimental research. Delft von O.R.V. et al. 

(Reference C-10) indicate that the UEG equations offer a good 

combination of accuracy and conservatism while the Efthymiou (i.e., 

Shell-SIPM) equations show a good comparison with experimental 

data. 

Ma and Tebbet (Reference C.11) report that there Is no consensus on 

whether a design SCF should represent a mean, lower bound or some 

other level of confidence. Tebbett and Lalani’s (Reference C.12) 

work on reliability aspects of SCF equations indicate that SCF 

equations underpredicting the 5CF values in less than 16% of the 

cases can be considered reliable. Thus, when presenting the findings 

of 45 elastic tests carried out on 15 tubular joints representing 

typical construction, Ma and Tebbet report that Wordsworth, UEG and 

Efthymiou equations meet this criteria and offer the best 

reliability. 

c-2

Ma and Tebbett also state that while both UEG and Wordsworth 

equations overpredict X joint SCFS, none of the equations overpredict 

the K joint SCFS. The comparative data indicate that the SCFS 

computed using Kuang and Gibstein equations for T/Y joints subjected 

to axial loading under predict the measured data in more than 16% of 

the cases. (See Figure Cl-l). 

Tolloczko and Lalani (ReferenceC.13) have reviewed all available new 

test data and conclude that reliability trends described earlier for 

simple joints remain valid and also state that Efthymiou equations 

accurately predict the SCFS for overlapping joints. 

c-3

C.2 STRESS CONCENTRATION FACTOR EQUATIONS 

C.2.1 

Kuang with Marshall Reduction 

The Kuang stress Concentration factor equations for simple 

unstiffened joints are shown on the following page. The brace stress 

Concentration factor equations include Marshall reduction factor, 

Qr. The validity ranges for the Kuang stress Concentration factor 

equations are: 

Term 

d/D 

T/l) 

t/T 

9/D 

D/L 

6 

Validity Range 

0.13 - 1.0 

0.015 - 0.06 

0.20 - 0.80 

0.04- 1.0 

0.05 - 0.3 

25-90 

. 

where, 

D = chord diameter 

T = chord thickness 

d = brace diameter 

t = brace thickness 

9 = gap between adjacent braces 

L = chord length 

e = angle between brace and chord 

c-4

C.2.2 


The Smedley-Wordsworth stress Concentration factor equations for 

simple unstiffened joints are shown on the following pages. The 

notes for the equations shown on the following pages include the 

Shell d/D limitation of 0.95. This interpretation is open to a 

project-by-projectreview. 

The validity ranges for the $medley-Wordsworthequations are: 

Term Validity Range 

d/D 0.13 - 1.0 

D/2T 12.0 - 32.0 

t/T 0.25 - 1.0 

91D 0.05- 1.0 

2L/D 8.0 - 40 

30 -90 

where, 

D = chord diameter 

T = chord thickness 

d = brace diameter 

t = brace thickness 

9 = gap between adjacent braces 

L = chord length 

= angle between brace and chord 

c-5

C.3 PARAMETRIC STUDY RESULTS . 

C.3.1 

= 

The Kuang and Smedley-Wordsworth chord stress Concentration factors 

for T joints are shown in Section C.3.l(a) and C.3.l(b), 

respectively. The Kuang and Smedley-Wordsworth chord stress 

Concentration factors for K joints are shown in Section C.3.l(C) and 

C.3.l(d), respectively. The Smedley-Wordsworth chord stress 

Concentration factors for X joints are shown in Section C.3.l(e). 

Since the chord side of the weld stress Concentration factor is 

generally higher than the brace side of the weld stress Concentration 

factor, only the chord side of the weld stress Concentration factors 

are shown. 

C-6

C.3.l(a) Kuang Chord SCF’S for T-Joints 

The Kuang chord SCF’S for T-joints are shown on the following 

pages. The following parameters are assumed for the Kuang figures: 

1) y = D/2T = 12.0 

2) Q = = 30.0 degrees 

3) = = D/L = 0.0571 

c-7

30. 

2s , 

20. 

15. 

10. 

5. & 

wORDSWORTH 

o 

05 IO IS 20 25 30 35 

Prod$ctOd SCF 

35- 

30. ● 

25, 

20- 

1s . 

10. 

5, 

KUANG 

o 

05 10 15 20 25 30 : 

Prmdmlod SCF 

359 

30. 

25. 

20. 

15. 

10. 

LEG 

o 

05 10 15 20 25 30 35 

Prmdxlod 5CF 

05 10 15 20 25 30 35 

PfOUctod 

Scf 

wJoInl ln$fd~ Oulsldo 

Tyoa V41#d,ly Vmllalty 

TIY ● ● 

K A b 

x o ● 

05 10 15 20 2s 30 : 

Prod)cltd EiCF 

Fig. 6-R~sulta o? compmnson—axial loading.

ChordSide 

BraceSide 

K-Joinlx 

SCFCX = 0.949‘y 4.666~4.059~1.IWq0.067sin1.521d SCFbX = 0s25y4“157g4.44170550~0.05S~1.44sin 

SCFW “ lao~ 

4.3 ~0.06 ~o.94 sin 0.9 e 

SCFbV = 2.827 B a-m To-% sin050 

—. 

for O“

ChordSide Brace Side 

K-Joints 

SCFU = 1.8(rsinflfi) SCFbx = 1.0+ 0.6 Qr [1.0 +{;. SCFCX] >1.8 

SCFCY = 1.2(7 sin6fi) SCFby = 1.0 +0.6 ~ [1.0+%; SCFCY] >1.8 

SCFU = 2.7(rsin6fi ) SCFbz = 1.0+0.6Qr [1.0+~j. SCFU] >1.8 

Y-BranchJoints 

SCF Kuang = 2.06yoS808e“l“2~ (sin 6) 1 “694 71.333 

SCFAWS = 14rsind fory 25 

SCF cxmod 

= SCFCX +TcOS0 

SCFTC = SCFKuang s SCFAWS 

scFTb = 1.0+0.6 Qr [1.0 +/#. SCFTC] >1.8 

>SCF cxmod 

> SCFbX 

SCFY 

= sameasfm K 

SCFY = same as for 

K 

SCFZ = same asforK 

SCFZ = sameasfor 

K 

UnreinforcedCrossJoin= 

SCFX = 1.333(SCFTC) ~ branch+ ~ 

. 

SCFbx = 1.0+ 0.6Qr [1. O+@ SCFXI >1.8 

SCFY 

= 1.333 (SCFCY) 

scFby = 1.0 +0.6 Qr [1.0 +3. SCFY]>1.8 

SCFZ = 1.333(SCFCZ) 

SCFbz = 1.0+0.6Qr[l.O+~. SCFz] >1.8 

angle betweenbraceandchord 

candiameter 

canthickness 

nominalchord thickness 

,, 

brace diameter 

stub thickness 

tA- 

(D–T)/2T 

dlD 

exp [-{0.5 T + t)~~t] 

MarshallFormulas Used for computingStressConcentration Factors 

-7 ‘3

Chord 

Sidg 

SCFCX= 1.7yT~(2.42 - 2.2S#2”2)sir$2(15 - 14”4P)6 

SCFCY=0.75y”*6r0”8(I .6#;14- 0.7~2)sin( 1.5– 1.66)6 

SCF~ =T@{l.56– 1.46~5)sh#2f15– 14.~)o 

Brace 

Side 

SCFbx= 1 + 0.63 

ScFby= 1+ 0.63 

SCFbz= 1+ 0.63 

SCFCX 

SCFCY 

SCFW 

Where 

~= BraceDiameter/ChordDiameter 

7=ChordRadius/ChordThicknes 

T= BraceThickness/Chord Thicknes 

O= AcuteAngleBetweenBraceandChord 

— 

SmedleyFormulasUsed for Computing Stress Concentration Factors 

for Unreinforced Cro= Joints

Definition of Parameters, Validitv Ranges and No:es OKI Tables 

o 

Definition of Tubular Joint Parameters 

~= 2L/D where D = chord outside diameter 

P = d/D T= chord vail thickness 

t = D12T L = chord length (distance between points of 

concraflexure) 

T = c}T d ● bkace outside diarnecer 

t ~ brace vail thickness 

~ ‘s/D g = gap between adjacenc braces 

Validitv Ranqes Eor Parametric !Zcuacions 

a ~4~&o 

O.lj:p:l.o 

12

(3) Table 2 only 

.. 

(l)-~f~ ~ 0.95 for out-of-plane bending then use ~ = 0.95. 

(2) The equations indicated for K and KT join~s apply only to 

loading on,all braces in che same direction for ouc-of-piane 

bending. 

(&) TabLe 3 only . 

(1) FOC K joints in ouc-of- 

(~ ~ l+t&’e”::: ; > 0 

by che carin i - . -“ 

ding replace the conscant 0.9 

(2) For KT joints in out-oi-ulane bending replace the conscant 0.8 

by the carm (1 - 0.1 1+4!J2 when < ~ O. 

....

-, 

l— 

I 

+ 

?1 

-— 

I 

. 

4> 

a ,- 

I 

I 

+ 

x 

N 

—4 ---- 

m 

/k - 

. . 

-c 

ii 

C.1 

I 

m 

Q 

; 

c-v 

:-: 

x 

w 

b 

u-l 

w 

o 

P 

-. 

“1 

+ 

(- 

a 

-— 

I 

I 

1 

I 

I 

! 

! 

1 

---

‘1 

——. -.— ——. . ..-—_____ . 

-- 

ICIIJT TYPE ~!ltI LO ADI:J(; 

,- 

Id.1-11 Ir t 

...- —..- .-. 

F1., 

.—. 

-:llnrJ 

.. 

—-. , 

-& ,. . :.:L 

‘L_ . _ 

— ..—.—-— .— 

+.3 

::-r 

Dr, X d::r,~$ .—. _ 

-...----- —- ——-— .- ——- -— ---- —- 

I: HORD, !i.lDDLE SCF 

— —-. — -- 

CHORD, CROWt4 SCF 

0.757 ‘6 ,0”5 (t.6&”25= 0.7f12) S,j’”5-J’6dh 

7Tfl(l.56- 

l.41j~5)S,,, 

(fJ7(15-14.4f3 ))0 

SCF=O 

K J() Ilfi. 

- .-- —__ —___ 

;(”I . ;IL15 

-. 

/ \ 

L- 

c-. ~ 

/q “ 

..-.’ 

—._ __ . .._- ,____ .- —---- . 

—-.. -— 

. 

-d 

%? 

-. . .. -. . .. --- ————— _______ -—. ..-__ ____ --- -----—-——--..---—— — __. — —,

Kuang SCF Computdion 

1 

L 

u 

UI 

\ 

f- 

1- 

0- 

0.2 0.4 0.6 

0.8 

Beta = d/D

5 

4 

L 

u 

w 3“ 

9 

t 

o 

-. ii 

Ic 

Kuang SCF Computation 

T 

2- 

1 

0 

0.2 0.4 0.6 

Beta = d/D 

O*8 

. 

1

., 

I 

, 

1- out— FIano SCF 

m 

tg 

n 

II 

~ 

J

C.3.l(b) Smedley-Wordsworth Chord SCF’S for T-Joints 

The Smedley-Wordsworth chord SCF’S for T-joints are shown on the 

following pages. The following parameters are assumed for the 

Smedley-Wordsworth figures: 

1) y = D/2T = 12.0 

2) Q = = 30.0 degrees 

3) = = 2L/D = 35.0 

The Shell d/D limitations have not been imposed for the SCF 

calculation. 

----- 

C-8

— 

6 

Smedley-Wordswoti 

SCF Computation 

c 

5“ 

!) 

IL 

9 

4- 

\ 

.,.. -, 

I 

I 

L 

u 

3“ 

4 

\ 

..> 

.-. \ 

u 

. 

“x 

< 

0.2 0.4 0.6 0.8 - 1

— 

&. 

15 

Smedley-Wordsworth SCF Computation 

14 

13 

12 

11 

1t 

10 

9 

8 

{ 

I ,,... 5’ I 

7 

. 

,,-.. 

“; 

(/l 

u 

“x 

< 

1- 

6- — — 

5 

4 

3 

2 

1 

0 

+ 

0.2 0.4 0.6 0.8 1 

Beta = d/D

T ln— Plan- SCF CrOwn POsltlon 

o - 

-s= 

u-l 

f 

,’)

— 

-. 

.... 

5 

Smedley-Wordswotih SCF Computation 

c 

o 

4 

3 

“-‘ : 

I 

I 

M 

2 

. 

L 

I 

4J 

i 

1 

0- 

0.2 0.4 0,6 0.8 

1 I i I 

1 

Beta = d/D

C.3.l(C) Kuang Chord SCF’S for T-Joints 

The Kuang chord SCF’S for K-joints are shown on the following 


1) y = D/2T = 12.0 

2) o = = 30.0 degrees 

3) a = D/L = 0.0571 

c-9

— 

5 


4 

IL 

L) 

(/l 

3- 

I 

1- 

kJ 

0“ 

0.2 

0.4 0.6 0.8 

Beta = d/D 

I

5 


4 

IL 

u 

M 3 

Q 

c 

i! 

—. 

-1 

c 

2 

Y 

( 

4 

[ 

1 

0- -44 

I 

0.2 

0.4 

i 

I 

0.6 0.8 1 

Beta = d/D

j 

K Out— ~lanq SCF 

‘?’ 

+ 

F 

.

C.3.l(d) Smedley-WordsworthChord SCF’S for 

K-Joints 

The Smedley-Wordsworth chord SCF’S for K-joints are shown on the 


Smedley-Wordsworthfigures: 

1) y = D/2T = 12*O 

2). o = 02 = 30.0 degrees 

3) ~ = 2L/D = 35.0 


calculation. 

— 

c-lo

, 

5 

Smediey-Wordswotih SCF Computation 

4< 

m 

3. 

2- 

1- 

Oj 

I i I 

0.2 0.4 0.6 0.8 1 

Beta = d/D

. 

,i 

5 

Smedley-Wordsworth SCF Computation 

s 

o 

4 

o 

u 

u 

u 

u) 

3 

I ,._.., I 

. ,- 

IL 

o 

u) 

2 

u 

!t 

1 

0 

1 1 I I I I I 

0.2 0.4 0.6 0.8 1 

Beta = d/D

Smedley-Wordswotih SCFComputation 

* 

i 

o 

L 

.—. 

1 

I 

IL 

u 

m 

/ 

/ 

I 

-’l 

0 

c 

u 

L 

I 

c 

0.2 

I--l 

0.4 0.6 0.8 1 

[

I 

I 

K Out— Plan= SCF —— Saddle Pos Itlon 

o 

L 

o - r= 

I 

t 

G-4 

+ 

m . 

.

C.3.l(e) Smedley-Wordsworth Chord SCF’S for X-Joints 

The Smedley-Wordsworth chord SCF’S for X-joints are shown on the 


Smedley-Wordsworth figures: 

1) y = D/2T = 12.0 

2) @ = = 30.0 degrees 

3) m = D/L = 35.0 


calculation. 

C-n

- 

10 

Smedley-Wordsworth SCFComputation 

9 

t 

o 

“n 

o 

n 

7 

8 

I 

I 

IL 

u 

ul 

u 

5 

4 

3 

–x 

2-— n 

1 

0 

O*2 0.4 0.6 0.8 1 

Beta= d/D

\ 

Smedley-Wordswoti 

SCF Computation 

4 

3 

2 

“1 

.. 

: 

0 

ii 

Ic 

x 

1“ 

o- 

Beta = d/D

‘\, 

?v 

x out— Plan- SCF —— Saddl= Position 

II 

I 

T 1 T I I 

/

C.3.2 

Tables 

The Kuang and Smedley-Wordsworth chord stress Concentration factors 

for T joints are shown in Section C.3.2(a) and C.3.2(b), 

respectively. Since the chord side of the weld stress Concentration 

factor is generally higher than the brace side of the weld stress 

Concentration factor, only the chord side of the weld stress 

Concentration factors are shown. 

.- . 

C-12

C.3.2(a) 

Kuang Chord SCF’S for T-Joints 

The Kuang chord SCF’S for T-joints are shown on the following 


1) = = D/L = 0.0571 

C-13

I@q W ~tim 

T-juint Axial W 

Owd Side114hld 

1 

I 1 1 ~. l~o : Sml = 15*O I h= 20.0 : -=.=0 i 

: 1 

l— 1 

1 I I I ! 

: Theta= :Tau=; Ma am : Ma 4m : Ha=d/R ! Ha =dIfi : 

I 

1 It/T: 0.3: 0.5: 0.7: 0.9!0. 3:0.5:0.7:0.9 !0,3:0.5; 0.7: 0,9: 0.3: 0,s1 om7:o.q: 

!1 — 1—1—l—!—i—l—l—l—l—l—;—l—l—!—!—!—:—! 

1 

:0.20 !O.bn OAK 0.432o,2n:o.7570.6730,5MO,ab:o.% 0.849o.b540.411:1.1441.0170.7830.492: 

# 

1 i— ! 

i I ! I 

! 30.OdegSO.40~1.593 1,416I,w o,~;~.~ i,~ lm~ 0,~~zM7 ~1~ Iaw I,~&~ 2.W 1,~ lm241~ 

! 0m524rad;-! I I I : 

1 

I /0.tiZ73h2.W 1A72l,17i3;3.Zb Z?1322421.411;4,1343.k75ZG?91.7EO;4SW4.4013.= ZIQ; 

i ;—; 1 ! 1 I 

1 

I0.~14.0143.%92.747l,rn;4.OMl 4,2743.~ Z070!6.W5.3934,151L612;7.2Mb.450 4.972 3.lZl; 

I 

i 

I 0:20 !1.137 1.011 0,~ 0.4W!1.U2 1.211 0.932 O,WH.71q l.= 1.176 0.740 :2ME 1.H30 1.W O,Mbl 

I _l 1 

i 45.Odeg; O.U&fjbb 2.549 1.96j L23&m 3.@ Zw 1.47614,331 3,Ei0 2.9b4 1.fh5;5.167 4.611 3.550 2.~ 

i O,~radi-! I I 1 

: :0. bO 14,921 4,375 WE 2,119 ;5.~ 5.Z9 4.033 MZ4;7.~ 6.bll 5.W 3.202 ;8.91H 7.917 b.M4 3.0S 

1 

t ;—; I 1 I 

.-, ! !O.~17,221 6.4~ 4.942 3.11O;U49 7.&E 5.919 3.7Z4;1O,91 9,7M 7.4b7 4.699 ;13,0b 11.61 H.943 5,b27 

i :m :1*W41,4%1.097 O,m!l.m1.7071.314 

O.m?:zm21541.b5E1.043:2.902 2.5E) 1.W Lao! 

I 1 I—1 1 ; I 1 

I 

1 bO.Odqi 0.40 !4,041 3.~ ~7fi l,740;4,~ 4.302 3.312 2.~ lb.1~ 5m4~ 4,179 2.~;7,312 hm~l S,w 3,149; 

! L047radj-! 1 I I I 

1 

! O.M ib.9U b.ltl 4.74H 2,9Wi3.XEI 7.3E7 uw 3.ai10.4E 9.320 7,174 4m51&i5 11.16 E.592 5.Mb; 

I 

1 

;—~ 

: i 

i 

I 

I 1 

I 0.&l IIO,lH 9.til 6.967 4.W4 :1219 10.83 8.344 $.ao 115.a 13967 10.Q 6,&L42 16.37 12.KI 7.933; 

1 

: 0.20 :2.OM 1.819 L4W O.ml KL451 2.in 1.677 1.055:3.092 Z74? 2116 1.33113.703 3.292 2.534 1.595: 

i ;—: 1 1 

I 

1 

I 

I 

1 

1 

90.Odegi 0.4 ;5.j5j 4,~ 3.= ~~;&.1~ S,#j 4,% 2&~7a790 6.% ~,~ 3m~~q,~ g,~ b.= 4m019 

i 1.571 radl-l 1 

I 1 

1 

! 0.bOM52 7470 ME 3.612 ;1O.M ‘?.4= 7.= 4.%5 !13,37 11.E9 9.154 5.7&4&Ol 14.24 10.96 6.6% 

1 1 l— i i 

1 

; 

1 

!o.81ilz9a 11.54 H.m 5.594 !15.5 13*U lo.b4 6.II W;19.U 17.44 13.43 B.m H3.54 m.w ltl.lm 10.12

KuwqSE _im 

T-joint In%neW 

UrrdSickofkld 

1 

I 

I I1 a = 12.0 ! a= 1s0 I ~. ~,o : h= ao ! 

1 I l— ! 

I ! ! I 

I llwta=!Tw=; W#D ~ Ma=d/D : W=dll : *W i 

I :tfl:o.3: 0.5:0.7:0.?!0.3:0.5:0,7:0.9!0.3:0.510.7:0.9!0.3: 0.5:0.7:0.9! 

~—;—~ — 1 —I—i—!—!—f—{—!—I—! —] —l—~—]—l—j 

: !0,~;0.551 ‘0.540 O.~ 0.S28:0.63;0.6180.410o.~ ;0.7490.7340.7240.717!0S70,640O.= O.E?O! 

) I_l 

: I 1 f 

! I 30*0dq;0,40h.ml 0.9Mom9M0.95E!1.145Lln 1.107i.m ;1.3?61 l.m 1.3151.302;1.5561.=41s041.469; 

! o.n4rdi—! : i i 1 

~ 

:0.60:1.419 1.391,3721.358!1.6231.901.5b~l.= !1,9291.8901.864l.Mb12203MO 2.1312J1O; 

1 ~—~ I I 1 1 

I 

:O.@!1.S181.781.7571.740ELOn2,036Zm 1.589;Z470Z4B 2.= 2Jb4;U24 Z767 2.7?4 2703 ; 

1 

:0.20 :o.&n O.= 0.650 0.643 !0.766 0.7s5 0,743 0.75:0.913 0.89s O.m 0.674:1.044 1.OZ 1.009 0,999: 

I_ I I 8 I 

i 

45.0 dq; 0,40 bII 1,155 1.179 1.16H;1,3% 1.367 1.349 l.= ;l.H 1.624 1.603 l.~ ;l.1%% l.~ 1.832 1.814! 

i 0,7WIrdi—i : # 1 

i 

1 

I :0.60 H.729 Lb94 1.672 1.655:1.977 LW I.fll i.~ ;~~ Lx 2,272 29249b ~b32 2.597 2S71 : 

! I~—; : 1 1 1 

I i O,m R215217021412120KLm 2.481 2AM 2A24 ;3.0102.?49L9W Zw A 3.3713.Q6 3*293i 

1 

! Oa !0.754 0.739 Omm 0.722:0.863 0.B45 0,E34 O,EH:1.025 i.w O*W1O.ml !Li72 L148 Li33 1.12 

i .~—~ 1 

: 

# 

! 60.0 deg! 0.40:1.370 1.342 1.Z!4 1.311;l.X4 1,S4 1.514 1.49911.861 1.623 1.799 L7Sl ;2.U3 2sW 2.057 2.036 

i 1,047radl-1 1 I 

i 

# 

1 

! O.M ;1.941 1.W 1.877 1.EH !’2.ZO Z175 2.146 2.124 ;2.t211 2.= 2.5W 2.Z4 :3.016 2.955 2.715 2.N 

1 :—j : 1 I 

1 

i O.M :2.486 2AM 2404 2sW HJ43 Z7H L748 2.721 ;3.~ 3.310 3.264 3.2S ;3.0S 3.704 3.734 3A9b 

1 

1 I 0.20:0.819 O.~ 0.792 0.7B4 10.936 0.917 0,9M 0.89611.113 1,090 l,07b 1.065M72 1.247 1.230 1.21B 

( I l— i : 

i 

I 

1 

90.0 degi 0.40 !1.487 1.457 1.437 1.423 ;1.700 l,b& 1.M 1.627 ;Zm 1,979 1,?53 1,~ H.31O 2.263 2.~ 2.210 ! 

1 1.571 radl-! 1 I , 1 , 1 

1 

! 0.64 !2J07 2.M 2037 2.o17 ;zW 2.361 z.~ 234 !zE63 2.KU 2.764 2.740 ;3.z74 3.B7 3.164 3.133i 

i I —1 I 1 I I 

1 

; O.W i2.6W 2.644 2.M9 2.W3 ;3.U36 3.023 2.%3 2~ ;3,647 3.593 3.545 3.W9 i4.193 4.lM 4.053 4,012~

-- -- -- .- -- -- -- -- -- -- .- -- -- . . -- -- -- -- -- -- -- -- .- -- -- -- -- -- 

“. -- -- -. 

as ------- -.-.- 

-.4’K.. 

..--.--..-k d=lw .- 

iniiii 

i? 

u 

.- -- .- .- -- -.. . . 

niini 

-- -- -- -- ..- -- -. 

iiiiiiik 

-- -- .- - -- . . -. 

glij$g 

-- -- -- .- -. -- -- 

iiiiiii 

ii 

-- -- .- .- -- -. -. 

NH 

-- -. -. -- -- -- -- 

Uinil 

iiiiiii 

Him 

ii 

.- - -. . . -. .- .- 

inib 

Uinii 

ii Fd iii 

uik ii 

. . -- -. -. -. .- . . 

USE 

.- -- .- -- . . -- .- 

Iii Uii 

iiviiii 

. 04 

-. -- -- -- -- -- .- 

-- -- -- -- -. -. -- 

.- -- -- -- -- -- -- 

.- -- -- -.. -- -- --

C.3.2(b) Smedley-HordsworthChord SCF’S for T-Joints 

The Smedley-Wordsworth chord SCF’S for T-joints are shown on the 


Smedley-Wordsworthfigures: 

1) = = 2L/D = 35.0 


calculation. 

C-14

— 

T-joint hid 

S5 Crm i%itim 

1 1 

1 i -= 120 : - = 15.0 ! ~= 20.0 j w=. a.o : 

1 ;—l I 1 

1 I t 

I 

: kh= ;Tw=l Ha 4/D ! b din : Ma*/o : h =dm 

I 

1 

I IWT : O*3!0.5: 0.710,9: 0,3! O,s: 0.7: 0.9: 0.3: 0.5: 0.7: 0.9: 0.3:0,5:0.7: 0.9; 

j—~— !— 1 

— 

1 

—1—l—!—l 

—l—l—l—l—!—l—l—l—l—! 

1 

I O.a :2447‘3.OSI ‘Mu 3.2H3 :2.929 3*N13.1773.21E :3J693*14a3.l&l3.166:3,207 3*m 3.* 3.145 ! 

I :—; I ! : I 

: W.o fkj 0.54 W23 5.7W Lm b.(m ;5.365.7195,9075*W1;sm~g~,~ 5,7935,~:5,716 5m~ 5,~ 5,=; 

I 0.S?4rad:-1 I 1 t 1 

: ! 0,25:8.15 9.361 %793 ?.~ k 140 %012 ?,ZJ1 9,015 ;8.276 E,W 8.891 R.= ;8.516 8.W7 8.7M MM ; 

{ 

i— r I ~ I 1 

f 

! 1*Mh 13.5 14.49 13.71ill.% 13.(U 13,44 1275 :11.4E 12.46 12.57 11.Q h 1M6 12J5 ilma ; 

.... 

..-, 

1 

1 i 0S 13.2U 3m&14.344 4.UO S294 3.W 4,320 4,7iZ :3.4~ 3.W 4,304 4.6W :3.E57 3.954 

4,311 4.651: 

I 

I —i ! 

I 1 

! 

1 M.O deq; 0,50 :5.74? 7.026 0.1~ 9.@ :5.06? 7,MI 7,% &EM ;kM4 7.(U3 7,905 MN k45 7.1~7,903 0,S1 ! 

I 1.047radi-! t 1 # 1 

) 

:0.75 :a.m10.M 12s27 13,52:s.643 10,47 11,95 13.10km 10.46 11,72 1273 k 10.57 11.66 i2.54 ; 

1 

1 

~—~ I 

i : : 

! lm~ :11.57 14.63 16.M 1H,33;11.65 14.~ 16.Z 17.ti :11.94 ]4.14 15.83 17.03:12.32 14.19 15.65 16.71; 

1 

i 0.3 i3.E14 3AM 4.6UI 5.W !3.1S 3.W 4S47 5.1?6 13.240 3.BW 4,511 5.CQ7!3S43 3.741 4.549 5.046i 

1 ;—{ t t 1 

i 

i W.Odeqi O.~ !5.%9 7,X5 H.6W 10.02;5.6!II 7.15# E.= %779;5.M2 7,184 8.422 9,= ;b.03S 7.2K 9.397 9.443i 

I 1.571radl-! I 

! i I 

I 

:0.75 :H.~ 10.81 13.ti 14.93;E.315 10,67 12.73 14,51:9.%4 10.64 12SI 14.13IH.E1410.71 12.41 13.93: 

I :—~ I I 

i 

i 

1 

: 1.M !!1.06 14.76 17.76 ZII,1O;11.14 14,45 17.22 !9.45 ;11.39 14.XI 16.7E 18.86:11.70 14,?3 MO 18.54!

T-joint Axial SF Saddle Posiiim

. 

T-joint 

In-PlaneSE UM P~itim 

., 

1 

~0.3 :0.M5 1.0)9 1.079 1,066loom 1.153 1.233 1.21? ;1,175 1.370 1.4M 1.449!1.343 1.567 1.h7b l,b7 : 

1 ;—~ : 1 1 I 

1 

45.0 dq; O,W ;I.w 1.7% 1,879 I.W 11,721 ?.~ 2.lW z.1~3 ;2,046 2.224 2.553 2.523:2.339 2.728 2,918 2.W5 ( 

I .0.785rad~—1 1 1 1 1 

i’ ~ 0.75 !2.083 2.429 2.599 2.5$9;2.331 2.778 2.971 2,931 ;2.830 3.301 3.ECfl3.490 ;3.25 3.774 4.037 3.’?91 i 

1 :—; I 1 1 ! 

n 

iLoo i2ab22 3.059 3.271 3.234;2.%113.497 3.740 3.W7 !3.%2 4.155 4,445 4.34 ;4,073 4.751 Lou 

5*OZ: 

1 

:0.25:1.063 1.162 L165 l.om !1.214 1.329 1.32 1.234;1,445 1.579 low 1.447:1.652 1.W 1*E1O1.577: 

I :—~ 1 

; 

1 1 

1 

60.0 deql 0,50 il.852 ?.024 2.029 I.w 12,117 2.314 2.~ 2.149 !2.516 2.755 2,757 ?.554 ;Z87k 5.144 3,152 2.9?0 ; 

I 

! 

i,C-47rad:—: 1 [ 1 

1 

1 ! 0.75 :2.5Li 2.W 2.907 2.6W :2.92j 3.201 3,.W 2.973 ;3.W3 3,!304LU4 :.533 h9 4.3XI 4,360 4.039; 

~—~ I 1 1 I 

: I.W !3.224 3.Z5 3,573 3,273!3.&4 4.030 4.04433.742 !4.381 4,7E9 4,801 4,440:5.009 5.475 5,449 5m’OK! 

1 

1 

: 0.25:1.231 1.% 

:—; 

1.231 1.OW!l.4c4 1.470 1.407 1.245!1.673 1,747 1,672 i.480 :1.913 i.W7 1.912 1.b92! 

1 1 1 1 

I 

90.0 dq.1 0,50 ;2.144 2.239 2.143 LW&;2.452 2.5? 1.450 I.IM ~Z.9143,~2 1.912 2.576 K3ZS 3.47H 3.329 2,9% ; 

I 1.571radl—1 I 

i 

1 ! 0.75 il.% 3,097 2.W5 2.h23 !3.391 3.540 Z.W 2.9W !4.034 4,207 +.02B 3.’%4:4.M9 4.010 Lb05 4.074; 

! {—; 1 z 1 1 

1 

: 1.00 !3.734 5.WR 3.TL 3.302!4.26’?4.457 4.267 :,775 !5.073 5.296 5.070 4,4S6;5.W 6.055 5.7W 5.129 ;

-— 

T-joint CtkuHlane ELFSaddlePcisitim 

;—~—j _~_~_ ~ —l— l—~— :— 1— I —;— ;—1— ,—, 1 

— j_ 

1 

I ! 0,5 !0,527 0.773 1).m O.w ;(),W ‘%%7 1.031 ().6% ;Omm ‘imm 1.375 O*9ZI;1s103 1.612 1,719 1.15’? 

I ;—: 1 1 1 

t 

?%0daq~0.50 !I.OEN1.547 l,b50 1.112;1.324 1.934 2.W 1,390!l.7& 2.579 2,755 1,E54:2.207 3.224 3.439 2.31E 

I 0,524rad:—; I 1 1 

I 

! 0.75 !1.58’+2.321 2.475 1,6M k 2.902 3.094 2.wb ;2,b47 3,@M4,125 ?.7E1;3,311 4,W7 5,157 3,477 

! 

:—! I t I x 

! ! 1,00:1.119 3,095 3.W 

1 

2,23 ;?aMq 3,~94.1~2,711 :3,532 ~=j5q5,5M3.709:4.415 b,~q~,g~b~a~: 

!O,fi;O.E72 1,347L5bl1,176 ;1,0%) 1.6841.9sl1,4711:1.454 

;—~ 1 1 

2,2+5 2.b02 1.%4 !lAIE 2.EJ17:.252 2.45fJ: 

# 1 

1 

45.0 deq! 0,50 !1.745 2,h74 3.122 2.352 ;2.1!313.W 3,9Q3 2,740 :2,90B 4,471 5,204 3.920!3.b3b 5.b14 b.~ 4,9@ : 

! 

f 0.7fi rad;—; 1 [ 

; 

1 

$ 

~0.75 ;2.610 4,042 Lb03 3,520k.2R s.0535.K44,410 ;4.3Hb.7377.00b5.M%4540.4219,757 

7.351 ! 

I ;—/ 1 1 ; 

1 

1 

! 1.C4!3.490 5.399 6.245 4,704 ;4.%3 6,737 7,W 5.W ;5.817 8.?03 10.40 7,B41;7.272 11Z2 13.01 ‘?.601; 

1 

: O.fi 11.169 1.EM 2.2b7 1.82 !l, %0 2,329 2.K3 2.2j% !1,?47 3,10h ;.7i0 3.037 !2.434 3,= 4,723 3.7% i 

! :—1 

; 

1 [ 

[ 

1 

60.0 dey 0.50 !2.237 3.7274,n4;.M4:2.’%?1 4,L595.6474,5%;3.m b.2127,557!5.074 :4.063 7.X5q.w 7.593: 

! 1.047 radi—i # ! 1 

1 

1 

:9.75 !3.505 5.591 4,MII 5.4b7 14,X2 .5.%Q E1.ml .5,e3.4 ;5.W2 ‘q,31E 11.33 ~,112 ;7,303 11.64 14.16 11.391 

1 :—/ f 1 I I 

1 

: I.@ !4.h74 7.%5 ?.W 7.LW%.842 q.31B 11.33 7,11217,790 12.42 15.11 12.14h7 15.= 1S,69 15.16I 

1 

! 0.25:1.437 2.344 2.9FA 2.4E4 ;1.7% 2,732 3.h92 3,10a :2,~q 3.710 4,923 4,144 !2.994 4.~ b.154 5.lM ; 

- :—; 1 1 

i 

!. 

1 

?0.0 dqi 0.54:2,874 4.692 5,X4 4,W3 ;3,593 5.W 7.= A.21b14.7?1 7.U 7,047 a.= ;5.989 7.775 12.W 10.3b; 

; 1.571racll-! I t 1 1 

i %75 :4.312 7,03E S.M2 7.457 ~5.390 0,797 11.b7 q,E4 ~7.107 11.73 14.77 12.43h.9B4 14.bb lB.4b 15.54; 

;—; 1 

i 

1 I 

1 

: 1.C4:%74q 7.X4 11.81 7.W :7,10] 11.73 14,77 12.43:q.~ 15.& 17.h9 16.57;11.’77 Iq.Zj 24.M X.72 :

— 

i : m ! 0.3: O*5: 0.7: o*?: 0.3: 0.5: 0.7: 0,9: 0,3; 0,5: 0.7: 0.9! 0.3! 0.5! 0.7: 0.9 

:—; —i—:—i— — — — — — —! —!—l—!—!— 

I ! 0.20:0.427 0.414 0.406 ‘0.40) ;0.4% ‘o*Ml 10.471‘0.464 ;0,600 ~’m;o.w !0.6% 0.676 o.bb2 O.m 

t 

1 :—l I 1 I 

1 30.0 I@; 0.40 10.91E0.6?! 0.E73 0,860;1.065 1.034 1.o13 0,99Eh?tl 1.252 LW l.~ h 1.453 1.424 1.403 

I 0.524rail-l I t i : 

t 

i0.60!1.4371.3941“371.347iLbb71.6181.3 1.%2:20191.9591.921.89223432.2132.2292.1?6i 

# I 1—1 : : 

I 1 

1 

!O.W!1.9741.9151.878l.~ KLm 2g~ 2.1792147!2,774Lb%?2A9 Zw ;3.2193.lZ3.M23’.017 ; 

! 

IO.~!0,7240.702Om~ 0.b7E:0.840 0,M5 0.7W 0,7B7:1.017 0.9H7 0,967 0.953:1.10 1.145 1.122 l.iti ! 

: :—l I 1 1 

1 

I 45.0 degl 0.40 :L~ 1.510 1.W 1.4% ;L8E 1,751 1.717 1.69212.186 2J21 2.W 2J49 k 2.461 2.413 2.37Ei 

! 0.7% rti:-1 i i 

1 1 

: i 0.60MM 2.3k231b2.202i2.~21412A872647!3,4213.3J03,Z43.W ;3,9bq 3.~ 3.77b3.720; 

1 

I —1 i I : 1 

! I ;O.~&345 3.2453.lD3.1S13.~3.7653.b913.637;4.700 4,%1 4.4714AM !%4535.2915.1B75.111i 

1 

1 !0.20!0.9%0.9560.937O.m :1.1431.lUI1.W 1.0711.W 1.3431.317l.m :1.646I.= l*52al.m I 

I 

:— 1 t 

i 

1< i 

1 60.0d~l0.40;Z1182.052.015l.~ ;2.4Z2.W Zm 2303%97bZm 2.KH2.7W;3.45J 3.3513.= 3.Zb! 

I 1.047 rxll-1 : i 

1 1 

i i 0.60!3.3143.2153.lD 3.106;3,B453.7313.6S73,604{4.6574,5194.4Y 4,365;5.4035.2435.1405.064; 

1 :—: I 1 t t 

1 

: O.~ :4.= 4.418 4.Q1 4,267 ;5.2W S.126 5.M 4.%! ;bm~ b,~ 6.(M6 5.996;7.4237,2037.061b.557 ; 

1 

:0.20 :1.z?b 1.190 1.1661.149!1.423 l,m l.m 1,353:1.723 1.672 1.639 1.615:1.999 1.940 1.902 1474: 

: 

I—1 

: 

1 1 1 

i 90.0 deg; 0.40 ;2.634 HE 2A07 2.470!3.MB 2.9L4 2.W 2.EM :3.704 3.94 3.24 3.472i4.2Xi 4.170 4.OW 4.02Ei 

; 1.571rdi—1 1 t I 1 

I 

i 0.60 !4.124 4.W 3.~ 3.EM;4.E 4,643 4,5s? 4,M ;5,Rb 5.b24 5.513 5.M ;b.Z?5 b.= b.397 b.W : 

i 

I —1 1 I : ! 

I 

! O.~ ;5.M45.4q5.~ 5.311 ;6.574 b.m b.m b.lK ;7.963 7,726 7,575 7.443 :9.Z9 8.965 8,7W %.bW;

I 1 1 

1 1 ~. l~o ~ ha= 1s0 : ~. ~J ; a=ao i 

i ;—{ I I 

1 \ 1 i 

! W= !Tw=i ti#D i ti=d/o : M=d/u : *=IVD : 

i ! tll : 0.3! 0.5: 0.7: o.? ! 0.3: 0.5I 0.7: 0.9! 0.3; 0,5: 0.7: 0.9: 0.3: 0.5: 0.7: 0.9: 

:—~— 1.— 1 I —i—I—!—I—!—!—!—i—I—: —l—i—!—l 

1 

I ! 0.20;0.s14‘0.S0 ‘0.5410.54910.559 0.5770,5890,598:0.6240,6440.6570.647!0.679o.7m0,7150.726: 

! i —t I I I 

: 

t 

30.Odtqi O.40;0.m 1.017l.~ M54;L074i.107l.1~1.147;Ll~1.ZSl.~ 1.279;1.304 1.3441.372l.~! 

: 0.!E4rtij-! 1 1 

: 1 

I 

!0.60:1.444 1.4891.S201.543;l.m 1.b21,6s4M&54 1*W 1,8451.873:1*WI.w 2.W 2.039; 

: 1,—1 1 I 1 I 

# 

;O.Ol&f l.~ 1.992.022;2.060 2.1242.16$2.201&l 210 2.41SZ~;2.S02La 2A32LbR; 

I 

i 0m3~0.702 0.724 0.739 0.Z4 :0.764 0,7M OM4 0,816 :0.~ 0.879 0,897 0.91110.928 0.957 0,977 O.Wl { 

i :—: I I [ I 

1 

# 45.0 deqi0,40U48 1.390 1.410 1.439;1,467 1.513 1,543 1,5b7;i.b3b 1.W 1.722 1.74&81 1.W 1.874 l.~; 

I 

! O.~raU—l 

I 1 

: 

i 10. M:l.w3 2&4 2m07b2.107;M8 U14 NM 2.Z4;U9b L470 2S21 2.S9hCtl 2.hW 2.744 L7M: 

1 

I 

1 

1 —t t : 

I # 

i 10mKk!3b 2M L7212.762;2s815L902 2.761 3.0u 13.140 3.m 3.304 3.354:394103.5243.36 3.651i 

# 

! 0.20:0.843 0.8M O.w O.m !o.917 0.946 0.965 O.w!l.oz 1.0551.077 1.093:1.114 1.149 1.172 1.190: 

1 

I i,—~ 1 t I 

! 

I 

bO,Odeqi0.40 !1.617 1.664 1.702 1.7ZI;I.761 1.815 1,~ i.mi ;1,?64 2JE 2,066 2.C49!2.138 2.204 2.249 2,284! 

! L047rad:-1 t 1 t t 

1 

: o.bo :2.3b8 2.442 2492 2.519 ;Z57112.H 2.712 2,~;ZE75 2.9~ 3.&5 3.071;S,130 3.W 3.293 3.343; 

1 f—~ i i 

i 

1 

1 

: 0.kl!3.103 3.~ 3.2LS”3.315:L~ S.m 3.54 3.LuJ:3.7M 3.W 3,9B 4.u:4.j~ 4,~ 4.31b 4.3E2;

Ku&W 

Cr@atim 

K-jrnntiht++laae SF 

M Sik 114Md 

t 1 1 ~. 1~~ : & ❑ 15.0 I -= 20.0 : bm=ao I 

I 

[ i —1 1 1 

I I 

: TMiI= :Tu=; mta#D ; Ma =dm i w =dm ! maw : 

1 

:UT ! 0.3! 0.5: 0.56 !0.75; o,3:o.55! o,5b; o.75: o*3:o.s: o.%: o.nio.310*5:om% :0.75: 

:—~_ I —i— 

I —i— l— i—i—i—l—:—l—l—i—l—;—l—! 

1 

:0.20 ;0.400 0.645 ‘o,ku 0.557 :0.w2 0.w9 o.~ o,hw ~o.672 Low w2 0.936!O.E43tJ59 1.407 1.174: 

i : —1 i i 

1 1 

t 

24).0dql 0,40 ;o,742 1.196 i,= LOS :o.~ 1.4w Im5521,~ :I,2M 2.007 2,0n 1.734!L5M L517 2.iM 2.174; 

! 0.=4 radl-! i i i i 

: : O*M:1.064 1.715 1.77s L48i :1.334 2*1W 2.m 1.= !1,786 2878 Zm 2.487EL240 3AM 3.737 3.118: 

1 

!—1 1 

i I 1 I 

I 

! O.MIM74 2.214 22?2 1.?13 ;1.723 L777 2675 2.399 ;%3)7 3.717 3s848 3.12 h93 4.662 4.026 4,027: 

1 

i 0.20 iOA07 1.107 1.146 0.957:Omlk?1.39 1.43a1,~ !1.154LK19 1,925l.bM ;1,447 2231 2.413 2014 i 

1 

1 

:—: 

1 

! 0.20 !0.942 1.519 1.512 1,312!l.IU 1.904 1,971 1.645:l,!E? 2S49 2A? 2.X? !l.9E4 3.197 3.309 2.7&2: 

I 

; 

i 

i 

1 

KMdq; 0.40:1.745 2.013 2.912 2.430 !~jw 3.527 3,M1 3,047 ;2.730 4,722 4,m 4,079 !3.b74 5.~ 6.12? 5.115: 

! 1.047rad:-: i i 

I 1 

i 

: OJJ) :2.~ 4nN 4,175 3.~ :3.139 5.059 5mZb 4,370 !4.202 b.771 7.(N9 5X4 !5,269 8.45V B.7B9?,= ; 

i I,—; 1 

1 

; 

i 

1 

I O.~ :3.~ 5.2W 5.392 4.5M ;4.054 b.Sj2 b.7b2 543 :S,4W 0.744 9,0Q 7,555;b.8)5 10.9b 11.35 9.473: 

1 

t ! 0.20 il.179 1.9M L9b7 1.M1 :1.478 2.~ 2.4bb 2.o5E:1.979 3,1W 3.302 2.E5 :2.M2 3.W 4.140 3.455: 

1 I,—j 1 1 I 

! 

t 

90.0 dqi 0.40 ;2.184 3.519 3.643 3.040 ;2.~ 4.412 4.% 3,812 ;3,W 5.907 kl15 5,1K3 :4.597 7.407 ].U b.3W : 

! 1.571rd:—! : I 1 1 

! I ~O.ti :3.131 5.046 5.224 4.359 !3,927 b.Q7 b,~ 5.447 ;5.257 S,471 9.769 7.318 ;b,5W 10.b2 10.W 9.lV” : 

I ;—; I 1 I 1 

1 

! O.B) :L044 6.517 6.746 5.bJl ;5.071 8.171 .9.459 7.Obo;b.7W 10.?3 11.32 %451;8.513 13.71 14.20 11.5 ;

1 

! 

! O.fi ;0.762 %841 0,769 O,= !0.881 0.973 o,m o,673 ~1,~ 1,1~ I,071 u,B1l !!.n 1,35$ i,2~ 0,9~ 

I I—; 1 1 

1 

1 

1 

I 30.0dq; 0,50:1,525 1,M3 1.537 1.164;1,7L3 1,?46 1.777 1,36 :2,M 2.347 2,143 1.b2212,4~ 2.7:3 2.477 1.876 

{ 0,524radl—! 

i 

1 ! 1 

>, 

I 

1 

~—; 1 I 

I 

1 

45;0 dql O,M :1,B!4 2.M2 l,&2B 1,JE4;2,097 2.315 2,1i4 l,W) ;2.5M 2,7?1 2.548 ~.Y~ :2.923:.~ ~.?~ 2,231 

! 0.765radi-; 1 1 1 

1 

45,0 dq: 0,75 !2,721 3,M)3 2,742 2.076 ;3,:46 3.472 3,!71 2.401 ;3,793 4.1B6 3.B23 2,W4 ;4,3!%I41~ 4.419 3.346 

! 0.7!35radl—! I 1 1 

1 I 1.00 ;3mb~ 4,005 LL7 2.7t9 ;4nlfi MJO 4,220 3,201 ;5.057 %= 5.097 5,SS9k.%? b.455 Z.N3 4,462

!WsA-MIEy 

SF bqutaticm 

K-joint 

Axial SK Saddlei%iticn 

1 

I 

: kfi 

~—: 

M.53i 0.57? MM 0,239 :0,61! 0.670 0.5?4 0.27b ;0,723 0.7B9 0,b24 0,3ZI \fh7W 0,671 0.690 0,’UO: 

I 1 1 I 

1 

:0,0 daqi 0.3 !1,062 1,15E 0,917 CI.47E;1,ZZ3 1,340 1.061 0,553 ;1.446 i.J~ 1,24? 0,651 :1.5~ 1s743 l.~ 0072f: 

: 0.524radi—1 

1 1 1 

! 

$ 30.0 dq; 9.75 !:.593 1.TM 1,37A 0.7!8 ;LE42 2.010 1,592 0,830 ;2,169 2.366 1,E74 0,?77 ;2,397 2.A15 2.571 :Sw : 

! 0,~4 rad;—~ I 

1 

1 r 1 

1.00 !2.124 2.317 1,635 0.937 !2,457 2.MO 2.122 1.107{2.~i 3.155 L4W !*X3 !:.1?6 3*M7 2.761 ;,440 [ 

1 

1 { 0.23 !0.?63 1,076 O,we 0,515:1.114 1,245 1,039 0.5% :1,3!1 1,465 1.223 0’701!1.449 1.619 !,32 0.774 ! 

I ~—~ 1 r ! 1 

! 45,1) rjq; O,m /Iu~~ ~.j~ 1,~ l,OM ~z,~ ~,490 2a079 1,191~2,b~ 2,931 2,447 1,402~2m5_99 3,239 ~,704 IE39 ~ 

1).7Wrad;—1 I t 1 I 

I 

t 45.0 deg! O.~ :2.~ 3,229 2,696 1.545;3,343 :,~ 3,119 1,~ ;:,935 4.397 3,b71 2,103;4,349 4,E59 4.055 2.324; 

! O.~ racil-! I 1 I t 

I 

1 ! 1.00 !3,B54 4,X)6 3,595 2.OM:4,458 4,9B0 4.159 2.3S3 ;5.247 5,243 4.355 2,M5 ;5,797 6.478 5.409 LW9 ;

Ikrdwth-kdlw 

SF l%quiaiifm 

K-joint IwPM 

ST Crew Pmitim 

I,M91.0791.066!0,9W1.1S 1,2S 1,219;1,175 1.370 1.466 L449!1,3431.%71.b7b 1.657: 

f 0 

I 

1 

1.7’55LB79 l,&57;1,721 2.008 2,14H 1,123;2.04S 2,386 2.Z3 2.523!2,33~ 2.72E 2.910 M35 : 

I I I 1 

2.429 2.99 2.M9 ;2,331 2,770 2,971 2.931 ;2,U.O 3.301 3.531 $4$0:3.235 2.774 4,037 Z.Ri ; 

1 I 1 8 

~.~ 3.271 :.2:4 ;2.99E Z,497 3,740 3.b97;3.562 4,155 4,445 4.394:4.073 4.751 5.062 5.(U3i 

...

-- ..—--- ------ -- ------ ------ 

in-3cl. 

2LLxi%.3 

------- ------ -- 

-1 ~ 

& 

ma 

----- ----- ---- -- 

-- -- -- ,.- 

S 

?# 

w 

------ ------ -- 

iiiwiii 

-- -- -- .- -- -- -- 

;;5s 

------ 

.- .- 

------ --- 

. 

~ 

* %. $= 

------ ------ -- 

*. 

s En 

-- -- .- -. -- -- -- 

------ ------ ---

hdsmthqwdhy W Camputatim 

l-joint Axial$# %ddleh51tl~ 

I 

1 

:—~ 

I 1 1 

1 

:0.0dql 0.50’:3,550 2.5391.&i2!,7M;4,437 3,1742,3152,232;5.9~64.2323.C%72.?77:7,3S LHO S,Hi? ;,721 

2.:24 radl—; 1 

) 1 

~0975:ZazzZBOB 2.7782.H7!6.6564,761?.4733,249!8,075L14B 4*M 4,465;11.097,?355,7895,32 

I ;—l 

1 1 I 

, 

1 

45;0dqi 0.50 :4.55 4,991 4,271 Ljt7 16s1916.29 5,339 3,959 ;8,~ %,:1? 7,:1? 5.278k31 10.39 9,BW 5.598 

! 0.7M radl—1 1 I 1 

I ! 0.75 !7.430 7,487 k407 4,73 ;9.237 7,3E4 E.(W?5.9?4 :12,38 12,47 10.67 ?,?10 :15.47 !5.59 15.34 9.E97 

) ~—~ 1 1 I 

1 

! 1.00 !9.906 9.%2 E.543 6,FA ;:2.Z !2.47 10A7 7,91BIIA.51 16.6.3 !4.23 10.55;20.LJ 23.79 17,79 !3,19

kbrdwmii%dl~y 

SCFComputation 

,..-,

Ejrnnt flkf+lane 

SF SaddlePmitim 

~, 

# 

45,0 d~j 0.50 :2.M7 2,:!: 2.:94 2,125 !2.509 2.W 2.7%2 2,656:3,346 5,852 Z,WO Z.542 ;4.MI 4.M5 4,7W 4,43 

~ 0.785 rad;—; 

1 1 1 

1 

i 0.7513.011 3.4% 3.591 3,W k,764 4,333 4.489 3,965k.!U95,7785.% 5.313 ;6.274 7.D27,4%?b.b42 

1 I ,—~ 1 1 1 

1 

! 

! 1,0014.015 4.6224.7E8 4.251 ;5.019 5.778 %985 5.313 k.t/72 7.704 ?,~l 7.0f5 ;8,U6 ‘?.634 f’,77k 0.256

C.4 FINITE ELEMENT ANALYSES RESULTS 

Finite element analyses were performed on the connections between the 

column tops and upper hull girders and between the corner columns and 

tubu1ar bracing of the column-stabilized, twin-hulled 

semisubmersible. The overall geometry and locations of the two 

connections are indicated in Figures C.4-1 and C.4-2. Longitudinal 

and transverse girders (8.2 m deep) coincide with the column faces. 

The columns are 10.6 by 10.6 m in cross section. 

Some dimensions of interest are: 

Overall length 

Overall width 

96.0 m 

65.0 m 

.,— 

Lower Hulls (two) 

Length 

Width 

Depth 

96.0 m 

16.5 m 

8.0 m 

Stability Columns (six) 

Size (square w/ rounded columns) 10.6x1O.6m 

Transverse spacing (center-to-center) 54.o m 

Longitudinal spacing 33.0 m 

Upper Hull 

Length 

Width 

Depth 

77.0 m 

65.0 m 

8.2 m 

C.4.1 

Column-Girder Connection 

The location of the connection is shown in Figure C.4-1. The joint 

dimensions are given in Figure C.4-3. The loading analyzed was a 

combined axial, shear and moment load. The .SCFis defined as: 

C-15

MAXIMUM PRINCIPAL STRESS 

SCF = -------------------------------------- 

NOMINAL STRESS IN GIRDER 

(P/A+M/S) 

The moment M Is due to a combination of moment and shear load. 

The maximum SCF was found in the gusset plate connecting the 

transverse girder and column top, at the edge of the gusset plate in 

the weld between the gusset web and flange. It was equal to 1.66. The 

SCF in the longitudinal girder at the windlass cutouts reached a 

value of 1.87. Figure C.4-4 shows the equivalent stress variation 

over the entire connection. The maximum stress, as already nokl, 

occurs in the crotch region. Figure C.4-5 shows an equivalent stress 

contour plot of the windlass holes. Table C.4-1 summarizes the SCFS. 

,.—. 

C-16

,. .. 

..-. __ _________ ._ _ _______ _______ ______ 

------ ________ _ _________ __________ 

I MEMBER LOCATION DIRECTION SCF I 

I 

TO WELD I 

I 

_____________________ 

-----_______________ __ _______________________ _--_+-+__________________ 

1 

I Center Column Middle of Parallel 1.66 I 

I Transverse Gusset 

I 

I 

I 

I Girder-Column Gusset-Girder Perpendicular 1.37 I 

I Connectlon Connection 

I 

I 

I 

I 2.3x2.3x1.1 m Gusset-Column Perpendicular 1.10 I 

I Gusset Connection 

I 

I 

I 

I 

Girder Flange Parallel 1.05 I 

I 

I -------------------_-...------------------------------- 

I 

I Longitudinal Middle of Parallel 1.52 I 

I Girder-Column Gusset 

I 

I Connection Gusset-Girder Perpendicular 1.14 I 

I 

Connection 

I 

I 

I 1.lxl.lx.55m Gusset-Column Perpendicular 1.05 I 

i 

Connection 

I 

I 

I 

I Girder Flange Parallel 1.01 I 

I 

I 

I------------------------ ----- .s.-.-+.- -------- ---------- i 

I 

I 

I EXteri or Bottom Right Parallel 1.87 I 

I Longitudinal Corner of 

I Girder Exterior Hole I 

i 

I 

] @ Windlass Upper Left Parallel 1.73 I 

I Holes Corner of 

I 

Interior Hole 

I 

I 

===-==============------—--------------------------------======== 

Table C.4-1 

Summary of SCFS for a Column - Girder Connection

‘-W, 

.\ I Ill I 

: II m 

-,, 

!) 

.—. --, — .’ 

.— --- . 

1 

—.. 

—..—- 

LOCATION OF 

FINITE ELEMENT 

MODEL 

=-mL 

-.— ---— . 

-4 

Figure C.4-1 

Overall Geometry of Vessel and Lacation of 

Column-to-Girder Connection 

— --, —

—..—.— 

-.. — 7 

a 

. 

LOWER HUL AN(I TuBULAR ERhCING PLAN B-Al 

o 

Hl 

.---------- — +----- . -..t-- . 5=1===- 

‘:& 

.. . . - ! .. ------- . . . . . . . . . . . . . . . --------- 

. . . . . . ..- . . . . . . . ------- . . . . . . . -------

’ \./ 

““’ w~”mm 

m ““- 

Y 

--+\ 

/ 

Figure C.4-3 

Finite Element Model and Dimensions of 

Col~-to-Girder Connection

. 

Loading ~ 

Figure C.4-4 

Equivalent Stress Contour Plot for the 

Column-to-Girder Connection

. . 

I 

Column 

L’ 

Longitudinal 

Girder> 

Figure C.4-5 Equivalent Stress Contour Plot Of Windlass Holes

C.5 REFERENCES 

C.1 

Kuang, J.G. et al., “stress Concentrations in Tubular 

Joints,” Proceedingsof Offshore Technology Conference, OTC 

Paper No. 2205, Houston, TX. 1975 (Revisions introduced in 

SPE Journal, pp. 287-299, August 1977). 

C.2 

Wordsworth, A.C., “Stress ConcentrationFactors at K and KT 

Tubular Joints,” Fatigue in Offshore Structural Steels, 

Institutionof Civil Engineers, London, February 1981. 

C.3 

Wordsworth, A.C., “Aspects of Stress Concentration Factors 

at Tubu1ar Joints,” TS8, Proceedings of the 3rd 

International Offshore Conference on Steel in Marine 

Structures, (SIMS 87), Delft, The Netherlands, June 1987. 

C*4 

Gibstein, M.B., “Parametric Stress Analyses of T Joints,” 

Paper No. 26, European Offshore Steels Research Seminar, 

Cambridge, November 1978. 

..—., 

C.5 

Gibstein, M.B., “Stress Concentration in Tubular K Joints 

with Diameter Ratio Equal to One,” TS1O, International 

Offshore Conference on Steel in Marine Structures (SIMS 

87), Delft, The Netherlands, 1985. 

C.6 

Efthymiou, M., et al. “stress concentrations in T/Y and 

Gap/Overlap K Joints,” The 4th InternationalConference on 

Behavior of Offshore Structures (BOSS 1985), Amsterdam, The 


C.7 

Marshall, P.W. and Luyties, W.H., “Allowable stresses for 

Fatigue Design,” International Conference on Behavior of 

Offshore Structures (BOSS 1982), Cambridge, Massachusetts, 

August 1982. 

C-17

C.8 Underwater Engineering Group, “Design of Tubular Joints for 

Offshore Structures,” UEG Publication, UR33, 1985. 

C.9 Kellogg, M.W., “Design of Piping Systems”, Second Edition, 

Wiley, 1956. 

C.lo 

Delft, van D.R.V. et al. “The Results of the European 

Fatigue Tests on Welded Tubular Joints Compared with SCF 

Formulas and Design Lives,” Paper No. TS 24, Proceedings of 

the 3rd International Conference on Steel in Marine 

Structures (SIMS 87), Delft, The Netherlands, June 1987. 

C*11 Ma, S.Y., Tebbett, I.E., “Estimations of Stress 

Concentration Factors for Fatigue Design of Welded Tubular 

Connections,” Proceedings of the 20th Annual Offshore 

Technology Conference, OTC Paper No. 5666, Houston, TX., 

May 1988. 

C.12 Tebbett, I.E., and Lalani, M., “A New Approach to stress 

Concentration Factors for Tubular Joint Design,” 

Proceedings of 16th Annual Offshore Technology Conference, 

ITC Paper No. 4825, Houston, TX, May 1984. 

C.13 Tolloczko, J.A., and 

Data on the Fatigue 

Proceedings of the 

Conference, OTC Paper 

Lalani, M., “The Implications of New 

Life Assessment of Tubular Joints,” 

20th Annual Offshore Technology 

No. 5662, Houston, TX, May 1988. 

C-18

(THIS PAGE INTENTIONALLY LE~ BLANK)

APPENDIX D 

VORTEX SHEDDING AVOIDANCE AND FATIGUE DAMAGE COMPUTATION 

CONTENTS 

NOMENCLATURE 

D. 

VORTEX SHEDDING 

D.1 

D*2 

D.3 

D.4 

D.5 

D*6 

D.7 

D*8 

D.9 

INTRODUCTION 

VORTEXSHEDDINGPARAMETERS 

SUSCEPTIBILITY TO VORTEXSHEDDING 

D.3.1 In-Line Vortex Shedding 

0.3.2 Cross-Flow Vortex Shedding 

D.3.3 Critical Flow Velocities 

AMPLITUDES OF VIBRATION 

0.4.1 In-Line Vortex Shedding Amplitudes 

0.4.2 Cross-Flow Vortex Shedding Amplitudes 

STRESSES DUE TO VORTEX SHEDDING 

FATIGUE LIFE EVALUATION 

EXAMPLE PROBLEMS 

D*7.1 Avoidance of Wind-Induced Cross-Flow Vortex Shedding 

D.7.2 Analysis for Wind-Induced Cross-Flow Vortex Shedding 

METHODS OF MINIMIZING VORTEX SHEDDING OSCILLATIONS 

0.8.1 Control of Structural Design 

D.8.2 Mass and Damping 

0.8.3 Devices and Spoilers 

REFERENCES

NOMENCLATURE 

co 

CLj 

CLO 

o 

‘tot 

DI 

D2 

E 

H 

I 

I 

Io 

K 

KS 

L 

N 

Re 

s 

s 

SCF 

‘t 

s~ 

T 

Te 

v 

Vm 

v max 

v min 

Vr 

Y 

Ym 

Y~ 

Coefficient of drag 

Design lift coefficient 

Base lift coefficient 

Fatigue damage 

Total fatigue damage 

Fatigue damage due to vortex shedding 

Fatigue damage due to storm 

Modulus of elasticity 

Submerged length of member 

Member moment of inertia 

Turbulence parameter 


Constant representingmember fixity 

Stability parameter 

Span between member supports 

Number of cycles to failure at hot spot stress range 

Reynolds number 

Hot spot stress range 

Member section modulus 

Stress concentration factor 

Strouhal number 

Correspondinghot spot stress range 

Wave period 

Time for which Vmin is exceeded 

Flow velocity normal to member axis 

Maximum orbital velocity due to wavemotion 

Maximum water particle velocity 

Minimum Vr, required for motion 

Reduced velocity 

Member midspan deflection 

Maximum member midspan deflection 

Refined maximum member midspan deflection

a 

an 

b 

d 

f“ 

f ar 

f~ 

‘bmax 

f~ 

fn 

f~ 

m 

z 

‘i 

‘j 

n 

‘e 

,--- no 

‘s 

‘w 

t 

v 

‘cr 

Vr 

w 

‘o 

WI 

y(x) 

y’(x) 

6 

E 

v 

‘N 

P 

Maximum modal amplitude 

Natural frequency coefficient 

Pit depth 

Member diameter 

Member vortex shedding frequency 


Member bending stress 

Member maximum bending stress 

Member maximum hot spot stress 

Member natural frequency 

Member vortex shedding frequency 

Mass of member per unit length excluding marine growth 

Effective mass per unit length 

Mass of member per unit length includingmarine growth 

Generalized mass per unit length for mode j 

Mode of vibration 

Member end condition coefficient 

Total number of occurrences per year 

Actual number of cycles at hot spot stress range 

Number of oscillations during one wave cycle 

Nominal caisson thickness 

Applied velocity 

Critical wind velocity 

Reduced velocity 

Load per unit length 

Weight per unit length of member 

Weight per unit length of supported Items 

Fundamentalmode shape 

Equivalent fundamental mode shape 

Logarithmic decrement of damping 

Damping ratio 

Kinematic viscosity 

Ratio of midspan deflection to member diameter (Y/d) 

Mass density of fluid

x 

(THIS PAGE INTENTIONALLY LEFT BIANK)

D. VORTEX SHEDDING 

0.1. INTRODUCTION 

When a fluid flows about a stationary cylinder, the flow separates, 

vortices are shed, and a periodic wake is formed. Each time a vortex 

is shed from the cylinder, the local pressure distribution is 

altered, and the cylinder experiences a time-varying force at the 

frequency of vortex shedding. 

In steady flows, vortices are shed alternately from either side of 

the cylinder producing an oscillating lift force transverse to the 

flow direction at a frequency equal to that at which pairs of 

vortices are shed. In the flow direction, in addition to the steady 

drag force, there is a small fluctuating drag force associated with 

the shedding of individual vortices at a frequency twice that of the 

lift force. 

As the flow velocity increases, the vortex shedding frequency 

increases. Thus, provided the flow velocity is high enough, a 

condition will be reached where the vortex shedding frequency 

coincides with the natural frequency of the flexible element. 

— 

In general, marine members and appurtenant pipework are of a diameter 

and length that preclude the occurrence of in-line vibrations induced 

by vortex shedding. However, all susceptible members must be 

analyzed to ensure that the stresses due to in-line vibrations and 

possible synchronized oscillations are small and do not result in a 


Response to vortex shedding cannot be predicted using conventional 

dynamic analysis techniques since the problem is non-linear. The 

motion of the structure affects the strength of the shedding which, 

in turn affects the motion of the structure. This feedback mechanism 

causes the response to be either significantly large or negligibly 

smal1. Once excited, there is also a tendency for the vortex 

D-1

shedding frequency to synchronize with the natural frequency of the 

structure. This results in sustained resonant vibration even if the 

flow velocity moves away from the critical velocity. 

Oscillations can be predominantly in-line with the flow direction or 

transverse to it. In-line motion occurs at lower flow velocities 

than transverse or cross-flow motion, but the latter is invariably 

more severe and can lead to catastrophic failure due to a small 

number of cycles of oscillation. 

Response to vortex shedding is further complicated as the 

excitational force is not necessarily uniform along the length of the 

members and the actual amplitude of oscillation depends to a large 

extent on the degree of structural damping. 

0.2. VORTEX SHEDDING PARAMETERS 

A number of parameters are common to this phenomenon: 

Reduced velocity (Vr) 

Vr = V/fnd 

where: 

v = flow velocity normal to the member axis 

fn = fundamental frequency of the member (Hz) 

d = diameter of the member 

Reynolds number (Re) 

where: 

Re = Vdi v 

w = kinematic viscosity of the fluid 

The Strouhal number (St) is a function of the Reynolds number for 

circular members. The Reynolds number for typical cylindrical 

members under storm current ranges from 3.5 x 105 to 1.0 x 106. The 

Strouhal number is reasonably approximated as 0.21 for this range of 

Reynolds numbers. 

D-2

Vortex Shedding Frequency 

(f”) 

fv=~= 

St v 

vortex 

shedding frequency of the member 

If 

the vortex shedding frequency of the member coincides with 

natural frequency of the member, resonance will occur. 

the 

Stability parameter 

(Ks) 

21iI& / P d 2 

21tE = logarithmic decrement 

damping ratio 

/-- 

mass density of the f’ uid 

Iii= 

effective mass per un” t length 

~~(m)[y(x)]2dx 

$ [Y’ (X)]% 

L 

span between member supports 

m 

mass of member per unit length 

y(x), 

&y’(x) = fundamental mode shapes as a function of the 

ordinate x measured from the lower support 

along the longitudinalaxis of the member 

As 

given in References 0.1 and 0.2, the effective mass is used to 

equate the real structure with an equivalent structure for which 

o-3

deflection and stability parameters are known. The deflected form of 

this equivalent structure is a cantilever, while typical structure 

members and appurtenancesdeflect as a simply supported beam. Hence, 

the equivalent structure has a mode shape given by: 

y’(x) = 

a- a cos(~) 

while the real structure has a mode shape given by: 

y(x) = 

a sin(~) 

Substituting into the effective mass formulation,we obtain: 

m= 

f~[m][a sin ~]2dx 

J: [a - a cos ~]2dx 

where: 

a = maximum modal amplitude 

Integration of the above equation leads to the relationship: 

i= 2.205 m for simple supported span 

i= 1.654 m for fixed supports 

ii= 

m for cantilever span 

Damping Ratio 

Welded marine structures exhibit very low values of structural 

damping. Vibratory energy is typically dissipated by material and 

aerodynamic (radiation) damping. Individual members subjected to 

large vibratory motions dissipate energy through the connections to 

the main structure largely as dispersive bending and compression 

D-4

waves. When only isolated members undergo large vibration response, 

energy dispersion exceeds reflected energy and represents a major 

source of damping. 

Structural members may be grouped Into two classes, depending on the 

fixity of their supports. Tubular braces welded on to regions of 

high rigidity, such as structure columns or legs, are defined as 

Class 1 members. Tubular braces welded on to regions of low 

rigidity, such as other braces, are defined as Class 2 members. The 

damping ratio applicable for structural members are: 

Structural Member - Class 

Structural Member - Class 

1 Damping ratio E = 0.0035 

2 Damping ratio E = 0.0015 

Although the recommended damping ratios are for vibrations in air, 

they may be conservativelyused for vibrations in water. 

Non-structural continuous members, such as tubulars supported by 

multiple guides, have both structural and hydrodynamic damping. The 

hydrodynamic damping occurs due to sympathetic vibration of spans 

adjacent to the span being evaluated for shedding. Recent work by 

Vandiver and Chung (Reference 0.3) supports the effectiveness of 

hydrodynamic damping mechanism. The lower bound structural damping 

ratio for continuous tubulars supported by loose guides is given as 

0.009 by Blevins (Reference0.4). The applicable damping ratios are 

assumed to be: 

Non-StructuralMembers - Continuous Spans 

Damping ratio E = 0.009 in air 

Damping ratio E = ().02 in k@t@r 

Natural Frequency 

The fundamental natural frequency (in Hz) for uniform beams may be 

calculated from: 

D-5

a 

fn = ~ (EI/mi L4)% 

where: 

the 

moment of inertia of the beam 

3.52 for a beam with fix-free ends (cantilever) 

9.87 for a beam with pin-pin ends 

15.4 for a beam with fix-pin ends 

22.4 for a beam with fix-fix ends 

1ength 

mode of vibration 

mass per unit length 

The amount of member fixity assumed in the analysis has a large 

effect on vortex shedding results, because of its impact on member 

stiffness, natural period, amplitude of displacement, and member 

stress. Hence, careful consideration should be given to member end 

conditions. Members framing into relatively stiff members can 

usually be assumed to be fixed. Other members, such as caissons and 

risers, may act as pinned members if supports are detailed to allow 

member rotation. 

For members with non-uniform spans, complex support arrangements or 

non-uniform mass distribution, the natural frequency should be 

determined from either a dynamic analysis or from Tables provided in 

References D.5 and D.6. Reid (Reference D.7) provides a discussion 

and a model to predict the response of variable geometry cylinders 

subjected to a varying flow velocities. 

The natural frequency of a member is a function of the member’s 

stiffness and mass. For the purposes of vortex shedding analysis and 

design, the member’s stiffness properties are computed from the 

D-6

member’s nominal diameter and thickness. The member mass per unit 

length m is taken to include the mass of the member steel including 

sacrificial corrosion allowance, anodes, and contained fluid. For 

the submerged portion of the member, the added mass of the 

surrounding water is also included. This added mass is the mass of 

water that would be displaced by a closed cylinder with a diameter 

equal to the nominal member outside diameter plus two times the 

appropriatemarine growth thickness. 

Because of insufficient knowledge of the effect of marine growth on 

vortex shedding, the member diameter “d” in vortex-shedding 

parameters Vr, Re, KS, and the member effective mass = in parameter 

Ks do not incluc(e any allowance for the presence of marine growth. 

D.3. 

SLISCEPTIBILITYTOVORTEX SHEDDING 

,/—. 

The vortex shedding phenomena may occur either in water or in air. 

The susceptibility discussed and the design guidelines presented are 

applicable for steady current and wind. Wave induced vortex 

shedding has not been investigated in depth. Since the water 

particle velocities in waves continually change both in magnitude and 

direction (i.e. restricting resonant oscillation build-up), it may be 

reasonable to investigate current-induced vortex shedding and 

overlook wave actions. 

To determine susceptibility of a member to wind- or current-induced 

vortex shedding vibrations, the reduced velocity (Vr) is computed 

first. For submerged members, the stability parameter (Ks) is also 

calculated. Vortex shedding susceptibility defined here is based 

upon the method given in Reference D.8, with a modified lower bound 

for current-induced shedding to reflect present thinking on this 

subject (ReferenceD.9). 

D-7

0.3.1 In-Line Vortex Shedding . 

In-1ine vibrations in wind and current environments may occur when: 

Current Environment 

Wind Environment 

1.2 ~ Vr< 3.5 1.7 < Vr< 3.2 

and KS 51.8 

The value of Vr may be more accurately defined for low KS values from 

Figure O-1, which gives the reduced velocity necessary for the onset 

of in-line motion as a function of combined mass and damping 

parameter (i.e. stability parameter). Corresponding amplitude of 

motion as a function of K5 is given on Figure D-2. As illustratedon 

this Figure, in-line motion is completely supressed for Ks values 

greater than 1.8. 

Typical marine structure members (i.e. braces and caissons on a 

platform) generally have values of Ks greater than 1.8 in air but 

less than 1.8 in water. Hence, in-line vibrations with significant 

amplitudes are often likely in steady current but unlikely in wind. 

0.3.2 Cross-Flow Vortex Shedding 

The reduced velocity necessary for the onset of cross-flow vibrations 

in either air or in water is shown on Figure D-3 as a function of 

Reynold’s number, Re, cross flow vibrations in water and in air may 

occur when: 

Current Environment 

Wind Environment 

3.95vr59 

and Ks s 16 

4.7

\Lf-! 

of cycles. Thus, the reduced velocity necessary for the onset of 

cross-flow vibrations in steady current should be avoided. 

0.3.3 Critical Flow Velocities 

The criteria for determining the critical flow velocities for the 

onset of VW can be expressed in terms of the reduced velocity 

(Section D.2): 

v cr = (Vr)cr (fn* d) 

where: 

(Vr) Cr = 1.2 for in-line oscillations in water 

= 1.7 for in-line oscillations in air 

= 3.9 for cross-flow oscillations in water 

= 

4.7 for cross-flow oscillations in air 

0.4. AMPLITUDES OF VIBRATION 

Amplitudes of vibrations can be determined by several methods. A DnV 

proposed procedure (Reference 0.8) is simple to apply and allows 

determination of member natural frequencies, critical velocities and 

maximum amplitudes of vortex-shedding induced oscillations. The 

procedure yields consistent results, comparable to the results 

obtained by other methods, except for oscillation amplitudes. The 

DnV calculation of oscillation amplitudes is based on a dynamic load 

factor of a resonant, damped, single-degree-of-freedomsystem. this 

approach is not valid unless the nonlinear relationship between the 

response and damping ratio is known and accounted for. Consequently, 

in-line and cross-flow vortex shedding amplitudes are assessed 

separately. 

D-9

0.4.1 In-LineVortex Sheddinq Amplitudes 

The reduced velocity and the amplitude of vibrations shown on Figures 

D-1 and D-2, respectively, as functions of stability parameter are 

based on experimental data. The experimental data obtained are for 

the cantilever mode of deflection for in-line and cross-flow 

vibrations. 

Sarpkaya (Reference D.1O) carried out tests on both oscillatory flow 

and uniform flow and observed smaller amplitudes of vibration for the 

oscillatory flow than for the uniform flow. It is also suggested by 

King (Reference 0.1) that the maximum amplitude for an oscillatory 

flow is likely to occur at a Vr value in excess of 1.5 (as opposed to 

1.0 assumed by DnV) and that an oscillation build-up of about 15 

cycles is required before “lock-in” maximum-amplitude vibration 

occurs. In light of this evidence, the amplitude of vibrations shown 

in Figure D-2 is based on Hallam et al (Reference D.2) rather than 

the DnV (ReferenceD.8). 

Since typical marine structure members have stability parameters (Ks) 

in excess of 1.8, in-line vibrations of these members in air are 

unlikely. 

D.4.2 

Cross-flow Vortex Shedding Amplitudes 

The amplitude of the induced vibrations that accompanies cross-flow 

vibration are generally large and creates very high stresses. 

Therefore, it is desirable to preclude cross-flow induced 

vibrations. Figure D-4 illustrates a curve defining the amplitude of 

response for cross-flow vibrations due to current flow and based on a 

cantilevermode of deflection. 

Cross-flowoscillations in air may not be always avoidable, requiring 

the members to have sufficient resistance. The DnV procedure 

(Reference 0.8) to determine the oscillation amplitudes is derived 

from a simplified approach applicable to vortex shedding due to 

D-lo

s ; 

J 

steady current, by substituting the mass density of air for the mass 

density of water. Hence, the oscillation amplitude is not linked 

with the velocity that causes vortex-induced motion. The resulting 

predicted amplitudes are substantially higher than amplitudes 

predicted based on an ESDU (Reference D.11) procedure that accounts 

for interactionbetween vortices shed and the forces induced. 

The iterative ESDU procedure to determine the amplitudes can be 

simplified by approximating selected variables. The peak amp1itude 

is represented in Equation 9 of the ESDU report by. 

● 

_=nN=— Y 0.00633 ~ —— d2 1 ~L. _ 0“0795 cLj 

d E ITlj 

KS $: 

Using this formulation, a corresponding equation can be established 

for a structure, while making assumptions about the individual 

parameters. Following step 3 of the procedure, the parameters may be 

set as: 

‘j = 

generalized mass/unit length for mode j 

= 2.205 m for pinned structure, 

= 1.654 m for fixed structure 

KS = stability parameter = y 

pd 

P 

= mass density of air = 1.024 kg/m3 

6 = decrement of damping = 21rE 

E = damping parameter = 0.002 for wind 

% = 

Strouhal Number = 0.2 

Q-11

CLO = base lift coefficient = 0.29 high Reynolds number 

= 0.42 low Reynolds number 

CLj = design lift coefficient = CLO X farX 10 X+ x 1.2 

f ar = 

turbulence parameter = 1.0 

~= 

turbulence parameter = 1.0 

10 = turbulence parameter = 0.45 

Evaluating the equation based on the high Reynolds number (Re > 

500,000) leads to: 

nN = 0.0795 (0.29 )(1.0 )(0.45 )(1.0 )(1.2 )/[ K~(0.2)2] 

or 

ON = 

~ (high Reynolds number, Re > 500,000) 

s 

0.4510 

~N ‘~ 

(low Reynolds number, Re < 500,000) 

The amplitude can also be determined iteratively by utilizing the 

ESDU recommended turbulence parameter and following steps 1 through 

5. 

Step 1: Determine correlation length factor, l.. Depending cm the 

end fixity, 10 

is: 

10 = 0.66 for fixed and free (cantilever) 

= 0.63 for pin and pin (simple beam) 

= 0.58 for fixed and pin 

= 0.52 for fixed and fixed 

step 2: Assume 1/10 = 1.0 and calculate the amplitude. 

D-12

Step 3: Obtain a new valueof 1/10 based on initial 

amplitude. 

Step 4: Recompute the amplitude based on 

the new value of l/l.. 

Step 5: Repeat Steps 3 and 4 until convergence. 

0.5. STRESSES DUE TO VORTEXSHEDDING 

Once the amplitude of vibration has been calculated, stresses can be 

computed according to the support conditions. For a simply supported 

beam with a uniform load w, the midspan deflection Y, and the midspan 

bending stress fb are given as follows: 

w 

Y 

a 

= 5 WL41 

m “T*T 

= 

384 EIY 

T“ ~ 

~ax 

= 

WL2= 384 EIY 

T m— ~2 

Md EDY 

‘bmax = ~*~=4”8~ at midspan 

Expressing fbmax = 

K . EDY 

~ 

The K value varies with support conditions and location as shown on 

Table D-1. 

Fixity Mid-Span Ends 

Fix Fix 8.0 16.0 

Fix Pin 6.5 11.6 

Pin Pin 4.8 0 

Fix Free N.A. 2.0 

Table D-1 K Values Based on Fixity and Location 

D-13

The vortex shedding bending stress is combined with the member axial 

and bending stresses due to global deformation of the marine 

structure. 

0.6. FATIGUE LIFE EVALUATION 

The fatigue life evaluation can be carried out in a conservative twostep 

process. First, the fatigue damage due to the vortex-induced 

oscillations is calculated as D1. Second, a deterministic fatigue 

analysis is performed by computer analysis. Hot spot stress range vs 

wave height (or wind velocity) for the loading directions considered 

is determined from the computer analysis. The critical direction is 

determined and a plot is made. From the plot of hot spot stress 

range vs wave height (or wind velocity), the stress ranges for the 

fatigue waves are determined. The maximum vortex-induced stress 

ranges for the fatigue environment are added to the deterministic 

fatigue stress ranges. Then, the standard deterministic fatigue 

analysis is performed using the increased stress range. The fatigue 

damage calculated in this second step is D2. Therefore the total 

fattgue damage is equal to the sum of D1 and D2, or Dtot = 01 + 02. 

The fatigue life fin Years is therefore calculated as l/Btot. 

A typical fatigue life evaluation procedure is given below: 

Step 1: 

a. 

Calculate the natural frequency fn (Hz) of the member. 

b. 

Calculate the stability parameter of the member. 

K5=~ 

pd2 

c. 

Determine the minimum Vr required for vibrations based on Ks in 

Figure D-1. 

d. 

Calculate Vmin, the minimum velocity at which current- or wind- 

0-14

vortex shedding will occur, i.e., Vmin = ‘r(req’d) x ‘n x ‘- 

e. 

Check the applied velocity profile to see if Vmax is greater 

than Vmin. If Vmax is less than Vmin, then no vortex 

oscillations can occur. 

f. 

For Vmax greater than Vmin, vortex oscillations can occur. The 

displacement amplitude is based on stability parameter Ks, and 

is determined from Figure O-2 for in-line vibration. A 

conservative approach is used to determine Y/d vs Ks. For Ks < 

0.6 the first instability region curve is used. For Ks > 0.6 

the second instability region curve is used. This 

conservatively represents an envelope of maximum values of Y/d 

vs Ks from Figure O-2. Displacement amplitude is normalized to 

Y/d. 

9* 

Given (Y/d), calculate the bending stress, fb. 

h. 

Multiply bending stress fb by an SCF of 1.S to produce hOt SpOt 

stress fH. A larger 

SCF will be used where necessary. 

i. 

From the maximum hot spot stress, the hot spot stress range is 

calculated as 2fH. 

j. 

Allowable number of cycles to failure (N) should be calculated 

using an applicable S-N curve (based on weld type and 

environment). 

k. 

Assume conditions conducive to resonant vortex shedding occur 

for a total time of T (seconds) per annum (based on current or 

wind data relevant to applicable loading condition). 

1. 

Hence, in time T, number of cycles n = fnT and the cumulative 

damage D1 = n/N = fnT/N in one year. 

Step 2: 

D-15

a. Depending on marine structure in service conditions (i.e. 

structure in water or in air) run an applicable loading 

analysis. Assuming a marine environment, run a storm wave 

deterministic fatigue analysis and obtain the results of hot 

spot stress range vs wave height for the wave directions 

considered and as many hot spots as are needed. 

b. Determine the critical hot spot and wave direction and draw the 

hot spot stress range vs wave height graph. 

c. Determine the hot spot stress range for each of the fatigue 

waves. 

d. For the larger fatigue waves in which vortex-induced 

oscillations occur, add the increase in stress range due to 

vortex-induced oscillations to the stress range from the 

deterministic fatigue analysis. 

e. Calculate the fatigue damage 02 over a 1 yr period for the full 

range of wave heights: 

f. Calculate the total fatigue damage: 

Dtot = DI + D2 

9= Calculate the fatigue life in years as: 

Life =~ 

‘tot 

D-16 

, ,

h. The fatigue life may -be modified to include the effects of 

corrosion pitting in caissons. Corrosion pitting produces an 

SCF at the location of the pit. The SCF is calculated as: 

SCF=~+— 

3 (:) 

(1-# (1-$2 

where: 

b = plt depth 

t 

= nominal caisson thickness 

The new life including corrosion damage is calculated as: 

Old Life 

New Life =— 

(SCF)3 

This estimate of fatigue damage can, if necessary, be refined by 

consideration of the number of wave occurrences for different 

directions and evaluation of the damage at a number of points 

around the circumference of the member. 

0.7. EXAMPLE PROBLEMS 

0.7.1 Avoidance of Wind-Induced Cross-Flow Vortex Sheddinq 

It 

can be shown that for a steel beam of circular cross section, the 

following relationship holds: 

where: 

c. Vrn~ W. 

v r— ]4 

cr = ‘W+WJ 

(L/d)2 0 1 

v cr = 

critical wind 

for the onset 

shedding 

velocity of the tubular necessary 

of cross-flow wind-induced vortex 

D-17

c 

constant (See 

Vr 

reduced velocity 

‘e 

member end efficiency 

1.5 fixed ends 

1.0 pinned ends 

‘o 

weight per unit length of tubular 

WI 

weight per unit length of supported item (e.g., 

anodes) 

L 

beam length 

d 

tubular mean diameter 

For Vr = 4.7, ne = 

1.5 (fixed condition), and WI = O, this reduces 

to: 

v = 97240/(L/d)~ ft/sec 

Cr = 29610/(L/d) m/see 

Hence, if maximum 

setting all brace 

cross-flow vortex 

are required. 

expected wind speed is 65.6 ft/s (20 m/s), then 

L/d ratios at 38 or less precludes wind-induced 

shedding, and no further analyses or precautions 

However, maximum wind speeds may be so high that the above approach 

may be uneconomical. In this case, either precautionary measures 

must be taken or additional analyses considering strength and fatigue 

must be undertaken. 

D-18 

./ 

‘-. -7 

[ J

NOTE: 

The relationship given is based on: 

44 

v cr 

=Vrfnd= Vr(~[EI/MiLl )d 

substituting 

an = (ne m)2 

ITli= (W. + Wi)/g 

I = T d3t/8 

E = 4176 X 

106 lbs/ft2 (200,000 MN/m2) 

9 = 32.2 ft/sec2 (9.806m/sec2) 

‘o = Ys ~dt 

= weight density of steel, 490 lbs/ft3 (0.077MN/m3) 

‘s 

2 .2 

Vcr= Vr (+) [ E (~d3t/8) ~]. + d 

(w. + Wl) L 

2, 

‘e E (wo/Ys) d2 9 ~ 

Vcr. Vr (~) [ ].d 

8 (WO+-, WI) L4 

Substituting for E, 

s, and g 

v 

cr 

where 

=Vr. 

C ne2 

(L/d)2 

constant C = 9195 for Vcr as ft/sec 

= 2800 for V~r as m/see 

D-19

D.7.2 Analysis for Wind-Induced Cross-flow Vortex Shedding 

Using procedures discussed in Section D.4 a flare structure bracing 

members are analyzed for crossflow oscillationsproduced by vortex 

shedding. The analysis is performed using a Lotus spreadsheet. The 

general procedure is as follows: 

(a) 

Member and environmental parameters are input. 

(b) Critical velocity, peak amplitudes of oscillation and 

corresponding stress amplitudes are computed. 

(c) The time (in hours) of crossflow oscillation required to cause 

fatigue failure is computed. 

Analysis Description 

The following is a detailed description of the spread sheet input and 

calculation. 

(a) Spread Sheet Terminology 

Columns are labeled alphabetically while rows are labeled 

numerically. A “cell” is identified by referring to a specific 

row and column. 

(b) General Parameters 

The following are parameters common to all members analyzed as 

given at the top of the spread sheet. 

CELL C5: DAMPING RATIO = E 

CELL C6: AIR MASS DENSITY = ~ 

0-20

CELL C7: KINEMATIC VISCOSITY = U 

CELL C8: STRESS CONCENTRATION FACTOR = SCF 

CELL C9: MODULUS OF ELASTICITY= E 

CELL K5: RATIO OF GENERALIZE MASS TO EFFECTIVE MASS = ( # ) 

e 

CELL K6: FIXITY PARAMETER INFORMUIA FOR CRITICAL VELOCITY = 

‘e 

CELL K7: FIXITY PARAMETER INFORMULA FOR STRESS AMPLITUDE = C 

CELL K8: FIXITY PARAMETER INFORMULA FOR MEMBER FREQUENCY = a n 

(c) Specific Member Analysis 

The following describes the content of each column in analyzing 

a specific member. Entries and formulas for vortex shedding 

analysis of member group HI on line 16 are also provided. 

Formula coding is described in the LOTUS 1-2-3 Users Manual. 

COLUMN A: 

ENTER THE MEMBER GROUP IDENTIFIER 

COLUMN B: 

ENTER THE EFFECTIVE SPAN OF THE MEMBER = L (m) 

COLUMN C: 

ENTER THE OUTSIOE OIAMETER OF THE-TUBULAR = d (mm) 

COLUMN D: 

ENTER THE TOTAL OUTSIOE DIAMETER = D (mm) INCLUDINGAS 

APPLICABLE, MARINE GROWTH, FIRE PROTECTION, ETC. 

COLUMN E: 

ENTER THE TUBULAR WALL THICKNESS = t (mm) 

COLUMN F: 

ENTER ADOED MASS (kg/m), IF APPLICABLE 

COLUMN G: 

THE MOMENT OF INERTIA OF THE TUBULAR = I (cm4) IS 

COMPUTED. 

D-21

I . + [ (+)-L (+ - t)4] (cm4) 

COLUMN H: THE TOTAL EFFECTIVE MASS IS COMPUTED 

me = , [(+)~.( + - t)2] (0.785) +ma (kg/m) 

COLUMNI: 

THE CRITICAL VELOCITYFOR CROSSFLOW OSCILLATION IS 

COMPUTED. 

COLUMNJ: 

13160 n: 

v= cr 

(m/s) 

(L/D)2 

ENTER THE THRESHOLDWINDVELOCITY= ‘thr 

COLUMN K: THE STABILITY PARAMETER IS COMPUTED 

Ks = 

2me (2~E) 

PD2 

COLUMN L: THE REYNOLDS NUMBER IS COMPUTED 

Before performing calculation in the following columns, the 

velocity is compared with the threshold velocity. If the 

velocity is larger, crossflow oscillations will not occur 

computations are supressed. An “N.A.” is then inserted 

column. 

critical 

critical 

and the 

in each 

If the critical velocity is less than the threshold value, the 

following computations are performed. 

COLUMN M: THE AMPLITUDE OF VIBRATION IS COMPUTED 

Y=& 

(~) Ks 

Where a = 0.04925 for Re 

and a = 0.07178 for Re 

> 500,000 

< 500,000 

D-22

COLUMN N: THE STRESS AMPLITUDE IS COMPUTED 

fb=y 

(MPa) 

where C depends on beam end fixity (see Section D.4) 

COLUMN O: THE HOT SPOT STRESS RANGE IS COMPUTED 

S = 2 (SCF)fb 

(MPa) 

COLUMN P: THE NUMBER OF CYCLES TO FAILURE UNDER THE HOT SPOT 

STRESS RANGE IS COMPUTED. 

N 

= 

~o(14.57 - 4.1 LogloS) (cycles) 

COLUMN Q: THE MEMBER NATURAL FREQUENCY IS COMPUTED 

a 

fn=~ (— %? 

~E:4 ) 

e 

(Hz) 

where an depends on beam end fixity (see Section D.2) 

COLUMN R: THE TIME IN HOURS TO FATIGUE FAILURE UNDER N CYCLES OF 

STRESS RANGE S IS COMPUTED 

T=+ 

n 

D.8. 

METHODS OF MINIMIZING VORTEX SHEDDING OSCILLATIONS 

D.8.1 

Control of Structural Design 

The properties of the structure 

velocity values in steady 

oscillations. 

can be chosen to ensure that critical 

flow do not produce detrimental 

D-23

Experiments have shown- that for a constant mass 

parameter (m/pd2 = 2.0), the critical velocity depends mainly on the 

submerged length/diameter (L/d) ratio of the member. 

Thus, either high natural frequency or large diameter is required to 

avoid VIV’S in quickly flowing fluid. A higher frequency will be 

obtained by using larger diameter tubes, so a double benefit 

occurs. An alternative method of increasing the frequency is to 

brace the structurewith guy wires. 

0.8.2 Mass and Dampinq 

Increasing the mass parameter, m/PdZ, and/or the damping parameter 

reduces the amplitude of oscillations; if the increase is large 

enough, the motion is suppressed completely. While high mass and 

damping are the factors that prevent most existing structures from 

vibrating, no suitable design criteria are presently available for 

these factors, and their effects have not been studied in detail. 

Increasing the mass of a structure to reduce oscillatory effects may 

not be entirely beneficial. The increase may produce a reduction in 

the natural frequency (and hence the flow speeds at which oscillation 

will tend to occur). It is thus possible that the addition of mass 

may reduce the critical speed to within the actual speed range. 

However, if increased mass is chosen as a method of limiting the 

amplitude of oscillation, this mass should be under stress during the 

motion. If so, the mass will also contribute to the structural 

damping. An unstressedmass will not be so effective. 

If the structure is almost at the critical value of the combined 

mass/damping parameter for the suppression of motion, then a small 

additional amount of damping may be sufficient. 

D-24

D.8.3 Devices and Spoilers 

Devices that modify flow and reduce excitation can be fitted to 

tubular structures. These devices (see Figure D-5) work well for 

Isolated members but are less effective for an array of piles or 

cylinders. Unfortunately, there is no relevant information 

describing how the governing stability criteria are modified. The 

most widely used devices are described below. 

Guy Wires 

Appropriately placed guy wires may be used to increase member 

stiffness and preclude wind-induced oscillations. Guy wires should 

be of sufficient number and direction to adequately brace the tubular 

member; otherwise, oscillations may not be eljmlnatecl completely and 

additional oscillations of the guys themselves may occur. 

Strakes or Spoilers 

$trakes and spoilers consist of a number (usually three) of fins 

wound as a helix around the tubular. These have proven effective in 

preventing wind-induced cross-flow oscillations of structures, and 

there is no reason to doubt their ability to suppress in-line motion. 

provided that the optimum stroke design is used. This comprises a 

three-star helix, having a pitch equal to five times the member 

diameter. Typically each helix protrudes one-tenth of the member 

diameter from the cylinder surface. To prevent in-line motion, 

strakes need only be applied over approximately in the middle onethird 

of the length of the tubular with the greatest amplitude. 

Elimination of the much more violent cross-flow motion requires a 

longer strake, perhaps covering the complete length of tube. The 

main disadvantage of strakes, apart from construction difficulties 

and problems associated with erosion or marine growth, is that they 

increase the time-averaged drag force produced by the flow. The drag 

coefficient of the straked part of the tube is independent of the 

Reynold’s number and has a value of CD = 1.3 based on the tubular 

diameter. 

D-25

Shrouds 

Shrouds consist of an outer shell, separated from the tubular by a 

gap of about 0.10 diameter, with many small rectangular holes. The 

limited data available indicates that shrouds may not always be 

effective. The advantage of shrouds over strakes is that their drag 

penalty is not as great; for all Reynold’s numbers, CD= 0.9 based on 

the inner tubular diameter. Like strakes, shrouds can eliminate the 

in-line motion of the two low-speed peaks without covering the 

complete length of the tubular. However, any design that requires 

shrouds (or strakes) to prevent cross-flow motion should be 

considered with great caution. Their effectiveness can be minimized 

by marine growth. 

Offset Dorsal Fins 

This is the simplest device for the prevention of oscillations. It 

is probably the only device that can be relied upon to continue to 

work in the marine environment over a long period of time without 

being affected adversely by marine growth: It has some drag penalty, 

but this is not likely to be significant for most designs. 

The offset dorsal fin is limited to tubular structures that are 

subject to in-line motion due to flow from one direction only (or one 

direction and its reversal, as in tidal flow). 

This patented device comprises a small fin running down the length of 

the tubular. Along with the small drag increase there is a steady 

side force. This may be eliminated in the case of the total force on 

multi-tubular design by placing the fin alternately on opposite sides 

of the tubulars. 

D-26

D*9 

REFERENCES 

D.1 

King, R., “A Review of Vortex Shedding Research and Its 

Application,” Ocean Engineering, Vol. 4, pp. 141-171, 

1977. 

D.2 

Hallam, M. G., Heaf, N.J.,Wootton, L.R., Dynamics of Marine 

Structures, CIRIA, 1977. 

D.3 

Vandiver, J.K., and Chung, T.Y., “Hydrodynamic Damping in 

Flexible Cylinders in Sheared Flow,” Proceedingsof Offshore 

Technology Conference, OTC Paper 5524, Houston, 1988. 

D.4 

Blevins, R.D., Flow Induced Vibrations, Van Nostrand 

Reinhold, 1977. 

,.—.> 

D.5 

Blevins, R.D., Formulas for Natural Frequency and Mode 

Shape, Van Nostrand Reinhold, 1979. 

D.6 

German, D.I.,Free Vibration Analyses of Beams and Shafts, 

Wiley-Interscience, 1975. 

0.7 

Reid, D.L., “A Model for the Prediction of Inline Vortex 

Induced Vibrations of Cylindrical Elements in a Non-Uniform 

Steady Flow,” Journal of Ocean Engineering, August 1989. 

D.a 

Det Norske Veritas, “Rules for Submarine Pipeline Systems,” 

Oslo, Norway, 1981. 

0.9 

Griffin, O.M. and Ramberg, S.E., “Some Recent studies of 

Vortex Shedding with Application to Marine Tubulars, and 

Risers,” Proceedingsof the First Offshore Mechanics and 

Arctic Engineering/Deep Sea Systems Symposium, March 7 - 

10, 1982, pp. 33 - 63. 

D.lo 

$arpkaya, T., Hydroelastic Response of Cylinders in 

D-27

Harmonic Flow, Royal Institute of Naval Architects, 1979. 

D.11 Engineering Sciences Data Unit, Across Flow Response Due to 

Vortex Shedding, Publication No. 78006, London, England, 

Clctober, 1978. 

D-28

Fint Insmbility Rtgion I !%mmd InatabtiwRagim 

I 

I 

I 

Motion 

I 

I 

I 

I 

No Motion 

I 

I 

I 

I 

. . .- .- 

--i 0.5 1.0 1.2 1.5 2 

/ 

I 

I 

o 

SmbiliPfParanww (KJ 

l.o

o.: 

Q., 

0“.. 

0.1 

0.1 

* 

REGION 

0 

9?* 1 ! 1 1 1$,, 

10’ 101 10] 

AND L4MINAR 

Of- TUR13ULENT VORTEX 

BOUNDARY IAYER 

CYLINDER 

TRAIL 

ON THE I / 

I ,’ : 

-“” “’ .:.. ..=. ...&. ~x--- 

1d 

REYNOLDS 

NUMDER, l_tC 

10s 

I 

REGION WHERETIIE 

VORTEX SHEDDING 

FREQUENCY UN K 

DEFINED AS THE 

DOMINANT FREQUENCY 

IN A SPECTRUM 

u 

10E 10’ 

Figure D-3 The Strou.halversus 

ReynoldIs Numbers 

for Cylinders 

..-.> 

1.8 

1.6. \ 

,’ . 

I # #’ 

,’ *’9 

., 

.-#-+- 

144- 

1,2 

1.0 

0.8 

0.6 

0.4 

0.2 

0 2.0 4.0 

StabilityPatwnemr 

(K$) 

Figure D-4 Amplitude of Response for cms$-FIOW Vibrations

.—____ 

*U.S. E.P.O. :1993-343-273:80117 

~’q

(THIS PAGE INTENTIONALLY LEFT BIANK)

COMMllTEE ON MARINE STRUCTURES 

Commission on Engineering and Technical Systems 

National Academy of Sciences - National Research Council 

The COMMITTEE ON MARINE STRUCTURES has technical cognizance over the interagency 

Structure Committee’s research program. 

Peter M. Palermo Chairman, Alexandria, VA 

Mark Y. Berman, Amoco Production Company, Tulsa, OK 

Subrata K. Chakrabarti, Chicago Bridge and Iron, Plainfield, IL 

Rolf D. Glasfeld, General Dynamics Corporation, Groton, CT 

William H. Hartt, Florida Atlantic University, Boca Raton, FL 

Alexander B. Stavovy, National Research Council, Washington, DC 

Stephen E. Sharpe, Ship Structure Committee, Washington, DC 

LOADS WORK 

GROUP 

Subrata K. Chakrabarti Chairman, Chicago Bridge and Iron Company, Plainfield, IL 

Howard M. Bunch, University of Michigan, Ann Arbor, Ml 

Peter A. Gale, John J. McMullen Associates, Arlington, VA 

Hsien Yun Jan, Martech Incorporated, Neshanic Station, NJ 

Naresh Maniar, M. Rosenblatt & Son, Incorporated, New York, NY 

Solomon C. S. Yim, Oregon State University, Corvallis, OR 

MATERIALS WORK GROUP 

William H. Hartt Chairman, Florida Atlantic University, Boca Raton, FL 

Santiago Ibarra, Jr., Amoco Corporation, Naperville, IL 

John Landes, University of Tennessee, Knoxville, TN 

Barbara A. Shaw, Pennsylvania State University, University Park, PA 

James M. Sawhill, Jr., Newport News Shipbuilding, Newport News, VA 

Bruce R. Somers, Lehigh University, Bethlehem, PA 

Jerry G. Williams, Conoco, Inc,, Ponca City, OK 

C-3 

*~117 LS7 

/

SHIP STRUCTURE COMMITTEE PUBLICATIONS 

SSC-351 An Introduction to Structural Reliability Theorv by Alaa E. Mansour 

1990 

SSC-352 Marine Structural Steel Touqhness Data Bank by J. G. Kaufman and 

M. Prager 1990 

SSC-353 Analysis of Wave Characteristics in Extreme Seas by William H. Buckley 

1989 

SSC-354 

SSC-355 

SSC-356 

SSC-357 

SSC-358 

SSC-359 

SSC-360 

SSC-361 

SSC-362 

SSC-363 

SSC-364 

SSC-365 

SSC-366 

None 

Structural Redundancy for Discrete and Continuous Svstems by P. K. 

Das and J. F. Garside 1990 

Relation of Inspection Findinqs to Fatique Reliability by M. Shirmzuka 

1989 

Fatique Performance Under Multiaxial Loai by Karl A. Stambaugh, 

Paul R. Van Mater, Jr., and William H. Munse 1990 

Carbon Equivalence and Weldability of Microalloyed Steels by C. D. 

Lundin, T. P.S. Gill, C. Y. P. Qiao, Y. Wang, and K. K. Kang 1990 

Structural Behavior After Fatique by Brian N. Leis 1987 

Hydrodynamic Hull Dampina (Phase 1~by V. Ankudinov 1987 

Use of Fiber Reinforced Plastic in Marine Structures by Eric Greene 

1990 

Hull Strappinq of Shim by Nedret S. Basar and Roderick B. Hulls 1990 

Shipboard Wave Heiqht Sensor by R. Atwater 1990 

Uncertainties in Stress Analysis on Marine Structures by E. Nikolaidis 

and P. Kaplan 1991 

Inelastic Deformation of Plate Panels by Eric Jennings, Kim Grubbs, 

Charles Zanis, and Louis Raymond 1991 

Marine Structural Inteqrity Proqrams (MSIP) by Robert G. Bea 1992 

Threshold Corrosion Fatique of Welded Shipbuilding Steels by G. H. 

Reynolds and J. A. Todd 1992 

Ship Structure Committee Publications - A Special Bibliography

4!! . 

,—.-.,

ssc-367 - Ship Structure Committee

Create successful ePaper yourself

Delete template?

Save as template?