5. Fatigue Design Fa

ABS TECHNICAL PAPERS 2005

Proceedings of OMAE 2005 24th International Conference on Offshore Mechanics and Arctic Engineering

June 12-17, 2005, Halkidiki, Greece

OMAE 2005 - 67488 FATIGUE DESIGN FACTORS AND SAFETY LEVEL IMPLIED IN FATIGUE DESIGN OF

OFFSHORE STRUCTURES

Xiaozhi Wang American Bureau of

Shipping 16855 Northchase Drive Houston, TX 77060, USA

[email protected]

Zhan Cheng American Bureau of


[email protected]

Paul H. Wirsching Aerospace and Mechanical

Engineering University of Arizona

Tucson, AZ 85721, USA [email protected]

Haihong Sun American Bureau of


[email protected]

Originally published by American Society of Mechanical Engineers (ASME), New York, NY and reprinted with their kind permission.

ABSTRACT

With the publication of the ABS Guide for Fatigue

Assessment of Offshore Structures (2003) and the Commentary to the Guide for the Fatigue Assessment of Offshore Structures (2004), application of the Fatigue Design Factor (FDF) is highlighted in fatigue assessments of offshore structures. Following review of FDF’s in available Rules/Guides from other authorities, FDF’s applied in the ABS Guide is presented and quantified with a corresponding safety level thus helping the user to relate FDF’s to estimated failure probability levels.

INTRODUCTION

For over a half century ABS has been involved in

the development of fatigue technology starting in 1946 with the formation of the Ship Structure Committee (SSC) for the specific goal of addressing avoidance of serious fracture in ships. The SSC, with strong financial support from ABS, has executed several fatigue research projects. Meanwhile, ABS has also provided support to numerous joint industry/agency fatigue projects in addition to independent investigators for their own in-house projects.

The current state of the art in fatigue technology

represents worldwide contributions of a large number of investigators from government agencies, professional organizations, classification societies, universities, and private industry, most notably petroleum companies. ABS has synthesized this body of knowledge to provide fatigue design criteria for marine structures, among them are the ABS published Guide for the Fatigue Assessment of Offshore Structures (2003) and the Commentary to the Guide for the Fatigue Assessment of

Offshore Structures (2004). The ABS Guide and Commentary not only provide the procedure for fatigue assessment and design requirement, but also the background to describe how the procedure was developed. One of the important aspects in fatigue design criteria is the introduction of Fatigue Design Factors (FDF).

In this paper, the definition of FDF is described

first, followed by a general review of FDFs in various Rules/Guides. The effect of applying FDF on safety or reliability point of view is then presented in terms of failure probability. The later provides quantitative result when applying different FDF. The importance of FDF in fatigue design is therefore emphasized.

FATIGUE DESIGN FACTOR The Fatigue Design Factor (FDF) is a parameter

with a value of 1.0 or more, which is applied to increase the required design fatigue life or to decrease the calculated permissible fatigue damage. The purpose of a fatigue design factor is to account for uncertainties in the fatigue assessment and design process. The process includes operations of estimating dynamic responses and stresses under environmental conditions.

The uncertainties include the following:

• Statistical models used to describe the sea states

• Prediction of the wave-induced loads from sea state data

• Computation of nominal element loads given the wave-induced loads

• Computation of fatigue stresses at the hot spot from nominal member forces

• Application of Miner’s rule

Fatigue Design Factors and Safety Level Implied in Fatigue Design of Offshore Structures 35


• Fatigue strength as seen in the scatter in test data, where a typical coefficient of variation on life is approximately 50-60%.

• Environmental effects on fatigue strength, e.g., corrosion

• Size effects on fatigue strength • Manufacturing, assembly and installation

operations In addition to uncertainties, the fatigue design

factor should also account for: • Ease of in-service inspection of a detail • Consequences of failure (criticality) of a

detail While reliability methods promise the most rational

way of managing uncertainty, the concept of a factor of safety on life, referred herein as a fatigue design factor (FDF), maintains universal acceptance.

SAFETY CHECK EXPRESSION The safety check expression can be based on

damage or life. While the damage approach is featured in the ABS Fatigue Guide (2003), either approach below can be used and are exactly equivalent.

When expressed in fatigue damage, the design is considered to be safe if:

D ≤ ∆ (1)

where

FDF0.1

=∆ (2)

=D the predicted fatigue damage of a detail

=∆ the maximum allowable fatigue damage of a

detail When expressed in fatigue life, the design is

considered to be safe if: N

f ≥ (FDF) (N

T) (3)

where

=fN the predicted fatigue life of a detail

=TN the structure design life The FDF is also referred to as a factor of safety on life.

Fatigue design factors specified in relevant documents are summarized in the following section.

FDFS SPECIFIED IN DOCUMENTS OTHER THAN ABS GUIDE

The following is a summary of factors of safety on

life that have been extracted from documents relevant to marine structural fatigue. The safety factors by themselves do not tell the whole story and may not address all of the issues raised above. However, it is instructive and helpful in the development of the Guide to review those factors that have been published in relevant documents.

It should be noted that safety factors associated with free corrosion in seawater and cathodic protection in seawater are not included in these factors and should be applied separately. API RP2T [API (1997)]

“General structure: In general, it is recommended that the design fatigue life of each structural element of the platform be at least three times the intended service life of the platform.”

“Tendons: … high uncertainties exist … The component fatigue life factor of ten is considered a reasonable blanket requirement.” API RP2A [API (2000)]

“In general, the design fatigue life of each joint and member should be at least twice the intended service life of the structure (i.e., FDF = 2.0).” Fatigue Design of Welded Joints and Components, [IIW (1996)]

For fatigue verification, it has to be shown that the total accumulated damage is less than 0.5, i.e., FDF = 2.0. ABS Rules for Building and Classing Steel Vessels, Part 5, American Bureau of Shipping [ABS (2004)]

No safety factor specified, i.e., an implied factor of safety on life of 1.0. However, since computed stress is based on “net” scantlings, the nominal FDF is greater than 1.0. Offshore Installations: Guidance on Design, Construction and Certification, UK Department of Energy [DEn (1990)]

No specific value given. “In defining the factor of safety on life, account should be taken of the accessibility of the joint and the proposed degree of inspection as well as the consequences of failure.” ISO CD 19902, International Standards Organization [ISO CD 19902 (2000)]

In lieu of more detailed fatigue assessment, the FDF can be taken from the following table:

Failure Critical

Inspectable Uninspectable

No 2.0 5.0 Yes 5.0 10.0



DNV RP-C203 Fatigue Strength Analysis of Offshore Structures, Det Norske Veritas [DNV (2000)]

“Design fatigue factor from OS-C101, Section 6, Fatigue Limit States”

Design Fatigue Factor (DFF) (Table A1 of DNV-

OS-C101 “Design of Offshore Steel Structures, General (LRFD Method)”, Section 6)

The following DFFs are valid for units with low

consequence of failure and where it can be demonstrated that the structure satisfies the requirement for the damaged condition according to the Accidental Limit State (ALS) with failure in the actual joint as the defined damage.

DFF Structural element 1 Internal structure, accessible and not

welded directly to the submerged part. 1 External structure, accessible for regular

inspection and repair in dry and clean conditions.

2 Internal structure, accessible and welded directly to the submerged part.

2 External structure, not accessible for regular inspection and repair in dry and clean conditions.

3 Non-accessible areas, areas not planned to be accessible for inspection and repair during operation.

Eurocode 3 Design of Steel Structures, BSI Standards [Eurocode 3, (1992)]

This document lists safety factors on stress. These are converted to FDF in the following table:

Inspection and access

Fail safe (a) Components

Non fail safe (b) components

Periodic inspection and maintenance (accessible joint)

1.00 1.95

Periodic inspection and maintenance (poor assessibility)

1.52 2.46

Notes: (a) Local failure of one component does not result

in failure of the structure (b) Local failure of one component leads rapidly to

failure of the structure

Fatigue Assessment of Ship Structures, Classification Notes No. 30.7, Det Norske Veritas [DNV (1998)]

“Accepted usage factor is defined as 1.0” (FDF = 1.0)

BS 7608 Fatigue Design and Assessment of Steel Structures, British Standards Institute [BS 7608 (1993)]

The standard basic S-N curves are based on a mean minus two standard deviations.... Thus, an additional factor on life, i.e., the use of S-N curves based on the mean minus more that two standard deviations should be considered for cases of inadequate structural redundancy.

FDF DEFINED IN ABS FATIGUE GUIDE The Fatigue Design Factor (FDF) is a parameter

with a value of 1.0 or more, which is applied to increase the required design fatigue life or to decrease the calculated permissible fatigue damage. Table 1 presents the FDF values for various types of offshore structures, structural details, detail locations and other considerations, defined in ABS Fatigue Guide (2003).

Table 1: Fatigue Design Factors in ABS Fatigue

Guide

Note: * The minimum Factor to be applied to

uninspectable ‘ordinary’ or uninspectable ‘critical’ structural details is 5 or 10, respectively.

1) The stated Factors presume that the detail can be

inspected at times of anticipated scheduled survey or when structural damage is suspected. The need to move equipment or covers to provide direct visual access or to employ inspection tools does not disqualify the detail as being ‘inspectable’. However where the ability to perform direct



visual inspection is not evident from the submitted design documentation, any ‘Inspection Plan’ as required by the applicable Rules is to address how it is intended that the required, effective inspection will be accomplished. The use of uninspectable details should be avoided as far as is practicable.

2) ABS S-N curves, in air, as presented in Table 2 and Figure 1

3) ABS S-N curves for tubular joints 4) ABS S-N curves for details cathodically protected in

seawater 5) C1 curve in Structural Welding Code – Steel (AWS,

1992) 6) X curve in API RP2A (2000)

Table 2: Parameters for ABS-(A) Offshore S-N Curves for non-tubular details in air

Note: For two segment S-N curves, the lower cycle

portion is N = AS-m and the higher cycle portion is N = CS-r. The intersection point of the two segments is (NQ,SQ), see Figure 1.

Figure 1: ABS-(A) Offshore S-N Curves for non-tubular details in air

SIMPLIFIED FATIGUE ASSESSMENT METHOD In the simplified fatigue assessment method, the

two-parameter Weibull distribution is used to model the long-term distribution of fatigue stresses. The cumulative distribution function of the stress range can be expressed as:

Fs(s) = P(S ≤ s) = 1 – exp⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−

γ

δs

, s > 0 (4)

Where

S = a random variable denoting stress range γ = the Weibull shape parameter δ = the Weibull scale parameter Based on the long-term distribution of stress range,

a closed form expression for fatigue damage can be derived. A major feature of the simplified method is that appropriate application of experience data can be made to establish or estimate the Weibull shape parameter thus, avoiding a lengthy spectral analysis.

The other major assumption underlying the simplified approach is that the linear cumulative damage (Palmgren-Miner) rule applies, and the fatigue strength is defined by the S-N curves.

The scale parameter, δ, which is also called the ‘characteristic value’ of the distribution, is obtained as follows.

Define a reference stress range, SR, which characterizes the largest stress range anticipated in a reference number of stress cycles, NR. The probability statement for SR is:

P(S > SR) = RN

1 (5)

where NR = number of cycles in a selected period of time SR = value which the fatigue stress range exceeds

on average once every NR cycles. For a particular offshore site the selection of an NR

and the determination of the corresponding value of SR can be obtained from empirical data, or from long-term wave data (using wave scatter diagram) coupled with appropriate structural analysis.

From the definition of the distribution function, it follows from Eqs. (4) and (5) that:

γδ

/1)(ln R

R

NS

= (6)

The shape parameter, γ, can be established from a

detailed stress spectrum analysis or the shape parameter may be assumed based on experience.

The results of the simplified fatigue assessment method can be very sensitive to the values of the Weibull shape parameter. Therefore where there is a need to refine the accuracy of the selected shape parameters, the performance of even a basic level global response analysis can be very useful in providing more realistic values. Alternatively, it is suggested that when the basis for the selection of a shape factor is not well known, then a range of probable shape factor values should be employed so that a better appreciation



of how selected values affect the fatigue assessment will be obtained.

The cumulative fatigue damage for the two-segment S-N curve is expressed as:

⎟⎟⎠

⎞⎜⎜⎝

⎛+Γ+⎟⎟

⎠

⎞⎜⎜⎝

⎛+Γ= zr

CNzm

AND

rT

mT ,1,1 0 γ

δγ

δ (7)

Γ(a,z) and Γ0(a,z) are incomplete gamma functions

(integrals z to ∞ and 0 to z, respectively). Values of these functions may be obtained from handbooks.

∫∞ −− Γ−Γ==Γz

ta zaadtetza ),()(),( 01 (8)

∫ −−=Γz ta dtetza

01

0 ),( (9)

γ

δ ⎟⎟⎠

⎞⎜⎜⎝

⎛= QS

z (10)

where SQ is the stress range at which the slope of

the S-N curve changes.

SAFETY LEVEL IMPLIED IN FATIGUE DESIGN Unlike ship structures, which have regular

inspection and on-site and port repair, offshore structures usually operate in a fixed location for 20 years without port repair. Due to the economic lose if the offshore structure has to stop operation for inspection or repair, or, if the environment impact due to leakage of the structure, which can result from fatigue cracks, applying FDF to reduce the risk of fatigue cracks is the common practice. However, the safety level in terms of failure probability by applying FDF is not easily understood by designers and users. In this Section, the failure probability of fatigue cracking is calculated with different FDFs.

With reference to Spencer, Wirsching, Wang & Mansour (2003), the event of failure is the event that the cycles to failure is less than the service life as:

sNN < (11) The probability of failure is then defined as:

)( sf NNPP <= (12)

Table 3: Failure probabilities when FDF = 1.0

S-N Curve

Weibull Shape

Parameter Permissible

Stress (MPa) Failure

Probability Pf

B 0.8 748.6562 0.1424 B 0.9 634.4500 0.1424 B 1 550.0418 0.1424 B 1.1 485.7730 0.1424 B 1.2 435.5799 0.1424 B 1.3 395.5199 0.1424 C 0.8 629.5654 0.1091 C 0.9 525.5799 0.1091 C 1 450.3771 0.1091 C 1.1 394.0867 0.1091 C 1.2 350.7259 0.1091 C 1.3 316.5092 0.1091 D 0.8 464.1185 0.0900 D 0.9 381.1272 0.0900 D 1 322.4626 0.0900 D 1.1 279.3334 0.0900 D 1.2 246.5895 0.0900 D 1.3 221.0579 0.0900 E 0.8 408.9674 0.0720 E 0.9 335.8375 0.0720 E 1 284.1435 0.0720 E 1.1 246.1392 0.0720 E 1.2 217.2860 0.0720 E 1.3 194.7882 0.0720 F 0.8 346.0310 0.0856 F 0.9 284.1539 0.0856 F 1 240.4143 0.0856 F 1.1 208.2579 0.0856 F 1.2 183.8446 0.0856 F 1.3 164.8087 0.0856

F2 0.8 304.6785 0.0798 F2 0.9 250.1980 0.0798 F2 1 211.6870 0.0798 F2 1.1 183.3743 0.0798 F2 1.2 161.8792 0.0798 F2 1.3 145.1187 0.0798 G 0.8 254.3003 0.1132 G 0.9 208.8295 0.1132 G 1 176.6872 0.1132 G 1.1 153.0567 0.1132 G 1.2 135.1162 0.1132 G 1.3 121.1273 0.1132 W 0.8 219.1767 0.1106 W 0.9 179.9908 0.1106 W 1 152.2910 0.1106 W 1.1 131.9264 0.1106 W 1.2 116.4652 0.1106 W 1.3 104.4095 0.1106



For a offshore structure having 20 years fatigue life

with no inspection and repair, Table 3 presents the failure probability implied in basic design with FDF = 1, corresponding to different Weibull parameter. It is shown that failure probability of fatigue design is independent of the variable of Weibull shape parameter. In-air S-N curve is used in this study.

Figure 2 shows the results of failure probability by applying different FDF listed in Table 3. It clearly shows the increase of safety by applying FDF > 1, e.g., for F curve, failure probability reduced from 8.56×10-2 to 3.47×10-6, according to Figure 2.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1 2 3 4 5 6 7 8 9 10

Fatigue Design Factor (FDF)

Pro

babi

lity

of F

ailu

re (P

f)

B

CD

E

F

F2

G

W

Figure 2: Relationship between probability of failure

and fatigue design factor

CONCLUSIONS Application of FDF in fatigue assessment of

offshore structures is described in detail in this paper. The effect of FDF is addressed by calculating failure probability of fatigue limit state. It is concluded that by applying FDF, the failure probability of fatigue cracking can be reduced depends on the FDF used. It is also showing that failure probability, however, is independent of Weibull shape parameter.

REFERENCES [1]ABS (2003), Guide for the Fatigue Assessment

of Offshore Structures, American Bureau of Shipping, Houston, TX

[2]ABS (2004), Commentary on Guide for the Fatigue Assessment of Offshore Structures, American Bureau of Shipping, Houston, TX

[3] ABS (2004), Rules for Building and Classing Steel Vessels, American Bureau of Shipping, Houston, TX

[4]API (2000), RP2A-WSD: Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms – Working Stress Design, Twenty-first Edition, American Petroleum Institute, Houston, TX

[5]API (1997), RP2T, Recommended Practice for Planning, Designing, and Constructing Tension Leg Platforms, Second Edition, American Petroleum Institute, Houston, TX

[6]AWS (1992), Structural Welding Code - Steel, American Welding Society Specification ANSI/AWS D1.1-92, American Welding Society.

[7]BS 7608 (1993), Code of Practice for Fatigue Design and Assessment of Steel Structures, British Standards Institution, 2 Park Street, London, W1A 2BS

[8]DEn (1990), Offshore Installations, Guidance on Design, Construction, and Certification, Department of Energy, UK, 4th Edition, London, HMSO

[9]DNV (2000), Fatigue Strength Analysis of Offshore Steel Structures, RP-C203, Det Norske Veritas, Hovik, Norway

[10] DNV (1998), Fatigue Assessment of Steel Structures, Classification Notes No. 30.7, Det Norske Veritas, Hovik, Norway

[11] Eurocode 3 (1992), Design of Steel Structures, European Committee for Standardization, Brussels, Belgium.

[12] IIW (1996), Fatigue Design of Welded Joints and Components, Report XIII-1539-96/XV-845-96, The International Institute of Welding, Abington Publishing, Cambridge, England

[13] ISO/CD 19902 (2000), Petroleum and Natural Gas Industries – Offshore Structures – Fixed Steel Structures, Section A16, International Standards

[14] Spencer, J. S., Wirsching, P. H., Wang, X. and Mansour, A. E. (2003), “Development pf Reliability Based Classification Rules for Tankers”, SNAME Annual Meeting, San Francisco, USA


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5. Fatigue Design Fa