Fatigue Lecture 2 2011

7/29/2019 Fatigue Lecture 2 2011

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Fatigue Analysis ofOffshore Structures

Rod Pinna

Platform, Pipeline and

Subsea Technology 415


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Miners Rule

Answer is the Palmgren-Miner linear cumulativefatigue damage hypothesis (Miners Rule)

A problem:

Fatigue data (S-N curves) are based onconstant amplitude fatigue tests

But engineering structures experience random

loading

So, how do we work out fatigue life?


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Miners Rule

...3

3

2

2

1

1 DN

n

N

n

N

n

N

n

i

i Damageratio


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Damage Ratio represents percentageof theoretical fatigue life under a givenloading regime

If D1, failure

Can be a way of introducing a fatiguesafety factor (e.g. D = 0.5 FoS = 2)

Miners Rule

...3

3

2

2

1

1 DN

n

N

n

N

n

N

n

i

i Damageratio


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Miners Rule

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Miner's Sum

Freq

uencyofOc

currence

0 1 2 3 4 5 6 7 8 9

Corresponding lognormal distribution

Comparison between calculation andobserved results (from tests)

But notethe scatter

About righton average


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Deterministic Time Domain

Spectral Frequency Domain

Types of FatigueAnalysis


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Steps:

1. Identify all phenomena which contribute tofatigue

2. Translate phenomena into loads onstructural members

3. Translate member loads into local stresses

4. Choose appropriate S-N curve

5. Carry out Damage calculation using MinersRule

6. Compare with design life accounting for

Factors of Safety

Deterministic Fatigue

Analysis


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1. Identify Phenomena which cause

fluctuating loads could be due to:

Construction, Transportation, Live Loads,

Environmental (Wave, Wind, Current)

Remember fatigue is a cumulativeprocess

Identify Phenomena


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For a specific period For a specific direction

Wave Occurrence Table


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2. Translate phenomena into member loads:

Hydrodynamic/structural analysis

Need loads for different wave positions

Member Loads


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Structural Dynamics may be important toinclude (e.g. by using DAFs)

Member Loads


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3. Translate member loads into local stresses

Hot Spot Stress Range

Local Stresses


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Hot Spot Stresses donot include localisedstress increase due toweld profile

Local Stresses viaAnalysis/Testing


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Parametric equations for Hot SpotSCFs (see Appendix A of notes)

Note: These equations use nominalstress (nominal axial stress ormaximum (outer fibre) bending stress

i.e. NOT just geometric stressconcentration factors

Local Stresses viaParametric Eqns


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Combination ofParametric equationsat mid-points

Local Stresses viaParametric Eqns

opopS

ipipC

axaxSaxCaxS

SCF

SCF

SCFSCFSCFHSS

cos

sin

90

1 5

3

7

2 4

8 6


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S-N Curves

4. Choose appropriate S-N curves

(API, UK Department of Energy)

Use consistent approach

Environment free corrosion orcathodic protection

Equation form: )(log)(log)(log1011010 B

SmKN

q

B

B

tt

SmKN 1011010 log)(log)(log For

Thickness

effect

Also bewareof dual slope

S-N Curves !


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5. Carry out Damage calculation usingMiners Rule

Damage Calculation

...3

3

2

2

1

1 D

N

n

N

n

N

n

N

n

i

i


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6. Compare with design life accountingfor Factors of Safety

e.g. API RP2A says fatigue life mustbe at least twice design life, so D


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Frequency domain calculation

Spectral Fatigue Analysis

Energy Spectrum

Energy in EachFrequency Band

Note Units !

)(

2

21

i

i

aS


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If one component of excitation is:

Then response at same frequency is:

Spectral Fatigue Analysis

Transfer Function

)cos()( iii tatx

)(

T)( txty


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The Transfer Function also relates the excitationspectrum and the response spectrum

Spectral Fatigue

Response

e.g.Hot spotstress range

)(T)(2

xy SS

Excitation


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Spectral Fatigue

Spectral Fatigue Damage:

where Tis time period in seconds

m0 and m2 are zero and second ordermoments of response spectrum

m and Kdescribe S-N curve

is the gamma function

2

2)m8(

m

mD

20

0

2 m

KT

m

See notes for

more detail


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Deterministic vs.Spectral ?

Spectral Fatigue Analysis can account

more completely for dynamics throughtransfer function

BUT assumes a linear relationshipbetween wave height and stress range(OK for large jackets but may be not OKfor shallow water structures)


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Deterministic ANDSpectral

Commonplace to carry out calc for 8

locations on brace and chord for waveheights over 8 directions

Computationally Intensive !

Despite the convenience of softwarea sound understanding of the

fundamentals of fatigue is essential


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Questions

?

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Fatigue Lecture 2 2011

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