fatigue ocean structures

7/21/2019 Fatigue Ocean Structures

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Eko B Djatmiko

Department of Ocean Engineering

Faculty of Marine Technology – ITSSurabaya – January !"

F#TI$%E #&#'(SIS

O& O)E#& ST*%)T%*ES



"+ I&T*OD%)TIO&

Damage and failure on ocean steel structures (OSS: offshore platforms,ships, etc): mainly due to fatigue; at primary, secondary or tertiarystructural elements (intensity increases with corrosion)

Fatigue damage is one of the most important failure modes in OSS,which are subject to continuous dynamic ariable amplitude loading,comprises of:• !ow fre"uency ("uasi#static) cyclical load brought about the wae e$citation,

at the rate of some %&' %& times during the operational life of the OSS (abt*& years)

• +igh fre"uency (dynamic) cyclical loads which can be classified into transientloads (slamming, wae slapping, hull whipping) and steady loads (engineibration, propeller, hull springing), at the rate of %& times during theoperational life of the OSS (abt *& years)

• -ery low fre"uency (static) cyclical load brought about the ariation of logisticloads and hydrostatic loads (tidal), at the rate of .&&& &&& times during theoperational life of the OSS (abt *& years)

• /yclic loads due to the irregular thermal gradient brought about the climate and cargo temperatures, at the rate of '&&& times during the operational lifeof the OSS (abt *& years)

","



0 large number of factors affect the fatigue damage on OSS, li1e:

2 3ean stresses and their redistribution2 4esidual stresses2 !oading of the structure including load se"uences2 5hic1ness of the structural joints2 /orrosie enironments and temperature of the surroundings

2 Design2 Fabrication and methods for improing fatigue performance2 Sensitiity of the material

Fatigue occurs mostly on the weld joints and structural elements

where stress concentration deelops

Failure commences with crac1 initiation (fatigue) followed with crac1growth up to fracture ta1e place on the structure6

4epair and maintenance costs for OSS: large proportion is

allocated to tac1le the failure and damage due to fatigue (mostly

related also to corrosion)



Fatigue analysis at the design stage is mainly directed towardsidentification of the structural parts which has a high probability to

suffer fatigue failure and further considered as the basis forredesign of the corresponding structures 4esult of final fatigue chec1s is necessary to establish an

inspection strategy for OSS Differences between analyses of fatigue limit state (F!S) and

wor1ing stress design (7SD), ultimate limit state (8!S), or

accidental limit state (0!S):

F'S -SD. %'S. #'S

• 5a1es into account all leels of load

intensities

• 5a1es into account only the

ma$imum loads, eg6 +ighest waeof %#year period and9or %&&#yearperiod

• 5a1es into account total cycleoccurences of all load leels duringthe operational life

• 5a1es into account only one cycleoccurrence of ma$imum load6

",



Fatigue Design /riteria of Offshore Structures according to 0 4 *0#

7SD and 0 4 *0#!4FD:

• A detailed fatigue analysis should be performed for template type structures.It is recommended that a spectral analysis technique be used.

• In general the design fatigue life of each joint and member should be at

least twice the intended service life of the structure (ie. SF = .!"

• For the design fatigue life# the design value damage ratio (damage inde$" %

should not e$ceed unity (&'.!"

• For critical elements whose sole failure could be catastrophic use of largerSF should be considered (eg. up to .!" applied also for members where

access for inspection and repair is restricted

<$ample of the re"uirement on the design fatigue life of the =elana1

FSO:

• %esign service life )! years

• Fatigue life of *! to )!! years ( '! times of service life ++ "

",/



0 year later in 3arch %@%, the inestigatie report concluded that the rig

collapsed owing to a fatigue crac1 in one of its si$ bracings (bracing D#),

which connected the collapsed D#leg to the rest of the rig6 5his was traced to

a small mm fillet weld which joined a non#load#bearing flange plate to this D#

bracing6 5his flange plate held a sonar deice used during drilling

operations6 5he poor profile of the fillet weld contributed to a reduction in itsfatigue strength6

Further, the inestigation found considerable amounts of lamellar tearing in

the flange plate and cold crac1s in the butt weld6 /old crac1s in the welds,

increased stress concentrations due to the wea1ened flange plate, the poor

weld profile, and cyclical stresses (which would be common in the >orth Sea),

seemed to collectiely play a role in the rigBs collapse6

",2



*' 3arch %@& at %6A&

/asualty: %*A men out of *%* men onboard

roduction loss

",3



Fractures on the right side of the Alexander L. Kielland rig

",4



Alexander L Kielland after accident Broken support bracing

Broken support bracing Alexander L Kielland salvaged

",5



+ S,& )%*6ES #&D $*#78S

S#> Eraphs contain scatter data obtained from fatigue tests on certainstructural joints (carried out in the laboratory) see Fig6 *6% and *6*

,"

Figure +"+ 5est on structural configuration

on a load frame with actuators

Figure ++ 5est on a specimen using

uniersal testing machine (853)



,

Figure +/+ Fatigue test on a comple$ structural configuration

(aeroplane structure)



5here are two general types of fatigue tests conducted6 One test focuses on

the nominal stress re"uired to cause a fatigue failure in some number of

cycles6 5his test results in data presented as a plot of stress (S) against the

number of cycles to failure (>), which is 1nown as an S#> cure6 0 log scale isalmost always used for >6

5he data is obtained by cycling smooth or notched specimens until failure6 5he

usual procedure is to test the first specimen at a high pea1 stress where

failure is e$pected in a fairly short number of cycles6 5he test stress is

decreased for each succeeding specimen until one or two specimens do not

fail in the specified numbers of cycles, which is usually at least %&' cycles6 5he

highest stress at which a runout (non#failure) occurs is ta1en as the fatigue

threshold6 >ot all materials hae a fatigue threshold (most nonferrous metallic

alloys do not) and for these materials the test is usually terminated after about

%& or $%& cycles6

Since the amplitude of the cyclic loading has a major effect on the fatigueperformance, the S#> relationship is determined for one specific loading

amplitude6 5he amplitude is e$pressed as the 4 ratio alue, which is the

minimum pea1 stress diided by the ma$imum pea1 stress6 (4Gmin9Gma$)6 t is

most common to test at an 4 ratio of &6%, but families of cures with each

cure at a different 4 ratio are often deeloped6

(source, www.ndt1ed.org" ,/



0 ariation to the cyclic stress controlled fatigue test is the cyclic strain controlled

test6 n this test, the strain amplitude is held constant during cycling6 Straincontrolled cyclic loading is more representatie of the loading found in thermal

cycling, where a component e$pands and contracts in response to fluctuations in

the operating temperature6

t should be noted that there are seeral short comings of S#> fatigue data6

First, the conditions of the test specimens do not always represent actualserice conditions6 For e$ample, components with surface conditions, such

as pitting from corrosion, which differs from the condition of the test

specimens will hae significantly different fatigue performance6

Furthermore, there is often a considerable amount of scatter in fatigue data

een when carefully machined standard specimens out of the same lot of

material are used6 Since there is considerable scatter in the data, areduction factor is often applied to the S#> cures to proide conseratie

alues for the design of components6

(source, www.ndt1ed.org"

,1



l o g S

log N

l o g S

log N

l o g S

log N

a) b) c)

Figure +1+ S#> Eraph: a) uncertainty due to the slope, b) uncertainty

due to intercept, c) total uncertainty

,2

S#> Eraphs shows the correlation between stress range, designated S or∆S (in 3a or >9mm*), and the number of cycles, >, of the load e$citationwhich causes fatigue failure6

S#> Eraphs is gien in a log H log scale (due to a large range of ∆S and >)

S#> /ure (also 1nown as 7Ihler cure) is the mean line of the scatterdata, deried from regression analysis

5he leel of reliability on the accuracy in the determination of S#> cure isinfluenced by the slope parameter and the intercept (or position) of thecure within the graph6 =oth parameters hae peculiar uncertainties6/ombination of uncertainties of the two parameters produces a total

uncertainty for the S#> cure (see Fig6 *6.)



Figure +2+ 4egression of S#> cure for: a) 3ean fatigue life

b) 3ean minus %$ standard deiation, c) 3ean minus *$ standard deiation

,3

l o g S

log N

a

bc

n practical design it is suggested to choose the cure haing @J leel ofconfidence (ie6 appro$imately e"ual to lowering the mean cure by * timesof the standard deiation), as shown in Fig6 *66



S#> cure for structural joint configuration with shorter fatigue life tend

to be leaner9lower slope (see Fig6 *6)

Figure +3+ /omparison of S#> cures with lower and higher slope

,4

l o g

S

log N

ab

N1 N2

N2

> N1

Si



where:

2 = cycles to failure

S = stress range A intercept of the log a$is

m slope of the S#> cure

(2.1)

/onsidering the form of the S#> cure, hence the appropriate e"uationto be used correspondingly is:

,5

+" #nalytical E9pre::ion of S,& )ur;e

S m A N

A NS m

logloglog

or

−=

=



D#T# O& S,& )%*6ES

CLASS log A m

B 15.!"#

$.%

C 1$.%$

&

.5

' 1&.!%%#

.%

( 1&.51!"

.%

F 1&.&#%

.%

F& 1&.%"%%

.%

11.#5&5 .%

* 11.5!!& .%

Department of <nergy, KEuidance >otesL 4eision

Drafting anel, 0ugust %@A, ssue >

Offshore nstallations: Euidance on Design and

/onstruction6 >ew Fatigue Design Euidance for

Steel 7elded Moints in Offshore Structures

Det nors1e -eritas, Fatigue Strength Analysis for

Mobile Offshore Unit , /lassification >otes >o6 A&6*,

%@.

5 : 0ll tubular joints

=,/,D,<,F,F*,E,7 : 0ll other joints depending ona) Eeometrical arrangement of the detail

b) 5he direction of fluctuating stress relatie to the detail

c) 5he method of fabrication and inspection of detail

(see also 0ppendi$ 0)

(see Fig6 *6', Fig6 *6 and 0ppendi$ 0)

,<



Figure +4+ S#> cures for non#tubular structural joints

,"!



Figure +5+ S#> cures for tubular structure joints

,""



Figure +<+ S#> cure for brittle aluminum with a 85S of A*& 3pa

(peculiar cure pattern in comparison to steel structure)

,"



+ Effect of Thickne:: on the S,& )ur;e

Data of S#> cure is deried from the material test with thic1nesses of:t A* mm for tubular joints (5 class)

t ** mm for other joints (=,/,D,<,F,F*,E and 7 classes)

f a standard S#> will be used for a structure haing different plate

thic1ness then a correction should be made as follows:

(2.2)

,"/

$,

%

%

$,

%%

hence

because

m

m

m

m

t

t

S

A N

S

A N

t

t N N

=

=

=



/omputation of fatigue on a structural joint is carried out on the basis of

almgren#3iner (%@.) cummulatie damage hypothesis, e$pressed as:

/+ F#TI$%E #&#'(SIS B( %SI&$

DETE*MI&ISTI) #77*O#)8

(3.1)

/,"

where:

ni number of cycles of stress range at intensity S i (>9mm*) which actually

occur on the structural joint brought about e$ternal load e$citation (wae)

N i number of cycles of stress range at intensity S i (>9mm*) which will yield

fatigue failure on the joint in "uestion6 5he figure may be obtained from anS#> cure for an appropriate joint

S i stress range (or ∆S i); twice of stress amplitude that is e$perienced by the

joint (>9mm*)

n accordance to almgren#3iner hypothesis, the failure of the joint ta1esplace when the damage inde$ D approaches alue of %6&.

∑=

+++==m

i m

m

i

i

N

n

N

n

N

n

N

n

N

n D

1

&

&

1

1 .........



5he alue of S i accounted for in the computation is the ma$imum stress

range on a certain location within the joint (ie6 hot spot stress) which can be

deried by magnifying the nominal stress range, S i(nom), by considering the

stress concentration factor (S/F)6 +ence the ma$imum stress range is

calculated as follows:

(3.2)

/,

5he nominal stress range, S i(nom), is obtained from the analysis of regularwae load (deterministic analysis) to generate internal forces and9ormoments on the structural components in "uestion, appropriatelycorrespond to the wae in the 3etocean data6

5he wae load so obtained is further accounted for in the structural analysis,for instance global analysis by using a conentional stress analysis or bymeans of global F<3 (eg6 S0, E5S548D!, etc) to derie the nominal

stress range, S i(nom)6 5he alue of S/F for a joint may be found by adopting peculiar formulae as

can be found in references by 0lmar#>aess (%@), 0 (%@&), 3unse(%@.), etc6

S/F is not necessary to be computed when the F<3 could directly producestresses on the detail structure (eg6 >0S540>, 0>SNS, 0=0/8S)

SCF S S nomii ×= )-



P i is the relatie fre"uency of occurrence of each wae, haingcharacteristic height H

i

(m) and period T i

(secs) which causes a stress S i to deelop6

-ariable T is the fatigue life of the structure after counting all stress cycles

(3.4)

/,/

(3.3)

5he number of cycles ni for any stress range S i which arises due to thewae load is characteri?ed by wae height H i (m) and period T i (sec) canbe calculated by using the following e"uation:

5he fatigue life T is finally found by soling the aboe e"6 (A6.) by ta1inginto account P i , N i and T i as shown in the e$ample contained in 5ableA6%6

=y substituting e"6 (A6A) into e"6 (A6%), the e"uation of structural fatiguefailure becomes:

1........

&&

&

11

1

=+++= mm

m

T N

T P

T N

T P

T N

T P

T N

T P

D

i

i

iT

T P n

×=



Hi (m) Ti (det) Pi Si (N/mm2) Ni Pi/(NixTi)

0.0 – 1.5 3 0.8781 11 1.059E+09 2.763E-10

1.5 – 3.0 5 0.1035 32 4.303E+07 4.811E-10

3.0 – 4.5 7 0.0124 79 2.860E+06 6.194E-10

4.5 – 6.0 9 0.0042 124 7.395E+05 6.310E-10

6.0 – 7.5 10 0.0011 158 3.575E+05 3.077E-10

7.5 – 10.0 11 0.0005 191 2.024E+05 2.246E-10

10.0 – 12.5 12 0.0001 226 1.222E+05 6.822E-11

0.999 otal ! 2.608E-09

S-N "#$%e&

NS3!1.41'1012

nown (3etocean Data)

/alculated from regular wae load analysis for

Hi and Ti (deterministic method) continued with

Stress analysis to obtain Si

/alculated from

S#> cure e"uation:

2i A9Si m

/,1

Table /+"+ <$ample of fatigue calculation by deterministic method

(ec) ! 3.834E+08

($) ! 12.157

/alculated by:

% year A%,A,&&& secs

∑=

=m

i i

ii

P

T N DT

1



0s a summary, the procedure in accomplishing the structural fatigue

calculation by the deterministic method is performed as follows:

a6 Find the wae distribution data containing the alues of H i (m), T i (secs) dan P i

b6 /alculate the wae load at any concerned joint as a function of wae

height H i (m) and period T i (secs) (by adopting the regular wae

theory deterministic method)

c6 /alculate the nominal stress range S i(nom) (>9mm*

) for any concerned joint (by means of stress analysis, or F<3)

d6 /alculate the S3F appropriately for the type of joint so concerned

e6 /alculate the ma$imum stress range S i (>9mm*) at the hot spot

f6 Select an appropriate S#> diagram related to the type of joint and

calculate alues of N i as functions of S i (>9mm*

); this can be readfrom the graph or deried from e"uation NS m=A

g6 /alculate all P i /(N i xT i ) and subsituted those into e"6 (A6.) to obtain

fatigue life of the joint, ie6 T (with final result in years) by inersing the

summation T = D ∑(Ni x Ti)/Pi

/,2



t should be noted that the deterministic approach has some drawbac1s, as

follows:

a6 5he wae loads applied on the structure are generated by regularwae, which is not essentially true in real operation6

b6 5he wae at any height interal H i (m) corresponds only to a single

period T i (secs)6 +ence this is not appropriate to be implemented on

structures which are sensitie to the wae period (or reersely

fre"uency) ariation, where resonant might deelop6

c6 oint b) also implies that the method is appropriate only if the

structure haing natural period (or fre"uency) outside the wae

periods commonly occur at sea6 Such structures are inherently stiff,

eg6 fi$ed jac1et platform and other robust offshore structures6

d6 For period (or fre"uency) sensitie structures the deterministic

method might gie an oer# or under#estimate results6 +ence itshould be used only for rough estimate of fatigue life in early design

stage6

/,2



1+ F#TI$%E #&#'(SIS O& OSS

B( F%'' S7E)T*#' MET8OD

5here are a number of aspects need to be comprehended as basic thoughts onthe necessity in performing fatigue analysis on OSS by employing the FullSpectral 3ethod, as follows: OSS are designed to be operated in real seas with the primary (dominant)

enironmental loads due to the wae e$citation6 5he real sea waes are random in nature, hence the responses of an OSS

due to the wae load e$citation will also be random; 5herefore the number of load cycles as well as intensities should be

computed by applying an appropriate method and procedures so thataccurate results of the analysis will be attained6

1,"

Figure 1+"+ 0n e$ample of a random wae time history



4andom waes (as in the case of any random signal), as shown by the time historyin Fig6 .6%, by means of Fast Fourier 5ransform could then be presented in the formof wae spectra (see references on sea waes)6

Following this, the random responses of an OSS could also be presentedin the form of response spectra6 5his is obtained by correlating theresponses in regular waes and the wae spectra6 (>ote: random waes as wellas random responses are composed by the superposition of a large9infinite number of regularcomponents)

From a spectra (either wae or response), and by applying certainformulations and algorithms, one may deries the statistical alue

(including the distribution) of the intensities as well as number of cycles that could possibly deelop during the lifetime of an OSS6 5he technical detail of the full spectral analysis is as described in the

following6

1,



First Stage: the distribution of fatigue load is computed on the basis

of loads on OSS due to regular waes e$citation, similar to thatcarried out in the deterministic approach (by employing 3orisonPstheory, *#D strip theory, or A#D diffraction theory), depending on theOSS configuration6• 5he difference in comparison to analysis in /hapter A is, here the load

computation is performed by arying the wae fre"uencies ω (commonly between &6% *6& rad9s at interal of &6* rad9s)6

• 4esults of the analysis are then presented in the form of transferfunction graph, which correlate between the ratio of load amplitude(bending moment, shear force, etc) to wae amplitude, designated asthe 40O (4esponse Amplitude 5perator ), for each incrementalfre"uency ω 6 (see Fig6 .6*)

• 40Os are computed for a number of wae directions (appropriatelyrepresenting the occurrence in the operational site of the OSS)6

• n some cases 40Os are also computed for a number internal loadconditions6 For e$ample analysis related to FSO may include: ballastcondition, %&J storage load, &J storage load, and %&&J storageload6

1,/



Second Stage: transforming the !oad 40O into Stress 40O for

particular joints under obseration by performing stress analyses(most appropriately applying F<3) see Fig6 .6*

1,/

*ave Load

Analsis-/egular)

Stress Analsis0

-F()

ω

/ A 2 3

ζ F 4

, ζ 4

ω

/ A 2 3

S , ζ

4

Figure 1++ !oad analysis to derie the Stress 40O

S*E , S*E ,,



5hird Stage: conducting the full spectral analysis, comprises of thefollowing steps: Step %: the definition of operational scenario (operational bo$)6 5his step include also the determination of probability related to the

occurrence of any sub#operational bo$, eg6 probability of waeoccurrences, probability of wae directions, probability of loadconditions, probability of adancing speeds, etc)

robability of wae occurrences may be obtained from the wae scatter

diagram, as e$hibited in Fig6 .6.6 5he (joint) probability of any singlecombination of + and 5 is the fraction of its occurrence relatie to thetotal wae occurrences6

robability of wae direction may be obtained from 3etocean data,which in most cases ery much related to the geographicalchracteristics, climate and (dominant) wind directions6

robability of load conditions is obtained from the fraction of certain

load condition (eg6 &J cargo load) relatie to the oerall loadoperation (say: ballast, %&J, &J, and %&&J load) robability of adancing speeds is related to the sea going ships, which

are operated at different speed leels6 For instance military essel maybe operated at speeds correspond to harboring, sureilance, chasing,combat, etc6

1,



a%e $.

a%e( )

oad "od.

30o

40o

2 m

3 m

#ll oad

Figure 1+/+ Operational scenario (bo$ of operation) of OSS

pi = probability of wave intensities (joint prob of H & T)

p j = probability of wave directions

pk = probability of load conditions

1,/



1,1

able 4.1. *S a%e Scatte$ ag$am o$ $et$cted Se$%ce "lacato

ABS0 67'( F2/ & S8(C+/AL9BAS(' FA+76( A:AL;S7S F2/ FL2A+7: 8/2'6C+72:0

S+2/A( A:' 2FFL2A'7: -F8S2) 7:S+ALLA+72:S0 a &%1%<

Wave Periods

Wave

Heights

(m)

3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5Sum

ver !""

Periods

0.5 8 260 1344 214 134 413 !6 10 1 0 0 "610

1.5"" 1223 "34 !"6 4!## 16# 3! 6 1 211"#

2.5

406 324" !#44 !!! 430" 14"# 3"1 6" 10 2"6!0

3.52 113 1332 4" 64## 4!16 202 642 14 2# 20161

4.530 46 2101 3!! 343 1#!6 66 12 43 1262"

5.5# 1"6 #"# 1#6! 2030 130! "64 1#0 46 !016

6.52 "2 336 #"6 10!! !" 30 140 40 36##

7.51 1# 132 3#3 "4" 4"2 24! # 30 106

8.56 "3 1!2 2!2 2"0 1"0 6" 22 0

9.5

2 22 !# 136 13! 0 42 1" "22



Figure 1+1+ 7ae scatter diagram (total wae data *%@)

1

2

3

4

5

6

7

8

2 4 6 8 10 12 14 16

1& &% " &# 55 ! 1%$ !! $ 1= &%

$ $1 5 !5 =& 11#1=! 1" "# 5 1&

$$ 5= $" !1 !" 1$$ $= &1 =

11 & 1 $% 5" $# 1$ 5 " &

1 = ! 11 1% = 1 $ 1

5 1 $ # 5 ! $ & 1

& & & $ & &

1 & 1 1

& 1

1 1 1

1 &

1 1

1

8: =m>

Tp :ec>

1,2



5hird Stage: conducting the full spectral analysis, comprises of thefollowing steps: Step *: conducting computations to generate the stress range spectra on the

basis of data yielded from the 40Os and wae spectra for eery element in thebo$ of operation6 5his step is basically identical with changing the information ofstresses in regular waes into stresses in random waes (sea waes)6

ω

/ A 2 3

S , ζ

4 &

/A2&-stress) > *ave Spectra 3 Stress Spectra

ω

S - ω )

?

ω

S S

- ω )

3

Figure 1+2+ /omputation to obtain the stress spectra

1,3



Figure 1+3+ /omputation of stress range short#term distribution

(4ayleigh distribution)

S

p S - S )

S1 S& S S$ Sm

:umber of ccles

Short9term

-1,det)

1,4

5hird Stage: conducting the full spectral analysis, comprises of thefollowing steps: Step A: conducting computations to obtain the number of cycles and followed by

computations of the distribution in the short#term scope, as shown in Fig6 .66

∫

∫

∞

∞

=

=

!

!

!

>=

>=

ω

ω

d S m

d S m

S

S

! ?

!

>= mS

s em

S S p

!

!

" mmnπ

=



Step.: /omputation of number of cycles in the long#term (operational life of

the structure) by:

(4.1)

(4.2)

1,5

where :

n number of stress cycles in the long#term

6 lifetime of the structure (secs)

no number of cycles per unit time (%9sec); can be found from the interal

operation in the short#term (see Fig6 .6):

mo area under the spectral cure (of stress response)

m second moment of area under the spectral cure (of stressresponse)

∑∑∑ ×=i j k

Lk ji L xT nn )- %

%

&%

&

1

m

m

n π =



Step : Determination of the probability density function (DF) for the

stress range S , in the long#term period (lifetime of the structure); which

could be appro$imated by 7eibull distribution, as follows (see Fig6 .6'):

(4.3)

(4.4)

where !(S) is the DF in the short#term; which is appro$imated by

the 4ayleigh distribution, as follows:

1,<

∑∑∑∑∑∑

×

××=

i j k

k ji

i j k

!k ji

L n

S n

S %

% )-

)-

%& &,

%)-

mS

! em

S

S

−

=



Figure 1+4+ /omputation of the long#term stress range distribution

(7eibull distribution)1,"!

- a %

e / $

.

0 / 1

/

oad cod

+ ++

+ +

n%1 n%& n%

n%m9& n%m91 n%m

> pi . p @ . pl

S

+otal number of occurence 3 n L1%% 1%1 1%& 1% 1%$ 1%5 1%! 1%# 1%=

* e i b u l l

d i s t r i b u

t i o n



S%MM#*( O&

T8E 7*O)ED%*E OF F%'',S7E)T*#' F#TI$%E #&#'(SIS

%6 erforming the regular wae load analysis to derie 40O of the structural responses(=ending 3oment, Shear Force); carried out for a number of appropriate wae directions(eg6 &, ., @&, %A, %& degs)

*6 5ransforming the structural response 40Os into the stress range 40Os (using stressanalysis, or F<3)

A6 Defining the operational scenario of the OSS by considering among others: the metoceandata (wae scatter diagram, joint probability of + Q 5, wae direction), loading conditions,adancing speeds (for traelling ships), spectral ariation (if any), and so on

.6 /omputing the stress spectra for all mode of operation as defined in point A)6 /omputing number of cycles (e"6 .6*) and distribution of stress cycles in the short#term as

can be represented by 4ayleigh distribution (e"6 .6.) for each operational mode in point A)6 /omputing the distribution of stress cycles in the long#term (which is the summation of all

the short#term stress cycle distributions) by considering the designed operational life 5 (inyears seconds) and all the probabilities of elements within operational mode in point A),and soling e"s6 (.6%) and (.6A) the long#term stress range distribution will follow the

theoretical 7eibull distribution'6 /orrelating results of the analysis and computation of stress cycle distribution in the long#term as obtained in point ) with the fatigue data represented by S#> cure byimplementing the almgren#3iner rule (e"6 .6%) to finally determine the fatigue life of thestructural joint under obseration6

1,""



2+ )'OSED,FO*M F#TI$%E E@%#TIO&

3ethod of predicting the fatigue damage on steel structure has beenintroduced by almgren#3iner through the accumulatie damagehypothesis:

f (S) is the stress pdf which can be defined in such a way hence (S i )dS is

e"uialent to the number of oscillation of stress component with the pea1

alue lies within an interal dS and with the mean alue of S i6 Further by

ta1ing " and T as the mean fre"uency which ary randomly and the oerall

operational time, respectiely, hence the increase of the damage due to S i which will ta1e place during an interal T is:

(5.1)

(5.2)

2,"

∑=

+++==m

i m

m

i

i

N

n

N

n

N

n

N

n

N

n D

1

&

&

1

1 .........

( )i

i

S N

dS S " T dD

)-××=



N(S i ) is number of cycle which would bring about damage at stress leel S i6

From e"6 (6*) the e$pected damage that would ta1e place in a certainperiod T , could then be obtained by integrating contributions of all cycles ofthe stress components, that is:

f T is the operational life of the structure as initially designed (ie6 T L), hence

T L3 n L /" 6 So e"6 (6A) could be rewritten by substituting N=A/S m , as follows:

(5.3)

(5.4)

2,

∫ ∞

×=% )-

)-)- d!

S N

S " T D # L

∫ ∞

=%

)-)- d!S S A

n D # m L



$t is i%portant to notice tat (S) is te contin'o's for%(teoretical) of L(S) in e (43)* wic represents a discrete

distrib'tion +ro% vario's investi,ation on te lon,-ter% wavedistrib'tion it as been concl'ded tat P L(S) co'ld be closely

appro.i%ated by /eib'll pdf* na%ely

where:

λ scale parameter

ξ

form parameter

5he alue of λ is a function of the e$treme stress range6

5he alue of ξ is a function of the structural configuration and operationalsea site; for the general e"uation ξ may range between &6' up to *6&; for

ocean structure ξ may range between &6@ (mostly for large structures) up

to %6%6 (mostly for small structures)6

(5.5)

2,/

−

=

− ξ ξ

λ λ λ

ξ S S S L e>p)-

1



f parameter Se is defined as the e$treme stress occurs once during oerall

cycles n L , thence λ could be calculated as:

(5.6)

arameter ξ will be obtained from iteration on the basis of results from

L(S) and n L 6

=y substituting e"6 (6) into e"6 (6.) we can find:

(5.7)

2,1

ξ

ξ ξ

λ

λ ,1)ln

or ln

−=

=

L

L

nSe(

nSe

S S

d!S S

S A

n D m L

−

=

−∞

∫ ξ ξ

λ λ λ

ξ e>p

1

%



ntegral in e"6 (6') could be simplified by implementing the gamma

function,Γ(n" and substituting into e"6 (6) as follows:

(5.8)

f the gamma funtion is defined as :

(5.9)

2,2

0ppro$imation of gamma

function:

Stirling Formula :

( )dx x x A

n D

xS

mm L −=

=

∫ ∞

−+ e>p

give 4ill+aking

%

1),1- ξ

ξ

λ

λ

∫ ∞

−−=Γ %

1)- dt t en nt

&!.1)!.1-e>p%%#!.%)- +≅Γ x x

( ) xe x x x ,&)1- π ≅+Γ



0nalogy of the factor within the integral in e"6 (6) and (6@) yields:

(5.10)

or, by substituting e"6 (6) into e"6 (6%&) finally we find:

(5.11)

this is referred to as

the )'OSED,FO*M F#TI$%E 'IFE E@%#TIO&

2,3

),1- ξ λ m A

n D m L +Γ =

),1-)-ln ,

ξ ξ

mn

Se

A

n D

m

L

m

L+Γ =



3+ *E'I#BI'IT( #$#I&ST F#TI$%E F#I'%*E

3argin of Safety :

Definition of margin of safety with regards to fatigue (by considering % from

e"6 6%%) is :

(6.1)

4 resistance or strength factor

load factor

(6.2)

3,"

LR M

) m! )" !ln

Se

A

" M

#M

mL

mL

F

F

ξ

ξ

"



Table 3+"+ Some references on ftigue failure inde$

" -

S: #; 0.90 0.67

S:#t< 1.00 0.60

Sc:llg 0.70 0.60

#$e 0.85 0.22

Ede e$ge 0.78 0.19

olme =e$$ 0.69 0.61

Table 3++ <$amples of uncertainty on ariables

*>,*E ?E*N " ,S @AE

N L

8.4'107 0.05 og-No$mal

A 1.51'1012 0.31 og-No$mal

m 3.0 0.03 No$mal

Se 200 0.20 og-No$mal

ξ

0.94 0.05 og-No$mal

3,



ol'tions + (mean value frst-order second moment )*5+ (advanced first1order second moment ), or 3onte /arlo

Simulation

+ & 7 are independents wit nor%al distrib'tion

(6.3)

(6.4)

(6.5) (6.6)

(6.7)

3,/

(6.9)

)! )R L! $ pf β

n>ke:elamata=in0ek: "

M M %

M =

σ

β

∑

i

i

i M

% M

x

x

M % &O%

x %

i

i i

σ

"

LR LR % %

LR

=

=

θ

θ

σ

β

L R



#77E&DIA #+

)'#SSIFI)#TIO& OF ST*%)T%*#' JOI&TS =refer al:o to Fig+ +5>

#,"



#,



#,/



#,1



#,2



#,3



#,4



#,5



#,<



#,"!



Fa1tor 1onsentrasi tegangan atau stress concentration factor (S/F)merupa1an perbandingan antara tegangan tertinggi di suatu posisi pada

sambungan (hot spot stress) dan tegangan nominal pada brace

(Eibstein, %@):

=esarnya S/F untu1 tiap sambungan a1an berbeda tergantung pada

geometrinya dan S/F ini merupa1an parameter yang dapat

mengindi1asi1an 1e1uatan sambungannya6 onsentrasi tegangan

menggambar1an suatu 1ondisi dimana telah terjadi tegangan lo1al

yang tinggi a1ibat dari geometri sambungan tersebut, sehinggadibutuh1an 1ea1uratan yang tinggi dalam penentuan nilai tegangan hot

spot , dan juga pennetuan S/F untu1 jenis sambungan yang berbeda6

#77E&DIA B

ST*ESS )O&)E&T*#TIO& F#)TO*

B,"

n

ma'sS&F

σ

σ



ada titi1 yang berde1atan di suatu sambungan antara chord dan brace nilai S/F yang terjadi a1an berbeda, 1arena 1edua member mempunyaiparameter#parameter dan orientasi yang berbeda6 S/F untu1 brace diberinotasi S/Fb dan untu1 chord diberi notasi S/Fc6

+ot spot adalah lo1asi pada suatu sambungan (tubular) dimana terjaditegagan tari19te1an ma1simum6 Secara umum diidentifi1asi sda tiga tipetegangan dasar yang menyebab1an munculnya hot spot (=ec1er, et al6,%@'&):

%6 5ipe 0, disebab1an oleh gaya#gaya a1sial dan momen#momen yangmerupa1an hasil dari 1ombinasi frame dan truss jac1et6*6 5ipe = disebab1an detail#detail sambungan stru1tur seperti geometri

sambungan yang 1urang memadai, ariasi 1e1a1uan yang berariasidisambungan dan lain#lain6

A6 5ipe /, disebab1an oleh fa1tor metalurgis yang dihasil1an dan 1esalahanpengelasan, seperti undercut, porosity, dan lain#lain6

8ntu1 mencari besar dari S/F dapat dila1u1an dengan pengu1uranlangsung yaitu dengan e1spenimen dengan mengguna1an strain gageatau dengan mengguna1an rumus#rumus pende1atan (1uang, semedleydil)6 =eberapa rumus pende1atan yang diberi1an oleh uang danSmedley sebagai beri1ut

B,



arameter 8tama:

! panjang 3hord

D diameter terluar chord

d diameter terluar brace

5 tebal chord

t tebal brace

g jara1 ujung 1e ujung antara

brace

arameter 5urunan:

α *!9D

τ t95

β d9D

ξ g9D

γ D9*5

θ sudut antara brace dan chord

$ambar B+"+ arameter tubular joint

74A30 74A30

5

D

t

=<=0>

0S0! =<=0>

0S0!

> !0><

=<>D>E> !0><

=<>D>E

O85 OF

!0><

=<>D>E

!

O85 OF

!0><

=<>D>E

g

θ

d

B,/



%6 ersamaan S/F Smedley

ersamaan Smedley diberi1an untu1 batasan parameter sebagai beri1ut:

ersamaan Smedley untu1 posisi sadel pada chord:

Dari hasil e1sperimen menunju11an bahwa bahan baja mencapai

1elelahan ditentu1an oleh besaran beda tegangan ma1simum terhadap

minimum yang berulang#ulang seperti dinyata1an pada 1ura S#>6B,1

&1&

"%%

%.11.%

1&5.%

$%=

%%

≤≤

≤≤

≤≤≤≤

≤≤

γ

θ

β

τ

α

θγτ

β

/4+!4+"2+!. ? :in1+345+3

( A* S&F

θγτ

β

/2+"2. ? :in"2+"3+"

( O$+S&F



.s 3 SCF at $%ord saddle.c 3 SCF at $%ord cro4n

.b 3 SCF at &ra$e

3 *eld correction factor 3 %.#"$

8ntu1 In1plane 7ending :

8ntu1 5ut1plane 7ending :

8ntu1 01sial:

*6 ersamaan S/F dari >aess (sambungan tubular N)

$ambar B++ Sambungan tubular tipe N

B,2

).!.%1-

)15.%).-cos&.1.-.%.%5.1B

,5.11

sin).sin,&,).-,.5.%.-

sinsin.&)).-1.-..#.1#.%-C

B.C

sin)..$&.!#=.!.-..

sorc

$5.11

5.%5.%

).#.%#.1-&,1

K K

K

K

K

K K K K

K

&

$

o

$

$o$$

!

+=+−+=

−−−

=−−+=

+=−=

−

+

θ β τ γ

γ

θ θ β α γ τ β τ

θ θ β τ γ

θ β β τ γ β $&

$

K K

K

.!.%1

sin)..#.%.!.1.-..#5.%).!.15.1-&&5.%=.%!.%

+=−= − θ β β τ γ β

K! K

K!

& .!.%1

sin)..15.1!.1.-.. )5.1-5 &

+=−= + θ β β τ λ β



A6 ersamaan uang

ersamaan uang untu1 para#

meter dengan batasan sbb:

• 8ntu1 /hord:

• 8ntu1 =race:

%% "%%

..=

%.1%&.%

=.%.%

=.%&.%

$%#

≤≤

≤≤≤≤≤≤≤≤

≤≤

θ

γ

ξ

β

τ

α

θ τ γ α β !"$.1.1%=.%&.1%5#.%

0, sin"=1.1−= ' T A SCF

θ τ γ β %5#=!%.=!.%$.%

0, sin#%&.% −=' T )P*SCF

θ τ γ β 55#.1==".%%1$.1#=#.%

0, sin%&%.1=' T +P*SCF

θ τ γ β

55#.1==".%%1$.1!1".%

0, sin$!&.%

−

=' T +P*SCF

θ τ γ α β "$.1.155%.%5..11&%.%

0, sin#51.−= ' T A SCF

θ τ γ β %&1=.%!.%&.%

0, sin%1.1=' T )P*SCF

θ τ γ β %.&5$.%=5&.%=%1.%

0, sin5&&.1=' T +P*SCF

θ τ γ β %.&5$.%=5&.%&=1.%

0, sin#"!.% −=' T +P*SCF

fatigue ocean structures

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