@

THE SOCIETY OF NAVAL ARCHITECTS AND MARINE ENGINEERS,@C.1w,.>e One World Trade Center, Suite 1369, New York, N,Y, 10048

>?”’

co

*3 PaPer$ to be presented at Extreme load. R,SPO”S, Symposium~

: Arli”ston, VA, October 19-20, 1981

;+ .5

% ,*L . ,*,,+\”+

Fatigue Criteria for Ship Structure DetailsW. H. Munse, University of Illinois, U;bana, IL

ABSTWCT

Fatigue criteria are presented forthe design of ship structures. l%ecriteria take into account the ships tructure details, the fatigue resis-tance of specific locations in thesedetails, the variable loading to whicha ship is subjected, and the desiredlevel of reliability (factor of safety)A design example indicates the simplemanner in which the criteria can beuseti.

NOMENCLATURE

log c

fs(s)

k

L(n)

m

N

(PF)

‘F

s

SD

(sD)all =

The life intercept of theS-N curve

Probability density function-Weibull distribution(Equation 2)

Shape parameter for theWeibull distribution

The probability of mfailure through a life, n(Equation 9)

Negative slope of S-N curve

The mean life necessary toproduce a useful life n witha reliability of L(n)

Probability of failure= [l-L(n)]

Reliability factor(Equation 13)

Stress range

Constant-cycle fatiguedesign stress range for auseful life n and reliabilityL(n)

The maximum allowablefatigue stress range(Equation 15)

(s~ax)N = The maximum stress range ofa variable Ioadi”g historythat is expec ed to produce

~failure in 10 cycles

‘N

‘Io8

w

‘L

r

us

E

5s

‘N

= Mean constant-cycle stressrange for failure at N cycles.

= The maximum stress range ex-pected to occur once in 108cycles, based o“ a Weibulldistribution.

= Characteristic value of S(Equation 5)

= Scatter factor (Equation 11)

= Gamma func tio”

= Mean stress of the Weibulldistribution (Equation 3)

= Random load factor (Equation7)

= Standard ieviation of theWeibull distribution.

= Total uncertainty in fatiguelife (coefficient ofvariation)

INTRODUCTION

Fatigue cracking in ships has beena serious problem for many years Asnoted by Vedeler (1)1 in 1962, ship-builders in Norway and Sweden consid-ered the problem of fatigue in shipsto be of more practical importance forordinary ships than the question ofbrittle fracture, He noted that fa-tigue cracks were often found in theforepeak region, bottom amidships, atthe bulwark at both ends of the bridge,and in the hatch corners In a recentstuciy it has been observed that shipsmay also have cracks at crossings offrames, longitudinal, and girders ,and many other locations (2, 3 and 4)

in

23.1

1Reference

parentheses.numbers are indicated

&

Since such cracks may be possiblepoints of initiation for catastrophicfailures and, since the repair of fa-tigue cracks can be very costly, it isessential that fatigue be given ade-quate consideration i“ the design ofship structures

In this paper criteria are pz-e-sented for the fatigue design of shipstructural details along with a briefdiscussion of the principal parametersincluded in the criteria. 2 An exampleof the application of these designcrireria is then presented to indicatethe simple manner in which the criteriacan be used to provide a verificationof the adequacy of a ship in fatigue.

FATIGUE DESIGN PARAMETERS

Fatigue design generally consistsof verifying that the details of astructure have sufficient resistanceto repeated loading to provide a fa-tigue life equal to or greater thanrequired: a wrifica, tion by checkingDrocess To achieve this for shiu;tructure details , criteria have ~eende”eloped which takes into account,(a) the basic fatigue behavior ofwelded structural details, (b) thetYPes Of details found in ship struc-tures at which cracking has been ob-served, (c) the loading histories towhich ships may be subjected, and (d)the level of fatigue safety to be in-cluded in the ship design.

There are other factors that canaffect the fatigue behavior of a struc-ture also ; however, their importanceor effect is not as great as the effectof those noted above and to includethem would have greatly complicatedthe overall design process. Theseneglected factors include, (a) themean stress effect, an effect that isrelatively small for welded detailsand is now neglected in most fatiguedesign specifications , (b) the tensilestrength of the steel, another factorthat is generally neglected in struc-tural fatigue design specificationsand considered to have relativelylittle effect in long life fatieue.and (c) tempera ture,-rate of lo~dapplication, residual stresses, andsize effect, again factors that areEenerally found toZmportanie

be of secondary

2The ship design criteria presentedherein were developed in an investi-gation conducted at the University ofIllinois and sponsored by tbe SnipStructure Committee,

Fatigue Behavior of Weldments

During the nearly 50 years oflaboratory studies conducted on weld-ments , numerous papers , conferenceproceedings and books have been pub-lished wherein detailed fatigue datafor welds and weldments may be found(5-11) Recently, much of this infor-mation has been re-examined to estab.lish basic S-N relationships fornumerous types of welded members anddetails (12) Nearlv 1500 S-N curveshave beerip;oduced, &ne example ofwhich is presented in Fig. 1. (Thisis the S-N curve for axially loaded lon-gitudinal fdl penetration groovewelds with the reinforcement intact;based on stress range; and for mild,high strength low alloy or quenchedand tempered steels. Identified byDAAAXB)

The solid line mean regressioncurve (50% reliability) of Fig. 1, asestablished by a least-square analysis ,can be given by,

Log N=log C-mlog SN (1)

~;or SN = (N) (la)

where,log c =

N=

m=

‘N =

the life intercept of theS-N curve

number of cycles to failurefor a constant cycle stressrange of SN,

the negatiw slope of theS-N curve

the constant-cycle stressrange for failure at Ncyci’es.

Using such straight-line relation-ships , the mean fati ue stress rangesfor lives of 105, 10~, 107, 108 cycles,have been established for numerouswelded members and details , and arepresented in Table 13, These mean fa-tigue strengths are for the numerousstructural fatigue details shown inFig. 2.

For each of the details shown inFig. 2, the location at “hich the fa-tigue strength applies is the pointwhere the greatest *tress concentrationexists and, except as noted, ca” be

3Under random loadings straight-

line S-N relationships are found toextend well beyond the fatigue limitsoften reported for constant cycletests (10) Therefore: in this devel-opment, the straight-line S-N relation-ship has been assumed to extend to 108cycles or more.

232

200

(OJ

m

60

1 I 1 1 1 1 ! Ill [ 1 1 1 1 1 1 111 1 1 ) 1 1 1 [ Iu 1 1J

1“

1 , 1 I ++~LB,,? TGLFF7CNU L ,“ !, s,,. 5..,, “K

t

4-

9,,: CO.r)[)[kct LCWL -

.

m.,, .

=-. --- =-—

-- =---

-.—- --------

._ . . .

1

++tHtH-–++ +-++-}+ H’, 5 , 10,!, : , , 5,,,,

CYCLES TO FF!lLL!RE,IN TH12U5RNC’5Fig. 1. S-N Relationship for a Weldment Containing a Longitudinal Groove

weld in the As-Welded Condition, (Detail No. 3)

considered to be a function of the prin-cipal tensile stress at that location.This location, for example, is at theend of the cover plate for detail No. 5,is at the toe of the butt weld for de-tail No. 10, and is at the side of thehole in detail No. 28.

The data in Table I and the dia-grams of Fig. 2 provide the basic fa-tigue information on which the fatiguedesign criteria presented herein arebased.

Ship Details

After the basic fatigue data hadbeen assenbled, the second phase inthe development of tbe fatigue designprocedure was the identification ofthose ship locations at which fatiguecrackine mi’zht occur. Two recent re-ports o; th~ in-service performance ofstructural ship details (3, 4) haveserved to define possible fatigue criti -cal locations in &hips These-reportscatalog and define the types and loca-tions of details at which failureshave occured in a variety of merchantand Naval vessels.

A total of 86 ships were includedin the surveys The details examinedwere separated into twelve generalfamilies (see Table II) and these werein turn divided into 56 zrouDs of 634separate configurations. - A ~otal of6856 failures were found in the 607584details observed. In the investigationon which this paper is based, the loca-tions in each of these confi~urationsat which fatigue might devel~p have

been identified and will provide gui-dance in locating the details for whichpossible fatigue failure should bechecked (22) AIIexample of a few ofthese families and configurations ofdetails is presented in Fig. 3.

The locations in Fig. 3 at whichfatigue cracking might develop are cir-cled and identified by the correspond-~g structural detail number from Fig,

(The basic fatizue resistance forthe ‘detail is provi~ed in Table 1)

Not all details in Fig, 2 are foundin ships and not all of the detailsused in the ships surveyed ha”e exhibi-ted cracks Only the thirty-seven de-tails listed in Table III are those forwhich cracking was reported and then,some of the details exhibited only avery limited number of cracks Thosefor which the largest number of crackswere found are those for which thesefstigue design criteria will be ofsvceatest value, However. in design a?atig”e evalwition shodd be made-ofall details for which fatigue crackingis a possibility,

Ship Loadings

To properly evaluate the fatigueadequacy of a ship detail requires arealistic estimate of the cvclic stresshistory to which the detail-will be sub-jected during its lifetime. Since theexisting full-scale ship loading dataare for a limited length of time. ithas been necessary to-extrapolate theavailable data to obtain an estimatedlifetime spectrum (13, 14) Such

233

TASLE I

Mean Fatigue Stress Range for Fatigue Details in Fig. 2

(Constant Cycle - 0,50 Reliability)

Detalil S-N Stress Range, ksi, for n cycles2Slope,

(seYIJig, 2) m ~ = 105 ~ = 106 “ = 107 ~ = 108

11(F)233(G)456

99(s)101O(G)1111(G)

12(G)12131415

:!(G)

17(s)

1818(s)1919(s)2020(s)2121(s)

2223242526A25B2627

27(S)2828(F)29

;;#)

29R230

5.734.806.055.775.946.083.256,08

4.116.549.648.857,449.326.136.65

5.663.984.237.433.484.636.973.739.52

4.039.227.497.533.946.443.947.36

3.153.263.267.098.533.953,464.85

4.487.744.81

2,83

69.467.161,544.141.241.426,441.4

39,855,832.64839.947.233.129.4

40,835,048.340,625,9832,832.827,828,9

20.3025.723.127,532.928.02(:;;:)

39,835.735.733.249.9(;::;)

22.8

22,840,1(29.4)

38~0

46,541.542,029,627.928,313.0228.3

22.7139,225,73729,336.922.7322.5

27,219.628.029,813.4019.9323,615,0022.7

11.4620.0217,0020,2818,3619.60(~M:36)

19,1617.617.624.038,1(;:::;)

14,17

13.8329.8(18.21)

16,83

234

31,125.728,719.919.019,46.42

19.41

12.9727,620.228.521.528.815,6217.26

18,0911.0016.2721.86,9112,1216.948.1017.81

6.4715.6012.4914.9310.2313.71(;;:;3)

9,228,688,6817.3629.1(M:j:)

8.81

8,1622,11(11,28)

7,46

20.815.919.6213,3312.8713.303.16

13.30

7.4119.415.9222.015,7622.4910.7313.23

12.056.179.44

16,033.577.37

12.174.3713.99

3.6512,159.1810,995.709.59(5,70)16.59

4,434,284.2812.5422.20(::~:)

5.46

4.8816.42(6,99)

3,31

TABLE I (CONTINUED)

Detail S-N Stress Range, ksi, for n cycles2

No .1 Slope,(See Fig. 2) m n = 105 ~ = 106 n=10

7 ~ = 108

30A31

;;A32B32c

::(s)

3434(s)353636A3737s38

:; (s)

39A39B39C404142

4343A4445464747A48

48R4950515253

(::;;)

3;483.53

3.6610.39

3.6610.393.553.953.95

3.71

10.23

3.53

5.02

4:35

(34.o)(20,16)

(;::g:)

21;3425,5

(21.34)(:::;)

34.934.9

32-

16.27

(21~50)

110,2

(20~16)

(23.5)(11.87)

(;:i;y)

11~3820,45

(11.38)(;;:$:)

19.5119,51

17.2

13,00

(11:21)

69;8

(11~87)

(16.1)(6.99)

(:;:;)

6;0716.38

(6.07)(1::::)

10,8910.89

9;24

10.37

(5;84)

44,08

(6:99)

1(S) Indicates

(F) Indicates

(G) Indicates

shear stress on fasteners or welds

flame cut surfaces.

the surfaces have been ground flush

(:;:;:]

(:;:;)

3;2313.12

(3.23)(1::l..)

6.086.08

4:97

8.28

(3:04)

27;88

(4112)

‘Estimated values are shown in parentheses ( )A dash is provided where no data are available

235

1“ ,“, -,” 7/’- L~#

ce=

c1 3

&&J-&.

‘f3==J-yp-13

Fig. 2, Structural Fatigue - Details

236

-==2-29( F)-29

29RI (Radi.3 = l14~,to1/2”)29 R2(Rodi. s ,1/2 Iol )

‘w.

C===D’>30A

c

32

c)

3;(s)-37

38( S)-38

_ —.

42

45A

n ct&Jl,

*+

L@ 51

‘k- –-#--52

r-l

L..

F/

“c3cJ-47

/53

(G) - Designates a ground surface(S) - Designates shear on weld or

fastener(F)

Fig,2,

Designates flame-cut edges f.ai-comparison with machined edges

Structural Fatigue-Details (cent

390

T

738 37

(a) Family No. I(AI)

7

b

‘\

7

25B 2130Zf(s)

(c) Family No, 2 (c2)

36 36

m49

(e)Family No,8 (A3)

39

T

-... . . . .26 26

20,21

(b) Family No,l(B4)

W_25 ; 3333s

(d) Family No. 3( AI)

7

III

f

(f) Family No, II(AIO)

Fig. 3. Examples of Configurations inship family details (3,4)

TABLE III

Details Exhibiting Failures i“ Ships

TotalDetail No. o

No. Crack—.

7

9

14

17

17s

19

19s

20

21

21s

26

28

28F

29

29R

29F

30

30A

272

7

7

2

‘2

42

40

318

1300

54

155

208

222

9

3

7

142

672

Detail&

32B

33

33s

34

34s

36

37

38

40

41

42

43

44

47

48R

50

51

52

53

TotalNo. ofCracks

2

36

20

23

17

600

462

8

2

11

7

75

14

29

25

2

687

105

8

i--237

1

~BLE II

Summary of Data for 12 Detail Families (Ref. 4)

Totals Observed

?amily Detail Family Total No, Total No,No, Name

zDetails Failures Failures

1 Beam Bracket 68,586 2,252 3.2B

2 Tripping Bracket 34,o12 1,587 4.67

3 Non-Tight Collar 20,974 33 0,16

4 Tight Collar 20,654 46 0.22

5 Gunwale Connect ion 172 5 2.91

6 Knife Edges o 0

7 Miscellaneous Cutouts 296,689 853 0.29

8 Clearance Cutouts 57,307 843 1.47

9 Deck Cutouts 7,534 29 0.38

10 Stanchion Ends 7,090 122 1.72

11 Stiffener Ends 40,729 298 0.73

12 Panel Stiffeners 53,827 788 1,46

Totals 607,584 6,856 1,13

)

238

extrapolations , plotted on a semi-logcumulative distribution basis for largetankers and dry cargo vessels are pre-sented in Fig, 4 and are based on thewave- induced longitudinal bendingstresses. A complete loading historyshould include also the high-frequencydynamic loadings However, since theseare generally of a relatively smallstress-range and would produce littledamage they have been neglected in thepresent study. (The somewhat conserva-tive previous assumption that the S-Ncurve is linear to 108 cycles tends tocompensate for this neglect of the high-frequency stresses. ) Nevertheless, ifit can be demonstrated that the stressranges for the expected high-frequencyloadings will not be small (above about6 ksi), then they should be included inthe total loading history,

To use the fatigue design criteriadeveloped herein requires that the load-ing history be represented in probabil-istic terms by a probability distribu-tion function. A variety of distribu-tion functions were investigated,including the Beta, Lognormal, Weibull,Exponential and Sayleigh distributions;however, the evaluation clearly indica-ted that the Weibull distributionwould most effectively define existingship loading data,

The two parameter Weibull probabil-ity distribution function can providemany shapes to model the loading his-tory, including those of the Exponentialand Sayleigh distributions , and is givenby:

fs(s) = $ ($k-1 exp [-(~)k] (2)

where:k = shape parameter

w = characteristic value of s

s = stress

The mea” stress of the distributicm is ,

us=wr(l+ l/k) (3)

and the standard deviation is ,

“s =w [r(l + Z/k) - rz(l + l/k)]1f2 (4)

where;r = Ganuna function

The general configurations of sevei--al Weibull distributions (various valuesof k) are shown in Fig, 5. These aresimilar to the distributions often re-ported for strain measurements made onships at sea, An indication of the ex-cellent fit of a Weibull distributionwith k = 1,2 and the data obtained fromSea-Lands SL-7 shipboard measurements(15) is presented in Fig. 6.

35 >.

F

...

30 “

5

t% f 765432[ o

- LOG “

(a ) Service Stresses In Large Tankers. (13)

.Q(x > Xj) TOTAL PROBABILITY OF EXCEEDING Xl

(b1 ServiceStressesInDry Cargo Vessels,(14)

Fig. 4. Long-Term Trends in ServiceStresses for Large Tankers and DryCargo Vessels (13,14)

Stress, S

Fig. 5. General Shapes of WeibullDistributions

239

30

20

10

0010 20 30 40

s(Max. Peak-to-Trough Stress, kei)

Fig. 6. SL-7 Scratch Gage Datawith Corresponding Iieihull Dis-tribution (16)

To obtain tieibull distributionsthat represent ship loading stress his-tories, the mean, the standard devia-tion and the coefficient of variacianfor the distributions are made equal tothe corresponding values for the shipdata. First, the appropriate value ofche Weibull distribution parameter kcan be obtained from Table IV by makingthe coefficient of variation for theWeibull distribution (standard devia-tionfmean) equal to the coefficient ofvariation fcm the histrograms, Next,the value of parameter w is obtainedfrom the following:

us“.r(l + I/k)

TABLE IV

Table of Weibull Shape ParameterValues and CorrespondingCoefficients of Variation

Weibull ShapeParameter

k

0,50,60.70,80.91.01.11.21.31,41.51,61.71.81.92,0

Coefficient ofVariation

6

2,2361.7581,4621,2611,1131,0000.9100.8370.7760,7240.6790,6400.6050.5750.5470.523

(5)

The above procedure has been fol-lowed to establish values of k for avariety of ships for which loading his-tOry data ~re available. These values~elg~en .LnTable V and ra~g~from 0.7

Tbe shapes of the functionsare presented in Fig, 7 and are similarto those for the ships shown in Fig. 4.It should be noted that the larger ships(tankers and bulk carriers) tend to haveloading shape parameters equal to orgreater than 1.0.

For the Weibull distribution func-tions, the maximum stress-range expectedtO be reached once in a ship, s lifetimeof 108 cycles (estimated to be a 20 yearlife) can be determined from the follow-ing equation:

S~08 = w [ln (52000)]1/k (6)

The predicted values of S~08 for theships for which loading history dataare available are give” in Table V andrange from 10 ksi to 34.1 ksi.

Random Load Factor

In the fatigue design procedurepresented herein tbe constant-cyclefatigue stress range in Eq. 1 must bemodified to account for the random load-ing represented by the Weibull distribu-tion functions This can be done readilyand simply by introducing a random load

factor, c (16).

The random load factor is based onthe assumption that the stress rangehistory can be modeled by the two-para-meter Weibull distribution functionwith a maximum stress range equal to

S108 and a minim~ stress range equalto zero and is given by:

C = (lnN)llk [r(l + m/k)] -l/m (7)

This factor, as developed by Ang andMunse (16), is based on the ap lication

I!”of Miner’s linear damage hypot C?SIS tothe random loading represented by theWeibull probability density function ofEq. 2. A tabulation of the random loadfactors for various values of k and mare presented in Table VI for a life of108 cycles. (A comparable table couldreadily be prepared for any other life.)

Using the random stress factor fromEq. 7 (Table VI) (a factor that corre-sponds to a specific Weibull distribu-tion and S-N curve slope) , and the meanfatigue stress range from Table I forspecific detail, one can readily obtainthe maximum stress of the variable load-ing that can be expected to producefailure at 108 cycles This maximumstress is :

(smax)N = SN E

.’

240

p.-

I.c

0,8

0,6_s_s.

0.4

0.2

0-( -b -> -4 -3 -2 -1 0

Log [1- FS(S)]

Fig. 7. Ship Loading Histories Nodeled by Weibull Distributions

TABLE V

Ship Loading His tories Compared With Weibull Distributions

Stress Change atWeibull Probability of

Type ofShip

Load EXCe danceName of Ship NOtes Shape,k 5= 10 ,S108 (ksi)

Dry Cargo Wolverine State 1.2California State l~;

16,51.0 18,0

Mormacs Can 1,5,7 1.3 12.0Mormacscan 1,5,6 1.0 10,0

Large Tankers Idemitsu Mar” 2,5 1.0 12.3R. G. Follis 2,5 0.8 30.0Esso Malaysia 2,5 0.8 21.8Universe Ireland 2,3,5, 0.7 18,7

Bulk Carrier Fotini L. 2,5 0,9 29,5

SL-7 Container- See Note 9 4,6,9 1.2 34.1ships

Data from ref. (14)Data from ref. (20)Data from ref. (21)Data from ref. (15)Load history is for wave-induceddynamic effects filtered.Load history is for wave-induceddynamic effeet included,Load history based on North Atlantic voyagesLoad history based on ,South American voyages.Load history hased on data collected from eight

containershipsSL-7

241

loading with

loading with

——

m

2.0

2,5

3.0

3.5

4.0

4.5

5.0

5,5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

TABLE VI

Random Load Factors

Random Load Factors , E

k=O.7 k=O.8 k=O .9 k=l.O k=l.1 k=l,2 k=l,3

28.63

23,12

19.23

16.35

14.15

12.41

11.01

9.87

8.91

8.11

7.42

6..S3

6.31

5,86

5.46

5.11

4.79

20.93

17.49

14.96

13.04

11.53

10.31

9.31

8.48

7.77

7.16

6.64

6.18

5.78

5.42

5,10

4,81

4.55

16,17

13.86

12.12

10.77

9.68

8.79

8.04

7.41

6.87

6.40

5.99

5.62

5.30

5.01

4.75

4.52

4,30

13.02

11.39

10.14

9.14

8.32

7.64

7.07

6,58

6.15

5.78

5.45

5.16

4,89

4.66

4.44

4.25

4,07

10.83

9.63

8.69

7.93

7,30

6.76

6.31

5.92

5.58

5.27

5.00

4,76

4.54

4.35

4.17

4.00

3.85

9.24

8.33

7.60

7.00

6.50

6,07

5.71

5.39

5.10

4,85

4,63

4,43

4.24

4.08

3.92

3.78

3.65

8.05

7.33

6.75

6.27

5.86

5.52

5.21

4,95

4.71

4.50

4.31

4.14

3.98

3.84

3.71

3.59

3.48

Values are based on a life of 108 cycles For any other life N,the values in this table would be multiplied by:

(,n N)ljk

(18,42)1/k

The term SN is the mean constant-cyclestress range from Table I that would be L(n)expected to produce a fatigue failure

{

-1,08in the selected detail at N cycles = expHowever,

-[~ r(l + nN1”08)]QNthe value so determined is the 1 (9)

mean value (50 percent level of reliabil - where:ity) and must be modified by a reliabil-ity factor (factor of safety) to obtain

N = mean life to fatigue failure

an appropriate maximum design stress ‘N= total uncertainty in fatigue

value.m

R~bility Factor (Factor of Safety)

The basic relationships for the fa-tigue reliability design criteria devel-oped herein have been presented by Ang(17) in his development of reliabilityanalysis for design. In this analysisit is recognized that the fatigue lifeOf a structural detail is a random vari -able and assumed that its distributioncan be represented by an approximationto the Weibull distribution (18) hthis basis , the reliability function(the probability of no failure througha life n) can be given by:

The total uncertainty is a func-tion of the uncertainly in the meanfatigue strength (Table I) , the uncer-tainty in the stress analysis, effectsof fabrication, workmanship, corrosion,etc. The uncertainty in the mean fa-tigue strength (standard deviationdivided by the mean) varies considerablyfrom one detail to the next b“c aver-ages about 0,50 (from 0.2 to 0.8 depend-ing upon the detail, the amount of data,etc.) for the details in Table 1, Rela-tively little is kmwn concerning tbeother factors, Nevertheless, untilbetter values can be established it isrecommended that an estimated value of~ uncertainty of 0.80 be used.

242

To utilize the reliability func-tion in design, the mean life N neces.ary to produce a useful life n with areliability of L(n) is obtained fromfrom the following:

N = nyL (lo)where yL is tbe scatter factor and isgiven by equation 11 (Fig. 8)

r(l+nN 1,08,~L =

1.08 (11)

‘N(PF)

where :(PF) = the probability of failure

and equal to [1 - L(II)].

In Fig. 8 it can be seen that a 99 per-cent level of reliability (one percentprobability of failure) , and an uncer-tainty in life $2N= O.50, would requirea design for a life N equal to about 8times the expected useful life n.

Under constant-cycle stress range,from equation (la), the required design

I041 1

5 \ I

~j= r(l+akoa)/

(P’P-w //103 1 ~f=lo->

/5 /[

/’

/’

Y~ // /

102 / “ ,/

/’ ,5 /[

/IfX[

r“ / /1

/i /“1/ r 1/5 —

/’ ‘.

// Y /“

/’

Io 0.2 0.4 0.6 0.8 1,0

fin

Fig. 8. Relationship Between theScatter Faccor and the Uncertaintyin Fatigue Life and Various Proba-bilities of Failure (17)

stress for a specified level of relia-bility will be given by:

SD = (f) Urn(12)

orSD = + lf~ (L)h

‘L(lza)

where:

‘D = constant cycle design stressrange for a useful life ~ anda specified reliability L(n)

Designating the Iast term of equation(1.2a)as the ‘Reliability Factor, , RF,

and the allowable constant-cycle designstress becomes,

‘D =SN. RF (14)

The value of RF for three levels ofreliability, various S-N curve slopes,and uncertainties $2Nequal to O.4, 0.6or O.8 can be obtained from Table VII.

FATIGUE DESIGN

With the relationships presentedabove a simple fatigue verification ordesign procedure that takes into ac-count the principal fatigue parameterscan now be provided. Table VIII showsthe six steps of the procedure to befollowed to verify the adequacy of agiven ship strueture detail in fatigue.

In step 1 the expected loading his-tory for the ship detail must be estab-lished (the shape factor for the Weibulldistribution selected) Some guidancecan be obtained from Table V, a summaryof the limited data now available. Asmore complete data are obtained concern-ing ship loading histories, the valuesin Table V can be expanded, improvedand updated to provide the designexwith the best possible guidance.

In the second step the ship detailsat which the fatigue resistance shouldbe checked must be identified. Thecritical locations in the ship assem-blies , such as shown in Fig, 3, can beused to identify the critical detailsin terms of the numerous details shownin Fig. 2, (k extensive summary of de-tails in the twelve families of TableII are presented in the Reference 22Report)

The third step is to obtain, forthe detail, the fatigue strength andslope of the S-N curve (this comes fromTable I). The fourth step is to obtainthe random load factor from Table VI,and the fifth step is to select the

243

TABLE VIII

Design Proceaure

1.

+

Ship LoadingDistribution Choose a loading shape parameter k,

of the Weibull distribution.

2. Ship Detail Identify the number designation ofCatalogs the critical details (Figs 2 and 3)

, 1

I

4.

YDesignTable 6

Find randomk-value and

SW curve slope, m, of detailNean fatigue stress-range,for detail.

load factor, C, based onm-”alue.

5.

z

Design Find reliability factor, Rf, baSed onTable 6 m-value and ~N-”al”e for desired le”el

of reliability,

6. Design Equation Cmnp”te allowable stress-range (SD)=ll,(SD)all=SN. c.RF for probability of exceedance

of 10-8.

appropriate reliability factor fromTable VII. The maximum allowable fa-tigue stress range, (sD)all

4, is rhenobtained from the following equation

(SD) =SN. L.+ (15)

This relationship, using Table VI, isbased on a desired life of 108 cycles.For any other life the values, as notedon Table VI, would need to be modified,

A design example for a beam bracketwith four structural details is presen-ted in Fig. 9. In this instance, theWeibull shape factor far the loadinghistory was taken as 1.0, the total “c-ertainty in fatigue life as O.80 andthe desired level of reliability wasassumed to be equal to 90 percent. Theresulting maximum allowable fatigwsstress range at the deck-bulkhead inter-section (detail 39B) is found to be31.8 ksi, This maximum stress-range

4.This maximum allowable stressrange at the point in question, is themaximum peak-to-trough stress range ex-pected under the most severe sea stateand during the entire life of the struc-ture.

provides only for fatigue; in addition,the maximum stress must not exceed thenominal permissible design stress pro-vided by the basic design rules (19)For detail number 7, at the toe of thestiffener weld in the web and flange,the maximum allowable fatigue stressrange is 39.7 ksi for a 20 year life,Similar calculaticms can readily bemade for details number 37 and 38.

SUNMARY AND CONCLUSIONS:

This paper summarizes a simple de-sign procedure that has been developedto provide for a fatigue strength veri-fication in ship design, The criteriaprovides for:

(a)

(b)

(c)

A large variety in ship strue-ture details.

The basic fatigue resistance ofthe numerous “elded details.

.1A distribution function thatcan be used to represent thelong life loading (1o8 cycles-20 years) for various typesof ships

244

Fig. 9. Design Example

Ship Assembly IA I - Beam Bracket (Fig, 3a)

*

Detail No. (S)]oe(See Fig. 2) (See Table H

7 7,41 4.11 Reliability - 90%

39 B 5.9 Est. 4.0 Est. Coef, of Var. -0.8037 5,0 Est. 3.7 Est,38 4.97

Weibull Dist, k = 1,03.71

~e - Detail 39B

(S)loa = 5.9 ksi Est. m = 4,0 Est. (Table 1)

Reliability Factor = 0.648 (Table 7)

Random Load Factor = 8.32 (Table 6)

Max. Allawable Stress Range = 5.9x 0,648x8.32 = 31.8 ksi

Considering Stiffener Detoil - Detail 7

(S)108= 741 ksi m =4.11

RF = 0.655 [ = 8.17Max. Allowable Stress Range = 7.41 x 0.655 x 8.17 = 39.7 ksi

i-

245

TABLE VII

Reliability Factors

I Reliability Factors, RF

m

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.o

6.5

7.0

7.5

8.0

8.5

9.0

I R = 90%I

K = 95%

‘N ‘N

0,40 0.60 0.80 0,40 0,60 0.80I

.691 .546 .420 .608 .447 .320

.744 .616 ,500 .671 .525 .402

.782 .668 .561 .717 .585 .468

.810 ,708 .609 .752 .631 .521

.831 .739 .648 .780 ,669 ,566

.849 .764 ,680 .8o1 ,699 .603

.863 ,785 .707 .819 .725 .634

,874 .602 .730 ,834 .746 .661

.884 .817 ,749 .847 .765 .684

.893 .830 .766 .858 .781 .705

.910 .841 .781 .867 .795 .722

.906 ..s51 .794 .876 .807 .738

.912 .860 .805 .883 ,818 .752

.917 .867 ,815 .889 .827 ,765

.921 .874 .825 .895 .836 ,776

R = 99%

‘N

0.40 0.60 0.80

.451 .281 .170

.528 .362 .242

.588 .429 .307

.634 .484 .363

.671 .530 .412

.702 .569 .455

,727 .602 .492

.748 .630 .525

.767 .655 .554

.782 .677 .580

.796 .696 .603

,808 .713 .623

.819 .728 .642

.829 .742 .659

.838 ,754 .675

(d) A random loading factor that the author and not necessarily thoseaccounts for the randomness of the Advisory Committee of the Shipof the loading during the life Structure Connnittee under whose guid-of the structure. ante the investigation on which this

(e) A reliability factor (Factor ofpaper is based was conducted.

Safety) that accounts for the KEFEKSNCESmany uncertainties that exist

The values of maximum allowablefatigue stress range obtained in thedesign example provides an excellentcalibration of the procedure and isconsidered very reasonable, based onthe history of such details in theships at sea. Additional evaluationsnow should be made of those details atwhich fatigue failures have developedto further evaluate and calibrate theDrocedure. After the rmocedure has~een further verified,’ it should bepossible also to use the procedure todevelop relative fatigue ratings forthe manv details used for shiD struc -tures.

The opinions herein are those of

246

1. Vedeler, G,,, “To What Extent DoBrittle Fracture and FatigueInterest Shipbuilders Today, ”Houdremont Lecture 1962,Sveiseteknikk 1962, No. 3.

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4. Jordan, C. R. and Knight, L. T.,“Further Survey of In-ServicePerformance of Structural De-tails,” SSC-294, 1980.

—

5

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7

8,

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u,

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247