Fatigue Assessment of Ship Structures using Hot Spot

Fatigue Assessment of Ship Structures using Hot Spot Stress andStructural Stress Approaches with Experimental Validation

Myung Hyun Kim (M), Pusan National University, Seong Min Kim (StM), Pusan National University, Jae Myung Lee(M), Pusan National University, and Sung Won Kang (M), Pusan National University

The aim of this study is to investiate fatigue assessment of typical ship structures employing structural stressapproach and to compare with hot spot stress approach. As an initial study of the systematic validation efforts onstructural stress method, an experimental investigation is performed on a series of edge details with welded gussetplates. Extrapolation based hot spot stress using converged mesh were also calculated for each specimen types.Having validated the application of structural stress for small edge detaIls, a systematic investigation is carried outfora fatigue assessment of typical ship structures employing structural stress approach. Fatigue strength of side shellconnection of a 8,100 TEU container vessel is evaluated using hot spot stress and structural stress employingsimpl/Iedfatigue analysis.

KEY WORDS: Ship structures, welded structure, fatiguedesign, structural stress, hot spot stress, fatigue life, finiteelement analysis

NOMENCLATUREa : Fatigue crack lengthC : Material constants for crack propagation modeld : Nodal displacementD Accumulated fatigue damage

f,, and f2 : Line force with respect to x, y and z axis

F : Vector of nodal force

F :Nodal force with respect to mid-plane of thickness

and F : New balanced force with respect to x, y and

zaxisWeibull stress range shape distribution parameter for

load condition n¡(r) : Dimensionless function of r

K : Stress intensity factor

Element stiffness matrix

M,,, : Notch induced stress intensity magnification factor

n0 : Total number of stress cycles associated with the

stress range level ic

nj Fatigue life

¡ : Element length

r Bending ratio( rYb / o)

SCF : Stress concentration factort : Plate thickness (mm)

Weibull stress range scale distribution parameter forload condition n

Average correlation between sea, pressure loads and

internal pressure loads

Paper No. Year- Last (family) name of the first author

c.s

HS

Top

°Bollom

o-n

°g1

o-w,

/t

eq

Lc7

&Tg

AOhg

Ao;

Average correlation between vertical and horizontal

wave induced bending stressBending stress (MPa)

Amplitude of stress due to dynamic external seapressure loads

Amplitude of stress due to dynamic internal

pressure loadsMembrane stress (MPa)

Structural stress (MPa)

Hot spot stress (MPa)

Measured stress at top surface

Measured stress at bottom surface

Nominal stress (MPa)

Bending stress of deck structure due to torsional

deformation of hatchWarping stress due to torsión at position considered

Usage factor

Equivalent structural stress (MPa)

Stress rangesGlobal combined stress range (MPa)

Range of stress due to wave induced horizontal hull

girder bending moment (MPa)Local combined stress range (MPa)

Reference stress range value at the local detail

exceeded once of n0 cycles

Range of stress due to wave induced vertical hullgirder bending moment (MPa)

Deift University of TechnologyShip HydromeChafl LaboratorY

LibraryMekelweg 2, 2628 CD Deift

The NetherlandsPhone: +31 15 2786873 - Fax: +31 15 2781836

INTRODUCTIONWelding is the most commonly employed process forfabricating steel structural joints, including those of ships andoffshore structures. Some of the advantages of welding arerelative ease of fabrication, high joint efficiency and watertightness (Matsubuchi 1980). However, stress concentrationsdue to the weld itself and because joints are generallydiscontinuous portions of a structure, welded joints tend tosuffer fatigue damage before other structural elements. Because,the fatigue life of a structure's welded joints is a keydeterminant of the service life of a structure subject to cyclicloading, it is very important to predict the fatigue life of weldedjoints in an accurate manner. The fatigue life of welded jòintsdepends on various factors such as weld quality and surfacefinish, and thejoint geometry and stress statesCurrently there exist three different methods for fatigue design;stress-based approach, strain-based approch and fracturemechanics approach (Cui 2002). Within the scope of stress-'based approach, different stress definition can be used such asnominal stress, hot spot stress and structural stress. Whilenominal stress is the most widely used in fátigue design, it isdifficult to define nominal stress value for çomplex structuressuch as ships (Maddox 1991). Hot spot stress is defined as astress value obtained by extrapolating stresses at certain distancefrom the weld toe based on finite element analysis (Niemi 1999).While hot spot stress approach is well accepted in offshoreindustry, it is well recognized that hot spot stress values mayvary for different elements and different extrapolationtechniques. On the other hand, structural tress approach isrecently proposed, and it is known as mesh-size insensitivefatigue assessment method by using finite element analyses. Thestructural stress definition is based on the elementary structuralmechanics theory and is known to provide an effective measureof a stress state in front of weld toe (Dong 2001).The aim of this study is to investigate fatigue assessment oftypical ship structures employing structural stress approach andto compare with hot spot stress approach. As an iñitial part ofthe systematic validation efforts on Battelle's structural stressmethod, a detailed experimental investigation is performed onedge fatigue details as a part of B attelle lIP program (Kang et al.2004).The S-N data generated from this investigation have shown thatthe structural stress based SCF (Stress Concentration Factors)are effective in correlating not only the S-N' data generated inthis detailed experimental investigation, but also all other S-Ndata from other joint types collected from various fatigue testliteratures. Extrapolation based hot spot stresses (HSS) usingconverged mesh were also calculated for each specimen types.Within the edge details tested in this investigation, the hot spotstresses based on three different extrapolation procedures arecompared and found to provide a good correlation of the S-Ndata. In the present work, hence, two different fatigueassessment procedures using hot spot stress and structural stressare compared and validated based on the series of fatigue testdata within similar jointtypes and thicknesses.Having validated the application of structural stress for smalledge details, a systematic investigation is carried out for a

fatigue assessment of typical ship structures employingstructural stress approach. Fatigue strength of side shellconnection of an 8,100 TEU containervessel is evaluated usingboth hot spOt stress and structural stress. Simplified fatigueanalysis is applied using typical lòading conditions defined byclassification societies. Finite element analysis is carried out forfull ship with respect to fatigue damage prone locations such asside-longitudinal located near design draft Fatigue lifecalculated using structural stress is compared with that of hotspot stress approach. For fatigue strength assessment of ships,structural stress approach is found to be a viable alternative asemploying the mesh size insensitive charaçteristics. Furtherstudy for the fatigue strength assessment of ship and offshorestructures are required with different mesh sizes and shapes.

COMPARISON OF STRUCTURAL STRESSAND HOT SPOT STRESS

Structura! stress definitionAs shown in Fig. 1, a typical through-thickness stressdistribution at the fillet weld toe is assumed to exhibit amonotonic through-thickness distribution with the peak stressoccurring at the weld toe (Niemi 1999). The self-equilibratingstress state induced by local geometry or notch effect isconsidered to be included in S-N data.

Fig. I Through-thickness structural stress distribution

The corresponding equivalent structural stress distribution isillustrated in Fig. 2, in the form of a membrane component(0m) and bending component (ab). The normal structural

stress (a5 ) is defined at a location of interest such as section A-A at the weld toe in Fig. 2 with a plate thickness of t. Thenormal and shear stress at the reference section B-B can bereadily obtained from either a finite element solutjon ormeasurements using strain gauges. The distance, 6, representsthe distance between sections A-A and B-B at the weld toe.The structural stress components am and ab can be calculatedimposing the following equilibrium conditions (Kang 2004).

Paper No. Year - Last name of first author Page number

;: Locui SfreB Diatributions alongA-A

>x

Fig. 2 Illustration of structural stress measurement

The strain gauge measurements obtained from the strain gaugepairs located both at the top and bottom edges of the specimenswas used to calculate the stnictural stress by means of Eq. (4).Note that the first and the last strain gauges were not used sincethey tend to exhibit more variability than the remaiñing straingauge measurements. The variation in the measured structuralstresses is due to the variations in the surface stresses measured,which are unavOidable in typical strain gauge basedmeasurements. To reduce the effects of the variation inestimating stress values at the weld toe, averaged valuesbetween the symmetric gauges in left and right sides of the testspecimens are used. In addition, a linear regression can then beused to represent the averaged strain distributions. The strainvalues based on the linear regression at each of the gauge pairpositions can then be used in Eq. (4) to determine the structuralstresses at the weld toe.

Structural stress using fiizite element analysisIn FE analysis using 2-D shell or plate element, balanced nodalforces can be derived from the element stiffness matrices andthe nodal displacements as described Eq. (5). The same appliesto the derivation of balanced nodal moments ûsing nodalrotational displacement..

(Fe) = [K]{d} (5)

where (Fe) = vector of nodal forces, [K] = element stiffnessmatrix, {d) = nodal displacement

Once the nodal forces (Fr1, F2) in y direction and moments withrespect to x axis are obtained as shown in Fig. 3, thecorresponding line forces (f, f) can be calculated withconsideration of the mechanical equilibrium as derived to Eqs.(6), (7) and (8). The derivation of line moments (m1, m2) arethe same as that of the line forces with respect to the nodalmoments (M1, M2)

+ ff(x)dxO (6)

Paper No. Year- Lst naine of first author Page number

m

0m + 0b = o-(y)ydy +.5t2 t2 r r

(1)

Here the first equation represents the force balance in x-direction evaluated along B-B section, and the second equationrepresents moment balance with respect to section A-A at yO.The mesh-insensitive structural stress can be calculated as longas the stress states at two sections at A-A and B-B are related toeach other in equilibrium sense (Dong 2001).

Structural stress from measurementsOn the other hand, as discussed by Dong et aI. (2004), themembrane and bending components in thè structural stressdefinition can be estimated by using a series of strain gauges onboth top and bottom surfaces, as shown in Fig. 2 for a fillet weld.1f the two rows of the strain gauges (B-B and C-C) are situatedapproximately within a linear surface stress distribution regimenear the weld toe, the bending stresses at Sections B-B and C-Ccan be calculated based on the measurements from both top andbottom surfaces as:

-:(2)dc

= .(oTOp -

It should be noted that if there exists no external loadingsbetween Sections B-B and C-C, the sectional moment changecan be expressed as:

AM (3)

where I represents the sectional moment :of inertia for unitlength in z direction in Fig. 2. Then, the strùctural stress at theweld (A-A) can be estimated by using extrapolations withrespectto bending stresses at B-B and C-C as:

Cb =-: +(of n.B)

OsYTop+j(Ob 0b)B L C B

(4)

In conjunction with fatigue testing of edge details, detailedstrain gauge measurements are collected before starting fatiguetest. The strain gauge readings were collected at two loadinglevels: (1) 20% of nominal yield strength and (2) 50% ofnominal yield strength.

F +Jfy(x).xdx=0

fi =(2F1 -Fr2), fy2

= (2Mri - M2), m2 = .(2At12 - 1W1)

where ¡ = element size along the weld line as described Fig. 3

Fig. 3 Local line force and the line moment frOm nodal forcesand moments for 4 node shell element

Along a weld line adjacent to multi-elements as shown in Fig. 4,a governing equation is given by Eq. (10) for four (4)-node sellor plate elements. The applied nodal forces are defined using theelement local coordinate (x', y', z').

Fig. 4 FE model with weld line using 4 node shell element

6 3_

Once the line force and the line moment are available, thestructural stress at each node can be given by Eq. (11).

fy6m (li)

Where, o, is stress concentration effects due to joint geometry

and °m are membrane and bending stress respectively.

Fatigue life evaluation from equivalent structuralstress and the master S-N curveFracture mechanics based prediction of fatigue life in cycles tofinal failure can be expressed as:

N= fda

a=aj

C(M,,)(tK)m(12)

where Mb, represents a notch-induced stress intensitymagnification factor defined as:

= - '-E"-¡((wifh Jô,nI notch effects)

K (considering only the far fl/ed stress coñtribution)

Rewriting Eq. (12) in terms of relative crack length form as:

aft=I m

N= i td(a/t) 1

tT(L,iO.$)_mI(r) (14)C(Mb,)(K) c

a, It-*O

where ¡(r) is a dimensionless function of r = crb /o and can beexpressed iii the following form under given m:

¡(r)=.1

d(a/t)

a fl_)OMbi[fm() - r(J'm(-) - fb(--)II

(15)

Here, the stress intensity factor K without notch effects for anedge crack is considered as:

K [CTmfm()Tbfh()] (16)

The paranietersfm(a/t) andf,('a./t) are well known dimensionlessfunction of alt corresponding to the membrane and bendingcomponents, which can be found in various fracture mechanicshandbook such as (Tada 1985).Rearranging Eq. (14) as in term of N with the givendimensionless ¡(r) function:

I 2-m I

Lo=C rnj 2m I(r)N (17)

An equivalent structural stress can be defined by normalizingthe structural stress range, Eq. (17), with two variablesexpressed in terms of the thickness t and the bending ratio r asfollows:

(13)

F2

n

!L !L3 6

!. (IIl2)o

'2

6

0

(in2 +

-o

0

'n-I

(10)=06 3

L.6

0

3

'n-I6

'n-I


where the thickness term /2m2m (m=3.6 according to Dong; theexponent of Paris crack propagation) becomes unity for t= I(unit thickness) and therefore, the thickness t can be interpreteda ratio of actual thickness t to a uñit thickness, rendering theterm dimensionless. With this interpretation, the equivalent JSeqretains a stress unit ¡(r) is the function ofbending ratio (r) whichindicates corrections depending on loading modes and cracktypes. Crack types should be classified into an edge crack or asemi-elliptical crack. As an edge crack grows, 1(r) can bedivided into load-controlled condition and displacementcondition and can be expressed as Eqs. (19) and (20),respectively.

¡(r)tm =-0.0732r6 +0.2132r5 -0.2063r4 (19)

+O.09lr3 +0.0193r2 -0.014r+l.1029

¡(r)tm = 2.4712r6 - 5.5828r5 + 5.0365r4 (20)

-l.9617r3 +0.4463r2 +0.035r+1.l392

In case of a semi-elliptical crack, ¡(r) can be divided into thefunction for small detail and for structural joint Approximatefunctions are expressed by Eqs. (21) and (22), respectively.

¡(r)tm =0.00llrt +0.0767r5 -0.0988r4

+ 0.0946r3 + 0.022 Ir2 + 0.014r + 1.2223

¡(r)tm =2.1549r6 -5.0422r +4.8002r4-2.0694r3 +0.561r2 +0.097r+1.5426

Since the thickness correction, the loading mode effects andgeometrical discontinuities have been already included in Eq.(18), any type of weld joints or loading modes can be evaluatedconsistently with the equivalent structural stress. Based on Eq.(18), over 2000 results of the existing fatigue tests for bothvarious weld joints and loading modes are fitted in Fig. 5 and amaster S-N curve is determined by Ha(2006). Based on Fig. 5,required parameters for S-N relationship can be obtained as Eq.(23) and Eq. (24). Here, the design master S-N curve is on thebasis of two standard deviation with respect to mean S-N curve.

For the mean master S-N curve, C=2 1672.4, m '=3.081ogA=13.33-3.O8logAScq

For the design master S-N curve, C=15465.6, m'3.08logA,-=1 2.88-3.O8logASeq

where, o and o correspond to measured stresses at 0.5t andI .5t in distance from the weld toe, respectively, as shown in Fig.6 (Niemi 1992).

Stress Notch stress

/Hot spot stress

Extrapolation of geometric stress to//derive the hot spot stress

1.E.Oß

I

Region effected bythe notch stress

Fig. 6 Calculation of hot spot stress based on linearextrapolation

These hot spot stresses are used for comparison purpose withstructural stress for interpreting fatigue test results in this study.


HS =1.5o (25)

I.EO4 1.EG1.E.O5

Bsduraece. cycles

Fig. 5 The master S-N curve by using equivalent structuralstress parameter

Hot spot stressHot spot stress is the most common to evaluating the fatiguestrength in ship and offshore structures because it includes thestress concentration due to geometric shape. There are threedifferent stress extrapolation techniques as commonlyrecommended procedures for the calculation of hot spot stressesin welded structures; 1) the linear extrapolation of stress overreference points at 0.5 and 1.5 of plate thickness away from thehot spot; 2) the linear extrapolation of stresses over referencepoints at 0.4 and 1.0 of plate thickness away from the hot spot;3) no extrapolatiòn but the use of the stress values at 0.5 of platethickness from the hot spot as the relevant hot spot stress(Mansour 2003). In this study, hot spot stress is calculated usingNiemi's guideline based on Eq. (25):

tri 3t/2Distance from hot spot

eq = 2-m I(18)

2m I(r)m

EXPERIMENTAL PROGRAMThe experimental investigation on edge details was set up toachieve the following major objectives:

Experimentally veri1,' the structural stresses calculatedusing the mesh-insensitive structural stress methodInvestigate fatigue crack behavior in edge details, effects ofplate thickness and failure definitions on S-N datagenerationExamine the applications of the extrapolation-based hotspot stress methods in interpreting the S-N data for edgedetailsExamine and demonstrate the validity of the structuralstress based master S-N curve approach in interpreting theS-N data for edge details

The detailed experimental investigation was focused on a totalof twelve specimen designs of edge details. The specimendesign involves a base plate and gusset attachment plate whichare welded to form an in-plane edge detail. Two differentthicknesses of the base plates were considered, i.e., 10mm and15mm. The widths for the base plates and the lengths of thegusset plates were varied to obtain a wide range of the hot spotand structural stresses based stress concentration factors at theweld ends considered as fatigue prone locations. All twelvespecimens (with unique combinations of plate thickness, width,and thicknesses) were fabricated and tested in duplicates.Typical shipyard welding procedures were used for fabricatingthe test specimens. Weld leg lengths and distortions in eachfabricated specimen were measured before fatigue testing for thelater interpretation of fatigue test data.Typically, six pairs of strain gauges were used on each side ofthe specimens. The strain gauge readings corresponding toapproximately linear distribution regime were used to calculatethe corresponding structural stresses according to the definitionsin the Battelle's structural stress definition and its measurementtechniques (Battelle 2004). For all specimens tested, anexcellent agreement between the measured and calculatedstructural stresses has been obtained, l-lot spot stressmeasurements based on 11W recommendations for edge detailswere also calculated from the strain gauge data and comparedwith the corresponding S-N curve.Fully reversed constant amplitude loading conditions were usedfor fatigue testing. The frequency of the cyclic load was 3Hz.Typical nominal stress range of I2OMPa was used throughoutthe test with a cyclic stress ratio of 0.4 under load-controlledconditions. During the fatigue testing of each specimen, bothstiffness, defined as load range/displacement range betweengrips, as well as instantaneous crack size as a function of cycleswere recorded at a fixed cycle interval. After final failuredefined as the separation of cross-section separation,photographs of the final fracture surfaces of the failed specimenwere also presented as a part of the test record.

EXPERIMENTAL SETUPThe dimension of the test specimen is shown in Fig. 7. The steelplates of thickness of both 10mm and 15mm are used as thethickness of the main plate of test specimens. The grip surfacedimension, indicated as dg (85mm) and W (100mm), are keptidentical for all specimens. The lengths of gusset plate (L2),which is welded on the side of the base plate, are designed tovary between 50, 100, 200 and 250 mm.

L,

Fig. 7 Dimension of test specimen

The material used in this research is a ship-structural mild steelof grade-A. The chemical composition and mechanicalproperties are summarized in Table 1. The design yield stress ofthe material is defined as 235MPa for ship-structural mild steelaccording to the specifications of classification societies.

Table I Major Chemical composition and mechanical propertiesof

(a) (b)Fig. 8 Grip location: (a) Base plate width 50mm (b) Base platewidth 90mm

C(%)Si(%) Si(%) Mn(%) P(%)

0.13 0.17 0.15 0.18 0.46 0.65 0.012 0.019

Yield Stress

(MPa)

Tensile Stress

(MPa)

Elongation

(%)

From Mill Sheet 299 336 441 - 468 28 - 30

From Tensile Test 290 - 299 427 457 34 36


T,

T,

a a

L,,

Fig. 8 shows a test specimen installed between grips. Note thatthe gusset plate is always located in the left side. Therefore, thefront side has the gusset plate always in the left side, and therear side has the gusset plate in the right side. The dimensionmatrix for the test specimens used in this study is summarized inTable 2. A series of proposed variations of some dimensions arealso given in the table as well.

Table 2 Test matrix

FCAW (Flux Cored Arc Welding) is used to attach the gussetplate into the main plate. V-shape groove was machined beforeweld. Gusset plate and main plate are welded by 3 - 5 passesunder flat position. During welding, additional jigs wereinstalled to prevent the specimen from any excessivedeformation. After welding the front side and backside, a filletwelding was formed at the ends of the gusset plates.Leg lengths of fillet welds at both sides of gusset plates arerecorded using Moire measurement technique. Moldingsreflecting the weld bead shapes are obtained using dental siliconrubber and sliced into 2mm thickness to obtain leg lengths ofboth the main plate and the gusset plate sides. Average leglengths of the main plate and the gusset sides are 5.52mm and5.57mm, respectively.

STATIC LOADING TEST RESULT ANDANAYSISPrior to fatigue test, surface stress distribution both at gusset andopposite sides are measured with remote nominal stresses at20% (47MPa) and 50% (1 17.SMPa) of yield stress (235MPa).Fig. 9 shows the typical placement of strain gauges. The straingauges near the weld toe are placed either 5mm or 8mm indistance from the toe. The remaining strain gauges are attachedeither 8mm or 10mm from each other. The fatigue test machineused in this study is a servo hydraulic fatigue test machine withmaximum load capacity of ±20 ton. Before setting a specimen,stress values measured using strain gauges at front and rear sidesof specimen are carefully observed in order to avoid anypossible pre-bending of the specimen.

-.-4544aC1 Os..-4--aV? 02.. -.-La,a?

#10 #7

4 54 54 54 54 10

fr t ta gma)12.10

DtttmIO. fl thi LU? OUI

54 54 C 54 54 lO O

#20 #19 #18 817 #10

.54."8lO54,al 0, + St .541 OSt1

...5po'4 O2.-a.Oøaa54-3 OSt,

O t

54

10 10

54r tho (Qe (QtO 14 54 54 C

Fig. 10 Stress distribution of specimens 2-1 and 2-2

a a----------*-Sto40Cl O54--Spl OStso a OSt:

No. TI T2 Li L2 WI W2 R do

1 10 10 350 50 50 25 45 150

2 10 10 350 100 50 25 45 125

3 10 10 350 200 50 25 45 75

4 10 10 350 250 50 25 45 50

5 10 10 350 50 90 25 145 150

6 10 10 350 100 90 25 145 125

7 10 10 350 200 90 25 145 75

8 10 10 350 250 90 25 145 50

9 15 10 350 50 50 25 45 150

10 15 10 350 100 50 25 45 125

11 15 10 350 200 50 25 45 75

12 15 10 350 250 50 25 45 50

a ,ya154

¶54

154

554

118

54

-54

-c8

'm

54

IS

¶54..

IC

54.

54

54

54-I Os-4-' St54554-1 lISt.lO StO5454554. 9 .O'4? OIS

- 84 84

Paper No. Year - Last naine of first author Page number

24 2424 21 24 19 13 14 15 16 17 18

Sbain ga.Jge Sbain

Fig. 9 Strain gauge locations in 10mm distance

Fig. 10 illustrates the surface stress distribution of the specimen2 along the edge surface on the base plate. Before cyclic fatiguetesting, each specimen was first tested under static loadingconditions with remote nominal stress at 20% and 50% of yieldstrength level, with fully instrumented strain gauges in pairsbetween both edges of the base plate placed at 5mm from theweld ends. On the gusset side, 12 strain gauges are placed while8 strain gauges are being placed on the opposite side. Stressvalues obtain from the measurement show similar values for theduplicate test, e.g. specimen #2-1 and #2-2. Also a symmetricstress distribution is observed for the both sides of the gussetplate.Fig. 11 and Fig. 12 present similar result for specimens 6 and 10,respectively. Fig. 11 corresponds to the stress distribution forthe specimen with identical dimension except for the width ofthe main plate (90mm), and Fig. 12 is that of the specimen withdifferent thickness of the main plate (15mm).

10 5454 ¿1

LIS 'ht (aO)

-..-i5n.,,*i O.1-...-inaiaint bi2..-n-n Q.S.

n n n si C a n n n i s s o g *

Distaacc frQmthc


-.-i.nnosiiß 02. -.--!ainJDi Qi.-'- taiflaiuI2 02,.- -Snaiaro2 *. -la ti,

#10

.r.Io

a oin ii a a n a a is t, i

Dn from the .; (mm)12O

Distance troni the too (mm)w n n n a a n ai ta i

ra ai

ai.ow.

'or,

to'.

a,

io g

#20 59 618 #17 #16o'

Diotance frani the toe (mon)

T1'lO

.WI 02.'---i.rinntanI ea.--troeoi12 Q2,-s-aiut3 COr,

-

o 'i a s a e so ro aDistance from tilo toe (mm)

Tlnt5

(Unit mm)

Distance from the toe (mm)i t, t, X a n i. s, n i

#12.....#13,. #14....#15.,.

so'

-I-5aC,MorC1 C2,,-w-OntnoCit iOr ., t- - ¡-n-iDrrnronffi.1 o2,... ps,ob.l bO.eo.J .. ia --io at.-la in


As noted in the previous section, hot spot stress values maybecome different depending on the extrapolation technique used.For instance, Fig. 13 illustrates hot spot stress obtained for testspecimen #2. Based on the measurement, hot spot stress is foundto be 161.O3MPa using the linear stress extrapolation at 0.5 and

1.5 plate thickness. On the other hand, hot spot stresses arecalculated as 153.67MPa and 164.S8MPa for extrapolation of(0.5/1.5t) and (0.411.Ot), respectively, based on the stressescalculated from finite element analysis. It is clearly seen that hotspot stress values exhibit noticeable difference between153.67MPa and 164.58MPa. This could result in significantlydifferent fatigue life estimation.

Fig. 13 Hot spot stress calculated from measurement and FEanalysis for test specimen #2

Average stress values measured at distances of 5mm and 15mmfrom both sides of weld toe are used to obtain hot spot stress.Fig. 14 illustrates the structural stress results based on the straingauge measurements for each given strain gauge pairs locatedboth at the top and bottom edges of the specimens by means ofEq. (4) and the hot spot stress obtained by extrapolating thestresses measured by strain gauges at 5mm and 15mm locationsusing Eq. (25) for the specimen 2. It is observed that hot spotstress values are typically higher than structural stress values.Note that the structural stress values using measurements 2, 3and 4 show a good agreement among each other.

2.6

2.0

1.5

LLC.,

0.5

0.0

-u- FE(mesli)-.-TEST#2'-s' HSS(co anar1

+-- HSS(a00s,)

#2-1 Reg(20%) #2-1 Reg(50%) #2-2 Reg(20%) #2-2 Reg(50%)

Fig. 14 Comparison of structural stress (SS) and hot spot stress(HSS) of specimen 2

ai

aioo

'ato'

an

¼

a

ai

ai11g

'a-

nio

n

-S-taintSI lia -.--o'ainS I iOOsiioO'2 Ca-s grsraiSO O

#12... .......


(UnIt mm)

Diotooloc from the toc (mon)i t ti io a n n n ii a st nThsmn from the toc (mmw n n e go n n a a ti ra

,g.2i.#19.#i.9 .#1716

...-. i.o nia-1 i -s.. Sgianr-1ct- -Sioga-2

ta'X

3.0!2.510.0! 0.51 1.0! 1.5! 2.01Distance from weld toe

Fig. 15 and Fig. 16 also present similar results for the specimen6 and 10, respectively. Stress concentration factors arecompared using both structural stress and hot spot stressobtained from strain measurements at two different loadinglevels

2.5

2.0

1.5

u-C.,

0.5

25

2.0

1.5

1.0

0.5

0.0#6-1 Reg(20%) #6.1 Reg(50%) #6-2 Reg(20%) #6-2 Reg(50%)


0.0#10-1 Reg(20%) #10-1 Reg(50%) #10-2 Reg(20%) #10-2 Reg(50%)


The structural stress and the hot spot stress values for the entirespecimen considered in this study are summarized in Table 3. Ingeneral, higher stress concentration values are obtained as thelength of gusset plates increases. Similar observation can bemade for both structural stress and hot spot stress. Within thespecimen with same gusset lengths, specimens with thicker baseplate (15mm) resulted lower stress concentration than that of thespecimen with 10mm thickness. Comparing the stressconcentration factors between different width of base plate(50mm and 90mm), it was found that 90mm indicated higherstress concentration. Also, hot spot stress values obtained fromthe measurement show slightly higher values than those of

structural stress. The number indicated as Test-1 and Test-2 inthe table represents the two duplicate tests, respectively.

Table 3 Stress concentration Ñctors of each specimen based onstrain measurements

CYCLIC FATIGUE TEST RESULTS ANDANALYSIS

Crack propagation measurementBefore the fatigue test, lines were drawn at 1mm uniformdistance using a height gauge for measuring fatigue crackpropagation. The initiation and propagation of crack wereobserved at every 5000 cycles corresponding to about every30mm. The crack propagations with respect to fatigue cycle forthe specimen 5-8 are presented in Fig. 17 as a typical exampleof the crack propagation. (U) and (L) corresponds to upper partand lower part of the gusset. And the numbers indicate thecycles at failure. Essentially, it is found that the crack size of0.4W corresponds to 10% reduction of stiffness. This stiffnessreduction can be used as a failure criterion, particularly usefulfor more complex specimen configurations and loadingconditions.

EE

a,Ca,

a)

Q

100

90

80-

70-

60-

50.

40-

30-

20

10-

0-

297,020(11 327,770(U) 433;910(U) 52 940(L)#6-1..........................

B.................532,820(U)

.

g

150000 200000 250000 300000 350000 400000 450000 500000 550000 600000

Number of cycle

Fig. 17 Crack propagation measurement with respect to fatiguecycle for specimen #5 - #8

SpecimenStructural StressTest i Test 2

Hot Spot StressTest i Test 2

1 1.04 1.13 - 1.592 1.11 1.24 - 1.523 - - 1.54 1.724 - 1.56 1.70 -

5 - 1.21 1.65 -6 1.18 1.20 1.71 1.557 - - 1.65 1.948 1.38 1.41 1.91 1.84

9 - 1.12 1.32 1.48lo 1.17 1.17 1.56 1.3811 - - 1.65 1.9412 1.38 1.28 1.73 1.72

#8-2 #5-2 #8-2 #5-1.F F ' .

.L01-..BB vB cB

Paper No. Year- Last name of first author Page number

Fracture surfaceThis section presents the crack initiation location and crackpropagation behavior by observing fracture surfaces of severaltest specimens after fatigue test. Typically most cracks initiatedin the middle of weld toe as indicated with an arrow. However,some cracks initiated at the edge of the weld bead, while someinitiated at multiple sites. In general, the crack initiation sites arestrongly depended on the weld bead shape (Suresh 2004).Fig. 18 shows the fracture surface of the specimen #1-2(thickness 10mm, width 50mm and gusset length 50mm). It canbe seen that the crack started at the middle of the weld bead.Red ink was injected with respect to both surfaces of testspecimen at a regular period. As the crack gradually growsthrough the fatigue test, fracture surface shows an elliptic shapeand then becomes a flat shape through the crack plane. As thecrack reaches approximately half of the width, a brittle fractureoccurred.

Fracture surface

Direction of fatigue crack propagation

Fig. 18 Fracture surface and final failure of specimen #1-2

Fatigue lifeFully reversed constant amplitude loading condition was usedfor the fatigue test. The frequency of the load was 3Hz, andtypical stress ratio R was set to 0.4. The fatigue loadingcondition for each specimen is summarized in Table 4.

icue test condition for each specimen

Each specimen is tested until final fracture. The stifThess curveis obtained dividing the load range by the displacement rangebased on Eq. (26) using the following relationship.

(Maximum load - Minimum load)(Maximum displacement - Minimum Displacement)

EDX-1 500A memory recorder/analyzer is employed to recordthe load and the displacement at every 990 cycles in order toobtain the stiffness curve. Normally, both load and displacementare recorded for I second at 100Hz sampling rate. Fig. 19illustrates a typical stiffness measurement for the specimen 8.

- . - Specimen #8-1 -. - Specimen #8-2 I

(26)

4-2 l2OMPa 10-2 I2OMPa

5-1 l2OMPa Il-1 12OMPa

5-2 l6OMiPa 0.2 lI-2 I2OMPa

6-1 I2OMPa 12-1 I2OMPa0.4

6-2 12OMPa 12-2 12OMPa

Spec.StressRange

StressRatio

Spec.StressRange

StressRatio

1-1 IOOMPa 0.4 7-1 I2OMPa 0.4(a,,,,1 a,,)

1-2 1 2OMPa 7-2 1 2OMPa

2-1 1 2OMPa 8-1 1 2OMPa

2-2 l2OMPa 8-2 I2OMPa

3-1 12OMPa 9-1 1IOMPa

3-2 12OMPa 9-2 12OMPa

4-1 1 2OMPa 10-1 12OMPa

Specimen Nf Specimen Nr

1-1 1,636,480 7-1 310,080

1-2 794,530 7-2 508,100

2-1 608,390 8-1 308,400


0 50000 100000 150000 200000 250000 300000 350000

Number of cyde

Fig. 19 Stiffness curve for specimen 8

S-N data correlationSummarizing the stress values presented in the previous sections,it was demonstrated that the structural stresses can be obtainedin consistent manner. In this regard, this section presents the S-N data obtained from the fatigue test. Fatigue test result withfinal fracture life for each specimen is summarized in Table 5.

le 5 Test result of fatigue life for each specimen

240

220

200

180

160

E 140z120

a 100--

80

60

40

20

o

Fig. 20 illustrates the fatigue life of each specimen in terms ofnominal stress versus cycles to failure. It should be noted thatnominal stress is calculated ignoring any bending inducedcontributions to the overall stress concentrations at weld end dueto the asymmetry of the specimen geometry. Therefore, the S-Ndata appeared in flat.

enQ-nen

C

61o,

en

enCgoz

1000

loo-

Io10' 10'

N, cycles

Fig. 20 Nominal stress range versus failure cycles

Fig. 21 presents S-N curve presented using hot spot stress. Hotspot stress is calculated as explained in previous section. Sincethe extrapolated hot spot stresses provide an indication of thestress concentration on the surface relatively close to the weldend, bending effects are captured in the hot spot stresscalculations. Thus, slightly improved correlation among the S-Ndata from the edge details can be seen. However, the overalldata scatter remains essentially the same as the case of nominalstresses.

u

10' 10'

1000

enQ.ns)a'C

¡100

10

1000

caO-nena,Caen

en

100

atCenca3-=a.w

10

#1-1 #1-2 £ #2.1 V #2-2 4 #3-1 #3-2#4.1 #5-1 5 #6-1 * #6-2 0 #1-1 U 47-2

S#a.1AI&2y#6-14 #6.2#10-1C#10-2#11-1 S #11-2 * #12-1 5 #12-2

- FAlSO

10' 10'

N, cycles

Fig. 21 Hot spot stress range based S-N data (20% loading)

Fig. 22 illustrates S-N plots using equivalent structural stress(ESS). Stress values for ESS are calculated based on the stressconcentrations calculated in the case of 20% tensile loadingaccording the methods explained in previous section. AIl dataessentially gathered into a single narrow band, as shown in Fig.22.

10'

J#1-1 #1-2

£ #2-1 V #2.2I #4-2 #5-2#6-1 5 #6-2#8-1 * #8-2#9-2 u #10-1 5 #10-2

A #12-1 V #12-2- Master S-N jrve

lo' 10'

N, cycles

Fig. 22 Equivalent structural stress range based S-N data (20%loading)

From the above discussion, it was demonstrated that structuralstress definition can be effectively applied to correlating fatiguetest data from various joint types, loading modes, and platethicknesses. The effectiveness of the equivalent structural stressparameter has been presented by consolidating S-N data into asingle narrow band, and this clearly implies that improvedfatigue life prediction can be achieved.

10' lo,

10'

2-2 737,150 - 8-2 297,020

3.-I 610,220 9-1 767,420

3-2 1,116,710 9-2 1,083,250

4-1 277,650 10-1 970,540

4-2 348,380 10-2 1,183,900

5-1 552,940 11-1 821,820

5-2 327,770 11-2 794,270

6-1 532,820 12-1 527,590

758,5806-2 433,910 12-2

* All cracks occurred at weld toe


#1-1 #1-2L #2-1 V #2-24 #3-1 #3-2

#4-1 C #4-2S #5-1 * #5-2

#6-1 #6-2#7-1 £ #7-2

y #6-1 4 #6-2#6-1 #6-2#10.1 S #10-2

* #11-1 5 #11-2#12-1 #12-2

- FATtO

FATIGUE ASSESSMENT OF TYPICAL SHIPSTRUCTURES EMPLOYING STRUCTURALSTRESS AND HOT SPOT STRESS APPROACHAs a later part of this study, a systematic investigation is carriedout for fatigue life assessment of side shell longitudinals on8,100 TEU container vessel employing structural stress.

Fatigue ljfe assessment procedure of ship structuresFatigue life assessment of welded joints in ship structures can becarried out using long term stress distribution and S-N curvas.In the case of simplified fatigue analysis, fatigue strength isanalyzed using loadings defined from classification societies,not using ship motion analysis. The fatigue damage ratio isfinally estimated using Palmgren-Miner rule with long-termstress range distribution. The long-term stress range distributionis defined by the Weibull distribution. The fatigue life iscalculated employing Weibull distribution factors (scale andshape parameter) and relevant S-N curves.Flow diagram over fatigue analysis procedures are shown in Fig.23 applyiñg equivalent structural stress and notch stress usingmaster S-N curve and DNV S-N curve. Load response in thediagram includes the loadings from internal or external pressureand hull girder wave bending moments. Using each equivalentstructural stress and notch stress defined with respect to loadcases, combined stress ranges can be obtained and fatiguedamage ratio is calculated from long-term stress rangedistribution and the master SN curve and DNV S-N curve.

JLoad response

Notch Stress

(Equivalent Structural Stress)

IStress components

Combination of stresses

(Stress range)

Long term stress

distribution

4

Fatigue Damage Calculation

Hot spot stress

(Structural Stress)

S-N curve

(Master S-N curve)

Fig. 23 Flow diagram over fatigue analysis procedures

In the simplified method, dynamic loading may be divided intoglobal wave bending moments and local load such as externalpressure and internal pressure.The following eight dynamic load cases have been applied to theFE model and the load cases applied are listed in Table 6.Boundary condition of the finite element model was applied as asimple support condition.

Paper No. Year - Last name of first author

Table 6. Load cases considered for fatigue calculation

Since global wave bending moments are based on vertical wavebending moment and horizontal wave bending moment atprobability level of exceedance from lACS, they are modified to10 probability level of exceedance to be compatible withpressure loading components defined at l0 probability level.Usiñg correlation factor (p) which considers phase difference forcombination of vertical and horizontal wave load, globalcombined stress range (Mg) is finally defined by Eq. (27).

2Jo-h + wl + °g1 +

(27)+ 2Pvhvh

where Ewg combined grobal stress range= range of stress due to wave induced vertical hull girder

bending moment (o =1/2 ¿sa,,)

= range of stress due to wave induced horizontal hull girderbending moment (0h =1/2 Mh)

= warping stress due to torsion at position consideredbending stress of deck structure due to torsional

deformation of hatch(0)Pvh = 0.10, average correlation between vertical and horizontalwave induced bending stress

External pressure is determined compariñg dynamic pressuresfrom ship rolling motion and ship pitching motion, whichever ishigher. The internal pressure is determined from the accelerationof liquid cargo or ballast water among three directions andselected from whichever is the highest.Local combined stress range (M,) is composed of external andinternal pressures with a correlation factor expressed in Eq. (28).Local combined stress range is divided into full loadedcondition and ballast condition.

Page number

Loading type Loading condition

LCIVertical wave bending

moment Fully loaded / Ballast

LC2Horizontal wave bending

momentFully loaded

LC3-

Horizontal wave bending- moment

Ballast

LC4 Torsional moment Fully loadedLC5 Torsional moment BallastLC6 External pressure Fully loadedLC7 External pressure BallastLC8 Internal pressure Ballast

Ao, = Jcr +c +2poo(28)

where 10-,= combined local stress range= amplitude of stress due to the dynamic external sea pressure

loads (tension=positive)= amplitude of stress due to the dynamic internal pressure

loads (tension=positive)

AOg = max

I

Pp = average correlation between sea pressure loads and internalpressure loads

i z + k + IyI xH2 iO.T, 4-L 4-B 5.L-T,

where L is rule length of ship in meter and T, is actual draft. Bis the greatest moulded breadth of the ship and x, y, x are thelongitudinal, transverse and vertical distance from the origin (atmidship, centerline, baseline) to the load point of the consideredstructural detail.

If a combined long term stress response analysis is not carriedout, the combined stress range response from the combinedglobal stress and local stress range responses is the largest of(Hovem 1993):

IO.6L\cr +\o&7o=fefmma

g

LOg +O.6-ia,

where f, is the operation route reduction factor and fm is themean stress reduction factor (JÇ,,=0.85 maybe applied on the longterm stress distribution). A reduction in the effective estimatedstress response is achieved for vessels that for longer periodsoperate in environments not as harsh as the North Atlantic. Forworld wide trade, the reduction factor may be taken as 0.8.

When the long-term stress range distribution is defined applyingWóibull distributions for the different load conditions, and aone-slope S-N curve is used, the fatigue damage is given by(DNV 2003),

T N,

D = p,,q"T(l !) 17

where, D = accumulated fatigue damagea, m = S-N fatigue parametersN, = total number load conditions consideredp,, = fractiOn of design life in load condition nTa = design life of ship in seconds

= Weibull stress range shape distribution parameter for loadcondition nqn = Weibull stress range scale distribution parameter for loadcoñdition n

V0 = long-term average response zero-crossing frequency

77 = usage factor. Accepted usage factor is defined as 77 =1.0

F(1 + -r-) = gamma function

The Weibull scale parameter is defined from the stress rangelevel, as

&70q

- (lnno)1Th(31)

Paper No. Year - Last name of first author

where, n0 is the number of cycles over the time period for whichthe stress level is defined.

Target structure and fatigue crack definitionIn this study, typical fatigue crack points are assumed in thevicinity of intersection of side longitudinals and transverse webframe for a 8,100 TEU class container carrier. Principaldimension of container vessel is listed in Table 7 and finiteelement model for full ship is shown in Fig. 24.

Fig. 24 Finite element model of target vessel

Table 7. Principal dimension of target vessel

FE analysis is carried out for full ship and structural stresses aswell as hot spot stresses are calculated in critical details of sidelongitudinals located between design draft (TF) and ballast draft(TB). Fig. 25 shows the concerned section of web frame andlocal area in finite element model, and Table 8 lists the designdetails.

Table 8. Geometry of stiffener considered

Page number

Length of ship 305.356m

Breadth of ship 42.8m

Depth of ship 246m

Draft, Fully loaded 14.47m

Draft, Ballast loaded 7.42m

Max. Speed 26.4knoi

Distance above keel 8.176m

Stiffener spacing 868rnm

Height of stiffener 300mm

Thickness of web 11mm

Width offlange 90mm

Thickness of flange Ï6mrn

u. IPUPlIpIupIgpp- U!uI.iupuii.11,1.-L!IUIIIIIL..III i

ILUUIpU IiiU iii U1I1 111111 11111 III ir".jI iu,ip 1111

Fig. 25 Section of midship in finite element model

Three possible crack points slot detail is defined as shown in Fig.26. For each HS (Hot Spot) point, semi-elliptical cracks areanticipated at HS 1 and HS 2 on the longitudinal face plate andcollar plate, whereas edge cracks are expected at HS 3.

Fig. 26 Configuration of longitudinal connection and definitionof fatigue crack points

FE models used in the fatigue strength assessment are classifiedinto 4 groups as shown in Figs. 27, 28, 29 and 30: 1 .Ot xl .Ot,2.01 x 2.0t, 2.Ot x 2.Ot(paver) and 3.Ot x 3.01 meshes for theparametric studies to veri1,' mesh-insensitivity. Fatigue liveswere calculated employing structural stress approach on everymesh size and shape which are mentioned above. In order tocompare with hot spot stress approach, mesh of i .Ot x 1.01 wascalculated by using hot spot stress.

Fig. 27 Finite element model of local detail (1 .Ot xl .01)

Fig. 28 Finite element model of local detail (2.Ot x 2.01)


"uiiFig. 29 Finite element model of local detail (2.Ot x 2.Ot Paver)

Fig. 30 Finite element model of local detail (3.01 x 3.01)

FATIGUE ASSESSMENT RESULTSFor the design life of 20 years, fatigue damage ratio has beencalculated with the equivalent structural stress (ESS) and thedesign master S-N curve. In order to compare with the fatiguelives from the hot spot stress (HSS) approach, the S-N curvefrom DNV Classification Note No. 30.7 was employed. Hot spotstress approach is applied to the FE model of which mesh size is1.Otx 1.01.Parameters for the use of design master S-N curve and DNVcurve are as given in Table 9. Palmgren-Miner rule was used tocalculate damage ratio.

Table 9. S-N narameters

Figs. 31, 32, and 33 show fatigue lives at HSI, HS2 and HS3,respectively. Each fatigue lives are normalized by calculatedfatigue life employing hot spot stress method.

IA

1.2

1.0

_i 0.8

60.4

0.2

0.0

Fig. 31 Result of fatigue life at HS I

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Fig. 32 Result of fatigue life at HS2

logN = logamlogologa m

Design master S-N curve (SS) 13.33 3.08DNV curve (HSS) 12.76 3.0


1.4

1.2

1.0

a)'I-0.8

0.6

0.4

02

0.0

Fig. 33 Result of fatigue life at HS3

Comparing with the results of 2 methods from1.0: x 1.0: meshed model, the fatigue lives from structural stressand hot spot stress give only a small difference. In consideringmesh shape insensitivity, result of fatigue lives from 2.0: x 2.0:and 2.Ot x 2.0: paver have good correlation, when structuralstress is used.in the case of HS1, the calculated fatigue life using structuralstress approach from I .0, x I .Ot meshed model is approximately10% less than larger meshed model. On the other hand, in thecase of HS2 and HS3, the calculated fatigue lives usingstructural stress approach from I.Otxl.Or are more thanmaximum 30% lager meshed models.In case of HS2, however, the calculated fatigue life usingstructural stress approach from 3.Ot x 3.0: meshed model isapproximately 30% less than those from the 1.0: x 1.0: one. It isconsidered that 3.0: x 3.0: meshed model is failed to representits own geometrical condition in the vicinity of concerned area.

CONCLUSIONSIn this study experimental structural stress measurementtechniques are investigated. The effectiveness of structural stressmethod is compared with that of hot spot stress. Themeasurement techniques are based on a series of strain gaugepairs placed on both sides of a specimen width to resolve bothmembrane and bending stress components. And also theparametric studies for mesh size and shape insensitivity ofstructural stress have been carried out. Fatigue strengthassessment of side shell longitudinal stiffener of 8,100 lEUcontainer vessel is performed. From this research followingconclusions are drawn.

Consistent structural stress values can be obtainedexperimentally using stress measurements in properdistance. Stress values obtained using linear regression areused to calculate structural stresses to minimize thefluctuation from experiments.Both hot spot stress and structural stress can besuccessfully obtained from the experiment. Structural stressvalues calculated based on the linear regression of

measured stresses result in lower stress value than those ofhot spot stress.Hot spot stress vs. life shows a reasonable consolidationbetween similar types of edge detail specimens. However,hot spot stress vs. life cannot show further consolidationwith those of different types/thickness of specimens.Equivalent structural stress with thickness correction versuslife shows a fairly good consolidation between edge detailtest results considered in this study.A consistent structural stress approach is employed for thefatigue strength assessment of side shell longitudinalstiffeners of an 8,100 TEU container vessel. The similarfatigue life results are compared with that of hot spot stressapproach.In case of structural stress approach, the stress values fromfinite element analysis for 2.Ot model are in generalapplicable to fatigue strength assessment. In consideringmesh shape insensitivity, result from different mesh shapemodels gives good correlation. From this result, it isconfirmed that modeling time associated with local fatiguemodel can be significantly reduced by using larger andirregular mesh types.For fatigue strength assessment of ships, structural stressapproach is found to be a viable alternative as employingthe mesh size insensitive characteristics.

ACKNOWLEDGEMENTSThis research is sponsored by Advanced Ship EngineeringCenter of Korea Science & Engineering foundation. Thefinancial support is gratefully acknowledged.

REFERENCES

Battelle Structural Stress uP Report (NO. N004431-01): Mesh-Insensitive Structural Stress Met hodfor Fatigue Evaluation ofWelded Structures, 2004. 2.

C. Guedes Soares and Y. Garbatov, "Reliability based fatiguedesign of maintained welded joints in the side shell of tankers",The 3td International Symposium on Fatigue Design, Editors:G. Marquis and J. Sohn, European Structural Integrity Society(ESIS), pp. 13-28, 1998

Cui, W. A state of the art review on fatigue ¡(fe predictionmethods for metal structures. Journal of Marine Science andTechnology, 2002, 7, 43-56.

Det Norske Ventas, Fatigue assessment of ship structure,Classification Notes No. 30.7, 2003

Det Norske Ventas, Rules for classification of ships-Part 3Chapter ¡ Hull structural design ships with length 100 metersand above, 2003

Dong, P. A structural stress definition and numericalimplementation for fatigue analysis of welded structures,International Journal of Fatigue, 2001, 23, 865-876

Dong P, Hong JK, Cao Z., Structural stress based master S-Ncurve foe weldedjoints, 11W Doc XIII- 193 0-02/X V- 1119-02,International Institute of Welding, 2002

Gurney, T. R. Fatigue of welded structures, Cambridgeuniversity press, 1979


Ha, C.!. A study on the fatigue strength of weldedjoints usingstructural stress with consideration of stress singularity andits application to the fatigue life assessment of ship structures,M.S. Thesis, Pusan National University, Busan Korea 2006

Hovem, L. Loads and load combination for fatigue calculations- Backgroundfor the wave load section for the DNVCclassification note Fatigue assessment of ships, DNVCReport No. 93-0314, Høvik, 1993

Kang, S.W., Kim, M.H., Kim, S.H., Ha WI. and Park, J.STesting andAnalysis offatigue analysis of edge details,Proceedings of OMAE: Specialty Symposium on Integrity ofFPSO Systems, Houston, TX, U.S.A., 2004. 8.

Kyuba, H. and Dong, P. Equilibrium-equivalent structural stressapproach lo fatigue analysis of a rectangular hollow sectionj oint, International journal of fatigue, pp. 8 5-94, 2004

Maddox, S.J. Fatigue strength of welded structuring, AbingtonPublishing, 1991.

Mansour, A.E. and Ertekin, R.C. Proceeding 0f151h

International Ship and Offshore structures congress, Elsevier,2003.

Masubuchi, K. Analysis of welded structures - residual Stresses,distortion, and their consequences, Pergamon Press Inc., 1980.

Niemi, E. and Tauskanen, P. Hot spot stress determination forwelded edge gussets, 1999., 11W XIII-1781-99.

Niemi, E. Recommendàtions Concerning Stress Determinationfor Fatigue Analysis of Welded Components, 11W-1458-92/XV-797-92, I 992.

Shin, C.H. Simplfiedfatigue strength assessment of shipstructures Journal of the Korean Welding Society, Vol. 16 ,No.5, pp.1 1-19, 1998 (Korean)

Suresh, S. Fatigue of materials, Cambridge University Press,2004.

Tada, H., Paris, P., and Irwiñ, G. The Stress Analysis of CracksHandbook, Paris Productions Incorporated, St. Louis,Missouri, 1985.

Paper No. Year - Last naine of first author Page number

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Fatigue Assessment of Ship Structures using Hot Spot