Fatigue Assessment of Ship Structures using Hot Spot Stress and Structural Stress Apporaches with Experimental Validation

Fatigue Assessment of Ship Structures using Hot Spot Stress and

Structural 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 stress approach and to compare with hot spot stress approach. As an initial study of the systematic validation efforts on structural stress method, an experimental investigation is performed on a series of edge details with welded gusset plates. 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 out fora fatigue assessment of typical ship structures employing structural stress approach. Fatigue strength of side shell

connection of a 8,100 TEU container vessel is evaluated using hot spot stress and structural stress employing

simpl/Iedfatigue analysis.

KEY WORDS: Ship structures, welded structure, fatigue

design, structural stress, hot spot stress, fatigue

life, finite element analysis

NOMENCLATURE

a

: Fatigue crack length

C : Material constants for crack propagation model

d

: Nodal displacement

D 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

zaxis

Weibull 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 factor

t : Plate thickness (mm)

Weibull stress range scale distribution parameter for

load 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 stress Bending stress (MPa)

Amplitude of stress due to dynamic external sea

pressure loads

Amplitude of stress due to dynamic internal pressure loads

Membrane 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 hatch

Warping stress due to torsión at position considered Usage factor

Equivalent structural stress (MPa) Stress ranges

Global 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 hull

girder bending moment (MPa)

Deift University of Technology

Ship HydromeChafl

LaboratorY

Library

Mekelweg 2, 2628 CD Deift

The Netherlands

INTRODUCTION

Welding is the

most commonly employed

process for

fabricating steel structural joints, including those of ships and offshore structures. Some of the advantages of welding are relative ease of fabrication, high joint efficiency and water tightness (Matsubuchi 1980). However, stress concentrations

due to the weld

itself and because joints

are generally

discontinuous portions of a structure, welded joints tend to

suffer fatigue damage before other structural elements. Because,

the fatigue

life

of a structure's welded joints

is

a key

determinant of the service life of a structure subject to cyclic

loading, it is very important to predict the fatigue life of welded

joints in an accurate manner. The fatigue life of welded jòints depends on various factors such as weld quality and surface

finish, and thejoint geometry and stress states

Currently there exist three different methods for fatigue design; stress-based approach,

strain-based approch and

fracture

mechanics approach (Cui 2002). Within the scope of stress-' based approach, different stress definition can be used such as

nominal stress, hot spot stress and structural stress. While

nominal stress is the most widely used in fátigue design, it is difficult to define nominal stress value for çomplex structures such as ships (Maddox 1991). Hot spot stress is defined as a

stress value obtained by extrapolating stresses at certain distance from the weld toe based on finite element analysis (Niemi 1999).

While hot spot stress approach is well accepted in offshore industry, it is well recognized that hot spot stress values may

vary for different elements and different extrapolation

techniques. On the other hand, structural tress approach is recently proposed, and it is known as mesh-size insensitive

fatigue assessment method by using finite element analyses. The structural stress definition is based on the elementary structural mechanics theory and is known to provide an effective measure of a stress state in front of weld toe (Dong 2001).

The aim of this study is to investigate fatigue assessment of

typical ship structures employing structural stress approach and

to compare with hot spot stress approach. As an iñitial part of

the systematic validation efforts on Battelle's structural stress method, a detailed experimental investigation is performed on

edge fatigue details as a part of B attelle lIP program (Kang et al. 2004).

The S-N data generated from this investigation have shown that

the structural stress based SCF (Stress Concentration Factors) are effective in correlating not only the S-N' data generated in this detailed experimental investigation, but also all other S-N data from other joint types collected from various fatigue test literatures. Extrapolation based hot spot stresses (HSS) using

converged mesh were also calculated for each specimen types. Within the edge details tested in this investigation, the hot spot

stresses based on three different extrapolation procedures are compared and found to provide a good correlation of the S-N

data. In the present work,

hence, two

different fatigue assessment procedures using hot spot stress and structural stress

are compared and validated based on the series of fatigue test

data within similar jointtypes and thicknesses.

Having validated the application of structural stress for small

edge details, a systematic investigation is carried out for a

fatigue assessment

of typical

ship structures employing structural stress approach. Fatigue

strength of side

shell connection of an 8,100 TEU containervessel is evaluated using

both hot spOt stress and structural stress. Simplified fatigue analysis is applied using typical lòading conditions defined by

classification societies. Finite element analysis is carried out for full ship with respect to fatigue damage prone locations such as side-longitudinal located near design draft Fatigue life

calculated using structural stress is compared with that of hot spot stress approach. For fatigue strength assessment of ships, structural stress approach is found to be a viable alternative as employing the mesh size insensitive charaçteristics. Further study for the fatigue strength assessment of ship and offshore

structures are required with different mesh sizes and shapes.

COMPARISON OF STRUCTURAL STRESS

AND HOT SPOT STRESS

Structura! stress definition

As shown

in Fig. 1,

a typical

through-thickness stress

distribution at the fillet weld toe is assumed to exhibit a

monotonic through-thickness distribution with the peak stress occurring at the weld toe (Niemi 1999). The self-equilibrating

stress

state induced by local geometry or notch effect

is

considered to be included in S-N data.

Fig. I Through-thickness structural stress distribution

The corresponding equivalent structural stress distribution is illustrated 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. The

normal and shear stress at the reference section B-B can be

readily obtained from either a finite element solutjon or

measurements using strain gauges. The distance, 6, represents

the distance between sections A-A and B-B at the weld toe.

The structural stress components am and ab can be calculated

;: Locui SfreB Diatributions alongA-A

>x

Fig. 2 Illustration of structural stress measurement

The strain gauge measurements obtained from the strain gauge pairs located both at the top and bottom edges of the specimens

was used to calculate the stnictural stress by means of Eq. (4).

Note that the first and the last strain gauges were not used since

they tend to exhibit more variability than the remaiñing strain gauge measurements. The variation in the measured structural

stresses is due to the variations in the surface stresses measured, which are unavOidable in typical strain gauge based

measurements. To reduce the effects of the variation

in

estimating stress values at the weld toe, averaged values

between the symmetric gauges in left and right sides of the test specimens are used. In addition, a linear regression can then be

used to represent the averaged strain distributions. The strain values based on the linear regression at each of the gauge pair

positions can then be used in Eq. (4) to determine the structural stresses at the weld toe.

Structural stress using fiizite element analysis

In FE analysis using 2-D shell or plate element, balanced nodal

forces can be derived from the element stiffness matrices and

the nodal displacements as described Eq. (5). The same applies

to the derivation of balanced nodal moments ûsing nodal

rotational displacement..

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

where (Fe) = vector of nodal forces, [K] = element stiffness

matrix, {d) = nodal displacement

Once the nodal forces (Fr1, F2) in y direction and moments with

respect to x axis are obtained as shown in Fig.

3, the

corresponding line forces (f, f) can be calculated with

consideration of the mechanical equilibrium as derived to Eqs.

(6), (7) and (8). The derivation of line moments (m1, m2) are the same as that of the line forces with respect to the nodal

moments (M1, M2)

+ ff(x)dxO

(6)

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

m

0m t2 + 0b t2 =

r

o-(y)ydy

+.5

r

(1)

Here the first equation represents the force balance in

x-direction evaluated along B-B section, and the second equation

represents moment balance with respect to section A-A at yO.

The mesh-insensitive structural stress can be calculated as long as the stress states at two sections at A-A and B-B are related to each other in equilibrium sense (Dong 2001).

Structural stress from measurements

On the other hand, as discussed by Dong et aI. (2004), the

membrane and bending components in thè structural stress

definition can be estimated by using a series of strain gauges on both 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 situated approximately within a linear surface stress distribution regime near the weld toe, the bending stresses at Sections B-B and C-C can be calculated based on the measurements from both top and bottom surfaces as:

-:

(2)

dc

=.(oTOp

-It should be noted that if there exists no external loadings

between Sections B-B and C-C, the sectional moment change

can be expressed as:

AM (3)

where I represents the sectional moment :of inertia for unit length in z direction in Fig. 2. Then, the strùctural stress at the

weld (A-A) can be estimated by using extrapolations with

respectto 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, detailed

strain gauge measurements are collected before starting fatigue

test. The strain gauge readings were collected at two loading

levels: (1) 20% of nominal yield strength and (2) 50% of

nominal 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 forces

and 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 sell or plate elements. The applied nodal forces are defined using the element 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, the

structural 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 structural

stress and the master S-N curve

Fracture mechanics based prediction of fatigue life in cycles to final failure can be expressed as:

N=

f

da

a=aj

C(M,,)(tK)m

(12)

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

= -¡((wif

'-E"-h Jô,nInotch 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 be

expressed 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 factorKwithout notch effects for an

edge crack is considered as:

K

_{[CTmfm()Tbfh()]}

(16)

The paranietersfm(a/t) andf,('a./t) are well known dimensionless

function of alt corresponding to the membrane and bending

components, which can be found in various fracture mechanics handbook such as (Tada 1985).

Rearranging Eq. (14) as in

term of

N

with the given

dimensionless ¡(r) function:

I 2-m I

Lo=C rnj 2m I(r)N

(17)

An equivalent structural stress can be defined by normalizing

the structural stress range, Eq.

(17), with two variables

expressed in terms of the thickness t and the bending ratio r as

follows: (13) F2 n

!L

!L 3 6

!.

(IIl2)

o '2 6 0 (in2 +

-o 0 'n-I (10)

=0

6 3 L. 6 0 3 'n-I 6 'n-I

where the thickness term/2m2m(m=3.6 according to Dong; the

exponent of Paris crack propagation) becomes unity for t= I

(unit thickness) and therefore, the thickness t can be interpreted

a ratio ofactual thickness t to a uñit thickness, rendering the

term dimensionless. With this interpretation, the equivalent JSeq retains a stress unit ¡(r) is the function

of

bending ratio (r) which

indicates corrections depending on loading modes and crack types. Crack types should be classified into an edge crack or a

semi-elliptical crack. As an edge crack grows, 1(r) can be

divided into load-controlled condition and displacement

condition 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 ofa semi-elliptical crack, ¡(r) can be divided intothe

function for small detail and for structural joint Approximate

functions 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 and geometrical discontinuities have been already included in Eq.

(18), any type of weld joints or loading modes can be evaluated consistently with the equivalent structural stress. Based on Eq.

(18), over 2000 results ofthe existing fatigue tests for both

various weld joints and loading modes are fitted in Fig. 5 and a

master 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 the

basis of two standard deviation with respect to mean S-N curve. For the mean master S-N curve, C=2 1672.4, m '=3.08

1ogA=13.33-3.O8logAScq

For the design master S-N curve, C=15465.6, m'3.08

logA,-=1 2.88-3.O8logASeq

where, o and o correspond to measured stresses at 0.5t and

I .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 by the notch stress

Fig. 6 Calculation

of hot

spot stress

based on

linear extrapolation

These hot spot stresses are used for comparison purpose with

structural stress for interpreting fatigue test results in this study.

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

HS=1.5o (25)

I.EO4 1.E.O5 1.EG

Bsduraece. cycles

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

stress parameter

Hot spot stress

Hot spot stress is the most common to evaluating the fatigue strength in ship and offshore structures because it includes the stress concentration due to geometric shape. There are three

different stress extrapolation techniques as commonly recommended procedures for the calculation of hot spot stresses

in welded structures; 1) the linear extrapolation of stress over

reference points at 0.5 and 1.5 of plate thickness away from the

hot spot; 2) the linear extrapolation of stresses over reference

points at 0.4 and 1.0 of plate thickness away from the hot spot; 3) no extrapolatiòn but the use ofthe stress values at 0.5 of plate

thickness from the hot spot as the relevant hot spot stress

(Mansour 2003). In this study, hot spot stress is calculated using Niemi's guideline based on Eq. (25):

tri 3t/2

Distance from hot spot

eq = 2-m I (18)

EXPERIMENTAL PROGRAM

The experimental investigation on edge details was set up to

achieve the following major objectives:

Experimentally veri1,' the structural stresses calculated

using the mesh-insensitive structural stress method

Investigate fatigue crack behavior in edge details, effects of plate thickness and failure

definitions on S-N data

generation

Examine the applications of the extrapolation-based hot spot stress methods in interpreting the S-N data for edge

details

Examine and demonstrate the validity of the structural

stress based master S-N curve approach in interpreting the S-N data for edge details

The detailed experimental investigation was focused on a total of twelve specimen designs of edge details. The specimen

design involves a base plate and gusset attachment plate which

are welded to form an in-plane edge detail. Two different

thicknesses of the base plates were considered, i.e., 10mm and 15mm. The widths for the base plates and the lengths of the

gusset plates were varied to obtain a wide range of the hot spot

and structural stresses based stress concentration factors at the weld ends considered as fatigue prone locations. All twelve

specimens (with unique combinations of plate thickness, width,

and thicknesses) were fabricated and tested

in duplicates. Typical shipyard welding procedures were used for fabricating

the test specimens. Weld leg lengths and distortions in each

fabricated specimen were measured before fatigue testing for the later interpretation of fatigue test data.

Typically, six pairs of strain gauges were used on each side of the specimens. The strain gauge readings corresponding to

approximately linear distribution regime were used to calculate the corresponding structural stresses according to the definitions in the Battelle's structural stress definition and its measurement techniques (Battelle

2004). For

all specimens tested, an

excellent agreement between the measured and calculated

structural stresses has been obtained, l-lot spot stress measurements based on 11W recommendations for edge details

were also calculated from the strain gauge data and compared

with the corresponding S-N curve.

Fully reversed constant amplitude loading conditions were used

for fatigue testing. The frequency of the cyclic load was 3Hz. Typical nominal stress range of I2OMPa was used throughout the test with a cyclic stress ratio of 0.4 under load-controlled conditions. During the fatigue testing of each specimen, both stiffness, defined as load range/displacement range between

grips, as well as instantaneous crack size as a function of cycles

were recorded at a fixed cycle interval. After final failure

defined as the separation

of

cross-section separation, photographs of the final fracture surfaces of the failed specimen were also presented as a part of the test record.

EXPERIMENTAL SETUP

The dimension of the test specimen is shown in Fig. 7. The steel

plates of thickness of both 10mm and 15mm are used as the thickness of the main plate of test specimens. The grip surface dimension, indicated as dg (85mm) and W (100mm), are kept identical for all specimens. The lengths of gusset plate (L2), which is welded on the side of the base plate, are designed to

vary between 50, 100, 200 and 250 mm.

L,

Fig. 7 Dimensionoftest specimen

The material used in this research is a ship-structural mild steel

of

grade-A. The chemical composition and mechanical properties are summarized in Table 1. The design yield stress

of

the material is defined as 235MPa for ship-structural mild steel according to the specifications of classification societies. Table I Major Chemical composition and mechanical properties

of

(a) (b)

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

width 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

Fig. 8 shows a test specimen installed between grips. Note that the gusset plate is always located in the left side. Therefore, the

front side has the gusset plate always in the left side, and the rear side has the gusset plate in the right side. The dimension

matrix for the test specimens used in this study is summarized in Table 2. A series of proposed variations of some dimensions are

also given in the table as well. Table 2 Test matrix

FCAW (Flux Cored Arc Welding) is used to attach the gusset

plate into the main plate. V-shape groove was machined before

weld. Gusset plate and main plate are welded by 3 - 5 passes

under flat position. During welding, additional jigs were

installed to prevent the specimen from any excessive

deformation. After welding the front side and backside, a fillet

welding was formed at the ends of the gusset plates.

Leg lengths of fillet welds at both sides of gusset plates are

recorded using Moire measurement technique. Moldings reflecting the weld bead shapes are obtained using dental silicon

rubber and sliced into 2mm thickness to obtain leg lengths of both the main plate and the gusset plate sides. Average leg lengths of the main plate and the gusset sides are 5.52mm and

5.57mm, respectively.

STATIC LOADING TEST RESULT AND

ANAYSIS

Prior to fatigue test, surface stress distribution both at gusset and

opposite sides are measured with remote nominal stresses at

20% (47MPa) and 50% (1 17.SMPa) of yield stress (235MPa).

Fig. 9 shows the typical placement of strain gauges. The strain gauges near the weld toe are placed either 5mm or 8mm in

distance from the toe. The remaining strain gauges are attached either 8mm or 10mm from each other. The fatigue test machine used in this study is a servo hydraulic fatigue test machine with maximum load capacity of ±20 ton. Before setting a specimen, stress values measured using strain gauges at front and rear sides

of specimen are carefully observed in order to avoid any

possible 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 (Qt

O 14 54 54 C

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

a a---*-Sto40Cl O54--Spl OSt

so 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 ,y a 154 ¶54 154 554 118 54 -54 -c 8 '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 specimen 2 along the edge surface on the base plate. Before cyclic fatigue

testing, each specimen was first tested under static loading

conditions with remote nominal stress at 20% and 50% of yield

strength level, with fully instrumented strain gauges in pairs between both edges of the base plate placed at 5mm from the

weld ends. On the gusset side, 12 strain gauges are placed while

8 strain gauges are being placed on the opposite side. Stress

values obtain from the measurement show similar values for the

duplicate test, e.g. specimen #2-1 and #2-2. Also a symmetric stress distribution is observed for the both sides of the gusset

plate.

Fig. 11 and Fig. 12 present similar result for specimens 6 and 10,

respectively. Fig. 11 corresponds to the stress distribution for the specimen with identical dimension except for the width of

the main plate (90mm), and Fig. 12 is that of the specimen with different thickness of the main plate (15mm).

10 54 54 ¿1

-..-i5n.,,*i O.1-...-inaiaint b

_i2..-n-n

Q.S.

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

Fig. 11 Stress distribution of specimens 6-1 and 6-2

-.-i.nnosiiß 02. -.--!ainJDi Qi.

-'- taiflaiuI2 02,.- -Snaiaro2 *. -la ti,

#10 .r.Io a o in 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 #16 o'

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 a Distance 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,MorC1C2,,-w-OntnoCit iOr

.,

t- - ¡-n-iDrrnronffi.1 o2,... ps,ob.l bO.

eo.J

-la

..

ia --io at.

in

Fig. 12 Stress distribution of specimens 10-1 and 10-2

As noted in the previous section, hot spot stress values may

become different depending on the extrapolation technique used.

For instance, Fig. 13 illustrates hot spot stress obtained for test

specimen #2. Based on the measurement, hot spot stress is found to be 161.O3MPa using the linear stress extrapolation at 0.5 and

1.5 plate thickness. On the other hand, hot spot stresses are calculated as 153.67MPa and 164.S8MPa for extrapolation of (0.5/1.5t) and (0.411.Ot), respectively, based on the stresses

calculated from finite element analysis. It is clearly seen that hot spot stress values exhibit noticeable difference between

153.67MPa and 164.58MPa. This could result in significantly

different fatigue life estimation.

Fig. 13 Hot spot stress calculated from measurement and FE

analysis for test specimen #2

Average stress values measured at distances of 5mm and 15mm from both sides of weld toe are used to obtain hot spot stress. Fig. 14 illustrates the structural stress results based on the strain

gauge measurements for each given strain gauge pairs located both at the top and bottom edges of the specimens by means of Eq. (4) and the hot spot stress obtained by extrapolating the

stresses measured by strain gauges at 5mm and 15mm locations

using Eq. (25) for the specimen 2. It is observed that hot spot stress values are typically higher than structural stress values. Note that the structural stress values using measurements 2, 3

and 4 show a good agreement among each other.

2.6 2.0 1.5 LL C., 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 a ioo 'a to' a n ¼ a ai ai 11g 'a-n io n

-S-taintSI lia -.--o'ainSI i

OOsiioO'2 Ca-s grsraiSO O

#1

2... ...

(UnIt mm)

Diotooloc from the toc (mon)

i t ti io a n n n ii a st n

Thsmn from the toc (mm

w n n e go

n n a a

ti ra

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

...-. i.o nia-1 i -s.. Sgianr-1

ct- -Sioga-2 ta 'X 3.0! 2.51 0.0! 0.51 1.0! 1.5! 2.01 Distancefromweld toe

Fig. 15 and Fig. 16 also present similar results for the specimen

6 and

10, respectively. Stress concentration factors are

compared using both structural

stress and hot spot stress

obtained from strain measurements at two different loading

levels 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%)

Fig. 15 Comparison of structural stress (SS) and hot spot stress (HSS) of specimen 6

0.0

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

Fig. 16 Comparison of structural stress (SS) and hot spot stress (HSS) of specimen 10

The structural stress and the hot spot stress values for the entire specimen considered in this study are summarized in Table 3. In

general, higher stress concentration values are obtained as the length of gusset plates increases. Similar observation can be made for both structural stress and hot spot stress. Within the

specimen with same gusset lengths, specimens with thicker base plate (15mm) resulted lower stress concentration than that of the specimen with 10mm thickness. Comparing the stress

concentration factors between different width of base plate (50mm and 90mm), it was found that 90mm indicated higher

stress concentration. Also, hot spot stress values obtained from

the measurement show slightly higher values than those of

structural stress. The number indicated as Test-1 and Test-2 in

the table represents the two duplicate tests, respectively.

Table 3 Stress concentration Ñctors of each specimen based on strain measurements

CYCLIC FATIGUE TEST RESULTS AND

ANALYSIS

Crack propagation measurement

Before the fatigue test,

lines were drawn at 1mm uniform

distance using a height gauge for measuring fatigue crack

propagation. The initiation and propagation of crack were

observed at every 5000 cycles corresponding to about every

30mm. The crack propagations with respect to fatigue cycle for

the specimen 5-8 are presented in Fig. 17 as a typical example

of the crack propagation. (U) and (L) corresponds to upper part

and lower part of the gusset. And the numbers indicate the

cycles at failure. Essentially, it is found that the crack size of 0.4W corresponds to 10% reduction of stiffness. This stiffness reduction can be used as a failure criterion, particularly useful

for more complex specimen

configurations and loading conditions. E E a, C a, a) Q 100 90 80- 70- 60-50. 40- 30-20 1 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 fatigue cycle for specimen #5 - #8

Specimen

Structural Stress

Test i

Test 2

Hot Spot Stress

Test i

Test 2 1 1.04 1.13 - 1.59 2 1.11 1.24 - 1.52 3 - - 1.54 1.72 4 - 1.56 1.70 -5 - 1.21 1.65 -6 1.18 1.20 1.71 1.55 7 - - 1.65 1.94 8 1.38 1.41 1.91 1.84 9 - 1.12 1.32 1.48

lo

1.17 1.17 1.56 1.38 11 - - 1.65 1.94 12 1.38 1.28 1.73 1.72 #8-2 #5-2 #8-2 #5-1

.F

F ' . .L01-..B B

vB

cB

Fracture surface

This section presents the crack initiation location and crack

propagation behavior by observing fracture surfaces of several test specimens after fatigue test. Typically most cracks initiated in the middle

of

weld toe as indicated with an arrow. However, some cracks initiated at the edgeofthe weld bead, while some initiated at multiple sites. In general, the crack initiation sites are strongly 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 can

be seen that the crack started at the middle

of

the weld bead.

Red ink was injected with respect to both surfaces of test

specimen at a regular period. As the crack gradually grows

through the fatigue test, fracture surface shows an elliptic shape

and then becomes a flat shape through the crack plane. As the

crack reaches approximately half of the width, a brittle fracture occurred.

Fracture surface

Direction of fatigue crack propagation

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

Fatigue life

Fully reversed constant amplitude loading condition was used for the fatigue test. The frequency of the load was 3Hz, and

typical stress ratio R was set to 0.4. The fatigue loading

condition for each specimen is summarized in Table 4.

icue test condition for each specimen

Each specimen is tested until final fracture. The stifThess curve

is obtained dividing the load range by the displacement range

based on Eq. (26) using the following relationship.

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

EDX-1 500A memory recorder/analyzer is employed to record

the load and the displacement at every 990 cycles in order to

obtain the stiffness curve. Normally, both load and displacement

are recorded for I second at 100Hz sampling rate. Fig. 19

illustrates 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 I2OMPa 0.4 6-2 12OMPa 12-2 12OMPa Spec. Stress Range Stress Ratio Spec. Stress Range Stress Ratio 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 correlation

Summarizing the stress values presented in the previous sections, it was demonstrated that the structural stresses can be obtained in consistent manner. In this regard, this section presents the

S-N data obtained from the fatigue test. Fatigue test result with

final 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 140

z

120 a 100 --80 60 40 20 o

Fig. 20 illustrates the fatigue life of each specimen in terms of nominal stress versus cycles to failure. It should be noted that nominal stress is calculated ignoring any bending induced

contributions to the overall stress concentrations at weld end due to the asymmetry of the specimen geometry. Therefore, the S-N

data appeared in flat.

en

Q-n

en C 61 o, en en C g o

z

1000 loo-Io 10' 10' N, cycles

Fig. 20 Nominal stress range versus failure cycles

Fig. 21 presents S-N curve presented using hot spot stress. Hot spot stress is calculated as explained in previous section. Since

the extrapolated hot spot stresses provide an indication of the stress concentration on the surface relatively close to the weld

end, bending effects

are captured in the hot spot stress

calculations. Thus, slightly improved correlation among the S-N

data from the edge details can be seen. However, the overall

data scatter remains essentially the same as the case of nominal stresses. u 10' 10' 1000 en Q. n s) a' C

¡

100 10 1000 ca O-n en a, C a en en 100 a

t

C en ca 3-= 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 stress concentrations calculated in the case of 20% tensile loading according the methods explained in previous section. AIl data

essentially gathered into a single narrow band, as shown in Fig. 22. 10'

J

#1-1 #1-2 £ #2-1 V #2.2

I

#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 structural

stress definition can be effectively applied to correlating fatigue

test data from various joint types, loading modes, and plate

thicknesses. The effectiveness of the equivalent structural stress

parameter has been presented by consolidating S-N data into a

single narrow band, and this clearly implies that improved

fatigue 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 12-1 527,590 758,580 6-2 433,910 12-2

* All cracks occurred at weld toe

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

#1-1 #1-2 L #2-1 V #2-2 4 #3-1 #3-2 #4-1 C #4-2 S #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 SHIP

STRUCTURES EMPLOYING STRUCTURAL

STRESS AND HOT SPOT STRESS APPROACH

As a later part of this study, a systematic investigation is carried

out for fatigue life assessment of side shell longitudinals on

8,100TEUcontainer vessel employing structural stress.

Fatigue ljfe assessment procedure of ship structures

Fatigue life assessment of welded joints in ship structures can be carried out using long term stress distribution and S-N curvas.

In the case of simplified fatigue analysis, fatigue strength is analyzed using loadings defined from classification societies, not using ship motion analysis. The fatigue damage ratio is finally estimated using Palmgren-Miner rule with long-term

stress range distribution. The long-term stress range distribution

is defined by the Weibull distribution. The fatigue life

is calculated employing Weibull distribution factors (scale and

shape parameter) and relevant S-N curves.

Flow diagram over fatigue analysis procedures are shown in Fig.

23 applyiñg equivalent structural stress and notch stress using master S-N curve and DNV S-N curve. Load response in the

diagram includes the loadings from internal or external pressure

and hull girder wave bending moments. Using each equivalent structural stress and notch stress defined with respect to load

cases, combined stress ranges can be obtained and fatigue

damage ratio is calculated from long-term stress range distribution and the master SN curve and DNV S-N curve.

JLoad response

Notch Stress (Equivalent Structural Stress)

I

Stress components

Combination of stresses (Stress range)

Long term stress distribution

4

Fatigue Damage Calculation

Hot spot stress (Structural Stress)

S-Ncurve (Master S-N curve)

Fig. 23 Flow diagram over fatigue analysis procedures

In the simplified method, dynamic loading may be divided into

global wave bending moments and local load such as external

pressure and internal pressure.

The following eight dynamic load cases have been applied to the

FE model and the load cases applied are listed in Table 6.

Boundary condition of the finite element model was applied as a simple support condition.

Table 6. Load cases considered for fatigue calculation

Since global wave bending moments are based on vertical wave

bending moment and horizontal wave bending moment at

probability level of exceedance from lACS, they are modified to

10 probability level of exceedance to be compatible with

pressure loading components defined at l0 probability level. Usiñg correlation factor (p) which considers phase difference for

combination of vertical and horizontal wave load, global

combined stress range(Mg) is finally defined by Eq. (27).

2Jo-h + wl+ °g1 +

(27)

+

_2Pvhvh

whereEwg 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 girder bending moment (0h=1/2Mh)

=warping stress due to torsion at position considered bending stress

of deck structure due to

torsional

deformation of hatch(0)

Pvh = 0.10, average correlation between vertical and horizontal

wave induced bending stress

External pressure is determined compariñg dynamic pressures

from ship rolling motion and ship pitching motion, whichever is higher. The internal pressure is determined from the acceleration

of liquid cargo or ballast water among three directions and

selected from whichever is the highest.

Local combined stress range (M,) is composed of external and internal pressures with a correlation factor expressed in Eq. (28).

Local combined stress range

is divided into full loaded condition and ballast condition.

Loading type Loading condition LCI Vertical wave bending

moment Fully loaded / Ballast LC2 Horizontal wave bending_moment Fully loaded LC3

-Horizontal wave bending

- moment

Ballast

LC4 Torsional moment Fully loaded

LC5 Torsional moment Ballast

LC6 External pressure Fully loaded

LC7 External pressure Ballast

LC8 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

Pp=average correlation between sea pressure loads and internal

pressure loads

i

z ₊

k

_{+ IyI}

xH

2

iO.T,

4-L

4-B

5.L-T,

where L is rule length of ship in meter and T, is actual draft. B is the greatest moulded breadth of the ship andx,y, x are the

longitudinal, transverse and vertical distance from the origin (at midship, centerline, baseline) to the load point of the considered structural detail.

If a combined long term stress response analysis is not carried out, the combined stress range response from the combined global stress and local stress range responses is the largest of

(Hovem 1993):

IO.6L\cr +\o

&7o=fefmma

_{LOg +O.6-ia,}g

where f, is the operation route reduction factor and fm is the

mean stress reduction factor(JÇ,,=0.85 maybe applied on the long term stress distribution). A reduction in the effective estimated stress response is achieved for vessels that for longer periods

operate in environments not as harsh as the North Atlantic. For world wide trade, the reduction factor may be taken as 0.8. When the long-term stress range distribution is defined applying

Wóibull distributions for the different load conditions, and a one-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 damage

a, m =S-N fatigue parameters

N, =total number load conditions considered p,,=fractiOn of design life in load condition n

Ta=design life of ship in seconds

= Weibull stress range shape distribution parameter for load conditionn

qn = Weibull stress range scale distribution parameter for load

coñditionn

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 range

level, as

&70 q

- (lnno)1Th

(31)

Paper No. Year - Last name of first author

where,n0is the number of cycles over the time period for which

the stress level is defined.

Target structure and fatigue crack definition

In this study, typical fatigue crack points are assumed in the

vicinity of intersection of side longitudinals and transverse web

frame for a 8,100 TEU class container carrier.

Principal

dimension of container vessel is listed in Table 7 and finite

element 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 as well as hot spot stresses are calculated in critical details of side longitudinals located between design draft (TF) and ballast draft

(TB). Fig. 25 shows the concerned section of web frame and

local area in finite element model, and Table 8 lists the design

details.

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

u.

_{IPUPlIpIupIgpp}

-

U!uI.iupuii.11,1.

-

L!IUIIIIIL..III

i

I

LUUIp

U Iii

U 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 are

anticipated at HS 1 and HS 2 on the longitudinal face plate and collar plate, whereas edge cracks are expected at HS 3.

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

FE models used in the fatigue strength assessment are classified

into 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 the parametric studies to veri1,' mesh-insensitivity. Fatigue lives were calculated employing structural stress approach on every mesh size and shape which are mentioned above. In order to

compare with hot spot stress approach, mesh of i .Ot x 1.01 was calculated by using hot spot stress.

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

"u

_ii

Fig. 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 RESULTS

For the design life of 20 years, fatigue damage ratio has been calculated with the equivalent structural stress (ESS) and the design master S-N curve. In order to compare with the fatigue lives from the hot spot stress (HSS) approach, the S-N curve

from DNV Classification Note No. 30.7 was employed. Hot spot stress approach is applied to the FE model of which mesh size is

1.Otx 1.01.

Parameters for the use of design master S-N curve and DNV

curve are as given in Table 9. Palmgren-Miner rule was used to calculate 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 calculated

fatigue life employing hot spot stress method.

IA 1.2 1.0 _i 0.8

6

0.4 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 = logamlogo

loga m

Design master S-N curve (SS) 13.33 3.08

DNV 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 from 1.0: x 1.0: meshed model, the fatigue lives from structural stress

and hot spot stress give only a small difference. In considering

mesh shape insensitivity, result of fatigue lives from 2.0: x 2.0:

and 2.Ot x 2.0: paver have good correlation, when structural

stress is used.

in the case of HS1, the calculated fatigue life using structural

stress approach from I .0, x I .Ot meshed model is approximately

10% less than larger meshed model. On the other hand, in the

case of HS2 and HS3, the calculated fatigue

lives using

structural stress

approach from I.Otxl.Or are more than

maximum 30% lager meshed models.

In case of HS2, however, the calculated fatigue life using

structural stress approach from 3.Ot x 3.0: meshed model is

approximately 30% less than those from the 1.0: x 1.0: one. It is

considered that 3.0: x 3.0: meshed model is failed to represent

its own geometrical condition in the vicinity of concerned area.

CONCLUSIONS

In this study experimental structural stress measurement techniques are investigated. The effectiveness of structural stress method is compared with

that of hot

spot stress. The

measurement techniques are based on a series of strain gauge pairs placed on both sides of a specimen width to resolve both membrane and bending stress

components. And also the

parametric studies for mesh size and shape insensitivity of

structural stress

have been

carried out. Fatigue strength

assessment of side shell longitudinal stiffener of 8,100 lEU container vessel is performed. From this research following

conclusions are drawn.

Consistent structural stress values can be obtained experimentally using stress measurements in proper distance. Stress values obtained using linear regression are

used to calculate

structural stresses

to minimize the

fluctuation from experiments.

Both hot spot stress and structural stress can be successfully obtained from the experiment. Structural stress

values calculated

based on the

linear regression of

measured stresses result in lower stress value than those of hot spot stress.

Hot spot stress vs. life shows a reasonable consolidation

between similar types of edge detail specimens. However,

hot spot stress vs. life cannot show further consolidation

with those of different types/thickness of specimens. Equivalent structural stress with thickness correction versus life shows a fairly good consolidation between edge detail test results considered in this study.

A consistent structural stress approach is employed for the

fatigue strength assessment of side

shell longitudinal

stiffeners of an 8,100 TEU container vessel. The similar

fatigue life results are compared with that of hot spot stress approach.

In case of structural stress approach, the stress values from

finite element analysis for 2.Ot model are

in general applicable to fatigue strength assessment. In considering

mesh shape insensitivity, result from different mesh shape

models gives good correlation. From this result,

it is

confirmed that modeling time associated with local fatigue

model can be significantly reduced by using larger and

irregular mesh types.

For fatigue strength assessment of ships, structural stress approach is found to be a viable alternative as employing

the mesh size insensitive characteristics.

ACKNOWLEDGEMENTS

This research is sponsored by Advanced Ship Engineering

Center of Korea Science & Engineering foundation. The

financial support is gratefully acknowledged.

REFERENCES

Battelle Structural Stress uP Report (NO. N004431-01): Mesh-Insensitive Structural Stress Met hodfor Fatigue Evaluation of

Welded Structures, 2004. 2.

C. Guedes Soares and Y. Garbatov, "Reliability based fatigue design 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 prediction methods for metal structures. Journal of Marine Science and Technology, 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 3 Chapter ¡ Hull structural design ships with length 100 meters and above, 2003

Dong, P. A structural stress definition and numerical implementation 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-N

curve foe weldedjoints, 11W Doc XIII- 193 0-02/X V- 1119-02, International Institute of Welding, 2002

Gurney, T. R. Fatigue of welded structures, Cambridge university press, 1979

Ha, C.!. A study on the fatigue strength of weldedjoints using structural stress with consideration of stress singularity and its 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

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

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Publishing, 1991.

Mansour, A.E. and Ertekin, R.C. Proceeding0f151h

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 for

welded edge gussets, 1999., 11W XIII-1781-99.

Niemi, E. Recommendàtions Concerning Stress Determination for Fatigue Analysis of Welded Components,

11W-1458-92/XV-797-92, I 992.

Shin, C.H. Simplfiedfatigue strength assessment of ship

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