LOCAL STRESS APPROACH FOR FATIGUE ASSESSMENT
OF WELDED JOINT
Hiroyuki YOKOTA and Kengo ANAMI
Kochi University of Technology
ABSTRACT:

Local stress approach can be a strong tool for assessing the fatigue

performance of welded joint in steel bridge structures, which is subjected tocomplicated stress field.

This paper surveys the effectiveness and remaining problemsof the local stress approaches.

Then, this paper examines a method, which utilizes themeasured stress, to evaluate fatigue strength of weld root of load carrying typecruciform welded joint.
KEYWORDS: fatigue, local stress approach load carrying cruciform welded joint

1. INTRODUCTION

S

S

One

of

the

most

importantmechanisms of steel bridge structures, which occurs
in-service condition, is fatigue.

mdeterioration

to initiate in steel bridge superstructures and even
Since such fatigue cracks may lead aN

SmN = AIn Japan, numerousNnumber of fatigue cracks has been recently reported
substructures.

A

1
S

N

Fig.1 S-N diagram; S: stress range, N: fatigue
life and A: representing fatigue strength

significant influence to the traffic and even collapse

applied stress range are known.

of the bridges if the cracks are left to propagate,

design is conducted with this fatigue design S-Nrepair and retrofitting works including investigation

diagram, which is expressed with fatigue strengthof fatigue mechanism for such fatigue damaged

categories specified with nominal stress range.

bridges are very urgent issues now.

Therefore, if nominal stress range is unknown or

As shown in Fig.1, relationship between the

Present fatigue

hard to determine, it should say that fatigue strength

stress range applied, S, fatigue life (loading cycle tocategory is also unknown.

failure), N and fatigue strength A is simply expressedcracks in steel bridges have been found to initiate at

by following equation (1);the area where nominal stress range is hard to be

SmN = A

(1)

where

However, most ofdetermined because of the complexity of stress field(complexity of stress field itself and complexity of

m: constant (=3 for weld subjected to cyclic

stress occurrence mechanism).

For this reason, it isnormal stress )now very difficult to evaluate the fatigue life of such

This equation, for an example, means that fatigue

areas in the steel bridges at the design term andlife can be calculated when fatigue strength andmaintenance term.

Therefore, it is very urgent

issue to establish a method to evaluate the fatigue
strengthofweldedjoint

subjected

toToe stresssuch

Stress concentration
due to toe geometrycomplicated stress field.

Stress concentration
due to joint geometry

Recently, local stress approach for assessing thefatigue strength of welded joint is investigated. This

Nominal stressapproach utilizes the stress in the vicinity of the

Weld toelocation of crack initiation, which can be obtainedTfrom stress measurement or numerical analysis likeFig.1 Schematic illustration of stressconcentration at weld toe

FE analysis.

Philosophy of local stress approachand many research works are well surveyed by RadajToe stressand Sonsino (1998).

Hot spot stressFirst part of this paper surveys

the effectiveness and remaining problems(recent

topics) of the local stress approaches.
A

As mentioned above, local stress approachesBautilize the stress in the vicinity of the location ofT

crack initiation.

Fig.2 Extrapolation to calculate hot
spot stress

In order to obtain a precise stressby calculation, it is necessary to know the detail
information of local structural geometry.

While thestrengthb

categoryof welded

joint,

isstressstress at cracked location is sometimes very sensitive

concentration (other factors are weld defect, welding

against the local geometry, but the structuralresidual stress, etc).

modeling of local geometry itself sometimes include

fatigue strength category of weld-attachment joint

very uncertainty.

In addition, local stress at cracked

results from the difference of stress concentration at

location cannot be sometimes evaluated without

crack initiation location, which depends on the size

considering the entire bridge behavior. In such area,

and configuration of the joint.

it needs numerous efforts to obtain the precise stressapproachanalytically. Thus, it is necessary to estimate theconcentration and evaluates the difference of themethod to evaluate the fatigue strength using

fatigue strength. In this section, hot spot stressmeasured stress.

approach and effective notch stress approach, which

For the welded root cracking,since the crack initiation location is embedded inside

focuses

Usually, the difference of

thisdifference

Local stressofstressare widely used recently, are briefly introduced.

the weld, it is not usually possible to measure thestress in the vicinity of the initiation point.

The

2-1 Hot spot stress approach

only method presently proposed to evaluate theStress concentration at weld toe can be divided

fatigue strength as a local stress approach is effective

into two parts as illustrated in Fig.1: stressconcentration K w depending on the size and typenotch stress method (which is explained later).

In

this study, a local stress approach which utilizes

of welded joint, and stress concentrationstress range measured in front of weld toe for load

depending on the local toe geometries, such as toe

carrying type cruciform welded joint is examined.

angle and toe radius (for example, Miki 1992).

2. LOCAL STRESS APPROACH

usually recognized that the influence of thedifference of K s results in the scatter in each fatigue

One of the factors, which dominate the fatigue

strength category.

Ks

It is

Hot spot stress aims to grasp thestructural stress K w . Since fatigue strength categories

Table 1 Examples of calculation methods of HSS

of weld-attachment joints are usually classified with

a

b

A

0.5T

1.0T

B

0.5T

1.5T

C

0.4T

2.0T

D

1.0T

3.0T

E

4.0mm

F

4

type and size of welded joint, it is said that fatigue
strength of weld-attachment joint can expressed with
only one fatigue strength category when using hot
spot stress range.
Several methods to calculate hot spot stress havebeen proposed.

2000000 Cycles

spot stress have been proposed and utilized in the
Also for the flat-plate welded joints,

which are usually used for bridge structures, several
methods to calculate hot spot stress are proposed.

Fatigue Strength [MPa]structures, several formulae for calculation of hot

Most of methods seem to obtain the stress at weld

100
90
80
70
60

For anexample, some extrapolation methods, which were
proposed by Yagi (1991) and Huther (1990), arelisted in Table 1. Miki (1992) also examined anotherextrapolation points, those are 4 mm and 6 mm from
Recently, International Institute of

Welding (IIW) recommends the extrapolation pointsof 0.4T and 1.0T far from weld toe, where T is baseplate thickness.

(Other methods are also proposed,such as one-point stress method where stress at one
location a certain distance (for example 0.3T: Nihei)
far from weld toe is decided as hot spot stress.)
As mentioned above, when using hot spot stress

Joint Specimen
TensionBending101Base Plate Thickness

10
[mm]

2

(a) with nominal stress range
Fatigue Strength (Hot Spot Stress Range) [MPa]front of weld toe as illustrated in Fig.2.

Girder Specimen
Pure–Bending
Shear–Bending200

toe by extrapolation from stresses at two point inweld toe.

3

4

4.9 T

For an example, for pipe (withhollow section)-welded joints in marine/off-shore

fatigue design.

1.57 T

10.0mm3

2 million cycles

200

100
90
80
70
60

Girder Specimen▲ Pure–Bending△ Share Bending

Small Specimen● Tension○ Bending
1

10

10

Base Plate Thickness [mm]2(b) with hot spot stress range
Fig.3 Fatigue strength of cruciform weld joint

strength of large-scale girder specimen is muchrange for the fatigue strength evaluation, the size

smaller than that of small joint specimen.

effect and shape effect can be eliminated.

this tendency disappears when hot spot stress range

Fig.3

shows an example, where the many results of thefatigue tests of cruciform welded joint specimens

However,is used instead of nominal stress range.
In order to use this hot spot stress range forhaving widely-scattered base-plate thicknesses are

fatigueevaluation,

arranged with (a) nominal stress range and (b) hot

specified with hot spot stress range is necessary as

spot stress range calculated from the stresses at 4 andillustrated in Fig.1.

6 mm away from weld toe (Anami, 2001).

It is(2002) proposed the fatigue strength category ofclearly observed if nominal stress range is used for

IIW-FAT100 or 90 (see the detail in the reference)vertical axis, fatigue strength decreases with an

specifiedincrease in the base plate thickness and fatigue

weld-attachment joints.

withfatiguestrength

category

Recently, Niemi and Marquis

hot

spot

stress

range

for

SYM

Advantages of the use of hot spot stress range

1/4 model(1/2 model for specimen
under combination load)

might be summarized as follows;○ hot spot stress can be calculated from stresses infront of weld toe, which can be obtained from

SYM

stress measurement in site (in real bridge
structures) and also stress analysis,
fictitious hole(r=1mm)incomplete penetration○ fatigue evaluation can be done for the weld joint
whose (nominal stress base)fatigue strength

SYM

category is unknown,

Fig.4

FE model for calculation of ENS○ since hot spot stress can be obtained in field,
fatigue evaluation can be conducted even after

Fictitious holechange of structural detail by repair and retrofit,○ since hot spot stress can be obtained frombase plate

structural analysis, this approach can contribute
the FEA (or other structural analysis)-based

Incomplete penetration

bridge design.

Distribution ofvon-Mises stress

ENS
Fictitious holeFig.5 Distribution of von-Mises stress aroundfictitious hole

Other than establishing the method to calculate hot
spot stress and establishing the fatigue strengthintersection of gusset centerline and boxer weld line,

category based on hot spot stress range, one of theand moves with the change in the ratio of shear

research topics with respect to the hot spot stress isstress and bending stress. The method for evaluating

the applicability of hot spot stress approach for thethe fatigue behavior of welded joint in such acomplex stress field.

Most of research works

complicated stress field has not been established yet,related to the fatigue strength focuses the fatigue

and this topic is now very hot issue also from thebehavior of welded joint subjected to in-plane stressview point of applicability of local stress approachnormal to the weld line.

for the fatigue evaluation.

However, as previously

mentioned, many fatigue cracks are found in the area
subjected to the complex stress field containing

2-2 Effective notch stress (ENS) approachIn

As mentioned above, while the hot spot stressaddition to this difficulty, in bridge structures, stressapproach is a strong tool to evaluate the fatigue

fluctuation, which causes fatigue cracks, mainly

strength, this approach is inapplicable for the root

results from vehicle and train passing through thecrack.

bridges.

This means that the loading point on thecase of crack initiation from weld root, effective

bridges moves so that the stress field, such as

notch stress (ENS) approach may be a useful tool.

principal stress direction, is possible to change even(this method is applicable also for weld toe cracking).

one load cycle.

For an example, Anami (2001)

Effective notch stress is defined as the maximum

investigate the stress condition around the boxer

von-Mises stress along the circumference of aweld of out-of-plane gusset welded to the girder web

fictitious hole which has a certain radius (IIWby FEM analysis with entire girder model. This

recommends the radius of 1mm, but there is also

reference concluded that the maximum stress aroundother radii proposed) installed at the crack initiation

the boxer weld of web gusset is not always at thelocation.

in-planeshear,

out-of-planebending/shear.

For the evaluation of fatigue strength in theFig.4 shows an example of FE model forcalculating ENS (This model is also utilized in
of incomplete penetration. Fig.5 shows an example

Crack from weld rootLchapter.3), where a fictitious hole is installed at a tip
Root gapof distribution of von-Mises stress in the vicinity of
the fictitious hole.

IP

IIW recommended that fatigue

strength of welded joint is categorized into IIW-FAT

IP: Incomplete penetration
L: Weld leg length

225 (fatigue strength at 2 million cycles is 225 MPa)
when using ENS (fictitious hole radius of 1mm) (forexample, Morgenstern, 2004).
Due to the recent development of computer

T

Fig.6 Crack from weld root of load carrying
cruciform welded joint
Fatigue strength

3.1

ENS

technology, it is now possible to conduct structural

3.2

stress analysis of complicated structural detail modelwith very fine mesh.

Toe stress

Recently, many researchers

focus this method and examine the reliability of this

3.3

method by discussing the ENS and fatigue

Stress in front of weld toe

experimental data.
However, this method relies on structural analysis,Fig.7 Illustration of purpose of this study

which needs detail structural information in order toobtain precise stress value.

Next chapter explainsan examination of local stress approach withmeasured stress in front of weld toe for fatigue
assessment of root cracking in load carrying
cruciform weld joint.
3.

2mm
groundout

LOCAL STRESS APPROACH OF LOADCARRYING CRUCIFORM WELDED JOINT

Membrane Combination

Load carrying cruciform weld joint is illustrated
in Fig.6.

Type-A
Fillet weld: Gap=0
Type-C
50% penetration
Gap=0
Type-D
50% penetration
Gap=3mmThis type of joint has two possible

locations of crack initiation, namely weld toe andweld root (tip of incomplete penetration).

Asmentioned above, while the fatigue strength of weld
toe can be evaluated by hot spot stress approach, thisapproach cannot be applied for the root cracking.
While it is proposed that effective notch stress (ENS)
approach can evaluate the root cracking, thisapproach relies on numerical analysis and needs
detailed information of welded joints.

However,

Fig.8 Specimens and Weld Details

there are some parameters which strongly affect theweld leg length (L).

These geometrical parameters

fatigue behavior of the weld root, such as length ofare usually very hard to grasp properly in site evenincomplete penetration (IP), root gap size (G), andby using non-destructive testing.

Therefore, it isnecessary to investigate the method for evaluating
the fatigue strength of the weld root of load carrying

Crack fromroot

cruciform welded joint using the stress in front of theweld bead/toe.

For this purpose, this study

Crack from toe

conducts following research works as illustrated in
Fig.7; (1) applicability of effective notch stress forthe crack from the weld root is examined
experimentally,(2)

relationshipbetweenFig.9 Fatigue cracks from root and toe

the

3

10

parametric analytical work and (3) method toevaluate the toe stress by using the stress in front of
weld toe is examined.
3-1 Applicability of ENS approach
Fatigue test specimens of load carrying

Nominal Stress Range (MPa)effective notch stress and toe stress is examined by

H
2

10

Type A
Type CType D

type cruciform welded joint used in this study isshown in Fig.8.

4

5

10

Fatigue tests of nine specimens are

Type A under Combination
Type D under Combination
Previous Data

JSSC A
B
C
D
E
F
G

6

10
10
Fatigue Life (Cycles)

done under uni-axial membrane loading, and fatigue(a) S-N diagram with nominal stress range

tests of other four specimens are carried out under10

bending loading.

One side of the surfaces of thespecimens under combination loading is reduced at
depth of 2 mm by grinding in order to apply an
eccentric load.

Calculated nominal out-of-planebending stress is about 30 % of nominal membranestress. Minimum loading of all of the fatigue tests
are 10 kN.

Figure 9 shows examples of fatigue

cracks observed in this series of fatigue tests.

3

Nominal Throat Area Stress Range (MPa)combination of membrane loading and out-of-plane

Examplesmesh size around the fictitious hole is about 0.08
mm that is less than 1/10 of the radius of thefictitious hole.
Fatigue test results are summarized in Fig.
10, where Kainuma’s (2000) fatigue test results arealso plotted with the results of FEM analysis carriedout in this study.

In the figure (a), nominal stressrange (load range/cross section area of base plate) is
for the vertical axis.

For the specimen tested under

H
2

10

Type A
Type CType D
Previous Data
4

10

5

6

10
10
Fatigue Life (Cycles)

7

10

3

10
Effective Notch Stress Range (MPa)of FE models are already shown in Fig.4. Minimum

JSSC AB
CDEF
G(b) S-N diagram with nominal throat area
stress range

FE analyses are also conducted in order toobtain the effective notch stress (ENS).

710IIW FAT225
Type A
Type CType D
Type A under Combination
Type D under Combination
Previous Data

2

10

4

10

5

6

10
10
Fatigue Life (Cycles)(c) S-N diagram with ENS range
Fig.10 Fatigue test results

7

10

the combination load, sum of the nominal membrane

minimum meshsize : 0.08mm

stress range and out-of-plane bending stress range isused for the vertical axis.

It is obviously observedthat fatigue test results are much scattered.

In thefigure (b), nominal throat area stress range is used
for

the

vertical

axis.

In

Fatigue

Incomplete
penetration

DesignFig.11 FE model for calculating toe stress

Recommendation from JSSC (Japanese Society of
Steel Construction, 1995), it is specified that thefatigue strength category of load carrying cruciform
welded joint is H class when evaluated with thisnominal throat area stress range. All results are

Table 2 Detail parameters for FEM
Base plate thickness T
Weld leg length L
Weld Gap G
Penetration ratio IP
IP=0 means fillet welding

11, 22, 33 mm
6.5, 13 mm
0, 1.5, 3, 4.5
0, 27, 50, 67 %(b) becomes much smaller than that in (a).

In thefigure (c), ENS range is used for the vertical axis.
While slight difference between the specimens withand without the weld gap, the scatter band is smaller
than that in (a).

In addition, the influence of theout-of-plane bending is also evaluated well by using
ENS range.

In this figure (c), line of IIW(International Institute of Welding) FAT-225 class is

Effective Notch Sterss / Nominal Stressplotted over the JSSC-H class and the scatter band in
15

10

IP=0, G=1.5

5

L
13
13

11
11

13
6.5

5
10
Toe Stress / Nominal Stressalso plotted. All fatigue test results including
previous data are plotted over this IIW-FAT 225 line.

T
33
22

15

Fig.12 Relationship between ENS and Toe stress

While the number of analysis cases (totally 54 cases)
3-2 Relationship between the toe stress and ENS

is not sufficient and all cases have equal weld

In order to find out the stress at the area

leg-length, the relationship between the toe stresswhere strain gages can be installed for predicting theand ENS can be described with one curve, which is

ENS, first the relationship between the toe stress andindependent of the parameters, namely base plate

ENS is discussed.

thickness, weld gap size and incomplete penetration.

For calculating the longitudinal

toe stress, the fictitious hole in each FE model usedin previous section (Fig.4) is eliminated as shown in
Fig.11.

The weld detail parameters examined inthis discussion is listed in Table 2.

The minimum

mesh size near weld toe is about 0.1 mm.

3-3 Relationship between the toe stress and stressin front of weld toe
Previous section explains the possibility to

Since theevaluate ENS and even fatigue strength from toe

toe radius is 0 in this model, the toe stress is strongly

stress, but it is impossible to measure directly toe

influenced by the mesh size around the weld toe.

stress itself.

However, since the mesh discretization near weld toe

predict the toe stress using stress in front of weld toe,is the same in all models, it is possible to discuss thewhich can be measured in field is examined.

change of toe stress with the weld detail parameters.

As mentioned before, stress concentration at
weld toe can be divided into two factors, K w

Relationship between ENS and toe stress obtained
from this series of FE analyses is shown in Fig.12.

and K s .

Thus, in this section, the possibility to

Since the FE mesh near weld toe is the15analytical cases. Thus, the difference of toe stressshown in Fig.12 results from the difference of K w .
On

the

other

hand, hotspot

stress(HSS)

concentration factor is defined as the factor
explaining structural stress concentration factor, K w .
Thus, the relationship between toe stress and HSS is

Toe Stress / Nominal Stresssame in all models, K s should be the same in all

10

5

T

L

33
22

13
13

11
11

13
6.5

examined here.
0

Fig. 13 shows the relationship between the toe
stress and HSS, which calculated from the stresses at(a) HSS from stresses at 4 and 6mm from toe
15

thickness, in Fig.(b).

While the results from thesame models are plotted in the both figure, (a) and(b), significant difference in HSS is observed.
In the figure (a), there is a circle drawn overthe 4 results (just as an example), which have theToe Stress / Nominal Stress4 and 6 mm from weld toe in Fig.(a) and from 0.4T
and 1.0T from weld toe, where T is base plate2
4
6
Hot Spot Stress (4–6mm) / Nominal Stress10

5

same length of incomplete penetration and different
0weld gap size. Relationship between HSS and toe
stress when only weld gap size is changed seems

T

L

33
22
11
11

13
13
13
6.5

2
4
6
Hot Spot Stress (0.4T–1.0T) / Nominal Stresslinear, but that relationship strongly depends on the(b) HSS from stresses at 0.4T and 0.6T from toe
Fig.13 Relationship between toe stress and HSS

base plate thickness, weld leg length and incomplete

evaluated using toe stress because fatigue life ofpenetration.

welded joint is usually dominated by crack

The variation of HSS calculated fromthe stresses at 0.4T and 1.0T from weld toe between

propagation life.

models is quite small compared to the variation ofpoints for calculating HSS are decided to evaluate

toe stress.

well the fatigue strength of welded joint.

In addition to that, in both figures (a)Usually, the stress extrapolation
Thus, itand (b), the change in HSS is quite small in themight be said that HSS currently proposed does notmodels having base plate thickness of 11 mm andrepresent directly the toe stress. In order to achieve

weld leg length of 13 mm.

This is because thethe goal of this study, it is necessary to find out thechanges in weld gap size and incomplete penetration

method to evaluate the toe stress by the stresssize are occurred at the weld root and stress points

measured in front of weld toe, but this topic is now

for the extrapolation are far from that point (weldon progress.

root).
Compared to Fig.12, the data plot is muchscattered.
HSS,

As mentioned above in the definition ofHSS

evaluates

thestructural

4. SUMMARY
Presently, development of useful method tostressevaluate the fatigue strength of welded joint

concentration. Since the toe configuration is the

subjected to complicated stress field is strongly

same in all models, it was expected that HSS and toe

demanded for the purposes of design and alsostress had a clear correlation.

maintenance of steel bridges.

It is well known thatfatigue strength of welded joint can not be directly

stressapproaches,

In this paper, local

advantages

andremainingproblems of use of hot spot stress approach andand Root Gap on Fatigue Strength of Load Carrying

effective notch stress approach, are introduced.

Fillet Welded Cruciform Weld Joint”, Journal of JSCE,

Then, local stress approach for fatigue assessmentof load carrying cruciform welded joint in the caseof fatigue cracking from weld root is examined.
From this discussion, the following remarks are

No.647/I-51: 435-445 (in Japanese) .
Japan Society of Steel Construction (JSSC), 1993,
Fatigue Design Recommendation for Steel Structures,
Gihodo-Shuppan (in Japanese).

obtained;(1) Effective notch stress approach is useful forevaluating the fatigue strength of load carrying
cruciform welded joint in case of root cracking
even when the joint is subjected to the
combinationofmembranestressandout-of-plane stress fluctuation.
(2) Extent of effective notch stress can be evaluatedby extent of longitudinal toe stress.

Thismeans, fatigue strength of weld root can beevaluated if toe stress can be predicted frommeasured stress.
(3) A good relationship between hot spot stresses
and toe stress is not found in this study.

This

study is now investigating the stress in front of
weld toe, which represent the toe stress and evencan be measured.

K. Anami, 2001, Fatigue Strength Improvement ofWelded Joints Made of High Strength Steel, Doctoral
Thesis in Tokyo Institute of Technology.
K. Anami and C. Miki, 2001, Fatigue Strength of
Welded Joint Made of High-Strength Steels,
Structure Engineering Mater, 86-94.
K. Nihei, 1996, Study on Unified Fatigue Strength
Assessment Method for Welded Structure – Hot SpotStress Evaluating Method for Various Combinationsof Plate Thickness and Weld Leg Length, Journal of
SNAJ (The society of Naval Architects of Japan), 179(in Japanese).
E. Niemi and G. Marquis, 2002, Introduction to the
Structural Stress Approach to Fatigue Analysis ofPlate Structures, Proc. of The IIW Fatigue Seminar,
IIW-Commission XIII, 73-90.

REFERENCES
C. Morgenstern et. al., 2004, Fatigue design of

C. Miki, K. Tateishi, Y. Yamamoto and M. Miyauchi,
1992, A Study on the Local Stress Approach to theFatigue Assessment, Journal of StructuralEngineering, JSCE (Japanese Society of Civil
Engineering), Vol. 38A: 989-997 (in Japanese).

aluminum welded joints by the local stress concept with
thefictitious

notchradiusof

rf=1mm,Doc.

XIII-2009-04, International Institute of Welding.
J. Yagi et. al, 1991, Definition of Hot Spot Stress inWelded Plate Type Structure for Fatigue Assessment,

D. Radaj and C. M. Sonsino, 1998, Fatigue
Assessment of Welded Joints by Local Approaches,
Abington Publishing.

IIW-XIII-1414-91
F. Huther, 1990, Recommendation for Hot Spot Stress
Definition in Welded Joints, IIW WG XIII/XV

S. Kainuma, et al., 2000, Influence of Welding Position