International Journal of Fatigue 33 (2011) 1118–1126

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International Journal of Fatigue

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Crane runways – Fatigue evaluation of crane rail welds using local concepts

M. Euler, U. Kuhlmann ⇑University Stuttgart, Institute of Structural Design, Pfaffenwaldring 7, 70569 Stuttgart, Germany

a r t i c l e i n f o

Article history:Received 27 October 2010Received in revised form 16 February 2011Accepted 20 February 2011Available online 23 February 2011

Keywords:Crane runwayCrane railsMultiaxial fatigueWheel loadsLocal concept

0142-1123/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijfatigue.2011.02.010

⇑ Corresponding author. Tel.: +49 711 685 66246.E-mail address: u.kuhlmann@ke.uni-stuttgart.de (

a b s t r a c t

The introduction of the wheel loads into a crane runway with a hot rolled I-section and a block rail fas-tened by longitudinal fillet welds forms a multiaxial fatigue problem. At the point of wheel load applica-tion the top region of the runway girder is subjected to a stress field comprising local stress componentsinduced by the concentrated load, i.e. local transverse pressure and local shear stress in addition to thedirect and shear stress components due to global bending. The superposition of all aforementioned stresscomponents (and stress ranges, resp.) during each single crane pass results in a so-called non-propor-tional cyclic stressing of the rail welds with alternating principal stress direction. Due to the variationof the principal stress direction the conventional fatigue evaluation procedures appear not to be reliable.To approach the complex issue two crane runway girders were tested under proportional multiaxial load-ing, i.e. under flexural bending and stationary wheel load, both simultaneously pulsating. The paper pre-sents the fatigue evaluation of these tests using different local concepts.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The vast majority of crane runways for top running overheadtravelling cranes are made of steel, Fig. 1a. Approximately 70% ofall crane runways are designed for light and moderate crane ser-vice and usually consist of a hot-rolled section (mild steel, steelgrade S 235, S 355) with a crane rail fastened to the top flangeby automatic fillet welds, Fig. 1b. Continuous static systems arequite common, Fig. 2.

At the point of wheel load application the top region of the run-way girder (Fig. 1b) is generally subjected to a stress field compris-ing local stress components induced by the concentrated load, i. e.local transverse pressure rz,local and local shear stress sxz,local, inaddition to the global stress components rx and sxz due to globalbending. For example the top region at location x of the continuouscrane runway shown in Fig. 2 is subjected to tensile bending stresssuperposed by the local stresses due to wheel load application.

1.1. Proportional and non-proportional loading

A stress history of two stress components rA and rB is referredto as proportional if it holds rA/rB = constant. That results in a con-stant direction of the principal stresses in time. In contrast, a stresshistory is called non-proportional if the direction of the principalstresses changes throughout the stress history. Fig. 3 illustrates

ll rights reserved.

U. Kuhlmann).

the stress history at particular locations of a two-span andsingle-span crane runway girder caused by a travelling craneassuming constant travelling velocity. Since the crane possessestwo crane wheels each passage of the crane causes two wheel pas-sages. Fig. 3a indicates that all stress components do not reachtheir amplitudes simultaneously for the two-span girder. In caseof the single-span girder (Fig. 3b) the amplitudes of rx and rz,local

appear at the same time despite that the frequency of rz,local istwice as large as for rx. The fact that the stresses rz,local and sxz,local

have to be inherently out-of phase is illustrated in Fig. 3c. Insummary, the stressing of both considered crane runway systemsindicates a permanent shift of the principal stress directions. Fromthat it can be concluded that crane runways are usually stressednon-proportionally.

1.2. Stress-rising effects of crane runways

Basically, the nominal stresses of a crane runway differ from thereal stressing for three reasons:

1. The welding of the crane rail leads to material homogeneities,and residual stresses are induced by the welding procedure.

2. The shape of the weld toes and roots forms geometric notchesamplifying the nominal stresses.

3. The concentrated load causes local stress peaks as describedabove.

Altogether, the crane runway undergoes a complex multiaxialstate of stress with several stress risers of different nature.

Nomenclature

Stressesrx, ry, rz normal stress componentssxz, syz shear stress componentsDr, Ds stress rangesDrc, Dsc fatigue strengths

Indices of stressesa amplitudeeq equivalent value due to DEHlocal due to wheel loadmean mean valueeff effective valuemod modifiednom nominalnotch related to effective notch stress concept

Other symbolsas notch stress concentration factor

d phase angleDMA multiaxial damage sumfs size factorF, G terms related to EESHF0, F1 single loadsk coefficientNf number of cycles to failurex angular velocityp normal stressPs probability of survivalqref fictitious notch radiusR stress ratios distanceh plane anglet time or notch deepth

z,local

xz,local

(a)

x

crane runway

crane wheels

crane

crane wheel

crane rail

continuous fillet weld

crane runway girder

x

(b)

y

zz

x

crane runway

xz xz

Fig. 1. Overhead travelling crane on crane runways (a) and typical cross section of acrane runway for light and moderate crane service (b).

x

Fig. 2. Multiple-span crane runway with two crane wheel loads.

xz,local

(a) x

wheel B passing

A B

2,00 m

wheel A passing

s

z,local

x

2,00 m

B A

wheel B passing

wheel A passing z,local

x

xz,local

s, t

s, t

s, t

s, t

s = travelled distancet = elapsed time

(b)

x

(c)

Fig. 3. Stress history caused by one crane passage at location x = 4.00 m in case of atwo-span runway (2 � 4.00 m) (a), at midspan location x = 2.00 m in case of asingle-span runway (b) and three states of stress for particular wheel locations (c).Remark: global shear stress sxz is not considered for the sake of simplicity.

M. Euler, U. Kuhlmann / International Journal of Fatigue 33 (2011) 1118–1126 1119

1.3. Current global approaches and conventional theories of failure

The nominal stress concept also known as classification methodis the most commonly used global approach to assess fatigue prob-lems. This method is called global since it refers to the nominal

stresses of the member rather than on the complex local stressesat the crack-causing notch. Its simplicity makes it favourable forthe practitioners while its limitation on only known and well-stud-ied constructional details (detail categories) forms its greatestdisadvantage.

To apply the nominal stress concept to a multiaxial stress prob-lem requires a failure hypothesis translating the multiaxial state ofstress into an equivalent uniaxial one. This is necessary since all

1120 M. Euler, U. Kuhlmann / International Journal of Fatigue 33 (2011) 1118–1126

strength parameters of the detail categories are obtained from uni-axial tests.

Principally, the choice of an appropriate failure hypothesis hasto account for the failure mechanism. From static tests on ductilematerials such as mild steel it is known that the damage is primar-ily initiated by shear stress. That is why the distortion energyhypothesis (DEH) of von Mises is commonly employed. It is alsoproven that this hypothesis holds for ductile materials under cyclicloading [11]. Moreover, Gough and Pollard recognized that the re-sults of combined stress fatigue tests of unwelded small-scalespecimens (normal stress due to bending, shear stress due to tor-sion) are in close agreement with the von Mises hypothesis thathas the form of an ellipse,

DrDrc

� �2

þ DsDsc

� �2

6 1 ð1Þ

The application of DEH for cyclic loaded structures with weldedjoints needs some adjustment to account for the material inhomo-geneity in the vicinity of welds. In detail, the assessment is sup-posed to differentiate in terms of the fatigue strengthsperpendicular to and parallel of the weld in form of Eq. (2) whereDrjj, Dr\ are the nominal stress ranges jj weld and ? weld, Ds isthe nominal shear stress range, and Drcjj, Drc\, Dsc are the corre-sponding fatigue strengths.

DrjjDrcjj

� �2

þ Dr?Drc?

� �2

� Drjj � Dr?Drcjj � Drc?

þ DsDsc

� �2

6 1 ð2Þ

It appears for several combined loadings (bending/axial loadingplus torsion) that the nominal stress concept in combination withDEH gives only reliable results for in-phase stressing, i.e. in caseof simultaneously occurring amplitudes of the stress componentsand therefore fixed principal stress directions. For out-of-phaseloading (i.e. shifting principal stress directions) this approach mightseverely overestimate the actual fatigue resistance since the equiv-alent stress becomes lower expecting a smaller fatigue damage.That is opposed to the experience that non-proportional loadinghas been identified to be more damaging than proportional loadingunder comparable conditions.

If the single stress components occur after each other in thecourse of time, the different stress components do not interactand therefore the damages done by the single stress componentscan be summed up provided all stress components contribute to

Fig. 4. Weld modelling for test girder No. 2: microsection of weld ‘A’ (a and b), correspmodelling (f).

the same fatigue failure. As a rule the summation of the individualdamages follows [3] according to Eq. (3) with Dr\ as nominalstress range perpendicular to the fatigue crack, Ds as nominalshear stress range and Drc\, Dsc as the corresponding fatiguestrengths [3].

DMA ¼Dr?Drc?

� �3

þ DsDsc

� �5

6 1 ð3Þ

Because of the required exclusion of simultaneously occurringamplitudes Eq. (3) is not able to evaluate multiaxial loadings safelywhere the single stress components interact [2].

In summary, the conventional global approaches seem to be notpromising to evaluate non-proportional loadings with out-of phaseacting stress components such as shown in Fig. 3.

1.4. Local approaches and modern theories of failure

The crack initiation is a local problem and requires local con-cepts. Local concepts can be based on structural stresses, notchstresses, notch strains as well as the crack propagation or stressintensity [10]. This paper focuses on the so-called effective notchstress approach.

In contrast to the global methods that refer to the member’snominal stress the notch stress method uses elastic stresses atweld notches, e. g. the weld toe. Since notch stresses are hardlymeasurable they are determined numerically for instance by a Fi-nite Element Analysis (FEA).

The appropriate modelling of the weld notches is the crucialpoint. The exact weld geometry can be obtained from measure-ments on microsections, Fig. 4. Alternatively, a concept of referenceradii can be applied, e.g. qref = 1 mm according to Radaj and Neuber.Through the FEA the local stresses can be computed and finallytransformed into an equivalent stress in terms of an appropriatefailure hypothesis.

In contrary of the notch strain approaches that account for elas-tic-plastic material behaviour in the vicinity of the notch (e.g. Neu-ber rule) the effective notch stress approach assumes fully elasticbehaviour resulting in an apparent conflict that the calculatedstresses at the notches partially exceed the yield stress. But thesecalculated stresses do not become completely effective since theless stressed material surrounding the maximum stressed notchregion induces a constraint leading to a multiaxial state of stress

onding modelling in FEA (c), microsection of weld ‘B’ (d and e) and corresponding

(a)

(b) (c)Fig. 5. Test set-up (a), cross section (b) and interface between crane rail and upperflange (c).

z = 178 N/mm²

x = 144 N/mm²

Fig. 6. State of stress in terms of nominal stresses.

(b)(a)

PC SC

M. Euler, U. Kuhlmann / International Journal of Fatigue 33 (2011) 1118–1126 1121

with a higher resistance compared with that of the unrestraineduniaxial one (micro-support effect) [13].

As pointed out before the conventional failure hypotheses can-not assess the damage due to out-of-phase loading causing chang-ing principal stress directions. A couple of new failure hypothesestries to overcome this shortcoming. Basically, the existing ap-proaches fall into two groups. While the first group, the so-calledintegral approaches, presumes that the overall damage is the inte-gration of the damages on different planes at a location, the criticalplane approaches forming the second group expect that the planewith the largest alternating shear stress (i.e. critical plane) controlsthe fatigue failure and coincides with the preferential orientationof the early crack growth [1].

The hypothesis of Findley [4] belongs to the oldest critical planeapproaches. It was originally derived for combined normal stressdue to bending/axial loading and shear stress due to torsion andassumes that the fatigue failure is initiated in the plane with themaximum alternating shear stress sa. Additionally, it accounts forthe influence of the normal stress rmax on this plane by calculatingan effective alternating shear stress seff,a, Eq. (4)

Dseff

2¼ seff ;a ¼ sa þ k � rmax ð4Þ

Note that sa is the shear stress amplitude (i.e. half the stress range)in contrary to rmax that is the sum of alternating and mean stress.For steel it holds k = 0.3 [4]. The effective alternating shear stressis increased by tensile (positive) normal stress and decreased bycompressive (negative) normal stress. Moreover, Findley’s hypothe-sis delivers reliable results under proportional but fails under non-proportional (out-of-phase) loading.

The hypothesis of the effective equivalent stress of Sonsino is afurther modern theory of failure [17]. It also expects that the fati-gue failure is initiated by shear stress. In contrast to Findley it ac-counts additionally for the interaction of the shear stress indifferent planes initiating corresponding dislocations [16]. That iswhy this hypothesis is an integral plane oriented approach [15].Its major scope is to evaluate out-of-phase loading, and its alge-braic algorithm is described in [17] for example.

Both hypotheses mentioned above will be applied for the par-ticular situation of crane runways in the following.

(c)

PC primary crack SC secondary crack

SC

Fig. 7. General failure mode: phase 1 (a), phase 2 (b) and phase 3 (c).

2. Experimental investigation

2.1. Test set-up

In a research project of the Deutsche Ausschuss für Stahlbau(DASt) under funding of AiF as part of the IGF-program of the Ger-man Federal Ministry of Economics and Technology (BMWi) the fa-tigue strengths of crane runway girders with particular focus onthe load application were determined [6]. Only the two test girdersNos. 2 and 3 with continuous rail welds are going to be consideredhere. The girders were tested in a servo-hydraulic test rig with twoaxial actuators under load control. The testing frequency amountedto about 1–2.5 Hz. The load ratio was R � 0.1. The applied loadranges measured DF0 = 460 kN and DF1 = 160 kN, Fig. 5a and b.All loads acted in phase with constant amplitudes.

The bottom rail surface (Fig. 5c) was recessed to avoid any con-tact between the rail and the girder and to ensure that the loadtransfer from the rail to the top flange was exclusively realizedby the rail welds. Hence, all loads acting on the top surface of therail were transmitted into the top flange by the rail welds. The trea-ted bottom rail surface was kept rough in order to simulate the de-fects of the mill scale. A more detailed description can be found in[6,7].

With the test set-up only an interaction of longitudinal normalstress rx and transverse pressure rz could be achieved at the pointof wheel load application, Fig. 6. It did not allow the superpositionof these stress components together with the local shear stresssxz,local, Fig. 3c.

2.2. Failure modes

The observed failure mode comprised three phases, Fig. 7; seealso Fig. 8. The so-called primary crack was initiated at the bottom

view

rail

flange

wheel

flange

rail

wheel

view

(b)(a)

Fig. 8. Failure of test girder No. 2 (a) and No. 3 (b).

1122 M. Euler, U. Kuhlmann / International Journal of Fatigue 33 (2011) 1118–1126

surface of the rail right below the wheel load (phase 1). After therail through-crack the rail welds failed in a ductile manner (phase2). Subsequently, the crack propagated into the top flange leadingto two crack growth centres (phase 3). Presumably, during phase 2,secondary cracks to each side of the rail developed right beneaththe wheel load along the weld toes, see Fig. 7b. These cracks werehardly detectable. Their fracture plane was oriented normal to thatof the primary crack. The number of load cycles at crack initiationin the rail was about 700,000 for test girder No. 2 and about640,000 for test girder No. 3. Note that in [6] and [7] the load cyclesto failure are 762,000 and 700,000 since the failure criterion wasrail through-cracking instead of crack initiation there.

3. Numerical investigation

3.1. Finite element analysis

The fully elastic notch stresses were computed by a FEA usingthe software package ANSYS Version 11. Basically, the stress

(a) (b)

(d) (c)

Fig. 9. Contours of global model (a) and of submodel (b), meshed weld of submod

determination was subdivided into two steps. Firstly, a globalmodel composed by solid elements (solid45) with a coarse meshwas set up comprising the tested crane runway girder betweenthe supports together with the crane wheel taking advantage ofthe symmetry, Fig. 9a. The external bending moments were simu-lated by pairs of equivalent forces. The wheel load at midspan wasintroduced through the crane wheel. The interface between cranewheel and crane rail were modelled by contact elements (con-tac174, target170).

Secondly, a 3-D submodel was created in order to refine the re-sults of the global model, Fig. 9b. The exact geometry of the weldswas obtained by an optical measurement, see Fig. 4. Moreover, theweld toes and the weld root were rounded off with a fictitious ra-dius qref = 1 mm according to Radaj and Neuber, Fig. 9c. Due to theirregular shape of the submodel tetrahedral solid elements (so-lid92) were used. The thickness of the submodel amounted to 6mm. The outer surfaces of the submodel were subjected to theboundary conditions caused by the global model. Consequently,unavoidable disturbances occurred there due to the interpolationbetween both models. Therefore, only the stresses at the centre

upper weld toe

lower weld toe

weld root

III

VIVII

Node y z yz ... ... II -41 -712 155 ... … ... ... ... ... VI -215 -446 305 ... VII -226 -343 273 ...

FE stresses

el (c) and paths of stress determination at the centre section of submodel (d).

Table 1Calculated notch stresses at the welds ‘A’ and ‘B’ [N/mm2]. Remark: the values of weld‘B’ in parentheses.

Weld root Weld toe low Weld toe up

rx 239 (235) 138 (136) �27 (32)ry �291 (�249) �82 (�96) �226 (�160)rz �827 (�748) �15 (�14) �712 (�609)sxy 0 (0) 0 (0) 0 (0)syz 312 (277) 29 (33) 305 (252)sxz 0 (0) 0 (0) 0 (0)

M. Euler, U. Kuhlmann / International Journal of Fatigue 33 (2011) 1118–1126 1123

section of the submodel were taken for the evaluation, Fig. 9d. TheYoung’s modulus of the girder and the wheel was 2 � 105 N/mm2.

The girder’s strains were recorded during the cyclic testing atparticular locations, e.g. at the flange to web junction at the loadingsection etc. These measurements served for the validation of thegenerated model. The FE strains of the global model and the mea-sured strains show a very good fit. See for more details in [6]. Theassessment of the local stresses was primarily carried out alongpaths at the weld notches. The FE stresses at 7 nodes along thepaths within the weld toes and at 43 nodes within the weld rootwere recorded, Fig. 9d. The maximum stress components per pathwere determined and combined for the assessment regardless ifthey occur on the same node along the path or not, compareFig. 9d.

The computed FE stresses are printed in Table 1. Because of thesmaller weld toe angle (Fig. 4) weld ‘A’ exhibits higher stresses. Aselection of the most important stress histories of the upper weldtoe of weld ‘A’ is given by Eq. (5). It can be seen that the stress ratioequals R = 0.

ryðtÞ ¼ ry;mean þ ry;a � sin x � t ¼ �113� 113 � sin x � trzðtÞ ¼ rz;mean þ rz;a � sin x � t ¼ �356� 356 � sin x � tsyzðtÞ ¼ syz;mean þ syz;a � sinx � t ¼ 152þ 152 � sin x � t

ð5Þ

Interestingly, the component rx of the lower weld toe is in goodcorrespondence with the nominal stress, Fig. 6. At the upper weldtoe and the weld root being closer to the point of loading the com-ponent rx differs from the nominal value. This is a strong onset for amultiaxial state of stress.

(d)

(f)

(a)18°

(b)

24°

(c)

w

5 mm

Fig. 10. Crack surfaces together with the early secondary crack growth

4. Fatigue evaluation of the girder tests

4.1. Objective

As mentioned before the primary crack was obviously initiatedat the rough bottom rail surface simulating the mill scale with itsdefects. In practice the greatest defect at the tensile stressed bot-tom rail surface will cause the primary crack.

The question arises whether the secondary crack is a conse-quence of the growing primary crack or whether the initiation ofthe secondary crack is independent of the primary one. So is it pos-sible that a rail with flawless surface fails through the secondarycrack, especially, in case of moving wheel loads, when the second-ary crack can grow in x-direction?

Of course the growth of both cracks will interact after exceedinga certain crack size. Concerning the crack initiation and early crackgrowth, however, both cracks might be independent of each other.In detail, the evaluation is supposed to answer two questions:

1. Are the notch stresses at the location of the secondary crack inthe uncracked rail sufficiently high to be the sole reason for thesecondary crack?

2. Is it possible to reveal any influence of the longitudinal stressesrx on the secondary crack? If so, there might be an interactionbetween the crack initiation of the primary crack mainly drivenby longitudinal stresses and that of the secondary crack.

4.2. Hypothesis of findley

Due to the outcome of the tests only planes at the upper weldtoe have to be considered making an angle with the y-axis, com-pare Fig. 11a and b. Eqs. (6) and (7) hold for the stresses at suchplanes.

rn ¼ ry � sin2 hþ rz � cos2 hþ 2 � syz � sin h � cos h ð6Þsn ¼ ðry � rzÞ � sin hþ 2 � syz � ðcos2 h� sin2 hÞ ð7Þ

The effective shear stress range Dseff,a can be computed based onEq. (4). According to Findley [4] rmax is referred to as the maximum(positive) normal stress at the considered plane. From the stresshistory in Fig. 11c it can be seen that the greatest positive normalstress becomes rn,max = 0 in all planes. Subsequently, the normalstress has no influence on the effective shear stress seff, Table 2. In

(e)

(g) 24°

24° 26°

20°

weld ’A’ weld ’A’

’B’dlew’B’dle

orientation of test girder No. 2 (a–c) and of test girder No. 3 (d–g).

t

-459

390

n,a

n,a

n

n

yz

z

y

zy

(c)

(b)(a)

+

y

z

-

+stre

ss-s

tress

n

n

n,max = 0 n,mean = -229,5

Fig. 11. Orientation of critical planes (a), stresses at any plane with angle h (b) and stress history of the components rn and sn of the plane with h = 20� (c).

1124 M. Euler, U. Kuhlmann / International Journal of Fatigue 33 (2011) 1118–1126

addition, a modified Dseff,mod is determined that is received if usingthe mean stress rn,mean instead of the maximum positive normalstress rn,max. The orientation of the critical plane in the first caseamounts to 20� and in the second case to 30�. That is in good agree-ment with the measurements, compare Fig. 10.

The effective shear stress ranges can be transformed in equiva-lent normal stress ranges according to DEH by applying Eq. (8).

Dreq ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 � Ds2

eff

q¼

ffiffiffi3p� Dseff ð8Þ

Table 3Fatigue strength [N/mm2] at Nf = 2 � 106 under shear loading, fillet welds, automaticwelding, R = �1, for different probability of survival Ps [12].

Ps (%) Dsnom acc. to [12] Calculated Dsnotch Calculated Dreq,DEH

50 140 280 48497.7 118 236 409

4.3. Effective equivalent stress hypothesis (EESH)

The loading of the test girders did not exhibit any phase shift(d = 0�), consequently, the computation of the effective equivalentstress according to EESH simplifies solely to (10) since the secondand third term of (9) become unity.

DreqðdÞ ¼ Dreqðd ¼ 0Þ � FðdÞFðd ¼ 0Þ �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiG1� d�90�

90�ð Þ2q

ð9Þ

Dreqðd ¼ 0Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2

x þ r2y � rx � ry þ fs � 3 � Ds2

xy

qð10Þ

fs ¼Dreq;axial

Dreq;shearð11Þ

Therefore, the effective equivalent stress depends only on the stressranges and the factor fs. This factor captures the so-called micro-support size effect. The size of the maximum stressed material vol-ume has a significant influence on the fatigue life. If only a smallvolume is subjected the maximum stress due to a steep stress gra-dient, the fatigue life will be longer due to the support effect of the

Table 2Notch stresses at the upper weld toe of weld ‘A’ at planes of different angle h [N/mm2]. R

h (�) �90 0 15 20

rn,min �226 �712 �527 �459rn,max 0 0 0 0Dsn 305 305 386 390Dseff 305 305 386 390 (337req – – – 675 (583Dseff,mod 237 91 228 252req,mod – – – –

less stressed surrounding material [14]. That explains why a mem-ber under uniform normal stress has a shorter fatigue life than thesame member under bending stress of the same magnitude.

The size effect is expressed by Eq. (11) with req,axial and req,shear

as the supportable effective equivalent stress with a survival prob-ability, Ps, of 50% under pure bending/axial loading and pure shearaccording to DEH. The exact computation of the size effect factor fs

requires statistically proven S�N curves for the considered con-structional detail under pure bending/axial loading and pure shear.Since such specific information is not available for the weldedcrane rail this factor has to be estimated.

In [12] fillet welds under pure shear stress Dsnom due to torsionwere tested, Table 3. The determined supportable shear stressranges indicate primarily weld root failure. Thus, these values areconservative concerning the fatigue strength of the weld toe. Thesupportable notch stress ranges Dsnotch and the correspondingequivalent stress ranges Dreq according to DEH can be computedas given by Eqs. (12) and (13). The stress concentration is esti-mated based on the notch stress concentration factor as of Neuber[9] for a shallow notch, Fig. 12b.

emark: the values of weld ‘B’ in parentheses.

25 30 35 90

�392 �326 �266 �2260 0 0 0382 363 333 305

) 382 363 333 305) – – – –

264 265 (237) 253 237– 459 (410) – –

(c) t/ = 2

t

max = 3.33 p

p

(b) t/ = 2

t

max = 2.0

(a)

Fig. 12. Stress concentration of moderately curved notches (a), under pure shear [9,p. 32] (b) and under pure tension [9, p. 141] (c).

Fig. 13. Haigh diagram with mean stress influence in fatigue tests under pure axialload or bending [13].

from torsion

from bending (a)

(b) (c)

Fig. 14. Typical test set-up with combined direct stress due to bending and shearstress due to torsion (a), crack opening modus III (b) and modus I (c).

M. Euler, U. Kuhlmann / International Journal of Fatigue 33 (2011) 1118–1126 1125

Dsnotch ¼ as � Dsnom ð12ÞDreq;shear ¼

ffiffiffi3p� Dsnotch ð13Þ

Fig. 13 summarizes the outcome of an extensive experimental anal-ysis of different chord-web junctions under pure bending or axialloading accounting for the mean stress influence [13]. The test re-sults for weld toe failure and weld root failure fall into the samescatter band of this analysis. Unfortunately, it is unclear what fail-ure hypothesis is used in [13] whether maximum principal stressor equivalent stress of DEH. Nevertheless, it can be stated thatFig. 13 is in close correspondence to the allowable notch stressranges for R = 0.5 proposed in [18] that amount to Drc = 225 N/mm2 in terms of DEH and Drc = 200 N/mm2 in terms of prinicipalstresses.

Since the mean stress influence in Fig. 13 is quite pronouncedand Table 3 only holds for R = �1, the estimated size effect factorfs is computed for R = �1 expecting no significant R-sensitivity of fs:

fs ¼494484

� 1:00

For comparison the tube-to-plate junctions in [17] have a compara-ble loading and a size factor fs = 1.39. Finally, the effective equiva-lent stress range at the upper weld toe (weld ‘A’) can becomputed using Eq. (10):

Dreqðd ¼ 0�Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2262 þ 7122 � ð�226Þ � ð�712Þ þ 1:00 � 3 � 3052

q

¼ 823 N=mm2 ð700 N=mm2at weld ‘B’Þ

4.4. Comparison

The comparison of all determined equivalent stress ranges Dreq

is illustrated in Fig. 15 together with a part of the scatter band forR = 0 according to [13] (compare Fig. 13) assuming an averagednumber of load cycles of the girder tests before failure,Nf = 670,000.

The EESH and the original formulation of Findley’s hypothesisestimate a shorter fatigue life (50% propability) than it was re-corded in the tests and give conservative results, consequently.The EESH results suggest that the crack initiation occurred slightlyearlier. Because the secondary cracks grew under compression(crack closing) they were very hard to detect. That is why an earliercrack initiation as recorded might be possible. Also the factor fs

being an important input parameter has to be estimated for theconsidered detail. For that reason the information for an assess-ment based on EESH might not be sufficient.

5. Conclusions

Crane runways are subjected to a complex multiaxial state ofstress due to geometric and metallurgic notch effects and the intro-duction of concentrated loads. The amplitudes of the stress compo-nents do not occur simultaneously resulting in an alternatingdirection of the shear stress that has been recognised to controlthe crack initiation.

To investigate this complex issue two girders with in-phaseinteraction of the global bending rx and the local wheel pressurerz,local were tested. The goal of this paper is to compute the corre-sponding equivalent notch stress ranges according to DEH applyingtwo different local approaches. On this basis the questions of Sec-tion 4.1 can be answered:

1. The notch stresses at secondary crack’s location can be consid-ered as sufficient to be its sole reason.

2. The calculated longitudinal stress rx that induces the primarycrack is quite low at the location where the secondary crack isinitiated (upper weld toe).

Altogether, the conclusion can be supported that the initiationof the secondary crack is independent of that of the primary crack.

Fig. 15. Scatter band of test results [13] for stress ratio R = 0, compare also Fig. 13.

1126 M. Euler, U. Kuhlmann / International Journal of Fatigue 33 (2011) 1118–1126

Findley’s hypothesis estimates obviously the fatigue life best.The computed orientation of the critical plane corresponds verywell with the measured early crack growth direction. Nevertheless,the results of the presented modified formulation of Findley’shypothesis suggest that the complete neglect of the compressivemean stress might be not reasonable.

The EESH results estimate that the crack initiation occurred ear-lier. As the secondary cracks grew under compression (crack clos-ing) they were very hard to detect. That is why an earlier crackinitiation as recorded might be possible. On the other hand the lackof fatigue strength values under pure axial loading and pure shearfor the considered constructional detail has not allowed a reliableapplication of the EESH, yet. Since the existing fatigue strengths forshear loading [12] were primarily determined under torsion lead-ing to crack opening modus III (Fig. 14a,b) their usage for shearloadings that do not arise from torsion might be questionable [8].It is known that combined stresses solely induced by bending leadto crack opening modus I, Fig. 14c.

Further testing especially for out-of-phase loading is necessary.In this case the secondary crack growth might be accelerated dueto an interaction with the local shear stress sxz,local caused by theload application [5]. In order to deepen the understanding of thewheel load introduction the authors plan tests on crane runwaygirders under moving (reciprocating) single loads for the nearfuture.

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