International Journal of Fatigue -...

International Journal of Fatigue 64 (2014) 97–113

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International Journal of Fatigue

journal homepage: www.elsevier .com/locate / i j fa t igue

Seismic low-cycle fatigue evaluation of welded beam-to-columnconnections in steel moment frames through global–local analysis

http://dx.doi.org/10.1016/j.ijfatigue.2014.03.0020142-1123/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel./fax: +86 10 6278 8623.E-mail addresses: [email protected] (H. Zhou), [email protected]

(Y. Wang), [email protected] (L. Yang), [email protected] (Y. Shi).

Hui Zhou a,c, Yuanqing Wang b,⇑, Lu Yang a, Yongjiu Shi b

a Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, Chinab Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Department of Civil Engineering, Tsinghua University, Beijing 100084, Chinac Beijing Collaborative Innovation Center for Metropolitan Transportation, Beijing 100124, China

a r t i c l e i n f o

Article history:Received 17 September 2013Received in revised form 27 February 2014Accepted 3 March 2014Available online 12 March 2014

Keywords:Seismic low-cycle fatigueSteel moment resisting frame (SMRF)Beam-to-column connectionGlobal–local modelCyclic void growth model (CVGM)

a b s t r a c t

A general methodology for seismic low-cycle fatigue assessment of welded beam-to-column connectionin steel moment resisting frames (SMRFs) is presented. Fatigue deformability curves of seven connectioncategories are elaborated using the available cyclic tests. Inter-storey drift history imposed on each con-nection of SMRF is generated by seismic dynamic analysis and adopted in fatigue damage calculationbased on Palmgren–Miner’s rule and the experimentally determined fatigue curve. The most critical con-nection identified by preliminary fatigue evaluation is refined with solid finite elements in global–localmodel where the cyclic void growth model is integrated to give a more accurate fatigue prediction includ-ing load sequence effects. The proposed approach is applicable to fatigue evaluation of welded connec-tions in SMRFs under earthquakes.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Following the 1994 Northridge earthquake in USA [1] and the1995 Kobe earthquake in Japan [2], brittle fractures were observedin a large number of beam-to-column connections in steel momentresisting frames (SMRFs). Extensive analytical and experimentalinvestigations [3] were carried out to explain the causes of frac-tures inspected in the connections. The poor fracture resistanceof the connection was mainly due to low material toughness, poorfield welding, severe geometric discontinuities and high strainrates, etc. Earthquake induced fracture could be categorized intolow-cycle fatigue (LCF) [4–9] or extremely low-cycle fatigue (ELCF)[10–14], which is characterized by large inelastic strain amplitudes(several times of the yield strain) and rather small number ofcycles to failure (usually less than 102 cycles).

In the current seismic design codes for steel structures, such asANSI/AISC 341 [15] and Eurocode 8 [16], provisions are mainlyreferred to stiffness, strength and ductility; while fatigue designis not required for steel structures subjected to seismic loadings,although welded connections are susceptible to LCF damage. Dur-ing numerous experimental tests performed on beam-to-columnconnections [17,18], results indicated that cracks typically

occurred at the beam flange welds, the heat affected zones andthe toe of weld access holes in the beam flanges. In some cases[17], crack growth led to a LCF failure of the connection at lowhinge rotation, while seismic energy dissipation depends on largeinelastic cyclic hinge rotations. Therefore, a practical approach isrequired to estimate LCF damage of connections in SMRFs sub-jected to the past earthquakes and to predict the remaining fatigueendurance that can be expended in the future seismic events.

Considerable researches [19–27] were concentrated on fractureand fatigue predictions of local details in individual beam-to-col-umn connection by using fracture mechanics or micro-mechanicsbased models. Fracture mechanics parameters, such as stressintensity factor, J-integral and crack tip opening displacementCTOD, provided effective approaches to predict fracture of thepre-Northridge connections with initial cracks at the weld roots[19–24]. As for improved connections (after Northridge and Kobeearthquakes) where initial flaws were absent, more generalizedmicro-mechanics based models were developed to predict ductilefracture initiation due to monotonic or cyclic loadings with largeplastic deformations [25–27]. These models were known as thevoid growth model (VGM) [25], the cyclic void growth model(CVGM) [26] and so on.

Low-cycle fatigue due to cyclic high stress is usually character-ized by Manson–Coffin [28,29] relationship which relates fatiguelife (number of cycles to failure) with plastic strain range. This rela-tionship was established for constant amplitude cyclic loading and

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could be extended to variable amplitude cyclic loading by usingPalmgren–Miner [30,31] cumulative damage rule. On the basis ofParis law [32] for high-cycle fatigue, J-integral range DJ wasapplied as an elastic–plastic criterion for low-cycle fatigue crackgrowth [33]. Based on Manson–Coffin strain-life concept, anempirical relationship between fatigue crack growth rate and plas-tic strain range was proposed by Krawinkler and Zohrei [34]. Acombined methodology of low-cycle fatigue concept and micro-mechanics based fracture model was developed by Iyama andRicles [35] to estimate the fatigue life of welded beam-to-columnconnections under inelastic loadings. Extremely low-cycle fatiguetests on thick-walled steel bridge piers were performed by Geet al. [13,14] and a damage index based on Manson–Coffin rela-tionship was adopted to predict ductile crack initiation. Alterna-tively, continuum damage mechanics based models [36,37] werealso efficient in predicting seismic damage at vulnerable locationsof welded connections in steel structures. Damage indices at threelevels, i.e. structure, section and material, can be defined as func-tions of deformation, energy dissipation or the combination ofboth. In order to consider the stiffness and strength degradationeffects caused by cyclic loading, a damage model for plane steelmembers based on plastic strains of the material was proposedby Shen et al. [38]. A numerical model that could simulate compo-nent deterioration and fracture of steel beam-to-column connec-tions due to LCF was developed by Lignos et al. [39] and theeffectiveness in quantification of seismic capacity of beam-to-col-umn connections was demonstrated through a full-scale shakingtable test of a high-rise steel building [40]. For plane SMRFs underseismic loading, a new damage index, which is defined at a sectionof steel member and takes into account the interaction betweenaxial force and bending moment, was proposed by Kamaris et al.[41] and its validity was verified by other well known damageindices.

Fatigue damage evaluations of beam-to-column connectionsfrom the perspective of global structural responses were proposedby several investigations [6,7,42–44]. In these studies, a similarapproach for the traditional high-cycle fatigue design of steelstructures was applied in the seismic low-cycle fatigue analysiswhere a generalized deformation range (such as strain or rotationrange) substitutes the stress range that is used in the stress-life S–N curve. In preliminary fatigue analysis, the aforementionedapproaches based on the structural deformation responses andthe fatigue curves of the connections are practical and efficient toevaluate general fatigue damage of connections in SMRFs underearthquakes. Several other methods, such as Manson–Coffinstrain-life approach [13], micro-mechanics based fracture model[26] and continuum damage mechanics [37], are also available topredict damage of materials and details in connections due toinelastic loadings. However, few works has been done to bridgethe gap between global fatigue analysis and local fracture predic-tion of the connection. Therefore, an attempt is made by the pres-ent study to propose a combined seismic LCF evaluation procedurein which fatigue critical connections are identified through globalanalysis and fatigue fracture prediction of the most critical connec-tion is performed by the refined global–local model.

In this study, LCF damage evaluations of welded beam-to-col-umn connections in SMRFs due to seismic loadings are carriedout through global and global–local analyses. In global fatigueanalysis, fatigue damage of the connection is calculated by usingPalmgren–Miner [30,31] cumulative damage rule based on thestructural deformation response and the fatigue curve specifiedby the connection category. The fatigue curves are elaborated bydata regressions of the available connection tests at constantamplitude cyclic loadings. The total rotation range Du (inter-sto-rey drift angle range) is selected as a generalized deformationparameter instead of stress range in S–N curve, so as to establish

the fatigue deformability curve (Du–Nf curve) of the connection.The cumulative fatigue damage of each connection is calculatedbased on the fatigue deformability curve and the inter-storey driftangle range spectrum (rotation range Dui versus the correspond-ing number of cycles ni) which is obtained through Rainflow cyclecounting [45] of the inter-storey drift angle history generated byseismic dynamic analysis of the global SMRF structure. Subse-quently, the most fatigue critical connection identified throughglobal analysis is substituted by solid elements in global–localfinite element model (FEM) of SMRF. A micro-mechanics basedfracture model termed as the cyclic void growth model (CVGM)is integrated into the refined local FEM to predict the most fatiguevulnerable location and the damage evolution under seismic load-ing. The presented procedure is practical and efficient to evaluatethe fatigue damage of the welded beam-to-column connectionsin the existing SMRFs experienced in the past earthquakes, andalso can be served as a basis for fatigue resistant design of weldedconnections in steel structures subjected to the future seismicevents.

2. Seismic fatigue damage assessment procedure

2.1. Fatigue curve and deformation parameter

In the traditional high-cycle fatigue design of steel structures[46–48], the prevalent method is based on the nominal stressranges of a classified constructional detail whose fatigue strengthis specified by the corresponding S–N curve. An S–N curve of aspecific detail category represents the quantitative relationship be-tween fatigue strength S and the number of cycles to failure N. It isexperimentally determined by a series of constant amplitudes fati-gue tests and the applied constant stress range in tests is adoptedas a representative parameter for fatigue strength.

As previously mentioned, field inspections after earthquakesrevealed that brittle failures occurred in beam-to-column connec-tions of steel structures subjected to strong ground motions.Besides, cyclic tests of connection subassemblages and shakingtable tests of steel moment frames [40] also indicated that fatiguefailure occurred due to crack initiation and propagation in regionswhere large inelastic deformations developed. From the engineer-ing point of view, a similar approach as for high-cycle fatiguedesign can be used to evaluate LCF damage of welded beam-to-column connections in SMRFs due to seismic loadings. Instead offatigue strength curves of the classified structural details forhigh-cycle fatigue design, it is possible to introduce fatigue defor-mability curves of the whole connections for seismic LCF assess-ment. It is widely accepted that when structural componentresponds in inelastic range, generalized deformations (such asstrain, displacement and rotation) are more representative thangeneralized strength (such as stress, force and moment). Therefore,it is straightforward to substitute the nominal stress range in thefatigue strength curve by appropriate structural deformationrange, so as to establish the fatigue deformability curve of theconnection.

Modern seismic resistant design relies on structural ductility toabsorb seismic energy. In SMRFs, the predominant mode of seismicenergy dissipation is the large inelastic cyclic deformations in theplastic hinge region, and the ductility could be represented bythe rotation capacity of beam-to-column connection. As shown inFig. 1a, the inter-storey drift angle u is a structural deformationparameter in seismic design of SMRFs and somewhat representsthe rotation intensity of the rigid connection. There are usuallytwo types of experimental setup for laboratory tests of connectionsubassemblages, i.e. one is horizontally loaded at the top of the col-umn as schematically shown in Fig. 1b, and the other is loaded at

Fig. 1. Deformation of steel moment frame under horizontal earthquake and deformations of connection subassemblages in laboratory tests.

H. Zhou et al. / International Journal of Fatigue 64 (2014) 97–113 99

the cantilever end of the beam with the column laid horizontallyon the reaction floor as shown in Fig. 1c. In the cyclic tests of steelmoment connections, the column drift angle u = D/H as shown inFig. 1b or the beam drift angle u = d/Lb as shown in Fig. 1c isadopted as a deformation controlling index in the loading protocol.The column or beam drift angle in the connection subassemblagetests is equivalent to the inter-storey drift angle in global steel mo-ment frame.

In inelastic range, strains are more representative than stresses,and strain ranges at the geometric discontinuities of the weldedconnections become the predominant indices that control thelow-cycle fatigue. When the connection responds in inelasticrange, strains and rotations are in a non-linear relationship, there-fore selecting rotation as a representative deformation parameterwill introduce additional inaccuracies but achieve simplifications.Regarding the cyclic tests of connection subassemblages for fatiguecurve elaboration, it is more appropriate and convenient to chooseglobal deformation parameters rather than local strains. Differentdeformation parameters were proposed to establish the seismic fa-tigue deformability curves of the beam-to-column connections,such as total rotation range including elastic part [42,44], or onlyplastic rotation range [34,43]. Both approaches based on total orplastic rotations are suitable, and limited influence on LCF damageof rigid connections is introduced by elastic rotations [42]. In thisstudy, regarding the global deformation parameter in steel mo-ment frames and the deformation controlling index in cyclic testsof connection subassemblages, the inter-storey drift angle u(equivalent to the total rotation of connection subassemblage) isselected as the generalized deformation parameter for the fatiguecurve, which can be easily measured during the connection testsand obtained from seismic analysis of global SMRF structures.

After the Northridge and Kobe earthquakes, considerable cyclicor dynamic tests were performed on beam-to-column connectionsof SMRFs. However, very limited connection tests were carried outat constant amplitude cyclic loadings, which are required by elab-orations of fatigue curves. As for elaboration of a fatigue curve, aseries of tests at different constant amplitudes are required for aparticular connection configuration. The available constant ampli-tude cyclic tests of the beam-to-column connections performed byresearchers all over the world are collected and the key results(such as the displacement amplitudes at the loading end and the

number of cycles to failure) are re-elaborated to establish theDu–Nf fatigue deformability curve, described as the followingexpression [43]:

DumNf ¼ K ð1Þ

where Du is the total rotation range; Nf is the number of cycles tofailure; m is the slope of the fatigue curve; and K is a constant. Theparameters m and K of a fatigue deformability curve are determinedby regression of test data for a specific connection category.

2.2. Proposed fatigue assessment procedure

In the present study, two general steps are sequentially carriedout to evaluate LCF damage of the welded connections in SMRFsdue to seismic loadings. The preliminary step is to identify themost fatigue critical connection in the whole structure based onthe Du–Nf fatigue curve method through global analysis, and theenhanced step is to predict crack initiation in the most fatigue crit-ical connection by using a micro-mechanics based fracture model(CVGM) through global–local analysis.

The proposed LCF assessment procedure for welded beam-to-column connections in SMRFs subjected to seismic loadings isshown in Fig. 2. Firstly, a global FEM of a plane SMRF with beamfinite elements is modeled and non-linear dynamic time historyanalysis is performed to simulate the global deformation responsedue to a seismic event. The time history of the inter-storey drift an-gle corresponding to each connection is extracted from global anal-ysis. Secondly, the Rainflow cycle counting method [45] is appliedto convert the irregular time history of inter-storey drift angle intothe equivalent rotation range spectrum, which consists of severalblocks of rotation range Dui versus number of cycles ni. The fatiguedeformability curve of the particular connection category adoptedin the investigated SMRF, which is elaborated by the available con-nection fatigue test data, is selected to determine the fatigueendurance Nfi at each rotation range Dui. Then, Palmgren–Miner’srule [30,31], shown in Eq. (2), is applied to calculate the cumulativefatigue damage of each connection.

D ¼Xk

i¼1

ni

Nf i¼Xk

i¼1

niDumi

Kð2Þ

Fig. 2. Low-cycle fatigue assessment procedure for welded connections of SMRFs under seismic loading.


where ni is the number of cycles for an applied level of rotationrange Dui; Nfi is the number of cycles to failure at the same rotationrange Dui; k represents the number of blocks with different rota-tion ranges; and D is the cumulative fatigue damage, ranges be-tween 0 (no damage) and 1 (complete damage).

The relative fatigue criticality of all connections in the steelframe is ranked based on the fatigue damage calculation. As shownin Fig. 2, a refined local model of the most fatigue critical connec-tion is integrated into the global steel frame model. A micro-mechanics based fracture model termed as CVGM is applied inthe refined local model to predict fracture initiations of vulnerablelocations in the most fatigue critical connection taking load se-quence effects into account. The CVGM model is realized by usingABAQUS [49] user subroutine in the refined local FEM of the con-nection and the time history of fracture index can be obtainedthrough seismic dynamic analysis of the global–local FEM of theSMRF.

2.3. Micro-mechanics based fracture model CVGM

Recently, a micro-mechanics based fracture model termed asthe cyclic void growth model (CVGM) [26], which represents theunderlying ductile fracture mechanism due to cyclic plastic strains,was developed to predict LCF fracture of steel structures subjectedto seismic loadings. The accuracy of the CVGM model was vali-dated through a series of cyclic tests of fourteen blunt notchedcompact tension specimens and four dogbone specimens [50].The variable amplitude cyclic tests of six full-scale column base-plate connections demonstrated the applicability of the CVGMmodel in fracture prediction of welded steel connections [51].Furthermore, the CVGM model was applied to predict extremelylow-cycle fatigue fracture in local buckling regions of the bracingmembers in steel frames under earthquakes [8,52]. The applicationof this micro-mechanics based model to a beam-to-column

connection with complex geometry requires an extremely finemesh and very high computational cost. Therefore, global–localanalysis provides a possible and efficient approach to adopt theCVGM model in predicting fatigue fracture of welded connectionsin the whole structure of SMRF due to seismic loadings.

The CVGM model was proposed by Kanvinde and Deierlein [26]based on the previous work of Rice and Tracey [53] and Hancockand Mackenzie [54]. For a single spherical void in an infinite con-tinuum, the void growth rate under cyclic reverse loading can beexpressed as [26]:

dr=r ¼ signðTÞ � C � expðj1:5TjÞdep ð3Þ

where r is the instantaneous void radius; T = rm/re is the stress tri-axiality (ratio of mean stress rm to effective stress re); C is a con-stant; dep ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2=3Þdep

ij � depij

qis the incremental equivalent plastic

strain; and sign(T) takes into account the sense of the stress triaxi-ality T. If the stress triaxiality is positive, the void will expanse un-der plastic straining, and if it is negative, the void will shrink. Themagnitude of triaxiality T and the equivalent plastic strain governthe rate of void growth or shrinkage.

Integrating Eq. (3) over tensile and compressive loading excur-sions, respectively, the cumulative void growth during a cyclicloading history can be given as:

ln ðr=r0Þcyclic ¼X

tensile

C1

Z e2

e1

expðj1:5TjÞdep �X

compressive

C2

Z e2

e1

� expðj1:5TjÞdep ð4Þ

The void size increases during intervals of positive triaxialityand decreases during intervals of negative triaxiality. The firstsummation on the right hand side of Eq. (4) represents the cumu-lative void growth over all cycles of positive triaxiality, whichrequires computation of the integral between plastic strains e1

and e2 at the beginning and the end of each tensile excursion.


The second term calculates the total void shrinkage over all cyclesof negative triaxiality. In Eq. (4), r0 is the initial void radius; theconstants C1 and C2 are used to distinguish different rates of voidgrowth and shrinkage. Here, C1 = C2 = C is assumed [26] as lack ofdata to determine the rates of void growth and shrinkage, respec-tively. Therefore, Eq. (4) is rewritten as the following expression atthe fracture critical instant:

lnðr=r0Þcriticalcyclic ¼ C

Xtensile

Z e2

e1

expðj1:5TjÞdep�X

compressive

Z e2

e1

expðj1:5TjÞdep

" #

ð5Þ

As per Eq. (5), the void growth ‘‘demand’’ VGD for a cyclic load-ing is defined as:

VGD ¼X

tensile

Z e2

e1

expðj1:5TjÞdep �X

compressive

Z e2

e1

expðj1:5TjÞdep

ð6Þ

The void growth ‘‘demand’’ VGD will alternatively increase anddecrease under a cyclic reversal loading. However, a restriction ismade on it, so that it never takes on negative value that correspondsto negative void size which has no physical sense. Therefore, whenthe result determined by Eq. (6) decreases below zero, it remains atzero until a subsequent tensile excursion increases its value abovezero. Under cyclic loading, LCF fracture is expected to initiate whenthe void growth ‘‘demand’’ VGD exceeds the void growth‘‘capacity’’, i.e. the cyclic fracture index FIcyclic P 1.0, defined as:

FIcyclic ¼ VGD=gcyclic ð7Þ

where gcyclic is the cyclic void growth capacity determined as adegraded fraction of the monotonic void growth capacity gmonotonic,described as:

gcyclic ¼ expð�kecÞ � gmonotonic ð8Þ

where an exponential decay function is used to degrade the mate-rial capacity under monotonic loading into its counterpart undercyclic loading, accounting for damage accumulation of inter-voidligaments; gmonotonic can be obtained by the monotonic tests ofsmooth notched round bars [25]; k is a material dependent damage-ability coefficient, calibrated by monotonic and cyclic material testsin combination of complementary finite element analyses [26]; andec is a damage variable defined as the compressive equivalentplastic strain that accumulates over all the preceding compressivecycles of the concerned loading instant.

In short, the CVGM model for predicting seismic fatigue crackinitiation is modeled from the two key aspects, i.e. the cyclicincreased void growth ‘‘demand’’ VGD and the progressively de-creased void growth ‘‘capacity’’ due to damage accumulation ofthe material. The CVGM model is realized by using ABAQUS [49]user subroutine and the time history of fracture index FIcyclic isautomatically calculated at each material point of the local FEMduring seismic time history analysis of the global–local model ofSMRF.

3. Fatigue curves of beam-to-column connections

3.1. Connection tests in Japan

Several series (a total of 72 specimens) of constant amplitude(CA) low-cycle fatigue tests of all welded beam-to-column connec-tions were performed by Japanese researchers between 1983 and2006, as summarized in Table 1.

A total of 19 connection subassemblages were tested byKuwamura and Suzuki [55] and Iyama et al. [56], which could beclassified into four series, i.e. HT60-NS, HT60-SC, SM50-NS and

SM50-SC. Each specimen consisted of a built-up welded H-shapedbeam section H200 � 100 � 9 � 9 mm and a 40 mm-thick endplate. The beam flange was welded to the end plate with completejoint penetration (CJP) and a reinforcing fillet weld was added afterthe removal of weld backing bar. The beam web was fillet weldedto the end plate which was connected to a strong column by usinghigh-strength bolts. Two varieties of structural steel denoted asHT60 and SM50 (known as SM490 now) were applied in the testspecimens. Connection configuration, either with weld access hole(scallop cut in the SC specimen) or without weld access hole (non-scallop cut in the NS specimen), was adopted in the specimen. Dif-ferent constant amplitude displacements were applied at the can-tilever beam ends until fracture failures of the specimens. Allspecimens collapsed due to fatigue fractures, which included twomanners, i.e. crack initiated from the beam flange edge in the NSspecimen and crack initiated from the beam flange center at thetoe of weld access hole in the SC specimen. The rotation rangeDui calculated from beam tip displacement range and the numberof cycles to failure Nfi obtained by each specimen is plotted in alog–log scale graph as shown in Fig. 3a. The fatigue curve parame-ters m and K of the four test series are obtained by linear regressionaccording to Eq. (1). As shown in Fig. 3a, when identical connectionconfigurations are adopted, the SM50 specimens fabricated withlower strength steel have relatively better fatigue deformabilitythan the HT60 specimens. Furthermore, the NS specimens withoutweld access holes achieve higher fatigue resistance than the SCspecimens with weld access holes.

As summarized in Table 1, four series of specimens denoted asSM490-NS-NB, SM490-NS-BB, SS400-SC-NB and SS400-SC-BB weretested under CA fatigue loadings by Akutsu and Mimura [57] andKanda et al. [58]. The connection subassemblage was composedof an H-shaped beam section H200 � 100 � 5.5 � 8 mm and abox column section h200 � 200 � 9 mm. The beam flange wasCJP welded to the diaphragm plate (which intersects across the col-umn) with gas metal arc welding (GMAW) procedure. Weld accessholes were not cut in the SM490 specimens, while they wereadopted in the SS400 specimens. Weld backing bar was either re-moved or retained in the SM490 specimens and the SS400 speci-mens. All specimens failed due to fatigue fracture and cracksinitiated from CJP weld toes, the ends of weld backing bars orthe toes of weld access holes. As shown in Fig. 3b, the backingbar detail seems to have no obvious effect on the fatigue resistanceof the connections. Therefore, only one fatigue curve is regressedfor the SM490 specimens or the SS400 specimens, respectively.Similar results as the tests of Kuwamura and Suzuki [55] and Iya-ma et al. [56] are obtained and it is indicated by Fig. 3b that the NSspecimens without weld access holes exhibit higher fatigue resis-tance than the SC specimens with weld access holes.

A total of 16 connections were tested under CA fatigue load-ings by Miura and Mimura [59], Kinoshita et al. [60], Sudo et al.[61] and Hayashi et al. [62,63], which could be categorized intothree series, i.e. SN490B-NS, SN490B-SC1 and SN490B-SC2. Eachconnection subassemblage consisted of an H-shaped beamH300 � 150 � 6 � 12 mm fabricated from SN490B steel and abox column h250 � 250 � 9 mm made of STKR490 steel. Thebeam flange was CJP welded to the diaphragm plate with backingbar left in place. The CA fatigue test data of the three series ofconnection subassemblages are plotted in Fig. 3c. Comparison offatigue curves between the SN490B-NS specimens and theSN490B-SC specimens further confirms that the NS specimenswithout weld access holes have higher fatigue resistance thanthe SC specimens with weld access holes. As indicated by thefatigue curves of SN490B-SC1 and SN490B-SC2 shown in Fig. 3c,the specimens with longer beams exhibit better fatigue deforma-bility than the specimens with shorter beams when other connec-tion configurations are identical.

Table 1Summary of constant amplitude fatigue tests of welded beam-to-column connections in Japan.

Investigator Series Number Beam (section/mm; aLb/mm) Column (section/mm; bLc/mm) Configuration

Kuwamura andSuzuki [55]

HT60-NS 7 H200 � 100 � 9 � 9; Lb = 1210;HT60, cfy, bf = 431 MPa

Not available; Lc = 1000; strongcolumn

dCJP weld; no eWAH; backing barremoved

Iyama et al. [56] HT60-SC 6 H200 � 100 � 9 � 9; Lb = 1210;HT60, fy, bf = 445 MPa

CJP weld; fillet weld reinforce; withWAH; backing bar removed

SM50-NS 3 H200 � 100 � 9 � 9; Lb = 1210;SM50, fy, bf = 335 MPa

CJP weld; no WAH; backing barremoved

SM50-SC 3 H200 � 100 � 9 � 9; Lb = 1210;SM50, fy, bf = 335 MPa

CJP weld; fillet weld reinforce; withWAH; backing bar removed

Akutsu andMimura [57]

SM490-NS-NB 6 H200 � 100 � 5.5 � 8; Lb = 1350;SM490, fy, bf = 398 MPa

h200 � 200 � 9; Lc = 1190;STKR400

CJP weld; no WAH; without backingbar

Kanda et al. [58] SM490-NS-BB 6 H200 � 100 � 5.5 � 8; Lb = 1350;SM490, fy, bf = 398 MPa

CJP weld; no WAH; backing bar left

SS400-SC-NB 6 H200 � 100 � 5.5 � 8; Lb = 1350;SS400, fy, bf = 443 MPa

CJP weld; with WAH; without backingbar

SS400-SC-BB 6 H200 � 100 � 5.5 � 8; Lb = 1350;SS400, fy, bf = 443 MPa

CJP weld; with WAH; backing bar left

Miura andMimura [59]

Kinoshita et al.[60]

SN490B-NS 4 H300 � 150 � 6 � 12; Lb = 1725;SN490B, fy, bf = 371 MPa

h250 � 250 � 9; Lc = 1190;STKR490


Sudo et al. [61] SN490B-SC1 4 H300 � 150 � 6 � 12; Lb = 1725;SN490B, fy, bf = 354 MPa


Hayashi et al.[62,63]

SN490B-SC2 8 H300 � 150 � 6 � 12; Lb = 1325;SN490B, fy, bf = 365–405 MPa


Akutsu et al.[64]

SS400-NS-BB 5 H200 � 100 � 5.5 � 8; Lb = 1350;SS400, fy, bf = 403 MPa

H200 � 200 � 8 � 12; Lc = 1270;SS400, ffy, cf = 294 MPa


Kaneta andKohzu [65]

SS41-SC-BB 3 H200 � 100 � 5.5 � 8; Lb = 1000;SS41, fy, bf = 273 MPa

H200 � 200 � 8 � 12; Lc = 1000;SS41


SS41-SC-NB 5 H200 � 100 � 5.5 � 8; Lb = 1000;SS41, fy, bf = 345 MPa

CJP weld; Fillet weld reinforce; withWAH; backing bar removed

a Lb denotes the beam length.b Lc denotes the column length.c fy, bf represents the yield strength of beam flange.d CJP is short for complete joint penetration.e WAH is short for weld access hole.f fy, cf represents the yield strength of column flange.


As shown in Table 1, LCF tests of five connection subassemblag-es denoted as SS400-NS-BB were performed by Akutsu et al. [64],and another two test series named SS41-SC-BB and SS41-SC-NBwere carried out by Kaneta and Kohzu [65]. The SS400-NS-BB spec-imen consisted of an H-shaped beam H200 � 100 � 5.5 � 8 mmand an H-shaped column H200 � 200 � 8 � 12 mm. The beamflange was CJP welded to the column flange with GMAW processand the weld backing bar was left. The beam and column sectionsof the SS41-SC specimens were identical to those of the SS400-NS-BB specimens. Two weld details, i.e. backing bar retained, andbacking bar removed in combination of a reinforcing fillet weld,were adopted in the SS41-SC-BB specimens and the SS41-SC-NBspecimens, respectively. The backing bar detail shows no remark-able effect on the fatigue performance as indicated by the fatiguetest data shown in Fig. 3d.

The aforementioned connection subassemblages all belonged tothe category of small-scale specimens, whose beam height rangedfrom 200 mm to 300 mm. As indicated by the previous analyses,the weld access hole detail showed great effects on the fatigueresistance of welded beam-to-column connections. All collected fa-tigue test data of 72 connection subassemblages are re-plotted inFig. 4a, divided into two groups, i.e. the NS specimens withoutweld access holes and the SC specimens with weld access holes.As shown in Fig. 4a, in log–log scale graph, a good linear relation-ship between the rotation range Du and the number of cycles tofailure Nf is presented both for the NS and SC specimens. The slopem of the fatigue curve equals to 2.96 and 2.92 for the NS specimensand the SC specimens, respectively, which is very close to the slopem = 3.0 of the traditional high-cycle fatigue design curve. In order

to keep the consistency with the high-cycle fatigue design curve,the previous LCF test data of the Japanese connections are re-re-gressed according to Eq. (1) with a fixed slope m = 3.0 as shownin Fig. 4b. Referring back to Fig. 2, the obtained mean fatigue curvesprovide fundamental inputs in LCF damage assessment of weldedbeam-to-column connections in steel moment frames subjectedto seismic loadings.

3.2. Connection tests in Europe

Table 2 summarizes the available LCF tests of rigid beam-to-col-umn connections in Europe. A total of 16 welded connection sub-assemblages were fabricated and tested up to failure at differentconstant amplitude loadings, which were performed by Ballioet al. [66] and Mele et al. [67]. The BCC4 specimens werewelded-flange bolted-web connections, consisting of small beamand column sections HE120A. The beam flange was welded tothe column flange by CJP single bevel groove weld in workshop.The BCC5, BCC6 and BCC8 specimens were composed of relativelylarge sections compared with the BCC4 specimens. These speci-mens were all welded connections, i.e. the beam flanges were con-nected to the column flange by means of CJP double bevel groovewelds, while fillet welds were applied between both sides of thebeam web and the column flange. The manual metal arc weldingprocedure with E7018-1 electrode was used and all welds weremade in horizontal position. No weld access holes and no weldbacking bars were used to make the CJP welds. The continuity plate(10 mm thick) across the column was fillet welded to the columnweb and flanges. As shown in Fig. 5a, the rotation range Du and

Fig. 3. Fatigue test data and fatigue curve fitting of the Japanese welded beam-to-column connections.

Fig. 4. Fatigue curve fitting with the collected connection test data in Japan.


the number of cycles to failure Nf obtained from each connectiontest is plotted in a log–log scale graph and linearly fitted as perEq. (1).

As summarized in Table 2, a total of 26 all welded beam-to-col-umn connection tests were carried out by Castiglioni et al. [68],among which 21 specimens were tested at five different constantamplitudes loadings and 5 specimens were tested at variableamplitudes (VA) loadings. The T-shaped connection subassemblageconsisted of an H-shaped beam IPE450A fabricated from S275-J0steel and an H-shaped column HE300B made of S355-J0 steel.The flux-cored arc welding (FCAW) technique was adopted in thebeam flange to column flange welds. Three sub-types were appliedin the CJP weld, i.e. type C1 was a single bevel groove weld withbacking bar left, type C2 was similar to type C1 but with a copperbacking bar easily removed after welding and type C3 was a doublebevel groove weld normally corresponding to shop welding.

Furthermore, other configurations, such as weld access hole andpanel zone doubler plate (with/without), were designed to evalu-ate their influence on the fatigue endurance of the connections.Through the analysis of the test results, it is found that the CJPweld details have no significant effects on the fatigue propertiesof the connections. To the contrary, the failure mode, which hassome relationships with the loading amplitudes, plays an impor-tant role in the fatigue resistance of the connections. The speci-mens loaded by large displacement amplitudes are more likely tofail accompanied with beam flange buckling. The tested connec-tions are classified into four series according to the failure modesand two fatigue curves as shown in Fig. 5b are obtained from theCA-SF1 specimens and the CA-M & CA-P specimens.

All collected European connection test data under CA fatigueloadings are re-plotted in Fig. 6 and the mean fatigue curve is ob-tained by regression analysis with a fixed slope m = 3.0. In order to

Table 2Summary of fatigue tests of rigid beam-to-column connections in Europe.

Investigator Series Number Beam (section; length; steel) Column (section; length; steel) Failure mode

Ballio et al.[66]

BCC4 4 HE120A; Lb = 943 mm; Fe360, fy, bf = 337 MPa HE120A; Lc = 1476 mm; Fe360,fy, cf = 337 MPa

Weld failure and panelzone shear mechanism

Mele et al.[67]

BCC5 4 IPE300; Lb = 862 mm; S235JR, fy, bf = 275 MPa HE160B; Lc = 1800 mm; S235JR,fy, cf = 323 MPa

Weld failure and panelzone shear mechanism


Base metal fracture inbeam flange


Base metal fracture inbeam flange

Castiglioniet al. [68]

CA-SF1 7 IPE450A (447 � 190 � 7.6 � 13.1 mm); Lb = 2000 mm;S275-J0 steel fy, bf = 318–486 MPa

HE300B (300 � 300 � 11 � 19 mm);Lc = 2400 mm; S355-J0 steel fy, cf = 486 MPa

Fracture from beamflange center

CA-SF2 4 Fracture from beamflange edge

CA-M 4 Mix of buckling andfracture

CA-P 6 Local bucklingVA 5 Mix of buckling and

fracture

Fig. 5. Fatigue test data and fatigue curve fitting of the European rigid beam-to-column connections.


prove the validity of the fatigue curve which is derived from CAfatigue tests in predicting fatigue failure under variable amplitudeloadings, test data of the VA specimens are plotted in Fig. 6 as well.The equivalent rotation range Dueq defined as Eq. (9) is adopted tosubstitute the rotation range Du in CA fatigue tests and the totalnumber of cycles to failure Rni is used to represent the fatigue lifeNf.

Dueq ¼P

niDu3iP

ni

� �1=3

ð9Þ

As shown in Fig. 6, the VA test data distribute along the meanfatigue curve, validating the applicability of fatigue curve in vari-able amplitude loading conditions. The test data shows a large dis-crepancy indicated by a low linear correlation coefficient R = 0.482.

Fig. 6. Fatigue curve fitting with the collected connection test data in Europe.

As a conservative way, the lowest boundary fatigue curve could beadopted in fatigue damage assessment or fatigue design ofbeam-to-column connections.

3.3. Connection tests in America

A total of ten T-shaped connection subassemblages comprisedA572 Gr. 50 W18 � 40 beams and W14 � 145 columns were cycli-cally tested at constant amplitude beam tip displacements, whichwere performed by Partridge et al. [69,70]. The beam-to-columnsubassemblages used basic ‘‘pre-Northridge’’ configuration withwelded-flange and bolted-web connections. The CJP welds werefilled with high toughness weld material E71-T8 and were ultra-sonically tested acceptable. In two of the ten specimens, weldbacking bars were left in place (denoted as the pre-N-BB speci-mens), and in eight specimens, backing bars were removed andfillet welds were reinforced at the weld roots (denoted as thepre-N-NB specimens). Another ten connection subassemblages,with the same sections and CJP weld details, were tested underCA fatigue loadings implemented by Richard et al. [71]. Three typesof connection configurations were adopted, i.e. Type I (SW-NB) hada slot cut in the beam web near the flange, Type II (RBS-NB) had aradius cut with 40% reduction of the beam flange and Type III (pre-N-NB) was identical to Partridge’s connection [69,70] with backingbar removed. All of the twenty specimens are classified into fourseries and the fatigue test data are plotted in Fig. 7. As indicatedby Fig. 7, the pre-N-BB specimens representing the non-improvedconnections as in the Northridge earthquake have the poorest

Fig. 7. Fatigue curve fitting with Partridge’s [69,70] and Richard’s [71] test data.


fatigue properties. The pre-N-NB specimens with improved welddetails exhibit a little higher fatigue resistance, while the RBS-NBand SW-NB specimens have much better fatigue properties thanthe pre-N connections.

Besides the limited constant amplitude fatigue tests, moreextensive full-scale beam-to-column subassemblages were testedunder variable amplitude loadings following the FEMA/SAC JointVenture Phase I and II projects. Specimen information and test re-sults of some experimental programs are available in the SAC Con-nections Database [72]. During Phase I project, welded-flangebolted-web connections representing the common pre-Northridgepractices, such as low toughness weld material E70T-4 and simu-lated field welding, were tested at the Earthquake Engineering Re-search Center (EERC), University of California Berkeley (UCB),University of California at San Diego (UCSD) and University ofTexas at Austin (UTA), respectively. Fifteen specimens followingsuch practices denoted as ‘‘non-improved’’ connections were avail-able with detailed test results [72] and the equivalent rotationrange Dueq of each specimen calculated as per Eq. (9) is plottedagainst the total number of cycles to failure Rni shown in Fig. 8a.In Phase II project, a total of ten T-shaped beam-to-column subas-semblages were tested in the Structural Laboratory at University ofMichigan [17]. These specimens were welded-flange bolted-webconnections with improved details, such as CJP weld with notch-tough electrodes E70TG-K2 and reinforcing fillet weld at weld rootafter backing bar removed. Another six single-sided and five dou-ble-sided connection subassemblages were tested at ATLSS Re-search Center, Lehigh University [18]. These specimens were allwelded connections with more improved details, such as notch-tough weld filler material E70TG-K2, modified weld access holes,polished weld toe, removal of backing bar and reinforcing fillet

Fig. 8. Fatigue curve fitting with the colle

weld. The test data of the VA specimens with improved detailsare plotted in Fig. 8a as well. Two mean fatigue curves are obtainedby regression analysis with a fixed slope m = 3.0 based on the CAfatigue tests of improved and non-improved connections. The VAtest data distribute along the mean fatigue curve, validating theapplicability of fatigue curve in predicting fatigue damage underVA loadings.

A total of eight double-sided RBS connection tests at variableamplitude loadings were conducted jointly at two universities,i.e. UTA and TAMU (Texas A & M University) [73]. All specimensconsisted of W36 � 150 beams and either W14 � 398 orW14 � 283 columns. The RBS radius cut was started at 230 mmdistance from the column flange and was 685 mm in length forall specimens. Two different reductions of beam flange, i.e. 40%and 50% were adopted. The beam flange groove welds were madeusing self-shielded flux-core arc welding (SS-FCAW) process withE70T-6 electrodes. Another seven single-sided RBS connectionswere tested under variable amplitude loadings performed at UCSD[74]. The RBS reductions ranged from 43% to 50%. The beam flangeCJP welds were performed using SS-FCAW process with E70T-6electrodes. As shown in Fig. 8b, the VA test data of RBS connectionsprovide validation of the mean fatigue curve derived from CA fati-gue tests.

3.4. Connection tests in China

A total of 8 single-sided beam-to-column subassemblages weretested under LCF loadings by Wang et al. [24]. The welded-flangebolted-web connection consisted of a welded beam H400 �150 � 8 � 12 mm and a welded column H450 � 200 �12 � 16 mm fabricated from Q235 steel. The beam flanges wereCJP welded to the column flange with GMAW process using E43electrodes. Almost identical configurations were adopted for allspecimens except a little difference in weld access holes. Amongthese specimens, two were tested under CA loadings and six weretested under VA loadings. Recently, another nine connection testswere conducted by Xiong [75]. These specimens used the identicalmember sections as Wang’s tests [24] but were made of Q345 steeland the beam flange CJP welds were performed with E50 elec-trodes correspondingly. Four of the nine specimens were testedunder CA fatigue loadings and five were tested under VA loadings.

The fatigue test data of six CA loaded specimens are plotted inFig. 9a and the mean fatigue curve is obtained by regression anal-ysis. As shown in Fig. 9b, the mean fatigue curve are re-fitted bythe CA test data with a fixed slope m = 3.0 and the VA test dataare plotted as well. Conservatively, the lowest boundary fatiguecurve is added below all CA and VA fatigue test data.

cted connection test data in America.

Fig. 9. Fatigue curve fitting with the collected connection test data in China.


3.5. Connection detail category and fatigue curve

The LCF resistance of beam-to-column connection largelydepends on the beam and column size, connection geometric con-figurations (such as RBS cut or not) and weld details (such as fieldor shop welding, weld material toughness, weld backing bar andweld access hole). Based on the collected fatigue test data andthe regressed fatigue deformability curves, a total of seven connec-tion detail categories are classified as listed in Table 3, includingtwo Japanese categories (JP-NS and JP-SC), one European category(EN-W), three US categories (US-NI, US-IM and US-RBS) and oneChinese category (CN-W). Several important observations can beobtained from Table 3, those are: (1) the Japanese and Europeancategories, which are based on small-scale test specimens, havebetter fatigue deformability than the other un-reduced connec-tions which consist of large-scale sections; (2) the JP-NS categorywithout weld access holes achieve higher fatigue resistance thanthe JP-SC category with weld access holes; (3) among the US cate-gories, the US-NI category with non-improved details has the poor-est fatigue property and the US-RBS category with reduced beamsection and improved details obtains the highest fatigue resis-tance; (4) the Chinese category CN-W has a comparative fatiguedeformability as the US-IM category. The mean fatigue curve andthe lowest boundary curve below any test point are provided foreach connection category. In fatigue damage assessment of theexisting SMRFs experienced in former earthquakes, the mean fati-gue curve is suggested; while in fatigue design of new SMRFs sub-jected to future seismic events, the lowest boundary fatigue curveis recommended as a conservative way.

4. Fatigue assessment of connections using global model

4.1. Seismic time history analysis of steel moment frame

As shown in Fig. 10, two steel moment frames, i.e. Frame I (5storeys) and Frame II (9 storeys), are selected as case studies topresent the general procedure of LCF assessment of weldedbeam-to-column connections in SMRFs under earthquakes. Thesame steel beam section H400 � 150 � 8 � 12 mm is adoptedthrough all storeys of both frames. In Frame I, steel column sectionH450 � 250 � 12 � 16 mm is applied through all storeys; while inFrame II, sections H450 � 250 � 16 � 20 mm and H450 � 250 �12 � 16 mm are used for columns from the ground to the thirdfloor and for those from the fourth floor to the roof, respectively.A common Chinese structural steel Q345 is applied in both frames.As for simplification, the plane frame model is adopted and a dis-tributed line load 42 kN/m along the beam is assumed to representthe vertical gravity load on each floor.

The finite element analyses of the two steel frames are imple-mented by ABAQUS/Standard [49]. Three-dimensional beam ele-ments B32 are used to model the columns and beams. Thecollected beam-to-column connections in Table 3 are either allwelded connections or welded-flange bolted web connections,which are commonly considered as rigid connections. Therefore, ri-gid joint is adopted to simulate the rotational behavior of beam-to-column connections in this study. The configurations that influencethe initial rotational stiffness of the connection, such as the panel-zone and the continuity plate, are not considered in the presentglobal model. The fundamental period obtained by frequency anal-ysis is 1.28 s and 2.39 s for Frame I and Frame II, respectively. Thenon-linear time history responses of the frames are calculated bydirect time integration method in �DYNAMIC IMPLICIT option ofABAQUS/Standard [49]. The geometric non-linearity is taken intoaccount and elastic–plastic material constitutive model of Q345steel reported by Zhou et al. [76] is adopted. The structural damp-ing matrix is defined by parameters a and b, which can be deter-mined by modal damping ratio and natural frequency. Thedamping matrix is proportional to the mass matrix and the stiff-ness matrix, expressed as [77]:

½C� ¼ a½M� þ b½K� ð10Þ

where [C], [M] and [K] are the damping matrix, mass matrix andstiffness matrix, respectively; a and b are the mass-proportionaldamping and the stiffness-proportional damping, respectively. Ifthe two reference modes are assumed to have the same dampingratio 1, then

a ¼ 12x1x2

x1 þx2; b ¼ 1

2x1 þx2

ð11Þ

where x1 and x2 are the natural angular frequencies of the first andthe second vibration modes of the considered frame, respectively.The modal damping ratio 1 = 3% is assumed for the first and the sec-ond vibration modes of both steel frames.

In the dynamic time history analysis, three ground motion re-cords, i.e. Northridge (1994), Kobe (1995) and El-Centro (1940)waves are selected to excite the seismic responses of the frames.The applied Northridge wave (NORTHR/MUL279 component) isadopted from Beverly Hills-Mulhol station and the peak groundacceleration (PGA) is 0.52 g. The Kobe wave (KOBE/NIS000 compo-nent) is recorded at Nishi-Akashi station and the PGA is 0.51 g. TheEl-Centro wave with the PGA = 0.35 g is recorded at Imperial ValleyIrrigation District substation. The acceleration response spectra ofthe ground motion records under consideration are shown inFig. 11 as well.

Table 3Summary of connection detail categories and fatigue deformability curves.

Detail category Schematic plot Detail description Mean fatigue curve Lower boundary

m K aR bSD m K

JP-NS

(1)/(2)

Strong box column;CJP shop welded flange;Fillet welded web;(1) JP-NS no weld access hole;(2) JP-SC weld access hole

3 7.03E�3 0.96 6.50E�4 3 2.82E�3JP-SC 3 1.22E�3 0.95 1.00E�4 3 3.87E�4

EN-W Weak H-section column;CJP shop welded flange;Double fillet welded web;No weld access hole

3 9.81E�3 0.48 2.09E�3 3 2.16E�4

US-NI

(1)/(2)

CJP field welded flange;Bolted or CJP welded web;(1) US-NI: Backing bar left,Brittle material, pre-N holes;(2) US-IM: Backing bar removed,tough material, modified holes

3 6.00E�5 c NA 1.00E�5 3 5.40E�5US-IM 3 5.10E�4 0.94 6.00E�5 3 2.49E�4

US-RBS Reduced beam section;40–50% reduction

3 1.93E�3 0.95 2.60E�4 3 1.63E�3

CN-W Strong H-section column;CJP welded flange;High-strength bolted web;Weld access holes; Weld backing bar left

3 5.90E�4 0.83 9.00E�5 3 7.87E�5

a R is the linear correlation coefficient.b SD is short for the standard deviation.c NA no linear correlation coefficient is available as there are only two points of test data.


4.2. Dynamic response and fatigue damage calculation

The time history of storey drift is extracted from each floor andthe maximum inter-storey drift angle range Dumax of each storeyis calculated by the drift history. As shown in Fig. 12a, the rangeDumax of each floor in Frame I under the Northridge earthquakeis larger than that under the Kobe or the El-Centro earthquake. Thisis mainly determined by the fundamental period of the structureand the response spectrum of the input ground motion. Referringback to Fig. 11, at the fundamental period of Frame I (1.28 s),acceleration response of the Northridge earthquake is relativelystronger than that of the Kobe or the El-Centro earthquake. Amongdifferent floors, the ranges Dumax of the second and the third floorsare relatively larger than those of the other floors, indicated by allthe three concerned earthquakes. As shown in Fig. 12b, the rangesDumax through the storeys of Frame II are comparable among thethree concerned earthquakes, which is due to the comparableacceleration responses of the three earthquakes at the fundamen-tal period of Frame II (2.39 s). Along the height of Frame II, seismicresponses of the third to the sixth floors are relatively strongerthan those of the other floors.

The time history of lateral displacement at the mid-height ofeach column between two floors is obtained from global dynamicanalysis and is converted into inter-storey drift angle history relat-ing to the beam-to-column connection. The inter-storey drift angle

u represents the global deformation imposed on the correspondingbeam-to-column connection. Typical time histories of inter-storeydrift angle u corresponding to the concerned connections are givenin Fig. 13, showing the results of connection A2 in Frame I. For clar-ity, the connection in the steel frames is denoted by the combina-tion of the column axis identifier (A, B, C, or D) and the floornumber (1–9).

The LCF damage of each connection caused by the experiencedearthquakes is calculated by firstly converting the predicted inter-storey drift angle history of the concerned connection into rotationrange spectrum using Rainflow cycle counting method [45], andthen applying Palmgren–Miner [30,31] cumulative damage ruleas per Eq. (2). As the deterministic approach based on the Du–Nf

fatigue curve and the linear Miner’s rule, the fatigue damage of aconcerned connection depends on the rotation range spectrum(rotation range Dui versus number of rotation cycles ni) and the fa-tigue curve specified by the connection detail category. Here, if theChinese design and fabrication practices are adopted in the beam-to-column connections of both steel frames, the mean fatiguecurve of connection detail category CN-W as listed in Table 3 isapplied to calculate the fatigue damage.

Fatigue damage of each connection in Frame I subjected to thethree concerned earthquakes is calculated and presented inFig. 14a. As the symmetry of fatigue damage distribution shownby Frame I, fatigue damage of only half number of connections in

Fig. 10. Elevations of the two steel frames for case studies.

Fig. 11. Acceleration response spectra of ground motion records.


the symmetrical structure Frame II is given in Fig. 14b. Fatiguedamage values of all the connections in Frame I and Frame II areless than 1.0, indicating that all the connections can survive fromany of the three concerned earthquakes. The fatigue criticalityranking of all the connections remains unchanged, though theabsolute fatigue damage value varies among different earthquakes.The beam-to-column connections suffer the most fatigue damagedue to the Northridge earthquake, indicated by both steel frames.It is very clear that connection A2 and A4 are the most fatigue crit-ical connection in Frame I and Frame II, respectively. Connectionsof the second and the third floors in Frame I, and connections of

Fig. 12. Envelope of maximum inter-storey drift angle range.

the third to the sixth floors in Frame II, sustain relatively largerfatigue damage than the other connections. The fatigue damagedistribution keeps consistent with the results of maximum inter-storey drift angle range Dumax as shown in Fig. 12.

4.3. Effects of PGA and connection detail category

Frame I is chosen for further investigations. The three originalground motion records are scaled with respect to peak groundacceleration (PGA) ranging from 0.1 g to 1.0 g, in order to evaluatethe effect of PGA on the fatigue damage of beam-to-column con-nections. The fatigue damage of beam-to-column connection in-duced by earthquakes depends on two key aspects, i.e. one is theinter-storey drift angle range which can be reflected by the defor-mation response, and the other is the loading cycles or the durationof strong ground motion. Fig. 15 shows the variation of fatiguedamage of connection A2 with peak ground accelerations. TheNorthridge and the El-Centro earthquakes seem to be moredestructive to the concerned frame when the same scaled PGA isadopted. As indicated by the fatigue damage versus PGA curves un-der the Northridge and the Kobe earthquakes, severer damage isinduced by the Northridge earthquake because much stronger re-sponse is excited by the Northridge earthquake than the Kobeearthquake when comparable cycles are suffered, indicated byFig. 13a and b. The El-Centro earthquake produces larger fatiguedamage than the Kobe earthquake, as its duration is much longeralthough the response intensities are comparable (shown inFig. 13b and c). Fig. 15 also indicates that connection A2 of FrameI will result in complete fatigue failure when the PGA of the El-Cen-tro earthquake increases above 1.0 g.

Fig. 16 shows the effect of connection detail category on the fa-tigue damage of connection A2 in Frame I under the excitation ofthe original Northridge earthquake. Seven detail categories as pre-sented previously in Table 3 are considered in turn for the beam-to-column connection practice in the steel frame. The mean fatiguecurves are adopted to calculate the LCF damage of the connection.As indicated by Fig. 16, connection A2 in Frame I will suffer fatiguefailure if the non-improved pre-Northridge connection categoryUS-NI is adopted, which is consistent with the observation thatfractures occurred in numerous connections of SMRFs in the prox-imity of the Northridge epicenter. However, connection A2 willsurvive if the improved connection category US-IM or the reducedbeam section connection US-RBS is applied. As for the US-RBS cat-egory, connection A2 accumulates only 8.6% of its complete fatiguedamage during one excitation of the original Northridge earth-quake. Connection A2 with the Japanese detail category (JP-NS orJP-SC) or the European detail category EN-W expends relativelyless fatigue life than the other standard connection category(US-NI, US-IM and CN-W).

5. Fracture prediction of critical connection using global–localmodel

5.1. Global–local model integrated with CVGM

The connection A2 is identified to be the most fatigue criticalbeam-to-column connection of Frame I through global dynamicanalysis. In order to give a more accurate fracture prediction ofthe critical connection, a refined local finite element model (shownin Fig. 17) simulated by solid elements is adopted to substitute thecorresponding beam elements of connection A2 in global model.The geometry and weld details of the local model are identical tothe connection reported in the previous research of authors [76].The global–local FEM contains a total of 23,202 eight-node solidelements (C3D8) and 187 beam elements (B32). The refined local

Fig. 13. Time history of inter-storey drift angle corresponding to connection A2 in Frame I.

Fig. 14. Fatigue damage of connections in Frame I and Frame II under the threeconcerned earthquakes.


brick model is connected to the global beam model by using�EQUATION constraints [49], where three translational degree offreedoms (DOFs) of the beam element node are set equal to those

Fig. 15. Effect of peak ground acceleration on fatigue damage.

of the solid element nodes at the interface section. The shear taband preloaded high-strength bolts are explicitly modeled to con-nect the beam web to the column flange. The surface-to-surfacecontacts are used to simulate contacts between beam web, sheartab and bolts. The hard contact and the Coulomb friction modelare adopted as the normal and the tangential behavior, respec-tively. The friction coefficient between the high-strength boltsand the steel plates is set to be 0.265, which is recommended byShi et al. [78]. The designed preload of 155 kN is applied on eachhigh-strength bolt M20 Gr. 10.9 by using �BOLT LOAD option[49]. Isotropic hardening is assumed for the material of bolts, withthe yield strength of 940 MPa and the ultimate strength of1040 MPa [78]. The fillet weld connection between shear tab andcolumn flange is assumed to be rigid, so that the �TIE option [49]is adopted to couple the corresponding nodes in all DOFs.

In the beam elements, the identical material model of Q345steel as used in the previous global frame model is adopted. Whilein the solid elements, the Lemaitré–Chaboche model [79] is appliedas the constitutive model for cyclic plasticity of Q345 steel basemetal and weld metal, which uses the von Mises yield surface com-bining non-linear isotropic and kinematic hardening. The isotropichardening component defines the size change of the yield surfacer0 as a function of equivalent plastic strain ep, described as:

r0 ¼ rj0 þ Q1½1� expð�bepÞ� ð12Þ

where r|0 is the initial size of the yield surface (the yield strength fy

is adopted); Q1 is the maximum change in the size of the yield

Fig. 16. Effect of connection detail category on fatigue damage.

Fig. 17. Refined local finite element model of the critical connection.

Fig. 18. Schematic plot of half-cycle stress–strain curve.

Fig. 19. Time history of inter-storey drift angle calculated by global and global–local models.


surface and b is the rate at which the yield surface size changes asplastic strain increases. The parameters Q1 = 21.0 MPa and b = 1.2for the material are suggested by Shi et al. [80], which are includedin the local FEM by using �CYCLIC HARDENING option [49].

The kinematic hardening component is defined by half-cycledata in material �PLASTIC option [49]. The half-cycle stress–straindata can be obtained from the first cycle of unidirectional tensiletest. A schematic plot of stress–strain curve is shown in Fig. 18and the key data points are listed in Table 4, which are adoptedfrom the previous research of authors [27,76].

Seismic time history analysis is re-performed on the global–local model of Frame I subjected to the original Northridge earth-quake. A comparison between the global and global–local modelsin terms of the deformation response is given in Fig. 19. The timehistory of inter-storey drift angle corresponding to connection A2obtained from global and global–local analyses almost overlaps,which demonstrates that the simplification of welded-flangebolted-web connections assumed as rigid joints in global modelhas little effect on the global deformation response and the cou-pling between the beam and the solid elements in global–localmodel is acceptable as well.

Table 4Half-cycle stress–strain data of Q345 steel base metal and weld metal [76].

Material fy (MPa) r1 (MPa) e1 r2 (MPa)

Base metal 359.9 367.7 0.010 646.6Weld metal 391.4 416.6 0.023 615.8

The stress and strain histories of all material points of the localFEM are monitored to calculate the fracture index FIcyclic accordingto the CVGM criterion. An ABAQUS user subroutine UVARM [49]coded by FORTRAN is utilized to integrate the CVGM criterion intothe refined local FEM of the beam-to-column connection. The usersubroutine UVARM is able to define output variables that are func-tions of any available parameters (such as von Mises stress, meanstress and equivalent plastic strain) at the integration points. Thefracture index FIcyclic of each material point within each incrementis calculated by subroutine UVARM as per Eqs. (6)–(8).In the CVGM model, the monotonic void growth capacitygmonotonic = 2.501 for Q345 steel base metal and gmonotonic = 2.626for weld metal are adopted from the previous research of authors[27], and the material dependent damageability coefficientk = 0.15 is suggested by Liao et al. [81]. During the earthquakeloading, the fracture index FIcyclic contour plot of the local connec-tion model can be obtained by using the visualization module inABAQUS to predict the fatigue critical point conveniently. Fatiguecrack will initiate when the fracture index FIcyclic of the criticalpoint exceeds 1.0.

5.2. Variations of fracture index with earthquake loadings

As shown in Fig. 20, several fracture vulnerable locations alongthe width of the beam flanges are monitored in the global–localanalyses. Path A represents the weld toe of beam top flange to col-umn flange and Path C indicates the weld root of beam bottomflange to column flange. Path B and Path D pass through the toesof weld access holes at the inner sides of the beam top and bottomflanges, respectively. As previously shown in Fig. 17, very refinedmeshes are employed along these paths at the beam end nearthe column face, and especially at the toes of weld access holes(element size is about 1.5 mm, which is sufficient to capture thestress and strain gradients). The fracture index FIcyclic (calculatedby the user subroutine UVARM) along these paths across the beamflange are extracted to identify the fatigue critical points in theconnection during the Northridge earthquake.

The time history of fracture index FIcyclic of each material pointalong the designated path is extracted from FEM analysis results toelaborate the contour plots as shown in Fig. 21. With the contourplots, fracture index FIcyclic of any point along the defined pathscan be obtained at each increment of the input earthquake loading.It is clearly seen from Fig. 21 that the fracture index FIcyclic is a littlelarger at the edges than that in the center of the beam flanges alongPath A and Path C. While along Path B and Path D, the maximumfracture index FIcyclic occurs at the toe of weld access hole in the

e2 rf (MPa) ef Kn (MPa) n

0.200 1224.6 1.330 875.6 0.18840.200 1168.4 1.330 823.6 0.1807

Beam

egnalfn

muloC

Top flange

Bottom flange

Path A

Path B

Path C Path D

Criticalpoint

Fig. 20. Fracture vulnerable locations along the width of the beam flange.


center of the beam flange. Through the loading history of theNorthridge earthquake, the connection is predicted to have higherfracture potentials during the time of 9–15 s as shown in Fig. 21.

Additionally, Fig. 22 gives the line plots of fracture index FIcyclic

varying with location and loading history, respectively. Fig. 22ashows the distributions of fracture index FIcyclic along paths acrossthe beam flange at a particular time increment (9.32 s for Path Aand B, 12.74 s for Path C and D). Along Path A and C, the edges

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50

75

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FIcyclic

Time [s]

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e fr

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lang

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0.0010.0020.0050.0100.0200.0500.1000.2000.400

-75

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-25

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25

50

75FI

cyclic

Path C

Time [s]

Dis

tanc

e fr

om f

lang

e ce

nter

[m

m]

0.0010.0020.0050.0100.0200.0500.1000.2000.400

0 5 10 15 20 25 30

0 5 10 15 20 25 30

Fig. 21. Contour plots of fracture index var

of the beam flanges are more critical to fatigue fracture than thecentral parts. Indicated by Path B and D, the centers of the beamflanges sustain the highest fracture potentials due to severegeometric discontinuities introduced by the weld access holes.Fig. 22b shows the time history of fracture index FIcyclic of the crit-ical point along each path. The critical points of Path C and D haverelatively higher level of fracture index compared with those ofPath A and B, indicating that fatigue fractures are more likely tooccur at the beam bottom flange (than the top flange) under hori-zontal seismic loadings. Among all the locations of the four paths,the toe of weld access hole in the beam bottom flange is the mostfatigue critical point in the connection, which is predicted by theline plot of Center of Path D as shown in Fig. 22b. Fracture indexFIcyclic of each material point through the entire loading history isbelow 1.0, indicating that no fatigue fracture will occur in theconnection subjected to the Northridge earthquake.

6. Summary and conclusion

The following conclusions can be drawn from this study:

1. A general methodology for low-cycle fatigue damage eval-uation of welded beam-to-column connections in SMRFssubjected to seismic loadings is proposed, including twosequential steps. The first step is to identify the most fati-gue critical connection in the whole structure based onthe Du–Nf fatigue curve method through global analysisand the second enhanced step is to predict fatigue crackinitiation in the most critical connection by using amicro-mechanics based fracture model CVGM throughglobal–local analysis.

2. Fatigue deformability curves of seven connection catego-ries are elaborated based on the available, constant ampli-tude cyclic test results of welded beam-to-columnconnection subassemblages. The Japanese categories

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0 5 10 15 20 25 30

0 5 10 15 20 25 30-75

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75

Time [s]

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e fr

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0.0010.0020.0050.0100.0200.0500.1000.2000.400

Path D

FIcyclic

ying with location and loading history.

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om f

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m]

Fracture index FIcyclic

Path A (9.32s) Path B (9.32s) Path C (12.74s) Path D (12.74s)

0.0 0.2 0.4 0.6 0.8 0 5 10 15 20 25 30

0.0

0.2

0.4

0.6

0.8

Frac

ture

inde

x FI

cycl

ic

Time [s]

Edge of Path A Center of Path B Edge of Path C Center of Path D

Fig. 22. Line plots of fracture index varying with location and loading history.


(JP-NS and JP-SC) and the European category EN-W, whichare based on small-scale specimen tests, have better fatiguedeformability than the other standard connection catego-ries. The reduced beam section connection US-RBS obtainsmuch higher fatigue resistance than the other US categories(US-NI and US-IM).

3. Time history of inter-storey drift angle relating to each con-nection is generated by dynamic time history analysis ofthe global steel frames and then converted into rotationrange spectrum by Rainflow cycle counting method. Seis-mic fatigue damage of each connection is calculated basedon Palmgren–Miner’s rule combined with the experimen-tally determined fatigue curve. The fatigue criticality rank-ing of all the connections remains unchanged underdifferent ground motions although the absolute fatiguedamage value varies from earthquake to earthquake. Theglobal analysis provides a practical and efficient approachto evaluate the LCF damage of steel moment connectionsdue to earthquakes.

4. The identified most critical connection of the whole steelframe is refined into details and a micro-mechanics basedfracture model CVGM is integrated in the local FEM byusing an ABAQUS subroutine. The toe of weld access holein the beam bottom flange is predicted to be the most frac-ture critical point in the identified critical connection sub-jected to the Northridge earthquake. The global–localanalysis provides a more accurate and detailed method topredict fatigue crack initiation of the welded connectiontaking the load sequence effects into consideration.

Acknowledgement

This study was financially supported by National Natural Sci-ence Foundation of China (Grant Nos. 51378289, 51178244 and51038006).

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