a state-of-the-art review on fatigue life assessment.pdf

8/17/2019 A State-of-the-Art Review on Fatigue Life Assessment.pdf

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Review Article A State-of-the-Art Review on Fatigue Life Assessment of Steel Bridges

X. W. Ye, 1 Y. H. Su, 2 and J. P. Han 2

Department o Civil Engineering, Zhejiang University, Hangzhou , ChinaKey Laboratory o Disaster Prevention and Mitigation in Civil Engineering o Gansu Province, Lanzhou University o echnology,Lanzhou , China

Correspondence should be addressed to X. W. Ye; [email protected]

Received October ; Revised December ; Accepted December ; Published February

Academic Editor: Stathis C. Stiros

Copyright © X. W. Ye et al. Tis is an open access articledistributed under the Creative Commons AttributionLicense, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fatigue is among the most critical orms o damage potentially occurring in steel bridges, while accurate assessment or predictiono the atigue damage status as well as the remaining atigue li e o steel bridges is still a challenging and unsolved issue. Terehave been numerous investigations on the atigue damage evaluation and li e prediction o steel bridges by use o deterministic orprobabilistic methods. Tepurpose o this reviewis devoted topresentinga summaryon thedevelopment history and current statuso atigue condition assessment o steel bridges, containing basic aspects o atigue, classical atigue analysis methods, data-driven

atigue li e assessment, and reliability-based atigue condition assessment.

1. Introduction

Fatigue is a localized and progressive process in which struc-tural damage accumulates continuously due to the repetitiveapplication o external loadings such as vehicles or steelbridges, winds or high-rise buildings, waves or offshoreplat orms, and temperature or turbine engines, while theseapplied loadings may be well below the structural resistancecapacity. Tis kind o process is extraordinarily dangerousbecause a single application o the load would not create

anyabnormal effects, whereas a conventionalstructuralstressanalysis might lead to a conclusion o sa ety that doesnot exist. Over a long period o time, the strength andserviceability modes o ailure have been well investigated inthe pro essional engineering communities. However, as oneo the most critical orms o damage and principal ailuremodes or steel structures, atigue is still less understood interms o the cause o ormation and ailure mechanism. It isthere ore essential to seek novel methodologies and developadvanced technologies or seizing the atigue phenomenonand conducting reliable assessment o atigue damage statuso steel bridges which serve as vital components in thetransportation in rastructure o a nation.

wo approaches are commonly employed or atiguedamage evaluation and li e prediction o bridge structures.Te rst approach is the traditional - curve method, inwhich the relationship between the constant-amplitude stressrange, , and the number o cycles to ailure, , is determinedby appropriate atigue experiments and described by an- curve. Te Palmgren-Miner linear damage hypothesis,

also called Miner’s rule [ ], extends this approach to vari-able-amplitude loadings. Te second method is the rac-ture mechanics approach which is dominantly dedicated toexploring the eatures and disciplines o crack initiation andgrowth in consideration o stress eld at the crack tip. Ingeneral, the two approaches are applied sequentially, with the- curve method being used at the bridge design stage or

preliminary evaluation o atigue li e and the racture mech-anics approach or more re ned crack-based remaining

atigue li e assessment or effective decision-making oninspection and maintenance strategies [ ].

Tere have been a lot o investigations and applicationson atigue damage evaluation and li e prediction o bridgestructures using the traditional - method or the racturemechanics approach. Some speci cations [ – ] adopt thetraditional nominal - method to guide bridge atigue

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 956473, 13 pageshttp://dx.doi.org/10.1155/2014/956473

http://dx.doi.org/10.1155/2014/956473http://dx.doi.org/10.1155/2014/956473


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Mathematical Problems in Engineering

design or evaluation. According to these speci cations, theatigue li e prediction o stochastically loaded structures is to

determine the correlation between the stress spectrum andthe material endurance. Te material endurance is generally given in the orm o - curves or constant-amplitude load-ings. Te stress spectrum is generally unknown and needs

to be evaluated by means o experiments or simulations. Inthe process o atigue li e prediction, the stress spectrum isderived by extracting the stress cycles rom a measured orsimulated stress time history with a suitable cycle countingmethod. Next, a proper atigue damage accumulative rule ischosen and the atigue damage caused by individual stresscycle is calculated. Te total atigue damage equals the sumo damage resulting rom individual stress cycle. One o themost widely used damage accumulative rules is the Miner’srule, and a rain ow cycle counting method is generally used

or extracting the stress cycles rom the stress time histories[ , ].

Te nature o atigue process anduncertaintiesassociatedwith the load histories and the estimation o uture loadsrequire eld inspectionas a necessary tool or atigue damagedetection and prevention. Te atigue damage conditionand atigue crack growth in bridge components are thenassessed with data and in ormation collected rom regular

eld inspection. Inspection may involve the visual exami-nation o structural components and/or the use o a variety o nondestructive evaluation (NDE) techniques, such asdynamic testing method, radiographic inspection method,electric inspection method, sonic and ultrasonic method,acoustic emission method, and dye penetration method [ ].Tey are conducted typically afer observing deteriorationand damage such as atigue cracking in local areas and ofenexpensive, time-consuming, and labor intensive to executeon large-scale bridges. When visual inspections withoutNDE techniques are used, the effectiveness o the inspectionprogram primarily depends on the inspector’s experience andthe type o damage observed in generic classes o structuresinspected. In cases where NDE techniques are used, theeffectiveness o the inspection process, to a great extent,depends on the reliability o the selected technique in atiguedamage detection. Tese tests may reveal a snapshot o the operating loads and the corresponding responses o thebridge to assess the atigue li e at atigue-sensitive (especially at racture-critical) details. However, some o the tests willrestrict normal operation o bridges.

Recently, long-term structural health monitoring (SHM)o bridges has been one o the major interests or researchersand engineers in civil, mechanical, material, and computerscience elds [ ]. Design and implementation o such asystem are an integration o analytical skills and instrumen-tation technologies with the knowledge and experience inbridge design, construction, inspection, maintenance, andmanagement. On-line SHM system is able to provide reliablein ormation pertaining to the integrity, durability, and relia-bility o bridges. Te in ormation can then be incorporatedinto bridge management and maintenance system (BMMS)

or optimizing the maintenance actions and to improvedesign standards, speci cations, codes, and guidelines. SHMis, in act, an augment but not a substitute o current practice

in bridge maintenance and management, not only throughthe use o advanced technologies in sensing, data acquisition,computing, communication, and data and in ormation man-agement, but also through effective integration o these tech-nologies into an intelligent system. An accurate estimation o theactual situation in atigue andremaining li e o thecritical

components is an important task o the SHM system, whichcan be achieved by use o the continuously measured data o dynamic strain rom the long-term SHM system.

Fatigue per ormance o steel bridges depends on a num-ber o actors such as material characteristics, stress history,and environment, and all these actors exhibit uncertainty and randomness during the service li e o the bridge. Onthe other hand, when the eld measurement data are used

or atigue condition assessment, the uncertainties relatedto the eld-measured data and the inaccuracies due to dataprocessing techniques are subsistent and hardly avoidable. In view o these acts, it is more appropriate to conduct atigueli e assessment in a probabilistic way than deterministicprocedures.

2. Basic Aspects of Fatigue

As a well-known phenomenon in metallic structures, atigueailures in service were already observed in the th century.

Te word “ atigue” was introduced in the s and sto describe ailures occurring rom repeated loads. Te

rst noteworthy investigation on atigue is generally datedrom the engineering research work o August Wöhler, a

technologist in theGermanrailroad systemin theearly s.Wöhler was concerned with the ailure o railroad axlesafer various times in service at loads considerably less thanthe static strength o the structures and undertook the rstsystematic study o atigue by per orming many laboratory

atigue tests under cyclic stresses. However, in the thcentury, atigue was thought to be a mysterious phenomenonin the material o an engineering structure because atiguedamage could not be seen and ailure apparently occurredwithout any early warning. In the th century, it has beenobserved that repeated load applications can start a atiguemechanism in the engineering material leading to nucleationo a microcrack, crack growth, and ultimately to complete

ailure o a structure.Te history o atigue covering a time span rom to

was reviewed in a survey paper byScḧutz[ ].Mann[ ]compiled , literature sources about atigue problems onengineering materials, components, and structures coveringthe period rom to in our books with an indexon subjects, authors, and years. A comprehensive survey o the historical development o the contributions to atigue onmetallic materials,nonmetallicmaterials,andcomposites canalso be ound in Suresh [ ]. Cui [ ] carried out a state-o -the-art review o metal atigue with particular emphasis onthe latest developments in atigue li e prediction methods.

. . Signi cance o Fatigue. Fatigue is one o the main causesinvolved in atal mechanical ailures o a wide range o struc-tures and in rastructures, such as aircrafs, ships, vehicles,offshore structures, pipelines, machinery, pressure vessels,


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cranes,power turbines, transmission towers,bridges,or otherengineering structures o high visibility. Such devastatingevents occur suddenly and result in heavy losses o li e andproperty. Even though no exact percentage is available on themechanical ailures due to atigue, many studies have sug-gested that to percent o all mechanical ailures are

atigue ailures [ ]. American Society o Civil Engineers(ASCE) Committee on Fatigue and FractureReliability statedthat about to percent o ailures in metallic structuresare related to atigue racture [ – ].

Te act that most mechanical ailures are associatedwith atigue is also testi ed by the results o an extensivestudy reported in by Battelle Columbus Laboratories inconjunction with the NationalBureau o Standards (currently NIS , National Institute o Standards and echnology) [ ].It is reported that out o the ailures (nearly %)were associated with atigue and three main causes o atigueare improper maintenance, abrication de ects, and designde ciencies. Te investigation also emphasized that the costo atigue-induced racture could be dramatically reducedby using proper atigue analysis methods and technologies.However, atigue ailure o metal materials, components, andstructures is very recondite and not well understood, norreadily predicted, by designers and engineers due to thecomplex nature o the atigue mechanism.

. . Mechanism o Metal Fatigue. Te mechanism o theatigue process is quite complicated and controversial which

is still only partially understood. However, understanding theatigue mechanism is a prerequisite or considering variousactors which affect atigue li e and atigue crack growth,

such as the material sur ace quality, residual stress, andenvironmental in uence. Tis knowledge is essential or theanalysis o atigue properties o an engineering structure.Generally, atigue is understood as a crack initiation process

ollowed by a crack growth period. Fatigue cracks caused by the repeated application o loads, which individually wouldbe too small to cause ailure, usually start rom the sur aceo a structural component where atigue damage initiatesas microscopic shear cracks on crystallographic slip planesas intrusions and extrusions, which is the rst stage calledcrack initiation (stage I). Te crack may then propagate romthe localized plastic de ormation to a macroscopic size in adirection perpendicular to the applied load, which is a crack propagation process (stage II). Finally the crack becomesunstable and the component may racture. Usually, it isdifficult to make an exact description and distinction o thetransition between twophaseso the atigue process since thisdistinction depends upon many actors, such as componentsize, material, and the methods used to detect cracks.

ypically, the crack initiation period accounts or mosto the atigue li e o a component made o steels, particularly in the high-cycle atigue (HCF) regime (approximately largerthan , cycles). In the low-cycle atigue (LCF) regime(approximately less than , cycles), most o the atigueli e is spent on crack propagation. Modern atigue theoriesprovide separate analyses or each phase o the atigue pro-cess. Crack initiation theories are based on the assumptionthat atigue cracksare initiatedby the local strains and stresses

concentrating on the sur ace o a structural component dueto geometric shapes such as holes, discontinuities, and lletradii. Crack propagation and nal ailure stages are analyzedby relating crack growth to the stresses in the componentusing racture mechanics.

3. Classical Fatigue Analysis MethodsHistorically, two overriding considerations have promotedthe development o atigue analysis methods. Te rst hasbeen the need to provide designers and engineers with meth-ods that are practical, easily implemented, and cost effective.Te second consideration has been the need to reconcilethese analytical approaches with physical observations. Oneo themost important physicalobservations is that the atigueprocess can generally be broken into two distinct phases:initiation li e and propagation li e. Tis paper introducesthree atigue analysis methods including stress-li e ( - )method, the racture mechanics approach, and strain-li e

( - )method. Tese methods have their ownregion o appli-cation with some degree o overlap among them.. . Fatigue Analysis Using Stress-Li e Method. Stress-li e

method is suited or HCF and mainly used or long atigueli e prediction where stresses and strains are elastic. It doesnot distinguish between crack initiation and propagationbut deals with a total li e or the li e to ailure o a struc-tural component.Stress-li e method represents a relationshipbetween the stress range and atigue ailure in the orm o - curves, attained by cycling test specimens at constant-

amplitude stresses until visible cracking occurs.Such tests arerepeated several times at different stress levels to establish the- curves. Running atigue tests is an expensive and time-

consuming process and curve tting o atigue data is alsotime-consuming. Fatigue analytical modelscan link theoreti-cal ideas with the observed data to provide a good predictiono uture observations. Wöhler was the pioneer researcherwho tried to quanti y the atigue strength in accordancewith the experimental results o the metal endurance andinvestigated the atigue ailure in railroad axles or GermanRailway Industry. His work also led to the characterizationo atigue behavior as the applied stress versus the cycles to

ailure and to the concept o atigue limit [ ].Basquin [ ] represented the nite li e region o the

Wöhler curve as log on the abscissa and log on the ordi-nate. Te Basquin unction can be expressed mathematically by

= ( )or

log = −log + log , ( )where and are positive empirical material constants.Obviously, log and are the intercept on the log axisand the constant slope o ( ), respectively.

Considering the existenceo atigue limit, Stromeyer [ ]modi ed ( ) by introducing an extra parameter as

log = −log − + log . ( )


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In cases where the optimum value o the parameter isnegative or insigni cant, it should be omitted since repre-sents the atigue limit stress.

o show the effect o stress ratio or mean stress onthe atigue li e, Walker [ ] proposed the equivalent stressmodel which is given by

log = −log − + log , ( )where

= 1 − . ( )Consider

= 2 1 + . ( )Substituting in ( ) with , then

= 2 − 2 , ( )where is a constant parameter.

Te stress-li e methods usually canbe divided into differ-ent categories depending on the stress analysis o the struc-tural details, mainly including nominal stress method, hotspot stressmethod, and effectivenotchstressmethod[ , ].

. . . Nominal Stress Method. As a common method or esti-mating the atigue li e o steel bridges, the nominal stressmethod has been widely used in most existent codes andstandards [ – ]. Tis method is based on a global consid-eration ocusing on the average stress in the studied crosssection according to the undamental theory o structuralmechanics. It is noted that the nominal stress is calculateddisregarding the local stress but involving the relative largestress o macrogeometric shape o studied component in the vicinity o welded joints. Te nominal stress can be deter-mined using linear elastic structural mechanics or simplestructural components or nite element method orrelatively complicated structures. Also, the nominal stress can bemeasured by use o strain gauges which are deployed outsidethe stress concentration eld o the welded joints.

In each code or standard, a variety o - curves relevantto speci c structural details and loading conditions are o great importance and necessity or atigue li e assessment o steel bridges by use o the nominal stress method. However,the nominal stress method is not suitable or the structural joint i the object detail is extraordinary complicated andincomparable to any classi ed joints, or the loadings arecomplex to make it difficult or impossible to determine thenominal stress [ ]. Moreover, it has an obvious drawback inthat it largely ignores the actual dimensional variations o aspeci c structural detail [ ]. Tere ore,as to some structuralcomponents o steel bridges, the atigue li e predicted by useo the nominal stress may be unreliable.

. . . Hot Spot Stress Method. An alternative method oratigue analysis o complicated welded joints is the hot spot

stress method which is more reasonable and accurate thanthe nominal stress method. Te International Institute o Welding (IIW) provides comprehensive rules and explicitrecommendations in computation o the hot spot stressinvolving the detailed process o experiments and modeling.Steel bridges are usually composed o lots o longitudinal and

transverse plate-type structural members with welded jointsat their intersections, or example, joints o main girdersand oor beams, oor beams and stringers in plate girderbridges, and longitudinal ribs and transverse ribs in steeldeck plates. Investigations on the atigue behavior o welded joints as well as undamentals o atigue strength assess-ment together with design rules and applications are numer-ous [ – ]. Te welded joints contain some orm o geo-metrical or microstructuraldiscontinuities, andthe weld toesin welded joints are the positions with the maximum localstresses where atigue cracks are most likely to occur. Tehot spot stress is the value o the structural stress at the hotspot usually located at a weld toe, which can be calculatedby multiplying the nominal stress by a stress concentration

actor (SCF) commonly obtained rom the nite elementanalysis or experimental measurements using strain gaugesor experiential ormulae [ ].

Numerical analyses have the distinct advantage o givingthe exact positions, directions, and magnitudes o highstresses and the patterns o stress distribution in the entirezone o the speci c joint being considered. When using the

nite element method to analyze the SCF, the structuralbehavior can be analyzed by a global nite element model(FEM). A part o the structure including the studied detail,that is large enough to prevent boundary interaction on stressdistribution at the welded joint with adequate boundary conditions, is extracted or a more detailed analysis. Tisselected area shouldbe newly modeled, in which themeshingis re ned to obtain enough ne meshes at the welded connec-tion provided with the boundary conditions rom the globalFEM calculation. Te local stress concentration at the weldtoe isheavily dependent, in physicalmodels, on the local weldpro le and, in numerical analysis, on the mesh re nement[ ]. Tere ore, it is necessary to nd a compromise betweenthe re nement o the meshing and the size in degrees o

reedom o the numerical model.When tests are per ormed and strain measurements are

used to determine the SCF, an elaborate and reasonableinstrumentation scheme o strain gauges is crucial [ ]. Teselectiono hotspot locations or instrumentationwith straingauges is improved and re ned based on experiences rom anumber o niteelement analyses o the typical details such asrib-to-diaphragm, rib-to-bulkhead, rib-to-stiffener, and dia-phragm-to-deck connections [ – ]. Te hot spot stress iscalculatedby extrapolation or regression o stress distributionoutside o the weld to the weld toe. For example, Puthli et al.[ ] investigated strain/stress concentration actors numeri-cally and experimentally on X, , and K joints using squarehollow steel sections and obtained parametric strain/stressconcentration actor ormulae using regression analyses.Fung et al. [ ] studied the SCFs o double plate rein orcedtubular -joints subjected to various types o basic loadingssuch as axial tension, axial compression, and in-plane and


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out-o -plane bending by using numerical and experimentalmethods. Other investigations can also be ound in Iida [ ],Karamanos et al. [ ], Gho et al. [ ], and Gao et al. [ ].

Te IIWrecommendations or determining thestructuralhot spot stress are based on the principle o sur ace extrapo-lation. Niemi [ ] and Niemi et al. [ ] gave detailed recom-

mendations concerning stress determination or the atigueanalysis o welded components and proposed distances o . and times plate thickness rom the weld toe and also

distanceso . and times plate thickness or coarser meshes.Yagi et al. [ ] proposed a de nition o hot spot stress or

atigue design o plate-type structures, and the hot spot stressshouldbe obtained bymeanso the linearextrapolation o thespeci c two points at 1.57 4√ 3 and 4.9 4√ 3 to the weld toe.Nonlinear extrapolation instead o the linear extrapolation isoccasionally applied by considering that the structural stressincrease in ront o the welded joint occurs with variousgradients and nonlinearities [ ].

Another method or determining structural hot spot

stress is through thickness-at-weld-toe method. Radaj [ ]demonstrated that structural hot spot stress could be eval-uated either by sur ace extrapolation or by linearizationthrough thepate thickness. Dong [ ] proposed an alternativestructuralhot spot stress computation methodcombiningthe

eatures o the sur ace extrapolation methods with those o the through thickness methods. Doerk et al. [ ] explainedand compared various procedures or evaluating structuralhot spot stress at different types o welded joints. Poutiainenet al. [ ] investigated the limits and accuracy o differentmethods or hot spot stress determination and comparedthem with nite element analysis results rom simple D andprecise D models. Xiao and Yamada [ ] proposed a new

method o determining structural hot spot stress in weldedconstructions based on the computed stress mm below thesur ace in the direction corresponding to the expected crack path.

Analysis and assessment o the hot spot stress withrespect to atigue have had a rather long history. Pioneeringinvestigations were made in the s by several researchersto relate the atigue strength to the local stress measuredat a certain point close to the weld toe [ ]. In s, thedevelopmento thehotspot stressmethodwith thede nitiono re erence points or stress evaluation and extrapolation atcertain distances away rom the weld toe was reviewed byvanWingerde et al. [ ], which was particularly success ul or

atigue strength assessment o tubular joints. First attemptsto apply the approach to welded joints at plates were seenin the early s, and CEN [] extended the hot spot stressmethodtoplate-typestructuresdueto the increasing demandalthough only limited guidance was provided [ ]. Up tonow, the hot spot stress method has been well accepted andrecommended by several national and international codesand standards [ , – ].

Little research has been per ormed on the applicationo the hot spot stress method to atigue damage evaluationo the welded plate joint o steel structures, especially orcable-supported steelbridge atigue evaluation[ ].Miki and

ateishi [ ] studied the atigue strength and local stress

or cope hole details existing in I-section beams by atiguetests, stress measurements, and stress analyses and proposeda simple equation or estimation o SCF based on the resultso nite element analysis which was veri ed by experimentalresults and con rmed to be accurate. Savaidis and Vormwald[ ] investigatednumerically andexperimentally the hotspot

stress and atigue li e o our different welded joints romthe oor structure o city buses under bending and tensionalcyclic loadings. Han and Shin [ ] derived a consistent anduni ed - curve by using the hot spot stress methodthrough a numerical and experimental analysis which can beapplied or atigue strength estimation and atigue design orgeneral welded steel structures. Chan et al. [ , ] reportedthat the hot spot stress method gave a more appropriate

atigue li e prediction than the nominal stress method or asteel suspension bridge.

. . . Effective Notch Stress Method. In contrast to the nomi-nalstressmethodandthe hotspot stressmethod, theeffective

notch stress method ocuses on initiation li e prediction or acrack at the root o a notch. Tis method was proposed by Radaj et al. [ , ] who were concerned with crack initiationand early growth phase on high-cycle regime using Neuberrule with a ctitious radius o mm or plate thicknesses o

mm and above. Zhang and Richter [ ] developed a new approach by considering the relationship between the stressintensity actor and the notch stress or numerical atigue li eprediction o spot welded structures using a ctitious radiuso . mm. Sonsino et al. [ ] investigated the applicability o our examples rom different industrial sectors in terms o notch stress concept with the re erence radius o mm orthick walled and . mm or thin walled welded steel con-

nections. Ayg ül et al. [ ] conducted a comparative study onve selected welded joints requently used in steel bridges toinvestigate the accuracy o three different stress-li e methods,that is, nominal stress method, hot spot stress method, andeffective notch stress method, and the results revealed thatthe effective notch stress method, despite its more efforts orboth modeling and computation, provides an inconspicuousimprovement in estimation o the atigue strength.

. .FatigueAnalysisUsing Fracture Mechanics Approach. Teracture mechanics approach is usually applied to predict the

propagation li e rom an initial crack or de ect. Te methodo linearelastic racturemechanics(LEFM) relates thegrowth

o an initial crack o size to the number o atigue cycles, .Te atigue crack growth is generally described by Paris’s rulewhich is expressed by Paris and Erdogan [ ]

= (Δ) , ( )where and are material-related parametersand the rangeo stress intensity actorΔ can be determined by Broek [ ]

Δ = ( )√ , ( )where ( ) is a unction o the crack geometry and is thestress range.


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Many investigations have been per ormed on bridge ati-gueconditionassessmentusing racturemechanicsapproach.Fisher [ ] illustrated more than twenty- ve case studieson atigue crack phenomena in steel bridges using ac-ture mechanics approach and other theories. Agerskov andNielsen [ ] carried out an investigation on atigue damage

accumulation o steel bridges under random loadings anddetermined the atigue li e o welded joints in steel highway bridges by a racture mechanics analysis. Applying a LEFMmodel to predict crack growth, MacDougall et al. [ ]quanti ed the differences in atigue li e o a short-span anda medium-span bridge under successive passages o either asteel-sprung vehicle or an air-sprung vehicle. Xiao et al. [ ]pointed out that lack o penetration zones o - mm resultedin low atigue strength o the buttwelded jointswith the aid o obtained experimental data o the structural components inKinuura Bridge and theoretical predictions based on LEFM.

. . Fatigue Analysis Using Strain-Li e Method. Te strain-li e method developed in the s is mainly concernedwith the crack initiation stage. It is used when the strain isno longer totally elastic but has a plastic component. Short

atigue lives in LCF regime generally occur under theseconditions. Tere have been some investigations on atigueper ormance assessment o steel bridges through low-cycle

atigue tests and theoretical strain-li e method [ , ]. Jesuset al. [ ] presented crack propagation atigue data rom vePortuguese ancient metallic riveted bridges, and the strain-li e atigue data were correlated using both deterministic andprobabilistic models. Up to now, only very limited amount o research hasbeen conducted on atigueli eassessmento steelbridges based on the strain-li e method, and the lack o suchinvestigations is mainly because most o the atigue issues insteel bridges pertain to HCF regime.

. . Fatigue Analysis Using Field Measurement Data. Whenthe stress-li e method is adopted or bridge atigue damageevaluation and li e prediction, the engineer must have themost realistic and precise load and resistance in ormation tomake an accurate atigue assessment, particularly when thelive load stresses are used in cubic equations [ ]. In thistype o analysis, a small variation in live load stress rangewill induce drastically different atigue assessment results.Analysis using computational models o load and structurecannot attempt to mimic the variation in stress range thata typical structural element will experience. Additionally, itwould be extremely time-consuming and almost impossibleto attempt to account or all o the variables in a conven-tional simulation analysis. Te only way to obtain precisein ormation that accounts or these variables is through the

eld measurement, where sensors are attached to the bridgeelements and the actual stresses and distribution o stressesthat the structural element experiences can be measuredand recorded. Consequently, it is considered that the eld-measured data would provide the simplest andmost accuratebasis or atigue assessment. Tis section provides a compre-hensiveoverview o atigue analysiso bridge structuresbasedon eld-measured data rom load-controlled diagnostic loadtesting and short-term in-service monitoring using NDE

techniques and long-term monitoring strategy dominated by SHM technologies.

. . . NDE-Based Fatigue Li e Assessment. As the traffic volume and truck weight continue to increase and as bridgeconditions continue to deteriorate, a lot o existing steel

bridges need to be strengthened, repaired, or reconstructedto insure an acceptable level o sa ety considering presentand uture traffic conditions [ ]. Furthermore, because o lack o unds and the high cost o reconstruction, NDEtechnology has been developed to improve the accuracy o bridge condition evaluation [ , ]. Among the methods,diagnostic load testing with controlled loadings and short-term in-service monitoring under normal traffic loadingscurrentlyare mainlyused and the atigue conditiono bridgesis then assessed with the obtained data and in ormation romthe deployed sensors and data acquisition systems.

Te load-controlled diagnostic load testing has theadvantages o using known loadings, which allows relatively

accurate quanti cation o the bridge response and the deter-mination o a airly comprehensive baseline model or abridge. Te limitation to this type o testing, asopposed to in-service monitoring, is that one must use some level o trafficcontrol during testing. Te time used or setup is longer,and the response represents only a snapshot in time. Teshort-term in-service monitoring, on the other hand, has theadvantages o not requiringtrafficcontrolduring monitoring,having a very rapid setup time, and recording the responsedue to ambient traffic, thereby providing statistical in orma-tion about actual responses and allowing the response to betracked over time. Te limitation o in-service monitoring isthat the weight and the classi cation o the truck loadings arenot speci cally known, and the limited data will not allow bridge parameters to be evaluated explicitly [ ].

Some investigations on bridge atigue analysis by useo NDE techniques have been made in recent years. Forexample, Hahin et al. [ ] presented the application o eldstrain data to condition assessment and prediction o the

atigue li e o feen highway bridges located in Illinois,and the results were urther used to study the signi canceo truck weight increase and traffic volume growth on the

atigue li e o the bridges. DeWol et al. [] evaluated theatigue li e ora variety o bridges using eld monitoring data

by a portable computer-based strain gauge data acquisitionsystem which has been extensively used in Connecticut toassist the Department o ransportation in evaluation andrenewal o the state’s bridge in rastructure and identi edcost-effective maintenance, repair, and replacement strategies[ ]. Peil [ ] studied the precision on li e cycle prediction o steel bridges under live loadings using strain monitoring atthe real critical points. Distortion-induced atigue problemsin steel bridges have been investigated by use o the eldmeasurement [ , ].

Chajes and Mertz [ ] discussed the diagnostic load testsper ormed at various stages throughout the process on deter-mining the circumstances leading up to the atigue crack andits cause and presented the temporary and permanent repairstrategies. Zhou [ ] proved that the atigue evaluation basedon eld-measuredstress range histogramsunder actual traffic


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loads was a more accurate and efficient method or existingbridges and applied this approach in assessing the remaining

atigue li e o aged riveted steel bridges. Ermopoulos andSpyrakos [ ] identi ed the structural components in needo strengthening or replacement or a th century railway bridgethrough staticanddynamic eld measurements aswell

as laboratory tests and proposed the strengthening schemesand predicted the remaining atigue li e o the bridge inits present condition and afer the suggested strengthening.Investigations into atigue evaluation o steel bridges by useo NDE techniques were also reported by Moses et al. [ ],Roeder et al. [ ], Abdou et al. [ ], Spyrakos et al. [ ],Alampalli and Lund [ ], and Malm and Andersson [ ].

. . . SHM-Based Fatigue Li e Assessment. o secure struc-tural and operational sa ety throughout the bridge li e-cyclesand issue early warnings on any deterioration or damage o bridges prior to costly repair or even catastrophic collapse,the signi cance o implementing long-term SHMsystems or

bridges has been increasingly recognized in USA [ – ],Europe [ – ], Japan [ , ], Korea [ , ], HongKong [ , ], Chinese mainland [ – ], and Canada[ – ], among others. A review o the literature indicatesthat there is a growing trend in incorporation o computer-and sensor-based long-term health monitoring systems intobridges especially or long-span bridges due to their largeinvestments, their signi cant roles in economics, and innovative techniques used to design and construct such bridges.

An important unction o SHM systems is to monitorstructural health and per ormance, as well as accurately estimating the actual status in atigue and remaining li e o the bridge [ ]. It has become an important issue o highresearch interest with the development o SHM systems orlarge complicated structures. However, little work on atigueanalysis and condition assessment o bridge structures basedon long-term monitoring data has been made in the pastdecade because SHM is a relatively new technology or appli-cations in civil engineering communities,andeven a compre-hensive de nition o SHM and the system design guidelineshave yet to be standardized; another important reason is thatsuch a complicated system has not been extensively installedin most o the bridges worldwide due to high cost.

However, investigations on atigue condition assessmentbased on long-term monitoring data still can be ound. Li etal. [ ] developed a methodology and strategy or atiguedamage analysis and li e prediction, and atigue conditionassessment o bridge-deck sections o the sing Ma Bridgewas carried out taking ull advantage o the on-line SHMdata. Connor et al. [ ] developed and implemented an in-depth instrumentation, testing, and monitoring program onthe Bronx-WhitestoneBridgeas parto a comprehensive ati-gue evaluation or the replacement orthotropic bridge deck.Xu et al. [ ] developed a systematic ramework or assess-ing long-term buffeting-induced atigue damage to a longsuspension bridge by integrating a ew important wind andstructural components with continuum damage mechanics-based atigue damage assessment method. Ye et al. [ ]presented a study on atigue li e assessment o the sing MaBridge using the standard daily stress spectrum method.

4. Reliability-Based FatigueCondition Assessment

In October , a paper entitled “Te Sa ety o Structures”appeared in the Proceedings o the ASCE. Tis historicalpaper was written by Freudenthal, and its purpose was to

analyze the sa ety actor in engineering structures in orderto establish a rational method o evaluating its magnitude. Itwas selected or inclusion with many discussions in the

ransactions o the ASCE [ ]. Te publication o this papermarked the beginning o structural reliability studies in theUnited States [ ]. Over thepast several decades, theconceptsand methods o structural reliability have developed rapidly and become more widely understood and accepted. Terehave been a lot o studies and applications [ – ] andcomprehensive books [ – ] on reliability-based structureanalysis.

Fatigue reliability evaluation is a very important task orthe design and management o bridges. For highway andrailway bridges, the techniques o atigue reliability havebeenapplied mainly in Mohammadi andPolepeddi [ ]andLukić and Cremona [ ]: (i) condition assessment and esti-mationo theremainingli etime o bridges,where probabilis-tic methods can be used to obtain estimates o the adequacy o the existing structure, need or increased inspection inthe uture to prevent ailure, and approximate remaining

atigue li etime based on projections o the uture loads, and(ii) development o probability-based design stress ranges

or atigue-critical bridge components, where accurate trafficload data can be acquired through weigh-in-motion (WIM)systems, rom which anextensiveamount o data are availableshowing distribution o loads by its time o appearance,transversal position, speed, number o axles, gross weight o axles, and distance between axles.

Most o the research work on reliability-based atigueanalysis has ocused on steel bridges. A comprehensiveliterature review on the existing atigue reliability approaches

or reassessment o steel structures, including railway andhighwaybridges, is available in Byerset al. [ , ].Te gen-eral approach oranalyzing reliabilityagainst atigue ailure is

rst to ormulate a mathematicalmodel, whether on the basiso mechanics or extensive observations o the phenomenon,which incorporates as many o the variables as practicalthat are known to affect atigue behavior. Te probabilisticand statistical analysis method then is per ormed within thisprovided analytical ramework.

. . Fatigue Reliability Assessment Using Stress-Li e Method.Fatigue load and resistance are two main variables whenthe stress-li e method is chosen or developing atigue reli-ability analytical models. Te atigue load model should bedetermined not only by magnitude but also by requency o occurrence which can be obtained by WIM measurements[ , ], and resistance model should be derived rom a loto atigue tests under varying amplitude loading [ ]. Usu-ally, the log-normal distribution and the Weibull distributionare used or load and strength probability distribution [ –

]. Murty et al. [ ] proposed a method to deal with thederivation o the atigue strength distribution as a unction


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o number o cycles to ailure. Zhao et al. [ ] developedan approach to determine an appropriate distribution rom

our possible assumed distributions o the atigue li e underlimited data. Lor én [ ] presented a model or calculatingthe atigue limit distribution based on the inclusion size.

Research efforts have been devoted by a number o inves-

tigators or modeling the stress range data by using varioussingle theoretical probability distributions. Beta distributionhas been suggested as a theoretical stress range distributionmodel to describe the eld data by Ang and Munse [ ] andWalker [ ]. Based on recorded stress range histograms,Yamada and Albrecht [ ] presented that the probability distribution o dimensionless stress range normalized by themaximum stress range could be expressed by a polynomialdistribution. Inorder to select a singlenondimensional math-ematical expression that can be used to represent the stresshistogram o highway bridges, a continuous two-parameterRayleigh curve wasused to model theprobabilitydistributiono stress range in the atigue test program [ ]. Wirsching[ ] assumed that the long-term stress range data wereWeibulldistributedandMadsen [ ] took thenominal stressrange as a random variable with normal distribution. Park et al. [ ] success ully expressed the stress range requency distributiono block loadingsbya log-normalprobability distribution. Ni et al. [ ] proposed a method or modelingo the stress spectrum using nite mixture distributions andlong-term monitoring data o dynamic strain.

Tere have been a number o studies on the reliability analysis or atigue damage and li e prediction o bridges[ – ]. Imam et al. [ ] presented a probabilistic atigueassessment methodology or riveted railway bridges andapplied this method to a typical, short-span, riveted UKrailway bridge under historical and present-day train load-ing. Kwon and Frangopol [ ] per ormed atigue reliability assessmento steelbridges using theprobabilitydensity unc-tion o the equivalent stress range obtained by monitoringdata. Ni et al. [ ] developed a atigue reliability model or

atigue li e and reliability evaluation o steel bridges withlong-term monitoring data, which integrates the probability distribution o hot spot stress range with a continuousprobabilistic ormulation o Miner’s damage cumulative rule.Researchefforts on probabilistic atigue li eestimation o steelbridges by use o a bilinear - approach can be ound inKwon et al. [ ] and Soliman et al. [ ].

. . Fatigue Reliability Assessment Using Fracture Mechanics Approach. A signi cant number o investigations on atiguereliability assessment o bridges have been conducted by useo the racture mechanics approach [ , , ]. Based on

eld-measured data rom nondestructive inspections, Zhaoand Haldar [ ] proposed a LEFM-based reliability modelconsidering uncertainties in different aspects includinginitial crack size, crack aspects ratio, material properties, andnumber o stress cycles. Lukíc and Cremona [ ] presenteda probabilistic assessment procedure o steel componentsdamaged by atigue using a racture mechanics-based crack growth model, which was applied to a transverse-stiffer-to-bottom- ange welded joint o a typical steel bridge.Righiniotis and Chryssanthopoulos [ ] conducted an

investigation on the application o probabilistic racturemechanics approach to predict the atigue li e o welded joints with initiation cracks through a bilinear crack growthlaw. Pipinato et al. [ ] applied a LEFM approach in a pro-babilistic content to evaluate the atigue reliability o steelbridges in the presence o seismic loading. Wang et al. [ ]

presented a procedure or assessing and updating the atiguereliability o existing steel bridge components using nondes-tructive inspection techniques and Bayes theorem based onthe probabilistic racture mechanics method. Guo and Chen[ ] per ormed an investigation on atigue reliability assess-ment o welded details o a -year-old steel box-girderbridge integrating the LEFM approach and eld dataobtained rom the long-term stress monitoring.

5. Conclusions

Tis paper provides a summary o research developmentsin the area o atigue li e assessment o steel bridges. Basedon the overall review o atigue-relevant theories, methods,technologies, and applications, the ollowing conclusions aremade: (i) the nominal stress-li e method is widely used

or atigue-related design and evaluation o steel bridges;however, theestimated atigue li e by useo thehotspot stressmethod has been proved to be more accurate and effective;(ii) eld measurement data will provide the most accuratein ormation orderivation o thekeyphysicalparameters andtheir statistical properties in atigue condition assessment,andthere ore it is crucial and desirableto develop data-drivenmethods or atigue li e assessment o steel bridges; and (iii)in recognition o the uncertainties and randomness inherentin the nature o atigue phenomenon and measurementdata, investigations or probabilistic atigue li e assessmento steel bridges are deemed to be reasonable. By so doing,reliable atigue condition assessment can be achieved orinstrumented steel bridges and rational strategies on bridgeinspection and maintenance can be executed in accordancewith the correlativity between reliability indices and prede-

ned inspection and/or maintenance actions.

Conflict of Interests

Te authors declare that there is no con ict o interestsregarding the publication o this paper.

Acknowledgments

Te work described in this paper was supported by theNational Science Foundation o China under Grant nos.

and U , the Research Fund or the DoctoralProgram o Higher Education o China under Grant no.

, the Fundamental Research Funds or theCentral Universitieso ChinaunderGrantno. QNA ,and the Department o Education o Zhejiang Province,China, under Grant no. Y .

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