Eurocodes for the design of bridges.pdf

7/22/2019 Eurocodes for the design of bridges.pdf

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Eurocodesforthedesignofbridges

TheEuropeanStandardFamily

Trafficactionsonbridge

Illustrationofbasicelementdesign

W.Hensen,M.Feldmann,G.Hanswille,G.Sedlacek

1. Introduction

(1) Sustainabilityisakeyissueforthedesignofbridgesincludingsteelbridges.Themost

importantsustainability indicatorforbridges isdurabilitywith itseffecton lifecycle

costsforanintendedservicelifeofabout100years.

(2) Durabilityisproducedbyvariouselementsincluding

asustainabledefinitionoftheserviceconditionincludingthebridgeloading,

choiceofthebridgesystem,itsstructuralandnonstructuralcomponentsand

productsandappropriatedetailingalsoconsideringfatigue,

designandexecutionforaqualityofstructurethateffectsdurability.

(3) Therefore this report does not focusonlyon design rules in Eurocode 3, but also

comprisestheotherelementsoftheEuropeanStandardFamilyaffectingdurability,amongstwhichEurocode3playsanimportantrole.

(4) AccordingtothegeneralconceptoftheEurocodesthesecodesconsistofaEuropean

part (the ENcodes) andNational Annexes to the ENcodes, that complement the

harmonizedEuropeanENcodesbyNationalchoices.

(5) In conclusion thepracticaldesignof abridgeon a certain territory isnotpossible

withouttheuseoftheNationalAnnexvalidforthatterritory.

(6) ThechoicesthatarecontainedintheEurocodescomprisethefollowing:

1. NationalresponsestoopeningnotestoEurocoderulesthat includetechnical

classesor factors related to safety, climatic, culturalandotheraspects (see

GuidancePaperLUseandapplicationofEurocodes).

2. Responsetoinformativeannexeswithtechnicalrulesandsetsofalternative

technical rules in the main codetext for which no agreement could be

achievedduring thecodewritingphaseand fromwhichCEN/TC250expects

eitherNationalacceptanceorbetterfoundedNationalAlternativesthatcould


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be used by CEN/TC250 for further harmonisation of the rules and the

reductionofcomplexityandvolume.

3. Non conflicting complementary informations, (NCCIs) that comprise

Nationalchoicesofadditionaltechnicalrulesnecessary for fillinggaps inthe

Eurocodes and tomake them fullyoperable.From theseNCCIsCEN/TC250

expectsimportantimpulsesforthefurtherdevelopmentoftheEurocodes.

(7) Therefore in this report reference is made to the Nationally Determined

Parameters, which are recommended in the Eurocodes for the design of Steel

bridges and in some cases to the draft German National Annex, that may be

considered as an example for the variations that may be induced by the many

NationalAnnexesintheEU.

2.

Contents

of

the

report

(1) Figure1givesthestructureofthereportwithashort introductiontotheEuropean

StandardFamily,theaspectofdurable loadassumption inparticularfromtrafficon

roadbridges,anexamplehow toovercomeshortcomings in theEurocoderules for

the technicalspecifications for thedeliveryofbearings, thebackgroundanduseof

EN 1993110 for the choice of steel to avoid brittle fracture and the core of the

designofsteelelements inbridges,thatencompassesthestabilityrules,thefatigue

rulesandrulesfortensionelements,e.g.forstayedcablebridge.

Dissemination of information for training Vienna, 4-6 October 2010 2

1. The European Standard Family and Steel bridges

2. Load assumptions for steel bridges

3. Modelling of steel bridges

4. Specification of bearings5. Choice of steel

6. Design of bridge elements

6.1. Stability rules

6.2. Fatigue rules

6.3. Rope structures

LIST OF CONTENTS

Figure1:


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3. GeneralremarkstotheEuropeanStandardFamilyforthedesignofsteelbridges

(1) Steel bridges for roads comprise full steel bridges with steel decks (orthotropic

plates)andsteelconcretecompositebridgeswithaconcretedeck,seeFigure2and

Figure3.


CROSS SECTION OF A BOX GIRDER BRIDGE WITH ANORTHOTROPIC DECK

Figure2


HASELTALBRCKE SUHL

Figure3


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(2) Inbothexamplesthemainstructureisastiffenedboxgirderwithcantileveringplates

withtheassemblyofsectionsprefabricatedintheworkshopononeshoreonsiteand

erectionbylaunching.

(3) There is a criticism that the design of bridges would become more and more

complicatedbecauseofthelargeamountandlargevolumesofthestandardsmaking

theuserslifedifficult.

Asthedetailingofrulesthatproducesthevolumesishoweverrequiredbytheusers

therearetwopossibilitiestocreateabettersurvey:

1. to develop appropriate navigation systems through the standards (as

practicede.g.fortheENstandardsforenergyefficiency),

2. to develop consolidated handbooks from the standards for particularapplication fieldsase.g.bridges, inwhich the technicalrulesandreferences

from the Eurocodes are assembled in a way suitable for watertight

contracting and security of use. Examples for such handbooks in bridge

designare

No.1: Basisanddesignofactionsforbridges

No.2: Designofconcretebridges

No.3: Designofsteelbridges

No.4: Designofcompositebridges

aspracticedinAustriaandGermany.


actionsEN 1990

G/Q-values

Safety aspects

EN 1990-A2

Load combination EN 1991-1-1

EN 1991-2

EN 1991-1-4

EN 1991-1-5

Self-weight

Traffic actions

Wind actions

Thermal actions

design

EN 1993-1-1

Seismic designEN 1998-3

Imperfections EN 1993-2

EN 1993-1-8

EN 1993-1-11

EN 1337

General

Connections

Ropes

Bearings

EN 1993-1-5

EN 1993-1-5

EN 1993-1-9 Fatigue

Stability of plates

execution

Materials

Welding

Corrosion protectionEN 1090-2

EN 1090-2

EN 10025 Prefabrication

Site work

Tolerances EN 1090-2

EN 1337

EN 1090-2

productconformity

CE-marking

TraceabilityEN 1337-6

EN 1090-2 Inspection

Maintenance EN 1337-10

EN 1090-2

NAVIGATION THROUGH STANDARDS

Figure4


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(4) Figure 4 shows a shortened example for a navigation system related to actions,

design,executionandproductconformitythatallowstheusertogoogletherulehe

needs.


EN 1990Eurocode: Basis of Design

Eurocode 1: Actions on Structures1-1 Sel f weight1-2 Fire Actions1-3 Snow1-4 Wind

1-5 Thermal Actions1-6 Construction Loads1-7 Accidential Actions2 Traffi c on br id ges3 L oads fr om cr an es4 Silo loads

EN 1991

Eurocode 2: Concrete structuresEurocode 3: Steel structuresEurocode 4: Composite structuresEurocode 5: Timber structureEurocode 6: Masonry structures

EN 1992 to EN 1996

EN 1997 and EN 1998

Eurocode 7: Geotechnical DesignEurocode 8: Design in seismic areas

EN 1999Eurocode 9: Aluminium structures

SURVEY OF THE EUROCODES

Figure5

(5) Figure5givesasurveyonallEurocodesfromwhichtheusershouldselectthoserules

relevanttohisdesignworks:

UnderthegeneralprinciplesinEN1990 BasisofDesign thereareononesidethe

variousgenericrules foractions(assnowandwind)andthespecificactionrulesas

e.g. traffic loadsonbridgesandon theotherside thematerialdependantrules for

variousmaterialsand typesof structures.EN1997 GeotechnicalDesign andEN

1998 Design inseismicareas comprisebothgenericrulesforactionsandspecific

rulesforresistancesandmaterials.


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Standardsystemf

or

steelstructures

hEN

product standards

for st eel materials,

semi- finishedproducts etc.

EN 1090 Part 2

Execution of

steel structures

EN 1090 Part 1 Delivery Conditio ns for prefabricated steel components

Eurocode: EN 1990 Basis of structural design

Eurocode 1: EN 1991 Actions on structures

Eurocode 3: EN 1993 Design rules for steel structures

HSS up to

S700

1.12

1. THE EUROPEAN STANDARD FAMILY AND STEEL BRIDGES

Figure6:

(6) Figure 6 shows theorganisationof the familyof standards for the designof steel

bridges.

TheumbrellastandardforDeliveryConditionsforprefabricatedsteelcomponents

ontheglobalmarketwithapartfortheconformityassessmentis EN1090Part 1.

Thisparttakesreferenceto

hEN product standards that give product properties from testingmethods

definedbystatisticalcharacteristicsthataresuitableforareliabledesign,

theEurocodesthatgivedesignrulesboth forprefabricatedcomponentsand

forstructuralworks,

EN10902thatcontainstherules forexecution intheworkshopandonsite

withrulesforgoodworkmanship,tolerancesetc.

(7) Eurocode3comprises inasimilarwayastheactioncodegenericdesignrules in its

centralpart1addressinge.g.platebucklingandfatigue,andspecificadditionalrules

inperiphericapplicationpartsasforbridges(Eurocode3 Part2),thattakereference

tothegenericrulesinPart1.


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actions

G/Q-values

Safety aspects

Load combination Self-weight

Traffic actions

Wind actions

Thermal actions

design

Seismic design

Imperfections General

Connections

Ropes

Bearings

Fatigue

Stability of plates

execution

Materials

Welding

Corrosion protection

Prefabrication

Site work

Tolerances

product

conformity

CE-marking

Traceability

Inspection

Maintenance

designer

contractor

Tasks for designer and contractor


Figure7:

(8) Inthisreportonlyrulesforactionsandfordesignareaddressedasdemonstratedin

Figure7,whereasrulesforexecutionandproductconformitythataremainlyusedby

thecontractorsarenotdealtwith.


Design rules for steel bridges in Eurocode 3


Figure8

(9) Figure8gives thedesign rules inEurocode3whichare relevant for thedesignof

steelbridges.


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ThecontrollingpartfordesignisEurocode3 Part2,withreferencetoEurocode3

Part 11, in particular to general rules for structural analysis, crosssectional

verifications, use of imperfections for stability checks e.g. flexural buckling, and

lateral torsional buckling, to Part 15 for plate buckling, to Part 18 covering

connections,toPart19forfatigue,toPart110forchoiceofmaterialandtoPart1

11forropestructures.

(10) EN19932hasanAnnexCwithrecommendationsforthedesignandtheexecutionof

orthotropicsteelbridgedeckscoveringnow50yearsofexperiencewithdurabledeck

plates,thatmaymakespecificnumericalfatiguechecksunnecessary.

(11) EN19932containsalsotheannexesAandBforthepreparationofspecificationsfor

the

delivery

of

bearings

and

transition

joints,

for

which

EN

1990

Annex

A

2

did

not

give specific rules. These annexes are material independent so that they are

applicable to concrete, steel andcompositebridges.Therefore in the future they

willbe transferred toEN1990,and the tentative titlesAnnexE1andE2havebeen

agreed.

(12) These new Annexes should in particular contain appropriate rules for the

representative values of actions and their combinations to give design values of

forcesandmovementsthatareincompliancewiththeevaluationsofmeasurements

as obtained from many decades of use; the values now recommended in the

Eurocodeswouldproducemovementsthatareintherangeof1.52.0ofthevalues

experienced in the past and alsowould not be suitable for the specification of

bearingcharacteristicsfromanintegralanalysisofthetotalsystemofsuperstructure,

bearings,piersandfoundations.

(13) ThereforethedraftofGermanNationalAnnexrelatedtoRequirementsforbearings

and transition joints is related to the future Annexes E1 and E2 and contains a

proposalthatpreventstheproblemsasdescribedabove.


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Limit State ConceptULS Ed RdSLS Ed CdFatigue E c

Choice of materialbased on fracture mechanics(EN 1993-1-10)

Stability of members and platesSingle -value for combinedactions,FEM-methods(EN 1993-1-1) (EN 1993-1-5)

Fatigue assessments unlessrecommended details are used

(EN 1993-2) (EN 1993-1-9)

Basic features of design rules for bridges


Figure9

(14) ThebasicassessmentsthatabridgedesignerhastoaccomplisharelistedinFigure9:

CheckscomprisetheLimitStatesULS,SLSandFatigue.

A particularity of steel structures exposed to external climate actions and

fatiguefromtraffic,windandrainisthechoiceofsteeltoavoidbrittlefailure.

Another particularity is the use of thinwalled slender components, which

needstabilitychecksforoutofplanestabilityaslateraltorsionalbucklingand

platebuckling,suitableforcomputeraideddesign.

Fatigue assessments are necessary because of the fatigue effects of traffic

actions,unlessstructuraldetailssuccessfully timetestedareused thatneed

nofurthernumericalfatiguecheck.

4. Howtogetasustainableloadingmodel

4.1 Loadingmodeland100yearsofservicelife

(1) The loadingmodel LM1 as specified in EN 1991Part 2 gives a European uniform

geometric pattern of concentrated loads and uniformly distributed loads the

magnitudesofwhichhavebeendecidedtoleavethemtothechoiceofeachMember

Statetoobtainasustainableloadingmodel,seeFigure10.


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900 kN

500 kN

275 kN

11,0 m

Load-model LM1

2. LOAD ASSUMPTIONS FOR STEEL BRIDGES

Figure10

(2) Theloadingpatternaswellastherecommendedvaluesfortheloadsoriginatefrom

acommonEuropeanstudymadeunder thechairmanshipofH.Mathieu in the1st

phaseandProf.J.A.Calgaro inthefinalphase,thatwascarriedoutbyspecialistsof

various EUmembers on the basis of measurements in the various countries

undertakeninthelate1980ths.

(3) Thecompositionof theroad traffic in theHighwayParisLyonatAuxerrehasbeen

decided to be the statistical basis for defining recommendations for characteristic

values,asthiscompositionseemedtoberepresentativeforfuturedevelopments in

allEurope.

(4) Thecharacteristicvaluesweredefinedwithareturnperiodof1000yearsinsteadof

theusualvaluesof50yearsbecauseof theprevailingrequirementofserviceability

onthislevelandsustainabilityofdecision.

Whereas a 50 yearsreturn periodwould havemeant a98%fractileof the annual

distributionofextremevaluesinthemean(i.e.for50%ofthebridgepopulation),the

1000yearsreturnperiodmeansa98%fractileoftheannualdistributionofextreme

valuesfor95%ofthebridgepopulation.

(5) TheresponsesofMemberStatesintheirNAsareexpectednottobehomogeneous,

because


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trafficconditionsareveryregional,

some countries use extraordinary loads in addition to the standard load

model,

somecountriesuseloadclassesfortheirroadnetwork.


1000 kN

600 kN

300 kN

11,0 m

12

6

3

3

Load-model LM1 (draft German NA)


Figure11

(6) Anexampleforaresponse isthedraft loadingmodel intheGermanNAasgiven in

Figure11.Itreflectsthefollowingconditions:

1. All values are equal or above 1.0 because the future trends in traffic

developmentsmust be taken into account. In comparing the characteristic

vehicleweightsforalengthof11mtheincreaseisabout10%.

2.

The

values

of

the

uniformly

distributed

loads

are

increased

by

1.30

except

forthesecondheavylanewheretheincreaseisby2.40.

This isdue to the resultsofevaluationsof trafficmeasurementsperformed

duringthedraftingworksandexplainedhereafter.

3. The increase of about 1.30 is justified by simulations of future traffic

compositions (including 60 t modular heavy vehicles) taking account of

rubbertrainswithafreightvolumesubstantiallylargerthanusedtodayand

withasmarterfreightmanagement.

(7) ThisexampleisspecificforGermanybeingthelargesttransitcountryatthecrossing

pointofNorthSouth andEastWesttrafficandwithlimitedcontrolsontheroads.


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4.2. Backgroundof the loadmodel LM1andof the recommended characteristic load

values

(1) The statisticalbackgroundof trafficmeasurementson thehighway inAuxerrehas

beendocumentedasgiveninFigure12.

(2) Ithasbeenusedwithotherstatisticaldatatoperformdynamicnumericalsimulations

withbridgesofvariousinfluencesurfacestoobtainarealisticviewonthestatisticsof

actioneffectsinthebridges.Tothisendthedynamicbehaviourofvehicleshasbeen

modelledbyrigidbodieswithnonlinearsprings,dampersandfrictionelementsand

thesurfaceroughnessof theasphaltwasartificiallygeneratedwithPowerSpectral

DensityclassificationsaccordingtoISOTC108,seeFigure13.


Statistical distribution of characteristics of vehicles


Figure12


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Modelling of vehicles and surfaces


Figure13


Modelling of bridges


Figure14

(3) Bridges were modelled as elasticmasssystems with an eigenfrequencyspan

characteristicgiveninFigure14.ThisFigurealsogivestheresultsofmodelcalibration

withtestscarriedoutatEMPAZrich.

(4) The results of the simulations are given in Figure 15 for the case of midspan

momentsofa three spancontinuousbridge.Apparently theeffectsof loadmodel


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LM1aresafesided inthiscasetocope forotherrequirementsfromother influence

lines.


Load-model and simulations


Figure15


Dynamic effects


Figure16

(5)

A

by

product

of

the

simulations

is

a

comparison

of

static

and

dynamic

action

effectsasgiven inFigure16.Thedistribution linesshowthatdynamiceffectscause


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anadditional M value (constantshift) rather thananamplificationbyadynamic

factor.ThatisthereasonwhydynamicfactorsareincludedinloadmodelLM1.

4.3 Reliabilityanalysisandpartialfactors

(1) Reliability analysis of loadmodel LM1was performedwith twomedium spanned

steelbridgeswithorthotropicdecks thatwerebuilt inGermanywith theNational

LoadingCodeDIN1072,seeFigure17.


K 210 K 138

Reference bridges for reliability analysis


Figure17


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Definition of target -value


Figure18

(2) A reliabilityanalysison thebasisof the statisticsof the traffic inAuxerre and the

statistics of largescale tests used to define characteristic values of resistancies in

Eurocode3givesthe values(reliabilityindices)asplottedinFigure18.

(3) TheFigureshowsthattheminimum valuefoundis =6.00.Thiswasthenused

asthetargetvalueforaprobabilisticdesignofbridgeswithvariousinfluencelinesto

identifyapartialfactor G fortheloadmodelLM1.


P r o b a b i l i s t i c d e s i g n E C 1 - P a r t 2 L o a d M o d e l

L M

QM

r eq u i r ed W

3 5.1

1 0.1

=

=

=

G

M

GG

M

r eq uy

Q dM

WfM

w h e r e L M

QQQ dMM =

LM

Q

Q d

QM

M=

Definition of Q-value


Figure19


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(4) Figure19givesthemethodforidentifying Q [Bez]:

Theprobabilisticdesigngives forvariousshapesof influence linesandspans

theresistances requiredW ofthemaingirdersthatcomplywith =6.00.

Inusingthedefinitions:

yf = yieldstrength

GM = momentforpermanentweightsasdefinedintheEurocodes

G = 1.35

M = 1.10

adesignvalue QdM canbedefinedfromtheprobabilisticdesignononehand.

In usingon theotherhand loadmodel LM1 themoment caused by traffic

loads LMQM can be determined and the design value is defined by

LM

QQQd MM = .

Fromacomparisonof QdM fromthetworoutesthevalue Q isobtained.


Q-values from LM1


Figure20


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Figure21

(5) Figure 20 gives the distributions of Q values obtained in this way for various

influence lines,spansandroadwidths. Itshowsthe largescatterofvaluesandalsothat Q =1.35isthemaximum.

(6) Figure 21 demonstrates what happens if in the load model LM1 the uniformly

distributedloadinlane1isslightlyreducedandinlane2enhancedbyafactorof2:

Thescatterof Q issmallerandthemaximumvaluesareintherangeof1.25,sothat

M couldbereducedto M =1.00.

(7) Thiseffectwasoneof the reasons for thechoiceof values in thedraftGerman

NA.

4.4 Tendencyoftrafficdevelopment

(1) Figure 22 gives a forecastof the year 2000 for the future developmentof freight

volumeofterrestictrafficthathasbeenexceeded in2010byfar.


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(2) Figure23givesthedevelopmentofrequestsforpermanenttravellingpermissionsfor

heavyvehiclesexceedingthelegalweightlimits,resultinginabout100requestsper

day.


Forecast of freight-volume


Figure22


Development of permits for heavy vehicles


Figure23


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(3) Figure24gives the vehicleandaxle loadsandaccumulatednumberof vehiclesas

measuredbyweighinmotion(WIM)methodsinanaccesshighwaytoRotterdamin

theNetherlandsfor1year.


Results of WIM-measurements in NL


Figure24

(4) Allthesemeasurementsshowthat

1. therecommendationsforLM1arenotovercautious,

2. therearetendanciestoincreasethetrafficloadsbydevelopinglargervehicles

toreduceCO2emissions,

3. a clear picture of a future loadmodel can only be obtained where clear

decisionsfromtransportpoliticsaremade.Suchdecisionsshouldnot ignore

the large impactofsuchdecisionsonthesustainabilityofthe loadingmodel

fortheexistinginfrastructure.

4.5 TheloadmodelFLM3forfatigueverifications

4.5.1 General

(1) Anumericalmeans toassessdurability is the fatigueassessment, that requires the

definitionofthetwodimensionalfatigueactionsintermsofapairofvalues:

the fatigue load, in general given with a frequency distribution or as a

constantdamageequivalentload,

thenumberofloadreversalsintherequiredservicetime.


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(2) EN19912specifiesadamageequivalentvehicleFLM3withasymmetricgeometric

loadingpattern,thatcontainstwotandemaxleloadswithanaxleloadof120kNand

avehicleloadof480kN.

EN19912alsogivestheannualnumberofheavyvehiclesdependingonthecategory

ofhighway,Figure25.


Fatigue load model specified in EN 1991

480 kN

Traffic Category Number of heavy vehicles N

1: 2-Lane Highways with a high rate ofheavy vehicles

2 106/ a

2: Highways and roads with a mediumrate of heavy vehicles

0,5 106/ a

3: Main roads with a low rate of heavyvehicles

0,125 106/ a

4: Country roads with a low rate ofheavy vehicles

0,05 106/ a

Number of expected trucks

per year for a single lane

Fatigue loading model FLM 3


Figure25

(3) Thisdamageequivalentvehiclerepresentsacertainfrequencydistributionofvarious

heavyvehicles in the trafficspectrum,evaluatedwith theslopem=5of the fatigue

resistance lines. For application in numerical fatigue assessments, which are not

based on fatigue damage (two dimensional), but on stressranges only (one

dimensional),themodelisusedinthefollowingway:

The stress range minmaxmax = is determined from the extreme

positionsofthevehiclesonthestaticinfluencesurface,

the values max aremodifiedwith equivalent factors fat and to take

accountofdynamiceffects and the specific characteristicsof the spectrum

consideredintheproject.

(4) Figure 26 gives the concept for this fatigue assessment, that usually works with

partial factorsFf

andMf

,dependingon the safety conceptapplied.Usually the

conceptofDamagetoleranceisused,whichrequires,thatanyfatiguedamage,i.e.

the formation and growthof cracks, canbedetected in regular inspectionsof the


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structure,beforethedamageattainsasizecriticalfortheultimateresistanceofthe

structure.


Conceptforfatigu

eassessmentwith

equivalentconsta

ntamplitudestressranges

MffatFf /

m ax

s a f e t y f a c t o r

f o r f a t i g u e s t r e n g t h

s a f e ty f a c to r

f o r f a t i g u e l o a d

d a m a g e e q u i va l e n t

i m p a c t f a c t o r

d a m a g e e q u i v al e n c e f a c to r

r e p r e se n t in g t h e s p e c t ru m

m a x im u m s t re s s r a ng e f ro m

E C 1 - 2 l oa d m od e l

r e fe r e n c e f a t i g u e s t r e ng t h

a t 2 1 0 c y cle s6

c

crack size a

time

critical

crack

size acrit

detectable

cracksize a0Ff= 1.00

Mf= 1.00 1.15 for damage tolerance

Mf= 1.25 1.35 for safe life method

Assessment method for FLM 3

Inspection interval


Figure26

(5) The fatigueresistances c arebasedonconstantamplitudetestswith largescale

specimens,thatcontainallfeaturesofweldedstructures(discontinuitiesandresidual

stresses). Figure 27 gives an example for detail categories c as specified in EN

199319andevaluationsoftestresultsthatsupportthechoiceof c made inEN

199319.

Thecomparison shows that for somedetails theremaybea large scatterof tests,

fromwhichthechoiceshavebeenmadeandthatforotherdetailsthebasisoftestsis

rathersmall.

Theremaybealsotheproblem,thatfordetailschoseninaprojecteitherthefatigue

loading or the fatigue resistancemay only be roughly estimated, so thatways of

fatigueassessmentotherthanbythenumericalwayarepreferred,e.g.prescriptive

rulesforfatigueorsubstitutiverulesforserviceability.


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Fatigue details welded attachments and stiffeners

EN 1993-1-9 - Fatigue resistance


Figure27

4.5.2. Examplefordescriptiverulesforsufficientfatigueresistance

(1) Anexample for thederivationof a descriptive rule for achieving sufficient fatigue

resistanceisgiveninFigure28.Incomparingthemomentresistancesofmaingirders

resultingfromULSverificationswithLoadmodelLM1andfromfatigueassessments

with Loadmodel FLM3 all for a certain minimum fatigue resistance, e.g. c =

71MPa,acertainmaximumspanlengthcanbedeterminedwherefatigueisnomore

relevant.


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Required moment of inertia from ULS and fatigue design for detail

category 71

= 1 ,0

= 0 , 8

U L S

Fat igue

S p a n L [ m ]

MomentofResistanceW/L[cm2m/m]

Span limits for fatigue design


Figure28

(2) Soadescriptiverulecouldbe

tospecifyaminimumrequirementforthefatigueresistanceofalldetails,e.g.

c =71MPa,

todefineaminimumspan length fromwhichonnumericalassessmentsare

necessary.

(3) Figure29givesanotherexamplefordescriptiverulesforcertaindetails. Inthiscase

theconnectionofhangersoftiedarchbridges,forwhichvariousdetailsarecommon

couldbestandardisedinsuchaway,thatfatiguefrom:

vortexinducedvibrations

rainwindinducedvibrations

fatiguefromimposeddeformationsfromthepassingoffatiguevehicleonthe

bridge

aretakenintoaccount.


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Joint for hanger

Recommendations for durable detailing

Alternatives for joints of hangers:

optimised joint:

continuously increasing stiffness (K90)

low curvature from bending end of hanger with hole and inclined cut

low stresses at end of hanger for

K50

ratio of inclined cut and connecting plate

avoiding of stress peak at end ofhanger


Figure29


1

2

4

3

Hanger connection for arch bridges

Substitution of fatigue checks for critical details


Figure30

(4) Figure30givessuchanexampleforastandardizedsolutionthatmaybedefinedby

geometric descriptions only. The background of these geometric descriptions are

fatigue assessments for the critical hot spots , , , that have been

undertakenforalargevarietyofbridgestoprovetheirsafety.


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(5) Aparticularcasefordescriptiverules istheorthotropicsteeldeckofbridges,see

Figure31.Themostcriticalhotspotforsuchplatesistheweldedconnectionofthe

deckplatetothetroughsortothewebsofthecrossbeams.


Standard orthotropic steel deck with continuous stringers with

cope holes in the web of the cross beam

Substitution of fatigue checks by structural detailing

rules


Figure31


Structural detailing for deck plate

design l ife load model 4without layer < 10 years

asphaltic

sealing

PmB 45

thermosetting

resin

PmB 25

30 - 50 years

70 - 90 years

connection of deck plate to troughs

Recommended details of orthotropic deck

75

12

300 300 300

HV HV HV14

fr t = 6 mm


Figure32

(6) The fatigue loading model FLM3 is not applicable for verifying these hot spots,

becauseitdoesnotsufficientlymodeltheeffectsofthetyrepressureofthewheels.


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Alsotheanalysismodelforfatigueisnotsufficient,ifitisrestrictedtomodellingthe

steelstructureonly.

(7) Figure32demonstrates inwhatway the steeldeckadhesivelyconnectedwith the

asphaltlayerisaffectedbythestiffnessofthelayeranditssensitivitytotemperature

andloadingfrequency.

TakingPolymermodifiedBitumenPmB45intoaccountproducesanenhancementof

servicelifebyafactorof3to5andPmB25generatesanenhancementbyafactorof

7to9.

(8) ThereforeAnnexCtoEN19932givesprescriptiverulesforthemostcriticaldetailsof

orthotropicplates,e.g.deckplate thickness,distanceoftroughs,weldpreparations

for

welded

joints

of

stiffeners

etc.

to

secure

a

sufficient

fatigue

life.


Structural detailing for cross beams

tLtrough = 6 mm

tweb = 10 - 16 mm; verification of net web section requiredhcrossbeam 700 mm

tSteg

h

75

12

T

25> 0,15 hT h

QTr


Figure33

(9) Anexampleforthestructuraldetailsdealtwith inAnnexCisthe interconnectionof

troughs andwebs of crossbeams according to Figure 33 and the definition of a

minimumdepthof crossbeamsandminimum thicknessofwebplate toavoid the

formation of cracks at the cutout forwhich a toothassessment in the critical

horizontalsectionbetweenthecutoutsisnecessary.


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28

4.5.3 Examplesforindirectfatigueassessments

(1) A particular protection aim for orthotropic steel decks is to avoid cracks in the

asphaltlayer that could lead to corrosion of the deckplate and in case of

disintegrationofthelayertosecurityproblemsoftheroadusers.

(2) Thecausesofsuchcracksare

insufficientstrainabilityoftheasphaltinparticularduringwinter,

excessive flexibility of the deckplate in particular due to differential

deflectionsofthetroughs,seeFigure34.


Potential positions of cracks in the asphalt layer

Durability of asphalt layer


Figure34

(3)

From

an

evaluation

of

the

ratio

of

the

frequency

of

occurrence

of

cracks

in

the

asphaltversusthemaximumstrainexertedfromdifferentialdeflectionsoftheribsa

minimum requirementof the stiffnessof troughshasbeenderived that isgiven in

Figure35.


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29


Steel bridges serviceability limit state

distancebetweencrossgirders

a[m]

0

3

4

5

1000 5000 15000 2000010000

AB

second moment of area IBof the stringers including deckplate [m4]

Condition for curve A

11,20m

2

IB

1 heavy traffic lane

2 web of main girder orlongitudinal girder

Requirements for the minimum stiffness of stringers

depending on the distance between crossbeams


Figure35

(4) Thisminimumstiffnessrequirement,specified inEN19932,alsoprotectsthedeck

platefromexcessivefatiguestresses.

(5) Another indirect fatigue assessment given in EN 19932 is the verification to

excessivewebbreathing,thatmayleadtocrackingattheweldededgesoftheweb

plateandalsoavoidsthehungryhorseappearance.

(6) Figure 36 shows the relevant platebucklingformula applied for stresses on the

servicelevel.


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30


stiffened panel length

sub-panel

longitudinal edge

stiffenedpanelwidth

transverseedge

y

x

aG

a1 a4a3a2

b21

bG

Definition of a plated

element

Verification to

web breathing

Plate buckling


15.1k

1.1k E

ser,Ed

2

E

ser,Ed,x

+

Figure36



Figure37

4.5.4 BackgroundinformationtotheEurocodespecificationsfortrafficloads

(1) TheJRChaspreparedabackgrounddocumenttoEN1991Part2Traffic loads for

road

bridges

and

consequences

for

the

design

,

see

Figure

37,

that

is

currently

being

extendedtoincludealsothebackgroundofthetrafficloadsforrailwaybridges.


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31

(2) Thatbackgrounddocumentgivestheorigineofthe loadspecificationsandcouldbe

usedasasourcefordeterminingtendenciesfrommorerecenttrafficmeasurements

orfromstudiesthatincludefurtherdevelopmentsofheavyvehicles.

5. Modellingofsteelbridgesfortheanalysis

5.1

General

(1) Twoexamples formodelsused forthedesignofsteelbridgesarepresented inthis

report,thatareconnectedwithdurabilitychecks:

Modelforshearlagforwideflangese.g.thebridgedeckcooperatingwiththe

maingirdersastopflange,

Modelforfatiguedesign.

5.2 Modelforshearlag

(1) The basis for themodel of shear lag in EN 199315, towhich EN 19932makes

reference,isthebeamtheoryextendedtocoversheardeformations.

(2) Figure38showstheprinciple:

thebendingtheoryofbeamswithloadsz

P andbendingmomentsz

M apply

to the full crosssectionwith the fullgeometric flangewidth b. Itgives the

warpingdistributionz,

anadditionalwarpingdistribution w forlongitudinalstresses x isfound,the

distributionofwhichcomplieswithalinearsheardistributions

w

inthewide

flangeandhasthefollowingproperties:

it isorthogonal to thewarpingdistributions 1w1= fornormal forces

andforbending zw2= ,inthattheequations:

0AkdAwdAw w10 =+=

0AkdAzwdAzw zzzw0 =+= apply,

it gives a vertical deformation v that can be determined from the

second order analysismodel of a beamwith the bending stiffness

wwAE where

= dAwA 2ww


32/118


33/118

33


Subdivision of a moment-distribution to elements with standard shape

3. MODELLING OF STEEL BRIDGES

Figure39

(3) Figure 39 shows amoment distribution for a continuous beamwhere thismodel

couldbeapplied:

z iscalculatedonthebasisof zM fromabeamanalysis

w is calculated from wM determined from 2nd order theory for a

continuousbeamwiththetensionforce SG .

(4) For the ease for use however themomentdistributionof the continuous beam is

divided into variousunitdistributions,eachofwhich canbemodelledby a simply

supportedbeamwithacombinationofuniformlydistributed loadandconcentrated

load,where istherelevantshapeparameterforthemomentshape.


34/118

34


-factor for shear lag


Figure40

(5) Figure40givesthealgebraicsolutionfor forvariousshapes takingaccountof

thepossibleorthotrophyofthewideflangeby b0 ,where

0 =1 forisotropicflangeplates

0 >1 fororthotropicflangeplates,wherethelongitudinalstiffnessislarger

thantheshearstiffness

0


35/118

35


Differences in modelling

Modelling for ULS Modelling for fatigue


Figure41

(2) Alsosmallcurvaturesofabridge inplanviewnormallyneglected intheanalysisfor

ULSmay induce lateral forces in the hogging and saggingmoment regions of the

maingirdersthatmayenhancetherestrainingmomentsinthetransverseframe.

(3) Fatigue damages have also been observed at the connections of longitudinal

stiffeners in webs of maingirders, that normally are designed for plate buckling

underperfectloadingconditionsforULS,howeverincaseofflexibledeckplatesmay

receive lateral imposed deformations from deflections of the crossbeams under

trafficloads,seeFigure42.


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36


Fatigue effects on web stiffenersModelling for ULS



Figure42


Frame and distorsional effectsModelling for ULS



Figure43

(4) A typicaldifference inmodelling forULS and fatigue isgiven in Figure43 forbox

girderbridges,where transverse frames are usually designed for load distributing

forcescalculatedon thebasisofrigidcrosssectionshapes,whereas for fatigue the

distortionofthecrosssectionandsecondarymoments inducedbythecontinuityof

deformationsofthedeckplateandthetransverseframemayberelevant.


37/118


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38


Design principles for individual bearings

- Permission of movements minimizing the reaction forces- No tensile forces

- No significant redistribution of forces to other bearings

from accomodation to installation tolerances

- Specification of installation conditions with details

of construction sequence and time variable conditions

- Measure to avoid unforeseen deformation of the bearings

(non uniform contact)

4. SPECIFICATION FOR BEARINGS

Figure44


Construction documents

Bearing plan (drawing of the bearing system) Bearing installation drawing (structural details) Bearing schedule (characteristic values from each

action, design values from combination of action)


Figure45

(2) Theconstructiondocuments,seeFigure45,are

thebearingplan,thatshowsthebearingsystem,

the

bearing

installation

drawing,

thebearingschedule.


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39

6.3 Preparationofbearingschedules

(1) Afterthechoiceofthebearingplanwithselectionofthetypesofbearing,seeFigure

46,bearingschedulesneed tobeprepared, forwhichFigure47andFigure48give

models.


sliding rolling deforming

displace-

ment

rotation

Functional principles of bearings


Figure46

(2) In Figure 47 the characteristic values of actioneffects (forces, moments and

movements)aregiven foreach individualaction,so that loadcombinationscanbe

performed that allow to define either extreme values togetherwith simultaneous

accompanyingactionsorconservativecombinationsofextremevaluesonly.


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40



Figure47



Figure48

(3) Figure48givesanexamplefortheindicationofdesignvaluesfromthecombination

ofextremecharacteristicvalues.

(4)

The

bearing

schedules

are

then

used

by

the

bearing

producers

to

design

the

bearings

accordingtotherulesinEN1337.


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41

(5) The reference standards for thepreparationof thebearing schedules are given in

Figure49andFigure50.Foraccidentaldesign situationsalsoEN19912 shouldbe

taken intoaccountwithparticular rules for the impact scenarios forbridges tobe

considered.TheNationalAnnexmaygivedescriptiverules (e.g. limitationofbridge

movementsbystructuralmeasures)thatapplyinsteadofnumericalassessments.


No. Action Eurocode

Reference to temperature T0

DIN EN 1991-1-5:2004-07

1.1

1.2

1.3

1.4

1.5

Self-weight

Dead loads

Prestressing

Creep concrete

Shrinkage of concrete

DIN EN 1991-1-7:2007-02

DIN EN 1991-1-7:2007-02

DIN EN 1992-1:2005-10 and

DIN EN 1994-2:2006-07

DIN EN 1992-1:2005-10

DIN EN 1992-1:2005-10

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

2.10

2.11

2.12

2.13

2.14

2.15

2.16

2.17

2.18

Traffic loads

Special vehicles

Centrifugal forces

Nosing forces

Brake and acceleration forces

Footpath loading

Wind on structure without traffic

Wind on structure with traffic

Range uniform temperature

Vertical temperature difference

Horizontal temperature difference

Soil Settlements

Bearing resistance/friction forces

Replacement of bearing

Pressure and suction from traffic

Wind during erection

Construction loads

Accidental actions

DIN EN 1991-2:2004-05

DIN EN 1991-2:2004-05

DIN EN 1991-2:2004-05

DIN EN 1991-2:2004-05

DIN EN 1991-2:2004-05

DIN EN 1991-2:2004-05

DIN EN 1991-4:2005-07

DIN EN 1991-4:2005-07

DIN EN 1991-1-5:2004-07, 6.1.3 and 6.1.5

DIN EN 1991-1-5:2004-07, 6.1.4 and 6.1.5

DIN EN 1991-1-5:2004-07, 6.1.4 and 6.2

DIN EN 1997-1:2009-09

DIN EN 1337, Part 2 to 8

DIN EN 1991-2:2004-05

DIN EN 1991-2:2004-05

DIN EN 1991-4:2005-07 and

DIN EN 1991-1-6:2005-09

DIN EN 1991-1-6:2005-09

DIN EN 1991-1-7:2007-02

For transient design situations reduction of variable actions due to limited duration EN 1991-2, 4.5.3. For steelbridges also actions from installation of hot asphalt according to technical project specifications.

Actions for permanent and transient design situations


Figure49


Actions in accidental design situations

Specifications according to EN 1991-2

Limitation of bridge movements by structural measures,

e.g. stop devices at abutments

Actions in seismic design situations

Specifications according to EN 1998-1 and EN 1998-2


Figure50


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42

6.4 Particularitiesofcombinationrules

(1) Figure51givestheprinciples for thedeterminationofdesignvaluesofmovements

andbearingforceswhenusingthecombinationrules.


Determination of design values of movements and bearing forces

Principles

Combination according to EN 1990, 6.5.3.2 (2) with partial factors according to

EN 1990, A.2 and particular rules for climatic temperature effects

Movements due to creep and shrinkage by multiplying mean values in

EN 1992-2 and EN 1994-2 by a factor of 1.35

Verification of static equilibrium (uplift of bearings) and anchoring devices

by applying 0.05 GK spanwise

Consideration of deformations of foundation, piers and bearings in the

modelling of the structure, see EN 1991-2, 6.5.4.2

Use of 2nd order theory for accounting for deformations of piers after

installation of bearings if required by EN 1992-1-1, 5.8.2 (6).For calculation of pier deformations ky = 0,5 may be applied to geometric

member imperfections in EN 1992-1-1, 5.2.


Figure51

(2) In order to comply with the requirement of realistic behaviour the following

particularitiesshouldbetakenintoaccount:

the F value for climatic temperature effects cannot exceed the value

35.1F= ,so that thisvalueshouldbechosen insteadof the recommended

value 5.1F= .

Creep and shrinkage should be taken into account by using mean values

multipliedwithafactorof1.35.

Non uniform distribution of permanent loads should be considered by

applying kG05.0 ontheinfluencelineforupliftandforanchoring.

Equivalentgeometricimperfectionswithonly50%ofthegeometricmember

imperfectionsspecifiedinEN199211,5.2shouldbeapplied.

(3) Fordeterminingthedesignvaluesofmovementsfromthedesignvaluesofextreme

temperatures min,EdT and max,EdT the safety system in Figure 52 should be used. It

comprisestwoelements

thedesignvalues NF T with 35.1F=


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43

the reference temperature TT0 with T from uncertainties of the

temperatureofthestructureduringinstallation,where NT dependsontype

ofconstructionand thetypicalhourofmeasurement (e.g.earlymorning for

steelstructures,afternoonforcompositestructures).


Determination of design values of movements and bearing forces

Maximum and minimum constant temperature component:

Climatic temperature effects

Ted, min = T0 -F TN,con -T0Ted, max = T0 + F TN,exp + T0

additional safety element

charact. Values EN 1991-1-5, 6.1.3.3

partial factor F = 1.35

reference temperature during installation of the bearings, e.g. +10C

Table E.4: Recommended values for T0

Case Ins ta lla ti on of bear in gT

0[C]

steel bridges composite b ridges concrete b ridges

1Installation with measured Temperature and with correction by

Resetting with bridge set at T0

0 0 0

2Installation with estimated T

0and without correction by resetting

with bridge set T0

10 10 10

3

Installation with estimated temperature T0

and without

correction by resetting and also one ore more changes in position

of the fixed bearing

25 20 20

Td = Ted,max -Ted,minFor non-linear behaviour stepwise determination

Td = F TN


Figure52


Reaction forces at fixed points resulting form resistance of the bearing system

For sliding bearings:

( )[ ]

+++=

kGr

kiiQikiQkGa

kQHG

QQGQF

d

inf,

01sup,

1

Forces from

acceleration and

braking

other variable actions

vertical actions of traffic load

self weight, dead loads

coefficient of friction according EN 1337-1, 6.2.

For PTFE sliding bearingsmax = 0.03

For elastomeric bearings

+=

inf,,infinf

sup,,supsup

1

dq

dq

kQH AG

AGQF

d

forces from

accelerationand braking

nominal values of shear modulus

Gsup = 1.05 N/mm2

Ginf= 0.75 N/mm2

Shear deformations of the bearings

according to EN 1337-3

plan shear area of bearings


Figure53


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45

ashapeandsizeofthecrackthatcomplieswithoberservationsintestingand

with the accuracy of the testing method as it should be at the limit of

detectability,

thefatigueloadingandinspectionmanagementtoaccountforpossiblecrack

growthinserviceuntilthecrackisdetected,

thelowesttemperatureinthecomponent.

(6) This fracture mechanics assessment is not a fitness for purpose check, as the

assumptionse.g.thepresenceofcracksareonlyhypothetical.Ithasthecharacterof

acheckforanaccidentaldesignsituationandhenceproducesrobustnessforthe

unprobablecasethatoneormoreofthehypotheticalassumptionswouldholdtrue.

(7) Whereastherequirementofrobustnessisoftendescribedinqualitativeterms,e.g.

by

the

requirement

to

avoid

progressive

collaps,

the

robustness

from

the

choice

of

materialtoavoidbrittlefractureisexpressedquantitatively.

7.2 Inputforthechoiceofmaterialforsteelbridges

(1) Aparticularityof thechoiceofmaterial forsteelbridges is that thedesignvalueof

crack da assumedatthehotspotofastructuralcomponentisverymuchaffectedby

fatigue,seeFigure54.

(2) Hencetheinitialcracksize 0a overlookedintestingafterfabricationisassumedtobe

enhanced by crack growth due to fatigue actions. The fatigue action taken into

accountisonequarterofthefullfatiguedamage

33c 102D =


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46


Choice of materialChoice of material

Safety assessment based on fracture mechanics

Assumption for a0

design crack

initial crack

fatigue loading

=

4

102faa

63c

0d

a0

ad

Kappl,d Kmat,d

Kappl,d (member shape, ad, 1Ed)

Kmat,d

(T27J

, TEd

)

5. CHOICE OF MATERIAL

Figure54

(3) Thefracturemechanicsassessmentisperformedwithstressintensityfactors K,one

fortheactionside

d,applK

whichisinfluencedbythemembershape,thecracksizeandthefrequentstresses

ULS,E1Ed =

according to the combination rules for accidental design situations, and on the

resistanceside

d,matK

which includesthetemperatureT27JfromCharpyVnotch impactteststhatproduce

animpactenergyof27Joule.

Thisassumptionmakesitpossibletoestablishalinkbetweenthefracturemechanics

assessmentand thenecessarynumberof inspectionsduring the service lifeof the

structure.

(5) It also produces structures that are damage tolerant, because the crack growth

fromhypotheticalcracksissufficientlyslow,toprovidelonginspectionintervals,and


47/118


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49


Choice of material to EN 1993-1-10


Figure57

(6) At present this table with maximum thickness values is extended to make it

applicabletocoldformedhollowsectionsstructures,stainlesssteelandalsoforthe

choiceofmaterialforplasticdesign(uppershelfbehaviour).

7.4

Requirementsfor

upper

shelf

behaviour

(1) Sofarafracturemechanicsproceduretoidentifythenecessarytoughnessproperties

intheuppershelfbehaviourisnotyetavailable.

(2) Therefore EN 1993Part 2 contains an opening for National decisions with a

recommendationthatmaybeattributedtothefollowingprocedure.

(3) Figure58 shows the characteristicofa nonharmonized threepointbending test

withamaterialsamplethathasgotaweldseamonthesurfaceintension.Thisseam

madewithanonductileelectrodeisintendedtoinitiateacrackduringbending.

(4) Featuresofthecrackgrowthuptoaplasticangle arethenusedtoclassifythetest

resultaspassedorfailed.


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50


AUBI-test according to SEP 1390 (1996)

National quality tests


Figure58


trend analysis for the AUBI correlation


Figure59

(5) Figure59givestheresultsofsuchtestsfromqualitytestsofsteelproducersrelated

to theCharpyVnotch impactenergyand the thicknessof theproduct fromwhich

thesamplesweretaken.


51/118

51

(6) The conclusion from Figure 59 is the recommendation in Figure 60, according to

whichthechoiceoffinegrainsteelsisnecessaryforproductthicknessesgreaterthan

30mm.

(7) ThischoicesupersedesthechoiceaccordingtothetableinFigure57.


Choice of material given in Table 3.1 of EN 1993-2


Figure60

7.5 ExamplesforuseofEN1993110forchoiceofmaterialinsteelbridges

(1) Aconventionalsteelbridge,withcompositeboxgirdersectionisgiveninFigure61.

Theplatethicknessoftheupperflangeandthebottomplateoftheboxgirderthat

attainvaluesupto135mmhavebeenchosentoEN1993110.


52/118

52


Bridge system and construction

Construction at supports

Cross section

125,28

Span

Upper chord

Bottom plates

Support Support

75

40

30 70 30 7070 95 45 70 9545

40

50 70 50

40

7 5 11 5 135 115 85 85 60 60 60 115 140 145 140 115 60 60 60 85 85115135115 75 75145

70

40

Plate thickness for S355 J2G3

Example: Thick plates for the composite Elbebridge Vockerode (EN 1993-1-10)


Figure61


Bridge St. Kilian


Figure62

(2) Anonconventionalcompositebridgeconsistingoftwoseparatebridgepartswitha

trianglecrosssection(andanopenjointbetweenthedecks inthemiddle) istheSt.

KilianbridgeinFigure62.

(3)

Thebottomchordof this trussbridgewithcircularhollowsections isasingle tube

withnodesmadeofcaststeel.


53/118

53

(4) The robustness of this structural concept is assured by the choice of material

according to EN 1993110 that produces damage tolerance together with the

usualinspectionregimeforbridges.

In conclusion the crosssection with a single bottom chord made of steel with

sufficient toughness is robustnessequivalentwith other crosssectionswithmore

than 1 bottom chord or bottom chords made of steel lamellas (because of

redundancies) that have low toughness values (as experienced forexisting riveted

bridges).

(5) A particular feature of this robustness concept is the appropriate choice of the

fatigueclass,whichismainlyinfluencedbytheexecutionquality.

(6)

Figure

63

gives

an

impression

of

the

erection

work,

Figure

64

shows

the

weld

preparationbetweenthecaststeelnodesandthetubes(withsmalltolerances)and

Figure65givesanimpressionofthecastnodes.



Bridge St. Kilian

Figure63


54/118


55/118


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56

k,ult = magnification factor to design action effects to obtain the

characteristic resistance kR without considering outofplane

imperfectionsandoutofplanebuckling.

crit = magnification factor to design action effects toobtain elastic critical

resistances critR

= globalslenderness

= reduction coefficient for buckling, depending on the buckling

phenomenon,theimperfectionfactor andtheslenderness.


lk

Ed E d

column buckling lat. tors. buckl. plate buckling shell buckling

0,00

0,20

0,40

0,60

0,80

1,00

1,20

0 0,5 1 1,5 2 2,5 3_

a0a

b

c

d

0,00

0,20

0,40

0,60

0,80

1,00

1,20

0 0,5 1 1,5 2 2,5 3_

a

b

c

d

EN 1993-1-1 EN 1993-1-1

0,0

0,2

0,4

0,6

0,8

1,0

1,2

0,0 0,5 1,0 1,5 2,0 2,5 3,0_p [-]

p[

-]

a0

b

EN 1993-1-5

M

kult

M

kd 1

RE

,

0,0

0,2

0,4

0,6

0,8

1,0

1,2

0 ,0 0 ,5 1,0 1,5 2,0 2,5 3,0

EN 1993-1-6

( )

===

=

=

crit

kult

crit

k

critdcrit

kdkult

R

R

RE

RE,,

skEd Ed

r

tEd E dEd/2

a

Ed

b

Common design rules for column, lateral torsional, plate and shell buckling

6. DESIGN OF BRIDGE-ELEMENTS6.1 STABILITY RULES

Figure67

(4) Forsteelbridgestheconditionsfortheapplicationofstandardformulasarerare,so

thata2ndorderassessmentorasimplified2

ndorderassessmentsarepreferred.

(5) Forsteelbridgesalso

columnbucklingandlateraltorsionalbucklingononesideand

platebucklingontheotherside

aretherelevantphenomena,andshellbucklingdoesingeneralnotoccur.

(6) Therefore this report gives thebackgroundof the imperfections to beused in2nd

order

analysis

and

a

simplified

2

nd

order

analysis

which

includes

the

application

of

such imperfections in the socalledGeneralmethod thatallows touse reduction


57/118


58/118

58

1. AunifiedEuropeancharacteristicresistance:

k,plk NR =

2. Anationaldesignvalue:

M

kd

RR

=


6.1 STABILITY RULES

Column buckling

Figure68

(3) AsaresultofthederivationinFigure68,Figure69givestheshapesofthereduction

factors forvariouscrosssectionalshapes,towhichvarious valuesbelong,see

Figure70.


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59


Column buckling curves

6.1 STABILITY RULES

Figure69


Selection of buckling curves

6.1 STABILITY RULES

Figure70

(4) Theratiosofexperimentalresults er andresultscalculatedwiththeformulaforthe

reductioncoefficient aregiveninFigure71forweakaxisbuckling.Figure72shows

thepartialfactors M thatresultfromtestevaluationaccordingtoEN1990Annex

D,toobtainthedesignvalues ( )03.38.38.0R == .


60/118


61/118


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62

Dissemination of information for training Vienna. 4-6 October 2010 76

d d d

dg=

0.5 0.685 0.870 0.477 0.661 0.895 1.03

1.0 1.136 0.597 0.953 1.082 0.627 1.05

1.5 1.846 0.342 1.43 1.734 0.369 1.08

2.0 2.806 0.209 1.906 2.605 0.228 1.09

3.0 5.476 0.10 2.859 5.039 0.109 1.09

M-values for 2nd order analysis

6.1 STABILITY RULES

Figure74

(3) Figure74givesthemodificationofthepartialfactortoobtain

M*M g = .

(4) InconclusiontherearetwopossibilitiesdependingonNationalChoice:

1. M ischosenequalto1,00andconsistencyisautomaticallyachieved,

2. incaseof 00.1M> ,e.g. 10.1M = ,thedifferencebetweenthefunctions M

and *M totheconstantvalue M issosmallthatbothfortheuseofbuckling

curves andfor2ndorderanalysiswithimperfections 0e thesame M factor

canbeused(withaslightadvantagesfor2ndorderanalysis inrelationtothe

useofvalues).

8.4 Extensiontootherboundaryconditions

(1) Theuseoftheelasticcriticalbucklingmode crit allowstoextendtheapplicabilityof

thecrosssectionalcheckinFigure68andhencethereductionfactor toanyother

boundaryconditionsasgiveninFigure75,e.g.bymodifyingthebucklinglength.


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63


x

EI

CNEdNEd

a1

max,crit

crit

2

crit

Ed

Edd0e

crit

max,crit

2

critd0ini

EI

N1

NeM

e

=

=

l

l

xsin

N

N1

1NeM

xsine

crit

EdEdd0e

d0ini

=

=

x

NEdNEd

Use of buckling mode as imperfection

Imperfections for members with various boundary conditions

6.1 STABILITY RULES

Figure75


Example for a column on elastic supports

6.1 STABILITY RULES

Figure76

(2) ThecomparisoninFigure75showsthat

the

initial

equivalent

geometric

imperfection

is

not

referred

to

max.

crit ,

but

tomax. //crit , and the shapeof//crit is the shapeof bendingmoment from

imperfections.Thereforetheequivalentgeometricimperfectionisnotanout


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of straightness imperfection in terms of displacement but a curvature

imperfection.

Theadvantageof taking thebucklingmode crit asshapeof imperfection is

thatwith crit alsothebendingmoment eM accordingto2ndordertheorycan

beeasilydetermined.

Theextensionoftheapplicationoftheflexuralbucklingcurveisnotlimitedto

onedimensionalstructuresascolumns,barsetc.,butalsototwodimensional

structuresasgrids,seeFigure76,forwhichtheconditionappliesthatexternal

forces do not change their value in dependance of buckling deformations

(conservativeloading).

8.5 Lateraltorsionalbuckling

(1) Abeamwithequalendmoments,whicheffects compression inone flangecanbe

assessedinasimilarwayasacolumn,iftheassessmentisperformedfortheflangein

compressionforoutofplanebuckling,seeFigure77.


Column buckling Lateral torsional buckling

1M

M

N

N

Rky

Ed

Rkpl

Ed =+,,

1M

M

N

NFl

Rky

Fl

Edy

Fl

Rkpl

Fl

Ed =+,

,

,

1

M

M1

1e

M

N

M

M

M

M

critz

Edz

Fl

Rky

Fl

crit

critz

Edz

Rkz

Edz =

+

,

,

*

,,

,

,

,1

N

N1

1

M

eN

N

N

crit

EdRk,y

*

Ed

Rk,pl

Ed =

+

FlRk,pl

FlRk,y

M*

N

M2.0e

=

Rk,pl

Rk,yN

*

N

M2.0e

=

11

12.0

*

2

MM

M2

Fl

2

M

MM =

=

+

876}1

1

12.0

2

NN

NNN =

=+

22

1

+=

( ) ++= 22.015,0

Equivalence of flexural and lateral torsional buckling

6.1 STABILITY RULES

Figure77

(2) Thehypothesisused in thederivation inFigure77 is that theequivalentgeometric

imperfection *e fortheflangeisthesameasforacolumnwithflexuraloutofplane

buckling.

(3) Thederivation shows that for lateral torsionalbuckling the sameexpressionas for

flexural buckling is obtained, however with the difference, that the imperfection


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65

factor isreducedto * bytheeffectoftheSt.Venanttorsionalrigidity,which is

determinedbytheratio

crit

*crit

2

Fl

2

M

=

where

2

M istheslendernessforthelateraltorsionalbucklingproblembasedon crit

2

Fl is the slenderness of the isolated flange in compression; that can also be

expressedby *crit calculatedwithoutSt.Venanttorsionalrigidity.

(4) Figure78givesthedifferencebetweentheflexuralbucklingcurvebandthe lateral

torsionalbucklingcurvewithreducedimperfectionfactor * foraHEB200beam.

(5) Testevaluationswithallavailabletestreportsforlateraltorsionalbucklingtestshave

proventhatthelateraltorsionalbucklingcurveasgiveninFigure77givesthebestfit

with M valuesintherangeof1.05.


0,0

1,0

0,0 1,0 2,0LT

LT

Lateral torsional buckling

for GIT=oo

Bc b

Lateral torsional

buckling for a beam

HEB 200

Bc a

Comparison of LTB-curves

6.1 STABILITY RULES

Figure78

(6) Ageneralisationoftheprocedure inFigure77 leadstotherule fordeterminingthe

reductionfactor foranyoutofplanestabilityproblem,thatmaybecomposedof


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66

mixedflexuralandlateraltorsionalbucklingandincludesanyoutofplaneboundary

condition,seeFigure79.


d

kkult

E

R=,

d

critcrit

E

R=

=

crit

*crit*

*crit DIG

( )[ ]2* 2.015,0 ++=

1,

M

kult

2. Modification of imperfection factor:

where is determined without effect of

3. Use of flexural buckling curve:

1. Input parameters:

4. Assessment for design point xd

22

1

=

critt

kult

,=

6.1 STABILITY RULES

Procedure for lateral torsional buckling assessments using the buckling curves:

Figure79

(7) Ifthedesignpoint dx isknown,wherethesumofinplanestressesandoutofplane

stressesfromimperfectionsgivetherelevantmaximumvalue,the inputparameters

canbecalculated.

Inthiscase k,ult isdeterminedatthepoint dx .

Ifthedesignpoint dx isnotknown, k,ult canbeconservativelyestimatedas min,k,ult .

(8) Ifthetwoelasticcriticalvalues crit withtorsionalrigidityand*crit withouttorsional

rigidityareavailablethemodified * valuecanbedetermined.

Aconservativeapproachis

=*

(9) Figure 80 shows an example for a beamwith unequal endmoments,where the

designpointisatadistance l155.0xd= fromthemaximumloadedend.


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67


Comparison of laterial torsional buckling curves

6.1 STABILITY RULES

Figure80

(10) If forconvenience theassessment iscarriedoutwith k,ult at themaximum loaded

end 0x= , the resultsareeither conservativeoramodifiedbucklingcurve mod is

used,that includesacorrectionwith onthebasisofknowledgewherethedesign

point dx is.

8.6 Determinationofthedesignpoint dx forlateraltorsionalbuckling

(1) Thelocationofthedesignpoint dx forlateraltorsionalbucklingwhereinplane and

outofplaneeffectssumuptoamaximumcanbedeterminedwiththeknowledgeof

thedistributionofinplaneeffectsandoutofplaneeffects.

(2) Figure 81 shows for a two span beam, the loaded top flange of which is to be

checked,thedistributionofinplanemomentsandinplanestressesintheflangeand

the modal outofplane displacements crit and modal outofplane flange

moments ( ) critxIE , that are produced togetherwith the elastic critical eigenvalue

crit .

(3) Therearetwopossibilitiesforthelateraltorsionalbucklingcheck:

eithertodeterminetheoutofplane2ndordermomentsfromthemodalout

ofplaneflangemoments ( ) //critxIE andtoperformacrosssectionalcheck,at

dx ,


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68

or to apply a check,where thedistributionsof the inplane andoutof

planestressessuggesttobethecriticalpoints dx .


Determination of design point xd

crit

kult

,=

( ) ,*=

1,

M

kult

check:

6.1 STABILITY RULES

Figure81

8.7 Examplesforlateraltorsionalbucklingverificationatthedesignpoint dx

(1) For awelded portal frame of an industrial hallwith the dimensions and support

conditions foroutofplanemovementsasgiven inFigure82 thedistributionof in

planeactioneffectsaccordingtoFigure83apply.


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69


S355J2G3

24420

8000

1068

kneepointLateralsupport

0

1

2

3 4

5

6

7

24015

5505

24015

5565

24012

24012

6.1 STABILITY RULES

Example: Portal frame

Figure82


Distribution of compression forces [kN]

Moment distribution [kNm]

ult.k.min=1.55

ult.k (xd)=1.94

6.1 STABILITY RULES

Figure83


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70


xd

6.1 STABILITY RULES

Example: Modal out-of-plane deformation crit=1.85

Figure84

(2) ThedistributionofbendingmomentsinFigure83givesthelocationfor 55.1min,k,ult =

and the maximum curvature in Figure 84 gives the design point dx , for which

( ) 94.1xdk,ult = applies.


1. Calculation w ith extreme value ult,k,min 2. Calculation design point xd

55.1, =kult

85.1=crit

84.1* =crit

915.085.1

55.1==

408.049.085.1

54.1** ===

crit

crit

( ) 064.12.015.0 2* =++= LT

50.0622.02

12

>=+

=

00.188.010.1

55,1622.0=

00.104.110.1

94.159.0, >=

=

M

kult

Check of out-of-plane stability

contact splice sufficient

6.1 STABILITY RULES

Figure85

(3) InFigure85twocalculationsarecarriedout:


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73


6.1 STABILITY RULES

Example: cross-beam at supports

Figure89


6.1 STABILITY RULES

Example: intermediate cross-beam all 7,50 m

Figure90

(8) Inthiscase1/3ofthewebshouldbetakenintoaccount.

(9) TheotherpossibilityistomodelthecrosssectionfullyorpartlywithFEM,toconsider

theeffectsoftorsionanddistorsionofthesteelcrosssection.


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74

(10) In Figure 91modal transverse displacements of the bottom flange of the critical

girder are given for the first 3 eigenvalues. The areawhere themodal transverse

momentsattaintheirmaximumvaluesaremarked.


critical area

critical area

critical area

6.1 STABILITY RULES

Example: crit-values and modal out-of-plane deformations

Figure91


295330

250

180

critical areas

6.1 STABILITY RULES

Example: Input for ult,k-values

Figure92


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75

(11) Figure92givestheinplanestressesinthecentrelineofthebottomflangeaswellas

the yield stresses from which k,ult values can be determined, that are possible

choicesforthedesignpoint dx .

(12) InFigure93twocalculationsarecarriedout

1. atthedesignpoint dx forthefirstmodaldisplacement(infield)

2. atthedesignpoint dx forthethirdmodaldisplacement(atthesupport).

In thesecalculationsalso themodificationof the imperfection factor by torsion

hasbeentakenintoaccount.


in field at point P1 at support (point P1)

83.1180

330k,ult ==

8576.8crit=

45.08576.8

83.1==

37.8*

crit

=

72.076.086.8

37.8* ==

69.0=

82.0=

00.137.110.1

89.182.0

M

k,ult >=

=

184.1250

295k,ult ==

489.17crit=

26.0489.17

184.1==

20.15*

crit=

66.076.049.17

20.15* ==

554.0=

96.0=

00.103.110.1

184.196.0

M

k,ult >=

=

6.1 STABILITY RULES

Checks for lateral-torsional buckling

Figure93

9.

Platebuckling

effects

9.1 General

(1) Itisacommonfeatureofcolumnbucklingandlateraltorsionalbuckling,thatinplane

stresses that initiate outof plane buckling are not affected by outof plane

deformations; i.e. the normal compression force in a column does not varywith

imperfectionsorbucklingdisplacementsandtheinplanestresssituationsinabeam

columndoesnotvary if lateraldeformations in termsof lateraldisplacementsand

torsion

take

place.


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78


Torsional buckling column-like behaviour plate-like behaviour

compression

stress

compression

strain

A

NN= EA

NN

=

response

strain

response

stress

( ) yM f1 =

bending

geometric strain effect:

( ) 2

222

1

2

4

=

crit

critcritogeom

N

N

N

N

N

N

b

s

l

es

6.1 STABILITY RULES

Figure96

(6) In torsional buckling a geometric strain effect occurs due to the torsional

deformations,that

incaseof loadingbyuniformlydistributedcompressionstresswouldcausea

parabolicdistributionofstrainsoverthecrosssectionand

incaseofloadingbyauniformlydistributedcompressionstrainwouldcausea

parabolicdistributionofstressoverthecrosssection.

(7) These different distributions of stress N from compression, either constant or

parabolic, are superimposedwith linear distribution of stresses M in the plated

elementsfromplatebending.


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79


( ) 2* 2.015.0 ++=

22

1

+

=

( ) 11

120

* =

+

~2

1+=k

( ) 11

17.0

*

*** =

+

( )

=

+20

*

1

1

( ) 11

17.0

* =

+

+=

2

* 1

( ) ++= 7.015.0 *

column buckling plate buckling

yf1 yf1

yf

yfk

yf

bending

compression

bending

compression

bsd=2.00=

bsd

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