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.
Dissemination of information for training Vienna, 4-6 October 2010 3
CROSS SECTION OF A BOX GIRDER BRIDGE WITH ANORTHOTROPIC DECK
Figure2
Dissemination of information for training Vienna, 4-6 October 2010 4
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.
Dissemination of information for training Vienna, 4-6 October 2010 5
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.
Dissemination of information for training Vienna, 4-6 October 2010 6
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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Dissemination of information for training Vienna, 4-6 October 2010 7
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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Dissemination of information for training Vienna, 4-6 October 2010 8
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
1. THE EUROPEAN STANDARD FAMILY AND STEEL BRIDGES
Figure7:
(8) Inthisreportonlyrulesforactionsandfordesignareaddressedasdemonstratedin
Figure7,whereasrulesforexecutionandproductconformitythataremainlyusedby
thecontractorsarenotdealtwith.
Dissemination of information for training Vienna, 4-6 October 2010 9
Design rules for steel bridges in Eurocode 3
1. THE EUROPEAN STANDARD FAMILY AND STEEL BRIDGES
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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Dissemination of information for training Vienna, 4-6 October 2010 10
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
1. THE EUROPEAN STANDARD FAMILY AND STEEL 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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Dissemination of information for training Vienna, 4-6 October 2010 11
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.
Dissemination of information for training Vienna, 4-6 October 2010 12
1000 kN
600 kN
300 kN
11,0 m
12
6
3
3
Load-model LM1 (draft German NA)
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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.
Dissemination of information for training Vienna, 4-6 October 2010 13
Statistical distribution of characteristics of vehicles
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
Figure12
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Dissemination of information for training Vienna, 4-6 October 2010 14
Modelling of vehicles and surfaces
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
Figure13
Dissemination of information for training Vienna, 4-6 October 2010 15
Modelling of bridges
2. LOAD ASSUMPTIONS FOR STEEL 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.
Dissemination of information for training Vienna, 4-6 October 2010 16
Load-model and simulations
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
Figure15
Dissemination of information for training Vienna, 4-6 October 2010 17
Dynamic effects
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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.
Dissemination of information for training Vienna, 4-6 October 2010 18
K 210 K 138
Reference bridges for reliability analysis
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
Figure17
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Dissemination of information for training Vienna, 4-6 October 2010 19
Definition of target -value
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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.
Dissemination of information for training Vienna, 4-6 October 2010 20
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
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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.
Dissemination of information for training Vienna, 4-6 October 2010 21
Q-values from LM1
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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.
Dissemination of information for training Vienna, 4-6 October 2010 23
Forecast of freight-volume
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
Figure22
Dissemination of information for training Vienna, 4-6 October 2010 24
Development of permits for heavy vehicles
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
Figure23
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(3) Figure24gives the vehicleandaxle loadsandaccumulatednumberof vehiclesas
measuredbyweighinmotion(WIM)methodsinanaccesshighwaytoRotterdamin
theNetherlandsfor1year.
Dissemination of information for training Vienna, 4-6 October 2010 25
Results of WIM-measurements in NL
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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.
Dissemination of information for training Vienna, 4-6 October 2010 26
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
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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.
Dissemination of information for training Vienna, 4-6 October 2010 27
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
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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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23
Dissemination of information for training Vienna, 4-6 October 2010 28
Fatigue details welded attachments and stiffeners
EN 1993-1-9 - Fatigue resistance
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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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Dissemination of information for training Vienna, 4-6 October 2010 29
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
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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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25
Dissemination of information for training Vienna, 4-6 October 2010 30
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
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
Figure29
Dissemination of information for training Vienna, 4-6 October 2010 31
1
2
4
3
Hanger connection for arch bridges
Substitution of fatigue checks for critical details
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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.
Dissemination of information for training Vienna, 4-6 October 2010 32
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
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
Figure31
Dissemination of information for training Vienna, 4-6 October 2010 33
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
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
Figure32
(6) The fatigue loading model FLM3 is not applicable for verifying these hot spots,
becauseitdoesnotsufficientlymodeltheeffectsofthetyrepressureofthewheels.
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27
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.
Dissemination of information for training Vienna, 4-6 October 2010 34
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
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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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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.
Dissemination of information for training Vienna, 4-6 October 2010 35
Potential positions of cracks in the asphalt layer
Durability of asphalt layer
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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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Dissemination of information for training Vienna, 4-6 October 2010 36
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
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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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Dissemination of information for training Vienna, 4-6 October 2010 37
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
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
15.1k
1.1k E
ser,Ed
2
E
ser,Ed,x
+
Figure36
Dissemination of information for training Vienna, 4-6 October 2010 38
2. LOAD ASSUMPTIONS FOR STEEL BRIDGES
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
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33
Dissemination of information for training Vienna, 4-6 October 2010 40
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.
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Dissemination of information for training Vienna, 4-6 October 2010 41
-factor for shear lag
3. MODELLING OF STEEL BRIDGES
Figure40
(5) Figure40givesthealgebraicsolutionfor forvariousshapes takingaccountof
thepossibleorthotrophyofthewideflangeby b0 ,where
0 =1 forisotropicflangeplates
0 >1 fororthotropicflangeplates,wherethelongitudinalstiffnessislarger
thantheshearstiffness
0
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35
Dissemination of information for training Vienna, 4-6 October 2010 42
Differences in modelling
Modelling for ULS Modelling for fatigue
3. MODELLING OF STEEL BRIDGES
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
Dissemination of information for training Vienna, 4-6 October 2010 43
Fatigue effects on web stiffenersModelling for ULS
Differences in modelling
3. MODELLING OF STEEL BRIDGES
Figure42
Dissemination of information for training Vienna, 4-6 October 2010 44
Frame and distorsional effectsModelling for ULS
Differences in modelling
3. MODELLING OF STEEL BRIDGES
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.
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38
Dissemination of information for training Vienna, 4-6 October 2010 45
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
Dissemination of information for training Vienna, 4-6 October 2010 46
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)
4. SPECIFICATION FOR BEARINGS
Figure45
(2) Theconstructiondocuments,seeFigure45,are
thebearingplan,thatshowsthebearingsystem,
the
bearing
installation
drawing,
thebearingschedule.
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6.3 Preparationofbearingschedules
(1) Afterthechoiceofthebearingplanwithselectionofthetypesofbearing,seeFigure
46,bearingschedulesneed tobeprepared, forwhichFigure47andFigure48give
models.
Dissemination of information for training Vienna, 4-6 October 2010 47
sliding rolling deforming
displace-
ment
rotation
Functional principles of bearings
4. SPECIFICATION FOR 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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Dissemination of information for training Vienna, 4-6 October 2010 48
4. SPECIFICATION FOR BEARINGS
Figure47
Dissemination of information for training Vienna, 4-6 October 2010 49
4. SPECIFICATION FOR BEARINGS
Figure48
(3) Figure48givesanexamplefortheindicationofdesignvaluesfromthecombination
ofextremecharacteristicvalues.
(4)
The
bearing
schedules
are
then
used
by
the
bearing
producers
to
design
the
bearings
accordingtotherulesinEN1337.
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(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.
Dissemination of information for training Vienna, 4-6 October 2010 50
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
4. SPECIFICATION FOR BEARINGS
Figure49
Dissemination of information for training Vienna, 4-6 October 2010 51
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
4. SPECIFICATION FOR BEARINGS
Figure50
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42
6.4 Particularitiesofcombinationrules
(1) Figure51givestheprinciples for thedeterminationofdesignvaluesofmovements
andbearingforceswhenusingthecombinationrules.
Dissemination of information for training Vienna, 4-6 October 2010 52
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.
4. SPECIFICATION FOR BEARINGS
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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the reference temperature TT0 with T from uncertainties of the
temperatureofthestructureduringinstallation,where NT dependsontype
ofconstructionand thetypicalhourofmeasurement (e.g.earlymorning for
steelstructures,afternoonforcompositestructures).
Dissemination of information for training Vienna, 4-6 October 2010 53
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
4. SPECIFICATION FOR BEARINGS
Figure52
Dissemination of information for training Vienna, 4-6 October 2010 54
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
4. SPECIFICATION FOR BEARINGS
Figure53
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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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Dissemination of information for training Vienna, 4-6 October 2010 55
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
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Dissemination of information for training Vienna, 4-6 October 2010 58
Choice of material to EN 1993-1-10
5. CHOICE OF MATERIAL
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
Dissemination of information for training Vienna, 4-6 October 2010 59
AUBI-test according to SEP 1390 (1996)
National quality tests
5. CHOICE OF MATERIAL
Figure58
Dissemination of information for training Vienna, 4-6 October 2010 60
trend analysis for the AUBI correlation
5. CHOICE OF MATERIAL
Figure59
(5) Figure59givestheresultsofsuchtestsfromqualitytestsofsteelproducersrelated
to theCharpyVnotch impactenergyand the thicknessof theproduct fromwhich
thesamplesweretaken.
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(6) The conclusion from Figure 59 is the recommendation in Figure 60, according to
whichthechoiceoffinegrainsteelsisnecessaryforproductthicknessesgreaterthan
30mm.
(7) ThischoicesupersedesthechoiceaccordingtothetableinFigure57.
Dissemination of information for training Vienna, 4-6 October 2010 61
Choice of material given in Table 3.1 of EN 1993-2
5. CHOICE OF MATERIAL
Figure60
7.5 ExamplesforuseofEN1993110forchoiceofmaterialinsteelbridges
(1) Aconventionalsteelbridge,withcompositeboxgirdersectionisgiveninFigure61.
Theplatethicknessoftheupperflangeandthebottomplateoftheboxgirderthat
attainvaluesupto135mmhavebeenchosentoEN1993110.
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Dissemination of information for training Vienna, 4-6 October 2010 62
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)
5. CHOICE OF MATERIAL
Figure61
Dissemination of information for training Vienna, 4-6 October 2010 63
Bridge St. Kilian
5. CHOICE OF MATERIAL
Figure62
(2) Anonconventionalcompositebridgeconsistingoftwoseparatebridgepartswitha
trianglecrosssection(andanopenjointbetweenthedecks inthemiddle) istheSt.
KilianbridgeinFigure62.
(3)
Thebottomchordof this trussbridgewithcircularhollowsections isasingle tube
withnodesmadeofcaststeel.
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(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.
Dissemination of information for training Vienna, 4-6 October 2010 64
5. CHOICE OF MATERIAL
Bridge St. Kilian
Figure63
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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.
Dissemination of information for training Vienna, 4-6 October 2010 68
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
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58
1. AunifiedEuropeancharacteristicresistance:
k,plk NR =
2. Anationaldesignvalue:
M
kd
RR
=
Dissemination of information for training Vienna, 4-6 October 2010 69
6.1 STABILITY RULES
Column buckling
Figure68
(3) AsaresultofthederivationinFigure68,Figure69givestheshapesofthereduction
factors forvariouscrosssectionalshapes,towhichvarious valuesbelong,see
Figure70.
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59
Dissemination of information for training Vienna, 4-6 October 2010 70
Column buckling curves
6.1 STABILITY RULES
Figure69
Dissemination of information for training Vienna, 4-6 October 2010 71
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 == .
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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
Dissemination of information for training Vienna, 4-6 October 2010 77
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
Dissemination of information for training Vienna, 4-6 October 2010 78
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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64
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.
Dissemination of information for training Vienna. 4-6 October 2010 79
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.
Dissemination of information for training Vienna, 4-6 October 2010 80
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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mixedflexuralandlateraltorsionalbucklingandincludesanyoutofplaneboundary
condition,seeFigure79.
Dissemination of information for training Vienna. 4-6 October 2010 81
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
Dissemination of information for training Vienna, 4-6 October 2010 82
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 .
Dissemination of information for training Vienna, 4-6 October 2010 83
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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Dissemination of information for training Vienna, 4-6 October 2010 84
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
Dissemination of information for training Vienna. 4-6 October 2010 85
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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Dissemination of information for training Vienna, 4-6 October 2010 86
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.
Dissemination of information for training Vienna, 4-6 October 2010 87
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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Dissemination of information for training Vienna, 4-6 October 2010 91
6.1 STABILITY RULES
Example: cross-beam at supports
Figure89
Dissemination of information for training Vienna, 4-6 October 2010 92
6.1 STABILITY RULES
Example: intermediate cross-beam all 7,50 m
Figure90
(8) Inthiscase1/3ofthewebshouldbetakenintoaccount.
(9) TheotherpossibilityistomodelthecrosssectionfullyorpartlywithFEM,toconsider
theeffectsoftorsionanddistorsionofthesteelcrosssection.
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(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.
Dissemination of information for training Vienna, 4-6 October 2010 93
critical area
critical area
critical area
6.1 STABILITY RULES
Example: crit-values and modal out-of-plane deformations
Figure91
Dissemination of information for training Vienna, 4-6 October 2010 94
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.
Dissemination of information for training Vienna. 4-6 October 2010 95
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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Dissemination of information for training Vienna, 4-6 October 2010 98
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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Dissemination of information for training Vienna. 4-6 October 2010 99
( ) 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