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Introduction, Traffic Loads onIntroduction, Traffic Loads on
Bridges & Combinations of actionsBridges & Combinations of actions
Jean-Armand Calgaro
Chairman of CEN/TC250
“ “ Application of Application of EurocodesEurocodes for bridgesfor bridges” ”
Athens, 20 October 2008 Athens, 20 October 2008
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BB
A A
BB
EE
LL
BELOWBELOW
ACCEPTABLE ACCEPTABLE
BASICBASIC
ENGLISHENGLISH
LANGUAGELANGUAGE
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Design of BridgesDesign of Bridges with the Eurocodeswith the Eurocodes
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EN 1991EN 1991--22
EurocodeEurocode 1 : Actions on1 : Actions onstructuresstructures – – Part 2:Part 2:
Traffic LoadsTraffic Loads onon
BridgesBridges
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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•• FOREWORDFOREWORD
•• SECTION 1SECTION 1 GENERALGENERAL
•• SECTION 2SECTION 2 CLASSIFICATION OF ACTIONSCLASSIFICATION OF ACTIONS
•• SECTION 3SECTION 3 DESIGN SITUATIONSDESIGN SITUATIONS
•• SECTION 4SECTION 4 ROAD TRAFFIC ACTIONS AND OTHERROAD TRAFFIC ACTIONS AND OTHER ACTIONS SPECIFICALLY FOR ROAD BRIDGES ACTIONS SPECIFICALLY FOR ROAD BRIDGES
•• SECTION 5SECTION 5 ACTIONS ON FOOTWAYS, CYCLE TRACKS ACTIONS ON FOOTWAYS, CYCLE TRACKS
AND FOOTBRIDGES AND FOOTBRIDGES
•• SECTION 6SECTION 6 RAIL TRAFFIC ACTIONS AND OTHERRAIL TRAFFIC ACTIONS AND OTHER ACTIONS SPECIFICALLY FOR RAILWAY BRIDGES ACTIONS SPECIFICALLY FOR RAILWAY BRIDGES
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ANNEX A (I) ANNEX A (I) Models of Models of special vehiclesspecial vehicles for road bridgesfor road bridges
ANNEX B (I) ANNEX B (I) Fatigue lifeFatigue life assessmentassessment for road bridgesfor road bridges – – Assessment Assessmentmethodmethod basedbased onon recordedrecorded traffictraffic
ANNEX C (N) ANNEX C (N) Dynamic factorsDynamic factors 1+1+ϕ for real trainsfor real trains
ANNEX D (N) ANNEX D (N) BasisBasis for for thethe fatiguefatigue assessmentassessment of of railwayrailway
structuresstructures
ANNEX E (I) ANNEX E (I)
LimitsLimits
of of
validityvalidity
of of
loadload
model HSLMmodel HSLM
andand
the selectionthe selection of of thethe criticalcritical universaluniversal traintrain
fromfrom HSLMHSLM-- A A
ANNEX F (I) ANNEX F (I) CriteriaCriteria toto bebe satisfiedsatisfied if aif a dynamicdynamic
analysis isanalysis is notnot requiredrequired
ANNEX G (I) ANNEX G (I) MethodMethod for for determiningdetermining thethe combined responsecombined response
of a structureof a structure andand tracktrack to variable actionsto variable actions
Annex Annex H (I)H (I) LoadLoad models for railmodels for rail traffictraffic loadsloads inin
transienttransient situationssituations
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TRAFFIC LOTRAFFIC LO AD MODELS FOR ROAD BRIDGES AD MODELS FOR ROAD BRIDGES
TrafficTraffic loadload modelsmodels
-- Vertical forces : LM1, LM2, LM3, LM4Vertical forces : LM1, LM2, LM3, LM4-- Horizontal forces :Horizontal forces : brakingbraking andand
accelerationacceleration,, centrifugalcentrifugal , transverse, transverse
Groups of Groups of loadsloads
-- gr1a, gr1b, gr2, gr3, gr4, gr5gr1a, gr1b, gr2, gr3, gr4, gr5
-- characteristiccharacteristic,, frequentfrequent andand
quasiquasi--permanent valuespermanent values
CombinationCombination withwith actionsactions other other thanthan
traffictraffic actionsactions
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•• LoadLoad ModelModel Nr Nr . 1. 1
ConcentratedConcentrated andand distributeddistributed loadsloads (main model(main model – – For For general andgeneral and locallocal verificationsverifications))
•• LoadLoad ModelModel Nr Nr . 2. 2
SingleSingle axleaxle loadload (semi(semi--locallocal andand locallocal verificationsverifications))
•• LoadLoad ModelModel Nr Nr . 3. 3Set of Set of specialspecial vehiclesvehicles ((general andgeneral and locallocal verificationsverifications))
•• LoadLoad ModelModel Nr Nr . 4. 4CrowdCrowd loadingloading : 5: 5 kNkN/m/m22 ((general verificationsgeneral verif ications))
ROAD BRIDGES : LOAD MODELS FOR LIMIT STATESROAD BRIDGES : LOAD MODELS FOR LIMIT STATESOTHER THAN FATIGUE LIMIT STATESOTHER THAN FATIGUE LIMIT STATES
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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TheThe mainmain loadload model (LM1)model (LM1)
TS : Tandem systemUDL : Uniformly distributed load
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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TheThe mainmain loadload model (LM1)model (LM1)
ExampleExample of values for of values for α
factorsfactors (National Annexes)(National Annexes)11stst class : internationalclass : international heavyheavy
vehicle trafficvehicle traffic
22ndnd class :class : «« normalnormal »» heavyheavy
vehicle trafficvehicle traffic
Classes 1Q 2iQi 1q 2iqi qr
1st class 1 1 1 1 1
2nd class 0,9 0,8 0,7 1 1
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Example of influence surface (transverse
bending moment) for a deck slab
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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LoadLoad modelmodel Nr Nr . 2 (LM2). 2 (LM2)
1QQ α=RecommendedRecommended valuevalue :: (National(National Annex Annex))
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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HORIZONTAL FORCES : BRAKING AND ACCELERATION (HORIZONTAL FORCES : BRAKING AND ACCELERATION (LaneLane Nr Nr . 1 ). 1 )
LwqQQ kq kQ k 11111 10,0)2(6,0 α+l kN Q kN kQ 900180 1 ≤
l
αQ1Q1 == αq1q1 = 1= 1
QQlklk = 180 + 2,7L= 180 + 2,7L
For 0For 0 ≤ LL ≤ 1,2 m1,2 m
QQlklk = 360 + 2,7L= 360 + 2,7L
For L > 1,2 mFor L > 1,2 m
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Group of Group of
loadsloads
gr1a :gr1a :
LM1 + «LM1 + « reducedreduced » value» value
of of pedestrianpedestrian loadload onon
footwaysfootways or cycleor cycle trackstracks
(3(3 kNkN/m/m22))
Group of Group of loadsloads gr1b : LM2gr1b : LM2
(single(single axleaxle loadload))
Group of Group of loadsloads gr2 :gr2 :
characteristiccharacteristic values of values of
horizontal forces,horizontal forces, frequentfrequent
values of LM1values of LM1
Groups of Groups of loadsloads
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Group of Group of loadsloads gr4 :gr4 :
crowdcrowd loadingloading
Group of Group of loadsloads gr5 :gr5 : specialspecial
vehiclesvehicles (+(+ specialspecial
conditions for normalconditions for normal traffictraffic))
Group of Group of loadsloads gr3 :gr3 :
loadsloads onon footwaysfootways andand
cyclecycle trackstracks
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CARRIAGEWAY FOOTWAYS
AND
CYCLE TRACKS
Load type Vertical forces Horizontal forces Vertical
forces only
Reference 4.3.2 4.3.3 4.3.4 4.3.5 4.4.1 4.4.2 5.3.2-(1)
Load system LM1
(TS and
UDL
systems)
LM2
(Single axle)
LM3
(Special
vehicles)
LM4
(Crowd
loading)
Braking and
acceleration
forces
Centrifugal
and
transverse
forces
Uniformly
Distributed
load
gr1a Characteristic
values
a aCombination
value b
gr1b Characteristicvalue
gr2 Frequentvalues
Characteristicvalue
Characteristicvalue
Groups of
Loads
gr3 d Characteristicvalue
c
gr4 Characteristic
value
Characteristic
value
gr5 See annex A Characteristicvalue
Dominant component action (designated as component associated with the group)a May be defined in the National Annex.
bMay be defined in the National Annex. The recommended value is 3 kN/m
2.
cSee 5.3.2.1-(2). One footway only should be considered to be loaded if the effect is more unfavourable than the effect of two loaded footways.
d This group is irrelevant if gr4 is considered.
TheThe ““ goodgood”” Table 4.4aTable 4.4a -- Assessment Assessment of groups of of groups of traffictraffic
loadsloads ((characteristiccharacteristic values of values of the multithe multi --component action)component action)
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•• LoadLoad ModelModel Nr Nr . 1 (FLM1) :. 1 (FLM1) : Similar Similar toto LoadLoad ModelModel Nr Nr . 1. 1
0,7 x0,7 x QQikik -- 0,3 x0,3 x qq ikik -- 0,3 x0,3 x qq rkrk
•• LoadLoad ModelModel Nr Nr . 2 (FLM2) : Set of «. 2 (FLM2) : Set of « frequentfrequent » lorries» lorries
•• LoadLoad ModelModel Nr Nr . 3 (FLM3) : Single. 3 (FLM3) : Single vehiclevehicle
•• LoadLoad ModelModel Nr Nr . 4 (FLM4) : Set of «. 4 (FLM4) : Set of « equivalentequivalent » lorries (to» lorries (to
createcreate anan artifical trafficartifical traffic))
•• LoadLoad ModelModel Nr Nr . 5 (FLM5) : Use of . 5 (FLM5) : Use of recorded traffic effectsrecorded traffic effects
FATIGUE LOAD MODELSFATIGUE LOAD MODELS
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FatigueFatigue LoadLoad ModelModel Nr Nr .3 (FLM3).3 (FLM3)
A second A second vehiclevehicle maymay bebe takentaken intointo accountaccount ::
RecommendedRecommended axleaxle loadload value Q = 36value Q = 36 kNkN
Minimum distanceMinimum distance betweenbetween vehiclesvehicles : 40 m: 40 m
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•• DeterminationDetermination of of thethe maximummaximum andand minimum stressesminimum stresses
resultingresulting fromfrom thethe transit of transit of thethe modelmodel alongalong thethe bridgebridge
•• TheThe stress variationstress variation isis multipliedmultiplied by a localby a local dynamicdynamic
amplificationamplification factor factor inin thethe vicinityvicinity of expansion jointsof expansion joints
•• TheThe modelmodel isis normallynormally centeredcentered inin everyevery slowslow lanelane
defineddefined inin thethe projectproject specificationspecification..
•• Design value of Design value of thethe stress variationstress variation
LM LM LM Min Max σ−
fat
VerificationVerification procedureprocedure withwith LoadLoad Model FLM 3Model FLM 3
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
LM fat fat σ∆
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s : gauge
u : cant
Qs: nosing force
(1) Running surface(2) Longitudinal forces acting along the centreline of the
track
RailRail traffictraffic actionsactions
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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The characteristic values are multiplied by a factor The characteristic values are multipl ied by a factor α α on lineson lines
carrying rail traffic which is heavier or lighter than normal racarrying rail traffic which is heavier or lighter than normal railil
traffic.traffic.
This factor This factor α α shallshall bebe oneone of of thethe followingfollowing: 0,75: 0,75 -- 0,830,83 -- 0,910,91 -- 1,001,00-- 1,101,10 -- 1,211,21 -- 1,331,33 – – 1,46.1,46.
TheThe valuevalue 1,331,33 isis normallynormally recommendedrecommended onon lineslines for for freightfreight
traffictraffic andand internationalinternational lineslines (UIC CODE 702, 2003).(UIC CODE 702, 2003).
LOAD MODEL 71LOAD MODEL 71
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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Load model qvk
[kN/m]
a
[m]
c
[m]
SW/0
SW/2
133
150
15,0
25,0
5,3
7,0
LOAD MODELS SW/0 & SW/2 (LOAD MODELS SW/0 & SW/2 (heavy trafficheavy traffic ))
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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ExampleExample of aof a heavyheavy weightweight waggonwaggon (DB, 32(DB, 32 axlesaxles,,selfweightselfweight 246 t,246 t, pay loadpay load 457 t, mass457 t, mass per per axleaxle 22 t ,22 t , LL tottot ==
63,3 m63,3 m
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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High speed trains : 2 load models HSLM-A and HSL-B
HSLM-A and HSLM-B together represent the dynamic load effects of articulated, conventional and regular high speed passenger trains inaccordance with the requirements for the European Technical Specification
for Interoperability
HSLMHSLM-- A : (1) Power car ( A : (1) Power car (leading and trailingleading and trailing power carspower cars identicalidentical) ; 2) End) ; 2) End
coach (coach (leading and trailingleading and trailing end coachesend coaches identicalidentical) ; (3)) ; (3) IntermediateIntermediate coachcoach
HSLMHSLM--BB
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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•• DynamicDynamic factorsfactors for for staticstatic calculationscalculations ::
Φ22 for for carefullycarefully maintainedmaintained tracktrack
Φ33 for standardfor standard tracktrack ((meansmeans :: poor trackpoor track))((determinant lengthsdeterminant lengths LLΦ due to table 6.2)due to table 6.2)
•• Dynamic enhancementDynamic enhancement for real trainsfor real trains
1 +1 + ϕ = 1 += 1 + ϕ ' + (½)' + (½) ϕ''''•• Dynamic enhancementDynamic enhancement for fatiguefor fatigue calculationscalculations
ϕ = 1 + ½(= 1 + ½(ϕ ' + (½)' + (½)ϕ '')'')
•• Dynamic enhancementDynamic enhancement for for dynamic studiesdynamic studies
1 / max' − stat dyn dyn y y
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
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•• Interaction model between the bridge and the trackInteraction model between the bridge and the track
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
(1) Track(1) Track
(2) Superstructure (a single deck comprising two spans and a sin(2) Superstructure (a single deck comprising two spans and a single deckgle deckwith one span shown)with one span shown)
(3) Embankment(3) Embankment
(4) Rail expansion device (if present)(4) Rail expansion device (if present)
(5) Longitudinal non(5) Longitudinal non--linear springs reproducing the longitudinal load/linear springs reproducing the longitudinal load/
displacement behaviour of the trackdisplacement behaviour of the track
(6) Longitudinal springs reproducing the longitudinal stiffness(6) Longitudinal springs reproducing the longitudinal stiffness K K of a fixedof a fixed
support to the deck taking into account the stiffness of the fousupport to the deck taking into account the stiffness of the fou ndation, piersndation, piers
and bearings etc.and bearings etc.
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ExampleExample of a real train for fatigueof a real train for fatigue
((Nr Nr . 1 of 12 types of trains. 1 of 12 types of trains defineddefined inin thethe EurocodeEurocode))
EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
EN 1991EN 1991 22 T ffi L dT ffi L d B idB id
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EN 1991EN 1991--22 «« Traffic LoadsTraffic Loads on Bridgeson Bridges »»
Groups of Groups of loadsloads
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Maximum permissible vertical deflectionMaximum permissible vertical deflection δ for railway bridges with 3 or for railway bridges with 3 or
more successive simply supported spans corresponding to amore successive simply supported spans corresponding to a
permissible vertical acceleration of permissible vertical acceleration of bbvv = 1 m/s= 1 m/s²² in a coach for speedin a coach for speed V V
[km/h][km/h]
EN 1990/A1EN 1990/A1 «« Application for Bridges Application for Bridges »»
EN 1990EN 1990 S ti 6S ti 6 AA A2A2
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EN 1990EN 1990 – – Section 6,Section 6, Annex Annex A2 A2
EN 1990EN 1990““ EurocodeEurocode ::
Basis of Basis of
Structural DesignStructural Design
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ForewordForeword
Section 1Section 1 :: GeneralGeneral
Section 2Section 2 :: RequirementsRequirements
Section 3Section 3 :: PrinciplesPrinciples of of limitlimit statesstatesSection 4Section 4 : Basic variables: Basic variables
Section 5Section 5 : Structural: Structural analysisanalysis andand designdesign assistedassisted byby
testingtesting
Section 6Section 6 :: VerificationVerification byby thethe partialpartial factor factor methodmethod
Annex Annex A1 A1 : Application for buildings (N): Application for buildings (N)
Annex Annex A2 A2 : Application for bridges (N) (EN 1990/A1): Application for bridges (N) (EN 1990/A1)
Annex Annex BB : Management of structural: Management of structural reliabilityreliability for for
constructionconstruction worksworks (I)(I)
Annex Annex CC :: BasisBasis for partialfor partial factor factor designdesign andand
reliabilityreliability analysisanalysis (I)(I)
Annex Annex DD : Design: Design assistedassisted byby testingtesting (I)(I)
EN 1990EN 1990 – – Section 6,Section 6, Annex Annex A2 A2
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Section 6Section 6 -- Verification by theVerification by the
partial factor methodpartial factor method
6.16.1 GeneralGeneral
6.26.2 LimitationsLimitations6.36.3 Design valuesDesign values
6.46.4 Ultimate limit statesUltimate limit states
6.56.5 Serviceabil ity limit statesServiceabil ity limit states
EN 1990EN 1990 – – Section 6,Section 6, Annex Annex A2 A2
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VerificationsVerificationsDesign situationsDesign situations
ULS,SLSULS,SLS
ULS,SLSULS,SLS
ULSULS
ULSULS
ULS, SLSULS, SLS
ULS, SLSULS, SLS
Normal useNormal use
During executionDuring execution
During executionDuring execution
SeismicSeismic
Normal useNormal use Accidental Accidental
ExecutionExecution,, temporarytemporary
conditions applicable tocondit ions applicable to
thethe structure, e.g.structure, e.g.
maintenance or maintenance or repair repair
TransientTransient
Normal useNormal usePersistentPersistent
TheThe selectedselected design situationdesign situation shallshall bebe sufficientlysufficiently severesevere andand soso variedvaried
as toas to encompassencompass all conditionsall condit ions whichwhich cancan reasonablyreasonably bebe foreseenforeseen totooccur occur duringduring thethe executionexecution andand use of use of thethe structure (3.2(3)P).structure (3.2(3)P).
EN 1990EN 1990 – – Section 6,Section 6, Annex Annex A2 A2
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Representative values of actions
EN 1990 – Section 6, Annex A2
EN 1990 – Section 6 Annex A2
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Turkstra’s ruleTurkstra’s rule (1972) :(1972) :within thewithin the set of variableset of variable
actions applicable to aactions applicable to a
structure, one of structure, one of them isthem is
selected and calledselected and called«« leadingleading variablevariable
actionaction » ;» ; the other the other
variable actions arevariable actions are
accompanyingaccompanying actionsactions
andand areare taken intotaken into
accountaccount inin thethe
combinationscombinations of actionsof actions
with their combinationwith their combination
values.values.
TheThe setset includingincluding all permanent actions,all permanent actions, the leadingthe leading variable actionvariable action
andand thethe relevantrelevant accompanyingaccompanying variable actionsvariable actions formsforms aa combinationcombination
of actions.of actions. The variousThe various values of actionsvalues of actions usedused inin the verificationsthe verifications areare
calledcalled «« representativerepresentative valuesvalues ».».
How to establish a combination of actions
EN 1990 – Section 6, Annex A2
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F F i i F F k k ,i ,i F F d d ,i ,i == ψγγ f,f,i i F F k k ,i ,i E( E( F F d d ,i ,i ; a; ad d ) )
E E d d == γSd Sd E E ( ( F F d d ,i ,i ; a; ad d ) ) E E d d = E( = E( ψγγF,F,i i F F k k ,i ,i ; a; ad d ) )
γγF,i F,i == γf,i f,i ×γγSd Sd
Action ActionCharacteristic Characteristic
value of value of thethe
actionaction
Design value of Design value of thethe actionaction Effect Effect of of
actionsactions
Design value of Design value of thethe effect effect of of
actionsactionsDesign value of Design value of thethe
effect effect of actionsof actions
( ( simplified simplified expression)expression)
EN 1990 – Section 6, Annex A2
ACTIONS ACTIONS
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aad d
Design value of Design value of geometrical geometrical datadata
γf f Uncertainty Uncertainty inin representativerepresentative valuesvalues
of actionsof actions
γSd Sd Model Model uncertainty uncertainty in actionsin actions and and
actionaction effectseffects
ψ Is either Is either 1,00 or 1,00 or ψ0,0,,, ψ1,1, or or ψ2,2,
EN 1990 – Section 6, Annex A2
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X X i i X X k k ,i ,i X X d,i d,i = ( = ( ηi i / / γm,i m,i ) ) X X k k ,i ,i R(X R(X d,i d,i ; a; ad d ) )
R R d d = (1/ = (1/ γRd Rd )R(X )R(X d,i d,i ; a; ad d ) ) R R d d = R(( = R(( ηi i / / γM,i M,i ) ) X X k k ,i ,i ; a; ad d ) )
γγM,i M,i == γm,i m,i ×γγRd Rd
Material Material
propertry propertry
Characteristic Characteristic
value of value of thethe
material property material property
Design value of Design value of thethematerial property material property Structural Structural
ResistanceResistance
Design value of Design value of thethe
structural structural
resistanceresistanceDesign value of Design value of thethe
structural structural resistanceresistance
( ( simplified simplified expression)expression)
EN 1990 – Section 6, Annex A2
RESISTANCES RESISTANCES
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aad d Design value of Design value of geometrical geometrical datadata
γmm Uncertainty Uncertainty inin material propertiesmaterial properties,,
including the randomincluding the random part of part of thethe
conversionconversion factor factor η
γRd Rd Model Model uncertainty uncertainty in structural in structural resistanceresistance
η The meanThe mean value of value of thethe conversionconversion factor factor
taking into account taking into account ::
-- volumevolume and scale effectsand scale effects,,-- effectseffects of of moisture and temperaturemoisture and temperature,, and and
-- any other any other relevant relevant parameters parameters
EN 1990 – Section 6, Annex A2
EN 1990 Section 6 Annex A2
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EEQQUU LLoossss oof f ssttaattiicc eeqquuii ll iibbr r iiuumm oof f tthhee ssttr r uuccttuur r ee oor r aannyy ppaar r tt oof f ii tt
ccoonnssiiddeer r eedd aass aa r r iiggiidd bbooddyy,, iinn wwhhiicchh ::
-- mmiinnoor r vvaar r iiaattiioonnss iinn tthhee vvaalluuee oor r tthhee ssppaattiiaall ddiissttr r iibbuuttiioonn oof f aaccttiioonnss f f r r oomm aa ssiinnggllee ssoouur r ccee aar r ee ssiiggnniif f iiccaanntt ;; -- tthhee ssttr r eennggtthhss oof f ccoonnssttr r uuccttiioonn mmaatteer r iiaallss oor r ggr r oouunndd aar r ee ggeenneer r aallllyy nnoott ggoovveer r nniinngg
SSTTRR IInntteer r nnaall f f aaiilluur r ee oof f tthhee ssttr r uuccttuur r ee oor r ssttr r uuccttuur r aall eelleemmeennttss,, iinncclluuddiinngg f f oooottiinnggss,, ppiilleess,, bbaasseemmeenntt wwaallllss,, eettcc..,, iinn wwhhiicchh tthhee ssttr r eennggtthh oof f ccoonnssttr r uuccttiioonn mmaatteer r iiaallss oor r eexxcceessssiivvee ddeef f oor r mmaattiioonn oof f tthhee ssttr r uuccttuur r ee ggoovveer r nnss
GGEEOO FFaaii lluur r ee oor r eexxcceessssiivvee ddeef f oor r mmaattiioonn oof f tthhee ggr r oouunndd iinn wwhhiicchh tthhee ssttr r eennggtthhss oof f ssooii ll oor r r r oocckk aar r ee ssiiggnniif f iiccaanntt iinn ppr r oovviiddiinngg r r eessiissttaannccee
FF A ATT FFaattiigguuee f f aaii lluur r ee oof f tthhee ssttr r uuccttuur r ee oor r ssttr r uuccttuur r aall eelleemmeennttss
Ultimate limit statesUltimate limit states
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EN 1990 – Section 6, Annex A2
Ultimate LimitUltimate Limit StatesStatesEQUEQU – – STRSTR – – GEO for aGEO for a
bridge.bridge.
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EQUEQU
STRSTR
GEOGEO
FATFAT
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6.4.26.4.2 VerificationsVerifications of of staticstatic equilibriumequilibrium and resistanceand resistance
UltimateUltimate limitlimit states of states of staticstatic equilibriumequilibrium (EQU) :(EQU) :
EEdd,dst,dst ≤ EEdd,,stbstb
UltimateUltimate limitlimit states of states of resistanceresistance (STR/GEO) :(STR/GEO) :
EEdd≤ RR
dd6.56.5 ServiceabilityServiceability limitlimit statesstates
EEdd ≤ CCdd
CCdd is the limiting design value of the relevantis the limiting design value of the relevant
serviceability criterion.serviceability criterion.EEdd is the design value of the effects of actions specified inis the design value of the effects of actions specified in
the serviceabil ity criterion, determined on the basis of thethe serviceabil ity criterion, determined on the basis of the
relevant combination.relevant combination.
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CombinationsCombinations of actions ULS)of actions ULS)
EN 1990 Section 6, Annex A2
CombinationReferenceEN 1990
General expression
6.10 ∑ ∑≥ >
+1 1
,,0,1,1, """""" j i
i kiiQ kQ P kjGj QQ PG ψ
Fundamental(for persistentand transientdesignsituations)
6.10 a/b⎪⎩
⎪⎨
⎧
+
+
∑∑
>
>
1
,,0,1,1,
1
,,
1
,,0,1,1,01,
1
,,
""""""
""""""
i
i kiiQ kQ P
j
j k jG j
i
i kiiQ kQ P
j
j k jG
QQPG
QQPG
ψ
ψ
00,185,0 ≤ j for unfavourable permanent
actions G
Accidental
(for accidentaldesignsituations)
6.11 ∑ ∑≥ ≥
+1 1
,,211,21,1 "")("""""" j i
i ki k d kj QQ ou A PG ψ
Seismic
(for seismicdesign
situations)
6.12 ∑ ∑≥ ≥
+1 1
,,2, """""" j i
i ki Ed j k Q A PG ψ
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6.5.36.5.3 ServiceabilityServiceability limitlimit states :states : combinationscombinations of of actionsactions
CharacteristicCharacteristic CombinationCombination ((irreversibleirreversible SLS)SLS)
FrequentFrequent CombinationCombination ((reversiblereversible SLS)SLS)
QuasiQuasi--permanentpermanent CombinationCombination ((reversiblereversible SLS)SLS)
∑ ∑≥ >
+1 1
,,01,, """""" j i
i ki k j k QQ PG ψ
∑ ∑≥ >
+1 1
,,21,1,1, """""" j i
i ki k j k QQ PG ψ
∑ ∑≥ ≥
+1 1
,,2, """" j i
i ki j k Q PG ψ
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DESIGN VALUES OF ACTIONSDESIGN VALUES OF ACTIONS
APPROACH 1 APPROACH 1
APPROACH 2 APPROACH 2
APPROACH 3 APPROACH 3
TABLESTABLES
A2.4(A) A2.4(B) A2.4(C) A2.4(A) A2.4(B) A2.4(C)ULS EQUULS EQU
ULS STRULS STRwithoutwithout
geotechnicalgeotechnicalactionsactions
ULS STRULS STRwithwith geotechnicalgeotechnical
actionsactions
ULS GEOULS GEO
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ExamplesExamples of of combinationscombinations of actionsof actions
for road bridgesfor road bridges
Note 1 :Note 1 : The combinationsThe combinations of actions areof actions are basedbased onon thethe
recommendedrecommended valuesvalues givengiven inin Annex Annex A2 A2Note 2 :Note 2 : ExceptExcept for for roofedroofed bridges,bridges, it is assumed thatit is assumed that
snow loadssnow loads on road bridgeson road bridges may be assessedmay be assessed asas
snow loadssnow loads onon the groundthe ground..
,
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Action Symbol ψ0 ψ1 ψ2
TS 0,75 0,75 0
UDL 0,40 0,40 0
gr1a
(LM1+pedestrianor cycle-track
loads)1) Pedestrian+cycle-track loads
2)
0,40 0,40 0
gr1b (Single axle) 0 0,75 0
Traffic loads gr2 (Horizontal forces) 0 0 0(see EN 1991-2,
Table 4.4)
gr3 (Pedestr ian loads) 0 0 0
gr4 (LM4 – Crowd loading) 0 0,75 0
gr5 (LM3 – Special vehicles) 0 0 0
Wk F
- Persistent design situations
- Execution0,6
0,8
0,2
-
0
0
Wind forces
∗W F
1,0 - -
Thermalactions
T k 0,63)
0,6 0,5
Snow loads Q Sn,k (during execution) 0,8 - -
Construction
loads
Q c 1,0 - 1,0
,
Table A2.1
Recommended
values of ψfactors for road
bridges
0,400,40
00
Too highToo high
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FundamentalFundamental combinationscombinations of actionsof actions basedbased on expression 6.10on expression 6.10
*
fkq ReducedReduced value of value of the loadthe load onon footwaysfootways for group gr1afor group gr1a – – ToTo bebedefineddefined inin thethe NationalNational Annex Annex (for (for exampleexample : 2,5: 2,5 kNkN/m/m22))
k P PrestressingPrestressing :: DefinitionDefinition in designin design EurocodesEurocodes.. UsuallyUsually P = PP = Pmm etet γPP = 1= 1
setG Uneven settlementsUneven settlements toto be taken into account wherebe taken into account where relevant,relevant, withwith γGsetGset
= 1,20 or 1,00 in case of = 1,20 or 1,00 in case of linear linear analysisanalysis..
gr1agr1a
ψ00gr1agr1a
⎪⎪
⎪
⎩
⎪⎪⎪
⎨
⎧
+
×
+⎭⎬⎫
⎩⎨⎧
+
=
≥∑
kSn
Wk
fk k
bi
trafficWk fk
k P kj kj
j
Q
F
qUDLTST
gri
FqUDLTS
PGG
,
*
5,4,3,2,1
,
*
inf ,sup,
1
5,1
5,1
)4,04,075,0(35,15,1
35,1
6,05,1)(35,1
"""")00,1""35,1( γ
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Representation of the action of uneven settlements Gset.
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CharacteristicCharacteristic combinationscombinations of actionsof actions
k P CharacteristicCharacteristic value of value of the prestressingthe prestressing forceforce
setG Uneven settlementsUneven settlements toto be taken into account wherebe taken into account where relevantrelevant
gr1agr1a
ψ00gr1agr1a⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
+++
+
+++
++⎭⎬
⎫
⎩⎨
⎧+
=
≥∑
k Sn
Wk
fk k
k bi
trafficWk fk
k kjkj j
Q
F
qUDLTS T
bgr
T gri
F qUDLTS
PGG
,
*
5,4,3,2,1
,
*
inf ,sup,1 )4,04,075,0(""
1
6,0""
6,0")"(
"""")""(
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QuasiQuasi--permanentpermanent combinationscombinations of actionsof actions
FrequentFrequent combinationscombinations of actionsof actions
⎪
⎪⎪
⎩
⎪⎪
⎪
⎨
⎧
+
+
+⎭
⎫
⎩
⎧+
≥
kSn
Wk
k
k
k
k kj kj
j
Q
F
T
T gr
b gr
T UDLTS
PGG
,
inf ,sup,
1
5,0
2,0
6,0
5,0""475,0
175,0
5,0")"4,075,0(
"""")""(
k k kj kj
j
T PGG 5,0"""")""( inf ,sup,
1
+⎭⎬⎫
⎩⎨⎧
+≥
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EN 1991EN 1991 11 6 : Actions6 : Actions during executionduring execution