Eurocod Misc

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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



BB

A A

BB

EE

LL

BELOWBELOW

ACCEPTABLE ACCEPTABLE

BASICBASIC

ENGLISHENGLISH

LANGUAGELANGUAGE



Design of BridgesDesign of Bridges with the Eurocodeswith the Eurocodes



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 »»



•• 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




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




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




•• 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




TheThe mainmain loadload model (LM1)model (LM1)

TS : Tandem systemUDL : Uniformly distributed load




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




Example of influence surface (transverse

bending moment) for a deck slab




LoadLoad modelmodel Nr Nr . 2 (LM2). 2 (LM2)

1QQ α=RecommendedRecommended valuevalue :: (National(National Annex Annex))




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




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






crowdcrowd loadingloading

Group of Group of loadsloads gr5 :gr5 : specialspecial

vehiclesvehicles (+(+ specialspecial

conditions for normalconditions for normal traffictraffic))


loadsloads onon footwaysfootways andand

cyclecycle trackstracks




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)



•• 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




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




•• 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


LM fat fat σ∆



s : gauge

u : cant

Qs: nosing force

(1) Running surface(2) Longitudinal forces acting along the centreline of the

track

RailRail traffictraffic actionsactions




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




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 ))




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




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




•• 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




•• Interaction model between the bridge and the trackInteraction model between the bridge and the track


(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.



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 T ffi L dT ffi L d B idB id







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



EN 1990EN 1990 – – Section 6,Section 6, Annex Annex A2 A2

EN 1990EN 1990““ EurocodeEurocode ::

Basis of Basis of

Structural DesignStructural Design



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)




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




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).




Representative values of actions

EN 1990 – Section 6, Annex A2

EN 1990 – Section 6 Annex A2



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




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)


ACTIONS ACTIONS



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,




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)


RESISTANCES RESISTANCES



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



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






Ultimate LimitUltimate Limit StatesStatesEQUEQU – – STRSTR – – GEO for aGEO for a

bridge.bridge.




EQUEQU

STRSTR

GEOGEO

FATFAT


EN 1990 – Section 6 Annex A2



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.





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




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





DESIGN VALUES OF ACTIONSDESIGN VALUES OF ACTIONS

APPROACH 1 APPROACH 1



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





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..

,




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




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




Representation of the action of uneven settlements Gset.





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")"(

"""")""(




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

+⎭⎬⎫

⎩⎨⎧

+≥

EN 1991EN 1991--11--6 : Actions6 : Actions during executionduring execution



EN 1991EN 1991 11 6 : Actions6 : Actions during executionduring execution



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