Introduction, Traffic Loads on Bridges & Combinations …library.tee.gr/digital/m2346/m2346_calgaro.pdf · Introduction, Traffic Loads on Bridges & Combinations of actions Jean-Armand

Introduction, Traffic Loads on Introduction, Traffic Loads on Bridges & Combinations of actions Bridges & Combinations of actions

Jean-Armand CalgaroChairman of CEN/TC250

““Application of Application of Eurocodes Eurocodes for bridgesfor bridges””

Athens, 20 October 2008 Athens, 20 October 2008

BB

AA

BB

EE

LL

BELOWBELOW

ACCEPTABLEACCEPTABLE

BASICBASIC

ENGLISHENGLISH

LANGUAGE LANGUAGE

Design of Bridges Design of Bridges with the Eurocodeswith the Eurocodes

EN 1991EN 1991--22EurocodeEurocode 1 : Actions on 1 : Actions on

structures structures –– Part 2:Part 2:Traffic Loads Traffic Loads on on

BridgesBridges

EN 1991EN 1991--2 2 «« 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 OTHER ROAD TRAFFIC ACTIONS AND OTHER ACTIONS SPECIFICALLY FOR ROAD BRIDGESACTIONS SPECIFICALLY FOR ROAD BRIDGES

•• SECTION 5SECTION 5 ACTIONS ON FOOTWAYS, CYCLE TRACKSACTIONS ON FOOTWAYS, CYCLE TRACKSAND FOOTBRIDGESAND FOOTBRIDGES

•• SECTION 6SECTION 6 RAIL TRAFFIC ACTIONS AND OTHER RAIL TRAFFIC ACTIONS AND OTHER ACTIONS SPECIFICALLY FOR RAILWAY BRIDGESACTIONS SPECIFICALLY FOR RAILWAY BRIDGES


ANNEX A (I)ANNEX A (I) Models of Models of special vehicles special vehicles for road bridgesfor road bridges

ANNEX B (I)ANNEX B (I) Fatigue life Fatigue life assessmentassessment for road bridges for road bridges –– Assessment Assessment method method basedbased on on recordedrecorded traffictraffic

ANNEX C (N)ANNEX C (N) Dynamic factorsDynamic factors 1+1+ϕϕ for real trainsfor real trains

ANNEX D (N)ANNEX D (N) BasisBasis for for thethe fatigue fatigue assessmentassessment of of railwayrailwaystructuresstructures

ANNEX E (I)ANNEX E (I) LimitsLimits of of validityvalidity of of loadload model HSLM model HSLM andandthe selectionthe selection of of thethe criticalcritical universaluniversal traintrainfromfrom HSLMHSLM--AA

ANNEX F (I)ANNEX F (I) CriteriaCriteria to to bebe satisfiedsatisfied if a if a dynamicdynamicanalysis is analysis is not not requiredrequired

ANNEX G (I)ANNEX G (I) MethodMethod for for determiningdetermining thethe combined responsecombined responseof a structure of a structure andand tracktrack to variable actionsto variable actions

AnnexAnnex H (I)H (I) LoadLoad models for rail models for rail traffictraffic loadsloads inintransienttransient situationssituations


TRAFFIC LOTRAFFIC LOAD MODELS FOR ROAD BRIDGESAD MODELS FOR ROAD BRIDGES

TrafficTraffic loadload modelsmodels

-- Vertical forces : LM1, LM2, LM3, LM4Vertical forces : LM1, LM2, LM3, LM4-- Horizontal forces : Horizontal forces : brakingbraking andandaccelerationacceleration, , centrifugalcentrifugal, transverse, transverse

Groups of Groups of loadsloads

-- gr1a, gr1b, gr2, gr3, gr4, gr5gr1a, gr1b, gr2, gr3, gr4, gr5-- characteristiccharacteristic, , frequentfrequent andandquasiquasi--permanent valuespermanent values

CombinationCombination withwith actions actions otherother thanthantraffictraffic actions actions


•• LoadLoad Model Model NrNr. 1. 1ConcentratedConcentrated andand distributeddistributed loadsloads (main model (main model –– For For general andgeneral and local local verificationsverifications))

•• LoadLoad Model Model NrNr. 2. 2Single Single axleaxle load load (semi(semi--local local and and local local verificationsverifications))

•• LoadLoad Model Model NrNr. 3. 3Set of Set of specialspecial vehicles vehicles ((general and general and local local verificationsverifications))

•• LoadLoad Model Model NrNr. 4. 4CrowdCrowd loadingloading : 5 : 5 kNkN/m/m22 ((general verificationsgeneral verifications))

ROAD BRIDGES : LOAD MODELS FOR LIMIT STATES ROAD BRIDGES : LOAD MODELS FOR LIMIT STATES OTHER THAN FATIGUE LIMIT STATESOTHER THAN FATIGUE LIMIT STATES


TheThe main main loadload model (LM1)model (LM1)

TS : Tandem systemUDL : Uniformly distributed load


TheThe main main loadload model (LM1)model (LM1)

ExampleExample of values for of values for ααfactorsfactors (National Annexes) (National Annexes)

11stst class : international class : international heavy heavy vehicle trafficvehicle traffic

22ndnd class : class : «« normalnormal »» heavy heavy vehicle trafficvehicle traffic

Classes 1Qα 2≥iQiα 1qα 2≥iqiα qrα

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 model model NrNr. 2 (LM2). 2 (LM2)

1QQ αβ =RecommendedRecommended valuevalue :: (National (National AnnexAnnex))


HORIZONTAL FORCES : BRAKING AND ACCELERATION (HORIZONTAL FORCES : BRAKING AND ACCELERATION (LaneLane NrNr. 1 ). 1 )

LwqQQ kqkQk 11111 10,0)2(6,0 αα +=l kNQkN kQ 900180 1 ≤≤ lα

ααQ1Q1 = = ααq1q1 = 1= 1

QQlklk = 180 + 2,7L= 180 + 2,7L

For 0 For 0 ≤≤ L L ≤≤ 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 on on footwaysfootways or cycle or cycle tracks tracks (3 (3 kNkN/m/m22))

Group of Group of loadsloads gr1b : LM2 gr1b : LM2 (single (single axleaxle loadload))

Group of Group of loadsloads gr2 : gr2 : characteristiccharacteristic values of values of horizontal forces, horizontal forces, frequentfrequentvalues of LM1values of LM1



Group of Group of loadsloads gr4 : gr4 : crowdcrowd loadingloading

Group of Group of loadsloads gr5 : gr5 : specialspecialvehiclesvehicles (+ (+ specialspecialconditions for normal conditions for normal traffictraffic))

Group of Group of loadsloads gr3 : gr3 : loadsloads on on footwaysfootways andandcycle cycle 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 a Combination value b

gr1b Characteristic value

gr2 Frequent values

Characteristic value


Groups of Loads

gr3 d Characteristic value c

gr4 Characteristic value


gr5 See annex A Characteristic value

Dominant component action (designated as component associated with the group) a May be defined in the National Annex. b May be defined in the National Annex. The recommended value is 3 kN/m2. c See 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.

The The ““goodgood”” Table 4.4a Table 4.4a -- AssessmentAssessment of groups ofof groups of traffic traffic loadsloads ((characteristiccharacteristic values ofvalues of the multithe multi--component action)component action)

•• LoadLoad Model Model NrNr. 1 (FLM1) : . 1 (FLM1) : SimilarSimilar to to LoadLoad Model Model NrNr. 1. 10,7 x 0,7 x QQikik -- 0,3 x 0,3 x qqikik -- 0,3 x 0,3 x qqrkrk

•• LoadLoad Model Model NrNr. 2 (FLM2) : Set of «. 2 (FLM2) : Set of « frequentfrequent » lorries» lorries

•• LoadLoad Model Model NrNr. 3 (FLM3) : Single . 3 (FLM3) : Single vehiclevehicle

•• LoadLoad Model Model NrNr. 4 (FLM4) : Set of «. 4 (FLM4) : Set of « equivalentequivalent » lorries (to » lorries (to create create an an artifical trafficartifical traffic))

•• LoadLoad Model Model NrNr. 5 (FLM5) : Use of . 5 (FLM5) : Use of recorded traffic effectsrecorded traffic effects

FATIGUE LOAD MODELSFATIGUE LOAD MODELS


Fatigue Fatigue LoadLoad Model Model NrNr.3 (FLM3).3 (FLM3)

A second A second vehiclevehicle maymay bebe takentaken intointo accountaccount : : RecommendedRecommended axleaxle loadload value Q = 36 value Q = 36 kNkNMinimum distance Minimum distance betweenbetween vehiclesvehicles : 40 m: 40 m


•• DeterminationDetermination of of thethe maximum maximum andand minimum stresses minimum stresses resultingresulting fromfrom thethe transit of transit of thethe model model alongalong thethe bridgebridge

•• TheThe stress variation stress variation isis multipliedmultiplied by a local by a local dynamicdynamicamplification amplification factorfactor in in thethe vicinityvicinity of expansion jointsof expansion joints

•• TheThe model model isis normallynormally centeredcentered in in everyevery slow slow lanelanedefineddefined in in thethe projectproject specificationspecification. .

•• Design value of Design value of the the stress variationstress variation

LMLMLM MinMax σσσ −=∆

fatϕ∆

VerificationVerification procedureprocedure withwith LoadLoad Model FLM 3Model FLM 3


LMfatfat σϕλσ ∆∆=∆

s : gaugeu : cantQs: nosing force

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

track

Rail Rail traffic traffic actionsactions


The characteristic values are multiplied by a factor The characteristic values are multiplied by a factor αα on lines on lines carrying rail traffic which is heavier or lighter than normal racarrying rail traffic which is heavier or lighter than normal rail il traffic.traffic.This factorThis factor αα shallshall bebe oneone of of thethe followingfollowing: 0,75 : 0,75 -- 0,83 0,83 -- 0,91 0,91 -- 1,00 1,00 -- 1,10 1,10 -- 1,21 1,21 -- 1,33 1,33 –– 1,46.1,46.TheThe valuevalue 1,33 1,33 isis normallynormally recommendedrecommended on on lineslines for for freightfreighttraffictraffic andand international international 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 a of a heavyheavy weightweight waggonwaggon (DB, 32 (DB, 32 axlesaxles, , selfweightselfweight 246 t, 246 t, pay loadpay load 457 t, mass 457 t, mass perper axleaxle 22 t , 22 t , LLtottot = =

63,3 m63,3 m


High speed trains : 2 load models HSLM-A and HSL-BHSLM-A and HSLM-B together represent the dynamic load effects ofarticulated, conventional and regular high speed passenger trains in

accordance with the requirements for the European Technical Specificationfor 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::ΦΦ22 for for carefullycarefully maintainedmaintained tracktrackΦΦ33 for standard for standard tracktrack ((meansmeans :: poor trackpoor track))((determinant lengthsdeterminant lengths LLΦΦ due to table 6.2)due to table 6.2)

•• Dynamic enhancementDynamic enhancement for real trainsfor real trains1 + 1 + ϕϕ = 1 + = 1 + ϕϕ' + (½) ' + (½) ϕϕ'' ''

•• Dynamic enhancementDynamic enhancement for fatigue for fatigue calculationscalculationsϕϕ = 1 + ½(= 1 + ½(ϕϕ' + (½)' + (½)ϕϕ'')'')

•• Dynamic enhancementDynamic enhancement for for dynamic studiesdynamic studies

1 /max ' −= statdyndyn yyϕ


•• Interaction model between the bridge and the trackInteraction model between the bridge and the trackEN 1991EN 1991--2 2 «« 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 deck gle deck with 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 KK of a fixed of a fixed support to the deck taking into account the stiffness of the fousupport to the deck taking into account the stiffness of the foundation, piers ndation, piers and bearings etc.and bearings etc.

ExampleExample of a real train for fatigueof a real train for fatigue((NrNr. 1 of 12 types of trains . 1 of 12 types of trains defineddefined in in thethe EurocodeEurocode))




Maximum permissible vertical deflection Maximum permissible vertical deflection δδ for railway bridges with 3 or for railway bridges with 3 or more successive simply supported spans corresponding to a more 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 speed in a coach for speed VV[km/h][km/h]

EN 1990/A1 EN 1990/A1 ««Application for BridgesApplication for Bridges »»

EN 1990 EN 1990 –– Section 6, Section 6, AnnexAnnex A2A2

EN 1990 EN 1990 ““EurocodeEurocode : :

Basis of Basis of Structural DesignStructural Design

ForewordForewordSection 1Section 1 : : GeneralGeneralSection 2Section 2 : : RequirementsRequirementsSection 3Section 3 : : PrinciplesPrinciples of of limitlimit statesstatesSection 4Section 4 : Basic variables: Basic variablesSection 5 Section 5 : Structural : Structural analysisanalysis andand design design assistedassisted byby

testingtestingSection 6Section 6 : : VerificationVerification by by thethe partial partial factorfactor methodmethod

AnnexAnnex A1A1 : Application for buildings (N): Application for buildings (N)AnnexAnnex A2A2 : Application for bridges (N) (EN 1990/A1): Application for bridges (N) (EN 1990/A1)AnnexAnnex BB : Management of structural : Management of structural reliabilityreliability forfor

construction construction worksworks (I)(I)AnnexAnnex CC : : BasisBasis for partial for partial factorfactor design design andand

reliabilityreliability analysisanalysis (I)(I)AnnexAnnex DD : Design : Design assistedassisted by by testingtesting (I)(I)


Section 6 Section 6 -- Verification by theVerification by thepartial factor methodpartial factor method

6.16.1 GeneralGeneral6.26.2 LimitationsLimitations6.36.3 Design valuesDesign values6.46.4 Ultimate limit statesUltimate limit states6.56.5 Serviceability limit statesServiceability 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 executionSeismicSeismic

Normal useNormal useAccidentalAccidental

ExecutionExecution, , temporary temporary conditions applicable to conditions applicable to thethe structure, e.g. structure, e.g. maintenance or maintenance or repairrepair

TransientTransient

Normal useNormal usePersistentPersistent

TheThe selectedselected design situation design situation shallshall bebe sufficientlysufficiently severesevere andand soso variedvariedas to as to encompassencompass all conditions all conditions whichwhich cancan reasonablyreasonably bebe foreseenforeseen to to occuroccur 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

Turkstra’s ruleTurkstra’s rule (1972) : (1972) : within thewithin the set of variable set of variable actions applicable to a actions applicable to a structure, one of structure, one of them is them is selected and called selected and called «« leading leading variable variable actionaction » ; » ; the other the other variable actions are variable actions are accompanying accompanying actions actions and and are are taken into taken into account account in in the the combinations combinations of actions of actions with their combination with their combination values. values.

TheThe set set including including all permanent actions, all permanent actions, the leading the leading variable action variable action andand thethe relevant relevant accompanyingaccompanying variable actions variable actions formsforms a a combinationcombinationof actions. of actions. The various The various values of actions values of actions used used in in the verifications the verifications are are called called «« representative representative valuesvalues ».».

How to establish a combination of actionsEN 1990 – Section 6, Annex A2

FFii FFkk,i,i FFdd,i,i = = ψγψγf,f,iiFFkk,i,i E(E(FFdd,i,i ; a; add))

EEdd = = γγSdSdEE((FFdd,i,i ; a; add)) EEdd = E(= E(ψγψγF,F,iiFFkk,i,i ; a; add)) γ γF,iF,i = = γγf,if,i ×γ×γSdSd

ActionActionCharacteristicCharacteristic

value of value of thetheactionaction

Design value of Design value of thethe actionaction EffectEffect of of

actionsactions

Design value of Design value of thethe effecteffect of of

actionsactionsDesign value of Design value of thethe

effecteffect of actions of actions ((simplified simplified expression)expression)


ACTIONSACTIONS

aadd Design value of Design value of geometrical geometrical datadata

γγff Uncertainty Uncertainty in in representative representative valuesvaluesof actionsof actions

γγSdSd Model Model uncertainty uncertainty in actions in actions andandaction action effectseffects

ψψ Is either Is either 1,00 or 1,00 or ψψ0,0,, , ψψ1,1, or or ψψ2,2,


XXii XXkk,i,i XXd,id,i = (= (ηηii//γγm,im,i))XXkk,i,i R(XR(Xd,id,i ; a; add))

RRdd = (1/= (1/γγRdRd)R(X)R(Xd,id,i ; a; add)) RRdd = R((= R((ηηii//γγM,iM,i))XXkk,i,i; a; add)) γ γM,iM,i = = γγm,im,i ×γ×γRdRd

Material Material propertrypropertry

CharacteristicCharacteristicvalue of value of thethe

material propertymaterial property

Design value of Design value of thethematerial propertymaterial property Structural Structural

ResistanceResistance

Design value of Design value of thethestructural structural resistanceresistance

Design value of Design value of thethestructural structural resistanceresistance

((simplified simplified expression)expression)


RESISTANCESRESISTANCES

aadd Design value of Design value of geometrical geometrical datadata

γγmm Uncertainty Uncertainty in in material propertiesmaterial properties,,including the random including the random part of part of thetheconversion conversion factor factor ηη

γγRdRd Model Model uncertainty uncertainty in structural in structural resistanceresistance

ηη The mean The mean value of value of the the conversion conversion factorfactortaking into account taking into account ::

-- volume volume and scale effectsand scale effects,,

-- effects effects of of moisture and temperaturemoisture and temperature, , andand

-- any other any other relevant relevant parametersparameters


EEQQUU LLoossss ooff ssttaattiicc eeqquuiilliibbrriiuumm ooff tthhee ssttrruuccttuurree oorr aannyy ppaarrtt ooff iitt

ccoonnssiiddeerreedd aass aa rriiggiidd bbooddyy,, iinn wwhhiicchh :: -- mmiinnoorr vvaarriiaattiioonnss iinn tthhee vvaalluuee oorr tthhee ssppaattiiaall ddiissttrriibbuuttiioonn ooffaaccttiioonnss ffrroomm aa ssiinnggllee ssoouurrccee aarree ssiiggnniiffiiccaanntt ;; -- tthhee ssttrreennggtthhss ooff ccoonnssttrruuccttiioonn mmaatteerriiaallss oorr ggrroouunndd aarree ggeenneerraallllyy nnoott ggoovveerrnniinngg

SSTTRR IInntteerrnnaall ffaaiilluurree ooff tthhee ssttrruuccttuurree oorr ssttrruuccttuurraall eelleemmeennttss,, iinncclluuddiinngg ffoooottiinnggss,, ppiilleess,, bbaasseemmeenntt wwaallllss,, eettcc..,, iinn wwhhiicchh tthhee ssttrreennggtthh ooff ccoonnssttrruuccttiioonn mmaatteerriiaallss oorr eexxcceessssiivvee ddeeffoorrmmaattiioonn ooff tthhee ssttrruuccttuurree ggoovveerrnnss

GGEEOO FFaaiilluurree oorr eexxcceessssiivvee ddeeffoorrmmaattiioonn ooff tthhee ggrroouunndd iinn wwhhiicchh tthhee ssttrreennggtthhss ooff ssooiill oorr rroocckk aarree ssiiggnniiffiiccaanntt iinn pprroovviiddiinngg rreessiissttaannccee

FFAATT FFaattiigguuee ffaaiilluurree ooff tthhee ssttrruuccttuurree oorr ssttrruuccttuurraall eelleemmeennttss

Ultimate limit statesUltimate limit states



Ultimate Limit Ultimate Limit States States EQU EQU –– STR STR –– GEO for a GEO for a bridge.bridge.

EQUEQU

STRSTR

GEOGEO

FATFAT


6.4.2 6.4.2 VerificationsVerifications of of staticstatic equilibriumequilibrium and resistanceand resistanceUltimateUltimate 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 ≤≤ RRdd

6.5 6.5 ServiceabilityServiceability limitlimit states states EEdd ≤≤ CCdd

CCdd is the limiting design value of the relevant is the limiting design value of the relevant serviceability criterion.serviceability criterion.EEdd is the design value of the effects of actions specified in is the design value of the effects of actions specified in the serviceability criterion, determined on the basis of the the serviceability criterion, determined on the basis of the relevant combination.relevant combination.


CombinationsCombinations of actions ULS)of actions ULS)EN 1990 – Section 6, Annex A2

Combination Reference EN 1990 General expression

6.10 ∑ ∑≥ >

+++1 1

,,0,1,1, """"""j i

ikiiQkQPkjGj QQPG ψγγγγ Fundamental (for persistent and transient design situations)

6.10 a/b ⎪⎩

⎪⎨

⎧

+++

+++

∑∑

∑∑

>≥

>≥

1,,0,1,1,

1,,

1,,0,1,1,01,

1,,

""""""

""""""

iikiiQkQP

jjkjGj

iikiiQkQP

jjkjG

QQPG

QQPG

ψγγγγξ

ψγψγγγ

00,185,0 ≤≤ jξ for unfavourable permanent actions G

Accidental (for accidental design situations)

6.11 ∑ ∑≥ ≥

++++1 1

,,211,21,1 "")(""""""j i

ikikdkj QQouAPG ψψψ

Seismic (for seismic design situations)

6.12 ∑ ∑≥ ≥

+++1 1

,,2, """"""j i

ikiEdjk QAPG ψ

6.5.3 6.5.3 ServiceabilityServiceability limitlimit states : states : combinationscombinations of of actionsactions

CharacteristicCharacteristic CombinationCombination ((irreversibleirreversible SLS)SLS)

FrequentFrequent CombinationCombination ((reversiblereversible SLS)SLS)

QuasiQuasi--permanent permanent CombinationCombination ((reversiblereversible SLS)SLS)

∑ ∑≥ >

+++1 1

,,01,, """"""j i

ikikjk QQPG ψ

∑ ∑≥ >

+++1 1

,,21,1,1, """"""j i

ikikjk QQPG ψψ

∑ ∑≥ ≥

++1 1

,,2, """"j i

ikijk QPG ψ


DESIGN VALUES OF ACTIONSDESIGN VALUES OF ACTIONS

APPROACH 1APPROACH 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

actionsactionsULS GEOULS GEO


ExamplesExamples of of combinationscombinations of actionsof actionsfor road bridgesfor road bridges

Note 1 : Note 1 : The combinations The combinations of actions are of actions are based based on on the the recommended recommended values values given given in in Annex Annex A2A2

Note 2 : Note 2 : Except Except for for roofed roofed bridges, bridges, it is assumed that it is assumed that snow loads snow loads on road bridges on road bridges may be assessed may be assessed as as snow loads snow loads on on the groundthe ground. .


Action Symbol ψ0 ψ1 ψ2 TS 0,75 0,75 0 UDL 0,40 0,40 0

gr1a (LM1+pedestrian or 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 (Pedestrian loads) 0 0 0

gr4 (LM4 – Crowd loading) 0 0,75 0 gr5 (LM3 – Special vehicles) 0 0 0

WkF - Persistent design situations - Execution

0,6 0,8

0,2 -

0 0

Wind forces

∗WF

1,0 - -

Thermal actions

Tk 0,6 3) 0,6 0,5

Snow loads QSn,k (during execution) 0,8 - - Construction loads

Qc 1,0 - 1,0

EN 1990 – Section 6, Annex A2Table A2.1

Recommended values of ψ

factors for road bridges

0,400,40

00

Too highToo high

FundamentalFundamental combinationscombinations of actions of actions based based on expression 6.10on expression 6.10

*fkq ReducedReduced value of value of the load the load on on footwaysfootways for group gr1a for group gr1a –– To To bebe

defineddefined in in thethe National National AnnexAnnex (for (for example example : 2,5 : 2,5 kNkN/m/m22) )

kP PrestressingPrestressing : : DefinitionDefinition in design in design EurocodesEurocodes. . UsuallyUsually P = PP = Pmm et et γγPP = 1= 1

setG Uneven settlements Uneven settlements to to be taken into account where be taken into account where relevant, relevant, withwith γγGsetGset= 1,20 or 1,00 in case of = 1,20 or 1,00 in case of linearlinear analysisanalysis..

gr1agr1a

ψψ00gr1agr1a⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

+++

×+++

++⎭⎬⎫

⎩⎨⎧

+=

≥∑

kSn

Wk

fkk

bi

trafficWkfk

kPkjkjj

QF

qUDLTST

gri

FqUDLTS

PGG

,

*

5,4,3,2,1

,*

inf,sup,1

5,15,1

)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 combinations combinations of actionsof actions

kP Characteristic Characteristic value of value of the prestressing the prestressing forceforce

setG Uneven settlements Uneven settlements to to be taken into account where be taken into account where relevantrelevant

gr1agr1a

ψψ00gr1agr1a⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

+++

+

+++

++⎭⎬⎫

⎩⎨⎧

+

=

≥∑

kSn

Wk

fkk

kbi

trafficWkfk

kkjkjj

QF

qUDLTSTbgr

Tgri

FqUDLTS

PGG

,

*

5,4,3,2,1

,*

inf,sup,1 )4,04,075,0(""

16,0""

6,0")"(

"""")""(


QuasiQuasi--permanent permanent combinations combinations of actionsof actions

FrequentFrequent combinations combinations of actionsof actions


⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

+

++

++⎭⎬⎫

⎩⎨⎧

+∑≥

kSn

Wk

k

k

k

kkjkjj

QFT

Tgrbgr

TUDLTS

PGG

,

inf,sup,1

5,02,06,0

5,0""475,0175,0

5,0")"4,075,0(

"""")""(

kkkjkjj

TPGG 5,0"""")""( inf,sup,1

++⎭⎬⎫

⎩⎨⎧

+∑≥

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

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Documents

Introduction, Traffic Loads on Bridges & Combinations …library.tee.gr/digital/m2346/m2346_calgaro.pdf · Introduction, Traffic Loads on Bridges & Combinations of actions Jean-Armand