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8/13/2019 Lecture 2- Bridge Superstructure (Deck Structural Forms & Behaviour)
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LECTURE2
BRIDGESUPERSTRUCTURE
(Structural
Form,
Behaviour
and
Idealization)
OBJECTIVE
Outlininggeneralconsiderationsneedforconceptualplanningandpreliminarydesignofabridgesuperstructure.
Understandingthedifferentdeckformsandtheir loaddistributionbehaviour.
Alookatwaysofidealizingthedifferentbridgedeckbehaviourforanalysispurpose.
Andthesuitableanalysismethodsrequiredforeachdeckform.
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1.2. DifferencebetweenBuildingSlabandBridgeDeck Loading are conventionally uniform in building but complex inbridgesduetoconstantvariableactionsofheavymovingloads.
Bridgedecksareconstantlyexposedtosevereenvironmentalactionsi.e.temperaturechanges,effectsofwindetc.
Bridge deck is very load sensitive hence, longitudinal and lateraldistributionofstressesbecomevitalforeconomicdesign.
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2.0 DECKGENERALCONSIDERATIONS2.1. ConceptualDesign
Conceptualdesignforbridgesdependsontheexperienceandintuitionof
thedesigner.The term conceptualdesign ismore crucial for large/long
spanbridgeswhosestructuralcomplexitiesincrease innonlinearmanner
withrespecttotheirspanlengths.
DeckGeometricEfficiency
Forcast insitubridges,deckdesign istotallygovernbythespan length.
For
shorter
spans,
simpler
and
heavier
shapes
are
mostly
preferred.
And
as span length increases, deck shapesmust bemademore efficient to
reducetheweightinordertolimitbendingforces.Butwhenspanlength
becomesverylarge,prioritymustbegiventostructuralefficiencyandto
reduce weight. This is the reason why deck shapes progresses from
rectangularslabs(forsmallerspans)toclassicalboxgirders.
Geometricefficiencycoefficient:
Where I= flexural inertia,A thecrosssectionareaofdeck,yandyarethedistances from thecentreofgravity to theextreme fibres. Itsvalue
variesfrom0.333forrectangularslabtoabout0.550.65forboxgirder.
Evidentofefficientshape forchangingcrosssection iswhenpermanent
loads producemore than 75 to 80% of the bendingmoments at the
criticalcrosssection.
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ConstructionMethods
Decktypesbasedonbridgeconstruction:
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AestheticRequirement
Basedonthefunctionalityofthebridgestructuresomeinherentaesthetic
featuresmayberequiredi.e.inlongspanbridgeswhichareoftenusedas
nations landmark structures. Hence this must be considered in the
detaileddesignandthisissometimesdevelopedwiththecollaborationof
anarchitect.
2.2. BridgeDeckIdealizationIdealization is the rational process ofmaking simplifications about the
behaviourofstructuresforthepurposeofstructuralanalysisanddetailed
design.
PurposeofIdealization
Todistilthekeymodesofcomplexstructuralbehaviourintopracticalanalysis.
Toidentifytheloadtransmissionandtravelpaths. Toensure thatprimarymodesarecapturedby thechosenanalysismodelandthesignificanceofsecondarymodesondesignforcesare
evaluated.
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3.0 DECKSTRUCTURALFORMSPrincipal types of bridge deck are divided into beam, grid, solid slab,
beamandslabdeck,andcellular/boxdeck inordertodifferentiatetheir
individualgeometricandbehaviourcharacteristic.
3.1. BeamDecksThesearebridgedeckswith the lengthsexceeding theirwidthsby such
amountthatunderloadstheybendandtwistalongtheirlengths.
Figures(a)(d)belowshowtypicalformsofbeamdeck:
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Theyaremostcommoninfootbridges. Caneitherbesteel,reinforcedconcreteorprestressedconcrete. Theyareoftencontinuousovertwoormorespans.
3.2. ConcreteSolidSlabDeckThe use of solid slab bridge deck today, provides the simplest form of
concretebridgedecks. Easeofconstructionresultingfromthesimplicity
makesthisthemosteconomictypeforshortspanstructures.
Concreteslabdecksarecommonlyusedforshortspansandcanspanupto15mlong.
Theycanbesimplysupportedfromabutmenttopiersorcontinuousoverintermediatesupportstoendabutments.
Thetypicalslabthicknessisbetween1/25and1/35ofthespan.
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The slab depth increases as the span increase. And hence, thematerialweightof a solid slabwill start tobecome excessive as it
exceeds15m.
The ability for the reinforced solid slab to carry sagging (+ve) andhogging(ve)moments,makesitadequateforcontinuousmultispan
bridgesandallowsfortheuseoflongprestressingtendons.
(a)Solidslab;(b)Voidedslab;(c)Compositesolid;and(d)Compositevoid
3.3. ConcreteVoidedSlabDeckDue to the increasing and excessivematerialweight as solid slab span
exceeds 15m it comes necessary to lighten itsweight by incorporating
voids.Voided slabdecks are frequently constructed as cast insituwith
permanent void formers or of precast prestressed concrete boxbeams
posttensionedtransverselytoensuretransversecontinuity.
If the void sizes are less than 60% of the overall deck depth, then the
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effectofvoidsonthedeckstiffnessisnegligiblysmall,hencethedeckcan
be analysed effectively as solid plate. Butwhen the void sizes exceeds
60%of thedeckdepth, thedeckcangenerallybeconsideredascellular
constructionwithbehaviourdifferentfromvoidedslab.
3.4. GridDecksTheprimary structural form for thisdeck type isagridof twoormore
longitudinal beams with transverse beams which support the running
slab.
Because of the amount of workmanship needed for fabricating or
shuttering the transversebeams, thisdeck type is lesspopularnowand
hasbeen replacedby slabandbeamandslabdeckswithno transverse
diaphragms.
3.5. ConcreteBeamandSlabDeckThis deck type consists of a number of longitudinal beams connected
transversely across their tops by a thin continuous concrete slab. This
decktypecouldalsobesimplysupportedorcontinuousatsupports.
When transferring load longitudinally to the support, the slab acts in
concertwith thebeamsas top flanges.Andgreaterdeflection from the
most heavily loaded beamswill cause the slab tobend transversely so
thatittransfersandshareoutloadtotheadjacentneighbouringbeams.
Conventionalconcretebeamandslabcanbeconstructedas:
Concreteinsituslaboninsitubeams Concreteinsituslabonprecastbeams
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Maineconomicadvantagesare:
I. The use of Isection steel girder will reduce the weight of thesuperstructureandhence,theoverallcostofthefoundation.
II. Foragivenspanandloadingsystemasmallerdepthofbeamcanbeusedthanforaconcretebeamsolution,whichleadstoeconomiesin
theapproachembankments.
III. Thesystemallowsforspeedconstructionandhence,savestime.IV. Thecrosssectionalareaofthegirdertopflangecanbereducedsince
insituconcretecontributestothestiffness.
V.Transverse
stiffening
for
the
top
compression
flange
of
the
steel
girdercanbereducedsincerestraintagainstbuckling isprovidedby
theconcreteslab.
3.7. BoxgirderDeckTheircomplexstructuraldeckformsaremadeupofanumberofthinslab
andwebs.Thesedeckformsarepreferableforspanover40m.
Inadditiontothelessmaterialandlowweightadvantages,theyhavehigh
longitudinalbendingstiffnessandtorsionalstiffnessandthesegivethem
betterstabilityandloaddistributioncharacteristics.
Aboxgirdersectioncouldbemadeofasingleboxormultibox.Theyare
practicallythemost feasibledeck forms for longerspanbridgesandthis
placethemincompetitionwithothertypesofdecks.
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4.0 DECKSTRUCTURALBEHAVIOURANDIDEALIZATIONDeckbehaviour in termof loaddistribution is such that traffic loadson
bridge decks are distributed according to the stiffness, geometry and
boundaryconditionsofthedeck.
Methodofanalysismostappropriatetoaparticulardeckdependsonthe
complexityofthestructuralform.
4.1. BeamDeckandFrameBeam deck behaves as a beam thatwhen loads causes it to bend and
twist
along
its
length,
its
cross
section
displaces
bodily
and
do
not
change
shape.
Hence itsbehaviourcanbe idealizedusingsimplebeamelastictheoryof
bendingandtorsion.Inthesimplebeamelastictheory,itisassumedthat
thedecksectionremainsplaneandthatthebeamiscomposedofdiscrete
linearfibres inwhichthe longitudinalbendingstress isproportionalto
longitudinalstrain inthefibre.
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Flexureabouttheprincipalaxisofthesectioncanbeexpressedas:
Most longspanbridgesbehavesasbeamsbecause thedominate load is
concentrated so that thedistortionof thecrosssectionundereccentric
loadshasrelativelylittleinfluenceontheprincipalbendingstress.
Analysisofbeam deck can bedone asdeterminate beam structure for
simply supported case and as indeterminate beam structure for
continuouscases.
Beam decks can also exhibit frame action in which the stiffness and
geometryof the supportshave significant influenceon theirbehaviour.
Hence,theycanbeidealisedandanalysedeitherasplaneor3Dframe.
4.2. SlabDeckDeck slab is structurally continuous in twoorthogonaldirectionsof the
slabsothatanappliedloadissupportedby2dimensionaldistributionof
shears,momentandtorqueeffects.
Classicalplatetheorycanbeusedfordeterminingthebehaviourofsolid
slab but for simplicity, deck slab can be idealized and analysed using
similarassumptionforelastictheoryofbendingasbeams.
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(a)Prototypesoliddeckand(b)equivalentgrillageGrillage idealizationcanbesuitable forthepurposesofanalysisand the
dispersedbendingandtorsionalstiffnessesineveryregionoftheslabare
assumedtobeconcentratedinthenearestequivalentbeam.
Ideally thebeam stiffness shouldbe such thatwhen theprototype slab
and its equivalent grillage are subjected to identical loads the two
structuresshoulddeflectidentically.
4.3. BeamandSlabDeckBehaviourof a typicalbeamandslabdeckunder anaxle load is shown
below:
Oneofthedisadvantagesofthisdecktypeispoorloaddistributioninthe
transversedirectionwhich iswhymost timestransversediaphragmsare
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introducedatpointsalongthedeckspan.
Forasinglespanrightdeckonsimplesupportswithdifferentstiffnessin
two orthogonal directions, it ispossible,using classical plate theory, to
determinetheloaddistributedforeachmember.Butgrillageidealization
isfoundtobeeffectiveforthispurposeandiftheamountofloadcarried
by the most heavily loaded member can be found then the bending
momentcanbeeasilycalculated.
Equivalentgrillageidealizationsareshownbelow:
4.4. CellularDecksIt isoftenconvenientandacceptable tousecellularstructuresandbox
sectiondeckswhichdistortsundershearand torsional loadingsand it is
then necessary to take into account this distortion in the method of
analysis.
Thedisplacementof thisdeckcrosssectionunder loads fallsunder four
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principalmodes.
Longitudinalbending Transversebending Torsion Distortion
The behaviour of cellular decks can be analysed with shearflexible
grillage. The shear flexibility in the grillage idealization reproduces the
distortionbehaviourofthecell.
In flexible grillage, the deck is simulated by a grid of beamswhich are
given high torsional stiffnesses of the cellular deck and the slope
deflection equation takes into account the shear deformation in the
beams.
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4.5. BoxgirderDecksBoxgirderisverystiffinpuretorsionandmostofthetwistinthedeckis
due to distortion unless the box is bracedwith diaphragm. The use of
transverse bracing or framing provides a very effective method for
stiffeningaboxgirderagainstdistortion.
Figuresbelowillustratethebehaviourofboxsectiontoloads:
(a)Plane, (b) section, (c) to (e) components of loads and (f) distortiondeflection
Theamountofstiffeningisequallybeneficialtoeffectiveloaddistribution
and distortional flexibilitywhich helps the structure to spread the load
betweenthesupports.
Grillagemethod can be used but the analysismay not give sufficient
detailed picture of the flexural and membrane stresses in the plate
elementandforthisadditional3dimenssionalanalysiswillbenecessary.
Foldedplateanalysiswillprobablyprovidemostaccurate information if
the deck crosssection is uniform from end to endwith few transverse
diaphragms.
For complicated variations in the deck section, finite element analysis
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methodwillbenecessary.
Belowisillustrationoftwodifferentanalysismethodsforboxgirderdeck:
(a)Finiteelementmodeland(b)to(d)framemodelTypical comparison of result for frame and grillage analysismethods is
illustratedinthefollowing:
Resultfromspaceframeanalysisofaconcreteboxgirderdeck
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Resultfromgrillageanalysisofaconcreteboxgirderdeck