Using Eurocodes and Aashto for assessing shear in slab bridges

13 Pages·2016·0.33 MB·English

Delft University of Technology

Using Eurocodes and Aashto for assessing shear in slab bridges
Lantsoght, Eva; van der Veen, Cor; de Boer, A; Walraven, Joost
DOI
10.1680/jbren.14.00022
Publication date
2016
Document Version
Final published version
Published in
Proceedings of the ICE - Bridge Engineering
Citation (APA)
Lantsoght, E., van der Veen, C., de Boer, A., & Walraven, J. (2016). Using Eurocodes and Aashto for
assessing shear in slab bridges. Proceedings of the ICE - Bridge Engineering, 1-13.
https://doi.org/10.1680/jbren.14.00022
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BridgeEngineering ProceedingsoftheInstitutionofCivilEngineers
http://dx.doi.org/10.1680/jbren.14.00022
UsingEurocodesandAashtofor Paper1400022
assessingshearinslabbridges Received02/06/2014 Accepted16/11/2015
Keywords:codesofpractice&standards/concretestructures/
Lantsoght,vanderVeen,deBoer
slabs&plates
andWalraven
ICEPublishing:Allrightsreserved
Using Eurocodes and
Aashto for assessing
shear in slab bridges
EvaO.L.LantsoghtBSc,MSc,PhD AnedeBoerBSc,MSc,PhD
Researcher,ConcreteStructures,DelftUniversityofTechnology,Delft, Senioradviser,MinistryofInfrastructureandtheEnvironment,Utrecht,
theNetherlands(correspondingauthor:[email protected]) theNetherlands
CorvanderVeenBSc,MSc,PhD JoostC.WalravenBSc,MSc,PhD
Associateprofessor,ConcreteStructures,DelftUniversityofTechnology, Emeritusprofessor,ConcreteStructures,DelftUniversityofTechnology,
Delft,theNetherlands Delft,theNetherlands
Reinforced concrete short-span solid-slab bridges are used to compare Dutch and North American practices. As an
assessment of existing solid-slab bridges in the Netherlands showed that the shear capacity is often governing, this
paper provides a comparison between Aashto (American Association of State Highway and Transportation Officials)
practice and a method based on the Eurocodes, and recommendations from experimental research for the shear
capacity of slab bridges under live loads. The results from recent slab shear experiments conducted at Delft
University of Technology indicate that slabs benefit from transverse force redistribution. For ten selected cases of
straight solid-slab bridges, unity checks (the ratio between the design value of the applied shear force and the
design beam shear resistance) are calculated according to the Eurocode-based method and the Aashto method. The
results show similar design shear forces but higher shear resistances in the North American practice, which is not
surprisingastheassociatedreliabilityindexforAashtoislower.
Notation E modulusofelasticityofreinforcingsteel
s
A areaofprestressingsteel e eccentricityofload
ps
A areaofreinforcingsteel F reactionforce
s
a shearspan f′ concretecompressivestrength
c
a maximumaggregatesize f characteristiccylindercompressivestrengthof
g ck
a clearshearspan concrete
v
b fullwidth f characteristiccubecompressivestrengthofconcrete
ck,cube
b edgedistance f parametertakenasthemodulusofelasticityof
edge po
b effectivewidthinshear prestressingtendonsmultipliedbythelocked-in
eff
b effectivewidthfromahorizontalloadspreading differenceinstrainbetweenprestressingtendons
eff1
under45°fromthecentreoftheload andsurroundingconcrete
b effectivewidthfromahorizontalloadspreading f characteristicyieldstrengthofreinforcementbar
eff2 yk
under45°fromfarcornersoftheload k sizeeffectfactor
b widthoftheload,takeninthespandirection l spanlength
load span
b distancebetweenthefreeedgeandthecentreof M factoredmoment,nottobetakenlessthanV d
r u u v
theload N factoredaxialforce
u
b effectivewidth:minimumwebwidthwithinthe s thelesserofd ormaximumdistancebetween
v x v
depthd or,forslabs,theeffectivewidth layersoflongitudinalcrackcontrolreinforcement
v
b webwidthofsectionor,forslabs,theeffectivewidth s crackspacingfactor
w xe
C factorfromNEN-EN1992-1-1:2005(CEN,2005) V shearcapacityaccordingtoAashtoLRFD(Aashto,
Rd,c c
expressionforshear 2015)
d thicknessofwearingcourse V designshearforce
asphalt Ed
d effectivedepthtomainflexuralreinforcement V componentofeffectiveprestressingforcein
l p
d effectivesheardepth:theinternalleverarm ≥ max directionoftheappliedshear
v
(0·9d,0·72h) V designshearcapacity
l Rd,c
E modulusofelasticityofprestressingsteel V factoredshearforce
p u
1
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BridgeEngineering UsingEurocodesandAashtofor
assessingshearinslabbridges
Lantsoght,vanderVeen,deBoer
andWalraven
v designshearresistanceaccordingtoAashto detailed analysis; for this, a fast, simple and conservative tool
c
v designshearstressaccordingtoEurocodes is required (e.g. the quick scan method (Lantsoght et al.,
Ed
v lowerboundofshearcapacity 2013a)).Thequickscanisaspreadsheet-basedmethod,similar
min
v designshearresistanceaccordingtoEurocodes to extended hand calculations (Vergoossen et al., 2013). The
Rd,c
v designshearstressaccordingtoAashto quick scans result in ‘unity check’ values; that is, the ratio
u
w widthofdesignlaneaccordingtoNEN-EN between the design value of the applied shear force resulting
th,1
1991-2:2003(CEN,2003)(typically3 m) from loads on the bridge according to current codes (dead
α factortomagnifytruckload loads, superimposed loads and live loads) and the shear resist-
Qi
α factortomagnifylaneload ance. The critical loading case on a slab occurs with a design
qi
β reductionfactorforloadsclosetothesupport truck close to the free edge parallel to the driving direction
β factorindicatingtheabilityofdiagonallycracked (Cope,1985),andthisisthecaseconsideredinthequickscan.
MCFT
concretetotransmittension
β reductionfactorforconcentratedloadsonslabs
new
closetothesupport 2. Literaturesurvey
β reliabilityindex Although slab bridges are calculated as beams with a large
rel
γ loadfactorfordeadload width without taking the beneficial effect of the extra dimen-
DL
γ loadfactorforsuperimposedload sionintoaccount,someresearchershavestudiedthebehaviour
DC
γ loadfactorforliveload of this bridge type and showed that the capacity is larger than
LL
Δq increasedlaneloadontheheavilyloadedlanein the rating (Aktan et al., 1992; Azizinamini et al., 1994a,
load
loadmodel1 1994b).
ε strainatmid-depthofthecross-section
x
ρ flexuralreinforcementratio The shear failure modes that need to be verified are flexural
l
σ axialstressonthecross-section(positivein shear and punching shear. Flexural shear failure results in an
cp
compression) S-shaped shearcrack at the side face of the slab, or, if the slab
τ shearstressduetoself-weightofslabandforceson is very wide, the crack can develop in the interior of the
add
prestressingbars slab (Figures 1(a)–1(c)). Punching shear failure results in the
τ sumofτ andτ punchingoutofaconcretecone.Ifsufficientflexuralreinforce-
combination conc line
τ shearstressduetoconcentratedloadoverthe mentisprovided,theconewillnotbeclearlyvisible,butcrack-
conc
effectivewidth ing on the opposite face of the load will indicate punching
τ shearstressduetodistributedloadoverthefull failure(Figures1(d)and1(e)).Thecheckforflexuralshearfor
line
width slab bridges can be carried out with the quick scan method,
τ ultimateshearstressinexperimentwith where the occurring shear stress from the loads is compared
tot,cl
concentratedloadonly with the flexural shear capacity. Punching checks are beyond
ϕ resistancefactor the scope of this paper, but need to be carried out on a per-
imeter around the loads, where the occurring shear loading is
1. Introduction comparedwiththepunchingshearcapacity.
A large number of existing reinforced concrete bridges in the
Dutch road network consist of short-span solid-slab bridges. For flexural shear in wide members, an effective width needs
As these bridges often have a simple geometry, they provide to be determined. The effective slab width in shear istheoreti-
an excellent case for a comparison between European and cally determined so that the reaction resulting from the total
North American practices. In the Netherlands, the Ministryof shear stress over the width of the support equals the reaction
InfrastructureandtheEnvironmentinitiatedaprojecttoassess from the maximum shear stress over the effective width.
the shearcapacityof existing bridges (60% of which werebuilt For design purposes, a method of horizontal load spreading
before 1975) under increased traffic loads as prescribed by the (depending on local practice) is chosen, resulting in the effec-
recently implemented Eurocodes. In total, the shear capacity tive width b at the support. In Dutch practice, horizontal
eff
of 600 reinforced concrete slab bridges needs to be studied. load spreading is assumed under a 45° angle from the centre
Preliminary calculations indicated that the shear capacity can of the load towards the support (Figure 2(a)) and, in French
be insufficient (Walraven, 2010) even though no signs of dis- practice, (Chauvel et al. 2007) from the far corners of
tressareobserved. the loading plate (Figure 2(b)). Currently, the only code that
prescribes an effective width for shear in wide members is
The large numberof solid-slab bridges to be assessed requires Model Code 2010 (fib, 2012) (Figure 2(c)). The UK currently
a systematic approach. The goal of the first round of assess- has no codified practice for determining the effective width in
ments is to determinewhich particular bridges require a more shear.
2
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BridgeEngineering UsingEurocodesandAashtofor
assessingshearinslabbridges
Lantsoght,vanderVeen,deBoer
andWalraven
a uniformly distributed load (design lane load). The tandem
system has a tyre contact area of 400mm(cid:1)400mm and
an axle load of α (cid:1)300kN in the first lane, α (cid:1)200kN
Q1 Q2
in the second lane and α (cid:1)100kN in the third lane. The
Q3
α are nationally determined parameters that can be used
Qi
to tailor the Eurocode load model to the traffic loading
situation of individual countries. All α equal the rec-
Qi
ommended value of 1. The uniformly distributed load is
appliedoverthefullwidthofthelaneandisα (cid:1)9kN/m2for
qi
the first lane and α (cid:1)2·5 kN/m2 for all other lanes, with α
q1 qi
being nationally determined parameters. In the Netherlands,
(a)
Centre of load for bridges with three or more notional lanes, α =1·15 and,
q1
fori>1,α =1·4.
qi
West InAashtoLRFD(AmericanAssociationofStateHighwayand
Transportation Officials load and resistance factor design)
(Aashto, 2015), a combination of a design truck or design
Centre of span
(b) Centre of support tandem with a design lane load is considered (Figure 4).
Thetyrecontactareais510mm(cid:1)250mmfordesigntruckand
Centre of load
tandem. The design truck has three axle loads: 35kN and
two times 145kN. The longitudinal spacing between the two
145kNaxlesisvariedbetween4300mmand 9000mmtopro-
East
duce extreme force effects. The transverse spacing is 1800mm.
The design tandem consists of a pair of 110kN axles spaced
Centre of span
Centre of support 1200mm apart and with a transverse spacing of 1800mm.
(c)
A dynamic load allowance (IM) of 33% has to be considered
Centre of load
for both the design truck and the design tandem (Aashto,
2015:table3.6.2.1-1).ThedesignlaneloadfromAashtoLRFD
consists of a load of 9·3N/mm uniformly distributed in the
longitudinal direction. Transversely, the design lane is assumed
(d) to be uniformly distributed over a 3m width, which is smaller
than the full lane width (3·6m). This width marks the largest
differenceinthewaytheEurocodeandAashtoprescribethelane
load.
3.2 Shearcapacity
According to §6.2.2(1) of NEN-EN 1992-1-1:2005 (CEN,
2005), the shear resistance for a member without stirrups is
calculatedas
(e)
h i
Feitgaul.r,e210.14O):n(ea-)wbaoyttsohmearf:accera;c(kbs)wafetestrsfaidileurfeacoef;B(cS)2eTa1st(Lsaidnetsfoagchet. 1: VRd;c ¼ CRd;ckð100ρlfckÞ1=3þk1σcp
Two-wayshear:cracksafterfailureofS9T1(Lantsoghtetal., (cid:1)bwdl (cid:2)ðvminþk1σcpÞbwdl
2013c):(d)frontface;(e)bottomface
sffiffiffiffiffiffiffiffi
3. Comparison of Eurocodes and 200
2: k¼1þ (cid:3)2(cid:4)0
NorthAmerican code provisions d
l
3.1 Liveload
In load model 1 of NEN-EN 1991-2:2003 (CEN, 2003) where all the terms are defined in the notation list, d is in
l
(Figure 3), a tandem system (design truck) is combined with mm and k =0·15. Equation 1 is an empirical relation, first
1
3
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BridgeEngineering UsingEurocodesandAashtofor
assessingshearinslabbridges
Lantsoght,vanderVeen,deBoer
andWalraven
Support Support
b b
eff,1 eff,2
45°
45°
Load Load
(a) (b)
Support
a av beff dl ≤ av/2
60°
Load
(c)
Figure2. Effectivewidth(a)assuming45°horizontalload
spreadingfromthecentreoftheload(b )and(b)assuming45°
eff1
horizontalloadspreadingfromthefarcornersoftheload(b );
eff2
(c)topviewofslabasprescribedbyModelCode2010(fib,2012)
proposed by Regan (1987) based on experimental results α Q
Qi ik
(Lantsoght et al., 2015d, 2015e). According to the Eurocode
procedures,thevaluesofthefactorCRd,c andthelowerbound αqiqik
of the shear capacity v may be chosen nationally. The
min
default values are C =0·18/γ with γ =1·5 and v (f in
Rd,c c c min ck 1·2 m
(a)
MPa)givenby
2 m 3 m
3: v ¼0(cid:4)035k3=2f1=2
min ck
The contribution of a load applied within a distance
0·5d ≤a ≤2d from the edge of a support to the shear force
l v l
V maybemultipliedbythereductionfactorβ=a/2d (CEN,
Ed v l 400 mm × 400 mm
2005: §6.2.2(6)) as a result of direct transfer of the load from
(b)
itspointofapplicationtothesupport.
Figure3. TrafficloadsaccordingtoNEN-EN1991-2:2003(CEN,
TheAashtoloadandresistancefactorrating(LRFR)(Aashto,
2003):(a)sideview;(b)topview
2011: §6A.5.8) mentions that in-service concrete bridges
showing novisible signs of shear distress need not be checked
for shear when rating for the design load. This code require-
ment is not in line with the current practice in several is given in §5.8.3. MCFT describes the stress–strain relation-
Europeancountries,whereallexistingbridgesneedtoberated ships for cracked concrete. In a member without transverse
for shear as a result of the increased live loads and new shear reinforcement,theshearcapacitydependsfullyontheconcrete
models. When shear rating is carried out, the critical section contributionV ,givenby
c
for shear is taken at the face of the support (Aashto, 2015:
pffiffiffiffiffi
§5.13.3.6.1). The sectional design model, based on modified 4: V ¼0(cid:4)083β f0b d
c MCFT c v v
compressionfieldtheory(MCFT)(VecchioandCollins,1986),
4
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BridgeEngineering UsingEurocodesandAashtofor
assessingshearinslabbridges
Lantsoght,vanderVeen,deBoer
andWalraven
where dv is the effective shear depth: the internal lever 110 kN 110 kN
arm ≥max(0·9d, 0·72h). The value of β can be found in
l MCFT
Aashto(2015:§5.8.3.4.2) 9·3 kN/m
4(cid:4)8 1300
5: β ¼ 1·2 m (a)
MCFT 1þ750εs990þsxe
dependingonthecrackspacingfactors andthestrainε 1·8 m 3·6 m 3 m
xe x
35
6: 300mm(cid:3)s ¼s (cid:3)2000mm
xe xa þ16
g
510 mm × 250 mm
where s is the lesser of either d or the maximum distance
x v
(b)
between layers of longitudinal crack control reinforcement, a
g
isthemaximumaggregatesizeand
35 kN 145 kN 145 kN
(cid:3) (cid:2) (cid:2) (cid:4)
jM j=d þ0(cid:4)5N þ(cid:2)V (cid:5)V (cid:2)(cid:5)A f 9·3 kN/m
7: ε ¼ u v u u p ps po (cid:3)6(cid:1)10(cid:5)3
x EA þE A
s s p ps
4·3 m 4·3 m – 9 m
Thesectionalmomenthastofulfil (c)
(cid:2) (cid:2)
8: jMuj(cid:2)(cid:2)Vu(cid:5)Vp(cid:2)dv 1·8 m 3 m 3·6 m
The resistance factor for shear is ϕ=0·90 (Aashto, 2015:
§5.5.4.2.1).
3.3 Loadfactors 510 mm × 250 mm
The Eurocode suite only provides load and resistance factors (d)
for design and the Eurocodes for rating and assessment
are under preparation. To allow for assessment according Figure4. LoadingasprescribedinAashto(2015)withdesign
to the basic assumptions and philosophy of the Eurocodes tandem((a)sideviewand(b)topview)andwithdesigntruck
(Lantsoghtetal.,2015c),asetofnationalcodesisbeingdevel- ((c)sideviewand(d)topview)
oped intheNetherlands:NEN8700forthebasic rules(NEN,
2011a), NEN 8701 for actions (NEN, 2011b), NEN 8702 for
(NEN, 2011a). Allowing unlimited numbers of vehicles to use
concrete structures (to be published) and so on. The load
thebridgeatoperatinglevelmayshortenthelifeofthebridge.
factors for the safety level ‘repair’, as used for bridge assess-
In table 6.A.4.2.2-1 of the bridge evaluation manual, the load
ment in the Netherlands, are given in tables A1.2(B) and (C)
factorsaregivenasγ =1·25forthedeadload,γ =1·50for
of NEN 8700 (NEN, 2011a). These factors correspond to a DL DC
superimposed loads and γ =1·35 for live loads. The defi-
reliability index β =3·6 for consequence class 3 (Steenbergen LL
rel nition of the operating level isthus similar to the ‘repair’ level
and Vrouwenvelder, 2010). This class (NEN-EN 1990:2002
fromNEN 8700.The target reliability indexof thesefactorsis
(CEN,2002):tableB1)definesahighconsequencefortheloss
β =2·5(Ghosnetal.,2010)(whichisconsideredasthelower
of human life or verygreat economic, social orenvironmental rel
boundforlossofhumanlifeinEuropeanpractice)andisthus
consequences. For dead loads, a factor γ =1·15 is used and,
DL considerably lower than the index related to the Dutch ‘repair’
forliveloads,γ =1·3.
LL level.
For LRFRs according to the Aashto bridge evaluation
4. Results from experimental research
manual(Aashto,2011),thefactorsfordesignloadattheoper-
ating level are used. Load ratings based on the operating 4.1 Experimentsonslabsfailinginshear
rating level generally describe the maximum permissible live Experimental research on a half-scale model of a solid-slab
load to which the structure may be subjected and, as such, is bridge was carried out at Delft University of Technology
described in a similar way as the repair level from NEN 8700 (Lantsoght et al., 2013c, 2014, 2015a). Slabs of dimensions
5
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BridgeEngineering UsingEurocodesandAashtofor
assessingshearinslabbridges
Lantsoght,vanderVeen,deBoer
andWalraven
m (E) Simple Continuous
m support support
8
3
4
Support 1 Support 2
s
ar
b
g m
Load n m
ssi 0
e 0
str 25
e
M) Pr
m ( Plywood
m
0 felt
125 m (E) Load
m
8
3
4
300 mm 300 mm
100 mm
300 mm 3600 mm 600 mm 500 mm
Figure5. Topviewoftestsetupforslabsunderaconcentrated loadclosetotheedgeandMindicatespositionofconcentrated
load:supportedbyelastomericbearingsontheleftandsupported loadinthemiddleofthewidth
byalinesupportontheright.Eindicatespositionofconcentrated
5m(cid:1)2·5m(cid:1)0·3m and slab strips of 5m(cid:1)0·3m with vari- elastomeric bearings; and a combination of loads (Lantsoght
able widths were tested. A top view of the experimental setup etal.,2012b,2013b).
ispresentedinFigure5,showingtwodifferentsupportlayouts.
A displacement-controlled concentrated load was placed at
4.2 Choiceofhorizontalloadspreadingmethod
different positions along the width and close to support 1 or
andminimumeffectivewidth
close to support 2 at avariable distance to the support. In a
Earlier research (Lantsoght et al., 2015b) showed that the
second series of tests, a force-controlled constant line load
effective width as used in French practice is to be preferred.
of 240kN/m at 1·2m from the support was added. Different
Thisconclusionwasbasedonstatisticalanalysisoftheratioof
support conditionswere also used – line support, three elasto-
the tested to the predicted values (based on the shear formula
meric bearings per side or a line of seven steel or elastomeric
from the Eurocode) and also on the results from the series of
bearings. Support 1 is a simple support and support 2 is con-
slab strips with increasing widths. The results of the exper-
sideredasacontinuoussupport.Prestressingbars,anchoredto
iments showed that the lower bound for the effective width
thelaboratoryfloor,wereusedtopartiallyrestraintherotation
(both for loading in the middle of the slab width and close to
atsupport2andthuscreateamomentoversupport2.
theedge)wasequalto4d.
l
Intotal,26slabs(18underaconcentratedloadonlyandeight
under a combination of loads) and 12 slab strips were tested. 4.3 Increaseincapacityclosetosupport:β
new
The properties of the specimens, the setup and loading were To take into account the higher shear capacities of slabs, an
varied such that the following parameters could be studied: additional enhancement factor reducing the contribution of
size of the loading plate; existing cracks and local failure; concentrated loads to the total shear force was proposed
transverse flexural reinforcement; moment distribution at the (Lantsoght et al., 2013a); this factor is equal to 1·25 (as a 5%
support; distance between the concentrated load and the sup- lower bound of the ratio of the tested to predicted values for
port; concrete compressive strength; overall width; reinforce- loads close to supports). The enhancement factor and the
menttype(smoothbarsordeformedbars),linesupportversus reduction factor β=a/2d can be combined into β =a/2·5d
v l new v l
6
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BridgeEngineering UsingEurocodesandAashtofor
assessingshearinslabbridges
Lantsoght,vanderVeen,deBoer
andWalraven
τ
τ τ conc τcombination
tot,cl
conc
τ
τ line
add
b b
(a)
b (b) b
eff eff
Figure6. Superpositionofshearstressduetoaconcentrated
loadovertheeffectivewidthtothedistributedloadoverthefull
slabwidth:(a)concentratedloadonly;(b)concentratedloadand
lineload
for the case of concentrated loads on slabs with elementsreinforcedwithlowerstrengthsteel,asflexuralfailure
0·5d ≤a ≤2·5d. will govern fora larger range of shear stresses. As a result, the
l v l
unity check for flexure for cross-sections with a low flexural
4.4 Thehypothesisofsuperposition capacity will be higherand the governing failure modewill be
flexure. Moreover, at the end supports, sufficient anchorage
Intheliteratureandtheresultingslabsheardatabase,noreports
needstobeprovidedtoapplyEquation9.
are made of experiments on slabs under a combination of con-
centrated and distributed loads. In some experiments (Reißen
andHegger,2013;RombachandLatte,2009),asmalllineload
5. Practical applications: the quick
(edgeload)wasappliedatthetipofacantileveringdeck,which
scan approach
is not representative of large distributed loads such asthe dead
load.Theexperimentscarriedoutonslabsunderacombination 5.1 Eurocodes,theNEN8700seriesand
ofloadsprovethatthehypothesisofsuperpositionisvalid;that recommendations
is,thesumoftheshearstressduetotheconcentratedloadover In 2008, a first quick scan method based on the Dutch
theeffectivewidth(τ )andtheshearstressduetothedistrib- codes was developed by Dutch structural engineering com-
conc
uted load at failure over the full width (τ ) is larger than or panies for the Ministryof Infrastructure and the Environment
line
equal to the ultimate shear stress in an experiment with a con- (Rijkswaterstaat). The Eurocodes, the NEN 8700 (NEN,
centratedloadonly(τ )(Figure6). 2011a) series and recommendations based on the experiments
tot,cl
were implemented into the quick scan (QS-EC). Materials
research on existing bridges indicated that, for the slabbridges
4.5 Theinfluenceofflexureonthelowerbound
ownedbyRijkswaterstaat (designedandbuiltinthesameera),
forshear
aminimumconcretecubecompressivestrengthof45 MPacan
The expression forv (Equation 3) is based on the ideathat,
min
beassumed(SteenbergenandVervuurt,2012).
for low reinforcement ratios, the capacity can never be lower
than the flexural capacity (Walraven, 2013) and assumesyield-
Forsuperimposedloads,thethicknessofthewearingsurfaceis
ing of the longitudinal reinforcement at a characteristic yield
assumed to be 120mm. Vertical stress redistribution through
strength f =500MPa (Walraven, 2002) as well as sufficient
yk
the asphalt layer is taken at a 45° angle, so that the Eurocode
anchorage capacity. However, most existing bridges are
wheel print of 400mm(cid:1)400mm is replaced by a fictitious
reinforced with lower grade steel. Before 1962, the standard
reinforcement in the Netherlands was a type ‘QR24’ wheelprintontheconcretesurfaceof640mm(cid:1)640mm.
(f =240MPa). Therefore, the expression for v is derived
yk min
All trucks are assumed to be centred in the fictitious lane.
as afunction of f (Walraven, 2013). The resulting expression
yk
Basedontherecommendationsdevelopedfromtheexperimen-
forv forlowergradesofsteel,assumingsufficientanchorage
min
tal research, the most unfavourable position (Figure 7) of the
capacity,wasfoundtobe
truck loadsto determine themaximumshear force atthe edge
9: v ¼0(cid:4)772k3=2f1=2f(cid:5)1=2 of the viaduct is obtained by placing the first design truck at
min ck yk a =2·5d. This distance is governing since the recommen-
v l
dations take the influence of direct load transfer into account
For f =500MPa, Equation 9 becomes Equation 3. The up to 2·5d (Rijkswaterstaat, 2013). For assessment of existing
yk l
lower bound of the shear capacity is thus increased for bridges, an asymmetric effective width is chosen in the first
7
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BridgeEngineering UsingEurocodesandAashtofor
assessingshearinslabbridges
Lantsoght,vanderVeen,deBoer
andWalraven
bside 1200 mm mm Lane 1
0
0
4
400 mm
m
m
0
0
0
2
a
v1,1
Lane 2
b + 3 m
side
m
3
=
beff2,1 av2,1 w th,2
a
2,1 b lload
load
b + 2 × 3 m Lane 3
side
Figure7. Mostunfavourablepositionofdesigntrucks
(cid:7) (cid:8)
lane. Use of an asymmetric effectivewidth results in the resul- 12: e¼ 1b(cid:5)b (cid:5)wth;1
tant force of the wheel load not coinciding with the resultant 2 edge 2
force of the distributed shear stress. In the second and third
lanes, the design truck is placed so that the effective width
(Figure7)ofthefirstaxlestartsattheedgeoftheviaduct.
1
The increased contribution of the lane load in the first lane to 13: y¼ b(cid:5)2d
2 l
the resulting shear stress can be approximated based on a tri-
angular distribution, as shown in Figure 8(a). The resulting
shearforceisthen
10: V ¼Fþ ðFeÞy 14: Δqload ¼αq1(cid:1)9kN=m2(cid:5)αq2(cid:1)2(cid:4)5kN=m2
addlane1 b 1=12b3
In the approach from Figure 8(a) it is assumed that the slab is
with infinitely stiff in the transverse direction but weak in torsion.
A slab bridge, however, has torsional stiffness, which can be
(cid:5) (cid:6)
estimated with the approach of Guyon–Massonet. The pro-
F ¼ αq1(cid:1)9kN=m2(cid:5)αq2(cid:1)2(cid:4)5kN=m2 wth;1 posed method from Figure 8(a) should give more conservative
11: (cid:7)l 1d 15 (cid:8) shear forces than the analysis based on the Guyon–Massonet
(cid:1) span(cid:5)2d þ lþ d
2 l 42 16 l method. To obtain this result, the maximum width b over
which the triangular distribution is used is limited to 0·72l
span
8
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BridgeEngineering UsingEurocodesandAashtofor
assessingshearinslabbridges
Lantsoght,vanderVeen,deBoer
andWalraven
τ l
∆qload b span
2d V edge
l addlane1
w ∆q
th,1 load
y b/2
e
12Fey/b3
b
F/b
(a) (b)
τ l
∆qload dasphalt bedge span
Vaddlane1 2 + w ∆q
d/l th,1 load
+ b/2
w th,1 e
+
b edge
b
(c) (d)
Figure8. Modelforcontributionofincreasedloadinginthefirst locationoffirstheavilyloadedlane;(c)assumedstressdistribution
heavilyloadedlaneassumingatriangularstressdistributionover (notethatthewidthisslightlylargerthanthelanewidthdueto
thesupport:(a)assumedstressdistributionτΔqloadduetoloadand theverticalstressdistributiontohalftheslabdepth);(d)sketchof
momentfromeccentricityofload;(b)sketchoftopviewwith associatedtopviewwithlocationoffirstheavilyloadedlane
(Lantsoght et al., 2012a). A model factorof 1·1 is added. The statically indeterminate case to the shear force in the statically
lower bound of this approach is determined byavertical load determinate case. The cases that were studied are applicable
distribution under an angle of 45° to half the slab depth d/2, within the scope of the quick scan: three or four spans, with
l
asshowninFigure8(c) end spans of 0·7l and 0·8l , cross-sectional depths of
span span
600–1000mm and edge distances (distance between the free
(cid:5) (cid:6)
Fmin¼ αq1(cid:1)9kN=m2(cid:5)αq2(cid:1)2(cid:4)5kN=m2 edge and the centre of the load, br) between 300mm and
15: (cid:9) (cid:7) (cid:8) (cid:10) 1400mm.
d d
(cid:1) min bedge;2lþdasphalt þwth;1þ 2lþdasphalt
5.2 AashtoLRFRandLRFD
A quick scan according to North American practice was
The quick scan method was developed for statically determi- also developed (QS-Aashto). Vertical force redistribution
nate structures. Asthe shear force at the mid-support for stati- through d =120mm is assumed at a 45° angle for the
asphalt
cally indeterminate structures can be larger, the quick scan axle loads and to d/2 for the lane load. The spreadsheet
l
method needsto be altered for these cases. The solution isthe selectswhether the design tandem ordesign truck, assumed to
use of correction factors, which were developed based on case be centred in the fictitious lane, results in the largest shear
studies of multiple-span structures (Lantsoght et al., 2012a). forces. The most unfavourable position of the vehicular loads
The correction factor is the ratio of the shear force in the to determine the maximum shear force at the edge of the
9
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