Bridge Abutment Design Example

11/14/2015 BridgeABUTMENTDESIGNEXAMPLE

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AbutmentDesignExampletoBD30

Designthefixedandfreeendcantileverabutmentstothe20mspandeckshowntocarryHAand45unitsofHBloading.Analysetheabutmentsusingaunitstripmethod.ThebridgesiteislocatedsoutheastofOxford(toestablishtherangeofshadeairtemperatures).Vehiclecollisionontheabutmentsneednotbeconsideredastheyareassumedtohavesufficientmasstowithstandthecollisionloadsforglobalpurposes(SeeBD60/04Clause2.2).

Thegroundinvestigationreportshowssuitablefoundingstrataabout9.5mbelowtheproposedroadlevel.Testresultsshowthefoundingstratatobeacohesionlesssoilhavinganangleofshearingresistance()=30oandasafebearingcapacityof400kN/m2.

BackfillmaterialwillbeClass6Nwithaneffectiveangleofinternalfriction(')=35oanddensity()=19kN/m3.

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Theproposeddeckconsistsof11No.Y4prestressedconcretebeamsandconcretedeckslabasshown.

LoadingFromtheDeck

Agrillageanalysisgavethefollowingreactionsforthevariousloadcases:

CriticalReactionUnderOneBeam

NominalReaction(kN)

UltimateReaction(kN)

ConcreteDeck

180

230

Surfacing

30

60

HAudl+kel

160

265

45unitsHB

350

500

TotalReactiononEachAbutment

NominalReaction(kN)



UltimateReaction(kN)

ConcreteDeck

1900

2400

Surfacing

320

600

HAudl+kel

1140

1880

45unitsHB

1940

2770

Nominalloadingon1mlengthofabutment:DeckDeadLoad=(1900+320)/11.6=191kN/mHAliveLoadonDeck=1140/11.6=98kN/mHBliveLoadonDeck=1940/11.6=167kN/m

FromBS5400Part2Figures7and8theminimumandmaximumshadeairtemperaturesare19and+37oCrespectively.ForaGroup4typestrucutre(seefig.9)thecorrespondingminimumandmaximumeffectivebridgetemperaturesare11and+36oCfromtables10and11.Hencethetemperaturerange=11+36=47oC.FromClause5.4.6therangeofmovementatthefreeendofthe20mspandeck=471210620103=11.3mm.Theultimatethermalmovementinthedeckwillbe[(11.3/2)f3fL]=[11.31.11.3/2]=8mm.

Option1ElastomericBearing:Withamaximumultimatereaction=230+60+500=790kNthenasuitableelastomericbearingwouldbeEkspan'sElastomericPad:BearingEKR35:

MaximumLoad=1053kNShearDeflection=13.3mmShearStiffness=12.14kN/mmBearingThickness=19mm

Note:therequiredsheardeflection(8mm)shouldbelimitedtobetween30%to50%ofthethickness



ofthebearing.Thefigurequotedinthecatalogueforthemaximumsheardeflectionis70%ofthethickness.Atoleranceisalsorequiredforsettingthebearingiftheambienttemperatureisnotatthemidrangetemperature.Thedesignshadeairtemperaturerangewillbe19to+37oCwhichwouldrequirethebearingstobeinstalledatashadeairtemperatureof[(37+19)/219]=9oCtoachievethe8mmmovement.Ifthebearingsaresetatamaximumshadeairtemperatureof16oCthen,byproportionthedeckwillexpand8(3716)/[(37+19)/2]=6mmandcontract8(16+19)/[(37+19)/2]=10mm.Letusassumethatthismaximumshadeairtemperatureof16oCforfixingthebearingsisspecifiedintheContractanddesigntheabutmentsaccordingly.

Horizontalloadatbearingfor10mmcontraction=12.1410=121kN.Thisisanultimateloadhencethenominalhorizontalload=121/1.1/1.3=85kNateachbearing.Totalhorizontalloadoneachabutment=1185=935kN935/11.6=81kN/m.

AlternativelyusingBS5400Part9.1Clause5.14.2.6:H=AGr/tqUsingtheEkspanbearingEKR35

MaximumLoad=1053kNArea=610420=256200mm2Nominlhardness=60IRHDBearingThickness=19mm

ShearmodulusGfromTable8=0.9N/mm2

H=2562000.910310/19=121kNThiscorrellateswiththevalueobtainedaboveusingtheshearstiffnessfromthemanufacturer'sdatasheet.

Option2SlidingBearing:Withamaximumultimatereactionof790kNandlongitudinalmovementof8mmthenasuitablebearingfromtheEkspanEASerieswouldbe/80/210/25/25:

MaximumLoad=800kNBasePlateAdimension=210mmBasePlateBdimension=365mmMovementX=12.5mm

BS5400Part2Clause5.4.7.3:Averagenominaldeadloadreaction=(1900+320)/11=2220/11=200kNContactpressureunderbaseplate=200000/(210365)=3N/mm2AsthematingsurfacebetweenthestainlesssteelandPTFEissmallerthanthebaseplatethenthepressurebetweentheslidingfaceswillbeintheorderof5N/mm2.FromTable3ofBS5400Part9.1theCoefficientoffriction=0.08forabearingstressof5N/mm2Hencetotalhorizontalloadoneachabutmentwhenthedeckexpandsorcontracts=22200.08=180kN180/11.6=16kN/m.

TractionandBrakingLoadBS5400Part2Clause6.10:NominalLoadforHA=8kN/m20m+250kN=410kNNominalLoadforHB=25%of45units10kN4axles=450kN450>410kNhenceHBbrakingiscritical.



Brakingloadon1mwidthofabutment=450/11.6=39kN/m.Whenthisloadisappliedonthedeckitwillactonthefixedabutmentonly.

SkiddingLoadBS5400Part2Clause6.11:NominalLoad=300kN300



LoadCombinations

Backfill+Constructionsurcharge

Backfill+HAsurcharge+Deckdeadload+Deckcontraction

Backfill+HAsurcharge+Brakingbehindabutment+Deckdeadload

Backfill+HBsurcharge+Deckdeadload



Backfill+HAsurcharge+Deckdeadload+HBondeck

Backfill+HAsurcharge+Deckdeadload+HAondeck+Brakingondeck(Notappliedtofreeabutmentifslidingbearingsareprovided)

CASE1FixedAbutment

Densityofreinforcedconcrete=25kN/m3.Weightofwallstem=1.06.525=163kN/mWeightofbase=6.41.025=160kN/mWeightofbackfill=4.36.519=531kN/mWeightofsurcharge=4.312=52kN/mBackfillForceFb=0.27197.52/2=144kN/mSurchargeForceFs=0.27127.5=24kN/mRestoringEffects:

Weight

LeverArm

MomentAboutA

Stem

163

1.6

261



Base

160

3.2

512

Backfill

531

4.25

2257

Surcharge

52

4.25

221

=

906

=

3251

OverturningEffects:

F

LeverArm

MomentAboutA

Backfill

144

2.5

361

Surcharge

24

3.75



91

=

168

=

452

FactorofSafetyAgainstOverturning=3251/452=7.2>2.0OK.Forslidingeffects:ActiveForce=Fb+Fs=168kN/mFrictionalforceonundersideofbaseresistingmovement=Wtan()=906tan(30o)=523kN/mFactorofSafetyAgainstSliding=523/168=3.1>2.0OK.

BearingPressure:Checkbearingpressureattoeandheelofbaseslab=(P/A)(Pe/Z)wherePeisthemomentaboutthecentreofthebase.P=906kN/mA=6.4m2/mZ=6.42/6=6.827m3/mNettmoment=3251452=2799kNm/mEccentricity(e)ofPaboutcentrelineofbase=3.2(2799/906)=0.111mPressureunderbase=(906/6.4)(9060.111/6.827)Pressureundertoe=142+15=157kN/m2



7.16

3.09

156

127

Case2

2.87

2.13

386

5

Case2a

4.31

2.64

315

76

Case3

3.43

2.43

351

39

Case4

4.48

2.63

322

83

Case5

5.22

3.17

362

81



Case6

3.80

2.62

378

43

FofSOverturning

FofSSliding

Case1

7.16

3.09

Case2

2.87

2.13

Case2a

4.31

2.64

Case3

3.43

2.43

Case4

4.48

2.63

Case5

5.22

3.17

Case6

3.80



2.62

BearingPressureatToe

BearingPressureatHeel

Case1

156

127

Case2

386

5

Case2a

315

76

Case3

351

39

Case4

322

83

Case5

362

81

Case6

378

43

FreeAbutment:



FofSOverturning

FofSSliding



Case1

7.15

3.09

168

120

Case2

2.91

2.14

388

7

Case2a

4.33

2.64

318

78

Case3

3.46

2.44

354

42

Case4

4.50

2.64



325

84

Case5

5.22

3.16

365

82

FofSOverturning

FofSSliding

Case1

7.15

3.09

Case2

2.91

2.14

Case2a

4.33

2.64

Case3

3.46

2.44

Case4

4.50

2.64

Case5

5.22

3.16





Case1

168

120

Case2

388

7

Case2a

318

78

Case3

354

42

Case4

325

84

Case5

365

82

Itcanbeseenthattheuseofelastomericbearings(Case2)willgovernthecriticaldesignloadcasesontheabutments.Weshallassumethattherearenospecificrequirementsforusingelastomericbearingsanddesigntheabutmentsforthelesserloadeffectsbyusingslidingbearings.

2)WallandBaseDesignLoadsonthebackofthewallarecalculatedusing'atrest'earthpressures.ServiceabilityandUltimateloadeffectsneedtobecalculatedfortheloadcases1to6shownabove.Again,thesearebestcarriedoutusingasimplespreadsheet.UsingtheFixedAbutmentLoadCase1againasanexampleofthecalculations:WallDesignKo=1Sin(')=1Sin(35o)=0.426



fLforhorizontalloadsduetosurchargeandbackfillfromBS5400Part2Clause5.8.1.2:Serviceability=1.0Ultimate=1.5f3=1.0forserviceabilityand1.1forultimate(fromBS5400Part4Clauses4.2.2and4.2.3)BackfillForceFbontherearofthewall=0.426196.52/2=171kN/mSurchargeForceFsontherearofthewall=0.426126.5=33kN/mAtthebaseoftheWall:Serviceabilitymoment=(1716.5/3)+(336.5/2)=371+107=478kNm/mUltimatemoment=1.11.5478=789kNm/mUltimateshear=1.11.5(171+33)=337kN/m

AnalysingthefixedabutmentwithLoadCases1to6andthefreeabutmentwithLoadCases1to5usingasimplespreadsheetthefollowingresultswereobtainedforthedesignmomentsandshearatthebaseofthewall:

FixedAbutment:

MomentSLSDead

MomentSLSLive

MomentULS

ShearULS

Case1

371

108

790

337

Case2a

829

258

1771

566

Case3

829



486

2097

596

Case4

829

308

1877

602

Case5

829

154

1622

543

Case6

829

408

1985

599

FreeAbutment:

MomentSLSDead

MomentSLSLive

MomentULS

ShearULS

Case1

394



112

835

350

Case2a

868

265

1846

581

Case3

868

495

2175

612

Case4

868

318

1956

619

Case5

868

159

1694

559

ConcretetoBS8500:2006UsestrengthclassC32/40withwatercementratio0.5andminimumcementcontentof340kg/m3forexposureconditionXD2.Nominalcovertoreinforcement=60mm(45mmminimumcoverplusatolerancecof15mm).ReinforcementtoBS4449:2005GradeB500B:fy=500N/mm2



DesignforcriticalmomentsandshearinFreeAbutment:ReinforcedconcretewallsaredesignedtoBS5400Part4Clause5.6.Checkclassificationtoclause5.6.1.1:Ultimateaxialloadinwallfromdeckreactions=2400+600+2770=5770kN0.1fcuAc=0.14010311.61=46400kN>5770designasaslabinaccordancewithclause5.4

BendingBS5400Part4Clause5.4.2forreisitancemomentsinslabsdesigntoclause5.3.2.3:z={1[1.1fyAs)/(fcubd)]}dUseB40@150c/c:As=8378mm2/m,d=10006020=920mmz={1[1.15008378)/(401000920)]}d=0.875d2175kNn/mOKCarryingoutthecrackcontrolcalculationtoClause5.8.8.2givesacrackwidthof0.2mm



EarlyThermalCrackingConsideringtheeffectsofcastingthewallstemontothebaseslabbycomplyingwiththeearlythermalcrackingofconcretetoBD28thenB16horizontallacerbars@150c/cwillberequiredinbothfacesinthebottomhalfofthewall.MinimumareaofsecondaryreinforcementtoClause5.8.4.2=0.12%ofbad=0.00121000920=1104mm2/m(useB16@150c/cAs=1340mm2/m)BaseDesignMaximumbendingandsheareffectsinthebaseslabwilloccuratsectionsnearthefrontandbackofthewall.Differentloadfactorsareusedforserviceabilityandultimatelimitstatessothecalculationsneedtobecarriedoutforeachlimitstateusing'atrestpressures'UsingtheFixedAbutmentLoadCase1againasanexampleofthecalculations:

CASE1FixedAbutmentServiceabilityLimitState

fL=1.0f3=1.0Weightofwallstem=1.06.5251.0=163kN/mWeightofbase=6.41.0251.0=160kN/mWeightofbackfill=4.36.5191.0=531kN/mWeightofsurcharge=4.3121.0=52kN/mB/fillForceFb=0.426197.521.0/2=228kN/mSurchargeForceFs=0.426127.51.0=38kN/mRestoringEffects:

Weight

LeverArm

MomentAboutA

Stem

163

1.6

261

Base

160



3.2

512

Backfill

531

4.25

2257

Surcharge

52

4.25

221

=

906

=

3251

OverturningEffects:

F

LeverArm

MomentAboutA

Backfill

288

2.5

570

Surcharge

38

3.75

143

=



266

=

713

BearingPressureattoeandheelofbaseslab=(P/A)(Pe/Z)P=906kN/mA=6.4m2/mZ=6.42/6=6.827m3/mNettmoment=3251713=2538kNm/mEccentricity(e)ofPaboutcentrelineofbase=3.2(2538/906)=0.399mPressureunderbase=(906/6.4)(9060.399/6.827)Pressureundertoe=142+53=195kN/m2

Pressureunderheel=14253=89kN/m2

Pressureatfrontfaceofwall=89+{(19589)5.3/6.4}=177kN/m2

Pressureatrearfaceofwall=89+{(19589)4.3/6.4}=160kN/m2

SLSMomentataa=(1771.12/2)+([195177]1.12/3)(251.01.12/2)=99kNm/m(tensioninbottomface).SLSMomentatbb=(894.32/2)+([16089]4.32/6)(251.04.32/2)(5314.3/2)(524.3/2)=443kNm/m(tensionintopface).

CASE1FixedAbutmentUltimateLimitState

fLforconcrete=1.15fLforfillandsurcharge(vetical)=1.2fLforfillandsurcharge(horizontal)=1.5Weightofwallstem=1.06.5251.15=187kN/mWeightofbase=6.41.0251.15=184kN/mWeightofbackfill=4.36.5191.2=637kN/mWeightofsurcharge=4.3121.2=62kN/m



BackfillForceFb=0.426197.521.5/2=341kN/mSurchargeForceFs=0.426127.51.5=58kN/mRestoringEffects:

Weight

LeverArm

MomentAboutA

Stem

187

1.6

299

Base

184

3.2

589

Backfill

637

4.25

2707

Surcharge

62

4.25

264

=

1070

=

3859

OverturningEffects:



F

LeverArm

MomentAboutA

Backfill

341

2.5

853

Surcharge

58

3.75

218

=

399

=

1071

BearingPressureattoeandheelofbaseslab=(P/A)(Pxe/Z)P=1070kN/mA=6.4m2/mZ=6.42/6=6.827m3/mNettmoment=38591071=2788kNm/mEccentricity(e)ofPaboutcentrelineofbase=3.2(2788/1070)=0.594mPressureunderbase=(1070/6.4)(10700.594/6.827)Pressureundertoe=167+93=260kN/m2

Pressureunderheel=16793=74kN/m2

Pressureatfrontfaceofwall=74+{(26074)5.3/6.4}=228kN/m2

Pressureatrearfaceofwall=74+{(26074)4.3/6.4}=199kN/m2



f3=1.1ULSShearataa=1.1{[(260+228)1.1/2](1.151.125)}=260kN/mULSShearatbb=1.1{[(199+74)4.3/2](1.154.325)63762}=259kN/mULSMomentataa=1.1{(2281.12/2)+([260228]1.12/3)(1.15251.01.12/2)}=148kNm/m(tensioninbottomface).ULSMomentatbb=1.1{(744.32/2)+([19974]4.32/6)(1.15251.04.32/2)(6374.3/2)(624.3/2)}=769kNm/m(tensionintopface).

AnalysingthefixedabutmentwithLoadCases1to6andthefreeabutmentwithLoadCases1to5usingasimplespreadsheetthefollowingresultswereobtained:

FixedAbutmentBase:

Sectionaa

ULSShear

SLSMoment

ULSMoment

Case1

261

99

147

Case2a

528

205

302

Case3

593

235

340

Case4

550

208



314

Case5

610

241

348

Case6

637

255

365

Sectionbb

ULSShear

SLSMoment

ULSMoment

Case1

259

447

768

Case2a

458

980

1596

Case3

553

1178

1834

Case4



495

1003

1700

Case5

327

853

1402

Case6

470

1098

1717

FreeAbutmentBase:

Sectionaa

ULSShear

SLSMoment

ULSMoment

Case1

267

101

151

Case2a

534

207

305



Case3

598

236

342

Case4

557

211

317

Case5

616

243

351

Sectionbb

ULSShear

SLSMoment

ULSMoment

Case1

266

475

816

Case2a

466

1029

1678

Case3

559



1233

1922

Case4

504

1055

1786

Case5

335

901

1480

DesignforshearandbendingeffectsatsectionsaaandbbfortheFreeAbutment:BendingBS5400Part4Clause5.7.3designasaslabforreisitancemomentstoclause5.3.2.3:z={1[1.1fyAs)/(fcubd)]}dUseB32@150c/c:As=5362mm2/m,d=10006016=924mmz={1[1.15005362)/(401000924)]}d=0.92d1922kNm/mOK(1983kNm/malso>1834kNm/mB32@150c/csuitableforfixedabutment.FortheServiceabilitycheckforCase3anapproximationofthedeadloadmomentcanbeobtainedbyremovingthesurchargeandbrakingloads.ThespreadsheetresultgivesthedeadloadSLSmomentforCase3as723kNm,thustheliveloadmoment=1233723=510kNm.CarryingoutthecrackcontrolcalculationtoClause5.8.8.2givesacrackwidthof0.27mm>0.25mmFail.Thiscouldbecorrectedbyreducingthebarspacing,butincreasethebarsizetoB40@150c/casthisisrequiredtoavoidtheuseoflinks(seebelow).UsingB40@150c/cthecrackcontrolcalculationgivesacrackwidthof0.17mm



ULSShearontoe=1.1{(620+599)0.50.1761.1510.17625}=112kN

v=V/(bd)=112103/(1000924)=0.121N/mm2Noshearreinforcementisrequiredwhenv0.121N/mm2OK

ShearonHeelUseFreeAbutmentLoadCase3:Shearrequirementsaredesignedatthebackfaceofthewalltoclause5.4.4.1:

Lengthofheel=(6.51.11.0)=4.4mULSShearonheel=1.1{3480.5(5.1852.1)1.1514.4251.24.4(8.6319+10)}=559kN

UsingB32@150c/cthen:v=V/(bd)=559103/(1000924)=0.605N/mm2Noshearreinforcementisrequiredwhenv



EarlyThermalCrackingConsideringtheeffectsofcastingthebaseslabontotheblindingconcretebycomplyingwiththeearlythermalcrackingofconcretetoBD28thenB16distributionbars@250c/cwillberequired.MinimumareaofmainreinforcementtoClause5.8.4.1=0.15%ofbad=0.00151000924=1386mm2/m(useB20@200c/cAs=1570mm2/m).

LocalEffectsCurtainWallThiswallisdesignedtobecastontothetopoftheabutmentafterthedeckhasbeenbuilt.Loadingwillbeappliedfromthebackfill,surchargeandbrakingloadsontopofthewall.

HBbrakingloadtoBS5400clause6.10=25%45units410kNon2axles=225kNperaxle.Toallowforloaddistributioneffectsassumea45odispersaltothecurtainwallanda45odispersaldownthewall,withmaximumdispersalofthewidthoftheabutment(11.6m).

Thiscrudeanalysiswillslightlyunderestimatethepeakvaluesinthewallbelowtheload,butallowancecanbemadewhendesigningthereinforcementtoensurethereissparecapacity.Then:1staxleloadonbackofabutment=225/3.0=75kN/mDispersedtothebaseofthecurtainwall=225/9.0=25kN/m2ndaxleloadonbackofabutment=225/6.6=34.1kN/mDispersedtothebaseofthecurtainwall=225/11.6=19.4kN/m

Forloadeffectsatthetopofthecurtainwall:Maximumloadonbackofabutment=75+34.1=109.1kN/mForloadeffectsatthebaseofthecurtainwall:Maximumloadonbackofabutment=25+19.4=44.4kN/m

BendingandShearatBaseof3mHighCurtainWall

HorizontalloadduetoHBsurcharge=0.426203.0=25.6kN/m



Horizontalloadduetobackfill=0.426193.02/2=36.4kN/mSLSMoment=(44.43.0)+(25.61.5)+(36.41.0)=208kNm/m(36dead+172live)ULSMoment=1.1{(1.144.43.0)+(1.525.61.5)+(1.536.41.0)}=285kNm/mULSShear=1.1{(1.144.4)+(1.525.6)+(1.536.4)}=156kN/m

400thickcurtainwallwithB32@150c/c:Mult=584kNm/m>285kNm/mOKSLSMomentproducescrackwidthof0.14mmv=0.48N/mm2ShearOK

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LastUpdated:01/05/15Formoreinformation:

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DavidChildsB.Sc,C.Eng,MICE

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