bridge abutment design example
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Bridge Abutment Design ExampleTRANSCRIPT
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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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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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)
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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.
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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Brakingloadon1mwidthofabutment=450/11.6=39kN/m.Whenthisloadisappliedonthedeckitwillactonthefixedabutmentonly.
SkiddingLoadBS5400Part2Clause6.11:NominalLoad=300kN300
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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LoadCombinations
Backfill+Constructionsurcharge
Backfill+HAsurcharge+Deckdeadload+Deckcontraction
Backfill+HAsurcharge+Brakingbehindabutment+Deckdeadload
Backfill+HBsurcharge+Deckdeadload
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
http://www.bridgedesign.org.uk/tutorial/abutex.html 9/33
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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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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:
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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FofSOverturning
FofSSliding
BearingPressureatToe
BearingPressureatHeel
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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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BearingPressureatToe
BearingPressureatHeel
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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
=
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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
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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:
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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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
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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
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495
1003
1700
Case5
327
853
1402
Case6
470
1098
1717
FreeAbutmentBase:
Sectionaa
ULSShear
SLSMoment
ULSMoment
Case1
267
101
151
Case2a
534
207
305
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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
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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
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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
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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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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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11/14/2015 BridgeABUTMENTDESIGNEXAMPLE
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