DESIGN OF DECK SLAB AND GIRDERS- BRIDGE ENGINEERING

BRIDGE ENGINEERING -KTU

1. Design of Deck Slab & Girders

2. DesignExample:
Design a RCC T beam girder bridge to suit the following data
Clear width of roadway –7.5 m
Span (c/c of bearings) –16 m
Live load –IRC class AA tracked vehicle
Average thickness of wearing coat –80 mm
Concrete mix –M25
Steel –Fe415 grade HYSD bars
UsingCourbon’smethod,computethedesignmomentsand
shearforcesanddesignthedeckslab,maingirderandcross
girderandsketchthetypicaldetailsofreinforcements.
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3. Design of Deck Slab
3

4. 1.Permissiblestresses:
Permissible flexural compressive stress (σ
cb) = 8.3 Mpa(table 9 of IRC
21-2000)
Permissible stress for Fe415 (σ
st) = 200 Mpa(table 10 of IRC 21-2000)
The modular ratio can be adopted as m = 10
Lever arm factor (j) =
Moment factor (Q) = 0.5σ
cbnj= 0.5x8.3x0.9x0.293 = 1.09
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3
n
1 9.0
3
293.0
1j
293.0
3.8x10
200
1
1
m
1
1
n
cb
st
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5. 2.Crosssectionofthedeck:
5
2.5 m
2.5 m
4.0 m 4.0 m 4.0 m 4.0 m
The depth of cross girder is taken as equal to the depth of main
girder to simplify the computations

6. 2.Crosssectionofthedeck:
6
0.08 m thick wearing coat
0.2 m
0.6 m
1.85 m 2.5 m 2.5 m
7.5 m
0.3 m
1.0 m
1.4 m
0.3 m

7. 3.Designofinteriorslabpanel:
Bendingmoments
Deadweightofslab=(1x1x0.2x24)=4.8kN/m
2
Deadweightofwc=(1x1x0.08x22)=1.76kN/m
2
Totaldeadload=4.8+1.76=6.56kN/m
2
7
B=2.5 m
L=4.0 m
3.60 m
0.85 m
u
=1.01 m
v=3.76 m

8. 3.Designofinteriorslabpanel:
Bendingmoments(liveload)
u/B=1.01/2.5=0.404
v/L=3.76/4.0=0.94
K=(B/L)=2.5/4.0=0.625
FromPigeaud’scurvesm
1=0.085andm
2=0.024
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Pigeaud'scurvesarebasedontheelasticanalysisofthinisotrpoicplates
withsimplesupportsonallthefoursides.However,adeckslabcannotbe
idealisedassimplysupportedpanel.TheprocessofreducingPigeaud‘s
momentvaluesby20%andassumingequalandsupportmomentsis
highlyconservative.Thedeckslabbehavesasafixedslabfortheusual
beamsizesofabridge.

9. 3.Designofinteriorslabpanel:
Bendingmoments(liveload)
Bendingmomentintheshortspandirection(M
S)
M
S=(m
1+μm
2)W=(0.085+0.15x0.024)350=31.01kNm
Bendingmomentinthelongspandirection(M
L)
M
L=(m
2+μm
1)W=(0.024+0.15x0.085)350=12.845kNm
Thedesignbendingmomentoveranintermediatesupportofa
continuousdecksupportedonbearingsmaybecalculatedby
equation.
M
1= (M –qa
2
/8) or 0.8M, whichever is greater,
where, M, = Design bending moment.
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10. 3.Designofinteriorslabpanel:
Bendingmoments(liveload)
Designbendingmomentincludingimpactintheshortspan
direction(M
S)=1.25x0.8x31.01=31.01kNm
Designbendingmomentincludingimpactinthelongerspan
direction(M
L)=1.25x0.8x12.845=12.845kNm
Bendingmoments(deadloads)
Deadload=6.56kN/m
2
Totalloadonpanel=(4x2.5x6.56)=65.6kN
u/B=1.0;v/L=1.0asthepanelisloadedwithuniformly
distributedload.
K=(B/L)=2.5/4.0=0.625and1/K=1.6
FromPigeaud’scurvesm
1=0.049andm
2=0.015
Bendingmomentintheshortspandirection(M
S)
M
S=(m
1+μm
2)W=(0.049+0.15x0.015)65.6=3.36kNm
Bendingmomentinthelongspandirection(M
L)
M
L=(m
2+μm
1)W=(0.015+0.15x0.049)65.6=1.468kNm
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11. 3.Designofinteriorslabpanel:
Bendingmoments(deadload)
Designbendingmomentintheshortspandirection
(M
S)=0.8x3.36=2.688kNm
Designbendingmomentinthelongerspandirection
(M
L)=0.8x1.468=1.174kNm
Totaldesignbendingmomentsintheshortspan
(M
S)=31.01+2.688=33.698kNm
Totaldesignbendingmomentsinthelongspan
(M
L)=12.845+1.174=14.019kNm
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12. 3.Designofinteriorslabpanel:
Shearforces
Dispersioninthedirectionofspan=0.85+2(0.08+0.2)=1.41m
Formax.shear,loadiskeptsuchthatthewholedispersionisin
span.Theloadiskeptat1.41/2=0.705mfromtheedgeof
beam.
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13. 3.Designofinteriorslabpanel:
Shearforces
Breadthofgirder=0.3m
Clearlengthofpanel(L’)=4.0-2(0.15)=3.70m
Clearbreadthofpanel(B’)=2.5-2(0.15)=2.2m
(B’/L’)=2.2/3.7=0.6
‘K’forcontinuousslabis1.84(IRC21-2000)
Effectivewidthofslab=1.84x0.705(1-0.705/2.2)+3.76=4.64m
Loadpermeterwidth=350/4.64=75.4kN
Shearforce=75.4(2.2-0.705)/2.2=51.23kN
Shearforcewithimpact=1.25x51.23=64kN
Deadloadshearforce=6.56x2.2/2=7.21kN
Totalshearforce=64+7.21=71.21kN
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14. 3.Designofinteriorslabpanel:
Designofsection
Effectivedepth
Adoptoveralldepth=200mm
Areaoftensionreinforcementisgivenby
Similarlycalculatereinforcementinlongerspandirection
14mm175
1000x1.1
10x698.33
Qb
M
d
6
 2
6
st
st mm1170
175x9.0x200
10x698.33
jd
M
A 
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15. 3.Designofinteriorslabpanel:
Checkforshearstress
Nominalshearstress
152
mm/N4.0
175x1000
1000x21.71
bd
V
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16. 3.Designofinteriorslabpanel:
Checkforshearstress
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Maximumpermissibleshear
stress
Permissibleshearstress
Hencesafeinpermissible
limits2
max mm/N9.1 2
c mm/N36.0

17. Design of Girders
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18. 4.Designoflongitudinalgirders:
Deadloadsfromslabforgirder
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0.2 m
0.6 m
1.85 m 2.5 m 2.5 m
0.3 m
1.0 m
1.4 m
0.3 m
W
1 W
2
W
1.2+2(0.85)
=2.05m
Axis of
bridge
CG of
loads
e=1.1 m

19. 4.Designoflongitudinalgirders:
Deadloadsfromslabforgirder
Weightof
1.Parapet=2x0.7=1.4kN/m
2.Wearingcoat=0.08x7.5x22=13.2kN/m
3.Deckslab=0.2x7.5x24=36kN/m
4.Kerb=2(0.5x0.6x24)=14.4kN/m
Totaldeadload=1.4+13.2+36+14.4=65kN/m
Itisassumedthatthedeadloadisequallysharedbyallgirders.
Deadloadpergirder=65/3=21.66kN/m
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20. 4.Designoflongitudinalgirders:
Reactionfactors
UsingCourbon’smethod,thereactionfactorsarecalculatedas
follows:
Where, R
x= Reaction factor for the girder under consideration
I = Moment of Inertia of each longitudinal girder
d
x= distance of the girder under consideration from the central
axis of the bridge
W = Total concentrated live load
n = number of longitudinal girders
e = Eccentricity of live load with respect to the axis of the
bridge.
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d
I
1
n
W
R
x
2
x
x

21. 4.Designoflongitudinalgirders:
Reactionfactors
Reactionfactorforoutergirder
Reactionfactorforinnergirder
SinceW
1=0.5W;R
A=0.48W;R
B=0.33W;
211
2
1
A W96.01.1x5.2
5.2Ix3
I3
1
3
W2
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1
1
B W66.001
3
W2
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22. 4.Designoflongitudinalgirders:
LiveloadBMs
Bendingmoment=4x700=2800kN.m
Bendingmomentincludingimpactfactorandreactionfactor=
Reactionfactor=2800x1.25x0.48=1680kNm(foroutergirder)
Bendingmomentincludingimpactfactorandreactionfactor=
Reactionfactor=2800x1.25x0.33=1155kNm(forinnergirder)
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23. 4.Designoflongitudinalgirders:
LiveloadShears
ReactionongirderB=(350x0.45)/2.5=63kN
ReactionongirderA=(350x2.05)/2.5=287kN
MaximumreactionongirderB=(63x14.2)/16=56kN
MaximumreactionongirderA=(287x14.2)/16=255kN
Consideringimpactfactor=56x1.25=70kN(girderB)
Consideringimpactfactor=255x1.25=318.75kN(girderA)
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24. 4.Designoflongitudinalgirders:
DeadloadBMandSFs
Thedepthofthegirderisassumedas1600mm.
Depthofrib=1.4m
Widthofrib=0.3m
Weightofrib=1x1.4x0.3x24=10.08kN/m(permeter)
Thecrosssectionisassumedtohavethesamecrosssection
dimensionofmaingirder.
Henceweightofcrossgirder=10.08kN/m(permeter)
Reactiononmaingirder=10.08x2.5=25.2kN
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10.08 kN/m

25. 25