concrete decks
DESCRIPTION
Concrete DecksTRANSCRIPT
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 116
573
151 Introduction
Bridge decks not only provide the riding surace or traffic but also support and transer live loads
to the main load-carrying members such as stringer and girders on a bridge superstructure Bridge
decks include cast-in-place (CIP) reinorced concrete precast concrete deck panel prestress con-
crete timber 1047297lled and un1047297lled steel grid and steel orthotropic decks Selection o bridge deck
types depends on locations spans traffic environment maintenance aesthetics and lie cycle costs
among other reasons
Tis chapter ocuses on concrete deck and emphasizes the cast-in-place reinorced concrete deck A
design example o a reinorced concrete bridge deck is provided in accordance with the AASHTO LRFD
Bridge Design Speci1047297cations (AASHO 2012) For more detailed discussion o the concrete deck reer-
ences are made to FHWA (2012) and Barker and Puckett (2007) Steel orthotropic decks are discussed
in Chapter 16
152 Types of Concrete Decks
1521 Cast-in-Place Concrete Deck
Te CIP concrete deck slab is the predominant deck type in highway bridges in the United States
Figure 151 shows a reinorcement layout in a CIP concrete deck on the steel plate girder Figure 152
shows a CIP concrete deck under construction Figure 153 shows a typical CIP concrete deck details Its
main advantages are acceptable skid resistance the easier 1047297eld-adjustment o the roadway pro1047297le during
concrete placement to provide a smooth riding surace commonly available materials and contractors
to do the work However CIP slabs have disadvantages including excessive differential shrinkage with
15Concrete Decks
John ShenCalifornia Department
of Transportation
151 Introduction 573
152 ypes o Concrete Decks 573
Cast-in-Place Concrete Deck bull Precast Concrete Deck 153 Materials 576
General Requirements bull Concrete bull Reinorcement bull Construct ion
Practices
154 Design Considerations 577General Requirements bull Design Limit States bull Analysis Methods
155 Design Example 579Bridge Deck Data bull Design Requirements bull Solution bull Calculate
Factored MomentsmdashStrength Limit State I bull Design or Positive
Flexure Design bull Design or Negative Flexure bull Check Service
Limit State-Cracking Control bull Determine the Slab Reinorcement
Detailing Requirements
Reerences 588
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 216
574 Bridge Engineering Handbook Second Edition Superstructure Design
the supporting girders and slow construction the tendency o the deck rebar to corrode due to deicing
salts In order to develop cost-competitive ast to construct and durable alternative systems recent
innovations on CIP decks are ocused on developing mixes and curing methods that produce peror-
mance characteristics such as reeze-thaw resistance high abrasion resistance low stiffness and low
shrinkage rather than high strength
FIGURE 151 Reinorcement layout in a cast-in-place concrete deck
FIGURE 152 A cast-in-place concrete deck under construction
Cont reinf
12 min
Min reinf in top slab4 cont 18
Detaildimension typ
Slabthick
8 min
Add reinf when ldquoSrdquo le 11ndash6
2 clear
1 clear4 bars
5 bars
Equal spacing
Extra 5 bars(tot 2 per bay)
Overhang
Max = Lesser of 05S or 6ndash0
Bottom bars
Truss bars
Top bars
ldquoSrdquoldquoSrdquo Girder C to C spacing L L
FIGURE 153 ypical cast-in-place concrete deck details
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 316
575Concrete Decks
1522 Precast Concrete Deck
Tere are two types o precast concrete decks ull-depth precast panels and stay-in-place (SIP) precast
prestressed panels combined with CIP topping
Figure 154 shows u ll-depth precast concrete deck panels under construction Te u ll-depth precast
panels have the advantages o signi1047297cant reduction o shrinkage effects and ast construction speed
and have been used or deck replacement with high traffic volumes NCHRP Report 407 (ardos and
Baishya 1998) proposed a ull-depth panel system with panels pretensioned in the transverse direction
and posttensioned in the longitudinal direction NCHRP Report 584 (Badie and ardos 2008) devel-
oped two ull-depth precast concrete bridge deck panel systems a transversely pretensioned system and
a transversely conventionally reinorced system and proposed guidelines or the design abrication and
construction o ull-depth precast concrete bridge deck panel systems without the use o posttensioning
or overlays and (2) connection details or new deck panel systems
Figure 155 shows a partial depth precast panel or SIP precast prestressed panes combined with
CIP topping Te SIP panels act as orms or the topping concrete and also as part o the structuraldepth o the deck Tis system can signi1047297cantly reduce construction time since 1047297eld orming is only
needed or the exterior girder overhangs It is cost-competitive with CIP decks or new structures and
deck replacement However the SIP panel system suffers re1047298ective cracking over the panel-to-panel
joints A modi1047297ed SIP precast panel system has been developed in NCHRP Report 407 (ardos and
Baishya 1998)
FIGURE 154 Full-depth precast concrete deck panels under construction (Courtesy o FHWA)
Cast-in-place concrete
Stay -in-place precast panel
FIGURE 155 ypical stay-in-place precast panel with cast-in-place concrete deck
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 416
576 Bridge Engineering Handbook Second Edition Superstructure Design
153 Materials
1531 General Requirements
Material characteristics in a bridge deck shall behave to reduce concrete distress and reinorcement
corrosion and lead to a long service lie with minimum maintenance Expected concrete deck should
behave with the ollowing characteristics (Russell 2004)
bull Low chloride permeability
bull A top surace that does not deteriorate rom reeze thaw or abrasion damage
bull Cracking that is limited to 1047297ne 1047298exural cracks associated with the structural behavior
bull Smooth rideability with adequate skid resistance
NCHRP Synthesis 333 (Russell 2004) recommended that use o the ollowing materials and practices
enhances the perormance o concrete bridge decks
1532 Concrete
bull ypes I II and IP cements
bull Fly ash up to 35 o the total cementitious materials content
bull Silica ume up to 8 o the total cementitious materials content
bull Ground-granulated blast urnace slag up to 50 o the total cementitious materials content
bull Aggregates with low modulus o elasticity low coefficient o thermal expansion and high thermal
conductivity
bull Largest size aggregate that can be properly placed
bull Water-reducing and high-range water-reducing admixtures
bull Air-void system with a spacing actor no greater than 020 mm (0008 in) speci1047297c surace area
greater than 236 mm2
mm3
(600 in2
in3
) o air-void volume and number o air voids per inch otraverse signi1047297cantly greater than the numerical value o the percentage o air
bull Water-cementitious materials ratio in the range o 040minus045
bull Concrete compressive strength in the range o 28minus41 MPa (4000minus6000 psi)
bull Concrete permeability per AASHO Speci1047297cation 277 in the range o 1500minus2500 coulombs
1533 Reinforcement
bull Epoxy-coated reinorcement in both layers o deck reinorcement
bull Minimum practical transverse bar size and spacing
1534 Construction Practices
bull Use moderate concrete temperatures at time o placement
bull Use windbreaks and ogging equipment when necessary to minimize surace evaporation rom
resh concrete
bull Provide minimum 1047297nishing operations
bull Apply wet curing immediately afer 1047297nishing any portion o the concrete surace and wet cure or
at least seven days
bull Apply a curing compound afer the wet curing period to slow down the shrinkage and enhance
the concrete properties
bull Use a latex-modi1047297ed or dense concrete overlay
bull Implement a warrant requirement or bridge deck perormance
bull Gradually develop perormance-based speci1047297cations
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 516
577Concrete Decks
154 Design Considerations
1541 General Requirements
bull Maintain a minimum structural depth o concrete deck o 70 in and a minimum concrete cover
o 25 in (64 mm) f cprime ge40 ksi
bull Use prestressing or depth o slabs less than 120 o the design span
bull Place the primary reinorcement in the direction o the skew or the skew angle o the deck less
than 25deg Otherwise place them perpendicular to the main supporting girders
bull Provide shear connectors between concrete decks and supporting beams
bull Provide edge beams at the lines o discontinuity For the deck supported in the transverse direc-
tion and composed with concrete barriers no additional edge beam is needed
1542 Design Limit States
Concrete decks must be designed or Strength I limit state (AASHO 2012) and are usually designed
as tension-controlled reinorced concrete components Strength II limit state o the permit vehicle
axle load does not typically control deck design Concrete decks are also required to meet the require-
ments or Service I limit state to control excessive deormation and cracking Te deck overhang shall
be designed to meet the requirements or Extreme Event II Concrete decks supported by multi-girder
systems are not required to be investigated or the atigue limit state
1543 Analysis Methods
15431 Approximate Method of Analysis
Approximate method o analysis is traditional ly used to design concrete bridge decks (AASHO 4621)
Te method assumes a concrete deck as transverse slab strips o 1047298exure members supported by the lon-
gitudinal girders Te AASHO speci1047297cations (AASHO 2012) require the maximum positive moment
and the maximum negative moment to apply or all positive moment regions and all negative moment
regions in the deck slab respectively Te width o an equivalent interior strip o a concrete deck is
provided in able 151 (AASHO 2012) For deck overhangs the AASHO Article 36134 may apply
For typical concrete deck supported on different girder arrangements with at least three girders and
the distance between the centerlines o the exterior girders not less than 140 f the maximum live load
moments including multiple presence actors and dynamic load allowance based on the equivalent strip
method are provided in AASHO A-4 (AASHO 2012) and are summarized in able 152
15432 Empirical Method of Analysis
Empirical method o analysis (AASHO 972) is a method o concrete deck slab design based on the
concept o internal arching action within concrete slabs In this method effective length o slab shal l be
taken as (1) or slabs monolithic with supporting members the ace-to-ace distance and (2) or slabs
supported on steel or concrete girders distance between the webs o girders Empirical design may beused only i the ollowing conditions are met
bull Cross-rames o diaphragms are used throughout the girders
bull Spacing o intermediate diaphragms between box beams does not exceed 25 f
bull Te deck is composed with supporting steel or concrete girders
bull Te deck is ully cast-in-place and water cured f cprimege 40 ksi
bull Deck o uniorm depth ge70 in except or hunched at girder 1047298anges and the distance between
extreme layers o reinorcement ge40 in
bull Effective length le135 f 60 le effective lengthdesign depth le180
bull Overhangslab depth ge50 or overhangslab depth ge30 with slab composites with continuous
concrete barrier
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 616
578 Bridge Engineering Handbook Second Edition Superstructure Design
15433 Re1047297ned Methods of Analysis
Re1047297ned methods o analysis or concrete deck speci1047297ed in AASHO 4632 (AASHO 2012) usually
consider 1047298exural and torsional deormation without considering vertical shear deormation Tey are
more suitable or a more complex deck slab structure or example the end zones o skewed girder decks
TABLE 152 Maximum Live Load Moment per Foot Width
Girder
Spacing
S (f)
Positive
Moment
M LL+IM
(kip-ff)
Negative M LL+IM (kip-ff)
Distance rom Centerline o Girder to Design Section or Negative Moment (in)
00 30 60 90 120 180 240
40 468 268 207 174 160 150 134 125
45 463 300 258 210 190 165 132 118
50 465 374 320 266 224 183 126 112
55 471 436 373 311 258 207 130 099
60 483 499 419 350 288 231 139 107
65 500 531 457 384 315 253 150 120
70 521 598 517 436 356 284 163 151
75 544 626 543 461 378 315 188 17280 569 648 565 481 398 343 249 216
85 599 666 582 498 414 361 296 258
90 629 681 597 513 428 371 331 300
95 659 715 631 546 466 404 368 339
100 689 785 699 613 526 441 409 377
105 715 852 764 677 589 502 448 415
110 746 914 826 738 650 562 486 452
115 774 972 884 796 707 719 552 487
120 801 1028 940 851 763 674 556 521
125 828 1081 993 904 816 728 597 554
130 854 1131 1043 955 867 779 638 586
135 878 1179 1091 1003 916 828 679 616
140 902 1224 1137 1050 963 867 718 645
145 925 1267 1181 1094 1008 921 757 672
150 947 1309 1223 1137 1051 965 794 702
TABLE 151 Equivalent Strips o Concrete Decks
ype o Concrete Deck Direction o Primary Strip
Relative to raffic Width o Primary Strip (in)
Cast-in-place Overhang 450 + 100 X
Cast-in-place Either parallel or
perpendicular
+ M 260 + 66 X
Cast-in-place with stay-in-place
concrete ormwork
Precast post-tensioned minus M 480 + 30S
S = spacing o supporting components (f)
X = distance rom load to point o support (f)
+ M = positive moment
minus M = negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 716
579Concrete Decks
155 Design Example
1551 Bridge Deck Data
A typical section o a steel-concrete composite plate girder bridge is shown in Figure 156
Concrete f c 4000 psiprime= (276 MPa) Ec = 3625 ksi (250 MPa)
Steel Reinorcement A706 Grade 60
f E y s( ) ( )= =60 ksi 414 MPa 29000 ksi 200000 MPa
n E
Es
c
= = 8
Loads Concrete Barrier weight wbarrier = 0410 kl
3 in Future wearing surace wws = 0140 kc (AASHO able 351-1)Reinorced Concrete unit weight wrc = 0150 kc (AASHO C351)
AASHO HL-93 + dynamic load allowance
1552 Design Requirements
Perorm the ollowing design calculations or concrete deck in accordance with the AASHTO LRFD
Bridge Design Speci1047297cations 2012 Edition
bull Select concrete deck thick ness and cover
bull Calcu late Unactored Dead Load Moments
bull Calcu late Unactored Live Load MomentsmdashEquivalent Strip Method
bull Calcu late Factored MomentsmdashStrength Limit State I
bull Design or Positive Flexure
bull Design or Negative Flexure
bull Check Service Limit State
bull Determine the Slab Reinorcement Detailing Requirements
58ndash0
Concretebarriertype 732(Typ)
2
4 12=48ndash0
structureCL
FIGURE 156 ypical section o composite plate girder bridge
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 816
580 Bridge Engineering Handbook Second Edition Superstructure Design
1553 Solution
15531 Select Concrete Deck Thickness and Cover
ry dec2k slab thickness t = 9125 in gt Minimum deck thickness = 70 in
DepthSpan= 9125 (144)= 0064 gt 1 20 = 005 No prestressing needed
Use deck top cover C top = 20 in
Use deck bottom cover C bot = 10 in
15532 Calculate Unfactored Dead Load Moments
Dead load or one oot length o concrete deck is calculated as ollows
Deck concrete weightmdashW DC1mdashdeck concrete weightmdash
W t wrc109125
12
(10) (015) 0114 kiptDC1 ( )( )= =
=
Barrier weight W DC2 (concentrate load applied at 7 in rom the edge o deck)
W w( ) ( )( )= = =10 10 041 041 kipDC2 barrier
Future wearing surace o 3 inmdashW DW
W wthickness o wearing surace 10
3
1210 014 0035 kiptDC2 ws( )( ) ( )( )= =
=
Te dead load moments or the deck slab can be calculated using a continuous beam as shown in
Figure 157able 153 lists unactored dead load moments Only the results or Spans 1 and 2 are shown in the
table since the bridge deck is symmetrical the centerline o the bridge
15533 Calculate Unfactored Live Load Moments
From able 152 unactored live load moments including multiple presence actors and dynamic load
allowance are obtained as ollows
For girder spacing S = 12 f maximum positive live load moments are as
M 801 kip-ttLL IM =+
For negative 1047298exure the design sections are located the ace o the support or monolithic concrete
construction 14 the 1047298ange width rom the centerline o the support or steel girder bridges and 13 the
1047298ange width not exceeding 15 in rom the centerline o the support or precast I-girders or open-boxgirders (AASHO 2012 Article 46216)
85
W DC2 W DC2
W DC1W DW
5ndash0 12ndash0Span 1
12ndash0Span 2
12ndash0Span 3
12ndash0Span 4
5ndash0
17
FIGURE 157 Concrete deck under unactored dead loads
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 916
581Concrete Decks
For this example assume steel girder 1047298ange width = 18 in the design section is at frac14(18)= 45 in rom
the centerline o steel girder as shown in Figure 158 Te negative moment can be obtained conservatively
as the moment at the centerline o the support or interpolated between moments at 3 in and 6 in
M 851
3 15
3940 851 896 kip-ttLL IM ( )minus = +
minusminus =+
1554 Calculate Factored MomentsmdashStrength Limit State IFor Strength Limit State I load combination actored moment ollows
( ) ( )= η γ + + γ + γ +DC DC1 DC2 DW DW LL LL IM M M M M M u
η= η η η ge 095D R I
For this example use η = 095 γ =125DC γ = 150DW and γ = 175LL
( )( )= + + + +095 [125 15 175 ]DC1 DC2 DW LL IM M M M M M u
TABLE 153 Unactored Dead Load Moments
Distancerom lef
support X
(f)
Location
XS
Deck Load DC1 M DC1 (kip-ff)
Barrier Load DC2 M DC2 (kip-ff)
Future Wearing Surace DW M DW (kip-ff)
Span 1 Span 2 Span 1 Span 2 Span 1 Span 2
00 00 minus1425 minus1352 minus1760 0496 minus0225 minus0475
12 01 minus0679 minus0616 minus1534 0422 minus0023 minus0240
24 02 minus0097 minus0044 minus1309 0348 0128 minus0055
36 03 0321 0365 minus1083 0273 0229 0079
48 04 0574 0608 minus0858 0199 0280 0163
60 05 0664 0688 minus0632 0125 0280 0196
72 06 0589 0604 minus0406 0051 0230 0179
84 07 0350 0355 minus0181 minus0023 0129 0112
96 08 minus0053 minus0058 0045 minus0097 minus0022 minus0006
108 09 minus0621 minus0635 0270 minus0171 minus0223 minus0174
120 10 minus1352 minus1376 0496 minus0245 minus0475 minus0393
Design
sectionC webL
bf = 18
14bf = 45
FIGURE 158 Design section or negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1016
582 Bridge Engineering Handbook Second Edition Superstructure Design
15541 Maximum Positive Factored Moments
From able 153 it is seen that the maximum unactored positive moments due to the concrete deckslab barrier and uture wearing surace is located in Span 2 at a distance o 05 S Te maximum live
load positive moment equals 801 kip-ff Tereore the maximum positive actored moment is
M u 095 (125)(0688 0125) (15)(0196) (175)(801) 14561kip-tt[ ]= + + + =
15542 Maximum Negative Factored Moments
From able 153 it is seen that the maximum unactored negative moments due to the concrete deck
slab barrier and uture wearing surace is located Span 1 at the centerline o exterior girder and can be
obtained conservatively as the moment at the centerline o the exterior support or interpolated between
00S and 01S as ollows
M 0679 12 45
12(1425 0679) 1145 kip-ttDC1 = minus minus minus minus = minus
M 1534
12 45
121760 1534 1675 kip-ttDC2 ( )= minus minus
minusminus = minus
M 0023
12 45
12(0225 0023) 0149 kip-ttDW = minus +
minusminus = minus
Te maximum actored negative moment is as
M u 095 (125)( 1145 1675) (15)( 0149) (175)( 896) 18457 kip-tt[ ]= minus minus + minus + minus = minus
1555 Design for Positive Flexure Design
ry 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashbottom covermdashhal bar diameter
( ) ( )= minus minus = minus minus =
bar diameter
29125 10
0625
27813 inbotd t C e
ry 58 in which is less than the maximum spacing 15t = 18 in = = As
12(031)
80465 in2
For a rectangular section with a width o b = 12 in and depth o t = 9125 inConcrete compression block depth
a
A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0465 60
085 40 120684 in
Distance rom the extreme compression 1047297ber to the neutral axis
=
β = =c
a 0684
0850801 in
1
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 216
574 Bridge Engineering Handbook Second Edition Superstructure Design
the supporting girders and slow construction the tendency o the deck rebar to corrode due to deicing
salts In order to develop cost-competitive ast to construct and durable alternative systems recent
innovations on CIP decks are ocused on developing mixes and curing methods that produce peror-
mance characteristics such as reeze-thaw resistance high abrasion resistance low stiffness and low
shrinkage rather than high strength
FIGURE 151 Reinorcement layout in a cast-in-place concrete deck
FIGURE 152 A cast-in-place concrete deck under construction
Cont reinf
12 min
Min reinf in top slab4 cont 18
Detaildimension typ
Slabthick
8 min
Add reinf when ldquoSrdquo le 11ndash6
2 clear
1 clear4 bars
5 bars
Equal spacing
Extra 5 bars(tot 2 per bay)
Overhang
Max = Lesser of 05S or 6ndash0
Bottom bars
Truss bars
Top bars
ldquoSrdquoldquoSrdquo Girder C to C spacing L L
FIGURE 153 ypical cast-in-place concrete deck details
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 316
575Concrete Decks
1522 Precast Concrete Deck
Tere are two types o precast concrete decks ull-depth precast panels and stay-in-place (SIP) precast
prestressed panels combined with CIP topping
Figure 154 shows u ll-depth precast concrete deck panels under construction Te u ll-depth precast
panels have the advantages o signi1047297cant reduction o shrinkage effects and ast construction speed
and have been used or deck replacement with high traffic volumes NCHRP Report 407 (ardos and
Baishya 1998) proposed a ull-depth panel system with panels pretensioned in the transverse direction
and posttensioned in the longitudinal direction NCHRP Report 584 (Badie and ardos 2008) devel-
oped two ull-depth precast concrete bridge deck panel systems a transversely pretensioned system and
a transversely conventionally reinorced system and proposed guidelines or the design abrication and
construction o ull-depth precast concrete bridge deck panel systems without the use o posttensioning
or overlays and (2) connection details or new deck panel systems
Figure 155 shows a partial depth precast panel or SIP precast prestressed panes combined with
CIP topping Te SIP panels act as orms or the topping concrete and also as part o the structuraldepth o the deck Tis system can signi1047297cantly reduce construction time since 1047297eld orming is only
needed or the exterior girder overhangs It is cost-competitive with CIP decks or new structures and
deck replacement However the SIP panel system suffers re1047298ective cracking over the panel-to-panel
joints A modi1047297ed SIP precast panel system has been developed in NCHRP Report 407 (ardos and
Baishya 1998)
FIGURE 154 Full-depth precast concrete deck panels under construction (Courtesy o FHWA)
Cast-in-place concrete
Stay -in-place precast panel
FIGURE 155 ypical stay-in-place precast panel with cast-in-place concrete deck
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 416
576 Bridge Engineering Handbook Second Edition Superstructure Design
153 Materials
1531 General Requirements
Material characteristics in a bridge deck shall behave to reduce concrete distress and reinorcement
corrosion and lead to a long service lie with minimum maintenance Expected concrete deck should
behave with the ollowing characteristics (Russell 2004)
bull Low chloride permeability
bull A top surace that does not deteriorate rom reeze thaw or abrasion damage
bull Cracking that is limited to 1047297ne 1047298exural cracks associated with the structural behavior
bull Smooth rideability with adequate skid resistance
NCHRP Synthesis 333 (Russell 2004) recommended that use o the ollowing materials and practices
enhances the perormance o concrete bridge decks
1532 Concrete
bull ypes I II and IP cements
bull Fly ash up to 35 o the total cementitious materials content
bull Silica ume up to 8 o the total cementitious materials content
bull Ground-granulated blast urnace slag up to 50 o the total cementitious materials content
bull Aggregates with low modulus o elasticity low coefficient o thermal expansion and high thermal
conductivity
bull Largest size aggregate that can be properly placed
bull Water-reducing and high-range water-reducing admixtures
bull Air-void system with a spacing actor no greater than 020 mm (0008 in) speci1047297c surace area
greater than 236 mm2
mm3
(600 in2
in3
) o air-void volume and number o air voids per inch otraverse signi1047297cantly greater than the numerical value o the percentage o air
bull Water-cementitious materials ratio in the range o 040minus045
bull Concrete compressive strength in the range o 28minus41 MPa (4000minus6000 psi)
bull Concrete permeability per AASHO Speci1047297cation 277 in the range o 1500minus2500 coulombs
1533 Reinforcement
bull Epoxy-coated reinorcement in both layers o deck reinorcement
bull Minimum practical transverse bar size and spacing
1534 Construction Practices
bull Use moderate concrete temperatures at time o placement
bull Use windbreaks and ogging equipment when necessary to minimize surace evaporation rom
resh concrete
bull Provide minimum 1047297nishing operations
bull Apply wet curing immediately afer 1047297nishing any portion o the concrete surace and wet cure or
at least seven days
bull Apply a curing compound afer the wet curing period to slow down the shrinkage and enhance
the concrete properties
bull Use a latex-modi1047297ed or dense concrete overlay
bull Implement a warrant requirement or bridge deck perormance
bull Gradually develop perormance-based speci1047297cations
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 516
577Concrete Decks
154 Design Considerations
1541 General Requirements
bull Maintain a minimum structural depth o concrete deck o 70 in and a minimum concrete cover
o 25 in (64 mm) f cprime ge40 ksi
bull Use prestressing or depth o slabs less than 120 o the design span
bull Place the primary reinorcement in the direction o the skew or the skew angle o the deck less
than 25deg Otherwise place them perpendicular to the main supporting girders
bull Provide shear connectors between concrete decks and supporting beams
bull Provide edge beams at the lines o discontinuity For the deck supported in the transverse direc-
tion and composed with concrete barriers no additional edge beam is needed
1542 Design Limit States
Concrete decks must be designed or Strength I limit state (AASHO 2012) and are usually designed
as tension-controlled reinorced concrete components Strength II limit state o the permit vehicle
axle load does not typically control deck design Concrete decks are also required to meet the require-
ments or Service I limit state to control excessive deormation and cracking Te deck overhang shall
be designed to meet the requirements or Extreme Event II Concrete decks supported by multi-girder
systems are not required to be investigated or the atigue limit state
1543 Analysis Methods
15431 Approximate Method of Analysis
Approximate method o analysis is traditional ly used to design concrete bridge decks (AASHO 4621)
Te method assumes a concrete deck as transverse slab strips o 1047298exure members supported by the lon-
gitudinal girders Te AASHO speci1047297cations (AASHO 2012) require the maximum positive moment
and the maximum negative moment to apply or all positive moment regions and all negative moment
regions in the deck slab respectively Te width o an equivalent interior strip o a concrete deck is
provided in able 151 (AASHO 2012) For deck overhangs the AASHO Article 36134 may apply
For typical concrete deck supported on different girder arrangements with at least three girders and
the distance between the centerlines o the exterior girders not less than 140 f the maximum live load
moments including multiple presence actors and dynamic load allowance based on the equivalent strip
method are provided in AASHO A-4 (AASHO 2012) and are summarized in able 152
15432 Empirical Method of Analysis
Empirical method o analysis (AASHO 972) is a method o concrete deck slab design based on the
concept o internal arching action within concrete slabs In this method effective length o slab shal l be
taken as (1) or slabs monolithic with supporting members the ace-to-ace distance and (2) or slabs
supported on steel or concrete girders distance between the webs o girders Empirical design may beused only i the ollowing conditions are met
bull Cross-rames o diaphragms are used throughout the girders
bull Spacing o intermediate diaphragms between box beams does not exceed 25 f
bull Te deck is composed with supporting steel or concrete girders
bull Te deck is ully cast-in-place and water cured f cprimege 40 ksi
bull Deck o uniorm depth ge70 in except or hunched at girder 1047298anges and the distance between
extreme layers o reinorcement ge40 in
bull Effective length le135 f 60 le effective lengthdesign depth le180
bull Overhangslab depth ge50 or overhangslab depth ge30 with slab composites with continuous
concrete barrier
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 616
578 Bridge Engineering Handbook Second Edition Superstructure Design
15433 Re1047297ned Methods of Analysis
Re1047297ned methods o analysis or concrete deck speci1047297ed in AASHO 4632 (AASHO 2012) usually
consider 1047298exural and torsional deormation without considering vertical shear deormation Tey are
more suitable or a more complex deck slab structure or example the end zones o skewed girder decks
TABLE 152 Maximum Live Load Moment per Foot Width
Girder
Spacing
S (f)
Positive
Moment
M LL+IM
(kip-ff)
Negative M LL+IM (kip-ff)
Distance rom Centerline o Girder to Design Section or Negative Moment (in)
00 30 60 90 120 180 240
40 468 268 207 174 160 150 134 125
45 463 300 258 210 190 165 132 118
50 465 374 320 266 224 183 126 112
55 471 436 373 311 258 207 130 099
60 483 499 419 350 288 231 139 107
65 500 531 457 384 315 253 150 120
70 521 598 517 436 356 284 163 151
75 544 626 543 461 378 315 188 17280 569 648 565 481 398 343 249 216
85 599 666 582 498 414 361 296 258
90 629 681 597 513 428 371 331 300
95 659 715 631 546 466 404 368 339
100 689 785 699 613 526 441 409 377
105 715 852 764 677 589 502 448 415
110 746 914 826 738 650 562 486 452
115 774 972 884 796 707 719 552 487
120 801 1028 940 851 763 674 556 521
125 828 1081 993 904 816 728 597 554
130 854 1131 1043 955 867 779 638 586
135 878 1179 1091 1003 916 828 679 616
140 902 1224 1137 1050 963 867 718 645
145 925 1267 1181 1094 1008 921 757 672
150 947 1309 1223 1137 1051 965 794 702
TABLE 151 Equivalent Strips o Concrete Decks
ype o Concrete Deck Direction o Primary Strip
Relative to raffic Width o Primary Strip (in)
Cast-in-place Overhang 450 + 100 X
Cast-in-place Either parallel or
perpendicular
+ M 260 + 66 X
Cast-in-place with stay-in-place
concrete ormwork
Precast post-tensioned minus M 480 + 30S
S = spacing o supporting components (f)
X = distance rom load to point o support (f)
+ M = positive moment
minus M = negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 716
579Concrete Decks
155 Design Example
1551 Bridge Deck Data
A typical section o a steel-concrete composite plate girder bridge is shown in Figure 156
Concrete f c 4000 psiprime= (276 MPa) Ec = 3625 ksi (250 MPa)
Steel Reinorcement A706 Grade 60
f E y s( ) ( )= =60 ksi 414 MPa 29000 ksi 200000 MPa
n E
Es
c
= = 8
Loads Concrete Barrier weight wbarrier = 0410 kl
3 in Future wearing surace wws = 0140 kc (AASHO able 351-1)Reinorced Concrete unit weight wrc = 0150 kc (AASHO C351)
AASHO HL-93 + dynamic load allowance
1552 Design Requirements
Perorm the ollowing design calculations or concrete deck in accordance with the AASHTO LRFD
Bridge Design Speci1047297cations 2012 Edition
bull Select concrete deck thick ness and cover
bull Calcu late Unactored Dead Load Moments
bull Calcu late Unactored Live Load MomentsmdashEquivalent Strip Method
bull Calcu late Factored MomentsmdashStrength Limit State I
bull Design or Positive Flexure
bull Design or Negative Flexure
bull Check Service Limit State
bull Determine the Slab Reinorcement Detailing Requirements
58ndash0
Concretebarriertype 732(Typ)
2
4 12=48ndash0
structureCL
FIGURE 156 ypical section o composite plate girder bridge
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 816
580 Bridge Engineering Handbook Second Edition Superstructure Design
1553 Solution
15531 Select Concrete Deck Thickness and Cover
ry dec2k slab thickness t = 9125 in gt Minimum deck thickness = 70 in
DepthSpan= 9125 (144)= 0064 gt 1 20 = 005 No prestressing needed
Use deck top cover C top = 20 in
Use deck bottom cover C bot = 10 in
15532 Calculate Unfactored Dead Load Moments
Dead load or one oot length o concrete deck is calculated as ollows
Deck concrete weightmdashW DC1mdashdeck concrete weightmdash
W t wrc109125
12
(10) (015) 0114 kiptDC1 ( )( )= =
=
Barrier weight W DC2 (concentrate load applied at 7 in rom the edge o deck)
W w( ) ( )( )= = =10 10 041 041 kipDC2 barrier
Future wearing surace o 3 inmdashW DW
W wthickness o wearing surace 10
3
1210 014 0035 kiptDC2 ws( )( ) ( )( )= =
=
Te dead load moments or the deck slab can be calculated using a continuous beam as shown in
Figure 157able 153 lists unactored dead load moments Only the results or Spans 1 and 2 are shown in the
table since the bridge deck is symmetrical the centerline o the bridge
15533 Calculate Unfactored Live Load Moments
From able 152 unactored live load moments including multiple presence actors and dynamic load
allowance are obtained as ollows
For girder spacing S = 12 f maximum positive live load moments are as
M 801 kip-ttLL IM =+
For negative 1047298exure the design sections are located the ace o the support or monolithic concrete
construction 14 the 1047298ange width rom the centerline o the support or steel girder bridges and 13 the
1047298ange width not exceeding 15 in rom the centerline o the support or precast I-girders or open-boxgirders (AASHO 2012 Article 46216)
85
W DC2 W DC2
W DC1W DW
5ndash0 12ndash0Span 1
12ndash0Span 2
12ndash0Span 3
12ndash0Span 4
5ndash0
17
FIGURE 157 Concrete deck under unactored dead loads
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 916
581Concrete Decks
For this example assume steel girder 1047298ange width = 18 in the design section is at frac14(18)= 45 in rom
the centerline o steel girder as shown in Figure 158 Te negative moment can be obtained conservatively
as the moment at the centerline o the support or interpolated between moments at 3 in and 6 in
M 851
3 15
3940 851 896 kip-ttLL IM ( )minus = +
minusminus =+
1554 Calculate Factored MomentsmdashStrength Limit State IFor Strength Limit State I load combination actored moment ollows
( ) ( )= η γ + + γ + γ +DC DC1 DC2 DW DW LL LL IM M M M M M u
η= η η η ge 095D R I
For this example use η = 095 γ =125DC γ = 150DW and γ = 175LL
( )( )= + + + +095 [125 15 175 ]DC1 DC2 DW LL IM M M M M M u
TABLE 153 Unactored Dead Load Moments
Distancerom lef
support X
(f)
Location
XS
Deck Load DC1 M DC1 (kip-ff)
Barrier Load DC2 M DC2 (kip-ff)
Future Wearing Surace DW M DW (kip-ff)
Span 1 Span 2 Span 1 Span 2 Span 1 Span 2
00 00 minus1425 minus1352 minus1760 0496 minus0225 minus0475
12 01 minus0679 minus0616 minus1534 0422 minus0023 minus0240
24 02 minus0097 minus0044 minus1309 0348 0128 minus0055
36 03 0321 0365 minus1083 0273 0229 0079
48 04 0574 0608 minus0858 0199 0280 0163
60 05 0664 0688 minus0632 0125 0280 0196
72 06 0589 0604 minus0406 0051 0230 0179
84 07 0350 0355 minus0181 minus0023 0129 0112
96 08 minus0053 minus0058 0045 minus0097 minus0022 minus0006
108 09 minus0621 minus0635 0270 minus0171 minus0223 minus0174
120 10 minus1352 minus1376 0496 minus0245 minus0475 minus0393
Design
sectionC webL
bf = 18
14bf = 45
FIGURE 158 Design section or negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1016
582 Bridge Engineering Handbook Second Edition Superstructure Design
15541 Maximum Positive Factored Moments
From able 153 it is seen that the maximum unactored positive moments due to the concrete deckslab barrier and uture wearing surace is located in Span 2 at a distance o 05 S Te maximum live
load positive moment equals 801 kip-ff Tereore the maximum positive actored moment is
M u 095 (125)(0688 0125) (15)(0196) (175)(801) 14561kip-tt[ ]= + + + =
15542 Maximum Negative Factored Moments
From able 153 it is seen that the maximum unactored negative moments due to the concrete deck
slab barrier and uture wearing surace is located Span 1 at the centerline o exterior girder and can be
obtained conservatively as the moment at the centerline o the exterior support or interpolated between
00S and 01S as ollows
M 0679 12 45
12(1425 0679) 1145 kip-ttDC1 = minus minus minus minus = minus
M 1534
12 45
121760 1534 1675 kip-ttDC2 ( )= minus minus
minusminus = minus
M 0023
12 45
12(0225 0023) 0149 kip-ttDW = minus +
minusminus = minus
Te maximum actored negative moment is as
M u 095 (125)( 1145 1675) (15)( 0149) (175)( 896) 18457 kip-tt[ ]= minus minus + minus + minus = minus
1555 Design for Positive Flexure Design
ry 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashbottom covermdashhal bar diameter
( ) ( )= minus minus = minus minus =
bar diameter
29125 10
0625
27813 inbotd t C e
ry 58 in which is less than the maximum spacing 15t = 18 in = = As
12(031)
80465 in2
For a rectangular section with a width o b = 12 in and depth o t = 9125 inConcrete compression block depth
a
A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0465 60
085 40 120684 in
Distance rom the extreme compression 1047297ber to the neutral axis
=
β = =c
a 0684
0850801 in
1
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 316
575Concrete Decks
1522 Precast Concrete Deck
Tere are two types o precast concrete decks ull-depth precast panels and stay-in-place (SIP) precast
prestressed panels combined with CIP topping
Figure 154 shows u ll-depth precast concrete deck panels under construction Te u ll-depth precast
panels have the advantages o signi1047297cant reduction o shrinkage effects and ast construction speed
and have been used or deck replacement with high traffic volumes NCHRP Report 407 (ardos and
Baishya 1998) proposed a ull-depth panel system with panels pretensioned in the transverse direction
and posttensioned in the longitudinal direction NCHRP Report 584 (Badie and ardos 2008) devel-
oped two ull-depth precast concrete bridge deck panel systems a transversely pretensioned system and
a transversely conventionally reinorced system and proposed guidelines or the design abrication and
construction o ull-depth precast concrete bridge deck panel systems without the use o posttensioning
or overlays and (2) connection details or new deck panel systems
Figure 155 shows a partial depth precast panel or SIP precast prestressed panes combined with
CIP topping Te SIP panels act as orms or the topping concrete and also as part o the structuraldepth o the deck Tis system can signi1047297cantly reduce construction time since 1047297eld orming is only
needed or the exterior girder overhangs It is cost-competitive with CIP decks or new structures and
deck replacement However the SIP panel system suffers re1047298ective cracking over the panel-to-panel
joints A modi1047297ed SIP precast panel system has been developed in NCHRP Report 407 (ardos and
Baishya 1998)
FIGURE 154 Full-depth precast concrete deck panels under construction (Courtesy o FHWA)
Cast-in-place concrete
Stay -in-place precast panel
FIGURE 155 ypical stay-in-place precast panel with cast-in-place concrete deck
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 416
576 Bridge Engineering Handbook Second Edition Superstructure Design
153 Materials
1531 General Requirements
Material characteristics in a bridge deck shall behave to reduce concrete distress and reinorcement
corrosion and lead to a long service lie with minimum maintenance Expected concrete deck should
behave with the ollowing characteristics (Russell 2004)
bull Low chloride permeability
bull A top surace that does not deteriorate rom reeze thaw or abrasion damage
bull Cracking that is limited to 1047297ne 1047298exural cracks associated with the structural behavior
bull Smooth rideability with adequate skid resistance
NCHRP Synthesis 333 (Russell 2004) recommended that use o the ollowing materials and practices
enhances the perormance o concrete bridge decks
1532 Concrete
bull ypes I II and IP cements
bull Fly ash up to 35 o the total cementitious materials content
bull Silica ume up to 8 o the total cementitious materials content
bull Ground-granulated blast urnace slag up to 50 o the total cementitious materials content
bull Aggregates with low modulus o elasticity low coefficient o thermal expansion and high thermal
conductivity
bull Largest size aggregate that can be properly placed
bull Water-reducing and high-range water-reducing admixtures
bull Air-void system with a spacing actor no greater than 020 mm (0008 in) speci1047297c surace area
greater than 236 mm2
mm3
(600 in2
in3
) o air-void volume and number o air voids per inch otraverse signi1047297cantly greater than the numerical value o the percentage o air
bull Water-cementitious materials ratio in the range o 040minus045
bull Concrete compressive strength in the range o 28minus41 MPa (4000minus6000 psi)
bull Concrete permeability per AASHO Speci1047297cation 277 in the range o 1500minus2500 coulombs
1533 Reinforcement
bull Epoxy-coated reinorcement in both layers o deck reinorcement
bull Minimum practical transverse bar size and spacing
1534 Construction Practices
bull Use moderate concrete temperatures at time o placement
bull Use windbreaks and ogging equipment when necessary to minimize surace evaporation rom
resh concrete
bull Provide minimum 1047297nishing operations
bull Apply wet curing immediately afer 1047297nishing any portion o the concrete surace and wet cure or
at least seven days
bull Apply a curing compound afer the wet curing period to slow down the shrinkage and enhance
the concrete properties
bull Use a latex-modi1047297ed or dense concrete overlay
bull Implement a warrant requirement or bridge deck perormance
bull Gradually develop perormance-based speci1047297cations
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 516
577Concrete Decks
154 Design Considerations
1541 General Requirements
bull Maintain a minimum structural depth o concrete deck o 70 in and a minimum concrete cover
o 25 in (64 mm) f cprime ge40 ksi
bull Use prestressing or depth o slabs less than 120 o the design span
bull Place the primary reinorcement in the direction o the skew or the skew angle o the deck less
than 25deg Otherwise place them perpendicular to the main supporting girders
bull Provide shear connectors between concrete decks and supporting beams
bull Provide edge beams at the lines o discontinuity For the deck supported in the transverse direc-
tion and composed with concrete barriers no additional edge beam is needed
1542 Design Limit States
Concrete decks must be designed or Strength I limit state (AASHO 2012) and are usually designed
as tension-controlled reinorced concrete components Strength II limit state o the permit vehicle
axle load does not typically control deck design Concrete decks are also required to meet the require-
ments or Service I limit state to control excessive deormation and cracking Te deck overhang shall
be designed to meet the requirements or Extreme Event II Concrete decks supported by multi-girder
systems are not required to be investigated or the atigue limit state
1543 Analysis Methods
15431 Approximate Method of Analysis
Approximate method o analysis is traditional ly used to design concrete bridge decks (AASHO 4621)
Te method assumes a concrete deck as transverse slab strips o 1047298exure members supported by the lon-
gitudinal girders Te AASHO speci1047297cations (AASHO 2012) require the maximum positive moment
and the maximum negative moment to apply or all positive moment regions and all negative moment
regions in the deck slab respectively Te width o an equivalent interior strip o a concrete deck is
provided in able 151 (AASHO 2012) For deck overhangs the AASHO Article 36134 may apply
For typical concrete deck supported on different girder arrangements with at least three girders and
the distance between the centerlines o the exterior girders not less than 140 f the maximum live load
moments including multiple presence actors and dynamic load allowance based on the equivalent strip
method are provided in AASHO A-4 (AASHO 2012) and are summarized in able 152
15432 Empirical Method of Analysis
Empirical method o analysis (AASHO 972) is a method o concrete deck slab design based on the
concept o internal arching action within concrete slabs In this method effective length o slab shal l be
taken as (1) or slabs monolithic with supporting members the ace-to-ace distance and (2) or slabs
supported on steel or concrete girders distance between the webs o girders Empirical design may beused only i the ollowing conditions are met
bull Cross-rames o diaphragms are used throughout the girders
bull Spacing o intermediate diaphragms between box beams does not exceed 25 f
bull Te deck is composed with supporting steel or concrete girders
bull Te deck is ully cast-in-place and water cured f cprimege 40 ksi
bull Deck o uniorm depth ge70 in except or hunched at girder 1047298anges and the distance between
extreme layers o reinorcement ge40 in
bull Effective length le135 f 60 le effective lengthdesign depth le180
bull Overhangslab depth ge50 or overhangslab depth ge30 with slab composites with continuous
concrete barrier
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 616
578 Bridge Engineering Handbook Second Edition Superstructure Design
15433 Re1047297ned Methods of Analysis
Re1047297ned methods o analysis or concrete deck speci1047297ed in AASHO 4632 (AASHO 2012) usually
consider 1047298exural and torsional deormation without considering vertical shear deormation Tey are
more suitable or a more complex deck slab structure or example the end zones o skewed girder decks
TABLE 152 Maximum Live Load Moment per Foot Width
Girder
Spacing
S (f)
Positive
Moment
M LL+IM
(kip-ff)
Negative M LL+IM (kip-ff)
Distance rom Centerline o Girder to Design Section or Negative Moment (in)
00 30 60 90 120 180 240
40 468 268 207 174 160 150 134 125
45 463 300 258 210 190 165 132 118
50 465 374 320 266 224 183 126 112
55 471 436 373 311 258 207 130 099
60 483 499 419 350 288 231 139 107
65 500 531 457 384 315 253 150 120
70 521 598 517 436 356 284 163 151
75 544 626 543 461 378 315 188 17280 569 648 565 481 398 343 249 216
85 599 666 582 498 414 361 296 258
90 629 681 597 513 428 371 331 300
95 659 715 631 546 466 404 368 339
100 689 785 699 613 526 441 409 377
105 715 852 764 677 589 502 448 415
110 746 914 826 738 650 562 486 452
115 774 972 884 796 707 719 552 487
120 801 1028 940 851 763 674 556 521
125 828 1081 993 904 816 728 597 554
130 854 1131 1043 955 867 779 638 586
135 878 1179 1091 1003 916 828 679 616
140 902 1224 1137 1050 963 867 718 645
145 925 1267 1181 1094 1008 921 757 672
150 947 1309 1223 1137 1051 965 794 702
TABLE 151 Equivalent Strips o Concrete Decks
ype o Concrete Deck Direction o Primary Strip
Relative to raffic Width o Primary Strip (in)
Cast-in-place Overhang 450 + 100 X
Cast-in-place Either parallel or
perpendicular
+ M 260 + 66 X
Cast-in-place with stay-in-place
concrete ormwork
Precast post-tensioned minus M 480 + 30S
S = spacing o supporting components (f)
X = distance rom load to point o support (f)
+ M = positive moment
minus M = negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 716
579Concrete Decks
155 Design Example
1551 Bridge Deck Data
A typical section o a steel-concrete composite plate girder bridge is shown in Figure 156
Concrete f c 4000 psiprime= (276 MPa) Ec = 3625 ksi (250 MPa)
Steel Reinorcement A706 Grade 60
f E y s( ) ( )= =60 ksi 414 MPa 29000 ksi 200000 MPa
n E
Es
c
= = 8
Loads Concrete Barrier weight wbarrier = 0410 kl
3 in Future wearing surace wws = 0140 kc (AASHO able 351-1)Reinorced Concrete unit weight wrc = 0150 kc (AASHO C351)
AASHO HL-93 + dynamic load allowance
1552 Design Requirements
Perorm the ollowing design calculations or concrete deck in accordance with the AASHTO LRFD
Bridge Design Speci1047297cations 2012 Edition
bull Select concrete deck thick ness and cover
bull Calcu late Unactored Dead Load Moments
bull Calcu late Unactored Live Load MomentsmdashEquivalent Strip Method
bull Calcu late Factored MomentsmdashStrength Limit State I
bull Design or Positive Flexure
bull Design or Negative Flexure
bull Check Service Limit State
bull Determine the Slab Reinorcement Detailing Requirements
58ndash0
Concretebarriertype 732(Typ)
2
4 12=48ndash0
structureCL
FIGURE 156 ypical section o composite plate girder bridge
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 816
580 Bridge Engineering Handbook Second Edition Superstructure Design
1553 Solution
15531 Select Concrete Deck Thickness and Cover
ry dec2k slab thickness t = 9125 in gt Minimum deck thickness = 70 in
DepthSpan= 9125 (144)= 0064 gt 1 20 = 005 No prestressing needed
Use deck top cover C top = 20 in
Use deck bottom cover C bot = 10 in
15532 Calculate Unfactored Dead Load Moments
Dead load or one oot length o concrete deck is calculated as ollows
Deck concrete weightmdashW DC1mdashdeck concrete weightmdash
W t wrc109125
12
(10) (015) 0114 kiptDC1 ( )( )= =
=
Barrier weight W DC2 (concentrate load applied at 7 in rom the edge o deck)
W w( ) ( )( )= = =10 10 041 041 kipDC2 barrier
Future wearing surace o 3 inmdashW DW
W wthickness o wearing surace 10
3
1210 014 0035 kiptDC2 ws( )( ) ( )( )= =
=
Te dead load moments or the deck slab can be calculated using a continuous beam as shown in
Figure 157able 153 lists unactored dead load moments Only the results or Spans 1 and 2 are shown in the
table since the bridge deck is symmetrical the centerline o the bridge
15533 Calculate Unfactored Live Load Moments
From able 152 unactored live load moments including multiple presence actors and dynamic load
allowance are obtained as ollows
For girder spacing S = 12 f maximum positive live load moments are as
M 801 kip-ttLL IM =+
For negative 1047298exure the design sections are located the ace o the support or monolithic concrete
construction 14 the 1047298ange width rom the centerline o the support or steel girder bridges and 13 the
1047298ange width not exceeding 15 in rom the centerline o the support or precast I-girders or open-boxgirders (AASHO 2012 Article 46216)
85
W DC2 W DC2
W DC1W DW
5ndash0 12ndash0Span 1
12ndash0Span 2
12ndash0Span 3
12ndash0Span 4
5ndash0
17
FIGURE 157 Concrete deck under unactored dead loads
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 916
581Concrete Decks
For this example assume steel girder 1047298ange width = 18 in the design section is at frac14(18)= 45 in rom
the centerline o steel girder as shown in Figure 158 Te negative moment can be obtained conservatively
as the moment at the centerline o the support or interpolated between moments at 3 in and 6 in
M 851
3 15
3940 851 896 kip-ttLL IM ( )minus = +
minusminus =+
1554 Calculate Factored MomentsmdashStrength Limit State IFor Strength Limit State I load combination actored moment ollows
( ) ( )= η γ + + γ + γ +DC DC1 DC2 DW DW LL LL IM M M M M M u
η= η η η ge 095D R I
For this example use η = 095 γ =125DC γ = 150DW and γ = 175LL
( )( )= + + + +095 [125 15 175 ]DC1 DC2 DW LL IM M M M M M u
TABLE 153 Unactored Dead Load Moments
Distancerom lef
support X
(f)
Location
XS
Deck Load DC1 M DC1 (kip-ff)
Barrier Load DC2 M DC2 (kip-ff)
Future Wearing Surace DW M DW (kip-ff)
Span 1 Span 2 Span 1 Span 2 Span 1 Span 2
00 00 minus1425 minus1352 minus1760 0496 minus0225 minus0475
12 01 minus0679 minus0616 minus1534 0422 minus0023 minus0240
24 02 minus0097 minus0044 minus1309 0348 0128 minus0055
36 03 0321 0365 minus1083 0273 0229 0079
48 04 0574 0608 minus0858 0199 0280 0163
60 05 0664 0688 minus0632 0125 0280 0196
72 06 0589 0604 minus0406 0051 0230 0179
84 07 0350 0355 minus0181 minus0023 0129 0112
96 08 minus0053 minus0058 0045 minus0097 minus0022 minus0006
108 09 minus0621 minus0635 0270 minus0171 minus0223 minus0174
120 10 minus1352 minus1376 0496 minus0245 minus0475 minus0393
Design
sectionC webL
bf = 18
14bf = 45
FIGURE 158 Design section or negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1016
582 Bridge Engineering Handbook Second Edition Superstructure Design
15541 Maximum Positive Factored Moments
From able 153 it is seen that the maximum unactored positive moments due to the concrete deckslab barrier and uture wearing surace is located in Span 2 at a distance o 05 S Te maximum live
load positive moment equals 801 kip-ff Tereore the maximum positive actored moment is
M u 095 (125)(0688 0125) (15)(0196) (175)(801) 14561kip-tt[ ]= + + + =
15542 Maximum Negative Factored Moments
From able 153 it is seen that the maximum unactored negative moments due to the concrete deck
slab barrier and uture wearing surace is located Span 1 at the centerline o exterior girder and can be
obtained conservatively as the moment at the centerline o the exterior support or interpolated between
00S and 01S as ollows
M 0679 12 45
12(1425 0679) 1145 kip-ttDC1 = minus minus minus minus = minus
M 1534
12 45
121760 1534 1675 kip-ttDC2 ( )= minus minus
minusminus = minus
M 0023
12 45
12(0225 0023) 0149 kip-ttDW = minus +
minusminus = minus
Te maximum actored negative moment is as
M u 095 (125)( 1145 1675) (15)( 0149) (175)( 896) 18457 kip-tt[ ]= minus minus + minus + minus = minus
1555 Design for Positive Flexure Design
ry 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashbottom covermdashhal bar diameter
( ) ( )= minus minus = minus minus =
bar diameter
29125 10
0625
27813 inbotd t C e
ry 58 in which is less than the maximum spacing 15t = 18 in = = As
12(031)
80465 in2
For a rectangular section with a width o b = 12 in and depth o t = 9125 inConcrete compression block depth
a
A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0465 60
085 40 120684 in
Distance rom the extreme compression 1047297ber to the neutral axis
=
β = =c
a 0684
0850801 in
1
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 416
576 Bridge Engineering Handbook Second Edition Superstructure Design
153 Materials
1531 General Requirements
Material characteristics in a bridge deck shall behave to reduce concrete distress and reinorcement
corrosion and lead to a long service lie with minimum maintenance Expected concrete deck should
behave with the ollowing characteristics (Russell 2004)
bull Low chloride permeability
bull A top surace that does not deteriorate rom reeze thaw or abrasion damage
bull Cracking that is limited to 1047297ne 1047298exural cracks associated with the structural behavior
bull Smooth rideability with adequate skid resistance
NCHRP Synthesis 333 (Russell 2004) recommended that use o the ollowing materials and practices
enhances the perormance o concrete bridge decks
1532 Concrete
bull ypes I II and IP cements
bull Fly ash up to 35 o the total cementitious materials content
bull Silica ume up to 8 o the total cementitious materials content
bull Ground-granulated blast urnace slag up to 50 o the total cementitious materials content
bull Aggregates with low modulus o elasticity low coefficient o thermal expansion and high thermal
conductivity
bull Largest size aggregate that can be properly placed
bull Water-reducing and high-range water-reducing admixtures
bull Air-void system with a spacing actor no greater than 020 mm (0008 in) speci1047297c surace area
greater than 236 mm2
mm3
(600 in2
in3
) o air-void volume and number o air voids per inch otraverse signi1047297cantly greater than the numerical value o the percentage o air
bull Water-cementitious materials ratio in the range o 040minus045
bull Concrete compressive strength in the range o 28minus41 MPa (4000minus6000 psi)
bull Concrete permeability per AASHO Speci1047297cation 277 in the range o 1500minus2500 coulombs
1533 Reinforcement
bull Epoxy-coated reinorcement in both layers o deck reinorcement
bull Minimum practical transverse bar size and spacing
1534 Construction Practices
bull Use moderate concrete temperatures at time o placement
bull Use windbreaks and ogging equipment when necessary to minimize surace evaporation rom
resh concrete
bull Provide minimum 1047297nishing operations
bull Apply wet curing immediately afer 1047297nishing any portion o the concrete surace and wet cure or
at least seven days
bull Apply a curing compound afer the wet curing period to slow down the shrinkage and enhance
the concrete properties
bull Use a latex-modi1047297ed or dense concrete overlay
bull Implement a warrant requirement or bridge deck perormance
bull Gradually develop perormance-based speci1047297cations
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 516
577Concrete Decks
154 Design Considerations
1541 General Requirements
bull Maintain a minimum structural depth o concrete deck o 70 in and a minimum concrete cover
o 25 in (64 mm) f cprime ge40 ksi
bull Use prestressing or depth o slabs less than 120 o the design span
bull Place the primary reinorcement in the direction o the skew or the skew angle o the deck less
than 25deg Otherwise place them perpendicular to the main supporting girders
bull Provide shear connectors between concrete decks and supporting beams
bull Provide edge beams at the lines o discontinuity For the deck supported in the transverse direc-
tion and composed with concrete barriers no additional edge beam is needed
1542 Design Limit States
Concrete decks must be designed or Strength I limit state (AASHO 2012) and are usually designed
as tension-controlled reinorced concrete components Strength II limit state o the permit vehicle
axle load does not typically control deck design Concrete decks are also required to meet the require-
ments or Service I limit state to control excessive deormation and cracking Te deck overhang shall
be designed to meet the requirements or Extreme Event II Concrete decks supported by multi-girder
systems are not required to be investigated or the atigue limit state
1543 Analysis Methods
15431 Approximate Method of Analysis
Approximate method o analysis is traditional ly used to design concrete bridge decks (AASHO 4621)
Te method assumes a concrete deck as transverse slab strips o 1047298exure members supported by the lon-
gitudinal girders Te AASHO speci1047297cations (AASHO 2012) require the maximum positive moment
and the maximum negative moment to apply or all positive moment regions and all negative moment
regions in the deck slab respectively Te width o an equivalent interior strip o a concrete deck is
provided in able 151 (AASHO 2012) For deck overhangs the AASHO Article 36134 may apply
For typical concrete deck supported on different girder arrangements with at least three girders and
the distance between the centerlines o the exterior girders not less than 140 f the maximum live load
moments including multiple presence actors and dynamic load allowance based on the equivalent strip
method are provided in AASHO A-4 (AASHO 2012) and are summarized in able 152
15432 Empirical Method of Analysis
Empirical method o analysis (AASHO 972) is a method o concrete deck slab design based on the
concept o internal arching action within concrete slabs In this method effective length o slab shal l be
taken as (1) or slabs monolithic with supporting members the ace-to-ace distance and (2) or slabs
supported on steel or concrete girders distance between the webs o girders Empirical design may beused only i the ollowing conditions are met
bull Cross-rames o diaphragms are used throughout the girders
bull Spacing o intermediate diaphragms between box beams does not exceed 25 f
bull Te deck is composed with supporting steel or concrete girders
bull Te deck is ully cast-in-place and water cured f cprimege 40 ksi
bull Deck o uniorm depth ge70 in except or hunched at girder 1047298anges and the distance between
extreme layers o reinorcement ge40 in
bull Effective length le135 f 60 le effective lengthdesign depth le180
bull Overhangslab depth ge50 or overhangslab depth ge30 with slab composites with continuous
concrete barrier
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 616
578 Bridge Engineering Handbook Second Edition Superstructure Design
15433 Re1047297ned Methods of Analysis
Re1047297ned methods o analysis or concrete deck speci1047297ed in AASHO 4632 (AASHO 2012) usually
consider 1047298exural and torsional deormation without considering vertical shear deormation Tey are
more suitable or a more complex deck slab structure or example the end zones o skewed girder decks
TABLE 152 Maximum Live Load Moment per Foot Width
Girder
Spacing
S (f)
Positive
Moment
M LL+IM
(kip-ff)
Negative M LL+IM (kip-ff)
Distance rom Centerline o Girder to Design Section or Negative Moment (in)
00 30 60 90 120 180 240
40 468 268 207 174 160 150 134 125
45 463 300 258 210 190 165 132 118
50 465 374 320 266 224 183 126 112
55 471 436 373 311 258 207 130 099
60 483 499 419 350 288 231 139 107
65 500 531 457 384 315 253 150 120
70 521 598 517 436 356 284 163 151
75 544 626 543 461 378 315 188 17280 569 648 565 481 398 343 249 216
85 599 666 582 498 414 361 296 258
90 629 681 597 513 428 371 331 300
95 659 715 631 546 466 404 368 339
100 689 785 699 613 526 441 409 377
105 715 852 764 677 589 502 448 415
110 746 914 826 738 650 562 486 452
115 774 972 884 796 707 719 552 487
120 801 1028 940 851 763 674 556 521
125 828 1081 993 904 816 728 597 554
130 854 1131 1043 955 867 779 638 586
135 878 1179 1091 1003 916 828 679 616
140 902 1224 1137 1050 963 867 718 645
145 925 1267 1181 1094 1008 921 757 672
150 947 1309 1223 1137 1051 965 794 702
TABLE 151 Equivalent Strips o Concrete Decks
ype o Concrete Deck Direction o Primary Strip
Relative to raffic Width o Primary Strip (in)
Cast-in-place Overhang 450 + 100 X
Cast-in-place Either parallel or
perpendicular
+ M 260 + 66 X
Cast-in-place with stay-in-place
concrete ormwork
Precast post-tensioned minus M 480 + 30S
S = spacing o supporting components (f)
X = distance rom load to point o support (f)
+ M = positive moment
minus M = negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 716
579Concrete Decks
155 Design Example
1551 Bridge Deck Data
A typical section o a steel-concrete composite plate girder bridge is shown in Figure 156
Concrete f c 4000 psiprime= (276 MPa) Ec = 3625 ksi (250 MPa)
Steel Reinorcement A706 Grade 60
f E y s( ) ( )= =60 ksi 414 MPa 29000 ksi 200000 MPa
n E
Es
c
= = 8
Loads Concrete Barrier weight wbarrier = 0410 kl
3 in Future wearing surace wws = 0140 kc (AASHO able 351-1)Reinorced Concrete unit weight wrc = 0150 kc (AASHO C351)
AASHO HL-93 + dynamic load allowance
1552 Design Requirements
Perorm the ollowing design calculations or concrete deck in accordance with the AASHTO LRFD
Bridge Design Speci1047297cations 2012 Edition
bull Select concrete deck thick ness and cover
bull Calcu late Unactored Dead Load Moments
bull Calcu late Unactored Live Load MomentsmdashEquivalent Strip Method
bull Calcu late Factored MomentsmdashStrength Limit State I
bull Design or Positive Flexure
bull Design or Negative Flexure
bull Check Service Limit State
bull Determine the Slab Reinorcement Detailing Requirements
58ndash0
Concretebarriertype 732(Typ)
2
4 12=48ndash0
structureCL
FIGURE 156 ypical section o composite plate girder bridge
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 816
580 Bridge Engineering Handbook Second Edition Superstructure Design
1553 Solution
15531 Select Concrete Deck Thickness and Cover
ry dec2k slab thickness t = 9125 in gt Minimum deck thickness = 70 in
DepthSpan= 9125 (144)= 0064 gt 1 20 = 005 No prestressing needed
Use deck top cover C top = 20 in
Use deck bottom cover C bot = 10 in
15532 Calculate Unfactored Dead Load Moments
Dead load or one oot length o concrete deck is calculated as ollows
Deck concrete weightmdashW DC1mdashdeck concrete weightmdash
W t wrc109125
12
(10) (015) 0114 kiptDC1 ( )( )= =
=
Barrier weight W DC2 (concentrate load applied at 7 in rom the edge o deck)
W w( ) ( )( )= = =10 10 041 041 kipDC2 barrier
Future wearing surace o 3 inmdashW DW
W wthickness o wearing surace 10
3
1210 014 0035 kiptDC2 ws( )( ) ( )( )= =
=
Te dead load moments or the deck slab can be calculated using a continuous beam as shown in
Figure 157able 153 lists unactored dead load moments Only the results or Spans 1 and 2 are shown in the
table since the bridge deck is symmetrical the centerline o the bridge
15533 Calculate Unfactored Live Load Moments
From able 152 unactored live load moments including multiple presence actors and dynamic load
allowance are obtained as ollows
For girder spacing S = 12 f maximum positive live load moments are as
M 801 kip-ttLL IM =+
For negative 1047298exure the design sections are located the ace o the support or monolithic concrete
construction 14 the 1047298ange width rom the centerline o the support or steel girder bridges and 13 the
1047298ange width not exceeding 15 in rom the centerline o the support or precast I-girders or open-boxgirders (AASHO 2012 Article 46216)
85
W DC2 W DC2
W DC1W DW
5ndash0 12ndash0Span 1
12ndash0Span 2
12ndash0Span 3
12ndash0Span 4
5ndash0
17
FIGURE 157 Concrete deck under unactored dead loads
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 916
581Concrete Decks
For this example assume steel girder 1047298ange width = 18 in the design section is at frac14(18)= 45 in rom
the centerline o steel girder as shown in Figure 158 Te negative moment can be obtained conservatively
as the moment at the centerline o the support or interpolated between moments at 3 in and 6 in
M 851
3 15
3940 851 896 kip-ttLL IM ( )minus = +
minusminus =+
1554 Calculate Factored MomentsmdashStrength Limit State IFor Strength Limit State I load combination actored moment ollows
( ) ( )= η γ + + γ + γ +DC DC1 DC2 DW DW LL LL IM M M M M M u
η= η η η ge 095D R I
For this example use η = 095 γ =125DC γ = 150DW and γ = 175LL
( )( )= + + + +095 [125 15 175 ]DC1 DC2 DW LL IM M M M M M u
TABLE 153 Unactored Dead Load Moments
Distancerom lef
support X
(f)
Location
XS
Deck Load DC1 M DC1 (kip-ff)
Barrier Load DC2 M DC2 (kip-ff)
Future Wearing Surace DW M DW (kip-ff)
Span 1 Span 2 Span 1 Span 2 Span 1 Span 2
00 00 minus1425 minus1352 minus1760 0496 minus0225 minus0475
12 01 minus0679 minus0616 minus1534 0422 minus0023 minus0240
24 02 minus0097 minus0044 minus1309 0348 0128 minus0055
36 03 0321 0365 minus1083 0273 0229 0079
48 04 0574 0608 minus0858 0199 0280 0163
60 05 0664 0688 minus0632 0125 0280 0196
72 06 0589 0604 minus0406 0051 0230 0179
84 07 0350 0355 minus0181 minus0023 0129 0112
96 08 minus0053 minus0058 0045 minus0097 minus0022 minus0006
108 09 minus0621 minus0635 0270 minus0171 minus0223 minus0174
120 10 minus1352 minus1376 0496 minus0245 minus0475 minus0393
Design
sectionC webL
bf = 18
14bf = 45
FIGURE 158 Design section or negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1016
582 Bridge Engineering Handbook Second Edition Superstructure Design
15541 Maximum Positive Factored Moments
From able 153 it is seen that the maximum unactored positive moments due to the concrete deckslab barrier and uture wearing surace is located in Span 2 at a distance o 05 S Te maximum live
load positive moment equals 801 kip-ff Tereore the maximum positive actored moment is
M u 095 (125)(0688 0125) (15)(0196) (175)(801) 14561kip-tt[ ]= + + + =
15542 Maximum Negative Factored Moments
From able 153 it is seen that the maximum unactored negative moments due to the concrete deck
slab barrier and uture wearing surace is located Span 1 at the centerline o exterior girder and can be
obtained conservatively as the moment at the centerline o the exterior support or interpolated between
00S and 01S as ollows
M 0679 12 45
12(1425 0679) 1145 kip-ttDC1 = minus minus minus minus = minus
M 1534
12 45
121760 1534 1675 kip-ttDC2 ( )= minus minus
minusminus = minus
M 0023
12 45
12(0225 0023) 0149 kip-ttDW = minus +
minusminus = minus
Te maximum actored negative moment is as
M u 095 (125)( 1145 1675) (15)( 0149) (175)( 896) 18457 kip-tt[ ]= minus minus + minus + minus = minus
1555 Design for Positive Flexure Design
ry 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashbottom covermdashhal bar diameter
( ) ( )= minus minus = minus minus =
bar diameter
29125 10
0625
27813 inbotd t C e
ry 58 in which is less than the maximum spacing 15t = 18 in = = As
12(031)
80465 in2
For a rectangular section with a width o b = 12 in and depth o t = 9125 inConcrete compression block depth
a
A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0465 60
085 40 120684 in
Distance rom the extreme compression 1047297ber to the neutral axis
=
β = =c
a 0684
0850801 in
1
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 516
577Concrete Decks
154 Design Considerations
1541 General Requirements
bull Maintain a minimum structural depth o concrete deck o 70 in and a minimum concrete cover
o 25 in (64 mm) f cprime ge40 ksi
bull Use prestressing or depth o slabs less than 120 o the design span
bull Place the primary reinorcement in the direction o the skew or the skew angle o the deck less
than 25deg Otherwise place them perpendicular to the main supporting girders
bull Provide shear connectors between concrete decks and supporting beams
bull Provide edge beams at the lines o discontinuity For the deck supported in the transverse direc-
tion and composed with concrete barriers no additional edge beam is needed
1542 Design Limit States
Concrete decks must be designed or Strength I limit state (AASHO 2012) and are usually designed
as tension-controlled reinorced concrete components Strength II limit state o the permit vehicle
axle load does not typically control deck design Concrete decks are also required to meet the require-
ments or Service I limit state to control excessive deormation and cracking Te deck overhang shall
be designed to meet the requirements or Extreme Event II Concrete decks supported by multi-girder
systems are not required to be investigated or the atigue limit state
1543 Analysis Methods
15431 Approximate Method of Analysis
Approximate method o analysis is traditional ly used to design concrete bridge decks (AASHO 4621)
Te method assumes a concrete deck as transverse slab strips o 1047298exure members supported by the lon-
gitudinal girders Te AASHO speci1047297cations (AASHO 2012) require the maximum positive moment
and the maximum negative moment to apply or all positive moment regions and all negative moment
regions in the deck slab respectively Te width o an equivalent interior strip o a concrete deck is
provided in able 151 (AASHO 2012) For deck overhangs the AASHO Article 36134 may apply
For typical concrete deck supported on different girder arrangements with at least three girders and
the distance between the centerlines o the exterior girders not less than 140 f the maximum live load
moments including multiple presence actors and dynamic load allowance based on the equivalent strip
method are provided in AASHO A-4 (AASHO 2012) and are summarized in able 152
15432 Empirical Method of Analysis
Empirical method o analysis (AASHO 972) is a method o concrete deck slab design based on the
concept o internal arching action within concrete slabs In this method effective length o slab shal l be
taken as (1) or slabs monolithic with supporting members the ace-to-ace distance and (2) or slabs
supported on steel or concrete girders distance between the webs o girders Empirical design may beused only i the ollowing conditions are met
bull Cross-rames o diaphragms are used throughout the girders
bull Spacing o intermediate diaphragms between box beams does not exceed 25 f
bull Te deck is composed with supporting steel or concrete girders
bull Te deck is ully cast-in-place and water cured f cprimege 40 ksi
bull Deck o uniorm depth ge70 in except or hunched at girder 1047298anges and the distance between
extreme layers o reinorcement ge40 in
bull Effective length le135 f 60 le effective lengthdesign depth le180
bull Overhangslab depth ge50 or overhangslab depth ge30 with slab composites with continuous
concrete barrier
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 616
578 Bridge Engineering Handbook Second Edition Superstructure Design
15433 Re1047297ned Methods of Analysis
Re1047297ned methods o analysis or concrete deck speci1047297ed in AASHO 4632 (AASHO 2012) usually
consider 1047298exural and torsional deormation without considering vertical shear deormation Tey are
more suitable or a more complex deck slab structure or example the end zones o skewed girder decks
TABLE 152 Maximum Live Load Moment per Foot Width
Girder
Spacing
S (f)
Positive
Moment
M LL+IM
(kip-ff)
Negative M LL+IM (kip-ff)
Distance rom Centerline o Girder to Design Section or Negative Moment (in)
00 30 60 90 120 180 240
40 468 268 207 174 160 150 134 125
45 463 300 258 210 190 165 132 118
50 465 374 320 266 224 183 126 112
55 471 436 373 311 258 207 130 099
60 483 499 419 350 288 231 139 107
65 500 531 457 384 315 253 150 120
70 521 598 517 436 356 284 163 151
75 544 626 543 461 378 315 188 17280 569 648 565 481 398 343 249 216
85 599 666 582 498 414 361 296 258
90 629 681 597 513 428 371 331 300
95 659 715 631 546 466 404 368 339
100 689 785 699 613 526 441 409 377
105 715 852 764 677 589 502 448 415
110 746 914 826 738 650 562 486 452
115 774 972 884 796 707 719 552 487
120 801 1028 940 851 763 674 556 521
125 828 1081 993 904 816 728 597 554
130 854 1131 1043 955 867 779 638 586
135 878 1179 1091 1003 916 828 679 616
140 902 1224 1137 1050 963 867 718 645
145 925 1267 1181 1094 1008 921 757 672
150 947 1309 1223 1137 1051 965 794 702
TABLE 151 Equivalent Strips o Concrete Decks
ype o Concrete Deck Direction o Primary Strip
Relative to raffic Width o Primary Strip (in)
Cast-in-place Overhang 450 + 100 X
Cast-in-place Either parallel or
perpendicular
+ M 260 + 66 X
Cast-in-place with stay-in-place
concrete ormwork
Precast post-tensioned minus M 480 + 30S
S = spacing o supporting components (f)
X = distance rom load to point o support (f)
+ M = positive moment
minus M = negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 716
579Concrete Decks
155 Design Example
1551 Bridge Deck Data
A typical section o a steel-concrete composite plate girder bridge is shown in Figure 156
Concrete f c 4000 psiprime= (276 MPa) Ec = 3625 ksi (250 MPa)
Steel Reinorcement A706 Grade 60
f E y s( ) ( )= =60 ksi 414 MPa 29000 ksi 200000 MPa
n E
Es
c
= = 8
Loads Concrete Barrier weight wbarrier = 0410 kl
3 in Future wearing surace wws = 0140 kc (AASHO able 351-1)Reinorced Concrete unit weight wrc = 0150 kc (AASHO C351)
AASHO HL-93 + dynamic load allowance
1552 Design Requirements
Perorm the ollowing design calculations or concrete deck in accordance with the AASHTO LRFD
Bridge Design Speci1047297cations 2012 Edition
bull Select concrete deck thick ness and cover
bull Calcu late Unactored Dead Load Moments
bull Calcu late Unactored Live Load MomentsmdashEquivalent Strip Method
bull Calcu late Factored MomentsmdashStrength Limit State I
bull Design or Positive Flexure
bull Design or Negative Flexure
bull Check Service Limit State
bull Determine the Slab Reinorcement Detailing Requirements
58ndash0
Concretebarriertype 732(Typ)
2
4 12=48ndash0
structureCL
FIGURE 156 ypical section o composite plate girder bridge
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 816
580 Bridge Engineering Handbook Second Edition Superstructure Design
1553 Solution
15531 Select Concrete Deck Thickness and Cover
ry dec2k slab thickness t = 9125 in gt Minimum deck thickness = 70 in
DepthSpan= 9125 (144)= 0064 gt 1 20 = 005 No prestressing needed
Use deck top cover C top = 20 in
Use deck bottom cover C bot = 10 in
15532 Calculate Unfactored Dead Load Moments
Dead load or one oot length o concrete deck is calculated as ollows
Deck concrete weightmdashW DC1mdashdeck concrete weightmdash
W t wrc109125
12
(10) (015) 0114 kiptDC1 ( )( )= =
=
Barrier weight W DC2 (concentrate load applied at 7 in rom the edge o deck)
W w( ) ( )( )= = =10 10 041 041 kipDC2 barrier
Future wearing surace o 3 inmdashW DW
W wthickness o wearing surace 10
3
1210 014 0035 kiptDC2 ws( )( ) ( )( )= =
=
Te dead load moments or the deck slab can be calculated using a continuous beam as shown in
Figure 157able 153 lists unactored dead load moments Only the results or Spans 1 and 2 are shown in the
table since the bridge deck is symmetrical the centerline o the bridge
15533 Calculate Unfactored Live Load Moments
From able 152 unactored live load moments including multiple presence actors and dynamic load
allowance are obtained as ollows
For girder spacing S = 12 f maximum positive live load moments are as
M 801 kip-ttLL IM =+
For negative 1047298exure the design sections are located the ace o the support or monolithic concrete
construction 14 the 1047298ange width rom the centerline o the support or steel girder bridges and 13 the
1047298ange width not exceeding 15 in rom the centerline o the support or precast I-girders or open-boxgirders (AASHO 2012 Article 46216)
85
W DC2 W DC2
W DC1W DW
5ndash0 12ndash0Span 1
12ndash0Span 2
12ndash0Span 3
12ndash0Span 4
5ndash0
17
FIGURE 157 Concrete deck under unactored dead loads
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 916
581Concrete Decks
For this example assume steel girder 1047298ange width = 18 in the design section is at frac14(18)= 45 in rom
the centerline o steel girder as shown in Figure 158 Te negative moment can be obtained conservatively
as the moment at the centerline o the support or interpolated between moments at 3 in and 6 in
M 851
3 15
3940 851 896 kip-ttLL IM ( )minus = +
minusminus =+
1554 Calculate Factored MomentsmdashStrength Limit State IFor Strength Limit State I load combination actored moment ollows
( ) ( )= η γ + + γ + γ +DC DC1 DC2 DW DW LL LL IM M M M M M u
η= η η η ge 095D R I
For this example use η = 095 γ =125DC γ = 150DW and γ = 175LL
( )( )= + + + +095 [125 15 175 ]DC1 DC2 DW LL IM M M M M M u
TABLE 153 Unactored Dead Load Moments
Distancerom lef
support X
(f)
Location
XS
Deck Load DC1 M DC1 (kip-ff)
Barrier Load DC2 M DC2 (kip-ff)
Future Wearing Surace DW M DW (kip-ff)
Span 1 Span 2 Span 1 Span 2 Span 1 Span 2
00 00 minus1425 minus1352 minus1760 0496 minus0225 minus0475
12 01 minus0679 minus0616 minus1534 0422 minus0023 minus0240
24 02 minus0097 minus0044 minus1309 0348 0128 minus0055
36 03 0321 0365 minus1083 0273 0229 0079
48 04 0574 0608 minus0858 0199 0280 0163
60 05 0664 0688 minus0632 0125 0280 0196
72 06 0589 0604 minus0406 0051 0230 0179
84 07 0350 0355 minus0181 minus0023 0129 0112
96 08 minus0053 minus0058 0045 minus0097 minus0022 minus0006
108 09 minus0621 minus0635 0270 minus0171 minus0223 minus0174
120 10 minus1352 minus1376 0496 minus0245 minus0475 minus0393
Design
sectionC webL
bf = 18
14bf = 45
FIGURE 158 Design section or negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1016
582 Bridge Engineering Handbook Second Edition Superstructure Design
15541 Maximum Positive Factored Moments
From able 153 it is seen that the maximum unactored positive moments due to the concrete deckslab barrier and uture wearing surace is located in Span 2 at a distance o 05 S Te maximum live
load positive moment equals 801 kip-ff Tereore the maximum positive actored moment is
M u 095 (125)(0688 0125) (15)(0196) (175)(801) 14561kip-tt[ ]= + + + =
15542 Maximum Negative Factored Moments
From able 153 it is seen that the maximum unactored negative moments due to the concrete deck
slab barrier and uture wearing surace is located Span 1 at the centerline o exterior girder and can be
obtained conservatively as the moment at the centerline o the exterior support or interpolated between
00S and 01S as ollows
M 0679 12 45
12(1425 0679) 1145 kip-ttDC1 = minus minus minus minus = minus
M 1534
12 45
121760 1534 1675 kip-ttDC2 ( )= minus minus
minusminus = minus
M 0023
12 45
12(0225 0023) 0149 kip-ttDW = minus +
minusminus = minus
Te maximum actored negative moment is as
M u 095 (125)( 1145 1675) (15)( 0149) (175)( 896) 18457 kip-tt[ ]= minus minus + minus + minus = minus
1555 Design for Positive Flexure Design
ry 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashbottom covermdashhal bar diameter
( ) ( )= minus minus = minus minus =
bar diameter
29125 10
0625
27813 inbotd t C e
ry 58 in which is less than the maximum spacing 15t = 18 in = = As
12(031)
80465 in2
For a rectangular section with a width o b = 12 in and depth o t = 9125 inConcrete compression block depth
a
A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0465 60
085 40 120684 in
Distance rom the extreme compression 1047297ber to the neutral axis
=
β = =c
a 0684
0850801 in
1
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 616
578 Bridge Engineering Handbook Second Edition Superstructure Design
15433 Re1047297ned Methods of Analysis
Re1047297ned methods o analysis or concrete deck speci1047297ed in AASHO 4632 (AASHO 2012) usually
consider 1047298exural and torsional deormation without considering vertical shear deormation Tey are
more suitable or a more complex deck slab structure or example the end zones o skewed girder decks
TABLE 152 Maximum Live Load Moment per Foot Width
Girder
Spacing
S (f)
Positive
Moment
M LL+IM
(kip-ff)
Negative M LL+IM (kip-ff)
Distance rom Centerline o Girder to Design Section or Negative Moment (in)
00 30 60 90 120 180 240
40 468 268 207 174 160 150 134 125
45 463 300 258 210 190 165 132 118
50 465 374 320 266 224 183 126 112
55 471 436 373 311 258 207 130 099
60 483 499 419 350 288 231 139 107
65 500 531 457 384 315 253 150 120
70 521 598 517 436 356 284 163 151
75 544 626 543 461 378 315 188 17280 569 648 565 481 398 343 249 216
85 599 666 582 498 414 361 296 258
90 629 681 597 513 428 371 331 300
95 659 715 631 546 466 404 368 339
100 689 785 699 613 526 441 409 377
105 715 852 764 677 589 502 448 415
110 746 914 826 738 650 562 486 452
115 774 972 884 796 707 719 552 487
120 801 1028 940 851 763 674 556 521
125 828 1081 993 904 816 728 597 554
130 854 1131 1043 955 867 779 638 586
135 878 1179 1091 1003 916 828 679 616
140 902 1224 1137 1050 963 867 718 645
145 925 1267 1181 1094 1008 921 757 672
150 947 1309 1223 1137 1051 965 794 702
TABLE 151 Equivalent Strips o Concrete Decks
ype o Concrete Deck Direction o Primary Strip
Relative to raffic Width o Primary Strip (in)
Cast-in-place Overhang 450 + 100 X
Cast-in-place Either parallel or
perpendicular
+ M 260 + 66 X
Cast-in-place with stay-in-place
concrete ormwork
Precast post-tensioned minus M 480 + 30S
S = spacing o supporting components (f)
X = distance rom load to point o support (f)
+ M = positive moment
minus M = negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 716
579Concrete Decks
155 Design Example
1551 Bridge Deck Data
A typical section o a steel-concrete composite plate girder bridge is shown in Figure 156
Concrete f c 4000 psiprime= (276 MPa) Ec = 3625 ksi (250 MPa)
Steel Reinorcement A706 Grade 60
f E y s( ) ( )= =60 ksi 414 MPa 29000 ksi 200000 MPa
n E
Es
c
= = 8
Loads Concrete Barrier weight wbarrier = 0410 kl
3 in Future wearing surace wws = 0140 kc (AASHO able 351-1)Reinorced Concrete unit weight wrc = 0150 kc (AASHO C351)
AASHO HL-93 + dynamic load allowance
1552 Design Requirements
Perorm the ollowing design calculations or concrete deck in accordance with the AASHTO LRFD
Bridge Design Speci1047297cations 2012 Edition
bull Select concrete deck thick ness and cover
bull Calcu late Unactored Dead Load Moments
bull Calcu late Unactored Live Load MomentsmdashEquivalent Strip Method
bull Calcu late Factored MomentsmdashStrength Limit State I
bull Design or Positive Flexure
bull Design or Negative Flexure
bull Check Service Limit State
bull Determine the Slab Reinorcement Detailing Requirements
58ndash0
Concretebarriertype 732(Typ)
2
4 12=48ndash0
structureCL
FIGURE 156 ypical section o composite plate girder bridge
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 816
580 Bridge Engineering Handbook Second Edition Superstructure Design
1553 Solution
15531 Select Concrete Deck Thickness and Cover
ry dec2k slab thickness t = 9125 in gt Minimum deck thickness = 70 in
DepthSpan= 9125 (144)= 0064 gt 1 20 = 005 No prestressing needed
Use deck top cover C top = 20 in
Use deck bottom cover C bot = 10 in
15532 Calculate Unfactored Dead Load Moments
Dead load or one oot length o concrete deck is calculated as ollows
Deck concrete weightmdashW DC1mdashdeck concrete weightmdash
W t wrc109125
12
(10) (015) 0114 kiptDC1 ( )( )= =
=
Barrier weight W DC2 (concentrate load applied at 7 in rom the edge o deck)
W w( ) ( )( )= = =10 10 041 041 kipDC2 barrier
Future wearing surace o 3 inmdashW DW
W wthickness o wearing surace 10
3
1210 014 0035 kiptDC2 ws( )( ) ( )( )= =
=
Te dead load moments or the deck slab can be calculated using a continuous beam as shown in
Figure 157able 153 lists unactored dead load moments Only the results or Spans 1 and 2 are shown in the
table since the bridge deck is symmetrical the centerline o the bridge
15533 Calculate Unfactored Live Load Moments
From able 152 unactored live load moments including multiple presence actors and dynamic load
allowance are obtained as ollows
For girder spacing S = 12 f maximum positive live load moments are as
M 801 kip-ttLL IM =+
For negative 1047298exure the design sections are located the ace o the support or monolithic concrete
construction 14 the 1047298ange width rom the centerline o the support or steel girder bridges and 13 the
1047298ange width not exceeding 15 in rom the centerline o the support or precast I-girders or open-boxgirders (AASHO 2012 Article 46216)
85
W DC2 W DC2
W DC1W DW
5ndash0 12ndash0Span 1
12ndash0Span 2
12ndash0Span 3
12ndash0Span 4
5ndash0
17
FIGURE 157 Concrete deck under unactored dead loads
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 916
581Concrete Decks
For this example assume steel girder 1047298ange width = 18 in the design section is at frac14(18)= 45 in rom
the centerline o steel girder as shown in Figure 158 Te negative moment can be obtained conservatively
as the moment at the centerline o the support or interpolated between moments at 3 in and 6 in
M 851
3 15
3940 851 896 kip-ttLL IM ( )minus = +
minusminus =+
1554 Calculate Factored MomentsmdashStrength Limit State IFor Strength Limit State I load combination actored moment ollows
( ) ( )= η γ + + γ + γ +DC DC1 DC2 DW DW LL LL IM M M M M M u
η= η η η ge 095D R I
For this example use η = 095 γ =125DC γ = 150DW and γ = 175LL
( )( )= + + + +095 [125 15 175 ]DC1 DC2 DW LL IM M M M M M u
TABLE 153 Unactored Dead Load Moments
Distancerom lef
support X
(f)
Location
XS
Deck Load DC1 M DC1 (kip-ff)
Barrier Load DC2 M DC2 (kip-ff)
Future Wearing Surace DW M DW (kip-ff)
Span 1 Span 2 Span 1 Span 2 Span 1 Span 2
00 00 minus1425 minus1352 minus1760 0496 minus0225 minus0475
12 01 minus0679 minus0616 minus1534 0422 minus0023 minus0240
24 02 minus0097 minus0044 minus1309 0348 0128 minus0055
36 03 0321 0365 minus1083 0273 0229 0079
48 04 0574 0608 minus0858 0199 0280 0163
60 05 0664 0688 minus0632 0125 0280 0196
72 06 0589 0604 minus0406 0051 0230 0179
84 07 0350 0355 minus0181 minus0023 0129 0112
96 08 minus0053 minus0058 0045 minus0097 minus0022 minus0006
108 09 minus0621 minus0635 0270 minus0171 minus0223 minus0174
120 10 minus1352 minus1376 0496 minus0245 minus0475 minus0393
Design
sectionC webL
bf = 18
14bf = 45
FIGURE 158 Design section or negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1016
582 Bridge Engineering Handbook Second Edition Superstructure Design
15541 Maximum Positive Factored Moments
From able 153 it is seen that the maximum unactored positive moments due to the concrete deckslab barrier and uture wearing surace is located in Span 2 at a distance o 05 S Te maximum live
load positive moment equals 801 kip-ff Tereore the maximum positive actored moment is
M u 095 (125)(0688 0125) (15)(0196) (175)(801) 14561kip-tt[ ]= + + + =
15542 Maximum Negative Factored Moments
From able 153 it is seen that the maximum unactored negative moments due to the concrete deck
slab barrier and uture wearing surace is located Span 1 at the centerline o exterior girder and can be
obtained conservatively as the moment at the centerline o the exterior support or interpolated between
00S and 01S as ollows
M 0679 12 45
12(1425 0679) 1145 kip-ttDC1 = minus minus minus minus = minus
M 1534
12 45
121760 1534 1675 kip-ttDC2 ( )= minus minus
minusminus = minus
M 0023
12 45
12(0225 0023) 0149 kip-ttDW = minus +
minusminus = minus
Te maximum actored negative moment is as
M u 095 (125)( 1145 1675) (15)( 0149) (175)( 896) 18457 kip-tt[ ]= minus minus + minus + minus = minus
1555 Design for Positive Flexure Design
ry 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashbottom covermdashhal bar diameter
( ) ( )= minus minus = minus minus =
bar diameter
29125 10
0625
27813 inbotd t C e
ry 58 in which is less than the maximum spacing 15t = 18 in = = As
12(031)
80465 in2
For a rectangular section with a width o b = 12 in and depth o t = 9125 inConcrete compression block depth
a
A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0465 60
085 40 120684 in
Distance rom the extreme compression 1047297ber to the neutral axis
=
β = =c
a 0684
0850801 in
1
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 716
579Concrete Decks
155 Design Example
1551 Bridge Deck Data
A typical section o a steel-concrete composite plate girder bridge is shown in Figure 156
Concrete f c 4000 psiprime= (276 MPa) Ec = 3625 ksi (250 MPa)
Steel Reinorcement A706 Grade 60
f E y s( ) ( )= =60 ksi 414 MPa 29000 ksi 200000 MPa
n E
Es
c
= = 8
Loads Concrete Barrier weight wbarrier = 0410 kl
3 in Future wearing surace wws = 0140 kc (AASHO able 351-1)Reinorced Concrete unit weight wrc = 0150 kc (AASHO C351)
AASHO HL-93 + dynamic load allowance
1552 Design Requirements
Perorm the ollowing design calculations or concrete deck in accordance with the AASHTO LRFD
Bridge Design Speci1047297cations 2012 Edition
bull Select concrete deck thick ness and cover
bull Calcu late Unactored Dead Load Moments
bull Calcu late Unactored Live Load MomentsmdashEquivalent Strip Method
bull Calcu late Factored MomentsmdashStrength Limit State I
bull Design or Positive Flexure
bull Design or Negative Flexure
bull Check Service Limit State
bull Determine the Slab Reinorcement Detailing Requirements
58ndash0
Concretebarriertype 732(Typ)
2
4 12=48ndash0
structureCL
FIGURE 156 ypical section o composite plate girder bridge
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 816
580 Bridge Engineering Handbook Second Edition Superstructure Design
1553 Solution
15531 Select Concrete Deck Thickness and Cover
ry dec2k slab thickness t = 9125 in gt Minimum deck thickness = 70 in
DepthSpan= 9125 (144)= 0064 gt 1 20 = 005 No prestressing needed
Use deck top cover C top = 20 in
Use deck bottom cover C bot = 10 in
15532 Calculate Unfactored Dead Load Moments
Dead load or one oot length o concrete deck is calculated as ollows
Deck concrete weightmdashW DC1mdashdeck concrete weightmdash
W t wrc109125
12
(10) (015) 0114 kiptDC1 ( )( )= =
=
Barrier weight W DC2 (concentrate load applied at 7 in rom the edge o deck)
W w( ) ( )( )= = =10 10 041 041 kipDC2 barrier
Future wearing surace o 3 inmdashW DW
W wthickness o wearing surace 10
3
1210 014 0035 kiptDC2 ws( )( ) ( )( )= =
=
Te dead load moments or the deck slab can be calculated using a continuous beam as shown in
Figure 157able 153 lists unactored dead load moments Only the results or Spans 1 and 2 are shown in the
table since the bridge deck is symmetrical the centerline o the bridge
15533 Calculate Unfactored Live Load Moments
From able 152 unactored live load moments including multiple presence actors and dynamic load
allowance are obtained as ollows
For girder spacing S = 12 f maximum positive live load moments are as
M 801 kip-ttLL IM =+
For negative 1047298exure the design sections are located the ace o the support or monolithic concrete
construction 14 the 1047298ange width rom the centerline o the support or steel girder bridges and 13 the
1047298ange width not exceeding 15 in rom the centerline o the support or precast I-girders or open-boxgirders (AASHO 2012 Article 46216)
85
W DC2 W DC2
W DC1W DW
5ndash0 12ndash0Span 1
12ndash0Span 2
12ndash0Span 3
12ndash0Span 4
5ndash0
17
FIGURE 157 Concrete deck under unactored dead loads
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 916
581Concrete Decks
For this example assume steel girder 1047298ange width = 18 in the design section is at frac14(18)= 45 in rom
the centerline o steel girder as shown in Figure 158 Te negative moment can be obtained conservatively
as the moment at the centerline o the support or interpolated between moments at 3 in and 6 in
M 851
3 15
3940 851 896 kip-ttLL IM ( )minus = +
minusminus =+
1554 Calculate Factored MomentsmdashStrength Limit State IFor Strength Limit State I load combination actored moment ollows
( ) ( )= η γ + + γ + γ +DC DC1 DC2 DW DW LL LL IM M M M M M u
η= η η η ge 095D R I
For this example use η = 095 γ =125DC γ = 150DW and γ = 175LL
( )( )= + + + +095 [125 15 175 ]DC1 DC2 DW LL IM M M M M M u
TABLE 153 Unactored Dead Load Moments
Distancerom lef
support X
(f)
Location
XS
Deck Load DC1 M DC1 (kip-ff)
Barrier Load DC2 M DC2 (kip-ff)
Future Wearing Surace DW M DW (kip-ff)
Span 1 Span 2 Span 1 Span 2 Span 1 Span 2
00 00 minus1425 minus1352 minus1760 0496 minus0225 minus0475
12 01 minus0679 minus0616 minus1534 0422 minus0023 minus0240
24 02 minus0097 minus0044 minus1309 0348 0128 minus0055
36 03 0321 0365 minus1083 0273 0229 0079
48 04 0574 0608 minus0858 0199 0280 0163
60 05 0664 0688 minus0632 0125 0280 0196
72 06 0589 0604 minus0406 0051 0230 0179
84 07 0350 0355 minus0181 minus0023 0129 0112
96 08 minus0053 minus0058 0045 minus0097 minus0022 minus0006
108 09 minus0621 minus0635 0270 minus0171 minus0223 minus0174
120 10 minus1352 minus1376 0496 minus0245 minus0475 minus0393
Design
sectionC webL
bf = 18
14bf = 45
FIGURE 158 Design section or negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1016
582 Bridge Engineering Handbook Second Edition Superstructure Design
15541 Maximum Positive Factored Moments
From able 153 it is seen that the maximum unactored positive moments due to the concrete deckslab barrier and uture wearing surace is located in Span 2 at a distance o 05 S Te maximum live
load positive moment equals 801 kip-ff Tereore the maximum positive actored moment is
M u 095 (125)(0688 0125) (15)(0196) (175)(801) 14561kip-tt[ ]= + + + =
15542 Maximum Negative Factored Moments
From able 153 it is seen that the maximum unactored negative moments due to the concrete deck
slab barrier and uture wearing surace is located Span 1 at the centerline o exterior girder and can be
obtained conservatively as the moment at the centerline o the exterior support or interpolated between
00S and 01S as ollows
M 0679 12 45
12(1425 0679) 1145 kip-ttDC1 = minus minus minus minus = minus
M 1534
12 45
121760 1534 1675 kip-ttDC2 ( )= minus minus
minusminus = minus
M 0023
12 45
12(0225 0023) 0149 kip-ttDW = minus +
minusminus = minus
Te maximum actored negative moment is as
M u 095 (125)( 1145 1675) (15)( 0149) (175)( 896) 18457 kip-tt[ ]= minus minus + minus + minus = minus
1555 Design for Positive Flexure Design
ry 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashbottom covermdashhal bar diameter
( ) ( )= minus minus = minus minus =
bar diameter
29125 10
0625
27813 inbotd t C e
ry 58 in which is less than the maximum spacing 15t = 18 in = = As
12(031)
80465 in2
For a rectangular section with a width o b = 12 in and depth o t = 9125 inConcrete compression block depth
a
A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0465 60
085 40 120684 in
Distance rom the extreme compression 1047297ber to the neutral axis
=
β = =c
a 0684
0850801 in
1
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 816
580 Bridge Engineering Handbook Second Edition Superstructure Design
1553 Solution
15531 Select Concrete Deck Thickness and Cover
ry dec2k slab thickness t = 9125 in gt Minimum deck thickness = 70 in
DepthSpan= 9125 (144)= 0064 gt 1 20 = 005 No prestressing needed
Use deck top cover C top = 20 in
Use deck bottom cover C bot = 10 in
15532 Calculate Unfactored Dead Load Moments
Dead load or one oot length o concrete deck is calculated as ollows
Deck concrete weightmdashW DC1mdashdeck concrete weightmdash
W t wrc109125
12
(10) (015) 0114 kiptDC1 ( )( )= =
=
Barrier weight W DC2 (concentrate load applied at 7 in rom the edge o deck)
W w( ) ( )( )= = =10 10 041 041 kipDC2 barrier
Future wearing surace o 3 inmdashW DW
W wthickness o wearing surace 10
3
1210 014 0035 kiptDC2 ws( )( ) ( )( )= =
=
Te dead load moments or the deck slab can be calculated using a continuous beam as shown in
Figure 157able 153 lists unactored dead load moments Only the results or Spans 1 and 2 are shown in the
table since the bridge deck is symmetrical the centerline o the bridge
15533 Calculate Unfactored Live Load Moments
From able 152 unactored live load moments including multiple presence actors and dynamic load
allowance are obtained as ollows
For girder spacing S = 12 f maximum positive live load moments are as
M 801 kip-ttLL IM =+
For negative 1047298exure the design sections are located the ace o the support or monolithic concrete
construction 14 the 1047298ange width rom the centerline o the support or steel girder bridges and 13 the
1047298ange width not exceeding 15 in rom the centerline o the support or precast I-girders or open-boxgirders (AASHO 2012 Article 46216)
85
W DC2 W DC2
W DC1W DW
5ndash0 12ndash0Span 1
12ndash0Span 2
12ndash0Span 3
12ndash0Span 4
5ndash0
17
FIGURE 157 Concrete deck under unactored dead loads
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 916
581Concrete Decks
For this example assume steel girder 1047298ange width = 18 in the design section is at frac14(18)= 45 in rom
the centerline o steel girder as shown in Figure 158 Te negative moment can be obtained conservatively
as the moment at the centerline o the support or interpolated between moments at 3 in and 6 in
M 851
3 15
3940 851 896 kip-ttLL IM ( )minus = +
minusminus =+
1554 Calculate Factored MomentsmdashStrength Limit State IFor Strength Limit State I load combination actored moment ollows
( ) ( )= η γ + + γ + γ +DC DC1 DC2 DW DW LL LL IM M M M M M u
η= η η η ge 095D R I
For this example use η = 095 γ =125DC γ = 150DW and γ = 175LL
( )( )= + + + +095 [125 15 175 ]DC1 DC2 DW LL IM M M M M M u
TABLE 153 Unactored Dead Load Moments
Distancerom lef
support X
(f)
Location
XS
Deck Load DC1 M DC1 (kip-ff)
Barrier Load DC2 M DC2 (kip-ff)
Future Wearing Surace DW M DW (kip-ff)
Span 1 Span 2 Span 1 Span 2 Span 1 Span 2
00 00 minus1425 minus1352 minus1760 0496 minus0225 minus0475
12 01 minus0679 minus0616 minus1534 0422 minus0023 minus0240
24 02 minus0097 minus0044 minus1309 0348 0128 minus0055
36 03 0321 0365 minus1083 0273 0229 0079
48 04 0574 0608 minus0858 0199 0280 0163
60 05 0664 0688 minus0632 0125 0280 0196
72 06 0589 0604 minus0406 0051 0230 0179
84 07 0350 0355 minus0181 minus0023 0129 0112
96 08 minus0053 minus0058 0045 minus0097 minus0022 minus0006
108 09 minus0621 minus0635 0270 minus0171 minus0223 minus0174
120 10 minus1352 minus1376 0496 minus0245 minus0475 minus0393
Design
sectionC webL
bf = 18
14bf = 45
FIGURE 158 Design section or negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1016
582 Bridge Engineering Handbook Second Edition Superstructure Design
15541 Maximum Positive Factored Moments
From able 153 it is seen that the maximum unactored positive moments due to the concrete deckslab barrier and uture wearing surace is located in Span 2 at a distance o 05 S Te maximum live
load positive moment equals 801 kip-ff Tereore the maximum positive actored moment is
M u 095 (125)(0688 0125) (15)(0196) (175)(801) 14561kip-tt[ ]= + + + =
15542 Maximum Negative Factored Moments
From able 153 it is seen that the maximum unactored negative moments due to the concrete deck
slab barrier and uture wearing surace is located Span 1 at the centerline o exterior girder and can be
obtained conservatively as the moment at the centerline o the exterior support or interpolated between
00S and 01S as ollows
M 0679 12 45
12(1425 0679) 1145 kip-ttDC1 = minus minus minus minus = minus
M 1534
12 45
121760 1534 1675 kip-ttDC2 ( )= minus minus
minusminus = minus
M 0023
12 45
12(0225 0023) 0149 kip-ttDW = minus +
minusminus = minus
Te maximum actored negative moment is as
M u 095 (125)( 1145 1675) (15)( 0149) (175)( 896) 18457 kip-tt[ ]= minus minus + minus + minus = minus
1555 Design for Positive Flexure Design
ry 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashbottom covermdashhal bar diameter
( ) ( )= minus minus = minus minus =
bar diameter
29125 10
0625
27813 inbotd t C e
ry 58 in which is less than the maximum spacing 15t = 18 in = = As
12(031)
80465 in2
For a rectangular section with a width o b = 12 in and depth o t = 9125 inConcrete compression block depth
a
A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0465 60
085 40 120684 in
Distance rom the extreme compression 1047297ber to the neutral axis
=
β = =c
a 0684
0850801 in
1
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 916
581Concrete Decks
For this example assume steel girder 1047298ange width = 18 in the design section is at frac14(18)= 45 in rom
the centerline o steel girder as shown in Figure 158 Te negative moment can be obtained conservatively
as the moment at the centerline o the support or interpolated between moments at 3 in and 6 in
M 851
3 15
3940 851 896 kip-ttLL IM ( )minus = +
minusminus =+
1554 Calculate Factored MomentsmdashStrength Limit State IFor Strength Limit State I load combination actored moment ollows
( ) ( )= η γ + + γ + γ +DC DC1 DC2 DW DW LL LL IM M M M M M u
η= η η η ge 095D R I
For this example use η = 095 γ =125DC γ = 150DW and γ = 175LL
( )( )= + + + +095 [125 15 175 ]DC1 DC2 DW LL IM M M M M M u
TABLE 153 Unactored Dead Load Moments
Distancerom lef
support X
(f)
Location
XS
Deck Load DC1 M DC1 (kip-ff)
Barrier Load DC2 M DC2 (kip-ff)
Future Wearing Surace DW M DW (kip-ff)
Span 1 Span 2 Span 1 Span 2 Span 1 Span 2
00 00 minus1425 minus1352 minus1760 0496 minus0225 minus0475
12 01 minus0679 minus0616 minus1534 0422 minus0023 minus0240
24 02 minus0097 minus0044 minus1309 0348 0128 minus0055
36 03 0321 0365 minus1083 0273 0229 0079
48 04 0574 0608 minus0858 0199 0280 0163
60 05 0664 0688 minus0632 0125 0280 0196
72 06 0589 0604 minus0406 0051 0230 0179
84 07 0350 0355 minus0181 minus0023 0129 0112
96 08 minus0053 minus0058 0045 minus0097 minus0022 minus0006
108 09 minus0621 minus0635 0270 minus0171 minus0223 minus0174
120 10 minus1352 minus1376 0496 minus0245 minus0475 minus0393
Design
sectionC webL
bf = 18
14bf = 45
FIGURE 158 Design section or negative moment
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1016
582 Bridge Engineering Handbook Second Edition Superstructure Design
15541 Maximum Positive Factored Moments
From able 153 it is seen that the maximum unactored positive moments due to the concrete deckslab barrier and uture wearing surace is located in Span 2 at a distance o 05 S Te maximum live
load positive moment equals 801 kip-ff Tereore the maximum positive actored moment is
M u 095 (125)(0688 0125) (15)(0196) (175)(801) 14561kip-tt[ ]= + + + =
15542 Maximum Negative Factored Moments
From able 153 it is seen that the maximum unactored negative moments due to the concrete deck
slab barrier and uture wearing surace is located Span 1 at the centerline o exterior girder and can be
obtained conservatively as the moment at the centerline o the exterior support or interpolated between
00S and 01S as ollows
M 0679 12 45
12(1425 0679) 1145 kip-ttDC1 = minus minus minus minus = minus
M 1534
12 45
121760 1534 1675 kip-ttDC2 ( )= minus minus
minusminus = minus
M 0023
12 45
12(0225 0023) 0149 kip-ttDW = minus +
minusminus = minus
Te maximum actored negative moment is as
M u 095 (125)( 1145 1675) (15)( 0149) (175)( 896) 18457 kip-tt[ ]= minus minus + minus + minus = minus
1555 Design for Positive Flexure Design
ry 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashbottom covermdashhal bar diameter
( ) ( )= minus minus = minus minus =
bar diameter
29125 10
0625
27813 inbotd t C e
ry 58 in which is less than the maximum spacing 15t = 18 in = = As
12(031)
80465 in2
For a rectangular section with a width o b = 12 in and depth o t = 9125 inConcrete compression block depth
a
A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0465 60
085 40 120684 in
Distance rom the extreme compression 1047297ber to the neutral axis
=
β = =c
a 0684
0850801 in
1
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1016
582 Bridge Engineering Handbook Second Edition Superstructure Design
15541 Maximum Positive Factored Moments
From able 153 it is seen that the maximum unactored positive moments due to the concrete deckslab barrier and uture wearing surace is located in Span 2 at a distance o 05 S Te maximum live
load positive moment equals 801 kip-ff Tereore the maximum positive actored moment is
M u 095 (125)(0688 0125) (15)(0196) (175)(801) 14561kip-tt[ ]= + + + =
15542 Maximum Negative Factored Moments
From able 153 it is seen that the maximum unactored negative moments due to the concrete deck
slab barrier and uture wearing surace is located Span 1 at the centerline o exterior girder and can be
obtained conservatively as the moment at the centerline o the exterior support or interpolated between
00S and 01S as ollows
M 0679 12 45
12(1425 0679) 1145 kip-ttDC1 = minus minus minus minus = minus
M 1534
12 45
121760 1534 1675 kip-ttDC2 ( )= minus minus
minusminus = minus
M 0023
12 45
12(0225 0023) 0149 kip-ttDW = minus +
minusminus = minus
Te maximum actored negative moment is as
M u 095 (125)( 1145 1675) (15)( 0149) (175)( 896) 18457 kip-tt[ ]= minus minus + minus + minus = minus
1555 Design for Positive Flexure Design
ry 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashbottom covermdashhal bar diameter
( ) ( )= minus minus = minus minus =
bar diameter
29125 10
0625
27813 inbotd t C e
ry 58 in which is less than the maximum spacing 15t = 18 in = = As
12(031)
80465 in2
For a rectangular section with a width o b = 12 in and depth o t = 9125 inConcrete compression block depth
a
A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0465 60
085 40 120684 in
Distance rom the extreme compression 1047297ber to the neutral axis
=
β = =c
a 0684
0850801 in
1
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1116
583Concrete Decks
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)(7813 0801)
0801(0003) 0026 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0465 60 7813
0684
21876 kip-inin
1563 kip-tt 14561kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
1556 Design for Negative Flexurery 5 bar size bar area = 031 in2 and bar diameter= 0625 in
Te effective depth d e = total slab thicknessmdashtop covermdashhal bar diameter
d t C e
( ) ( )= minus minus = minus minus =
bar diameter
29125 20
0625
26813 intop
ry 55 in which is less than maximum spacing 15t = 18 in = =12(031)
50744 in2 As
For a rectangular section with a width o b = 12 in and depth o t = 9125 in
Concrete compression block depth
a A f
f b
s y
c
( )( )
( )( )( )=
prime = =
085
0744 60
085 40 121094 in
Distance rom the extreme compression 1047297ber to the neutral axis
=β
= =c a 1094
0851287
1
ensile strain o rebar is
ε =
minus=
minus= gt
d c
ct
e (0003)6813 1287
1287(0003) 0013 0005
Tereore the section is tension controlled resistance actor ϕ = 09
M M A f d a
M
r n s y e
u
209 0744 60 6813
1094
225174 kip-inin
2098 kip-tt 18457 kip-tt
( )( )( )= φ = φ minus
= minus
=
= gt =
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1216
584 Bridge Engineering Handbook Second Edition Superstructure Design
1557 Check Service Limit State-Cracking Control
Concrete cracking is controlled by the proper distribution o 1047298exure reinorcement at service limit state
AASHO (2012) requires steel reinorcement spacing s o the layer closet to the tension ace to satisy
the ollowing
s f
d e
s ssc ( )le
γ β
minus700
2 AASHO 5734-1
in which
( )β = +
minusd
h d s
c
c
107
where γ e is 075 or Class 2 exposure conditions d c is thickness o concrete cover measured rom extreme
tension 1047297ber to the center o the 1047298exural reinorcement f ss is tensile stress in steel reinorcement at ser-
vice limit state and h is overall thickness o the deck
15571 Service I Load Combination
( )= + + +10 10 10DC1 DC2 DW LL+IM M M M M M s
Maximum positive moment
M s 10 (10)(0688 0125) (10)(0196) (10)(801) 9019 kip-tt[ ]= + + + =
Maximum negative moment
M u 10 (10)( 1145 1675) (10)( 0149) (10)( 896) 11929 kip-tt[ ]( )= minus minus + minus + minus = minus
15572 Positive Flexure Cracking Control
= + = + =10bar diameter
210
0625
21313ind c
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangu-lar concrete section with b = 12 in d e = 7813 in = =n
E
Es
c
8 we have
+ minus =b
y nA y nA d s s e2
02
= minus + minus
y B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1316
585Concrete Decks
For bottom reinorcement designed or positive 1047298exure As = 0465 in2
= = = A b
2
12
26
= = =B nAs 8(0465) 372
( )= minus = minus times times = minusC nA d s e 8 0754 675 29064
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
372 372 4 6 29064
2 61912 in
2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
( )
( )( )( )( )( )= + minus = + minus =
3
12 1912
38 0465 7813 1912 157496 incr
32
32 4I
by nA d y s e
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )
= minus
= minus
=8 9019 12 7813 1912
213463244 ksi
cr
f nM d y
I ss
s e
( ) ( )β = +
minus = +
minus =
d
h d s
c
c
107
11313
0 07 (9125 1313)1240
( )=
γ β
minus = minus =s f
d e
s ss
c
7002
700 (075)
(1240)(3244)(2)(1313) 1043in
It is obvious that 5 8 in meets cracking control requirement
15573 Negative Flexure Cracking Control
= + = + =d c 25bar diameter
225
0625
22813in
Assume y is the distance o the neutral axis to extreme compression 1047297ber or the transormed rectangular
concrete section with b = 12 in d e = 6813 in = =n EE
s
c
8 we have
+ minus =b
y nA y nA d s s e2
02
=
minus + minus y
B B AC
A
4
2
2
in which = A b
2 =B nAs = minusC nA d s e
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1416
586 Bridge Engineering Handbook Second Edition Superstructure Design
For top reinorcement designed or negative 1047298exure As = 0744 in2
= = = A b
2
12
26
( )( )= = =B nAs 8 0744 5952
( )( )( )= minus = minus = minusC nA d s e 8 0744 6813 40551
( ) ( )( )( )
( ) ( )=
minus + minus=
minus + minus minus=
4
2
5952 5952 4 6 40551
2 62151in
2 2 2
y B B AC
A
Moment o inertia o cracked or the transormed section I cr is
I by
nA d y s e( ) ( )( )
( )( )( )= + minus = + minus =3
12 2151
38 0744 6813 2151 16917 incr
32
32 4
ensile stress f ss in the steel reinorcement at service limit state is
( ) ( )( )( )( )=
minus=
minus=
8 11929 12 6813 2151
1691731561ksi
cr
f nM d y
I ss
s e
( ) ( )( )
β = +minus
= +minus
=d
h d s
c
c
107
125
07 9125 28131637
( )= γ
β minus = minus =s
f d e
s ss
c700 2 700 (075)
(1637)(31561)(2)(2813) 454 in
ry 545 in or negative moment in the top reinorcement
Use 59 in (truss Bar) and 59 in (straight bar) or both top and bottom reinorcement in the
transverse direction as shown in Figure 159
Bottom bars 59
Top bars
Truss bars
59
59
Extra 5 bars(tot 2 per bay)
2ndash0 typ
12ndash0
4 cont 18
115 barsEqual spacing
9125 2 clear
1 clear
FIGURE 159 Bridge deck reinorcement detail
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1516
587Concrete Decks
1558 Determine the Slab Reinforcement Detailing Requirements
15581 Top of Slab Shrinkage and Temperature Reinforcement
Te top slab distribution reinorcement is or shrinkage and temperature changes near the surace o the
exposed concrete slab AASHO Article 5108 (AASHO 2012) requires the area o reinorcement in
each direction and each ace As shall meet the ollowing requirements
ge+
A bh
b h f s
y
13
2( )
le le As011 060
where b is the least width o component section h is least thickness o component section f y is speci1047297ed
yield strength o reinorcing bars less than 75 ksiry 418 in bar cross section area = 02 in2
As
12(02)
180133in t2= =
A
bh
b h f s
y
13
2( )
13(12)(9125)
2(12 9125)(60)0056in t2gt
+ =
+ =
As ge 011in t2
Using 418 in or longitudinal distribution reinorcement and 545 in or ransverse primary
reinorcement meets this requirement15582 Bottom of Slab Distribution Reinforcement
Te distribution reinorcement on the bottom o the slab is placed in the perpendicular direction to
the primary reinorcement or positive moment and calculated based on whether the primary rein-
orcement is parallel or perpendicular to traffic (AASHO 2012) For this example the primary rein-
orcement is perpendicular to traffic AASHO Article 9732 requires that bottom slab distribution
reinorcement ratio shall be larger than S lt220 67 where S is the effective span length taken as the
distance between the 1047298ange tips plus the 1047298ange overhang For steel girder S is taken as girder spacing
o 12 f conservatively
= = lt
220 220
12635 67
S
Bottom primary reinorcement 545 in As
12(031)
450827 in t2= =
Since bottom distribution reinorcement usually placed within the center hal o the deck span total
required distribution reinorcement area
A ( )= =0635 0827 (6) 315inrequired
2
ry 115 bar ( )( )= = gt =11 031 341 in 315 in2required
2 A As
Figure 159 shows the detailed deck reinorcement or the design example
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC
7212019 Concrete Decks
httpslidepdfcomreaderfullconcrete-decks 1616
588 Bridge Engineering Handbook Second Edition Superstructure Design
References
AASHO 2012 AASHTO LRFD Bridge Design Speci1047297cations Customary US Units 2012 American
Association o State Highway and ransportation Officials Washington DC
Badie S S and ardos M K 2008 Full-Depth Precast Concrete Bridge Deck Panel Systems NCHRP
Report 584 ransportation Research Board Washington DC
Barker R M and Puckett J A 2007 Design o Highway Bridges 2nd Edition John Wiley amp Sons Inc
New York NY
FHWA 2012 Concrete Deck Design Example Design Step 2 httpwwwwadotgovbridgelrdus_ds2
htmdesignstep21_0
Russell H G 2004 Concrete Bridge Deck Perormance NCHRP Synthesis 333 ransportation Research
Board Washington DC
ardos M K and Baishya M C 1998 Rapid Replacement o Bridge Decks NCHRP Report 407
ransportation Research Board Washington DC