lecture no.4b

8/3/2019 Lecture No.4B

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Introduction to

Bridge Engineering

Lecture 4 (II)

CONCRETE BRIDGES


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Presented By:

YASIR IRFAN BADRASHI&

QAISER HAYAT

Presented To: PROF. DR. AKHTAR NAEEM KHAN

&

CLASSMATES

CONCRETE BRIDGES


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Topics to be Presented:

Example Problem on:

(i). Concrete Deck Design(ii). Solid Slab Bridge Design

(iii). T-Beam Bridge Design

CONCRETE BRIDGES


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7.10.1

CONCRETE DECK DESIGN


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CONCRETE DECK DESIGN

Use the approximate method ofanalysis [4.6.2] to design the deckof the reinforced concrete T-Beambridge section of Fig.E-7.1-1 for aHL-93 live load and a PL-2performance level concrete barrier

(Fig.7.45).The T-Beams supporting the deckare 2440 mm on the centers andhave a stem width of 350 mm. Thedeck overhangs the exterior T-Beam approximately 0.4 of the

distance between T-Beams. Allowfor sacrificial wear of 15mm ofconcrete surface and for a futurewearing surface of 75mm thickbituminous overlay. Use fc=30MPa, fy=400Mpa, and compare theselected reinforcement with that

obtained by the empirical method[A9.7.2]

Problem Statement:


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The minimum thickness for concrete deck slabs is 175 mm [A9.7.1.1].

Traditional minimum depths of slabs are based on the deck span length Sto control deflection to give [ Table A2.5.2.6.3-1]

A. DECK THICKNESS

Use hs = 190 mm for the structural thickness of the deck. By adding the15 mm allowance for the sacrificial surface, the dead weight of the deckslab is based on h= 205mm. Because the portion of the deck that

overhangs the exterior girder must be designed for a collision loadon the barrier, its thickness has been increased by 25mm to ho=230mm

mmmm

S

h 17518130

30002440

30

3000

min


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B. WEIGHTS OF THE COMPONENTS[ TABLE A3.5.1-1 ]

For a 1mm width of a transverse strip.

Barrier

Pb = 2400 x 10-9 Kg/mm3 x 9.81 N/Kg x 197325 mm2

= 4.65 N/mm

Future Wearing Surface

WDW = 2250 x 10-9 x 9.81 x 75 = 1.66 x 10-3 N/mm

Slab 205mm thick

Ws = 2400 x 10-9 x 9.81 x 205 = 4.83 x 10-3 N/mm

Cantilever Overhanging

Wo = 2400 x 10-9 x 9.81 x 230 = 5.42 x 10-3 N/mm


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C. BENDING MOMENTFORCE EFFECTS GENERAL

An approximate analysis of strips perpendicularto girders is considered acceptable [A9.6.1]. Theextreme positive moment in any deck panelbetween girders shall be taken to apply to allpositive moment regions. Similarly, the extremenegative moment over any girder shall be takento apply to all negative moment regions[A4.6.2.1.1]. The strips shall be treated ascontinuous beams with span lengths equal to thecenter-to-centre distance between girders. Thegirders are assumed to be rigid [A4.6.2.1.6]

For ease in applying the load factors, thebending moments will separately be determinedfor the deck slab, overhang, barrier, future

wearing surface, and vehicle live load.


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1. DECK SLAB

h = 205 mm,

Ws = 4.83 x 103 N/mm,S = 2440 mm

Placement of the deck slabdead load and results of amoment distribution analysis fornegative and positive momentsin a 1-mm wide strip is given infigure E7.1-2

A deck analysis design aidbased on influence lines is givenin Table A.1 of Appendix A. Fora uniform load, the tabulatedareas are multiplied by S forShears and S2 for moments.

mmNmmWsS

FEM /239612

)2440)(1083.4(

12

232

Fig.E7.1-2: Moment

distribution for deck slabdead load.


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R200 = Ws (Net area w/o cantilever) S= 4.83 x 10-3 (0.3928) 2440 = 4.63 N/mm

M204 = Ws (Net area w/o cantilever) S2

= 4.83 x 10-3 (0.0772) 24402

= 2220 N mm/mm M300 = Ws (Net area w/o cantilever) S2

= 4.83 x 10-3 (-0.1071) 24402= - 3080 N mm/mm

Comparing the results from the design aid with thosefrom moment distribution shows good agreement. Indetermining the remainder of the bending momentforce effects, the design aid ofTable A.1 will beused.

1. DECK SLAB


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2. OVERHANG

The parameters are

ho = 230 mm,Wo = 5.42 x 10

-3 N/mm2

L = 990 mm

Placement of the overhang dead load is shown in the figure E7.1-3. Byusing the design aid Table A.1, the reaction on the exterior T-Beamand the bending moments are:

Fig.E7.1-3

Overhangdead loadplacement


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2. OVERHANG

R200 = Wo (Net area cantilever) L= 5.42 x 10-3 (1+ 0.635 x 990/2440) 990 = 6.75 N/mm

M200 = Wo (Net area cantilever) L2

= 5.42 x 10-3 (-0.5000) 9902 = -2656 N mm/mm


= 5.42 x 10-3 (-0.2460) 9902 = -1307 N mm/mm


= 5.42 x 10-3 (0.1350) 9902 = 717 N mm/mm


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3. BARRIER The parameters are

Pb = 4.65 N/mmL = 990 127 = 863 mm

Placement of the center of gravity of the barrier dead load isshown in figure E7.1-4. By using the design aid Table A.1 for theconcentrated barrier load, the intensity of the load is multiplied

by the influence line ordinate for shears and reactions. Forbending moments, the influence line ordinate is multiplied by thecantilever length L.

Fig.E7.1-4

Barrierdead loadplacement


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3. BARRIER

R200 = Pb (Influence line ordinate)= 4.65(1.0+1.27 x 863/2440) = 6.74 N/mm

M200 = Pb (Influence line ordinate) L

= 4.65(-1.0000) (863) = -4013 N mm/mm


= 4.65 (-0.4920) (863) = -1974 N mm/mm


= 4.65 (0.2700) (863) = 1083 N mm/mm


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4. FUTURE WEARING SURFACE

FWS = WDW = 1.66 x 10-3 N/mm2

The 75mm bituminous overlay is placed curb to curb asshown in figure E7.1-5. The length of the loaded cantilever isreduced by the base width of the barrier to giveL = 990 380 = 610 mm.

Fig. E7.1-5: Future wearing surface dead load placement


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If we use the design aid Table A.1, we have

R200 = WDW [(Net area cantilever) L + (Net area w/o cantilever) S]= 1.66 x 10-3 [(1.0 + 0.635 x 610/2440) x 610 + (0.3928) x 2440)]= 2.76 N/mm

M200 = WDW (Net area cantilever) L2

= 1.66 x 10-3 (-0.5000)(610)2 = -309 N mm/mm

M204 = WDW [(Net area cantilever) L2 + (Net area w/o cantilever) S2 ]

= 1.66 x 10-3 [(-0.2460)(610)2 + (0.0772)24402 ] = 611 N mm/mm

M300 = WDW [(Net area cantilever) L2 + (Net area w/o cantilever) S2 ]

= 1.66 x 10-3 [(0.1350)(610)2 + (-0.1071)24402 ] = -975 N mm/mm

4. FUTURE WEARING SURFACE


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D. VEHICULAR LIVE LOAD

Where decks are designed using the

approximate strip method [A4.6.2.1], and thestrips are transverse, they shall be designedfor the 145 KN axle of the design truck[A3.6.1.3.3]. Wheel loads on an axle areassumed to be equal and spaced 1800 mmapart [Fig.A3.6.1.2.2-1]. The design truckshould be positioned transversely to producemaximum force effects such that the centerof any wheel load is not closer than 300mm

from the face of the curb for the design ofthe deck overhang and 600mm from theedge of the 3600 mm wide design lane forthe design of all other components[A3.6.1.3.1]


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The width of equivalent interior transverse strips

(mm) over which the wheel loads can be considereddistributed longitudinally in CIP concrete decks isgiven as[Table A4.6.2.1.3-1]

Overhang, 1140+0.883 X Positive moment, 660+0.55 S Negative moment, 1220+0.25 S

Where X is the distance from the wheel load tocenterline of support and S is the spacing of the T-Beams. Here X=310 mm and S=2440 mm(Fig.E7.1-6)


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Figure E 7.1-6 : Distribution of Wheel load

on Overhang


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Tire contact area [A3.6.1.2.5] shall beassumed as a rectangle with width of 510mm and length given by

P

IM

l

100128.2

Where is the load factor, IM is the dynamicload allowance and P is the Wheel load.

Here = 1.75, IM = 33% , P = 72.5 KN.


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Thus the tire contact area is510 x 385mm

with the 510mm in thetransverse direction asshown in Figure.E7.1-6


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Figure E 7.1-6 : Distribution of Wheel loadon Overhang

Back


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3


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mm

m


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Fig.E7.1-7: Live load placement for maximum positive moment

(a) One loaded lane, m = 1.2

(b) Two loaded lanes, m = 1.0


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If we use the influence line ordinates fromTable A-1, the exterior girder reaction andpositive bending moment with one loaded lane(m=1.2) are

200

204


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For two loaded lanes(m=1.0)

Thus, the one loaded lane case governs.


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3. MAXIMUM INTERIOR NEGATIVE LIVE LOAD MOMENT.

the critical placement of live load for maximum negativemoment is at the first interior deck support with oneloaded lane (m=1.2) as shown in Fig.E7.1-8.

The equivalent transverse strip width is

1220+0.25S = 1220+0.25(2440) = 1830 mm Using Table A-1, the bending moment at location 300 is


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4. MAXIMUM LIVE LOAD REACTION ON EXTERIOR GIRDER


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E. STRENGTH LIMIT STATE

The gravity load combination can be statedas [Table A.3.4.1-1]

P P


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The T-Beam stem width is 350mm, so the design

sections will be 175mm on either side of the supportcenterline used in the analysis. The critical negativemoment section is at the interior face of the exteriorsupport as shown in the free body diagram

[Fig. E7.1-10]


Back


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The values of the loads in Fig E7.1-10 are for a 1-

mathematical model strip. The concentrated wheelload is for one loaded lane, that is,

W = 1.2(72500)1400 = 62.14 N/mm

1. Deck Slab:


s


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2. Overhang

3. Barrier


o

200


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4. Future Wearing Surface

5. Live Load



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6. Strength-I Limit State



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F. Selection Of Reinforcement

The effective concrete

depths for positive andnegative bending will bedifferent because of thedifferent coverrequirements as indicated

in this Fig shown.


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u


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Maximum reinforcement keeping in view theductility requirements is limited by [A5.7.3.3.1]

Minimum reinforcement [5.7.3.3.2] forcomponents containing no prestressing steel issatisfied if

da 35.0

y

cs

f

f

bd

A '03.0

)(


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1. POSITIVE MOMENT REINFORCEMENT :


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Check Ductility

Check Moment Strength


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2. Negative Moment Reinforcement

Back


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Check Moment Strength

For transverse top bars,

Use No. 15 @225 mm.


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3. DISTRIBUTION REINFORCEMENT:

Secondary reinforcement is placed in the bottom of the slab todistribute the wheel loads in the longitudinal direction of the bridgeto the primary reinforcement in the transverse direction. Therequired area is a percentage of the primary positive momentreinforcement. For primary reinforcement perpendicular to traffic

[A9.7.3.2]

Where Se is the effective span length [A9.7.2.3]. Se is the distanceface to face of stems, that is,

Se=2440-350= 2090mm

%673840

eS

Percentage

%67%,842090

3840UsePercentage


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So

Dist.As = 0.67(Pos.As)=0.67(0.889)

= 0.60 mm2/mm

For longitudinal bottom bars,Use No.10 @ 150 mm,

As = 0.667 mm2/mm



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F. Selection Of Reinforcement4. SHRINKAGE AND TEMPRATURE REINFORCEMENT.

The minimum amount of reinforcement in each direction shall be[A5.10.8.2]

Where Ag is the gross area of the section for the full 205 mm thickness.

For members greater than 150 mm in thickness, the shrinkage andtemperature reinforcement is to be distributed equally on both faces.

Use No.10 @ 450 mm, Provided As = 0.222 mm2/mm

y

g

sf

AATemp 75.0.

mmmmATemp s /38.0200

)1205(75.0. 2

mmmmATemp s /19.0).(2

12


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G. CONTROL OF CRACKING-GENERAL

Cracking is controlled by limiting the tensile stress in

the reinforcement under service loads fs to an allowabletensile stress fsa [A5.7.3.4]

WhereZ = 23000 N/mm for severe exposure conditions.dc =Depth of concrete from extreme tension fiber to

center of closest bar 50 mmA = Effective concrete tensile area per bar having thesame centroid as the reinforcement.

y

c

sas f

Ad

Zff 6.0

)(

3/1


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M = MDC + MDW + 1.33 MLL

c


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c

.2770030)2400(043.0 5.1 MPaEc

Where

= density of concrete = 2400 Kg/m3.

fc = 30 MPa.

So that

Use n = 7

,2.7

27700

200000n


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1. CHECK OF POSITIVE MOMENT REINFORCEMENT.

The service I positive moment at Location 204 is

The calculation of the transformed section properties is based on a 1-mm widedoubly reinforced section shown in the Figure E7.1-12


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Sum of statical moments about the neutral axis yields


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The positive moment tensile reinforcement of No.15 bars at 25mm

on centers is located 33 mm from the extreme tension fiber.Therefore,

c

sa y

sa y s


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2. CHECK OF NEGATIVE REINFORCEMENT:

The service I negative moment at location 200.72 is

The cross section for the negative moment is shown in Fig.E7.1-13.


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Balancing the statical moments about the

neutral axis gives


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The negative moment tensile reinforcement of

No.15 bars at 225 mm on centers is located 53mm from the tension face. Therefore dc is themaximum value of 50mm, and

sa

sa


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H. FATIGUE LIMIT STATE

The investigation for fatigue is notrequired in concrete decks formultigirder applications [A9.5.3]

I TRADITIONAL DESIGN FOR INTERIOR


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I. TRADITIONAL DESIGN FOR INTERIORSPANS

The design sketch in Fig.E7.1-14 summerizes the

arrangement of the transverse and longitudinalreinforcement in four layers for the interior spans of thedeck. The exterior span and deck overhang have specialrequirements that must be dealt with separately.

J EMPERICAL DESIGN OF CONCRETE DECK


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J. EMPERICAL DESIGN OF CONCRETE DECKSLABS

Research has shown that theprimary structural action of theconcrete deck is not flexure, but

internal arching. The archingcreates an internal compressiondome. Only a minimum amount of

isotropic reinforcement is requiredfor local flexural resistance.



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1. DESIGN CONDITIONS [A9.7.2.4]

Design depth excludes the loss due to wear,h=190mm. The following conditions must be satisfied:



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2. REINFORCEMENT REQUIREMENTS [A9.7.2.5]

J. EMPERICAL DESIGN OF CONCRETE DECK


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3. EMPERICAL DESIGN SUMMARY

while using the empirical design approach there is no need of usingany analysis. When the design conditions have been met, theminimum reinforcement in all four layers is predetermined. Thedesign sketch in the Fig.E7.1-15 summarizes the reinforcementarrangement for the interior deck spans.

K. COMPARISON OF REINFORCEMENT


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K. COMPARISON OF REINFORCEMENTQUANTITIES

The weight of reinforcement for the traditional and

empirical design methods are compared in Table.E7.1-1for a 1-m wide transverse strip. Significant saving, inthis case 74% of the traditionally designedreinforcement is required, can be made by adopting theempirical design method.

(Area = 1m x 14.18m)

L DECK OVERHANG DESIGN


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L. DECK OVERHANG DESIGN

The traditional and the empirical methods

does not include the design of the deckoverhang.

The design loads for the deck overhang areapplied to a free body diagram of a

cantilever that is independent of the deckspans.

The resulting overhang design can then beincorporated into either the traditional or the

empirical design by anchoring the overhangreinforcement into the first deck span.



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Two limit states must be investigated.

Strength I [A13.6.1] and ExtremeEvent II [A13.6.2]

The strength limit state considersvertical gravity forces and it seldomgoverns, unless the cantilever span isvery long.



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The extreme event limit stateconsiders horizontal forces causedby the collision of a vehicle with

the barrier.

The extreme limit state usually

governs the design of the deckoverhang.



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1. STRENGTH I LIMIT STATE:

The design negative moment is taken at theexterior face of the support as shown in theFig.E7.1-6 for the loads given in Fig.E7.1-10.

Because the overhang has a single load pathand is, therefore, a nonredundant member,then 05.1R



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2. EXTREME EVENT II LIMIT STATE

the forces to be transmitted to the deck overhanddue to a vehicular collision with the concrete barrierare determined from a strength analysis of thebarrier.

In this design problem, the barriers are to bedesigned for a performance level PL-2, which issuitable for

High-speed main line structures on freeways,

expressways, highways and areas with a mixture ofheavy vehicles and maximum tolerable speeds



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The maximum edge thickness of the deck overhand is

200mm[A13.7.3.1.2] and the minimum height of barrierfor a PL-2 is 810mm.

The transverse and longitudinal forces are distributedover a length of barrier of 1070mm. This length

represents the approximate diameter of a truck tire,which is in contact with the wall at the time of impact.

The design philosophy is that if any failures are to occurthey should be in the barrier, which can readily be

repaired, rather than in the deck overhang. The resistance factors are taken as 1.0 and the

vehicle collision load factor is 1.0

M CONCRETE BARRIER STRENGTH


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M. CONCRETE BARRIER STRENGTH

All traffic railing systems shall be proven

satisfactory through crash testing for adesired performance level [A13.7.3.1]. If apreviously tested system is used with onlyminor modification that do not change itsperformance, then additional crash testing is

not required [A13.7.3.1.1] The concrete barrier shown in the

Fig.E7.1-17 (Next Slide) is similar to theprofile and reinforcement arrangement to

traffic barrier type T5 analyzed byHirsh(1978) and tested by Buth et al (1990)



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c t

Fig. W7.1-17 (Concrete Barrier and connection to deckoverhang.)



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H

LMHMMLLR

ccwb

tc

w

2

882

2..(E7.1-8)



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t

t



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1. MOMENT STRENGTH OF WALL ABOUT

VERTICAL AXIS,MWH.

The moment strength about the verticalaxis is based on the horizontal

reinforcement in the wall. The thickness ofthe barrier wall varies and it is convenientto divide it for calculation purposes intothree segments as shown in Fig. E7.1-18



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Neglecting the contribution of compressive

reinforcement, the positive and negative bendingstrengths of segment I are approximately equal andcalculated as

nI



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For segment II, the moment strengths are slightly

different. Considering the moment positive if it producestension on the straight face, we have

n neg

n pos

n II



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For segment III, the positive and negative

bending strengths are equal and

nIII

nIInI nIII



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Now considering the wall to have uniform

thickness and same area as the actual wall andcomparing it with the value of MwH.

This value is close to the one previously calculated and is

easier to find



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2. MOMENT STRENGTH OF WALL ABOUT HORIZONTAL

AXISThe moment strength about the horizontal axis isdetermined from the vertical reinforcement in thewall.

The yield lines that cross the vertical reinforcement(Fig.E7.16-16) produce only tension in the slopingwall, so that the only negative bending strengthneed to be calculated.

Matching the spacing of the vertical bars in thebarrier with the spacing of the bottom bars in thedeck, the vertical bars become No.15 at 225mm

(As = 0.889 mm2/mm) for the traditional design

(Fig.E7.1-14).



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For segment I, the average wall thickness is 175mm

and the moment strength about the horizontal axisbecomes

At the bottom of the wall the vertical reinforcement atthe wider spread is not anchored into the deckoverhang. Only the hairpin dowel at a narrower spreadis anchored. the effective depth of the hairpin dowel is[Fig.E7.1-17]

d=50+16+150+8 = 224 mm



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II+III



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3. CRITICAL LENTH OF YIELD LINE PATTERN,LC

Now with moment strengths and Lt=1070mm known,Eq.E7.1-9 yields

c

t t b w

c



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4. NOMINAL RESISTANCE TO TRANVERSE

LOAD,RWFrom Eq.E7.1-8, We have

w c tb w

cc



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5. SHEAR TRANSFER BETWEEN BARRIER AND DECK

The nominal resistance Rw must be transferred acroass a cold jointby shear friction. Free body diagrams of the forces transferred fromthe barrier to the deck overhang are shown in the Fig.E7.1-19

c



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The nominal shear resistance Vn of the

interface plane is given by [A5.8.4.1]

cvn vf c



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The last two factors are for concrete placed

against hardened concrete clean and free oflaitance, but not intentionally roughened.Therefore for a 1-mm wide design strip

n cv

vf fy



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The minimum cross-sectional area of dowels

across the shear plane is [A5.8.4.1]

vf

y

v



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The basic development length lhb for a hooked bar with

fy = 400 MPa. Is given by [A5.11.2.4.1]

and shall not be less than 8db or 150mm. For a No.15bar, db=16mm and

which is greater than 8(16) = 128mm and 150mm. Themodifications factors of 0.7 for adequate cover and 1.2

for epoxy coated bars [A5.11.2.4.2] apply, so that thedevelopment length lhb is changed to

lhb=0.7(1.2)lhb = 0.74(292) = 245mm

'

100

fc

dl bhb

mmlhb 292

30

)16(100



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c c w



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The standard 90o hook with an extension of 12db=12(16)=192mm atthe free end of the bar is adequate [A5.10.2.1]



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CO C S G

6. TOP REINFORCEMENT IN DECK OVERHANG

The top reinforcement must resist the negative bendingmoment over the exterior beam due to the collision andthe dead load of the overhang. Based on the strength ofthe 90o hooks, the collision moment MCT (Fig.E7.1-19)

distributed over a wall length of (Lc+2H) is



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The dead load moments were calculated

previously for strength I so that for the ExtremeEvent II limit state, we have

u



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Bundling a No.10 bar with No.15 bar at 225mm

on centers, the negative moment strengthbecomes

s

n



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this moment strength will be reduced because

of the axial tension forceT = Rw/(Lc+2H)

By assuming the moment interaction curve

between moment and axial tension as a straightline (Fig.E7.1-20]



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u

st



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The development length available for the hook in the overhang before reachingthe vertical leg of the hairpin dowel is

available ldh=16+150+8=174mm>155mm



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db



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7.10.2: SOLID SLAB BRIDGE DESIGN


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PROBLEM STATEMENT:

Design the simply supported solid slab bridgeof Fig.7.2-1 with a span length of 10670mmcenter to center of bearing for a HL-93 liveload. The roadway width is 13400mm curb to

curb. Allow for a future wearing surface of75mm thick bituminous overlay. Usefc=30MPa and fy=400 MPa. Follow the slabbridge outline in Appendix A5.4 and the

beam and girder bridge outline in section 5-Appendix A5.3 of the AASHTO (1994) LRFDbridge specifications.

7.10.2: SOLID SLAB BRIDGE DESIGN


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A. CHECK MINIMUM RECOMMENDEDDEPTH [TABLE A2.5.2.6.3-1]


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DEPTH [TABLE A2.5.2.6.3 1]

B. DETERMINE LIVE LOAD STRIPWIDTH [A4.6.2.3]


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WIDTH [A4.6.2.3]

1. One-Lane loaded:

Multiple presence factor included [C4.6.2.3}

1 1

B. DETERMINE LIVE LOAD STRIPWIDTH [A4.6.2.3]


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WIDTH [A4.6.2.3]

C. APPLICABILITY OF LIVE LOADS FOR DECKSAND DECK SYSTEMS


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1. MAXIMUM SHEAR FORCE AXLE LOADS [FIG.E7.2-2]



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1. MAXIMUM BENDING MOMENT AT MIDSPAN-

AXLE LOADS [FIG.E7.2-3]

D. SELECTION OF RESISTANCEFACTORS (Table 7.10 [A5.5.4.2.1]


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FACTORS (Table 7.10 [A5.5.4.2.1]

E. Select load modifiers [A1.3.2.1]


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F. SELECT APPLICABLE LOAD COMBINATION(TABLE 3.1 [TABLE A3.4.1-1])


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1. STRENGTH I LIMIT STATE

2. SERVICE I LIMIT STATE

3. FATIGUE LIMIT STATE

G. CALCULATE LIVE LOAD FORCEEFFECTS


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1. INTERIOR STRIP.



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2. EDGE STRIP [A4.6.2.1.4]



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H. CALCULATE FORCE EFFECTS FROM

OTHERloads


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1. INTERIOR STRIP, 1-mm WIDE

H. CALCULATE FORCE EFFECTS FROM

OTHERloads


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2. EDGE STRIP, 1-MM WIDE

I. INVESTIGATE SERVICE LIMIT STATE


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1. DURIBILITY



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a. MOMENT- INTERIOR STRIP

s y



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b. MOMENT-EDGE STRIP



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2. CONTROL OF CRACKING

a. INTERIOR STRIP

s sa

r

c r

c

s



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Location of neutral axis

cr



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STEEL STRESS

s

s y

c

y

sa



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b. EDGE STRIP

(103)(x2) = (35 x 103)(510-x)

cr



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STEEL STRESS

s



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3. DEFORMATIONS [A5.7.3.6]

e

c e

cr

a

cr

crae



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t

g

cr

e


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4607mm



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Back



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DESIGN LANE LOAD

Lane



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The live load deflection estimate of 17mm is

conservative because Ie was based on themaximum moment at midspan rather than anaverage Ie over the entire span.

Also, the additional stiffness provided by the

concrete barriers has been neglected, as wellas the compression reinforcement in the topof the slab.

Bridges typically deflect less than the

calculations predict and as a result thedeflection check has been made optional.



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5. Concrete stresses [A5.9.4.3].

As there is no prestressing thereforeconcrete stresses does not apply.



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5. FATIGUE [A5.5.3]

Fatigue load should be one truck with 9000-mm axle

spacing [A3.6.1.1.2]. As the rear axle spacing is large,therefore the maximum moment results when the twofront axles are on the bridge. as shown in Fig.E7.2-8,the two axle loads are placed on the bridge.

No multiple presence factor is applied (m=1). FromFig.E7.2-8



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a. TENSILE LIVE LOAD STRESSES:

One loaded lane, E=4370mm

s


b [ ]


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b. REINFORCING BARS:[A5.5.3.2]

min

J. INVESTIGATE STRENGTH LIMIT STATE

[ ]


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1. FLEXURE [A5.7.3.2]

RECTANGULAR STRESS DISTRIBUTION [A5.7.2.2]

a. INTERIOR STRIP:

(2/7)



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For simple span bridges temperature gradient effect


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For simple span bridges, temperature gradient effectreduces gravity load effects. Because temperature gradientmay not always be there, so assume = 0TG



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So the strength limit state governs.

Use No.30 @ 150 mm for interior strip.


b


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b. EDGE STRIP


STRENGTH I


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STRENGTH I:

Use No. 30 @ 140mm for edge strip.


2 SHEAR


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2. SHEAR

Slab bridges designed for moment inconformance with AASHTO[A4.6.2.3]

maybe considered satisfactory forshear.

K. DISTRIBUTION REINFORCEMENT[A5.14.4.1]

Th t f b tt t


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The amount of bottom transverse

reinforcement maybe taken as a percentageof the main reinforcement required forpositive moment as.


a INTERIOR SPAN:


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a. INTERIOR SPAN:


b EDGE STRIP


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b. EDGE STRIP:

L. SHRINKAGE AND TEMPRATURE REINFORCEMENT

Transverse reinforcement in the top of the slab


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Transverse reinforcement in the top of the slab

[A5.10.8]

M. DESIGN SKETCH


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TABLE A-1


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BACK


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162BACK


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lecture no.4b

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