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NOTICE

This

ocuments

isseminated

nderhe

ponsorship

f

he

.S .

Department

ofTransportation intheinterestofinformation exchange. he

United

tates

Government

ssumes

o

iability

or

the

ontents

r

se

thereof.

he

United

tates

Government

oes

ot

ndorse

roducts

r

manufacturers.rade rmanufacturer's ames ppearerein olely

because

theyareconsideredessentialto

the

objectiveofthisreport.

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Techn ica lRepor t

Documenta t ion

Pag

1.

eport

N o.

DOT/FAA/AR-95/85

2.

Government AccessionNo .

3.ecipient's CatalogNo .

4.

itlean d

Subtitle

A D VA NCE DP A V E M E N T

DESIGN:

Finite

ElementModelingfo r

Rigid Pavement

Joints

Report

I:

ackgroundInvestigation

S.

eport

Date

April1997

6.

erformingOrganization

Code

7.

uthor(s)

Michael

I .

Hammonsand Anastasios M .

Ioannides

8.

erforming

Organization

Report

No .

9.

erforming

Organization

Name

an dAddress

U.S.

Army EngineerWaterways

Experiment

Station

3909HallsFerry Road

Vicksburg,

M S

39180 -6199

10.Work

Unit

No .

(TRAIS)

11 .

ontractor Grant

No .

DTFA03-94-X-00010

12.ponsoring

Agency

N am e

an dAddress

U.S.

Department

of

Transportation

FederalAviationAdministration

Officeof Aviation

Research

Washington,D C20591

13.

yp e

of

Report

an d

Period

Covered

Final

Report

14.

ponsoring

Agency

Code

AAR-410

15 .

upplementary

Notes

FA A

William

J.

Hughes

Technical

Center

Contract

Officer

(COTR)

Technical

Representative

is

Xiaogong

Lee

16 .

bstract

The

objective

of

this

researchproject

is

to

develop

an

analytical

model

fo r

rigid

pavementjoints

that

ca n

be

implemented

into

advancedpavementdesign

models.his

reportdocuments

a

background

investigation

including

a

comprehensive

reviewofrigid

pavementjo intmodels

ith

articular

mphasis n

heir

jo int

ndoundationmodeling

apabilities.

T he

major

istorical

developments

in

airportrigid

pavementdesignar e

discussed.

losed-formsolutionsakintothosebyWestergaardwere

derivedin

this

study

fo rth emaximumresponsesonth e

unloaded

sideofarigidpavementslab

edge

capable

ofadegreeof

load

transfer.

W henusedtogether

with

Westergaard's

ow nclosed-form

equations

fo r

th e

free-edge

problem,

th e

formulae

derived

in

thisstudy

constitute

a

complete

solutionofth eedge

load

transferproblem,

ecognized

overth e

years

asacriticalonsideration

in

rigid

pavement

design.he

newlyderived

solution

is

presented

inconvenientformfo r

routine

engineeringapplication

an d

iscompared

to

earlier

finite

element

data.

he

improvement

in

ease

of

application

and

precision

is

considerable.

17 .

Keywords

Analysis

Responsemodels

Design Rigid

pavements

Joints

Testing

18.

istribution

Statement

Document

isavailabletoth epublic

through

th e

National

TechnicalInformation

Service,Springfield,

V A

2161

19.ecurity Classif.(o fthisreport)

Unclassified

20 .ecurity

Classif.

(o fthis

page)

Unclassified

21 .o.

of

Pages

107

22 .

rice

Form

DOT

F1700.7

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T A B L E

O F

C O N T E N T S

Page

E X E C U T I V E

S U M M A R Y i

I N T R O D U C T I O N

Background

Object ive

Scope

P R O B L E M

S T A T E M E N T

T heRigidPave me n tSystem

L o a dTrans fe r

Defini t ions

Rigid

Pave me n t

Foundat ions

M o d e lRequi remen t s

H I S T O R I C A L B A C K G R O U N D

Genera l

Response

M o d e l

0

Cri t ica l

Des ign

Stresses

0

Accelerated

Traff ic

Tests 1

Subgrade

Characterizat ion

2

RigidPave me n t

Joints

2

C L A S S I C A L

R E S P O N S EM O D E L S 7

Weste rgaardTheory

7

Response

Charts

8

Compute r i zed

Solut ions 9

Weste rgaardTheoryLimita t ions 9

ElasticLaye r

Model s 0

M ode l s

fo r

D o w e lStresses 1

Finite

Difference

M o d e l 4

F IN IT E

E L E M E N T

R E S P O N S E

M O D E L S 5

Genera l

5

T w o-Di me n s i on a lFiniteElementModel s

6

JJLLI-SLAB

7

DenseLiquidSubgrade 3

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Elastic

Sol id

Subgrade 3

Resi l ient

Subgrade

M o d e l

4

VlasovT w o-Pa rame t e r

Foundat ion

5

K er r

Three -Paramete r

Founda t ion 5

Zhemochkin -Sin i t syn -Shtae rmanFounda t ion

6

J S L A B

7

W E S L I Q I D

and

K E N S L A B S 7

F E A C O N S

III

9

W E S L A Y E R

and

K E N L A Y E R

1

Three -Dimens iona l

FiniteElemen t

Model s 2

G E O S Y S

M o d e l 2

A B A Q U S

Model s 3

A

W E S T E R G A A R D - T Y P E

S O L U T I O N

F O R

T H E

L O A D

T R A N S F E R

P R O B L E M

6

Genera l

6

Genera lSolut ionfo r

L o a d

Transfer

6

In terpolat ionFormulae

1

Free -Edge

Deflect ion 1

Free -EdgeBend ingStress 2

U n loade d

Side

Deflect ion

2

Unloaded

SideBending

Stress

4

LoadTransfer

Efficiency 6

S u mma ry 9

S M A L L - S C A L E

P H Y S I C A LM O D E LS T U D I E S

9

Genera l 9

Single-SlabMode ls

9

Tes t

Descript ion

9

Tes t

Resul ts

and

Analys i s 1

Dow e l e dJointModel s 3

Tes t

Descript ion 3

Tes t

Resul t s

5

Analys is 6

V I

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C O N C L U S I O N S

A N DR E C O M M E N D A T I O N S 0

Conclusions

0

Recommendat ions 1

Pavemen t

Perfo rmance

Model ing

1

Materia lModel ing

1

Mult iple-Wheel

L o a d

Model ing

2

JointModel ing 2

R E F E R E N C E S 3

Vll

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LIST

O F

I L L U S T R A T I O N S

Figure

age

1ypicalRigidPavement

System

2oncep t

ofLoad

Transfer

3

ffectof

LoadTransferEfficiency

on

Pavement

Perfo rmance

4

o we l

Installat ions

atLockbourn e

and

Sharonville

Tes t

Tracks

5

5riberg's(1940)

Analysisof

D o w e l

B ar

Suppor t 3

6

our -N ode

PlateBendingElement

6

7

inite

Element

M ode l

inI L L I -S L A B

8

8

quivalent

Sect ions

fo r

a

Two -L a ye r

System 9

9

L L I -S L A B

Joint

Mo d e l 0

10

ointEfficiencyas

a

Funct ionof

Dimensionless

Joint

Stiffness

fo rAggrega te

Interlock

Joint

0

1 1oint

Efficiency

as

a

Funct ion

of

Dimensionless

Joint

Stiffness

fo r

D o we l ed

Joint

2

12ound

Displacement

U n de r

a

L o a d ed

Plate

fo r

Winkle rand

Elastic

Solid

Foundat ions

4

1 3

lasov

o r

Plas ternak

Founda t ion

5

14

err

Foundat ion

Mo d e l 6

15oint

M ode l

inWesliq idandWeslaye r

8

16

eomet ryof

Shear

Transferat

a

Doweled

Joint

in

Wesliq idand

Weslayer

9

17

inite

Element

Model ing

inFeacons

III

1

18ffectiveJoint

StiffnessWith

Relative

Displacementin

FeaconsII I2

19

ariat ion

of

Unloaded

Side

Maximum

Dimensionless

Deflect ion

With

Dimensionless

Joint

Stiffnessand

el

8

20

ariat ion

ofUnloaded

Side

Maximum

Dimensionless

BendingStress

Wi t h

Dimensionless

Joint

Stiffnessand

el

9

21ariat ionof

Max imum

Dimensionless

Deflectiono r

Free

E d g e

Wi t hel

t

0

vm

8/10/2019 Ada 325108

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22

ariation

of

Ma x i mu m

Dimensions

Bending

Stress

fo rFreeE d g eWi t h

elt

0

23ariat ion

of

L T E

S

With D imensionlessJointStiffnessande/1 7

2 4

elat ionshipBetween

L T E

8

and

L T E

a

With

e/ 7

25

ompar i sonof

Newl yDerived

Solut ion

With

Earlier

Finite

ElementResul ts

8

2 6

hotograph

ofSmall-ScalePhysicalModel sTestSetup 1

27

dge

Load ing

Deflect ion

Contours

FromSmall-Scale

M o d e lStudy2

28

ompar i sonofE d g e

Load ingDeflection

Basins

From

Exper imentand

I L L I -S L A B

63

2 9

ypical

Small-Scale

D o w e l

Joint

Tes t

SlabShowingApprox imate

Strain

Ga g e

Posi t ions 5

30

ackcalculated

Dimensionless

Joint

Stiffness

From

Small-Scale

M o d e l

Tests

8

31

ackcalculated

Mo d u l u s

of

D o w e lReact ionFromSmall-Scale

M o d e lTests

9

IX

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LIST

OF

TABLES

Table

age

1

imensionsand

Spacings

of

Steel

Dowels(FAA,

1978)

2

ummary

ofCorps

of

Engineers

Load

TransferMeasurements

fo r

Full-Scale

Test

SectionsandIn-ServicePavements(Rollings,

1989)

3

3

verviewofFinite

Element

Models

fo r

Rigid

Pavements 5

4mall-Scale Doweled

JointModelTest

Parameters

4

5

ackcalculatedDoweled

Joint

ResponseParameters 7

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E X E C U T I V E

S U M M A R Y

Arigidpave me n tsys temcons is t s

of

a

n umbe r

of

relat ivelythinPort landcemen tconcre te

slabs ,

finite

n

ength

nd

idth,ver

ne

r

more

oundat ion

ayers.

hen

lab-on-grades

subjectedo heeload,

t

evelopsendingt resses

nd

is tributes

heoadverhe

foundat ion.

owever ,

he

esponse

f

hese

inite

labs

s

ontrolled

y

oint

r

dge

discontinuities.y

heir

ature,

joints

re

t ructurally

eakening

omponen t s f

th eystem.

Thus ,heesponsendeffect iveness

f

joints

re

primary

oncernsn

rigid

pavemen tnalysis

and

des ign.

Curren t

F A Astructuraldes ign

criteria

are

based

ei ther

uponth eWeste rgaard

response

mo d e l

or

th eayeredlastic

esponseodel .l thoughvailable

estergaard

olutions

aveeen

extensivelyused,they

arel imited

bytw o

significantshortcomings :

a)

only

a

singleslab

pane l

is

accommoda t e din

th eanalysis;therefore,loadt ransfer

at

jointsisnotaccounted

for,and

(b )

th e

layerednatureofth epavemen tfoundat ionis otexplici t lyreflectedinth eWinkle r

foundat ion

model .

ult i layered,

inear

elast ic

models ,

s

used

in

th e

new

F A A

des ign

method

released

in

1994,

ons ide r

he

ompleteayeredystem

n

he ert ical i rection,herebyddress ing

he

second

imi ta t ion.

nhe orizonta l

i rection,

owever ,

he

ayers

re s sumedto

be

infinitely

longwi th

no

discontinuities

uchs

edges

or

joints.onsequent ly,he

load

t ransfer

l imitation

remains

unresolved.

O v erth epas t

tw o

decades ,

everal

two-d imens iona l

( 2D)

finite

element

analysisprogramshave

been eveloped

hich

ncorporate

oad

ransfer

t

oints.

hese

rog rams

se hin-plate

e lemen tormulat ionorhe

lab.

om e rograms llowhe

ser

ohoosero m ibrary

f

foundat ionmodels .

ew

esearchers

ave

t tempted

o

se

hree-dimensional3D )finite

e lemen t

model s

or

igid

a v emen tnalysis

ncludingom e

oadransfer

mechan i sms

the

joint.

ven

state-of-the-art

2 D

finite

e lement

model ing

involves ,

at

leas t

implici t ly,

assumptions

wh i ch

l imi t

th e

precis ion

ofes t imates

concerning

th eloadcarried

by

eachdowel .

h is

problem

is

ven

urtheromplicated

y

he

nteraction

f

oadsrom

mult iple-wheel

anding

ears.

Adopt ing

a3D

finite

element

model

m ay

clarifysuch

issuesfurther.

Closed- formsolutions

akinto

those

byWes tergaa rd

were

derivedinthis

study

fo rth emaxi mum

responses

onth e

unloaded

side

of

a

rigidpavementslab

edge

capable

of

a

degreeof

load

t ransfer.

W h e n

sedtogetherwi thWestergaard'sw n

closed-form

equat ionsorth eree-edge rob lem,

th e

ormulaeerivedn

his

tudy

onsti tute

omple t e

olution

f

hedge

oad

ransfer

problem,

ecognized

verhe ears s cri t ical

onsiderat ion

n

igid

ave me n t

esign.

he

newlyderived

solution

is

presentedinconvenient

form

fo r

rout ine

engineeringapplication

andis

compared

to

earlier

finite

e lement

data.

he

improvement

in

ease

of

appl ica t ion

and

precis ion

is

cons iderable .

xi/xii

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I N T R O D U C T I O N

B A C K G R O U N D .

T hecommercia l

aviation

indus t ry

has

responded

to

increased

demandfo r

air

t ravel

by

developing

longer ,

ider ,

nd

eavier

i rcraft

it h

ncreas ing

umbers

f

wheel s

o

uppor t

he

i rcraft

whi lein

ground

operat ion.n

order

tomaximizeusablespacefo r

passengersand

cargo,

as

well

as

to

reduce

weigh t ,aircraft

des igners

aredevelopinglanding

gear

layouts

that

are

qui te

different

fromthose

on

previous

commerc i a l

aircraft.new

generat ion

ofsuch

aircraftdebutedin

995

with

th e

in t roduct ion

of

th e

Boeing

B -777 .

he

2 ,630 -kN

(592,000-lb)B - 7 7 7featurestw o

main

landing

gear

assembl ies ,each

ina

triple-tandem

configurat ion.

he

M cDon a ld -Doug l a sM D - 1 2 ,

wh i ch

has

growth

vers ions

f

up

to

, 780

kN

1 ,300 ,000

lb) ,

s

ls o

envis ionedin

n

effort

to

meet

future irt raveldemands .hesenew enerationaircraftm ay

precipitate

he

requirement

fo r

adjustments

toai rport

pavemen t

th ickness

to

ensure

serviceable

pavement s

over

des ign

l ives

of

2 0 ,30,

or

even40years.

M a n y

es ign

riteria

sed

y

he

ederal

viation

dministration

F A A )

or

igid

i rport

pave me n tthickness es ign avetheirorigininresearchconducted

b y

th e .S .A rmy orps

f

Engineersbe tween

1941

and

1955 .

urrent

methodsof

selecting

pavemen tthicknesses

arebased

uponheore t icaltudies,

mall-scaleodel

tudies,

ull-scale

cceleratedraffic

ests ,nd

variousther

ieldtudies ,ncludingoni toring

f

erformance

f

n-serviceigidi rport

pavemen t s

(Hutch inson , 966) .

owever ,

since

955

aircraft

landing

geargeometry

has

beco me

more

complex

as

loadshavecont inuedtoincrease.

n

th e 970 ' s ,aseries

of

accelera tedtraffic

tests

ereonductedo

erifyxtrapolations

eyondheriginal

xperimentalatabase

or

specific

loadsand

condi t ions

(Ahlvin,

971 ) .

ecent

deve lopment

of

new-generat ion

aircraft

has

caused

someconcernsregardingth eadequacyandapplicabil i ty

of

current

methods

of

structural

des ign

fo rai rportpavement s .

T he

esponse

odel

hich

ormshe

asis

or

he

A A

igidavemen ttructural

es ign

procedure

s

heestergaarddealization.

n

926,

estergaardeveloped ethod

or

comput ingth e

response

of rigidpavemen t

s labs-on-grade

subjected

towh ee lloadsby

model ing

th epave me n t

as

thin,infiniteorsemi-infiniteplaterest ingonab ed

of

springsWes tergaa rd ,

1926) .l t houghavailableWeste rgaardsolutions

havebeen

extens ivelyused,they

are

l imited

by

tw o ignificanthortcomings :a) nly inglela b anels

ccommodated

nhenalysis;

therefore,loadtransfer

at

joints

is

no t

accounted

for,

and

(b )

th elayered

nature

ofth e

pavemen t

foundat ion

s

ot

xplici t lyeflectednheWinkle roundat ionmodel .

ulti layered,

inear

elast icmodel s ,

as

usedin

th enewF A Adesignmethodreleasedin 994,

consider

th e

complete

layeredsys tem

inth evert ica ldirection,

hereby

ddress ingth esecondl imitationParkeret

al.,

1979 ) .

n

th ehorizontal

direction,

however ,

th e

layersareas sumed

to

be

infinitely

longwi th

no

discontinuitiesuch

s

dges

r

oints.

onsequent ly,heoadransfer

imitationemains

unresolved.

Advances

n

lectronic

omput ingaveevolutionized

odern

ociety,

ndheracticef

engineering

hasbenefi tedfrommu ch

of

thisrevolution.hefinitee lemen t

model ing

technique

has

matured

as

a

powerfu l

and

efficient

analysis

tool

for

boundary

value

prob lems

in

engineering .

F or

ver

wenty

ears ,

avemen tngineers aveealized

he otential f

hree-dimensional

(3D)

finite

e lemen t

analyses

of

jointed

concretepavements .he

s lab-join t -foundat ion

sys tem

fo r

8/10/2019 Ada 325108

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a

rigidpave me n t

is

D

in

nature;hus ,

omprehens iverepresentation

of

this

ys tem

requires

3D

analytical

approach .

O B J E C T I V E .

T heobject iveofthisresearch

is

todevelop

an

analytical

mo d e l

fo rconcre te

pave me n tjointsthat

can

be

readily

implemen ted

into

advanced

pavemen t

des ign

model s

currentlyunder

deve lopmen t

by

th e

F A A .hebas iccriteriato

be

used

fo rthismo d e ldeve lopmen t

wil l

be

(a)

soundness

of

th e

theory

and

(b )

precis ionofth e

mo d e l

consis tentwithth erequirements

of

th eF A Apavemen t

des ignmodel .hemo d e l evelopedhouldbecapable

f

model inghe lab-join t -foundat ion

sys temanderves

n

nalyticalteppings tonetoincreasedunders tandingof

th ebehaviorof

rigid

ave me n t

ys tems.

yjudiciously

pplying

his

ncreased nders tanding

f

ehavior,

improved

des ign

criteriacan

be

developedresulting

in

enhancedrigid

pave me n t

performance

in

th efield.

T he

object ives

listedabovewil lbe

accomplished

by

complet ingth e

fol lowing

tasks:

1 .

ask1 :eviewand

Evaluat ion

of

Exis t ing

Joint

Model s .

2.

ask

2:

erform

a

Response

and

Sensit ivi ty

Analys isof

Rigid

Pave me n tSys t ems .

3.

ask

3:

evelop

a

Genera l3DAnalyt ica l

Model .

4.

ask

4:

erformLabora tory -Sca le

Test ing.

5.

ask

5:

ode l

Appl icat ion.

6.ask

6:

odel

Simpli f icat ion

fo r

Implementat ion

into

F A ADes ignProcedures .

S C O P E .

Thi s

epor t

escribes

he

ask

fforttoeview

nd

evaluate

xisting

rigid

pave me n t

model s

with

art icular

mphas i s

n

hei r

oint

nd

oundat ion

odel ing

apabil i t ies .

lso,

et

unpubl i shedmall-scaleodela ta eveloped

y

heorpsf ngineersnhe950 ' ss

documen tedandanalyzedusing

moderntechniques .

closed-formsolution

fo r

rigidpavemen t

response

basedupon

th e

Weste rgaardas sumpt ionscoupled

with

an

elast icconnect ionat

th e

joint

is

presented

and

discussed .

P R O B L E M

S T A T E M E N T

T H ER IG IDP A V E M E N T

S Y S T E M .

A

rigid

pave me n t

sys tem

consists

of

a

n umbe r

ofrelat ively

thinPort land

ce me n t

concre te

slabs ,

finite

in

length

and

wid th ,

over

one

or

more

foundat ion

layers.igure h o w sa

representat ion

of

ypical

igid

ave me n t

ys tem

ubjected

o

tatic

oading.

hen

lab-on-grade

s

subjected

o

heeload,

t

evelops

endingt resses

ndistributes

heoadverhe

foundat ion.

owever ,he

esponse

f

hese

inite

labs

s

ontrolled

y

oint

r

dge

discontinuities.

y

heir ature,joints re

t ructurally eakening

omponen t s

fth e

ys tem.

Thus ,he

response

nd

effectiveness

f

joints

reprimary

concerns

nrigidpave me n tanalys is

anddes ign.

8/10/2019 Ada 325108

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1 .

ire

Pressure

2.

earing

Stresses

Caused

by

Tire

3.

lexural

Stresses

(Compression)

4.

lexural

Stresses

(Tension)

5 .

tresses

atthe

Slab-BaseInterface

6.

ertical

andHorizontal

Stresses

(Base)

7.

ertical

and

Horizontal

Stresses(Subbase)

8 .

ertical

andHorizontal

Stresses

(Subgrade)

9.

tresses

atConcrete-Dowel

Interface

F I G U R E

1 .

YP I CA L

RIGIDP A V E M E N T

S YS TE M

( A F T E RL A R R A L D E

A N D

C H E N ,

985)

Figure

2

presentsaconceptualview

of

the

mechani sm

ofload

t ransfer

at

a

joint .

he

concept

of

loadt ransferisverysimple:

tressesanddeflectionsinaloadedslab

are

reducedif

aport ionof

th e

load

istransferred

to

an

adjacentslab.oadt ransfer

isveryimpor t an tandfundamenta lto

th e

F A A

rigidpavemen t

des ign

procedure.oad

t ransfer

is

a

complexmechan i smtha t

can

vary

with

concre te

avemen tempera tu re ,ge,oistureontent ,onstruct ionuali ty,

agni tudend

repetit ion

ofload,and

type

of

joint

(Ha mmo ns ,Pi t tman,

and

Ma t h ews ,

995).

8/10/2019 Ada 325108

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Loaded

Edge

Deflection

Wheel

Load

Unloaded

Edge

Deflection

PC C

Slab

.

oaded

0

oa

Base

Course

Unloaded

Edge

Stress

C T

Subgrade

o

/V/XsW

F I G U R E

2 .

O N C E P TO F L O A D

T R A N S F E R

W h e n

a

joint

is

capable

of

t ransferring

load,stat icsdictatethat

th etotalload

(P )

m u s tbeequa lto

th e

su m

of

thatport ion

of th eload

supportedbyth eloadedslab

(P

L

)and

th e

port ion

of th e

load

suppor t ed

by

th e

unloaded

slab

(Py),

i.e.,

PiP u =

(1 )

Load

m ay

e

ransferred

cross joint

y

hear

rbend ing

moment s .owever ,t

as

een

common ly

rguedhat

oad

ransfer

s

rimarily

aused

y ert icalhear.

n

i ther

ase

he

fol lowingrelationship

applies:

G

L

5 u

=.

(2)

wherea

L

is

th emaxi mum

bend ing

stress

inth e

loadedslab,

u

is

th e

m a x i m u mbendingstress

in

th e

djacent

nloaded

lab,

nd

f

ishe

maxi mum

endingt ress

or

he

ree-edge

oading

condi t ion.

Becausemaxi mum

slab

deflect ions

are

also

directly

proport ional

to

applied

load

under

th e

stated

condi t ions ,

it

fo l lows

fromequat ion tha t

W

L

Wu

=

W

f

(3 )

wherew

L

is

th emaxi mumedge

deflection

of

th e

loadedslab,

w u

is

th emaxi mumedge

deflection

ofth eadjacentunloaded

slab ,

and

W f

is

th e

ma x i mu m

edge

deflection

wi th

no

joint.

L O A D

T R A N S F E R

D E F I N I T I O N S .

Deflect ionload

transfer

efficiency(LTE)is

definedasth erat io

of

th e

deflection

of

th eun loaded

slab

( w u )

to

th e

deflection

ofth e

loaded

slab

(w

L

)

as

fol lows:

LTE*

=

Wu

WL

(4 )

8/10/2019 Ada 325108

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Similar ly,

t ress

load

transfer

efficiency

LT E

a

)

is efinedasherat ioof

th e

edge

t ress

nth e

un loaded

slab

to

edge

stress

in

th e

loaded

slab

as

fol lows:

LTE

C

=

o .

(5 )

L o a d

t ransfer

LT )

nhe A Arigidpavement

esign

procedures

efined

s

hat ortion

he

edge

stress

thatis

carried

b y

th e

adjacentunloaded

slab:

LT

=

o

V/

a