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Load Models for Fatigue DesignLoad Models for Fatigue Designof Highway Bridgesof Highway Bridges

CE671CE671Lecture 28Lecture 28

Design vs. EvaluationDesign vs. Evaluation

We will consider:We will consider:

Loads for fatigue designLoads for fatigue design

Response of bridge elementsResponse of bridge elements

How many cycles per passageHow many cycles per passage

Must Distinguish between Loads forMust Distinguish between Loads for

Fatigue vs. Other LimitFatigue vs. Other Limit--statesstates

Limit State:Limit State:Condition beyond which the bridge orCondition beyond which the bridge or

component ceases to satisfy the provisionscomponent ceases to satisfy the provisions

for which it was designedfor which it was designed

(from AASHTO LRFD)(from AASHTO LRFD)

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Common LimitCommon Limit--statesstates

Service limitService limit--statestate

Relates to stress, deformation, cracking,Relates to stress, deformation, cracking,

relies somewhat on experiencerelies somewhat on experience

Strength limitStrength limit--statestate

Relates strength & stabilityRelates strength & stability

Extensive distress & structural damageExtensive distress & structural damage

Structural integrity is maintainedStructural integrity is maintained

Common LimitCommon Limit--statesstates

Extreme eventExtreme event

Unique occurrenceUnique occurrence

collision, flood, earthquakecollision, flood, earthquake

Ensure survival of structureEnsure survival of structure

Fatigue and fracture limitFatigue and fracture limit--statestate

Limit cracking under repeated loadsLimit cracking under repeated loads

Prevent fracturePrevent fracture

Clearly, structures areClearly, structures are

subjected to many differentsubjected to many different

types of loads for each limittypes of loads for each limit--

statestate

This limit-state vs. .

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This limit-state !

But itBut its still standing!!s still standing!!

Fatigue LimitFatigue Limit--statestate

Considers stresses induced byConsiders stresses induced by

repeated loadsrepeated loadsmillions of cyclesmillions of cycles

Maximum loading conditions notMaximum loading conditions notappropriateappropriate

e.g., permit loads in all lanese.g., permit loads in all lanes

However, fatigue damageHowever, fatigue damage isis the resultthe result

of the entire variable load spectrumof the entire variable load spectrum

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Design LoadsDesign Loads

for any Limitfor any Limit--statestate

Desirable to use a minimumDesirable to use a minimum

number of different trucksnumber of different trucks

However, design vehicles shouldHowever, design vehicles should

produce reasonably similar effectsproduce reasonably similar effects

as real trucksas real trucks

Loads forLoads for

Fatigue LimitFatigue Limit--statestate

Desirable to use one type of vehicleDesirable to use one type of vehicle

This results in constant amplitude fatigueThis results in constant amplitude fatigue

Easiest to work withEasiest to work with

Vehicle must produce the sameVehicle must produce the sameequivalent fatigue damage as entireequivalent fatigue damage as entirevariable live load spectrumvariable live load spectrum

Development ofDevelopment of

Fatigue TruckFatigue Truck

Developed based on:Developed based on:

WIM studiesWIM studies

FHWA loadometer dataFHWA loadometer dataField testing of inField testing of in--service bridgesservice bridges

Led to truck proposed in NCHRPLed to truck proposed in NCHRP

Report 299Report 299

Developed for longitudinal and transverseDeveloped for longitudinal and transverse

members of girder bridgesmembers of girder bridges

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Comparison of Gross Vehicle Weight DistributionComparison of Gross Vehicle Weight Distribution

from 1970 FHWA Nationwide Loadometer Surveyfrom 1970 FHWA Nationwide Loadometer Survey

with Bridge Weighwith Bridge Weigh--inin--Motion SurveyMotion Survey

Fatigue TruckFatigue Truck

Truck which produces equivalentTruck which produces equivalent

fatigue damage as variable amplitudefatigue damage as variable amplitude

spectrumspectrum

Does not included panel, pickDoes not included panel, pick--up, & otherup, & other

22--axle 4axle 4--wheel vehicleswheel vehicles

GVW > 20 kipsGVW > 20 kips

These contribute little to fatigue damageThese contribute little to fatigue damage

AASHTO LRFDAASHTO LRFD

Fatigue TruckFatigue Truck(Equivalent to HS15 w/ fixed trailer length)(Equivalent to HS15 w/ fixed trailer length)

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How should the FatigueHow should the Fatigue

Truck be applied?Truck be applied?

Depends on bridge and elementDepends on bridge and element

Most short to medium span bridgesMost short to medium span bridgesdamage caused by individual trucksdamage caused by individual trucks

One primary cycle produced per truckOne primary cycle produced per truck

Use only a single truck for fatigueUse only a single truck for fatigue

Multiple presence can be consideredMultiple presence can be consideredif necessaryif necessary

Time (sec)

Stress(ksi)

Bottom chord of continuous deck truss

0.9 ksi

(594 ft. span)

Primary Member

Time (sec)

Stress(ksi)

Diagonal of continuous deck truss

1.1 ksi

(594 ft. span)

Primary Member

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Time (sec)

Stress(ksi)

Bottom flange of plate girder

1.1 ksi

(end span of 4 span unit

125 ft. span)

Primary Member

Transverse Member -Floorbeam

Arch BridgesArch Bridges

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Tie Girder Response

Tie Girder Response

Influence ofInfluence of

Multiple PresenceMultiple Presence

Multiple presenceMultiple presencemore than one truck onmore than one truck on

the bridgethe bridge

What is the effect on damage?What is the effect on damage?

Influence is typically small in terms ofInfluence is typically small in terms of

cumulative fatigue damagecumulative fatigue damage

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Influence ofInfluence of

Multiple PresenceMultiple Presence

ExampleExampletwo trucks sidetwo trucks side--byby--sideside Assume ADTT of 10%Assume ADTT of 10%

Assume trucks sideAssume trucks side--byby--side 10% of ADTTside 10% of ADTT

Assume static stress increases by 80% due toAssume static stress increases by 80% due to

adjacent truckadjacent truck

Influence of Multiple TrucksInfluence of Multiple Trucks

What is effect on damage?What is effect on damage?

Use MinerUse Miners Rule to calculate equivalents Rule to calculate equivalentdamagedamage

SSreffreff = [(0.1)(1.8S= [(0.1)(1.8Srr))33 + 0.9(S+ 0.9(Srr))

33]]1/31/3 = 1.14S= 1.14Srr

SSreffreff increased by less than 15% due toincreased by less than 15% due to

presence of second truckpresence of second truck

Two Trucks One Truck

Special ConsiderationsSpecial Considerations

for Deck Elementsfor Deck Elements

Fatigue truck developed to produceFatigue truck developed to produce

cumulative damage in main memberscumulative damage in main membersAxles of fatigue truck actually represent aAxles of fatigue truck actually represent a

tandem for simplicitytandem for simplicity

This simplification is not appropriate forThis simplification is not appropriate for

deck elementsdeck elements

Orthotropic decksOrthotropic decks

Modular bridge expansion jointsModular bridge expansion joints

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Five Axle Truck IdealizedFive Axle Truck Idealized

as Three Axle Truckas Three Axle Truck

P PR R

R2 P

P PR R

R2 P

Simplified

Actual

Response of Deck ElementsResponse of Deck Elements(Steel Orthotropic Closed Rib Deck)(Steel Orthotropic Closed Rib Deck)

Deck Plate

RibFloorbeam

DiaphragmCritical DetailCritical Detail

HSHS Series TruckSeries Truck(Short Trailer)(Short Trailer)

MPa

Seconds

CH27 Diaph.

CH89 on

Deck

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HSHS Series truckSeries truck(Long Trailer)(Long Trailer)

CH27

Diaph.

CH89 on Deck

Sec

MPa

Summary of Fatigue DesignSummary of Fatigue Design

Summary of Fatigue DesignSummary of Fatigue Design

FatigueFatigue designdesign

Usually concerned with 75Usually concerned with 75--100 yr. life100 yr. life

Desire very low probability of crackingDesire very low probability of crackingUse lowerbound curvesUse lowerbound curves

May wish include traffic growthMay wish include traffic growthIncreases in ADTTIncreases in ADTT

Increases in GVWIncreases in GVW

Load spectrum is conservatively assumedLoad spectrum is conservatively assumed

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QuestionsQuestions ??