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Session 4ession 4
Loads for Fatigue Designoads for Fatigue Design
orr
What is the AASHTOhat is the AASHTO
Fatigue Truck?atigue Truck?
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Must Distinguish between Loads forust Distinguish between Loads for
Fatigue vs. Other Limitatigue vs. Other Limit-statestates
Limit State:Limit State:
“ “ Condition beyond which the bridge or Condition beyond which the bridge or
component ceases to satisfy the provisions component ceases to satisfy the provisions
for which it was designed for which it was designed ” ”
(from AASHTO LRFD)(from AASHTO LRFD)
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Common Limitommon Limit-statestates
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
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Common Limitommon Limit-statestates
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
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Clearly, structures are subjected toClearly, structures are subjected to
many different types of loads for many different types of loads for
each limiteach limit--statestate
This limit-state vs. …….
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This limit-state !
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But itut it ’s still standing!!still standing!!
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Fatigue Limitatigue Limit-statetate
Considers stresses induced byConsiders stresses induced byrepeated loadsrepeated loads……millions of cycles millions of cycles
Maximum loading conditions notMaximum loading conditions not
appropriateappropriate 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 Loadsesign Loadsfor any Limitor any Limit-statetate
Desirable to use a minimumDesirable to use a minimum
number of different trucksnumber of different trucks Design vehicles should produceDesign vehicles should produce
reasonably similar effects asreasonably similar effects as
real trucksreal trucks
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Load foroad for
Fatigue Limitatigue Limit-statetate
Desirable to use one vehicleDesirable to use one 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 same
equivalent fatigue damage as entireequivalent fatigue damage as entire
variable live load spectrumvariable live load spectrum
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Development ofevelopment of
“Fatigue Truckatigue Truck”
Developed based on:Developed based on:
WIM studiesWIM studies
FHWA loadometer dataFHWA loadometer data Field testing of inField testing of in--service bridgesservice bridges
Led to truck proposed in NCHRP Report 299Led to truck proposed in NCHRP Report 299
Developed for longitudinal and transverse membersDeveloped for longitudinal and transverse membersof girder bridgesof girder bridges
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Objective of the Fatigue Truck is Representbjective of the Fatigue Truck is Represent
Equivalent Cumulative Damagequivalent Cumulative Damage?
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AASHTO Fatigue TruckASHTO Fatigue Truck
Truck which produces equivalentTruck which produces equivalentfatigue damage as variable amplitudefatigue damage as variable amplitude
spectrumspectrum
Does not included panel, pickDoes not included panel, pick--up, & other up, & other
22--axle 4axle 4--wheel vehicleswheel vehicles
GVW > 20 kipsGVW > 20 kips
These contribute little to fatigue damageThese contribute little to fatigue damage
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AASHTOASHTO
“Fatigue Truckatigue Truck”(Equivalent to HS15 w/ fixed trailer length)Equivalent to HS15 w/ fixed trailer length)
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AASHTO LRFDASHTO LRFD
LoadingLoading
Damage produced byDamage produced by ““Fatigue Truck Fatigue Truck ””
Equivalent to HS15 (54 kip GVW)Equivalent to HS15 (54 kip GVW) Constant axle spacingConstant axle spacing
Produces theProduces the ““Effective Stress RangeEffective Stress Range””
Developed from WIM DataDeveloped from WIM Data NCHRP 299NCHRP 299
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Two Approaches to Designwo Approaches to Design
Finite life if:Finite life if: SSr r from HS15 > CAFL / 2.0from HS15 > CAFL / 2.0
Defined number of cycles or yearsDefined number of cycles or years
Infinite life if:Infinite life if:
SSr r from HS15 < CAFL / 2.0from HS15 < CAFL / 2.0
Unlimited cycles requiredUnlimited cycles required
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Finite Lifeinite Life(Design for Specific Number of Cycles)Design for Specific Number of Cycles)
Must forecast expected spectrumMust forecast expected spectrum
Stress and # cyclesStress and # cycles
HS15 truck yields effective stress rangeHS15 truck yields effective stress range Use it just like a constant amplitudeUse it just like a constant amplitude
stress range with the Sstress range with the S--N curve for N curve for
number of cycles desirednumber of cycles desired Finite Finite - - life only useful if ADTT less than life only useful if ADTT less than
550 (gives 10 million cycles in 50 years) 550 (gives 10 million cycles in 50 years)
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Infinite Lifenfinite Life(Design Below Threshold)Design Below Threshold)
Design so thatDesign so that fatigue limitfatigue limit--statestate
stress rangestress range is below the constantis below the constant--
amplitude fatigue limit (CAFL)amplitude fatigue limit (CAFL)
Cracks will not propagate significantlyCracks will not propagate significantly
in the life of the structurein the life of the structure
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But, it is well known that there are trucks heavierut, it is well known that there are trucks heavier
than the 54 kip fatigue truckhan the 54 kip fatigue truck…...
Note many trucks areheavier than fatigue truck
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Fatigue Limitatigue Limit-Statetate-Loadoad(AASHTO LRFD)AASHTO LRFD)
HS15 results inHS15 results in effectiveeffective stress rangestress range(i.e., equivalent cumulative damage)(i.e., equivalent cumulative damage)
Recognized that many trucks in theRecognized that many trucks in the
spectrum are heavier than HS15 andspectrum are heavier than HS15 andcan produce damagecan produce damage
Fatigue limitFatigue limit--state load defined as:state load defined as: Upper bound load with minimum frequencyUpper bound load with minimum frequency
sufficient to produce fatigue damagesufficient to produce fatigue damage Expressed asExpressed as XX x HS15 = HSXXx HS15 = HSXX
XX > 1.0> 1.0
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Development of theevelopment of the
Fatigue Limitatigue Limit-State Loadtate Load
Based on testing (NCHRP Report 354)Based on testing (NCHRP Report 354) 0.05% exceeded CAFL, cracks observed0.05% exceeded CAFL, cracks observed
0.001% exceeded the CAFL, no cracks0.001% exceeded the CAFL, no cracks
Concluded infinite life if fewer than 0.01%Concluded infinite life if fewer than 0.01%exceed CAFL (exceed CAFL (1 in 10,000 1 in 10,000 ))
Fatigue limitFatigue limit--state stress range is stress rangestate stress range is stress rangewith 0.01% exceedencewith 0.01% exceedence
‘‘XX’’ can now be definedcan now be defined
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GVW
%
O c c u r r e n c
e
How does this relate toow does this relate to
live load spectrum?ive load spectrum?
Sreff Srmax
0.01% prob. ofexceedence
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Magnitude ofagnitude ofFatigue Limitatigue Limit-State Loadtate Load
WIM data suggest that the GVW of 0.01%WIM data suggest that the GVW of 0.01%exceedence truck is closer to 150 kipsexceedence truck is closer to 150 kips
3.0 x HS15 or HS45 (162 kips)3.0 x HS15 or HS45 (162 kips)
- - However However - -
AASHTO fatigue limit AASHTO fatigue limit--state load range is:state load range is:
2 x HS15 or HS30 (108 kips)2 x HS15 or HS30 (108 kips)
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GVW
%
O c c u r r e n c
e
How does the AASHTO LRFDow does the AASHTO LRFDfatigue limitatigue limit-state load relate totate load relate to
live load spectrum?ive load spectrum?
Sreff Srmax
0.01% prob. ofexceedence
Srmax
(LRFD)
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Why the discrepancy?hy the discrepancy?
Actual stress ranges in primary members Actual stress ranges in primary members are often much less than predicted using are often much less than predicted using
conservative design equations conservative design equations
LRFD calibrated to experience and LRFD calibrated to experience and
observed cracking observed cracking
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AASHTO LRFD SpecificationASHTO LRFD Specification(Infinite life checknfinite life check)
Compares calculated effective stressCompares calculated effective stressrange to CAFL / 2range to CAFL / 2
Factor of 2 accounts for SFactor of 2 accounts for Srmaxrmax/S/Sreff reff (i.e., X(i.e., X = 2.0)= 2.0) Intended to account for increase in load or loadIntended to account for increase in load or load
effects (i.e., stress range)effects (i.e., stress range)
Implies that the resistance is reducedImplies that the resistance is reduced
Uses fatigue load factor of 0.75 on HS20Uses fatigue load factor of 0.75 on HS20 0.75 x HS20 = HS150.75 x HS20 = HS15
Impact factor of 15%Impact factor of 15%
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AASHTO LRFD SpecificationASHTO LRFD Specification(Finite life checkinite life check)
Compares calculated effective stressCompares calculated effective stress
range to Srange to S--N curveN curve
Fatigue load factor of 0.75 on HS20Fatigue load factor of 0.75 on HS20
0.75 x HS20 = HS150.75 x HS20 = HS15
Impact factor of 15%Impact factor of 15%
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AASHTO LRFD SpecificationASHTO LRFD Specification(Finite life checkinite life check)
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Equation for Fatigue Designquation for Fatigue Design
TH nF
N
AF )(
2
1)(
3
1
Δ≥⎟ ⎠
⎞⎜⎝
⎛ =Δ
Existing Eq.Existing Eq.
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How should the Fatigueow should the FatigueTruck be applied?ruck be applied?
Depends on bridge and elementDepends on bridge and element
Most short to medium span bridges damageMost short to medium span bridges damage
caused by individual truckscaused 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
Single lane distribution factorsSingle lane distribution factors
Multiple presence can be considered if Multiple presence can be considered if
necessarynecessary
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Influence ofnfluence of
Multiple Presenceultiple Presence
Influence is typically small in terms of cumulativeInfluence is typically small in terms of cumulative
fatigue damagefatigue damage
ExampleExample – – two trucks sidetwo trucks side--byby--sideside
Assume ADTT of 10% Assume ADTT of 10% Assume trucks side Assume trucks side--byby--side 10% of ADTTside 10% of ADTT
Assume static stress increases by 80% due to Assume static stress increases by 80% due to
adjacent truckadjacent truck
What is the effect on damage?What is the effect on damage?
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Influence of Multiple Trucksnfluence of Multiple Trucks
What is effect on damage?What is effect on damage? Use Miner Use Miner ’’s Rule to calculate equivalents Rule to calculate equivalent
damagedamage
SSreff reff = [(0.1)(1.8S= [(0.1)(1.8Sr r ))33 + 0.9(S+ 0.9(Sr r ))
33]]1/31/3 = 1.14S= 1.14Sr r
SSreff reff increased by less than 15% due toincreased by less than 15% due topresence of second truckpresence of second truck
Two Trucks One Truck
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Special Considerationspecial Considerations
for Deck Elementsor Deck Elements
Fatigue truck developed to produceFatigue truck developed to produce
cumulative damage in main memberscumulative damage in main members
Axles of fatigue truck actually represent a Axles of fatigue truck actually represent atandem for simplicitytandem for simplicity
This simplification is not appropriate for This 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 Idealizedive Axle Truck Idealized
as Three Axle Trucks Three Axle Truck
P PR R
R2 P
P PR R
R2 P
Simplified
Actual
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Questionsuestions ??