AASHTO

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AASHTO LRFD OF STEEL BEAM BRIDGES Fatigue and
Fracture
Special course on of AASHTO LRFD
Specifications Workshop 4 Day 2
by, Amit H. Varma
May 2, 2003 Michigan Department of
Transportation Conference Room
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INTRODUCTION

• Structural components and details of steel beam
  bridges are susceptible to localized failures
  (cracking) due to fatigue and brittle fracture.
• Fatigue crack propagation usually precedes
  brittle fracture with a few exceptions.
• Fatigue is caused by the stress range (Sr)
  experienced by the component / detail due to
  applied cyclic live loading combined with
• Stress concentrations at weld toes in poorly
  designed details
• Internal defects and heat affected zones in
  welded connections
• Detail configurations that simulate a large
  initial pre-crack
• Out-of-plane distortion of girder web gaps due to
  unaccounted secondary lateral forces.
• Careful site inspections indicate that several
  components and details of the same bridge may
  develop localized fatigue distress (cracks).

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INTRODUCTIONSome examples of fatigue prone
details
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FUNDAMENTAL FATIGUE OF METALS

• Metal fatigue is a well-known phenomenon
• Wohler - German engineer fatigue of railroad
  car axles
• Alternating cyclic stresses (even in the elastic
  range) cause fatigue failure in metal components
  or details.
• Fatigue crack initiation
• Fatigue crack propagation
• Brittle fracture
• The cyclic stress range causes the initiation of
  fatigue cracks, fatigue crack propagation, and
  eventually brittle fracture of the cracked
  component.
• Fundamental fatigue behavior of a metal is
  expressed in terms of a constant amplitude cyclic
  stress range vs. number of cycles to failure (Sr
  - N) curve.

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FUNDAMENTAL FATIGUE OF METALS

• The Sr N curve for a metal can be developed by
  conducting four-point rotating bending tests
  according to ASTM Standards.
• Test specimen is an unnotched mirror-polished
  smooth cylindrical bar 0.25 in. in diameter
• Sr N curve is a straight line in log-log
  coordinates
• ENDURANCE LIMIT Se below which infinite fatigue
  life

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Standard rotating bending fatigue test
Stress range vs. Number of cycles (Sr N) to
failure.
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FATIGUE CRACK INITIATION

• Structural components and welded details have
  inherent flaws or defects, which serve as initial
  cracks.
• These initial cracks propagate to larger sizes
  and eventually fracture under cyclic fatigue
  loading.
• Smooth structural components with notches or
  discontinuities
• Strain concentrations and localized plastic
  strains occur at the notches / discontinuities
• Alternating cyclic plastic strains cause fatigue
  crack initiation.
• Fundamental constant amplitude strain range (De)
  versus number of reversals (Nf) to crack
  initiation for a metal experimentally
• These De Nf curves can be used to predict crack
  initiation in smooth components with notches or
  geometric discontinuities.
• Not of much use for bridge structural components
  and details, which have inherent flaws or defect
  serving as initial cracks.

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FATIGUE CRACK INITIATION

• Total strain elastic strain plastic strain.
• When elastic strains dominate, behavior is
  similar to the Sr N behavior of metal.
• When plastic strains dominate, the slope of the
  De Nf curve changes becomes more steep
  indicating reduced fatigue life
• Usually occurs for 1 lt Nf lt 1000 called low
  cycle fatigue

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Fatigue crack initiation at notches or
discontinuities
Strain amplitude (De/2) vs. number of reversals
(Nf) to failure
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FATIGUE CRACK PROPAGATION

• Initiated cracks propagate to larger sizes under
  cyclic loading
• Stable fatigue crack propagation or crack growth
• Fatigue cracks become large cause unstable
  crack growth Fracture
• Propagation of fatigue cracks due to cyclic
  loading can be predicted and understood using
  fundamentals of fracture mechanics.
• Fracture mechanics relates the stress-field in
  the vicinity of a crack tip to the nominal
  stress, size, shape, orientation of the crack,
  and material properties.
• Consider the stress state in the vicinity of the
  crack tip in a structure subjected to tensile
  stresses normal to the plane of the crack
• magnitude described by the stress intensity
  factor KI , which implicitly accounts for the
  effects of stress, crack size and geometry, and
  structure

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Stress state in the vicinity of a crack tip
loaded in tension
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FATIGUE CRACK PROPAGATION

• KI can be calculated analytically for various
  structural configurations, crack geometries, and
  loadings
• For all cases KI C s
• KI has units of ksi
• Unstable crack growth occurs when KI exceeds
  KIc, which is the critical stress intensity
  factor for the material
• KIc represents the fundamental fracture
  toughness of the material, it ability to crack
  without brittle fracture
• ASTM E399 to determine KIc
  experimentally
• Stable crack propagation occurs under cyclic
  loading if KI lt KIc

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FATIGUE CRACK PROPAGATION

• Stable crack propagation rate Paris Law
• where, a flaw or crack size N number of
  fatigue cycles
• A and m are material constants
• Fatigue crack propagation is linear with respect
  to (DKI) in log-log coordinates

Material A m
Martensitic steels 0.66 x10-8 3.25
Ferrite-Perlite steels 3.6 x 10-10 3.0
Austenitic steels 3.0 x 10-10 3.25
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TOTAL FATIGUE LIFE

• The total fatigue life of a component is equal to
  the sum of the crack initiation life and the
  crack propagation to fracture life
• N Ni Np
• For bridge components and details, initial crack
  or defects are present in the form of flaws or
  defects
• Crack initiation life is negligible
• Crack propagation life dominates (N Nf)
• If the initial flaw size is ai and the final flaw
  size at fracture is af
• Therefore
• Let A1 Therefore
• And

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FATIGUE LIFE

• where, m 3 for
  ferrite-perlite steels
• The constant A1 depends significantly on the
  value of the initial flaw or defect ai, which
  cannot be estimated easily or accurately
• Therefore, A1 is calibrated to experimental
  results for various structural components and
  details
• This equation is identical to the one recommended
  by AASHTO for fatigue life prediction and design
• Experimental results indicate the existence of an
  endurance limit (Ds)TH below which fatigue crack
  propagation does not occur

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FATIGUE DESIGN PROVISIONS

• AASHTO provisions (2000) are based on the load
  and resistance factored design (LRFD) philosophy
• Current LRFD provisions recommend that fatigue
  should be categorized as load induced fatigue
  or distortion-induced fatigue
• Previous standard specification focused on
  load-induced fatigue only
• Distortion induced fatigue caused by unaccounted
  cyclic stresses produced by distortion or
  out-of-plane deflections that induced by
  secondary members (diaphragms or lateral bracing
  frames)
• Load induced fatigue quantitative analysis
• Distortion induced fatigue qualitative only
  detailing practices

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FATIGUE LOADING

• Fatigue loading for design consists of two parts,
  namely, the applied cyclic stress range (Df) and
  the frequency of occurrence or the number of
  fatigue cycles.
• The live-load stress range is used as the
  relevant force effect for designing bridge
  details for fatigue.
• Research has shown that the total stress is not
  relevant for welded details
• Residual stresses are not considered explicitly
  for fatigue design
• Using the stress range as the design parameter
  implicitly includes the effects of residual
  stresses on welded details
• Fatigue design load vehicular live load (LL)
  due to fatigue design truck and the corresponding
  impact factor (IM) and centrifugal force (CE)
• Q
• where, hi load modifiers, gi load factor
  0.75 and
• The load factor of 0.75 reflects a load level
  representative of the truck population with large
  number of repetitive cycles and fatigue effects.

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FATIGUE DESIGN TRUCK

• Steel bridges are designed for the live-load (LL)
  stress range caused by the fatigue design truck,
  which has a set distance of 30 ft. between the 32
  kip loads, and is slightly different than the
  design truck
• The live load stress due to the passage of the
  fatigue load is approx. one-half of the heaviest
  truck expected to cross the bridge in 75 years.
• Only one fatigue truck is considered for design
  irrespective of the number of design lanes.
• No multiple presence of live load and no lane
  loads are considered.
• Dynamic load allowance (IM). The live load stress
  caused by the fatigue design truck is to be
  increased by the dynamic load allowance factor of
  15

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FATIGUE LOADING

• The frequency of occurrence of the fatigue design
  load is estimated as the single-lane annual daily
  truck traffic (ADTT)SL
• In the absence of better information ADTT)SL can
  be estimated as
• (ADTT)SL p x ADTT
• ADTT number of trucks per day in one direction
  averaged over the design life
• ADTT can be estimated as the limiting value of
  average daily traffic multiplied by the fraction
  of trucks in the traffic

Number of Lanes available to Trucks p
1 1.00
2 0.85
3 or more 0.80
Highway Fraction of trucks
Rural Interstate 0.20
Urban Interstate / other rural 0.15
Other urban 0.10
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FATIGUE LOADING

• Fatigue design life 75 years
• Total number of fatigue cycles over the design
  life
• N (365) (75) n (ADTTSL)
• Where, n number of stress range cycles per
  truck passage
• For continuous spans, a distance equal to
  one-tenth of the span either side of the interior
  support ? near the support
• n 5 for cantilever girders due to the
  vibrations as the truck leave

Span length gt 40 ft. Span length lt 40 ft.
Simple span girder 1.0 2.0
Continuous girder near interior support 1.5 2.0
Continuous girder elsewhere 1.0 2.0
Trusses 1.0 1.0
Transverse members Span gt 20 ft. ? 1.0 Span lt 20 ft. ? 2.0
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FATIGUE DESIGN CRITERIA

• Fatigue design criteria for load-induced fatigue
  in a component
• h g (Df) j (DF)n
• g load factor 0.75 and j 1.0 for the
  fatigue limit state
• (Df) maximum stress range (LL, IM, CE) due to
  the fatigue truck
• (DF)n nominal fatigue resistance of the
  structural component or detail.
• The nominal fatigue resistance for structural
  components / details
• (DF)n (DF)TH
• where N (365)(75) n (ADTTSL) number of cycles
  over design life
• (DF)TH is the constant amplitude fatigue
  threshold in ksi
• Commonly existing components and details
  categorized into detail categories A .. E
• Values of A and (DF)TH are specified for these
  detail categories

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FATIGUE RESISTANCE
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Stress range vs. number of cycles for various
detail categories
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FATIGUE RESISTANCE

• (DF)TH is the constant amplitude fatigue
  threshold below which the component or detail
  will theoretically have infinite fatigue life.
• (DF)TH values correspond to the allowable fatigue
  stress range specified by the previous AASHTO
  standard specifications for more than 2 million
  cycles on a redundant load path structure
• Why is (DF)TH multiplied by ½ ?
• to account for the possibility of the heaviest
  truck in 75 years being double the weight of the
  fatigue truck used in calculating stress range
• Logically, this effect should be present on the
  load side (Df) instead of the resistance side
  (DF)n
• When (DF)TH controls the resistance, the LRFD
  equation becomes
• ½ (DF)TH g (Df) or (DF)TH 2 g
  (Df)
• Thus, the effect of double-heavy trucks on the
  design for theoretically infinite fatigue life is
  accounted for by multiplying the fatigue
  threshold (DF)TH by ½ instead of multiplying the
  applied stress (Df) range by 2

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COMPARISON WITH AASHTO Standard

• In the previous AASHTO standard specifications,
  allowable stress ranges were specified for both
  redundant and non-redundant member.
• The allowable for non-redundant members were
  arbitrarily specified as 80 of those for
  redundant members due to more severe consequences
  of their failure.
• However, greater fracture toughness was also
  specified for non-redundant members.
• This double-penalty has been rectified in the
  LRFD specifications by maintaining only the
  requirement for greater fracture toughness for
  non-redundant members.
• The same fatigue resistance curves are applicable
  to both redundant and non-redundant members.      

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FATIGUE DETAIL CATEGORIES

• Structural components and details are grouped
  into eight detail categories according to their
  fatigue resistance
• A and B detail categories are for plain members
  and well-prepared welded connections in built-up
  members without attachments
• D and E detail categories are assigned to
  fillet-welded attachments and groove-welded
  attachments without adequate transition radius or
  with unequal plate thickness
• C detail category can apply to welded attachments
  with transition radius greater than 150 mm and
  proper grinding of welds.

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FATIGUE DETAIL CATEGORIES
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FATIGUE DETAIL CATEGORIES
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FATIGUE DETAIL CATEGORIES
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FATIGUE DETAIL CATEGORIES
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COVER PLATED DETAIL CATEGORY EFATIGUE CRACK
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FATIGUE CRACKING
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DISTORTION INDUCED FATIGUE

• Rigid load paths are required to prevent the
  development of significant secondary stresses.
• Transverse members should be connected
  appropriately to the longitudinal members
• Transverse connection plates should be welded or
  bolted to both the compression and tension
  flanges of the cross-section, where
• Connecting diaphragms or cross-frames are
  attached
• Internal or external diaphragms or cross-frames
  are attached
• Floor-beams are attached
• Corresponding connection should be designed for a
  force of 20 kips for straight, non-skewed bridges

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DISTORTION INDUCED FATIGUE

• Lateral connection plates should be attached to
  the flanges of the longitudinal member, otherwise
• Lateral connection plates attached to stiffened
  webs should be located at a distance of at least
  the flange width divided by two (bf /2) from the
  flange-web interface
• Connection plates attached to unstiffened webs
  must be located at a distance of at least 6.0 in.
  or bf /2 from the flange-web interface
• This will reduce out-of-plane distortions of the
  web-gap between the lateral connection plate and
  the flange-web interface to a tolerable value
• It will also move the connection plate closer to
  the neutral axis, thus reducing the impact of
  weld termination on fatigue strength

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DISTORTION INDUCED FATIGUE

• Lateral bracing members should be attached to
  lateral connection plates at a minimum distance
  of 4.0 in. from the web or any transverse
  stiffener.
• Reduce distortion-induced stresses in the gap in
  the lateral connection plate between the
  web/stiffener and the lateral bracing members
• If web stiffener is present at the same location
  at the lateral connection plate, then the plate
  should be centered on the stiffener
• irrespective of whether the plate and stiffener
  are the same side of web
• If the lateral connection plate and the
  stiffeners are on the same side
• lateral connection plate should be attached to
  the stiffener
• stiffener should be continuous and attached to
  both flanges

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DISTORTION INDUCED FATIGUE FATIGUE CRACK
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FATIGUE DETAILS
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BRITTLE FRACTURE CONSIDERATIONS

• Materials in components and connections subjected
  to tensile stresses due to the Strength I
  limit-state must satisfy supplemental impact
  requirements
• These impact requirements relate to minimum
  energy absorbed in a Charpy V-notch test at a
  specified temperature
• Minimum service temperature at a bridge site
  determines the temperature zones for the Charpy
  V-notch requirements
• Michigan is zone 2

Minimum service temperature Temperature zone
18 C and above 1
19 C to 34 C 2
34 C to 51 C 3
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BRITTLE FRACTURE CONSIDERATIONS

• Fracture-critical member (FCM) is defined as a
  member with tensile stress whose failure is
  expected to cause the collapse of the bridge
• material in a FCM is required to exhibit greater
  toughness and ability to absorb more energy
  without fracture than a non-fracture critical
  member
• Charpy V-notch fracture toughness requirements
  for welded components are given below for
  different plate thicknesses and temperature
  zones.
• FCM values for absorbed energy are approximately
  50 greater than for non-FCM values at the same
  temperature

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FATIGUE OF SHEAR CONNECTORS

• Shear connectors are designed to achieve
  composite action between the steel beam and the
  concrete deck.
• The number of shear connectors should satisfy the
  strength and the fatigue limit states
• The pitch of shear connectors determined to
  satisfy fatigue
• p lt
• where, p pitch of shear connectors along
  longitudinal axis
• n number of shear connectors in a
  cross-section
• I moment of inertia of the short-term
  composite section
• Q Ay first moment of the transformed area of
  the slab about the
• n.a.of the short-term composite
  section
• Vr shear force range under LL IM determined
  for the fatigue limit
• Zr shear fatigue resistance of an individual
  shear connector
• The c-to-c pitch of shear connectors shall not
  exceed 24.0 in. and shall not be less than six
  stud diameters

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FATIGUE OF SHEAR CONNECTORS

• The fatigue resistance of an individual shear
  connector
• Zr a d2 gt 2.75 d2
• where a 34.5 2.28 Log N
• d diameter of stud and N number
  of cycles
• Stud shear connectors shall not be closer that
  4.0 d c-to-c transverse to the longitudinal axis
  of the supporting member
• The clear distance between the edge of the top
  flange and the edge of the nearest shear
  connector shall not be less than 1.0 in.
• The clear depth of concrete cover over the tops
  of the shear connectors should not be less than
  2.0 in.
• Shear connectors should penetrate at least 2.0
  in. into the deck

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FATIGUE DESIGN

• We have already designed a composite steel
  bridge. The span length of the bridge is 34 ft.
  The roadway width is 44 ft.
• The selected beam is W24 x 68 with a ½ in. thick
  cover plate narrower than the flange
• Clearly the bending moment is smaller at the ends
  and we can curtail the cover-plate to save some
  money. Lets see?
• The cover plate can be curtailed to the point
  where the moment is small enough for the steel
  beam alone to carry it
• But, the fatigue stress range at the end of the
  cover plate must be OK!

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Partial-length? Cover plate
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FATIGUE DESIGN

• Step I Estimate number of fatigue cycles
• Limiting value of annual daily traffic (ADT)
  20,000 per lane
• Highway bridge is on rural interstate with two
  truck lanes
• Therefore, annual daily TRUCK traffic (ADTT)
  0.20 x 20000 x 2 8000
• (ADTT)SL p x ADTT
• where p 0.85 for 2 lanes available to trucks
• (ADTT)SL 0.85 x 8000 6800
• Number of fatigue cycles N (365) (75) n
  (ADTTSL)
• N 186.15 x 106 x n
• For a simply supported girder with span length lt
  40 ft., n 2
• Therefore, N 372.3 x 106 cycles

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FATIGUE DESIGN

• Step II. Estimate the fatigue strength (DF)n
• (DF)n (DF)TH
• Cover plate (narrower than the flange) with
  flange thickness lt 0.8 in.
• Therefore, Category E detail
• From the table A 11.0 x 108 and (DF)TH 4.5
  ksi
• Therefore, (DF)n (11.0 x 108)/(3.723 x
  108)1/3 1.43 ksi,
• but (DF)n gt ½ (4.5) 2.25 ksi
• Therefore, the constant amplitude fatigue
  threshold controls
• The applied fatigue stress range (Df) must be lt
  2.25 ksi
• The cover-plate can be curtailed to the point
  where the stress range in the steel beam alone is
  less than 2.25 ksi !!!!!!

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