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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 – PowerPoint PPT presentation

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Title: AASHTO


1
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
2
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).

3
INTRODUCTIONSome examples of fatigue prone
details
4
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.

5
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

6
Standard rotating bending fatigue test
Stress range vs. Number of cycles (Sr N) to
failure.
7
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.

8
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

9
Fatigue crack initiation at notches or
discontinuities
Strain amplitude (De/2) vs. number of reversals
(Nf) to failure
10
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

11
Stress state in the vicinity of a crack tip
loaded in tension
12
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

13
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
14
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

15
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

16
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

17
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.

18
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

19
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
20
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
21
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

22
FATIGUE RESISTANCE
23
Stress range vs. number of cycles for various
detail categories
24
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

25
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.      

26
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.

27
FATIGUE DETAIL CATEGORIES
28
FATIGUE DETAIL CATEGORIES
29
FATIGUE DETAIL CATEGORIES
30
FATIGUE DETAIL CATEGORIES
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COVER PLATED DETAIL CATEGORY EFATIGUE CRACK
43
FATIGUE CRACKING
44
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

45
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

46
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

47
DISTORTION INDUCED FATIGUE FATIGUE CRACK
48
FATIGUE DETAILS
49
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
50
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

53
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

54
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!

?
Partial-length? Cover plate
55
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

56
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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