Effects Of Multiple Heat Straightening On The Structural

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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
                          INTRODUCTION
                 Some examples of fatigue prone details
Component / Detail         Initial Defect or           Fatigue Category
                           Condition
Cover-plated beams         Weld toe                    E
Flange gussets             Weld toe                    E or E
Eyebars                    Stress corrosion, Forge     Initial crack
                           laps
Longitudinal stiffener     Lack of fusion /poor weld   Large initial crack
Box girder corner welds    Transverse weld             Large-initial crack
Coped Members              Flame-cut notch             Initial defect
Pin Plates                 Frozen pins                 Out-of-plane
Transverse stiffeners      Shipping and handling       Out-of-plane
Diaphragm connection       Web gaps                    Out-of-plane
plates
Gusset plates              Lateral bracing             Out-of-plane
    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.
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
        Standard rotating bending fatigue test




Stress range vs. Number of cycles (Sr – N) to failure.
          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.
       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 < Nf < 1000 – called low cycle fatigue
                              Fatigue crack initiation at
                              notches or discontinuities




Strain amplitude (De/2) vs.
number of reversals (Nf) to
failure
         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
Stress state in the vicinity of a crack tip loaded in tension
       FATIGUE CRACK PROPAGATION
•   KI can be calculated analytically for various structural
    configurations, crack geometries, and loadings
     – For all cases KI = C s  a
     – KI has units of ksi in
•   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 < KIc
      FATIGUE CRACK PROPAGATION
                                                        A DK I 
                                                    da
•   Stable crack propagation rate – Paris’ Law
                                                                  m

                                                    dN
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
                      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
                                                   af                         Nf

                                                                    Ds   dN
     da                                                     da              m
                                                    
                          m
          A C Δσ  a               Therefore       ai A ( C  a )
                                                                   m
                                                                              Ni
     dN

                                                     A1  Ds    N 
                af
                         da                                    m
    Let A1 =                       Therefore
                ai   A( C  a )m
                                                 1
                                         A1    m
                     And           Ds   
                                        N
                       FATIGUE LIFE
                 1

• Ds   A1 
        
                 m
                       where, m = 3 for ferrite-perlite steels
           N
•   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
         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
                       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 = h i g i Qi
        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.
                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




                                       30’-0”
•   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%
                      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
                      Number of Lanes                p
                     available to Trucks
                               1                   1.00
                               2                   0.85
                           3 or more               0.80
    – ADTT can be estimated as the limiting value of average daily traffic
       multiplied by the fraction of trucks in the traffic
                       Highway                  Fraction of trucks

                    Rural Interstate                     0.20
             Urban Interstate / other rural              0.15
                     Other urban                         0.10
                      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

                                       Span length > 40 ft.    Span length < 40 ft.
           Simple span girder                  1.0                     2.0
     Continuous girder near interior           1.5                     2.0
               support
      Continuous girder elsewhere              1.0                     2.0
                Trusses                        1.0                     1.0
          Transverse members           Span > 20 ft.  1.0     Span < 20 ft.  2.0

    –    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
            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
                     1
                 A 31
    – (DF)n =       (DF)TH
                 N   2

    – 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
      FATIGUE RESISTANCE

  Detail Category       Constant A x   (DF)TH
                            108         (ksi)
         A                 250.0        24.0
         B                 120.0        16.0
        B’                  61.0        12.0
         C                  44.0        10.0
        C’                  44.0        12.0
         D                  22.0         7.0
         E                  11.0         4.5
        E’                  3.9          2.6
M164 (A 325) bolts in       17.1        31.0
   axial tension
M253 (A 490) bolts in       31.5        38.0
   axial tension
Stress – range vs. number of cycles for various detail categories
                   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
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.
         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.
FATIGUE DETAIL CATEGORIES
FATIGUE DETAIL CATEGORIES
FATIGUE DETAIL CATEGORIES
FATIGUE DETAIL CATEGORIES
            PLAIN MEMBERS                              BUILT-UP MEMBERS


           A    Rolled surface                         B
                                                              Cont. welded
           B    Painted weath.                        B’

           E      Eyebars                              E
                                                             Cover plates
                                                      E’


            Splice connection                                Fastened connections


Same sections               Unequal sections                  Bolted         Riveted


     B           Width transition     Transitions in width      B               D
                   2 ft. radius          or thick 1:2.5


                        B                      B
                                               B’
                                                         LONGITUDINALLY LOADED ATTACHMENTS

                         Groove welded                                                                                    Fillet welded


                  Detail length                           Transition radius              Detail length                            Transition radius


                               End welds                          End welds not                            End welds                      End welds not




                                                                                  Longer is worse
                    C                                                                               C
Longer is worse




                             ground smooth                        ground smooth                          ground smooth                    ground smooth
                    D                                                                               D
                              Larger radius better




                                                                                                          R > 2 in. not req
                    E                                B                  E                           E                         D                 E
                    E’                               C                                              E’                        E
                                                     D
                                                     E
                             TRANSVERSE LOADED ATTACHMENTS


                                                              Groove welded


                          Equal plate thick                                                        Unequal plate thickness


Weld rft. removed              Weld rft. not removed
                                    Rad. > 6.0 not help                  Weld rft. removed                      Weld rft. not removed




                                                                              R > 2 in. not bet.
                      B
  Larger rad.better




                                                          C                                         D                        E
                      C                                   D                                         E
                      D                                   E
                      E
                               TRANSVERSE LOADED ATTACHMENTS


                                              Fillet welded
                                   Welds parallel to direction of stress


Transition radius and                                      Transition radius and Welds
Welds ground smooth                                            not ground smooth
      Rad. > 2.0 in. no help




                               D                                            E
                               E



                                                    FILLET WELDED CONNECTION


                                                              Welds normal to stress     C at base metal


                                                      Welds normal or par. to stress      E in the weld
COVER PLATED DETAIL CATEGORY E
          FATIGUE CRACK
FATIGUE CRACKING
      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
         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
      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
DISTORTION INDUCED FATIGUE
       FATIGUE CRACK
FATIGUE DETAILS
    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
    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
    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
          n Zr I
       p<
          V sr Q
    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
      FATIGUE OF SHEAR CONNECTORS
•   The fatigue resistance of an individual shear connector
    – Zr = a d2 > 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
                       FATIGUE DESIGN




                                       30’-0”

                ?                                Partial-length? Cover plate
•   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!
                    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 < 40 ft., n = 2
    – Therefore, N = 372.3 x 106 cycles
                         FATIGUE DESIGN
Step II. Estimate the fatigue strength (DF)n
                     1

     – (DF)n =  A 
               
                    3
                         
                             1 (DF)
                                    TH
                 N         2

     – Cover plate (narrower than the flange) with flange thickness     < 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 > ½ (4.5) = 2.25 ksi
     – Therefore, the constant amplitude fatigue threshold controls
     – The applied fatigue stress range (Df) must be < 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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