Effects Of Multiple Heat Straightening On The Structural

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            Fatigue and Fracture

 Special course on of AASHTO LRFD Specifications
              Workshop # 4 – Day 2

                 Amit H. Varma

                   May 2, 2003
      Michigan Department of Transportation
                Conference Room
                 Some examples of fatigue prone details
Component / Detail         Initial Defect or           Fatigue Category
Cover-plated beams         Weld toe                    E
Flange gussets             Weld toe                    E or E
Eyebars                    Stress corrosion, Forge     Initial crack
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
Gusset plates              Lateral bracing             Out-of-plane
•   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.
•   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.
•   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.

•   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

•   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
•   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

•   Stable crack propagation occurs under
    cyclic loading if KI < KIc
                                                        A DK I 
•   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
                      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
          A C Δσ  a               Therefore       ai A ( C  a )

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

• Ds   A1 
        
                       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

•   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

•   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
      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 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
                 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

  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
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

  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.

•   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.
            PLAIN MEMBERS                              BUILT-UP MEMBERS

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

           E      Eyebars                              E
                                                             Cover plates

            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
                                                         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
                             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.
  Larger rad.better

                                                          C                                         D                        E
                      C                                   D                                         E
                      D                                   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

                                                    FILLET WELDED CONNECTION

                                                              Welds normal to stress     C at base metal

                                                      Welds normal or par. to stress      E in the weld
•   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

•   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
•   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

•   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
•   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
•   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
          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
•   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


                ?                                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

     – (DF)n =  A 
                             1 (DF)
                 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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