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
Lateral bracing
Out-of-plane
plates
Gusset plates
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
•
Stable crack propagation rate – Paris’ Law
da
m
 A DK I 
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
da
m
m
da
 Ds   dN

 A C Δσ  a
Therefore
m
ai A ( C  a )
Ni
dN


af
Let A1 = 
ai
da
A( C  a )m
And
A1  Ds   N 
m
Therefore
 A1 
Ds   
N
1
m
FATIGUE LIFE
• Ds
•
•
•
•
 A1 
 
N
1
m
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
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 = hi 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
available to Trucks
p
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
support
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
•
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 =
1
A 3
1

   (DF)TH
2
N
– 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
A
B
B’
C
C’
D
E
E’
M164 (A 325) bolts in
axial tension
M253 (A 490) bolts in
axial tension
Constant A x
108
250.0
120.0
61.0
44.0
44.0
22.0
11.0
3.9
17.1
(DF)TH
(ksi)
24.0
16.0
12.0
10.0
12.0
7.0
4.5
2.6
31.0
31.5
38.0
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 nonredundant 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
BUILT-UP MEMBERS
PLAIN MEMBERS
A
Rolled surface
B
B
Painted weath.
B’
E
E
Eyebars
E’
Splice connection
B
Cover plates
Fastened connections
Unequal sections
Same sections
Cont. welded
Bolted
Width transition
2 ft. radius
Transitions in width
or thick 1:2.5
B
B
B’
B
Riveted
D
LONGITUDINALLY LOADED ATTACHMENTS
Groove welded
E
E’
B
C
D
E
E
C
End welds
ground smooth
End welds not
ground smooth
D
E
E’
R > 2 in. not req
End welds not
ground smooth
D
Larger radius better
Longer is worse
End welds
ground smooth
Transition radius
Detail length
Longer is worse
Transition radius
Detail length
C
Fillet welded
D
E
E
TRANSVERSE LOADED ATTACHMENTS
Groove welded
Unequal plate thickness
Equal plate thick
C
D
E
C
D
E
Weld rft. removed
R > 2 in. not bet.
B
Weld rft. not removed
Rad. > 6.0 not help
Larger rad.better
Weld rft. removed
D
E
Weld rft. not removed
E
TRANSVERSE LOADED ATTACHMENTS
Fillet welded
Welds parallel to direction of stress
Rad. > 2.0 in. no help
Transition radius and
Welds ground smooth
D
Transition radius and Welds
not ground smooth
E
E
FILLET WELDED CONNECTION
Welds normal to stress
Welds normal or par. to stress
C at base metal
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 flangeweb 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 nonFCM 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
p<
n Zr I
Vsr 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
•
(ADTT)SL = p x ADTT
•
Number of fatigue cycles = N = (365) (75) n (ADTTSL)
•
For a simply supported girder with span length < 40 ft., n = 2
– Highway bridge is on rural interstate with two truck lanes
– Therefore, annual daily TRUCK traffic (ADTT)= 0.20 x 20000 x 2= 8000
– where p = 0.85 for 2 lanes available to trucks
– (ADTT)SL = 0.85 x 8000 = 6800
– N = 186.15 x 106 x n
– Therefore, N = 372.3 x 106 cycles
FATIGUE DESIGN
Step II. Estimate the fatigue strength (DF)n
– (DF)n = 
1
A 3
1
  (DF)TH
2
N
– Cover plate (narrower than the flange) with flange thickness
– 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,
< 0.8 in.
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 !!!!!!