Title: AASHTO
1AASHTO 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
2INTRODUCTION
- 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).
3INTRODUCTIONSome examples of fatigue prone
details
4FUNDAMENTAL 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.
5FUNDAMENTAL 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
6Standard rotating bending fatigue test
Stress range vs. Number of cycles (Sr N) to
failure.
7FATIGUE 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.
8FATIGUE 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
9Fatigue crack initiation at notches or
discontinuities
Strain amplitude (De/2) vs. number of reversals
(Nf) to failure
10FATIGUE 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
11Stress state in the vicinity of a crack tip
loaded in tension
12FATIGUE 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
13FATIGUE 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
14TOTAL 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
15FATIGUE 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
16FATIGUE 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
17FATIGUE 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. -
18FATIGUE 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
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19FATIGUE 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
20FATIGUE 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
21FATIGUE 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
22FATIGUE RESISTANCE
23Stress range vs. number of cycles for various
detail categories
24FATIGUE 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
25COMPARISON 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. Â Â Â Â Â
26FATIGUE 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.
27FATIGUE DETAIL CATEGORIES
28FATIGUE DETAIL CATEGORIES
29FATIGUE DETAIL CATEGORIES
30FATIGUE DETAIL CATEGORIES
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42COVER PLATED DETAIL CATEGORY EFATIGUE CRACK
43FATIGUE CRACKING
44DISTORTION 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
45DISTORTION 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
46DISTORTION 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
47DISTORTION INDUCED FATIGUE FATIGUE CRACK
48FATIGUE DETAILS
49BRITTLE 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
50BRITTLE 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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52FATIGUE 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
53FATIGUE 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
54FATIGUE 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
55FATIGUE 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
56FATIGUE 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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