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PPT – AASHTO LRFD OF STEEL BEAM BRIDGES Fatigue and Fracture PowerPoint presentation | free to download - id: 3aeacd-ODc2N

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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

- 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).

INTRODUCTIONSome examples of fatigue prone

details

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 lt Nf lt 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
- 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

FATIGUE CRACK PROPAGATION

- Stable crack propagation rate Paris Law
- where, a flaw or crack size N number of

fatigue cycles - A and m are material constants
- Fatigue crack propagation is linear with respect

to (DKI) in log-log coordinates

TOTAL FATIGUE LIFE

- The total fatigue life of a component is equal to

the sum of the crack initiation life and the

crack propagation to fracture life - N Ni Np
- For bridge components and details, initial crack

or defects are present in the form of flaws or

defects - Crack initiation life is negligible
- Crack propagation life dominates (N Nf)
- If the initial flaw size is ai and the final flaw

size at fracture is af - Therefore
- Let A1 Therefore
- And

FATIGUE LIFE

- where, m 3 for

ferrite-perlite steels - The constant A1 depends significantly on the

value of the initial flaw or defect ai, which

cannot be estimated easily or accurately - Therefore, A1 is calibrated to experimental

results for various structural components and

details - This equation is identical to the one recommended

by AASHTO for fatigue life prediction and design - Experimental results indicate the existence of an

endurance limit (Ds)TH below which fatigue crack

propagation does not occur

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
- 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 - ADTT can be estimated as the limiting value of

average daily traffic multiplied by the fraction

of trucks in the traffic

FATIGUE LOADING

- Fatigue design life 75 years
- Total number of fatigue cycles over the design

life - N (365) (75) n (ADTTSL)
- Where, n number of stress range cycles per

truck passage - For continuous spans, a distance equal to

one-tenth of the span either side of the interior

support ? near the support - n 5 for cantilever girders due to the

vibrations as the truck leave

FATIGUE DESIGN CRITERIA

- Fatigue design criteria for load-induced fatigue

in a component - h g (Df) j (DF)n
- g load factor 0.75 and j 1.0 for the

fatigue limit state - (Df) maximum stress range (LL, IM, CE) due to

the fatigue truck - (DF)n nominal fatigue resistance of the

structural component or detail. - The nominal fatigue resistance for structural

components / details - (DF)n (DF)TH
- where N (365)(75) n (ADTTSL) number of cycles

over design life - (DF)TH is the constant amplitude fatigue

threshold in ksi - Commonly existing components and details

categorized into detail categories A .. E - Values of A and (DF)TH are specified for these

detail categories

FATIGUE RESISTANCE

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

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COVER PLATED DETAIL CATEGORY EFATIGUE 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

BRITTLE FRACTURE CONSIDERATIONS

- Fracture-critical member (FCM) is defined as a

member with tensile stress whose failure is

expected to cause the collapse of the bridge - material in a FCM is required to exhibit greater

toughness and ability to absorb more energy

without fracture than a non-fracture critical

member - Charpy V-notch fracture toughness requirements

for welded components are given below for

different plate thicknesses and temperature

zones. - FCM values for absorbed energy are approximately

50 greater than for non-FCM values at the same

temperature

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FATIGUE OF SHEAR CONNECTORS

- Shear connectors are designed to achieve

composite action between the steel beam and the

concrete deck. - The number of shear connectors should satisfy the

strength and the fatigue limit states - The pitch of shear connectors determined to

satisfy fatigue - p lt
- where, p pitch of shear connectors along

longitudinal axis - n number of shear connectors in a

cross-section - I moment of inertia of the short-term

composite section - Q Ay first moment of the transformed area of

the slab about the - n.a.of the short-term composite

section - Vr shear force range under LL IM determined

for the fatigue limit - Zr shear fatigue resistance of an individual

shear connector - The c-to-c pitch of shear connectors shall not

exceed 24.0 in. and shall not be less than six

stud diameters

FATIGUE OF SHEAR CONNECTORS

- The fatigue resistance of an individual shear

connector - Zr a d2 gt 2.75 d2
- where a 34.5 2.28 Log N
- d diameter of stud and N number

of cycles - Stud shear connectors shall not be closer that

4.0 d c-to-c transverse to the longitudinal axis

of the supporting member - The clear distance between the edge of the top

flange and the edge of the nearest shear

connector shall not be less than 1.0 in. - The clear depth of concrete cover over the tops

of the shear connectors should not be less than

2.0 in. - Shear connectors should penetrate at least 2.0

in. into the deck

FATIGUE DESIGN

- We have already designed a composite steel

bridge. The span length of the bridge is 34 ft.

The roadway width is 44 ft. - The selected beam is W24 x 68 with a ½ in. thick

cover plate narrower than the flange - Clearly the bending moment is smaller at the ends

and we can curtail the cover-plate to save some

money. Lets see? - The cover plate can be curtailed to the point

where the moment is small enough for the steel

beam alone to carry it - But, the fatigue stress range at the end of the

cover plate must be OK!

?

Partial-length? Cover plate

FATIGUE DESIGN

- Step I Estimate number of fatigue cycles
- Limiting value of annual daily traffic (ADT)

20,000 per lane - Highway bridge is on rural interstate with two

truck lanes - Therefore, annual daily TRUCK traffic (ADTT)

0.20 x 20000 x 2 8000 - (ADTT)SL p x ADTT
- where p 0.85 for 2 lanes available to trucks
- (ADTT)SL 0.85 x 8000 6800
- Number of fatigue cycles N (365) (75) n

(ADTTSL) - N 186.15 x 106 x n
- For a simply supported girder with span length lt

40 ft., n 2 - Therefore, N 372.3 x 106 cycles

FATIGUE DESIGN

- Step II. Estimate the fatigue strength (DF)n
- (DF)n (DF)TH
- Cover plate (narrower than the flange) with

flange thickness lt 0.8 in. - Therefore, Category E detail
- From the table A 11.0 x 108 and (DF)TH 4.5

ksi - Therefore, (DF)n (11.0 x 108)/(3.723 x

108)1/3 1.43 ksi, - but (DF)n gt ½ (4.5) 2.25 ksi
- Therefore, the constant amplitude fatigue

threshold controls - The applied fatigue stress range (Df) must be lt

2.25 ksi - The cover-plate can be curtailed to the point

where the stress range in the steel beam alone is

less than 2.25 ksi !!!!!!

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