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Bridge Engineering 1

Chapter 9Fatigue and Brittle Fracture


Fatigue - theory

Initiation of microscopic cracks and/or propagation of such cracks into macroscopic cracks, due to repeated loadsStress rangeType of structural detailConsider only tension or reversal stress cycles


Fatigue strength prediction

maxσ

minσσ∆

iσ∆

minσ

a) Constant

amplitude

a) Random

amplitude


Fatigue strength predictionThe relationship between the number of fatigue cycles and stress range is a linearone.For constant-amplitude cyclic stresses, specific number of stress cycles can be expressed as:

N: number of fatigue cycles, : fatigue stress range, c: material constant, m: an integer number

mcN −∆= σ

σ∆


Fatigue - Design

m: usually considered to be 3For random amplitude vibrations

is the equivalent stress range, are individual stress ranges and are the corresponding frequency of occurrenceFatigue tests on, weld joints and memberswith connection configurations

eσ∆ iσ∆


Fatigue S-N curve for steel


Fatigue strength

Other factors affectingResidual stress – The slope of the S/N relationship is steepended and the fatigue strength is reduced significantly at longer lives (fatigue strength – the stress to produce a given life)Weld leg length / plate thickness andthickness of the plate – if w/t is the same, the fatigue strength for thick plate is lower than the fatigue strength of thinner plate


Fatigue - strength

Other factors affecting – (cont.)Frequency

Rest-periods – Resting period cause increase in endurance

σ∆


Fatigue - Design

Fatigue strength, not a material property like yield strengthDepends on:

joint configuration residual stressweld leg length per plate thickness and thickness of the platerest periodsEtc.


Fatigue - Design

Load-induced fatiguea connection detail goes under repetitivenet tensile stress

Distortion-induced fatiguecross frames or diaphragms are connectedto girder webs, restricting movements


Issues and Design

Fatigue limit state , limits crack growthConsider the vehicular load onlyOne truck only placed at the center of one traveled lane No lane load is considered


Fatigue design of components

ComponentsConnectionsMechanical fastenersWelds

Design such that computed tensile stressrange does not exceed the allowable stress for various elements

srF


Live load induced fatigue

Code provision applies, only if the detail is expected to go under a net tensilestress

except in bridge decks

in bridge decksWhere : the calculated stress rangeat the detail due to passage of the CL-Wtruck, and : the fatigue resistance

srsr

srsr

Ff

Ff

<

<

62.0

52.0

srf

srF


Live load induced fatigueFatigue stress range resistance, except for shear studs and cables:

Where : is the fatigue life constant for the detail category, : constant amplitude threshold stress range and : the specified number of design stress cycles calculated as follows:

2

31

srt

csr

FNF ≥⎟

⎠⎞⎜

⎝⎛= γ

γsrtF

cN





y : the design life of the bridge (75 years, unless otherwise specified), is a factor to recognize different stress ranges produced by single pass of a truck and is the average daily truck traffic in a single lane.

is given in the following table

( )fdc ADTTyNN 365=

dN

fADTT

dN





Average daily truck traffic:Site-specific traffic forecast

P : the fraction of multiple lanes of traffic in a single lane, and ADTT is the average daily traffic

fADTT

( )ADTTpADTTf =




















High strength bolts

High-strength bolts subjected to cyclic tensile load shall be pre-tensioned to a minimum pre-load specified in code.Connected parts shall be arranged so that prying forces are minimized, and in no case shall the calculated prying force exceed 30% of the externally applied load.


High strength bolts

Common type of bolts (ASTM designation)A307 low carbon steel, square heads and nuts, 60 ksiA325 heat-treated carbon steel

120 ksi (up to 1” diameter)105 ksi (1”-1 ½” diameter)

A490Heat-treated high strength alloy steel, 150 ksi(up to 1-1 ½” diameter)


Reinforcing Bars

Crack starts at the base of transversedeformationThe higher the stress range S, the fewer the number of cycles N before failureThe higher the min. stress level, the higher the average tensile stress, the lower the fatigue strength


Reinforcing Bars

Arching action reduces the stress in rebars, lowering the stress range

Fatigue not considered in deck slabs designed in accordance with empirical method

When rebars part of longitudinal or transverse beams, consider fatigue (8.5.3.1)The stress range in straight bars shall notexceed 125 MPa


Reinforcing Bars

For anchorage, connections and bends, reduce permissible stress range to 65MPa.


Welded reinforcement

Bars containing complete jointpenetrating groove welds (CSA-W186), the stress range in the vicinity welds shall not exceed 100MpaFor other types of welds (tack welding is not permitted for primary reinforcement), the stress range shall not exceed 65 Mpa.


Stud shear connectorsTransfer load between the steel beams and the top concrete slab

where:

:permissible range of interface shear stress

:number of load cycles

:nominal diameter of the stud

22 38)log5.29238( ddNz csr ≥−=

d

srz

cN


Stud shear connectors

The permissible shear force will be:

Where: is the permissible shear force

is range of shear force at FLS resulting from passage of CL-W truck, n is the number of connectors on a transverse section at a given location, Q is the static moment about the neutral axis, is the moment of inertia of the composite section

srV

srqt

srsr nI

QsVq 52.0=

tI


Shear stud connectors

Simple and continuous span, install connectors all alongIf no stud at negative moment regions:

Extra ones at contraflexure regionsIn a distance equal to one-third of the effective slab width on each side of dead load contraflexure point. Their number:


Shear stud connectors

Where::is the number of extra the studs

:is calculated fatigue limit state stress range at the detail due to passage of the CL-W truck

:is the area of reinforcing steel within the effective width of concrete slab

: is the permissible range of interface shear stress

sr

srra Z

fAN =

aN

rA

srf

srZ


Cable-stays and cable-stayed bridge tie downs

Inspectable cable-stays and tie-downsReplaceableNo significant loss of function of the bridgeWire breaks, detectable in service

Fatigue stress < fatigue stress resistance from tests

Test, two million cycles of stress rangeTested sample has at least 0.95 of breaking strengthLowest stress range of three successful tests is the fatigue stress range resistance


Cable-stays and cable-stayed bridge tie downs

If secondary (bending stresses) exceeds of 50MPa, then add to primary (tension) stress to derive the test fatigue stress rangeIf non-replaceable cable-stays and tie-downs and if breaks are non-detectable

Stress range < 0.75 of fatigue stress from test


Prestressing Tendons

If pre-stress so high that concrete cross section remains un-cracked, no fatigueprovisionPartial pre-stressing, where concretecracks under service load and neutralaxis moves, then fatigue is criticalTendons are most critical, especially when under curvature


Pre-stressing TendonsStrands stress range in corrugated steel ducts or pre-tensioning strands to be less than:

125 MPa, when radii 10m or more70 Mpa for radii of 3.5m or lessInterpolate in between

For strands in plastic corrugated ducts, stress range to be less than 125 MPaStress range in deformed and smooth high-strength bars, less than 70 MpaStress range in tendons at couplers less than 70 Mpa


Distortion-Induced Fatigue

Interaction between longitudinal and transverse members, can generate high-magnitude secondary stresses in bridge bending. When superimposed on primary stress, early fatigue may happenConsider diaphragms, cross-frames, lateral bracings, floor beams, etc and study both the members and interconnection components



Connection to transverse membersThe connection of diaphragms, cross frames, lateral bracings, floor beams, etc., to main members shall be made using transverse connection plates that are welded or bolted to thetension and compression flanges of the member For straight, non-skewed bridges, the connection shall be designed to resist a factored horizontalforce of 90 KN



Connection to lateral elementsIf connections of lateral elements to members that are parallel to longitudinal axis of main element, the lateral connection plates shall be attached to both the tension and compression flanges of the main member.


Brittle Fracture

A failure of a steel element under a condition of brittle behavior


Brittle Fracture

Brittle behavior of the super-structure(factors contributing to the possibility of brittle

fracture)Use of higher-strength steelIncreased thickness of steelReduced safety factorMore complex details, with possible stress concentrationIncreased use of welding


Brittle fracture

Cracks are present no matter how good installation, workmanship and inspectionThe issue is they should not propagate under load and passage of timeSteel behaves more brittle in colderweatherCharpy V-notch test to measure fractureenergy


Fracture mechanics

Fracture mechanics is a method of characterizingfracture behavior in terms of structure parameters, namely stress and flaw size.


Fracture mechanics

Fracture behavior is a function of stressand flaw size

Defined in terms of stress intensity factor Its units areTests and theories have resulted in expressions for

κinchksi /

κ

Opening Mode I Tearing Mode III Edge Sliding Mode II


Brittle fracture

σ

σ

Through thickness crack Edge crack Surface crack

aI πσκ = aI πσκ 12.1= Qa

I σπκ 1.1=

Q is a function of a and c


Brittle fracture

σ

aI πσκ =

σ


Brittle fracture

The critical value of is It is the value at failure for a given steel of particular thickness and at a specific temperature and loading stateIf is known, then

Find critical flaw size at a particular stresslevelFind design stress for a given flaw size

κ cκ

cκ


Notch toughness and ductility

The capacity to absorb energy before fractureIn room temperature, steel has hightoughness and behaves ductileIn lower temperature, however, it becomes more brittleThe Charpy V-notch impact test


Temperature effects

Temperature Transition Curve


Brittle Fracture

CHBDCFracture control (10.23.3)

Fracture toughness requirementsThe Charpy V-notch requirements are for standard specimenFor plates from 8 to 11 mm thick, sub-size specimen with adjusted energy levels may be used as permitted by CAN/CSA G40.20Requirements apply to both bolted and welded connections


Brittle Fracture

The fracture toughness must be enough to ensure ductile behavior1) Fracture-critical members, single load path structures (10.23.3.1)

Charpy test per plate frequency

2) Primary tension members (10.23.3.2)Charpy test per heat frequencySteel shall meet the specified impact energy requirements


Brittle FractureFracture control, fracture-critical members


Brittle FractureFracture control, primary tension members


Brittle FractureFracture control, welded metal members


Structural steel materials standards

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