Structural Engineering Lab 3.1 kind of fatigue design. (1) Safe life design (2)Fail safe design (3)...

Structural Engineering Lab

3.1 kind of fatigue design.

(1) Safe life design

(2) Fail safe design

(3) Damage tolerance design

(4) Fracture controlled design

3. Fatigue Design3.1 Kind of Fatigue Design


3.2 Fatigue Design of Bridge.Actual stress (Sɑ) is function of next factor as follows:

Sɑ = f (Sn, Ktd , Ktw)

Where ,

Sɑ : actual stress(2nd stress) which is considered cause of all stress concentration.

Sn : nominal stress(first stress) which is decided by area and section factor of member for load

Ktd : elastic stress concentration which is decided by geometric type of structural member

Ktw : elastic stress concentration which is dominated by welding(such as welding type, welding defect,

fabrication error, etc) and fabricating.

To prevent fatigue crack initiation, Sɑ have to control less than limit value.If possible, Sn , and Ktd , Ktw should be reduced.

3. Fatigue Design3.2Fatigue Design of Bridge.


3.2.1 Allowable stress based on crack initiation life

In fatigue strength analysis, it is reasonable to decision on the basis of P-S(Q)-N curve that fatigue life relates load density to fracture probability.

Fatigue strength analysis which is based S-N curve and statistical data and cumulative damage data is carried out.

For fatigue crack initiation is local behavior, So, it is recommended to use of SA-N curve which related fatigue life and local stress and strain than S-N curve which related fatigue life and nominal stress(first stress).



Setting up Fatigue design of structural member

Fatigue strength of structural member

External force estimation

S-N curve decision

Structural member or model test

SA-N curve decision

Mean stressestimation

Fluctuating stress estimation

Fatigue strength curve estimation of structural member

Fatigue strength curve of basic

specimen

local stress frequencyDistribution of

structural member

The law of accumulated damage

Accumulated damage value

Allowable stress calculation

Setting up of limitsaccumulated value

Safety, economy

Allowable stress determination


(Fig 3.1 Estimation procedure of allowable stress for safe life design)


(Fig 3.2 Flow chart for crack propagation life design)

Setting crack propagation path

Analysis of stress intensity factor

Setting up Structural member for analysis of fatigue crack propagation

Stress analysis of structural member estimation of external force(random load)

estimation of mean stress estimation of fluctuation stress

Equation of crack propagation rate

Stress frequency distribution of structural member

Calculation of crack propagation quantity,

Assumption of initial crack

l

Setting limit crack size,

Calculation of crack propagation life

cl

cll



3.3 Allowable stress and safety factor(Empirical safety factor)

In strength design, allowable stress is decided by divide criterion strength by empirical safety factor. Load is respectively using another safety factor according to static, dynamic, impact load etc.Criterion strength take static fracture strength.This is not so good. because of make down the accuracy of allowable stress.Fatigue strength is effected by notch effect, size effect, surface finishing etc.So, Recently, criterion strength take actual load and actual fracture strength.

Relation allowable stress σɑl and safety factor S and fatigue limit σu is as follows:

Where, σu : fatigue limit of standard specimen which finishing surface

S = σm + σs

σm : safety factor for fatigue limit of material (1.1 ~1.2, 1.5)

σs : safety factor for stress(1.1, 1.5 ~ 2)

3. Fatigue Design3.3 Allowable and safety factor.

u

al S 21

1


3.4 Fatigue Safety of Steel Bridge

In Korea used allowable stress design method, acquirement of safety is only dependent on safety factor .In countries used limit state design method, acquirement of safety is mainly described as partial safety factor, reliability index, fatigue damage parameter, uncertainty of service load etc.


d


3.4 Fatigue Safety of Steel Bridge3.4.1 Partial Safety Factor (In here, JSSC and EUROCODE are present as follows)In fatigue design by JSSC, fatigue safety is determined from

Where, and are the design stress range and the allowable fatigue stress range. γb ,γw ,γi are the partial safety factors to consider fatigue loads and uncertainty of structures.

γb = factor for influence partial fatigue damage on safety strength and performance of structures (strength reduction factor) γw = factor for social influence when structures cause fatigue fracture (significance factor) γi = factor for possibility to find a fatigue damage by inspecting before fatigue failure (inspection factor) Value of partial safety factor is determined by engineers. In JSSC, reference values for partial safety factor are presented but the magnitude of failure probability is not obvious.


( )b w i d a

d

d a

b


3.4 Fatigue Safety of Steel Bridge

[Partial Safety Factor]In EUROCODE, fatigue safety is determined from

Where, Δσe is the equivalent stress range related to spectrum of the design frequent stress range, Δσa is the allowable fatigue stress range.γf ,γm are the partial safety factors for fatigue load and strength, respectively.

γf is factor related to uncertainty which can be included the magnitude of fatigue load, the transfer of stress range from fatigue load, the effect of spectrum of design frequent stress range on equivalent stress range, the design life, the increase of fatigue load and etc.γm is uncertainty included into fatigue strength and factor in relation to error of the fatigue life.


db

af e

m


3.4 .2 Fatigue damage parameter

Value of “m” at Eq. is approximately 3 based on the Paris’s fatigue crack propagation.

Therefore, slope of S-N curve obtained from integral Eq. is approximately -1/3.

As sample size for the fatigue test results of one structural detail increases gradually,

slop of the S-N curve calculated by least Square Method is tend to converge into approximately -1/3.

From two reasons above mentioned, slop of the S-N curve is -1/3, not a random variable.

Therefore, parameter defined by next equation can be applied.

Variable of C is calculated by this equation in accordance with cycle number ( N) and stress range (Δσ)

for the each fatigue specimens.


db

( )mc N 3m

)( KCm

dN

da

)( KCm

dN

da


3.4 .2 Fatigue damage parameter

In case of frequent stress range, Ci is considered and defined as follows

Where, Δσi : one of stress range components at the spectrum of frequent stress range

ni : cycle number of Δσi

It is assumed that fatigue failure is occurred if follow condition is satisfied.

Constant stress range (Δσe) caused fatigue failure can be described

using frequent stress range, ( ) as follows


db

( )mi i ic n

1

k

ii

c c

1

k

ii

N n

( )mec N


3.4 .2 Fatigue damage parameterFollow equation can be obtained by substituting Eq. and Eq.

to Eq. .

This equation is similar form with equivalent stress range of Eq. .

Eq. describes that fatigue failure occurs when total cumulative of Ci is equal to C.

Therefore, Ci presents a part of fatigue damage. Such a feature of Ci , C is called fatigue damage parameter.


db

1

k

ii

c c

( )mec N ( )mi i ic n

1/

1

{ ( ) }k

m mie i

i

n

N

a

me cN )(

1

k

ii

c c


4. Fatigue Standard of Various countries(KOREA, USA, BS, JAPAN, CANADAetc)

5

1) KOREA : Korea Bridge Design Code Korea Railway bridge design code.2)USA : AASHTO(American Association of State Highway and Transportation Officials )

3) BS (Eurocode)

4)JAPAN

5)CANADA


5

[Korea] Korea Bridge Design Code1) Design stress range should not exceeds allowable fatigue stress range.2) Maximum stress of joint part should not exceeds allowable fatigue stress range. 3) Cycles number of maximum stress range(load number) - Primary member : 2 million (truck (DB) load), 500 thousand(lane load) - Transverse member, structure detail part : 2 million (truck load) 4) Allowable fatigue stress are made by combined load including live load and wind load. *(This is a little different that the wind load is not included in Eurocode BS 5400 part 10)

Korea Railway bridge design code 1) Allowable fatigue stress range : 95% of nondestructive probability. *(This is a little different from 97.7% of Eurocode BS 5400) 2) Grade classification of joint part : 4 grade(for vertical stress), 3 grade(for shear stress). *(This is not detailed compare with Japan, USA, BS, CANADA.)

Fatigue Standard of (KOREA)


5

[AASHTO]Fatigue design criteria of AASHTO = AWS until 1965.

1) Design stress range should not exceeds allowable fatigue stress range.2) Primary load transfer member is applied to allowable fatigue stress range of singular loading path3) Cycles number of maximum stress range(load number) - Primary member : 2 million (truck (DB) load), 500 thousand(lane load) - Transverse member, structure detail part : 2 million (truck load) 4) Allowable fatigue stress are made by combined load including live load and wind load. *(This is a little different that the wind load is not included in Eurocode BS 5400 part 10)

Fatigue Standard of (AASHTO, USA)


5

[BS]Fatigue design standard(BS) was printed as BS 5400 Part 10 in 1980.

1) Permissible value of stress is prescribed as stress range not stress limit value. When strength of fatigue is evaluated, magnitude of stress by dead load is no relation.

2) Fatigue strength evaluation method which considered actual stress for weld structure is adopted.

3) Design life is guaranteed until 97.7% of nondestructive probability and design life is until120 years.

4) It is possible to calculate fatigue strength for any design life.

5) Definition of design life is defined as safely serviceable period.

Fatigue Standard of (BS)


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[BS]--- LOAD---I] Load of railway bridge : 1) Standard railway load is considered including double track loading. 2) Specially, Dead load is not considered in weld joint. But, Dead load is considered in non-welded part. 3) Effective stress range is calculated by sum of maximum tensile stress and 60% of maximum

compressive stress.

II] Load of highway bridge : 1) Total weight of live load is 320kN(32.6ton). 2) One vehicle is loading at one bridge. 3) Lane driving by Standard vehicle is limited by slow lane and adjacent to the slow lane. 4) Effective stress range is same with railway bridge case.



5

[BS][Categories of Structural detail]

1) Joint part is classified by non-welded details, welded details on surface of member, welded details at end of member etc.

2) Also, it is subdivided by location of potential crack initiation, dimensional

requirement, manufacturing requirement, inspection requirement, etc.3) Fatigue strength is divided by 10 grade : A ~ F, F2, G, S,W.4) Also, non-welded details is sub divided by 12 grade.5) welded details on surface of member is sub divided by 12 grade.6) welded detail on end of connection of member is sub divided by 15 grade.

[Assessment of Fatigue strength]

There are three method.1) the method which not required calculation of fatigue damage.2) the method which calculated fatigue damage due to standard vehicles loading method.3) the method which calculated fatigue damage due to load spectra method.



5

[JAPAN]

[Japan Bridge design code]

Fatigue design is not so much allocating in Japan bridge design code. Because the result of study from railway association and JSSC can be used as manual.

[Japan Railway design code] 1) Joint details is divided by 5 grade. 2) Fatigue strength cycles are number of 2 million.3) The kind of steel is 400MPa and 490MPa.

Fatigue Standard of (JAPAN)


5

[CANADA][Calculation of stress range]1) This is calculated using ordinary elastic analysis and the principles of mechanics of materials. 2) More sophisticated analysis is required only in case not covered in table 9. eg: major access holes and cut-offs.

3) Stress range is the algebraic difference between the maximum stress and minimum stress at a given location. : thus, only live load induces stress range.

4) Stress range need be applied only at location that undergo a net applied tensile stress. So, stress ranges that are completely in compression need not be investigated for fatigue.

Fatigue Standard of (CANADA)


5

[CANADA][Design Criteria]

Where, fatigue resistance.

where, fatigue life constant, number of stress range cycles number of application of load constant amplitude threshold stress range calculated stress range at the detail due to passage of the fatigue load.

F sr fsr

F sr

FnN

srt

3

1

nNF srt

fsr



5

[CANADA][Cumulative fatigue damage]The total damage that results from fatigue loading, not applied at constant amplitude, shall satisfy

Where, number of expected stress range cycles at stress range level i.

number of cycles that cause failure at stress range level i.

0.1

NnN

fi

i

nNi

N fi



5

[CANADA]

[Cumulative fatigue damage]The summation shall include low-stress cycles with stress range less than Fsrt

in accordance with the requirement that for such cycles the fatigue resistance F`sr

shall be taken as :

Where , is obtained by setting for value of at which

The fatigue constant, and are given in next table.

nN' 5

1

'

NnNn '

'

'

51

31

NnnN' FF srtsr

Nn' '



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1)To establish the Fatigue Analysis Tools2)To work out Prediction Method of Remaining Fatigue Life by Fatigue Analysis 3) To provide the Fracture Prevention Plan4)To develop an adequate Analysis Tools for Fatigue and Fracture 5)The Problem of stress and deformation in welding part.6)The Problem of the behavior of stress and deformation in steel member welding joint under cycle loading. 7)To develop model of cycle loading

5. Current Research of Fatigue


5

1

• Stress history measurement and fatigue life assessment of coped stringers of steel railway bridge under being in service.• Estimation methods for strain-life fatigue properties from hardness• Evaluation of fatigue damage

• A study on characteristics of Fatigue crack growth in SM570 steel•A study on parameters affected the fatigue crack growth in steel structure member.•An experimental study on fatigue crack growth characteristic of welded high-strength steel.•Fatigue Crack Growth and Crack closure Behavior of Structural Materials• Fatigue Crack Propagation and Crack Closure under Random Loading• Elastic-Plasic Fatigue Crack Growth Behavior under Repeated Two-Step Loading• estimation of probabilistic distribution of fatigue crack propagation using the first-order taylor expansion of crack geometry

• An experimental study on the fatigue of torque shear type high tension bolted joint.• A study on fatigue crack at coped stringer of the plate girder subway bridge.• behavior od the crack initiation, transition and fatigue crack growth of rail steel.• The Cyclic Plastic Strain and Cumulative Fatigue Damage• The Cyclic Plastic Strain and Cumulative Fatigue Damage Under Actual Loading



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•Iterative modeling scheme of 2-D mixed fatigue crack growth •Fatigue crack growth analysis of steel deckplates under bending stress.•fatigue crack growth analysis of high strength steel(posten 80) with out-of-plane gusset.•The computational model for fracture and fatigue of structure steel member under random loads•analysis of two-dimensional fatigue crack growth under mixed mode loading.•Finite Element Analysis of Closure Behaviour of Fatigue Cracks in Residual Stress Fields

•data base for fatigue strength•development of software for damage evaluation

•An Expert System for Estimation of Fatigue Properties of Metallic Materials

• J-INTEGRAL for a 3 D interface crack configuration in welds of dissimilar steels

• COD


Structural Engineering Lab 3.1 kind of fatigue design. (1) Safe life design (2)Fail safe design (3)...

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Transcript of Structural Engineering Lab 3.1 kind of fatigue design. (1) Safe life design (2)Fail safe design (3)...