suscos m emmc co3 bridges fatigue l4

8/10/2019 Suscos m Emmc Co3 Bridges Fatigue l4

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Introduction la mcanique de la rupture


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CONCEPTUAL DESIGN OF BRIDGES

Luis Borges

Lecture 27: 20/11/2012European Erasmus Mundus Master Course

Sustainable Constructionsunder Natural Hazards and Catastrophic Events

520121-1-2011-1-CZ-ERA MUNDUS-EMMC


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L27 Fatigue and fracture of steel structures

European Erasmus MundusMaster Course

Sustainable Constructionsunder Natural Hazards

and Catastrophic Events

Contents

L26 Basis of fatigue design in steel structures

Definitions and application range

L27 Fatigue loads and determination of stresses and stress ranges

Cycles and stress ranges

L28 Fatigue strength

Fatigue strength curves

Fatigue details

L29

Reliability and verification Application to Road Bridges

Application to Rail Bridges

L30 Introduction to Fracture mechanics and Brittle fracture


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Contents

Variable stress range

Equivalent/simplified stress range VA, damageaccumulation

Verification under fatigue variable amplitudeloading

Damage equivalent factor l


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Road bridge under heavy traffic


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Variable stress range

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8/33L27 Fatigue and fracture of steel structures




Traffic evolution in Switzerlandstations Weigh-in-Motion in nationalroads

8

Mattstetten (A1)Bern Solothurn

Gschenen (A2)Gotthard

Denges (A1)Lausanne Morges

Trbbach (A13)St-Margrethen Chur

Oberbren (A1)Zurich St.-Gallen

Plazzas (A13)Chur Thusis

Ceneri (A2)Bellinzona Lugano

St-Maurice (A9)

Schafisheim (A1)Solothurn - Zrich

Donnent le trafic sous formede

Composition du traficGomtries des vhiclesPoids des axes


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0

1

2

3

4

5

6

0 100 200 300 400 500

D

i s t r i b u t

i o n

( % )

total weight (kN)

Ceneri-2003 Ceneri-2005 Ceneri-2007Truebbach-2003 Truebbach-2005 Trubbach-2007Mattstetten

Histograms of vehicles totalweights

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+53% in 5years


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Load histograms examples

10


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Variable loading spectrum simplification VA,damage accumulation

1. Reduce the spectrum to a series of constantamplitudes with a cycle counting method

2. Create a load histogram with load cycles from

the spectrum

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Cycle counting: reservoir method(or Rainflow)

12

2 large cycles


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Histogram resulting from cyclecounting

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Cycle counting: reservoir method(or Rainflow)

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0

5 0

1 0 0

1 5 0

1

2

3

4

5

6

7

t

[N/mm ]

8 trains per hour Calculate fatigue load histogram for 100 years service life


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the spectrum3. With the adapted fatigue curve, for each

stress range, compute the damage for therespective number of cycles (Miner law)

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No cycles to collapse

S t r e s s r a n g e

Ultimate strength Finite service life

Infinite service lifeFatigue Limit (CAFL)

N C m

Test results

Fatigue testing and detailcategories


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N cycles to collapse

S t r e s s r a n g e

N C m

Test results

Low Cycle Fatigue High Cycle Fatigue

Fatigue testing and detailcategories (Whler)


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N C m

No cycles to collapse

S t r e s s r a

n g e

Mean results

Results statisticaldistribution

C

2 .10 6

S-N Curves


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Damage accumulation n i, i

20

d i 1 N i

Di n i d i n i N i

1,0

Dtot Di 1,0

Linear damage accumulation


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Fatigue limit verification

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i,max

Ff i,max D

Mf

0.74 C Mf

Max of histogram


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the spectrum3. With the adapted fatigue curve, for each

stress range, compute the damage for therespective number of cycles (Miner law)

4. Combine individual damage to obtain totaldamage accumulated and proceed with theverification

22


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Histogram i and fatigue curve

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Extreme positions

Fatigue verification:damage equivalent factor

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Trains passing over the bridge

Histogram of Stress ranges

Damage accumulation

Service loads Code load model

Bridge detail

Qk max Qk min Qk

l E 2 Qk 2 E E

Difficulties linked to VA in development ofstandards


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Ff E 2 C Mf

E 2 l Qk Actions

Category = Resistenceat 2 million cycles

Resistance factor

Load

factor

Fatigue verification:damage equivalent factor concept

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28

l l 1 l 2 l 3 l 4 l maxwith:l 1 factor accounting for the span length (a relation which is function of

the influence line lengthl

2 factor accounting for the traffic volumel 3 factor accounting for the design working life of the structure(e.g. the working life of 100 years for a bridge leads to 3 =1)

l 4 factor accounting for the influence of more than one load on thestructural member, function of structure type and definition of the fatigue load model for computing 1 (if more than one)

l max maximum damage equivalent factor value, taking into accountthe fatigue limit.


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Example: compute damageaccumulation

29source: Trait de Gnie Civil vol. 10


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Results

30Fonte: Trait de Gnie Civil vol. 10


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What are the best details??

A

B

C

D

E


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CAT 160-125

CAT 125-100

CAT 100-80

CAT 63-50

CAT 71-36

B

A

D

E

C

What are the best details??


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[email protected]

http://steel.fsv.cvut.cz/suscos
mailto:[email protected]:[email protected]

suscos m emmc co3 bridges fatigue l4

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