2010 bridges analysisandmodelling ldavaine

8/12/2019 2010 Bridges AnalysisandModelling LDavaine

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Composite bridge design (EN1994-2)

Bridge modelling and structural analysis

Laurence DAVAINE

French Railwa s SNCF

Bridge Engineering Department (IGOA)


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Dissemination of information for training Vienna, 4-6 October 2010 3

Twin-girder bridge modelling

C3

G P2

P1xy

simply supported bar model (dz=0 for every support)

half-bridge cross-section represented by its centre of gravity G

(neutral fibre)

C0

structural steel alone, or composite, mechanical properties

according to the construct ion phases of the bridge slab


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Concrete slab thickness

Actual slab Computed slab

Sactual = Scomputed (same area)

actual = computed (same location of the slab gravity centre Gc)


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Shear lag in the concrete slab according to EN 1994-2

effb

,maxxx

xx Non-uniform transversedistribution of the

longitudinal stresses

750 mmb

1 1eb

2 2eb

13.125 mb

22.125 mb 0b

0eff i ei

i

b b b

min ;8

e

ei i

Lb b

0.55 0.025 1.0e

i

ei

L

b


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Shear lag in the concrete slab according to EN 1994-2

Equivalent span length Le

Global analysis (calculation of internal forces and moments) : constant

along each span (equal to the value at mid-span)

Section analysis (calculation of stresses) : linearly variable along Li/4

surrounding the internal supports


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Application to the twin-girder bridge example

C0 P1 C3P2

60 m 80 m 60 m

L m 0.85x60 = 51 0.7x80 = 56 0.85x60 = 510.25 x (60+80) = 35 0.25 x (60+80) = 35

e e e 1 2 e

In-span 1 and 3 48 3.125 2.125 1 1 6.0

In-span 2 56 3.125 2.125 1 1 6.0

. . .

End supports C0 and C3 48 3.125 2.125 0.958 1.15 but < 1.0 5.869 < 6.0


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P1 P2 C3C0

2

0

11 12

L2/4L2/4L1/4L1/4 L1/4 L1/4

-2

-1

-3

-4


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Composite cross-sections mechanical properties

effb

Un-cracked behaviour (mid-span regions, Mc,Ed > 0)

caA A

n

A elastic

neutral axis

c

GGy

Gcy

e n orcemen neg ec e n compress on

cG a Ga Gc

AAy A y

ny

22 1( )a a G Ga c c G GcI I A y y I A y

n

y

aG

Gay

Cracked behaviour (support regions, Mc,Ed < 0)

effb

Ea = Es = 210 000 N/mm (n = 1)

elasticneutral axis

s

GGsy a sA A A G a Ga s GsAy A y A y

a

GayGy ( )a a G Ga s s G GsI I A y y I A y y

0sI


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Modular ratios (creep effect)

a

0

cm

En

EShort-term modular ratio:

0.3

cm

cm

fE 22000

10

L 0 L tn n . 1

t 0t t

ong- erm mo u ar ra o:

Creep coefficient according to EN 1992-1-1 with :

t = age of concrete at the considered time during the bridge life

t0 = age of concrete when the considered loading is applied to the bridge

t0 = 1 day for shrinkage

t0 = mean value of age of concrete segments, in case of composites structurescast in several sta es ermanent load

L depends on theload case :

Permanent loads 1.1

Imposed deformations 1.5


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Creep coefficient according to Annex B in EN 1992-1-1

000

0.3

t 0 c 0 0

H

t

t. t .

t

tt

t

(end of bridge life)

18H 0 3 31.5. 1 0.012 RH .h 250. 1500.

00

0 RH cm 1 2 0.2

3 0 cm

RH1

16.8 1100. f . 1 . . . .

0.11 tf

t

0 . 0 h

with : RH = 80 % (relative humidity in the bridge area)

c0h

u notional size (u is the concrete slab

perimeter exposed to drying)

0.7

1

cm

350.8658

f

0.2

2cm

350.9597

f

0.5

3

cm

350.9022

f


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Short-term modular ratio

aE

Long-term modular ratio

0cm

.E

Load case L t0 (days) t = 0 nL

Concrete slab segment (selfweight)

Settlement

Shrinka e

1.10

1.50

0.55

35.25

49.25

1

1.394

1.291

2.677

15.61

18.09

15.24

Bridge equipments 1.10 79.25 1.179 14.15


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Application to the traffic load model LM1

1. Conventional traffic lanes positioning

0.5 m1 m

3 m3 m 3 m 2 m

. . .

Bridge axle

girder no. 2Girder no.1

(modeled)3.5 m 3.5 m


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2. Tandem TS

Bridge axle

TS 1 per axle :

=

TS 2 per axle :

1.0 x 200 = 200 kNTS 3 per axle :

1

.1.0 x 100 = 100 kN

0

Influence line of the

support reaction on

girder no. 1

0.5 m 1 m 2 m

Support reaction on each main girder : R1 = 471.4 kN

R2 = 128.6 kN


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3. Uniform Design Load UDL

Bridge axle

Load on lane no.1 :1.0 x 9 x 3 = 27 kN/ml

Load on lane no.2 :1.0 x 2.5 x 3 = 7.5 kN/ml

1

Load on lane no.3 :

1.0 x 2.5 x 3 = 7.5 kN/ml

LANE 1

LANE 2 LANE 3

R1

0Influence Line

R2

0.5 m 1 m 2 m

Support reaction for each main girder : R1 = 35.36 kN/ml

R2 = 6.64 kN/ml


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Contents

1. Bridge modelling

Geometry

Effective width (shear lag effect) Cross-sectional

Transversal distribution

mechanical properties

2. The global cracked analysis according to EN 1994-2

Results from the global analysis


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1Global cracked analysis

Stress distribution c in the concrete slab for the characteristic SLScombination of actions assuming the concrete resists in every cross

1

In the zones where c < - 2 fctm , the concrete is assumed to be cracked(and then neglected) for the bending stiffness distribution (EI2)

EI1

EI2

EI1= un-cracked composite second moment of area

+

EI2= cracked composite second moment of area

(structural steel + reinforcement in tension)

This approach is not iterative (the cracked zones are

determined only once).!


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Global cracked analysis 1

Simplified method is possible if :

- no re-stress

EI2

0.15 (L1+ L2)

- Lmin/Lmax > 0.6

s

EI1

L1 L2

Ac = 0

concrete in tension is neglected

reinforcement are included


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In-span steel yielding 2

Mid-span eventual yielding is taken into account if : Class 1 or 2 at mid span (and MEd > Mel,Rd )

Lmin/Lmax < 0.6

max min

Class 1 or 2 Class 3 or 4

As Lmin/Lmax > 0.6 in the example, the redistribution due toyielding near mid-span is not taken into account.


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1 2 3 16 15 14 4 5 6 7 13 12 11 10 9 8

Concreting phases, Slab segments order:

5

N/mm)

ination

0

0 20 40 60 80 100 120 140 160 180 200

ncreteslab

icS

LScomb

-10

-5

2

ctm2f 6.4 N/mm

tressesinc

Characterist

-15

x = 35.0 m x = 76.0 m x = 124.0 m x = 152.0 m

Cracked zone for P1

41.0 % 19.5 %

Cracked zone for P2

19.5 % 20.0 %


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SLS and ULS shear force distribution VEd

10

6.02 5.98

.

4.83

.

6

8 Characteristic SLS

Fundamental ULS

2.78

2

4

es(MN)

-1.90-2

0

0 20 40 60 80 100 120 140 160 180 200

Shearforc

-6.04

-5.74

-6

-4

-8.14-8.01

-10

-


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400

ULS stresses (N/mm) along the steel flanges, calculated without concrete resistance

272.6277.5

200

300

100

-100

0

0 20 40 60 80 100 120 140 160 180 200

-287.1-300

-200

- .

-400


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Thank you for your kind attention !

2010 bridges analysisandmodelling ldavaine

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