Eurocodes dealing with steel andcomposite bridgesJoël Raoul

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Main selected features

• General presentation and scope of EC’srelated to steel and composite bridges

• Materials• Structural analysis• Cross-section analysis at ULS and SLS• Treatment of instabilities• Fatigue

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railwayrailwaybridges(TGV)bridges(TGV)

• TGV south (Lyon)(1981) and west(1990): no steelbridge

• TGV north : 13000 t(3600 m) (1993)

• TGV south of Lyon :42000 t (9500 m)(2001)

• TGV east : all the noncommon bridges26000 t (5790 m)

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40cm slab

Bracing systemDiaphragm

RailwayRailway bridgesbridgesballast

Inspection path

2 I girders

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• Steel bracing

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• Concrete slabbracing

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2 types of cross-sectionCross girder not connected to the slab

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Cross-girders connected

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2 x 2 lanes

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Box girder bridges

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Box girder bridges (truss)

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EN 1992 : concrete

�EN 1992-1-1 general rules�EN 1992-2 bridges

Partie2

bridges

Partie7.1

pylons

Partie7.2

chimneys

Partie 6

Cranes

Partie4.2

tanks

Partie4.3

Pipelines

Partie 5

pilingapplications

Partie1.1

General rulesbuilding

Partie1.2

fire

Partie1.3

sheetings

Partie1.4

Stainless steel

Partie1.5

Plated elements

Partie1.6

shells

Partie1.7

Plated elementsloaded transv.

Partie1.8

joints

Partie1.9

Fatigue

Partie1.10

Brittlefracture

Partie1.11

cables

Partie4.1

Silos

genericrules

Partie1.12 S500 to S690

Eurocode 3 : steel structures

EN 1994 : steel and concrete composite structures

�EN 1992-1-1 general rules�EN 1992-2 bridges

EN 1994-2 : composite structures

�EN 1994-2 general rules and bridges

Avoid cascades ofreferences

EN 1994-2 : rules for drafting (to get a self-sufficient document)The paragraphs specific to buildings in EN 1994-1-1 are put

at the end to be easily modified

EN 1994-1-1

The paragraphs specific to bridges are added at the end ofthe clauses to get a self-sufficient document

EN 1994-2

EN 1994-2 : rules for drafting (to get a self-sufficient document)

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Scope of EN1994-2

• Composite bridges

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Scope of EN1994-2

• Composite members (cross beam)

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Scope of EN1994-2

• Tension members (tie of bowstring arch)

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Scope of EN1994-2

• Composite plates

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Scope of EN1994-2

• Filler beam decks

In transversal direction In longitudinal direction

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Scope of EN1994-2• Composite columns

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Materials

• Concrete :– Between C20 and C60 for composite bridges (C 90

for concrete bridges)

• Steel :– up to S460– S 500 to S 700 in a separate part for steel bridges

(due to lack of knowledge for composite bridges ⇒elastic design)

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t

∆σ=56 Mpa

B

L

t

2c

a

T

Initial defect a/c=0.4 et a0 = 0.5 ln t (if t=80mm a0=2.2mm2c0=11mm)

Damage Dmax=1

Paris law : da/dN = C ∆Km with m=3 and C=1.83 10-13

∆K = ∆σ (πan)0.5 Y Mk with Y=f(a,c,B,t) and Mk=f(T,L,B,θ,a,t)

Final critical defect given by : K1=K1C

Toughness requirement to EN 1993-1-10

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Toughness requirement to EN 1993-1-10

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Structural analysis (steel and composite)

�1st order� 2nd order (deformed structure)

1st or 2nd

order ?αcr ≥ 10

1st order 2nd order

yes no

αcr=Ncr / NEd

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Structural analysis�linear

(material)� non linear

steel

concrete

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Structural analysis

�Elastic

�Plastic (buildings, bridges in accidental situations)

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θ

Class of a steel cross-sectionCl.1

Cl.2Cl.3

Cl.4

Mpl

Mel

θ1 3 6

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Class of webs

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Sections class 1 : plastic analysis (not for bridges)

Sections class 2 : elastic analysis up to Mpl,Rd

Sections class 3 : elastic analysis up to Mel,Rd

Large composite bridges (in general)

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Class of a cross section• Corresponds to the largest class of all the

elements• A composite section is generally class 1 under

positive moment due to the location of thePNA (the web is in tension)

compression

tension

PNA (+)

(−)

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Global analysisIn the global analysis, two aspects are considered.

Cracking of concreteon support

Mel,Rd

Mpl,Rd

θ

Class 1

Non linear behaviourat mid span

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• Redistribution due to plastification at mid-span isneglected except if :– Class 1 or 2 at mid-span (if MEd > Mel,Rd )– Class 3 or 4 on support– Lmin/Lmax < 0.6

• Non-linear elastic analysis or• Linear elastic analysis with MEd < 0.9 Mpl,Rd in

sagging moment regions

Cl.1/2

Cl.3 / 4

M

θ

Linear elastic analysis of a composite bridge

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Cracking of concrete in a composite bridge

If under characteristic combination 2fctm ≤ σc⇒cracked global analysis

EI1EI2

EI1

Cracked zone

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Cracking of concrete in a composite bridge

• Alternative if– No prestressing (tendons or jacking on supports)– lmin/lmax>0.6

EI1EI2

EI1

Imin Imax

0.15Imax

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Modular ratio used in a composite section( )L 0 L tn n . 1= +ψ φ

Value of t0 : t0 = 1 day for shrinkaget0 = a mean value in case of concrete cast in several stages

a0

cm

EnE

= ( )t 0t tφ = φ − creep coefficient given by EC2 :and

{Lψ is given by : Permanent loads

shrinkageImposed deformations

1,10,551,5

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Concreting the slab

Segment 12.5 m

Type of loading

Concretingshrinkageequipment

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Example of cracked zones in a compositebridge 60-80-60

17 % 15,6 % 23 % 17,7 %

ctm2f 6,4MPa− = −

-12

-10

-8

-6

-4

-2

0

2

4

6

8

0 20 40

60

80 100 120

140

160 180200

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Plate buckling and shear lag

Effectivep width(plate buckling)

effectives width(shear lag)

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Equivalent spans for slab effectives width

eei i

Lb min( ; b )8

=

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Cross-section verification at ULS (M>0)

PNA

Elastic resistance(for class 1, 2, 3)

plastic resistance(for classes 1/2)

0,85 fck/γcfck/γc

(+)

fy/γM

(+)

(−)(−)

ENA

fy/γM

compression

tension

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Cross-section verification at ULS (M<0)

PNA

ENA

Elastic resistanceclass 1, 2, 3

Plastic resistance(Classes 1 and 2)

fsk/γs (−)

(−)

(+)

fy/γMfy/γMcompression

(+)

fy/γM

fsk/γs

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• uncracked section analysis (even in the crackedzone)

• Particular rules where Mel,Rd < MEd < Mpl,Rd

Longitudinal shear

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Studs

hd21 uRk

dP 0,8 f 4= π 2 2 cmRk ckP 0,29 d f E= α

1 2Rk Rk RkP min(P ;P )=

and

h0,2. 1d

α= + if h3 4d≤ ≤

1α=If not

RdP75.0

25.1Rk

RdPP =At U.L.S.

At S.L.S.

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Resistance of 4 studs @300 mm

Resistance of 4 studs @410 mm

Shear flow at SLS inMN/m

Shear flow at ULS inMN/m

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Verification at ULS

P1 B

MplRd

MEd

A

Plastification of a fibre

Elasticcalculation

Elasto-plasticcalculation

FB interaction diagrammeFC

P2C

FB

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Verification at SLS

• Limitation of stresses– As in EN1992-2 and EN1993-2 (fy in the steel part)

• Limitation of crack widths– As in EN1992-2 with tension stiffening

(wk=0.3mm in general)– Using a simplified method

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Simplified method• Minimum reinforcement (to put in general in all the sections)

As.σs = ks.kc.k.fct,eff.Act

ks=0.9 ; k=0.8 ; fct,eff=fctm ; kc depends on the stress distribution, in generalkc=1

σs may be given by a table to limit the crack width

That leads to about 1% of reinforcement

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Simplified method

• Control of cracking (in all the sections subjected to directloading)– Maximum bar diameter– Or maximum spacing

depending on σs = σs,0 + ∆σs with :

For a medium span bridge ∆σs ≅ 100 MPa

aast

sst

ctms

IAIA

f

⋅⋅=

=∆

α

ρασ 4,0

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Instabilities : two possibilities

• Verification formulae

• Second order calculations– Equivalent geometric bow (or

buckling shape) imperfection

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expérimental behaviour mechanical model

M

V

P

Aeff

τ

σ1σ2=-τcr

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Non-dimensional slenderness

for all the instabilitiescr

u

ααλ =

Ncr

y

cr

u fNN

σλ ==

cr

uF

FF=λP

M

3y

ycr

yW

f== τ

ττ

λV

cr

y

cr

uLT

fMM

σλ ==

αu=Fult / FEd

αcr=Fcr / FEd

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Principle of verification

λ )(λχ f=Test /theory

uRk PP χ=PRd=PRk/γM

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χ

λ

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Fatigue verification in EC3

• Calculation of ∆σE,2 under a fatigue loading

• Influence of the type of influence line• Influence of the type of traffic• Influence of the number of lanes

P = 480kN

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Fatigue verification in EC3

• verification

partial factor forloading= 1,0

Category ofdetail

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∆σC for each detail

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Choice of detailings