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Eurocodes dealing with steel andcomposite bridgesJoël Raoul
EC3/4 bridges 2008 2
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
EC3/4 bridges 2008 3
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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EC3/4 bridges 2008 6
• 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
EC3/4 bridges 2008 32
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
EC3/4 bridges 2008 36Cl.1 Cl.3 / 4
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
EC3/4 bridges 2008 60
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
EC3/4 bridges 2008 63
Fatigue verification in EC3
• verification
partial factor forloading= 1,0
Category ofdetail
EC3/4 bridges 2008 64
∆σC for each detail
EC3/4 bridges 2008 65
Choice of detailings