eurocodes dealing with steel and composite bridgeslibrary.tee.gr/digital/m2346/m2346_raoul.pdf ·...
TRANSCRIPT
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Eurocodes dealing with steel andcomposite bridgesJoël Raoul
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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
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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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EC3/4 bridges 2008 4
40cm slab
Bracing systemDiaphragm
RailwayRailway bridgesbridgesballast
Inspection path
2 I girders
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EC3/4 bridges 2008 5
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EC3/4 bridges 2008 6
• Steel bracing
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EC3/4 bridges 2008 7
• Concrete slabbracing
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EC3/4 bridges 2008 8
2 types of cross-sectionCross girder not connected to the slab
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EC3/4 bridges 2008 9
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EC3/4 bridges 2008 10
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EC3/4 bridges 2008 11
Cross-girders connected
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EC3/4 bridges 2008 12
2 x 2 lanes
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EC3/4 bridges 2008 13
Box girder bridges
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EC3/4 bridges 2008 14
Box girder bridges (truss)
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EC3/4 bridges 2008 15
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EN 1992 : concrete
�EN 1992-1-1 general rules�EN 1992-2 bridges
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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
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EN 1994 : steel and concrete composite structures
�EN 1992-1-1 general rules�EN 1992-2 bridges
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EN 1994-2 : composite structures
�EN 1994-2 general rules and bridges
Avoid cascades ofreferences
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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
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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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EC3/4 bridges 2008 22
Scope of EN1994-2
• Composite bridges
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EC3/4 bridges 2008 23
Scope of EN1994-2
• Composite members (cross beam)
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EC3/4 bridges 2008 24
Scope of EN1994-2
• Tension members (tie of bowstring arch)
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EC3/4 bridges 2008 25
Scope of EN1994-2
• Composite plates
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EC3/4 bridges 2008 26
Scope of EN1994-2
• Filler beam decks
In transversal direction In longitudinal direction
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EC3/4 bridges 2008 27
Scope of EN1994-2• Composite columns
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EC3/4 bridges 2008 28
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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EC3/4 bridges 2008 29
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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EC3/4 bridges 2008 30
Toughness requirement to EN 1993-1-10
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EC3/4 bridges 2008 31
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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EC3/4 bridges 2008 32
Structural analysis�linear
(material)� non linear
steel
concrete
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EC3/4 bridges 2008 33
Structural analysis
�Elastic
�Plastic (buildings, bridges in accidental situations)
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EC3/4 bridges 2008 34
θ
Class of a steel cross-sectionCl.1
Cl.2Cl.3
Cl.4
Mpl
Mel
θ1 3 6
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EC3/4 bridges 2008 35
Class of webs
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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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EC3/4 bridges 2008 37
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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EC3/4 bridges 2008 38
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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EC3/4 bridges 2008 39
• 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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EC3/4 bridges 2008 40
Cracking of concrete in a composite bridge
If under characteristic combination 2fctm ≤ σc⇒cracked global analysis
EI1EI2
EI1
Cracked zone
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EC3/4 bridges 2008 41
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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EC3/4 bridges 2008 42
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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EC3/4 bridges 2008 43
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EC3/4 bridges 2008 44
Concreting the slab
Segment 12.5 m
Type of loading
Concretingshrinkageequipment
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EC3/4 bridges 2008 45
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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EC3/4 bridges 2008 46
Plate buckling and shear lag
Effectivep width(plate buckling)
effectives width(shear lag)
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EC3/4 bridges 2008 47
Equivalent spans for slab effectives width
eei i
Lb min( ; b )8
=
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EC3/4 bridges 2008 48
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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EC3/4 bridges 2008 49
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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EC3/4 bridges 2008 50
• uncracked section analysis (even in the crackedzone)
• Particular rules where Mel,Rd < MEd < Mpl,Rd
Longitudinal shear
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EC3/4 bridges 2008 51
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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EC3/4 bridges 2008 52
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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EC3/4 bridges 2008 53
Verification at ULS
P1 B
MplRd
MEd
A
Plastification of a fibre
Elasticcalculation
Elasto-plasticcalculation
FB interaction diagrammeFC
P2C
FB
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EC3/4 bridges 2008 54
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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EC3/4 bridges 2008 55
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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EC3/4 bridges 2008 56
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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EC3/4 bridges 2008 57
Instabilities : two possibilities
• Verification formulae
• Second order calculations– Equivalent geometric bow (or
buckling shape) imperfection
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EC3/4 bridges 2008 58
expérimental behaviour mechanical model
M
V
P
Aeff
τ
σ1σ2=-τcr
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EC3/4 bridges 2008 59
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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EC3/4 bridges 2008 60
Principle of verification
λ )(λχ f=Test /theory
uRk PP χ=PRd=PRk/γM
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EC3/4 bridges 2008 61
χ
λ
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EC3/4 bridges 2008 62
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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EC3/4 bridges 2008 63
Fatigue verification in EC3
• verification
partial factor forloading= 1,0
Category ofdetail
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EC3/4 bridges 2008 64
∆σC for each detail
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EC3/4 bridges 2008 65
Choice of detailings