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Dissemination of information for training Brussels, 2-3 April 2009
EUROCODESBridges: Background and applications
1
EN 1992-2
EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Approved by CEN on 25 April 2005Published on October 2005
Supersedes ENV 1992-2:1996
Prof. Ing. Giuseppe Mancini
o ecn co or no
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
-EN 1992-2 contains principles andapplication rules for the design of bridges
in addition to those stated in EN 1992-1-1
-Scope: basis for design of bridges in
plain/reinforced/prestressed concrete
made with normal/light weight aggregates
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EUROCODEEUROCODE 22 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Section 3Section 3 MATERIALSMATERIALS- Recommended values for Cmin and Cmax
C30/37 C70/85
(Durability) (Ductility)
- cc coe c ent or ong term e ects an un avoura eeffects resulting from the way the load is applied
Recommended value: 0.85 high stress values during construction
- Recommended classes for reinforcement:
B and C
(Ductility reduction with corrosion / Ductility for bending and shear mechanisms)
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reinforcementreinforcement
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Penetration of corrosion stimulating
components in concrete
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Deterioration of concrete
Corrosion of reinforcement by chloride penetration
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Avoiding corrosion of steel in concrete
Design criteria
- Aggressivity of environment- Specified service life
Design measures
- Sufficient cover thickness- Sufficiently low permeability of concrete (in combination with cover
thickness)- Avoiding harmfull cracks parallel to reinforcing bars
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Aggressivity of the environment
Main exposure classes:
The exposure classes are defined in EN206-1. The main classes are:
XO no risk of corrosion or attack
XC risk of carbonation induced corrosion
XD risk of chloride-induced corrosion (other than sea water)
XS risk of chloride induced corrosion (sea water)
XF risk of freeze thaw attack XA chemical attack
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Aggressivity of the environment
Further specification of main exposure classes in subclasses (I)
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Procedure to determine cmin,dur
EC-2 leaves the choice of cmin,dur to the countries, but gives the followingrecommendation:
The value cmin,dur depends on the structural class, which has to be
determined first. If the specified service life is 50 years, the structural class
is defined as 4. The structural class can be modified in case of the
- The service life is 100 years instead of 50 years
- The concrete strength is higher than necessary
- a s pos t on o re n orcement not a ecte y construct on process- Special quality control measures apply
.
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Table for determinin final Structural Class
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Final determination of cmin,dur(1)
The value cmin,duris finally determined as a function of the structuralclass and the exposure class:
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Special considerations
In case of stainless steel the minimum cover may bereduced. The value of the reduction is left to the decision
.
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-
waterproofing
Exposed concrete surfaces within (6 m) of the
carriage way and supports under expansion
oints: directl affected b de-icin salt
- When de-icing
salt is used Recommended classes for surfaces directly- ,
covers given in tables 4.4N and 4.5N for XD
classes
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Section 5Section 5 Structural analysisStructural analysis- Linear elastic analysis with limited redistributions
Limitation of due to uncertaintes on size effectand bending-shear interaction
.
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-
Restrictions due to uncertaintes on size effect and bending-shear
interaction:
. or concree s reng casses uxd 0.10 for concrete strength classes C55/67
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- Rotation capacity
Restrictions due to uncertaintes on size effect and bendin -shear
interaction:
0.30 for concrete strength classes C50/60x
hinges
d 0.23 for concrete strength classes C55/67
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Numerical rotation capacity
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- Nonlinear analysis Safety format
Reinforcing steel Prestressing steel Concrete
Mean values
Mean values Sargin modified
mean values
.yk
.yk
.pk
cffck
cf= 1.1 s / c
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Design format
Incremental analysis from SLS, so to reachG Gk + Q Q in the same step
Continuation of incremental procedure up to the
peak strength of the structure, in corrispondance
of ultimate load qud
Evaluation of structural strength by use of a
global safety factor0
udq
0
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Verification of one of the following inequalities
ud Rd G QO
q E G Q R
udG Q
q E G Q R
. Rd O
udqR (i.e.)
'O
q Rd Sd g q
O
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Rd = 1.06 partial factor for model uncertainties (resistence side)
With Sd = 1.15 partial factor for model uncertainties (actions side)
0 = 1.20 structural safety factor
If Rd = 1.00 then 0 = 1.27 is the structural safety factor
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Safety formatApplication for scalar combination of internal actions
and underproportional structural behaviour
ADE
E,R
udqR
Rd
OudqR
F G
SdRd
Oudq
BCH H
qqud
O
udq
max
QG qg
maxQG QG
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Safety formatApplication for scalar combination of internal actions
and overproportional structural behaviour
,
A
E D
O
udqR
F
G Rd
OudqR
OudqR
F
G
H C B
SdRd
H
qudq
O
udq
maxQG QG
max
QG qg
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Safety formatApplication for vectorial combination of internal
actions and underproportional structural behaviour
sd, rd
IAP
A
ud
O
udqM
C
D
aRd
O
udqM
Nsd,Nrd
b
udqNq O
O
udq
N Rd
O
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Safety formatApplication for vectorial combination of internal
actions and overproportional structural behaviour
a
sd , rd
IAP
A udqM
C
B
O
udqM
N sd,N r
D
udRd
udqM
udq O
OO
O
udqN
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
For vectorial combination and = = 1.00 the safet
check is satisfied if:
0 '
ud
ED Rd
qM M
and
0 '
u
ED Rd N N
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Concrete slabs without shear reinforcement
Shear resistance VRd,c governed by shear flexure failure:
s ear crac eve ops rom exura crac
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Concrete slabs without shear reinforcement
Prestressed hollow core slab
Shear resistance VRd,c governed by shear tension failure:
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Shear design value under which no shear
re n orcemen s necessary n e emen s
unreinforced in shear (general limit)
CRd,c coefficient derived from tests (recommended 0.12)
k size factor = 1 + (200/d) with d in meter
lon itudinal reinforcement ratio 0,02
fck characteristic concrete compressive strengthbw smallest web width
d effective height of cross section
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EUROCODEEUROCODE 22 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Shear design value under which no shear
re n orcemen s necessary n e emen s
unreinforced in shear (general limit)
Minimum value for VRd,c
VRd,c= vminbwd
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Axial actions and bending
moments in the outer la er
Membrane shear actions and
twisting moments in the outer layer
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Edx Edy
with lever arm zc, determined with reference to the centroid of theappropriate layers of reinforcement.
For the design of the inner layer the principal shearvEdo and itsdirection o should be evaluated as follows:
EUROCODE 2EUROCODE 2 D i fD i f
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beam and the appropriate design rules should therefore be applied.
EUROCODE 2EUROCODE 2 D i f t t tD i f t t t
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
When shear reinforcement is necessary, the longitudinal force
resulting from the truss model VEdocot gives rise to the followingmembrane forces in xand ydirections:
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The outer layers should be designed as membrane elements, using
the design rules of clause 6 (109) and Annex F.
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
EdyEdxy
- Membrane elements
Edxy
Edx
Edx
Edxy
Edxy
Edy
Compressive stress field strength defined as a function
of principal stresses
If both principal stresses are comprensive
1 3,800.85
1 is the ratio between the two
principal stresses ( 1)
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EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Where a plastic analysis has been carried out with = eland at least one principal stress is in tension and no
reinforcement yields
max 0,85 0,85s
cd cd f
yd
is the maximum tensile stress
value in the reinforcement
Where a plastic analysis is carried out with yielding of any
reinforcement
max 1 0,032cd cd elf
is the angle to the X axis of plastic
is the inclination to the X axis of
principal compressive stress in
the elastic analysis
(principal compressive stress)
15el degrees
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Model by Carbone, Giordano, Mancini
Assumption: strength of concrete subjected to biaxialstresses is correlated to the angular deviation
between angle el which identifies the
principal compressive stresses in incipientu
inclination of compression stress field in
concrete at ULS
With increasin concrete dama e increasesprogressively and strength is reduced accordingly
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Plastic equilibrium condition
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0.50
Graphical solution of inequalities system
0.30
0.35
0.40
0.45
Eq. 69
Eq. 70
Eq. 71
Eq. 72
x = 0.16
0.10
0.15
0.20
0.25v
E . 73
y = 0.06nx = ny = -0.17
el = 45
0.00
0.05
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0
pl
.
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xper men a versus ca cu a e pane s reng y ar an au mann a
and by Carbone, Giordano and Mancini (b)
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U OCOU OCO es g o co c ete st uctu eses g o co c ete st uctu esConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Skew reinforcement
yrxyr
xr xr conventions
xyrY r
Thickness = tr
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ggConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
br
rsrbr
1
E uilibrium of the
rsr ar xr sinr
ar
sinr
xyr sinr
section parallel to
the compression
fieldryr cosr xyr cosr
cosr
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ggConcrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
br
rsr br
cr
cosrxr cosr
xyr cosr
r ar rsr ar
1
section orthogonal to
the compression
field
r sinrxyr sinr
sinr
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Use of genetic algorithms (Genecop III) for the optimization ofreinforcement and concrete verification
Objective: minimization of global reinforcement
Stabilit : find correct results also if the startin oint is ver
far from the actual solution
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Section 7Section 7 Serviceability limit state (SLS)Serviceability limit state (SLS)
- 1 ck
classes XD, XF, XS (Microcracking)
k1 = 0.6 (recommended value)
=1 .
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Reinforced members and Prestressed members with
- Crack control
Classprestressed members with
unbonded tendons
bonded tendons
Quasi-permanent loadFrequent load combination
X0, XC1 0,31 0,2
, ,
0,3
,
XD1, XD2, XD3
XS1, XS2, XS3Decompression
Note 1: For X0, XC1 exposure classes, crack width has no influence on durability and
this limit is set to guarantee acceptable appearance. In the absence of
appearance conditions this limit may be relaxed.
Note 2: For these exposure classes, in addition, decompression should be checked
under the quasi-permanent combination of loads.
Decompression requires that concrete is in compression within a distance
of 100 mm (recommended value) from bondend tendons
EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresC b id d i d d ili lC b id d i d d ili l
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
For skew cracks where a more refined model is not available,
the following expression for the may be used:
1
rm
cos sins
rm,x rm,y
where srm,x and srm,y are the mean spacing between the cracks
.opening of cracks can than evaluated as:
w s ,
where and c, represent the total mean strain and the mean,
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structuresC t b id d i d d t ili lC t b id d i d d t ili l
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Expressing the compatibility of displacement along the
crack, the total strain and the corresponding stresses in
reinforcement in x and y directions may be evaluated, as
,respectively orthogonal and parallel to the crack direction.
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Moreover, by the effect of w and v, tangential and
orthogonal forces along the crack take place, that can be
the interlock effect.
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Finally, by imposition of equilibrium conditions between
internal actions and forces along the crack, a nonlinear
sys em o wo equa ons n e un nowns w an v may e
derived, from which those variables can be evaluated.
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Annex BAnnex B Creep and shrinkage strainCreep and shrinkage strain
HPC, class R cement, strength 50/60 MPa with orwithout silica fume
Thick members kinetic of basic creep and drying
Autogenous shrinkage:related to process of hydratation
Drying shrinkage:related to humidity exchanges
Specific formulae for SFC (content > 5% of cement by
weight)
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
- Autogenous shrinkage
For t < 28 days fctm(t) / fck is the main variable
t
cmf t 6( )cmf t
0.1ckf
,ca ck
.ckf
, . .ca ck ck ckf
For t 28 days
6( , ) ( 20) 2.8 1.1exp( / 96) 10ca ck ck t f f t
97% of total autogenous shrinkage occurs
within 3 mounths
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
- Drying shrinkage (RH 80%)
0 2
0
exp .( , , , , )
( )
ck ck s
cd s ck
s cd
t tt t f h RH
t t h
with: ( ) 18ckK f if fck 55 MPa
30 0.21K if f > 55 MPac c
concretefumesilicanonfor
concretefumesilicaforcd
021.0
007.0
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
- Creep
0t28
, , ,cc dcE
Basic creep Drying creep
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Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
- Basic creep
0
0 0 0
0
, , ,b ck cm bbc
t t
t t f f t t t
0,37
3.6for silica fume concrete
cm 0
b0
1.4 for non silica fume concrete
with:
cm 0ck
bc
f t0.37exp 2.8 for silica fume concretef
cm 0
ck
f t0.4exp 3.1 for non silica fume concrete
f
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g g gg g g
0 0 0 0( , , , , , ) ( , ) ( , )d s ck d cd s cd st t t f RH h t t t t
concretefume-silicafor1000
concretefume-silicanonfor3200
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g g gg g g
- Experimental identification procedure
At least 6 months
- Long term delayed strain estimation
FormulaeExperimental
determination
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g g gg g g
- t
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Annex KKAnnex KK Structural effects of timeStructural effects of timeepen en e av our oepen en e av our o
concreteconcrete
Creep and shrinkage indipendent of each other
Assumptions Average values for creep and shrinkage withinthe section
Validity of principle of superposition (Mc-Henry)
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Type of analysis Comment and typicalapplication
- -
method applicable to all structures. Particularly
useful for verification at intermediatestages of construction in structures in
(e.g.) cantileverconstruction.
Methods based on the theorems of linear
viscoelasticity
Applicable tohomogeneous structures with
rigidrestraints.
Theageingcoefficient method This mehod will be useful when only the
long -term distribution of forces and
.
bridges with composite sections (precast
beamsandin-situconcreteslabs).
Simplifiedageingcoefficient method Applicable to structures that undergo
changes in support conditions (e.g.) span-
to- spanor freecantilever construction.
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- General method
0 001
( , )1( ) ( , ) ,28 28
n ic i cs s
i
t tt t t t t t E t E E t E
A step by step analysis is required
- Incremental method
At the time t of application of the creep strain cc(t),the potential creep strain cc(t) and the creep rate arederived from the whole load history
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The potential creep strain at time t is:
28
( ) ( , )cc
c
d t d t
dt dt E
e
under constant stress from te the same cc(t) and
cc
,cc c e cct t t t
Creep rate at time t may be evaluated using the creepcurve for te
,( ) c ecc
cc
t td tt
dt t
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For unloading procedures
|cc(t)| > |cc(t)| e
( ) ( ) ( ) ( ) ,
ccMax cc ccMax cc c et t t t t t
( ) ( ) ,( ) ( )
ccMax cc c e
ccMax cc
d t t t t t t
dt t
where ccMax(t) is the last extreme creep strain reached before t
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- Application of theorems of linear viscoelasticity
J(t,t0) an R(t,t0) fully characterize the dependent propertiesof concrete
Structures homogeneous, elastic, with rigid restraints
Direct actions effect
elt t
( ) ,t
C elD t E J t dD 0
Di i ti f i f ti f t i i Vi 4 6 O t b 2010 69
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Indirect action effect
el
0
1( ) ,
t
elS t R t dSE
Structure subjected to imposed constant loads whose initial
statical scheme (1) is modified into the final scheme (2) by
n ro uc on o a ona res ra n s a me 1 0
2 ,1 0 1 ,1, ,el elS t S t t t S
0 1 01
, , , ,
t
t
t t t R t dJ t
0
0 0
0
,, , 1
C
t tt t t
E t
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When additional restraints are introduced at different times
t t the stress variation b effect of restrain introduced attj is indipendent of the history of restraints added at ti < tj
j
, ,1
e ei
- ge ng coe c en me o
Integration in a single step and correction by means of
(28) (28)t c cE Et d t t t t
0
00( ) ( )t c c E E t
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- Simplified formulae
( , ) ( , ) ( )t t t E t
0 1 0 1 01 , ( )ct E t
where: S0 and S1 refer respectively to construction and
t1 is the age at the restraints variation
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ENEN 19921992--22 A new design code to help inA new design code to help inconceiving more and moreconceiving more and more
en ance concre e r gesen ance concre e r ges
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g
Thank you for the
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Durability cover to reinforcement
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Structural class (table 4.3 N)
To face of the slab : Bottom face of the slab :
XC3 XC4
Final class : 3 4
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cmin,dur(table 4.4 N)
Top face of the slab :
XC3 str. class S3
Bottom face of the slab :
XC4 str. class S4
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cnom = cmin + cdev (allowance for deviation, expr. 4.1)cdev = 10 mm (recommended value 4.4.1.3 (1)P ) dev . . . in case of quality assurance system with measurements of the
concrete cover, the recommended value is:
mm cdev mm
min,b min,dur dev nomTop face of the slab 20 20 10 30
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The verifications of transverse bending and vertical
representing a 1-m-wide slab strip. Anal sis: For permanent loads, which are uniformly distributed over the length of
the deck, the internal forces may be calculated on a simplified model:
isostatic beam on two supports.
For traffic loads, it is necessary to take into account the 2-dimensional
behaviour of the slab. For the design example, the extreme values of
transverse internal forces and moments are obtained reading charts
es a s e y e ra or e oca en ng o e s a n w n-g r er
composite bridges. These charts are derived from the calculation ofinfluence surfaces on a finite element model of a typical composite
.
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Analysis - Transverse distribution of permanent loads
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Analysis - transverse bending moment envelope due to permanent loads
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Analysis - Maximum effect of traffic loads
Influence surface of the
transverse moment above
the main girder
transverse momentabove the main girder vs.
width of the cantilever
Position of UDL
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Combination of actions
Transverse bending moment
QuasiCharacteristic
m m permanenSLS
requenSLS
Section above
the main
-46 -156 -204 -275girder
Section at
mid-span 24 132 184 248
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Bending resistance at ULS (EN1992-1-1, 6.1)Stress-strain relationships:
for the concrete, a simplified rectangular stress distribution: = 0,80 and = 1,00 as fck= 35 MPa 50 MPa
fcd= 19,8 MPa (with cc= 0,85 recommended value)cu3 = 3,5 mm/m
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Bending resistance at ULSStress-strain relationships: for the reinforcement, a bi-linear stress-strain relationship with strain
hardening (Class B steel bars according to Annex C to EN1992-1-1):
fyd
= 435 Mpa, k= 1,08, ud
= 0,9.uk
= 45 mm/m (recommended value)
s yd s s ss fors fyd/ Es s = fyd+ (k 1) fyd(s fyd/ Es)/ (uk fyd/ Es)
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Verification of the transverse reinforcement
B di i t t ULS
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Bending resistance at ULS s = cu3 (d x)/x s = yd+ yd s yd s uk yd s nc ne op ranc Equilibrium : NEd = 0 Ass = 0,8b.x.fcd where b = 1 m
Then, xis the solution of a
uadratic e uation The resistant bending moment
is given by:0,8x
MRd = 0,8b.x.fcd(d 0,4x)
=Ass(d 0,4x)
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Verification of the transverse reinforcement
B di i t t ULS d i l
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Bending resistance at ULS design exampleSection above the main steel girder (absolute values of moments)
w = , m an s= , cm every , m : x= 0,052 m , s = 20,6 mm/m (< ud) and s = 448 Mpa
Rd , . Ed , .
- with d= 0,26 m andAs= 28,87 cm
2 (25 every 0,17 m): x= 0,08 m , = 7,9 mm/m (< ) and = 439 MPa Therefore MRd = 0,289 MN.m > MEd = 0,248 MN.m
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Stress limitation nder SLS characteristic combination
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Stress limitation under SLS characteristic combination The following limitations should be checked (EN1992-1-1, 7.2(5) and7.2(2)) :
s k3fyk = 0,8x500 = 400 MPa
c k1fck = 0,6x35 = 21 MPa
where k1 and k3 are defined by the National Annex to EN1992-1-1
e recommen e va ues are 1 = , an 3 = ,
These stress calculations are performed neglecting the tensile
. s the reinforcement are generally provided by the long-term
calculations, performed with a modular ratio n
compressive stresses c
in the concrete are generally provided by
the short-term calculations, performed with a modular ratio
n = E /E = 5,9 (E = 200 GPa for reinforcing steel and E = 34 GPa
for concrete C35/45).
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Stress limitation under SLS characteristic combination
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Stress limitation under SLS characteristic combination
The design example in the section above the steel main girder givesd= 0,36 m,As = 18,48 cm
2 and M= 0,204 MN.m.
Using n = 15, s = 344 MPa < 400 MPa is obtained.
Using n = 5,9, c= 15,6 MPa < 21 MPa is obtained.
The design example in the section at mid-span between the steelmain girders gives d= 0,26 m,As = 28,87 cm
2 and M= 0,184 MN.m.
, s .Using n = 5,9, c= 20,0 MPa < 21 MPa is obtained.
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Crack control (SLS)
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Crack control (SLS)
According to EN1992-2, 7.3.1(105), Table 7.101N, the calculatedcrack width should not be greater than 0,3 mm under quasi
permanent combination of actions, for reinforced concrete,
whatever the exposure class.
Exposure
Class
Reinforced members and prestressed
members with unbonded tendons
Prestressed members with
bonded tendons
Quasi-permanent load combination Frequent load combination
X0, XC1 0,31 0,2
XC2, XC3, XC4 0,22
0,3XD1, XD2, XD3 XS1,
XS2, XS3
Decompression
Note 1: For X0, XC1 exposure classes, crack width has no influence on durability and this limit is set to
guarantee acceptable appearance. In the absence of appearance conditions this limit may
e re axe .
Note 2: For these exposure classes, in addition, decompression should be checked under the quasi-
permanent combination of loads.
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Crack control (SLS)
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Crack control (SLS)
In the design example, transverse bending is mainly caused by liveloads, the bending moment under quasi-permanent combination is
far lesser than the moment under characteristic combinations. It is
the same for the tension in reinforcing steel. Therefore, ther is no
problem with the control of cracking.
The concrete stresses due to transverse bending under quasipermanent combination, are as follows:
M= - 46 kNm/m c = 1,7 MPa
at mid-span between the main girders: c ,
Since
c > - fctm , the sections are assumed to be uncracked(EN1992-1-1, 7.1(2)) and there is no need to check the crack
o enin s. A minimum amount of bonded reinforcement is re uired
in areas where tension is expected (EN1992-1-1, 7.3.2)
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Crack control (SLS) - design example
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Crack control (SLS) - design example Minimum reinforcement areas (EN1992-1-1 and EN1992-2 , 7.3.2)
As,mins = kc k fct,effAct ( 7.1)
For the design example:
ct = = m ; = , m a ove ma n g r er an , m a m -span s = fyk (lower value only when control of cracking is ensured by limiting bar
size or spacing according to 7.3.3)
= =, , k= 0,65 (flanges with width 800 mm) kc = 0,4 ( expression 7.2 with c mean stress of the concrete = 0)
The following areas of reinforcement are obtained:
As,min = 5,12 cm2
/m on top face of the slab above the main girder As,min = 4,10 cm
2/m on bottom face of the slab at mid-span
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Local justification of the concrete slab
Verification of the transverse reinforcement
Resistance to vertical shear force - ULSA i th f i f t i t i ( Fi 6 3 i EN1992
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Resistance to vertical shear force ULS Asl is the area of reinforcement in tension (see Figure 6.3 in EN1992-1-1 for the provisions that have to be fulfilled by this reinforcement).
For the design example,Asl represents the transverse reinforcing
steel bars of the upper layer in the studied section above the steel
main girder. bw is the smallest width of the studied section in the
ens e area. n e s u e s a w = mm n or er o o a n a
resistance VRd,c to vertical shear for a 1-m-wide slab strip
(rectangular section).
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Resistance to vertical shear force ULS
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Resistance to vertical shear force ULS
According to EN1992, shear reinforcement is needed in the slab,near the main girders. With vertical shear reinforcement, the shear
design is based on a truss model (EN1992-1-1 and 1992-2, 6.2.3, fig.. :
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Resistance to vertical shear force ULS
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es sta ce to e t ca s ea o ce U S
For vertical reinforcement = 90 the resistance V is the smallervalue of:
VRd,s = (Asw/s).z.fywd.cot and= + ,max cw w c where: z is the inner lever arm (z= 0,9dmay normally be used for members
without axial force)
,chosen such as 1 cot 2,5 Asw is the cross-sectional area of the shear reinforcement s is the spacing of the stirrups yw 1 is a strength reduction factor for concrete cracked in shear, the
recommended value of1 is = 0,6(1-fck/250) cw is a coefficient taking account of the interaction of the stress in the
recommended value ofcw is 1 for non prestressed members.
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Resistance to vertical shear force ULS
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In the desi n exam le choosin cot = 2 5 with a shearreinforcement areaAsw/s = 6,8 cm
2/m for a 1-m-wide slab strip:
VRd s = 0,00068x(0,9x0,36)x435x2,5 = 240 kN/m > VEd
VRd,max = 1,0x1,0x(0,9x0,36)x0,6x(1 35/250)x35/(2,5+0,4)
= 2,02 MN/m > Ved
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Verification of the transverse reinforcement
Resistance to longitudinal shear stress - ULS
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gThe longitudinal shear force per unit length at the steel/concrete
n er ace s e erm ne y an e as c ana ys s a c arac er s c an
at ULS. The number of shear connectors is designed thereof, to resist
to this shear force per unit length and thus to ensure the longitudinal.
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Resistance to longitudinal shear stress - ULS
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At ULS this longitudinal shear stress should also be resisted to for any
po en a sur ace o ong u na s ear a ure w n e s a .
Two potential surfaces of shear failure are defined in EN1994-2, 6.6.6.1,
fig 6.15:
surface a-a holing only once by
the two transverse
reinforcement layers,
As = Asup + Ainfthere are 2 surfaces a-a.
sur ace - o ng w ce y e
lower transverse reinforcementlayers, As = 2.Ainf
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Resistance to longitudinal shear stress - ULS
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The maximum longitudinal shear force per unit length resisted to by
, .
verifying shear failure within the slab. The shear force and on each
potential failure surface is as follows
surface a-a, on the cantilever
side : 0,59 MN/m
- ,side : 0,81 MN/m
- ,
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Verification of the transverse reinforcement
Resistance to longitudinal shear stress - ULSFailure surfaces a-a:
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a u e su aces a a The shear resistance is determined according to EN1994-2, 6.6.6.2(2), which
refers to EN1992-1-1, 6.2.4, fig. 6.7 (see below), the resulting shear stress is :
vEd = Fd/(hf x)where:
f xis the length under consideration, see Figure 6.7Fd is the change of the normal force in the flange over the length x.
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Dissemination of information for training Vienna, 4-6 October 2010 37
Local justification of the concrete slab
Verification of the transverse reinforcement
Interaction shear/transverse bending - ULSTh t ffi l d d l h th t th b d th
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The traffic load models are such that they can be arranged on the
pavemen o prov e a max mum ong u na s ear ow an a
maximum transverse bending moment simultaneously. EN1992-2,
6.2.4 (105) sets the following rules to take account of this
the criterion for preventing the crushing in the compressive struts isverified with a height hfreduced by the depth of the compressive
concrete is worn out under compression, it cannot simultaneously
take up the shear stress);
the total reinforcement area should be not less thanA +A /2whereAflex is the reinforcement area needed for the pure bending
assessment andAshearis the reinforcement area needed for the purelongitudinal shear flow.
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Local justification of the concrete slab
Verification of the transverse reinforcement
Interaction shear/transverse bending - ULSCrushing in the compressive struts
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Crushing in the compressive struts
. fis not a problem therefore.
shear plane a-a:hf red = hfxULS = 0,40-0,05 = 0,35 mvEd,red = vEd.hf/hred = 0,81/0,35 = 2,31 MPa 6,02 MPa
shear plane b-b:hf,red = hf 2xULS = 1,185 2x0,.05 = 1,085 m
Ed,red Ed. f red , , , ,
Total reinforcement area:
Aflex = 18,1 cm2/m required
Ashear= 14,9 cm2/m required
Ashear/2 +Aflex = 25,6 cm2
/mAs = 30,3 cm2/m : the criterion is saatisfied
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Local justification of the concrete slab
Verification of the transverse reinforcement
ULS of fatigue transverse bending
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The slow lane is assumed to be close to the safet barrier and the the
fatigue load is centered on this lane
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Local justification of the concrete slab
Verification of the transverse reinforcement
ULS of fatigue transverse bendingFatigue load model FLM3 is used Verification are performed by the damage
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Fatigue load model FLM3 is used. Verification are performed by the damage
- - , . . - ,
FLM3 (Axle loads 120 kN)
Variation of transverse bending
39 kN.m/m
girder during the passage of
FLM 3
s(FLM3) = 63 Mpa
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Local justification of the concrete slab
Verification of the transverse reinforcement
ULS of fatigue transverse bendingDamage equivalent stress range method
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Damage equivalent stress range method
EN1992-1-1, 6.8.5:
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Local justification of the concrete slab
Verification of the transverse reinforcement
ULS of fatigue transverse bendingDamage equivalent stress range method
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Damage equivalent stress range method
F,fat s e par a ac or or a gue oa - - , . . . . erecommended value is 1,0
Rsk (N*) = 162,5 MPa (EN1992-1-1, table 6.3N) s,fat is the partial factor for reinforcing steel (EN1992-1-1, 2.4.2.4). The
recommended value is 1,15.
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Local justification of the concrete slab
Verification of the transverse reinforcement
ULS of fatigue transverse bendingAnnex NN NN.2.1 (102)
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Annex NN NN.2.1 (102)
s,equ = s,Ec.swhere
s,Ec = s , . s ress range ue o , mes , n e case
of pure bending, it is equal to 1,4 s(FLM3) . For a verification of fatigue
on intermediate supports of continuous bridges, the axle loads of FLM3
,s is the damage coefficient.s = fat.s,1. s,2. s,3. s,4where is a d namic ma nification factor
s,1 takes account of the type of member and the length of the influenceline or surfaces 2 takes account of the volume of traffics,3 takes account of the design working lifes,4 takes account of the number of loaded lanes
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Local justification of the concrete slab
Verification of the transverse reinforcement
ULS of fatigue transverse bendingAnnex NN NN.2.1 (104)
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Annex NN NN.2.1 (104)
s,1 is given by figure NN.2, curve 3c) . In the design example, the lengthof the influence line is 2,5 m. Therefore s,1 1,1
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Local justification of the concrete slab
Verification of the transverse reinforcement
ULS of fatigue transverse bendingAnnex NN NN.2.1 (105)
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( )
k = 9 table 6.3 N N = 0 5.106 EN1991-2 table 4.5 Q = 0 94
s,2 = 0,81
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Local justification of the concrete slab
Verification of the transverse reinforcement
ULS of fatigue transverse bendingAnnex NN NN.2.1 (106) and (107)
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( ) ( )
s,3 = 1 (design working life = 100 years)s,4 = 1 (different from one if more than one lane are loaded)fat ,where fat = 1,3
s = 0,89 (1,16 near the expaxsion joints)s,Ec = 1,4x63 = 88 MPas,eq = 78 MPa (102 near the expansion joints)Rsk/ s,fat = 162,5/1,15 = 141 MPa > 102 MPaThe resistance of reinforcement to fatigue under transverse bending is
verified
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Second order effects in the high piers
Pier height : 40 m
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external diameter : 4 m
wall thickness : 0,40
lon itudinal reinforcement: 1 5%
Ac = 4,52 m2
Ic = 7,42 m4
As = 678 cm2
Is = 0,110 m4Pier head:
volume : 54 m 3
e g : ,
Concrete
C35/45
ck
Ecm = 34000 MPa
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Second order effects in the high piers
The second order effects are analysed by a simplifiedmethod: EN1992-1-1, 5.8.7 - method based on nominal
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.
direction.
Geometric imperfection (EN1992-1-1, 5.2(5):l = 0hwhere
0 = 1/200 (recommended value)h = 2/l1/2 ; 2/3 h 1lis the height of the pier = 40 m
l = 0,0016 resulting in a moment underpermanent combination M0Eqp = 1,12 MN.m at the
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Second order effects in the high piers
First order moment at the base of the pier: M0Ed = 1,35 M0Ed + 1,35 Fz (0,4UDL + 0,75TS).l.l
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, x . , , x k .
M0Ed
= 28,2 MN.m
Effective creep ratio (EN 1992-1-1, 5.8.4 (2)):
ef= 2.(1,12/28,2) = 0,08
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Second order effects in the high piers
Nominal stiffness (EN1992-1-1, 5.8.7.2 (1)
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Ecd= Ecm/cE = 34000/1,2 = 28300 MPa
Ic = 7,42 m4
s
Is = 0,110 m
4
Ks = 1
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Dissemination of information for training Vienna, 4-6 October 2010 54
Second order effects in the high piers
.Moment magnification factor (EN1992-1-1, 5.8.7.3)
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Second order effects in the high piers
Moment magnification factor (EN1992-1-1, 5.8.7.3)
0Ed
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0Ed , . = 0,85 (c0 = 12)NB = 2EI/l02 = 118 MNNEd = 26 MN (mean value on the height of the pier)
MEd = 1,23 M0Ed = 33,3 MN.m
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Thank ou for our kind attention
Dissemination of information for training Brussels, 2-3 April 2009
EUROCODESBridges: Background and applications
1
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steelsteel--concrete composite two girder bridgeconcrete composite two girder bridge
Prof. Ing. Giuseppe Mancini.Politecnico di Torino
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Span Distribution
Basic geometry of crosssection
Dissemination of information for training Vienna, 4-6 October 2010 3
Application of external prestressing toApplication of external prestressing tosteelsteel--concrete composite two girder bridgeconcrete composite two girder bridge
Structural steel distribution for main girder
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Dissemination of information for training Vienna, 4-6 October 2010 4
Application of external prestressing toApplication of external prestressing tosteelsteel--concrete composite two girder bridgeconcrete composite two girder bridge
The not prestressed original solution has beencompare w t 4 erent so ut ons w t externa
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compare w t 4 erent so ut ons w t externaprestressing.
Comparison has been done taking into account only:
1. SLU bending and axial force verification during constructionphases and in service
. at gue ver cat on3. SLS crack control
1. Reduction of steel girder
2. Reduction of slab longitudinal ordinary steel.
Dissemination of information for training Vienna, 4-6 October 2010 5
Application of external prestressing toApplication of external prestressing tosteelsteel--concrete composite two girder bridgeconcrete composite two girder bridge
1st
prestressing layout4x22 0.6 strand tendons on green layout
100% t i li d t t l i d
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100% prestressing applied to steel girder
1.5
2
2.5
0
0.5
1
0 20 40 60 80 100 120 140 160 180 200
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Application of external prestressing toApplication of external prestressing tosteelsteel--concrete composite two girder bridgeconcrete composite two girder bridge
2nd
prestressing layout2x22 0.6 strand tendons on green layout
.
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100% prestressing applied to steel girder
1.5
2
2.5
0
0.5
1
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Application of external prestressing toApplication of external prestressing tosteelsteel--concrete composite two girder bridgeconcrete composite two girder bridge
3rd
prestressing layout4x22 0.6 strand tendons on green layout
50% prestressing applied to steel girder
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50% prestressing applied to steel girder +50% prestressing applied to steel composite section
1.5
2
2.5
0
0.5
1
0 20 40 60 80 100 120 140 160 180 200
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4th
prestressing layout2x22 0.6 strand tendons on green layout
.
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50% prestressing applied to steel girder +
50% restressin a lied to com osite section
2
2.5
0.5
1
1.5
0 20 40 60 80 100 120 140 160 180 200
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Application of external prestressing toApplication of external prestressing tosteelsteel--concrete composite two girder bridgeconcrete composite two girder bridge
SLU internal actions on NOT prestressed girder at t0
120
mMN
100 Mmax
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MN80
60
Mmin
Resistantbendingmoment(Mmax)
N(Mmax)
40
20
0
0 10 20 30 40 50 60 70 80 90 100
N Mmin
20
40
60
80
100
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SLU internal actions with 1st
prestressing layout at t0
120
mMN 100
Mmax
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MN 100
80
60
Mmin
Resistantbendingmoment(Mmax)
N(Mmax)
40
200 10 20 30 40 50 60 70 80 90 100
N(Mmin)
20
40
60
80
100
Dissemination of information for training Vienna, 4-6 October 2010 11
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SLU actions with 2nd
prestressing layout at t0
mMN 100
Mmax
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MN 100
80
Mmin
Resistantbendingmoment(Mmax)
N(Mmax)
40
200 10 20 30 40 50 60 70 80 90 100
N(Mmin)
0
20
40
60
80
100
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SLU internal actions with 3rd
prestressing layout at t0
120
mMN 100 Mmax
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MN
80
Mmin
Resistantbendingmoment(Mmax)
N(Mmax)
40
200 10 20 30 40 50 60 70 80 90 100
N(Mmin)
0
20
40
60
80
100
Dissemination of information for training Vienna, 4-6 October 2010 13
Application of external prestressing toApplication of external prestressing tosteelsteel--concrete composite two girder bridgeconcrete composite two girder bridge
SLU internal actions with 4th
prestressing layout at t0
mMN
120
100 M
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MN100
80
Mmax
Mmin
Resistantbending
moment(Mmax)
60
40
200 10 20 30 40 50 60 70 80 90 100
N(Mmin)
0
20
40
60
80
100
Dissemination of information for training Vienna, 4-6 October 2010 14
Application of external prestressing toApplication of external prestressing tosteelsteel--concrete composite two girder bridgeconcrete composite two girder bridge
ConclusionsThe following quantities have been obtained
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QuantitiesNo Prestressinglayout
.
Girdersteel [kg/m2] 256 202 194 190 201Prestressingsteel [kg/m2] 0 16.0 11.6 16.0 11.6Slablongitudinalordinary
. .
TopslabinSLSfrequent[status] cracked cracked cracked
Compres Compres
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Thank you for the