2010 Bridges EN1992 GMancini EBouchon

8/8/2019 2010 Bridges EN1992 GMancini EBouchon

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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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Dissemination of information for training Vienna, 4-6 October 2010 2


-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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Penetration of corrosion stimulating

components in concrete


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Deterioration of concrete

Corrosion of reinforcement by chloride penetration


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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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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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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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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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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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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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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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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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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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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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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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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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When shear reinforcement is necessary, the longitudinal force

resulting from the truss model VEdocot gives rise to the followingmembrane forces in xand ydirections:

EUROCODE 2EUROCODE 2 Design of concrete structuresDesign of concrete structures


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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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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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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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Section 7Section 7 Serviceability limit state (SLS)Serviceability limit state (SLS)

- 1 ck

classes XD, XF, XS (Microcracking)

k1 = 0.6 (recommended value)

=1 .

EUROCODEEUROCODE 22 Design of concrete structuresDesign of concrete structures


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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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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,

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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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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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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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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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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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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- 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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- 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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- Creep

0t28

, , ,cc dcE

Basic creep Drying creep



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- 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

Dissemination of information for training Vienna 4 6 October 2010 70



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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

Dissemination of information for training Vienna 4-6 October 2010 71



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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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Dissemination of information for training Vienna, 4 6 October 2010 72

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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Local justification of the concrete slab

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



Verification of the transverse reinforcement


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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)




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)




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).




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.




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.




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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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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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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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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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




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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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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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

- ,




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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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.




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




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




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




ULS of fatigue transverse bendingDamage equivalent stress range method


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Damage equivalent stress range method

EN1992-1-1, 6.8.5:




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.




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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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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( )

k = 9 table 6.3 N N = 0 5.106 EN1991-2 table 4.5 Q = 0 94

s,2 = 0,81




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


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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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



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



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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.Moment magnification factor (EN1992-1-1, 5.8.7.3)


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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


Application of external prestressing toApplication of external prestressing tosteelsteel--concrete composite two girder bridgeconcrete composite two girder bridge


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Span Distribution

Basic geometry of crosssection



Structural steel distribution for main girder


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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.



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



2nd


.


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1.5

2

2.5

0

0.5

1



3rd




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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



4th


.


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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



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



SLU internal actions with 1st

prestressing layout at t0

120

mMN 100

Mmax


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MN 100

80

60

Mmin


N(Mmax)

40

200 10 20 30 40 50 60 70 80 90 100

N(Mmin)

20

40

60

80

100



SLU actions with 2nd


mMN 100

Mmax


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MN 100

80

Mmin


N(Mmax)

40

200 10 20 30 40 50 60 70 80 90 100

N(Mmin)

0

20

40

60

80

100



SLU internal actions with 3rd


120

mMN 100 Mmax


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MN

80

Mmin


N(Mmax)

40

200 10 20 30 40 50 60 70 80 90 100

N(Mmin)

0

20

40

60

80

100



SLU internal actions with 4th


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



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

Documents

2010 Bridges EN1992 GMancini EBouchon