en1992 2 mancini
TRANSCRIPT
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EN 1992-2
EUROCODE 2EUROCODE 2 – – Design of concrete structuresDesign of concrete structures
Concrete bridges: design and detailing rulesConcrete bridges: design and detailing rules
Approved by CEN on 25 April 2005
Published on October 2005
Supersedes ENV 1992-2:1996
Prof. Ing. Giuseppe Mancini
Politecnico di Torino
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-EN 1992-2 contains principles and
application rules for the design of bridgesin 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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SectionSection 33 ⇒ MATERIALSMATERIALS
- Recommended values for Cmin and Cmax
C30/37 C70/85
- αcc coefficient for long term effects and unfavourable
effects resulting from the way the load is applied
Recommended value: 0.85 → high stress values during construction
- Recommended classes for reinforcement:“B” and “C”
(Durability) (Ductility)
(Ductility reduction with corrosion / Ductility for bending and shear mechanisms)
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SectionSection 44 ⇒ DurabilityDurability and coverand cover toto
reinforcementreinforcement
- XC3 class recommended for surface protected by
waterproofing
- When de-icing
salt is used
Exposed concrete surfaces within (6 m) of the
carriage way and supports under expansion joints: directly affected by de-icing salt
Recommended classes for surfaces directly
affectd by de-icing salt: XD3 – XF2 – XF4, withcovers given in tables 4.4N and 4.5N for XD
classes
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- Bare concrete decks without waterproofing or
surfacing should be classified as abrasion class XM2
- When concrete surface is subject to abrasion by iceor solid transportation in running water → increase
the cover by 10 mm, min
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SectionSection 55 ⇒ Structural analysisStructural analysis
- Geometrical imperfections
Piers
0l nϑ ϑ α =
1/200
(recom.)2 1l ≤
Arches Shape of imperfections based on
the shape of first horizontal and
vertical buckling mode, idealised by
a sinusoidal profile having amplitude
2l
l a ϑ =
(l = half wavelength)
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- Linear elastic analysis with limited redistributions
Limitation of δ due to uncertaintes on size effect
and bending-shear interaction
(recommendedvalue)δ ≥ 0.85
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- Plastic analysis
Restrictions due to uncertaintes on size effect and bending-shear
interaction:
0.15 for concrete strength classes ≤ C50/60
≤u x
d 0.10 for concrete strength classes ≥ C55/67
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- Rotation capacity
0.30 for concrete strength classes ≤ C50/60
≤u x
d 0.23 for concrete strength classes ≥ C55/67
in plastic
hinges
Restrictions due to uncertaintes on size effect and bending-shear
interaction:
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Numerical rotation capacity
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- Nonlinear analysis ⇒ Safety format
Reinforcing steel
1.1 f yk
Mean values
1.1 k f yk
Prestressing steel
1.1 f pk
Mean values
Concrete
γcf f ck
Sargin modified
mean values
γcf = 1.1 γs / γc
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Design format
Incremental analysis from SLS, so to reach
γG Gk + γQ 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 factor γ0
0
ud q Rγ
⎛ ⎞⎜ ⎟⎝ ⎠
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Verification of one of the following inequalities
( ) ud Rd G Q
O
q E G Q Rγ γ γ
γ
⎛ ⎞+ ≤ ⎜ ⎟
⎝ ⎠
( ).
ud G Q
Rd O
q E G Q Rγ γ
γ γ
⎛ ⎞+ ≤ ⎜ ⎟
⎝ ⎠
'
ud
O
q R
γ
⎛ ⎞⎜ ⎟⎝ ⎠
( ) ud Rd Sd g q
O
q E G Q Rγ γ γ γ
γ
⎛ ⎞+ ≤ ⎜ ⎟⎝ ⎠
(i.e.)
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With
γRd = 1.06 partial factor for model uncertainties(resistence side)
γSd = 1.15 partial factor for model uncertainties (actionsside)
γ0 = 1.20 structural safety factor
If γRd = 1.00 then γ0’ = 1.27 is the structural safety factor
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Safety format
A
BC
DE
F’’ G’’
H’’
E,R
qqud
O
udq
γ
⎟ ⎠ ⎞
⎜⎝ ⎛
O
ud qR
γ
( )Rd
Oud qR γ
γ
( )Sd Rd
Oud qR γ γ
γ
F’ G’
H’
( )γ γ +
( )γ γ +
Application for scalar combination of internal actions
and underproportional structural behaviour
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Safety format Application for scalar combination of internal actions
and overproportional structural behaviour
H’’
E,R
F’’
G’
E
C
q
B
D
A
O
udq
γ
⎟ ⎠ ⎞
⎜⎝ ⎛
O
ud qR
γ
( )Rd
Oud qR γ
γ
( )Sd Rd
Oud qR γ γ
γ
F’
H’
G’’
( )γ γ +
( )γ γ +
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Safety format Application for vectorial combination of internal
actions and underproportional structural behaviour
Msd,M rd
C
Nsd,Nrd
BD
A
a
b
( )ud q M
⎟⎟ ⎠
⎞⎜⎜⎝
⎛
O
ud qN
γ
( )ud q N
⎟⎟ ⎠
⎞⎜⎜⎝
⎛
O
ud qM
γ
Rd
O
ud qN
γ
γ ⎟⎟ ⎠
⎞⎜⎜⎝
⎛
Rd
O
ud qM
γ γ
⎟⎟
⎠
⎞⎜⎜
⎝
⎛
IAP
O
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Safety format Application for vectorial combination of internal
actions and overproportional structural behaviour
a
C
b
N sd,N r
M sd ,M rd
B
D
A( )ud q M
( )Rd
O
ud qM γ
γ ⎟⎟ ⎠
⎞⎜⎜⎝
⎛ Rd
O
ud qN γ
γ ⎟⎟ ⎠
⎞⎜⎜⎝
⎛
⎟⎟ ⎠
⎞
⎜⎜⎝
⎛
O
ud q
M γ
O
⎟⎟ ⎠
⎞⎜⎜⎝
⎛
O
ud qN
γ
IAP
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For vectorial combination and γRd = γSd = 1.00 the safety
check is satisfied if:
0'
ud ED Rd
q M M
γ
⎛ ⎞≤ ⎜ ⎟
⎝ ⎠
0 '
ud ED Rd
q N N
γ
⎛ ⎞≤ ⎜ ⎟
⎝ ⎠
and
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Example 1:
Two spans R. C. bridge (l = 20 + 20 m)
Advance shoring (20+5 m / 15 m)
Dead load at t0 = 28 days and t1 = 90 days
ξ (28, 90, ∞) = 0.51
N. L. analyses att1 (no redistribution due to creep)
t∞ (full redistributiondueto creep)
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60 115 300 115 60
650
50 50
3 0
1
1 0 1
4 0
300125 125
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8 9 10 11 20 21 22 23 24 30 31
8,00
9,20
300 kN 300kNq = 32.75 kN/m
g = 101.4 kN/m
98 1110 31302423222120
300 kN 300kNq = 32.75 kN/m
g = 101.4 kN/m
10,80
12,00Load distribution for the design of the region close to the central support
Load distribution for the design of the midspan
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Incremental loading process
Application of self weight in different statical schemes with γG = 1
Modification of internal actions by creep by means of ξ function
(γG = 1) only for t = t∞
Application of other permanent actions (γG = 1) on the final statical
scheme
Application of live loads with γG = 1
Starting of incremental process so that γG = 1.4 and γQ = 1.5
is reached in the same step
Continuation of incremental process up to attainment of peak load
(Critical region: central support section)
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Safety format : γ Gl
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Safety format : γ gl
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Critical section : number 22
Reduction of gain by application of model uncertaintes only incase Y due to the increase of negative bending moment by
creep and consequent translation of N.L. behaviour
Gain =1.51.4
1.4 1.5
QuGu γ γ −−
=
14000
1.00 1.20 1.40 1.60 1.80 2.00 γG
140 00
1.00 1.20 1.40 1.60 1.80 2.00 γG
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-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
10000
12000
14000
Section 30
Section 31
Sect io n 10
Sect io n 11
Section 20
Section 21
Section 22
Section 23
Section 24
1.00 1.28 1.50 1.71 1.93 2.14 γQ
Bending moment for load case X (max. negative t = t 1)
-1400 0
-1200 0
-1000 0
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
100 00
120 00
140 00
Section 8
Section 9
Sect ion 10
Sect ion 11
Section 20
Section 21
Section 22
Section 23
Section 24
1.00 1.28 1.50 1.71 1.93 2.14 γQ
Bending moment for load case W (max. positive t = t 1)
14000
1.00 1.20 1.40 1.60 1.80 2.00 γG
1400 0
1.00 1.20 1.40 1.60 1.80 2.00 γG
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-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
10000
12000
14000
Sectio n 30
Sectio n 31
Sect ion 10
Sect ion 11
Sectio n 20
Sectio n 21
Sectio n 22
Sectio n 23
Sectio n 24
1.00 1.28 1.50 1.71 1.93 2.14 γQ
Bending moment for load case Y (max. negative t = ∞ )
-1400 0
-1200 0
-1000 0
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
1000 0
1200 0
Section 8
Section 9
Sect ion 10
Sect ion 11
Section 20
Section 21
Section 22
Section 23
Section 24
1.00 1.28 1.50 1.71 1.93 2.14 γQ
Bending moment for load case Z (max. positive t = ∞ )
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Example 2: Set of slender piers with variable section
Depth: 82 / 87 / 92 / 97 m
Unforeseen eccentricity: 5/1000 x depth
γG = γQ = 1.5 (for semplification)
Critical section at 53.30 m from plinth in
which both thickness and reinforcementundergo a change
Safety format applied tothat section
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Safety format : γ Gl
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Safety format : γ gl
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0.0E+00
5.0E+04
1.0E+05
1.5E+05
2.0E+05
2.5E+05
3.0E+05
3.5E+05
4.0E+05
-4.0E+05-3.5E+05-3.0E+05-2.5E+05-2.0E+05-1.5E+05-1.0E+05-5.0E+040.0E+00
Axial force N [kN]
B e n
d i n g m o m e n t [ k N m ]
Collapse surfacefor section1182 m Pier
87 m Pier
92 m Pier
97 m Pier
Safety format : γ gl
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Example 3: Continous deep beam experimentally tested
(Rogowsky, Mac Gregor, Ong)
Adina N.L. code
Concrete strength criterion by
Carbone, Giordano, Mancini
Peak load reached at the crushing of secondelement (model unable to reach the equilibrium
for further load increments)
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R/C deep beam: FE half mesh (right) load-displacement curve of point A (left)
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Resisting interaction surfaceσ x, σ y, τ xy
Application of safety format in the
vectorial space of internal actions
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Set of external and internal actions
Behaviour with limited non linearity
Very limited effect ofmodel uncertaintes
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SectionSection 66 ⇒ UltimateUltimate limitlimit state (ULS)state (ULS)
- Robustness criteria for prestressed structures
3 different approaches
) V ifi ti f l d it ith d d f
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a) Verification of load capacity with a reduced area of
prestressing
Evaluation of bending moment in frequent combination of
actions: Mfreq
Reduction of prestressing up the reaching of f ctm at the extreme
tensed fibre, in presence of Mfreq
Evaluation of resisting bending moment MRd with reducedprestressing and check that:
MRd > Mfreq
Redistributions can
be applied
Material partial safety
factors as for accidental
combinations
b) Verification with nil residual prestressing
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b) Verification with nil residual prestressing
Provide a minimum reinforcement so that
,min
rep p p
s s yk yk
M A A
z f f
σ ⎛ ⎞⋅ Δ= −⎜ ⎟
⎜ ⎟⎝ ⎠
where Mrep is the cracking bending moment evaluated with f ctx
(f ctmrecommended)
c) Estabilish an appropriate inspection regime(External tendons!)
Δσ p < 0.4 f ptk and 500 MPa
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Tendon layout
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Brittle failure
1. Reduction of prestressing up to reaching of f ctm at the
extreme tensed fibre in presence of Mfreq
In such condition add ordinary reinforcement so that
M Rd ≥ M freq, with γ C = 1.3 and γ S = 1.0
T k f l ti f th t ib ti f t d t
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Take care of preelongation for the contribution of tendons to
the evaluation of MRd
Such condition is reached for an addition of 1φ 14 / 150 mm in the
bottom slab and 1φ 12 / 150 mm in the webs and top slab
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2. Provide a minimum reinforcement evaluated as
,min
rep
s s yk
M A
z f =
Mrep = cracking moment evaluated with f ctm and nil prestressing
zs = lever arm at USL = 1.62 m
The required ordinary reinforcement results
1φ 12 / 150 mm in the bottom slab
- Shear design of precast prestressed beams
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High level of prestress → σcp/ f cd > 0.5
Thin webs
End blocks
Redundancy in compressed and tensed chords
Web verification only for compression field due to shear (αcw = 1)
Pd
Pd,c
Pd,t
Pd = Pd,c + Pd,t
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- Superimposition of different truss models
θ1
θ2
- Bending–shear behaviour of segmental precast
bridges with external prestressing (only)
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Axes of theoreticaltension tie Axes of theoretical
compression struts
Tension chord of truss(external tendon)
Field A
Field B
θmin θmax
hred
Field A : arrangement of stirrups with θmax (cot θ = 1.0) Field B : arrangement of stirrups with θmin (cot θ = 2.5)
bridges with external prestressing (only)
( )cot tan Ed red
w cd
V h
b f θ θ
ν = +
cot sw Ed
red ywd
A V s h f θ
=
hred,min = 0.5 h
(recommended value)
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Application of Miner rule
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11
m
i
i i
n
N = ≤∑
Ni ⇒
Given by national authorities (S-N curves)
,max,110 exp 14
1
⎛ ⎞−⎜ ⎟= ⋅⎜ ⎟−⎝ ⎠
cd i
i
i
E N
R
where: ,min,
,max,
cd i
i
cd i
E R
E =
,min,
,min,
,
cd i
cd i
cd fat
E f
σ = ,max,
,max,
,
cd i
cd i
cd fat
E f
σ =
( )
; ;
⎛ ⎞= −⎜ ⎟⎝ ⎠
f f k β t f ckcd,fat 1 cc 0 cd 1
250
K1 =0.85 (Recommended value)
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Plastic equilibrium condition
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Skew reinforcement
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Thickness = tr
τxyr
Y
σ
yr
θr
σxr
σ
yr
σxr
τxyr
X
Plates
conventions
b
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cosθr
ρ
rσ
s r ar
θr
σxr sinθr
ar
br
sinθr
σ
yr cosθ
r
τxyr cosθr
τxyr sinθr
ρ
rσs r br
1
Equilibrium of the
section parallel to
the compression
field
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Use of genetic algorithms (Genecop III) for the optimization of
reinforcement and concrete verification
Objective: minimization of global reinforcement
Stability: find correct results also if the starting point is very
far from the actual solution
SectionSection 77 Serviceability limitServiceability limit state (SLS)state (SLS)
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SectionSection 77 ⇒ Serviceability limitServiceability limit state (SLS)state (SLS)
- Compressive stresses limited to k1f ck with exposure
classes XD, XF, XS (Microcracking)
k1 = 0.6 (recommended value)
k1 = 0.66 in confined concrete (recommemded value)
Exposure
Reinforced members and Prestressed members with
- Crack control
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Exposure
Class prestressed members with
unbonded tendons
bonded tendons
Quasi-permanent load
combinationFrequent load combination
X0, XC1 0,31 0,2
XC2, XC3, XC4
0,3
0,22
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 becheckedunder the quasi-permanent combination of loads.
Decompression requires that concrete is in compression within a distance
of 100 mm (recommended value) from bondend tendons
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Baricentric prestressing, two coupled tendons over two
t = 14 gg
deformationσx σy
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Baricentric i o n
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prestressing two coupled tendons
over two d e f o r m a
t
t = 42 gg
σx σy
Baricentrico
n
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prestressing
two coupled tendons
over two d e f o r m a t i
t = 70 gg
σx σy
Baricentric
prestressing t i o n
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prestressing
two coupled tendons
over two d e f o r m a
t
t =∞
σx σy
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Baricentric
prestressing t i o n
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two anchored
tendons over two d e f o r m at = 41 gg
σ
x σ
y
Baricentric t i o n
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prestressing two anchored
tendons over two d e f o r m at = 70 gg
σx σy
Baricentric
t i t i o n
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prestressing
two anchored
tendons over two d e f o r m a
σx
t = ∞
σy
Baricentric
t i Z d
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prestressing two anchored
tendons over two
σ
x
t = ∞
σy
Zoomed areas
near anchorages
SectionSection 113113⇒ DesignDesign forfor thethe execution stagesexecution stages
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Take account of
construction
procedure
Construction stages
Redistribution by creep in the section
Redistribution by creep for variation of
statical scheme
- Actions during execution Cross reference to
EN1991-1-6
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Statical equilibrium of cantilever bridge → unbalanced
wind pressure of 200 N/m2 (recommended value)
For cantilever constructionFall of formwork
Fall of one segment
For incremental launching → Imposed deformations!
In case in SLS decompression is required, tensile stresses
less then f ctm (recommended value) are permitted during theconstruction in quasi-permanent combination of actions
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- Basic creep
( )( ) 0t t
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( )( ) 0
0 0 0
0
, , ,b ck cm b
bc
t t t t f f t
t t φ
β
−Φ =⎡ ⎤− +⎣ ⎦
( )
0,37
cm 0
b0
3.6for silica fume concrete
f t
1.4 for non silica fume concrete
φ
⎛ −⎜⎜=⎜⎜
−⎝
( )
( )
cm 0
ck
bc
cm 0
ck
f t0.37exp 2.8 for silica fume concrete
f
f t0.4exp 3.1 for non silica fume concrete
f
β
⎛ ⎛ ⎞−⎜ ⎜ ⎟
⎝ ⎠⎜
⎜= ⎜⎛ ⎞⎜ −⎜ ⎟⎜ ⎝ ⎠⎝
with:
- Drying creep
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0 0 0 0( , , , , , ) ( , ) ( , )d s ck d cd s cd st t t f RH h t t t t φ ε ε Φ = −⎡ ⎤⎣ ⎦
⎜⎜
⎜
⎝
⎛
=concretefume-silicanonfor 3200
concretefume-silicafor 1000
0d φ with:
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Annex Annex JJ ⇒ Detailing rules for particularDetailing rules for particular
situationssituations
Bearing zones of bridges
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Consideration of brittleness of HSC with a factor to beapplied to f cd
2 / 30,46.
.1 0,1.
ck cd
ck
f
f +
Edge sliding
AS . f yd ≥ FRdu / 2
(≤ 1)
Bearing zones of bridges
ϑ = 30°
- Anchorage zones of postensioned members
Bursting and spalling in anchorage zones controlled by
reinforcement evaluated in relation to the primaryregularisation prism
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p yregularisation prism
)(6,0
'
max t f
cc
P ck ⋅≤
⋅where c,c‘ are the dimensions of the associate rectangle
'1,25
'
c c
a a
⋅≤
⋅
similar to anchorage plate
c/a
c’/a’
being a,a‘ the dimensions of smallest rectangle including
anchorage plate
Primary regularisation prism represents the volume in which
the stresses reduce from very high values to acceptable
values under uniaxial compression
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values under uniaxial compression
The depth of the prism is 1.2 max(c,c’)
Reinforcement for bursting and spalling
(distributed in each direction within the prism)
Surface reinforcement at the loaded face
max,0,03 surf P unf
yd
P A
f γ ≥ (in each direction)
max ,0,15S P unf
yd
P A
f γ = (with γP,unf = 1.20)
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Type of analysis Comment and typical
application
General and incremental step-by-step
method
These are general methods and are
applicable to all structures. Particularlyuseful for verification at intermediate
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useful for verification at intermediate
stages of construction in structures in
which properties vary along the length
(e.g.) cantilever construction.
Methods based on the theorems of linear
viscoelasticity
Applicable to homogeneous structures with
rigid restraints.
The ageing coefficient method This mehod will be useful when only the
long -term distribution of forces andstresses are required. Applicable to
bridges with composite sections (precast
beams and in-situ concrete slabs).
Simplified ageing coefficient method Applicable to structures that undergochanges in support conditions (e.g.) span-
to- span or free cantilever construction.
- General method
( ) ( )0 0 ( , )1( ) ( )
nit t σ σ ϕ ⎛ ⎞
Δ⎜ ⎟∑
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( ) ( ) ( )0 0
010
( , )( ) ( , ) ,
( ) (28) (28)
ic i cs s
ic c c i c
t t t t t t E t E E t E
ϕε ϕ σ ε
=
⎛ ⎞= + + + Δ +⎜ ⎟⎜ ⎟
⎝ ⎠∑
A step by step analysis is required
- Incremental method
At the time t of application of σ the creep strain εcc(t),
the potential creep strain ε∝cc(t) and the creep rate are
derived from the whole load history
The potential creep strain at time t is:
28
( ) ( , )cc
c
d t d t
dt dt E
ε σ ϕ ∞ ∞=
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t ⇒ te
under constant stress from te the same εcc(t) andε∝cc(t) are obtained
( ) ( ) ( ),cc c e cct t t t ε β ε ∞ ⋅ =
Creep rate at time t may be evaluated using the creep
curve for te
( ) ( ),( ) c ecccc
t t d t t dt t
β ε ε ∞ ∂=∂
For unloading procedures
|ε
cc(t)| > |ε
∝cc(t)|
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and te accounts for the sign change
( ) ( )( ) ( ) ( ) ( ) ,ccMax cc ccMax cc c et t t t t t ε ε ε ε β ∞− = − ⋅
( )
( )
( )( ) ( ) ,( ) ( )
ccMax cc c e
ccMax cc
d t t t t t t
dt t
ε ε β ε ε
∞
− ∂= − ⋅
∂
where εccMax(t) is the last extreme creep strain reached before t
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When additional restraints are introduced at different times
ti ≥ t0, the stress variation by effect of restrain j introduced at
t j is indipendent of the history of restraints added at ti < t j
j
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( )1 ,1 0 ,1
, , j
j el i el ii
S S t t t S ξ +=
= + Δ∑
- Ageing coefficient method
Integration in a single step and correction by means of χ(χ≅0.8)
( ) ( ) ( ) ( )28 0 28 0 000
(28) (28)
, , ,( ) ( )
t c c
t t
t c c
E E
t d t t t t E E t τ ϕ τ σ τ χ ϕ σ τ →
=
⎡ ⎤ ⎡ ⎤
+ = + Δ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦∫
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Annex Annex LLLL⇒ ConcreteConcrete shell elementsshell elements
A powerfull tool to design 2D elements
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Axial actionsand bending
moments in the outer layer
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Membrane shear actionsandtwisting moments in the outer layer
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RANTIVA BRIDGE
Sandwich model:
Numerical example
Mesh
2215 shell elements
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2285 nodes
6 D.o.F. per node
13710 D.o.F. in total
Element chosen: n°682
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X = 22
Y = 33
Symbols, conventions
and general data
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α = 0 ⇒ transverse reinforcement, Asx, direction 22
β= 0 ⇒ longitudinal reinforcement, Asy, direction 33
Concrete properties f cd = 20.75 MPa
f ctm = 3.16 MPa
f ctd = 1.38 MPa
Steel properties f yd = 373.9 MPa
Dimensioning of
α reinforcement (transverse)
in the inferior layer
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Distance of reinforcement from the outer surface = 6 cm
Nsd22 Nsd33 Nsd23 Msd22 Msd33 Msd23 Vsd12 Vsd13Combination
type (KN/m) (KN/m) (KN/m) (KNm/m) (KNm/m) (KNm/m) (KN/m) (KN/m)
Max M33 277 -5134 -230 616 1121 -476 95 -212
Load combination that maximizes this reinforcement
Layers
thicknessesH sez. tsup tinf
(m) (m) (m)
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(m) (m) (m)
1.0000 0.23 0.18
Increment of internal actions
due to shear
(for the single layer)
nsd22 nsd33 nsd23
(KN/m) (KN/m) (KN/m)
0 0 0
Upper layer verif ication
Internal actions on the
layer Cracked
?
Concrete
parameters
Actions in
reinforcement
at tsup/2
Reinforcement
calculated at
c+φ/2nsd22 nsd33 nsd23 case θ ν f
cd σ
c(f) n
R1(x)n
R2(y) A
s(x)nec A
s(y)nec
(KN/m) (KN/m) (KN/m) (-) (°) (N/mm²) (kN/m) (kN/m) (cm2/m) (cm2/m)
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
119
(KN/m) (KN/m) (KN/m) ( ) ( ) (N/mm ) (kN/m) (kN/m) (cm /m) (cm /m)
-633 -4070 481 no. 65.0 17.6 17.6 0.0 0.0 15.7 15.7
Lower layer verification
Internal actions on the
layer Cracked
?
Concrete
parameters
Actions in
reinforcement
at tsup/2
Reinforcement
calculated at
c+φ/2
nsd22 nsd33 nsd23 case θ ν f cd
σc(f) n
R1(x)n
R2(y) A
s(x)nec A
s(y)nec
(KN/m) (KN/m) (KN/m) (-) (°) (N/mm²) (kN/m) (kN/m) (cm2
/m) (cm2
/m)
909 -1064 -711 yes 23.1 11.1 11.1 1212.0 607.2 31.3 15.7
Minimum reinforcement φ 20/20 = 15.7 cm2 /m
Minimum reinforcement φ 20/20 = 15.7 cm2 /m
Dimensioning of
β reinforcement (longitudinal)
in the inferior layer
8/10/2019 EN1992 2 Mancini
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120
Distance of reinforcement from the outer surface = 6 cm
Nsd22 Nsd33 Nsd23 Msd22 Msd33 Msd23 Vsd12 Vsd13Combination
type (KN/m) (KN/m) (KN/m) (KNm/m) (KNm/m) (KNm/m) (KN/m) (KN/m)
Max M22 261 -5134 -219 657 1014 -464 79 -197
Load combination that maximizes this reinforcement
Layers
thicknessesH sez. tsup tinf
(m) (m) (m)
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121
(m) (m) (m)
1.0000 0.23 0.19
Increment of internal actions
due to shear
(for the single layer)
nsd22 nsd33 nsd23
(KN/m) (KN/m) (KN/m)
0 0 0
Upper layer verif ication
Internal actions on the
layer
Cracked
?
Concrete
parameters
Actions in
reinforcement
at tsup/2
Reinforcement
calculated at
c+φ/2nsd22 nsd33 nsd23 case θ ν f
cd σ
c(f) n
R1(x)n
R2(y) A
s(x)nec A
s(y)nec
(KN/m) (KN/m) (KN/m) ( ) (°) (N/mm²) (kN/m) (kN/m) (cm2/m) (cm2/m)
8/10/2019 EN1992 2 Mancini
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
122
(KN/m) (KN/m) (KN/m) (-) ( ) (N/mm ) (kN/m) (kN/m) (cm2/m) (cm2/m)
-695 -3904 474 no 45.0 17.6 17.6 0.0 0.0 15.7 15.7
Lower layer verification
Internal actions on the
layer Cracked
?
Concrete
parameters
Actions in
reinforcement
at tsup/2
Reinforcement
calculated at
c+φ/2
nsd22 nsd33 nsd23 case θ ν f cd
σc(f) n
R1(x)n
R2(y) A
s(x)nec A
s(y)nec
(KN/m) (KN/m) (KN/m) (-) (°) (N/mm²) (kN/m) (kN/m) (cm2
/m) (cm2
/m)
956 -1229 -693 yes 20.6 11.1 11.1 1216.7 611.5 31.3 15.7
Minimum reinforcement φ 20/20 = 15.7 cm2 /m
Minimum reinforcement φ 20/20 = 15.7 cm2 /m
Dimensioning of
α reinforcement (transverse)
in the superior layer
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
123
Distance of reinforcement from the outer surface = 6 cm
Nsd22 Nsd33 Nsd23 Msd22 Msd33 Msd23 Vsd12 Vsd13Combination
type (KN/m) (KN/m) (KN/m) (KNm/m) (KNm/m) (KNm/m) (KN/m) (KN/m)
Max M22 261 -5134 -219 657 1014 -464 79 -197
Load combination that maximizes this reinforcement
Layers
thicknessesH sez. tsup tinf
(m) (m) (m)
8/10/2019 EN1992 2 Mancini
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
124
( ) ( ) ( )
1.0000 0.23 0.19
Increment of internal actions
due to shear
(for the single layer)
nsd22 nsd33 nsd23
(KN/m) (KN/m) (KN/m)
0 0 0
Upper layer verif ication
Internal actions on the
layer Cracked
?
Concrete
parameters
Actions in
reinforcement
at tsup/2
Reinforcement
calculated at
c+φ/2nsd22 nsd33 nsd23 case θ ν f cd
σc(f) n
R1(x)n
R2(y) A
s(x)nec A
s(y)nec
(KN/m) (KN/m) (KN/m) (-) (°) (N/mm²) (kN/m) (kN/m) (cm2/m) (cm2/m)
8/10/2019 EN1992 2 Mancini
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
125
-695 -3904 474 no 45.0 17.6 17.6 0.0 0.0 15.7 15.7
Lower layer verification
Internal actions on the
layer Cracked
?
Concrete
parameters
Actions inreinforcement
at tsup/2
Reinforcementcalculated at
c+φ/2
nsd22 nsd33 nsd23 case θ ν fcd σc(f) nR1(x) nR2(y) As(x)nec As(y)nec
(KN/m) (KN/m) (KN/m) (-) (°) (N/mm²) (kN/m) (kN/m) (cm2/m) (cm2/m)
956 -1229 -693 yes 20.6 11.1 11.1 1216.7 611.5 31.3 15.7
Minimum reinforcement φ 20/20 = 15.7 cm2 /m
Minimum reinforcement φ 20/20 = 15.7 cm2 /m
Dimensioning of
β reinforcement (longitudinal)
in the superior layer
8/10/2019 EN1992 2 Mancini
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
126
Distance of reinforcement from the outer surface = 6 cm
Nsd22 Nsd33 Nsd23 Msd22 Msd33 Msd23 Vsd12 Vsd13Combination
type (KN/m) (KN/m) (KN/m) (KNm/m) (KNm/m) (KNm/m) (KN/m) (KN/m)
Max M22 261 -5134 -219 657 1014 -464 79 -197
Load combination that maximizes this reinforcement
8/10/2019 EN1992 2 Mancini
http://slidepdf.com/reader/full/en1992-2-mancini 127/138
Upper layer verif ication
Internal actions on the
layer Cracked
?
Concrete
parameters
Actions in
reinforcement
at tsup/2
Reinforcement
calculated at
c+φ/2nsd22 nsd33 nsd23 case θ ν fcd σc(f) nR1(x) nR2(y) As(x)nec As(y)nec
(KN/m) (KN/m) (KN/m) (-) (°) (N/mm²) (kN/m) (kN/m) (cm2/m) (cm2/m)
8/10/2019 EN1992 2 Mancini
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
128
-695 -3904 474 no 45.0 17.6 17.6 0.0 0.0 15.7 15.7
Lower layer verification
Internal actions on the
layer Cracked
?
Concrete
parameters
Actions in
reinforcement
at tsup/2
Reinforcement
calculated at
c+φ/2
nsd22 nsd33 nsd23 case θ ν fcd σc(f) nR1(x) nR2(y) As(x)nec As(y)nec
(KN/m) (KN/m) (KN/m) (-) (°) (N/mm²) (kN/m) (kN/m) (cm
2
/m) (cm
2
/m)
956 -1229 -693 yes 20.6 11.1 11.1 1216.7 611.5 31.3 15.7
Minimum reinforcement φ 20/20 = 15.7 cm2 /m
Minimum reinforcement φ 20/20 = 15.7 cm2 /m
Annex Annex MMMM⇒ ShearShear andand transverse bendingtransverse bending
8/10/2019 EN1992 2 Mancini
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
129
Webs of box girder bridges
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
130
Modifiedsandwich model
Annex Annex NNNN⇒ Damage equivalent stressesDamage equivalent stresses
for fatigue verificationfor fatigue verification
8/10/2019 EN1992 2 Mancini
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
131
Unchanged with respect to ENV 1992-2
To be used only for simple cases
Annex OO Annex OO⇒ Typical bridge discontinuityTypical bridge discontinuity
regionsregions
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
132
Strut and tie model for a solid
type diaphragm without manhole
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
133
Strut and tie model for a solid
type diaphragm with manhole
Diaphragms with indirectsupport. Strut and tie model
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
134
Diaphragms with indirect
support. Anchorage of the
suspension reinforcement
reinforcement
Diaphragms with indirect
support. Links assuspension reinforcement
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
135
diaphragm
pier
longitudinal section
Diaphragm in monolithic joint with double diaphragm:
Equivalent system of struts
and ties.
Torsion in the deck slab andreactions in the supports
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
136
Model of struts and ties for a
typical diaphragm of a slab
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EUROCODES - Background and Applications - Brussels 18-20 February 2008Prof. Ing. Giuseppe Mancini - DISTR - Politecnico di Torino
137
EN 1992EN 1992--22 ⇒ A new design code to help in A new design code to help in
conceiving more and moreconceiving more and more
enhanced concrete bridgesenhanced concrete bridges
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138
Thank you for thekind attention