gothenburg diana users meeting april 25-26 2013 final-1
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International DIANA Users Meeting
Chalmers University of Technology
Gothenburg, Sweden
Opening - WelcomeInternational
DIANA Users Meeting
Ane de Boer
DIANA Users Association &Ministry of Infrastructure, The Netherlands
International DIANA Users Meeting
Chalmers University of Technology
Gothenburg, Sweden
Why Gothenburg-Sweden after
London-UK, NijmegenNL, Essen-Germany, Porto-Portugal,
Trondheim-Norway, Delft-NL, Brescia-Italy
-- DIANADIANA UsersUsers inin SwedenSweden
-- LocalLocal arrangementsarrangements:: LundgrenLundgren andand HanjariHanjari
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International DIANA Users Meeting
Chalmers University of Technology
Gothenburg, Sweden
Gothenburg well-known city
Volvos hometown & Factories
Ferry link to Danmark
Chalmers University of Technology
Sport events like: Indoor European Championship Athletics
Speed skating track
International DIANA Users Meeting
Chalmers University of Technology
Gothenburg, Sweden
Activities Users Association
in cooperation with TNO DIANA BVDevelopment meetings:
Since 1984, the foundation year of the Users Association
-General meetings at the Users offices in The Netherlands,
including Technical meetings in the Netherlands twice a year since 2000
-International Users Meeting since London 2004
- Users Association open for International Members since 2005,
so join us, a registration form at the registration desk of this Meeting!
-Activities:In cooperation with CUR-NL: Concrete Mechanics Applications 2003 [CD],
Advanced FE analyses (CUR2003-1;NL) & Design in 3D(2008-1;NL)
Wish Lists: International User Wish List since User Meeting 2005
DIANA User Advisory Board: short, mid and longterm wishes
Set-up of a User Database of articles, presentations around DIANANLFEA Guideline: Girders published 18 April 2013!!
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International DIANA Users Meeting
Chalmers University of Technology
Gothenburg, Sweden
NLFEA Guidelines / Safety Formats EC2-MC2010
Safety Formats Slabexperiments Stevinlab; Framcos8 - Belletti etc.
Pu/Pu,experiment
E
C
2
0
20
40
60
80
100
LevelI
LevelII
LevelIV
-PF
LevelIV-GRF
LevelIV
-ECO
V
Run-Mea
n
Experim
ent
NumericalAnalytical
MC2010
Henrik Schlune: Chalmers PhD Thesis Alternative Safety Formats
Experiment
International DIANA Users Meeting
Chalmers University of Technology
Gothenburg, Sweden
Location of this meeting Hosting this meeting:
Chalmers University of Technology
Concrete Structures, Division of Structural Engineering
Chalmers Teknik Park
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International DIANA Users Meeting
Chalmers University of Technology
Gothenburg, Sweden
Social Event
17:00 City / Harbour guided Tour
start: Teknik Park
finish: Tvkanten
19:30 Dinner Restaurang Tvkanten
International DIANA Users Meeting
Chalmers University of Technology
Gothenburg, Sweden
Wijtze Pieter Kikstra, Scientific Employee
Gerd-Jan Schreppers, General Director
Opportunity meeting TNO DIANA BV people
Opportunity meeting DIANA Users Association people
Nynke Vollema Henco Burggraaf
Ane de Boer
Opportunity to meet other DIANA Users !!
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
[mm]
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Structural Engineering Concrete Structures
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20
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60
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0 2 4 6 8 10
Active slip [mm]
Without stirrups
Load [kN]
0
20
40
60
80
100
0 2 4 6 8 10
Load [kN]
Active slip [mm]
With two stirrups
0
20
40
60
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Load [kN]
Active slip [mm]
With four stirrups
FEAExp.
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Structural Engineering Concrete Structures
z
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tt[MPa]
tt[MPa]
ut[mm]
ut[mm]
s
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
0
50
100
150
200
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0 5 10
Load [kN]
l+ r[mm]
B, B
S
S Exp.
FEA, edge
FEA, centre
720720
l r
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
Bond - slip in centre slice(2)
0
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
Structural Engineering Concrete Structures
Force [kN]
0
20
40
60
80
100
120
140
0 2 4 6 8 10Slip [mm]
Exp.
FEA
Yield force
/
Force [kN]
0
20
40
60
80
100
120
140
0 2 4 6 8 10Slip [mm]
Exp.
FEA
Yield force
,
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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crack width [mm] crack width [mm] crack width [mm]
Analysis, corrosion equal around the rebar
Analysis, corrosion localized at the crackExp. Andrade et al.
1 2 3 1 2 3 1 3Mass loss [%]
II: c = 20mm, 100Acm-2
Mass loss [%]III: c = 30mm, 100Acm
-2Mass loss [%]
IV: c = 20mm, 10Acm-2
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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Structural Engineering Concrete Structures
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Fibre reinforced concrete in dapped-end
beams
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Fibre reinforced concrete in dapped-end beams
Introduction
E.V. Sarmiento et al.
> Motivation
Application for FRC
/
K
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Dapped-end beams project > Previous experience(1)
witho
utfibres
1% Steel fibres
4Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
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/
K
D
W
Dapped-end beams project > Previous experience(2)
1% Steel fibres
5Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
1%Steelfibres
/
K
D
W
Dapped-end beams project > Previous experience(3)
Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
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/
K
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>
Fibre reinforced concrete in dapped-end beams
Dapped-end beams project
E.V. Sarmiento et al.
> Limitations(1)
>
K
K
&
8
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K
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>
Fibre reinforced concrete in dapped-end beams
Dapped-end beams project
E.V. Sarmiento et al.
> Limitations(2)
&
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9
/
K
D
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>
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Fibre reinforced concrete in dapped-end beams
Finite Element Analysis
E.V. Sarmiento et al.
> Study case(1)
10
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Fibre reinforced concrete in dapped-end beams
Finite Element Analysis
E.V. Sarmiento et al.
> Study case
^WE
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K
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Model descriptionFinite Element Analysis
Supports and loading
Simple supports
Interface elements
Loading control
Force load
Displacement load
Mesh size
Element size 25x25
Element size12.5x12.5
12
/
K
D
W
>
&
^
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Materials / geometries(1)Finite Element Analysis
Concrete in tension
Multi-linear tension softening curve
Fibre reinforced concrete
Crack modeling
Semeared crack approach with Rotating crack model
Concrete in compresionIdeal
Elements
Eight-node quadrilateral plane stress elements (CQ16M)
RILEM Design methods for steel fibre
reinforced concrete. --design method
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/
K
D
W
>
&
^
D
D
Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Materials / geometries(2)Finite Element Analysis
Reinforcement
Strain hardening model
Yield stress: 566 Mpa
Modulus of elasticity: 200 000 MPa
Ultimate strain and stress at ultimate strain: 7.5, 589 MPa
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/
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>
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^
D
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Materials / geometries(3)Finite Element Analysis
Bond properties
All Embedded reinforcement
Option 2 - BAR in Plane stress
Reinf with slip: Truss elements (CL6TR)
Line-plane interface elements (CQ22IF)
Bond-slip + Embedded reinforcement
Option 1
Reinf with slip: Truss elements (CL6TR)
Line interface elements (CL12I)
David Fall et al.Non-linear finite element analysis of steel fibre
reinforced beams with conventional r einforcement. BEFIB2013
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>
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Control method
Step size
Convergence norm
Mesh size
Concrete strain limit
Bond properties
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>
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Control method
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Control method
Displacement control Force control
Principal strain
4mm deflection
Principal strain6mm deflection
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>
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Step size
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K
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>
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Step size
0.5mm step size
0.1mm step size
0.2mm step size
Principal strain5mm deflection
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>
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D
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Convergence norm
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>
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Convergence norm Principal strain6.8mm deflection
Displ norm0.05
Displ norm0.02
Displ norm0.01
Force norm0.1
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Mesh size
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K
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>
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D
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Mesh size
25x25mm el. size 12.5x12.5 el. size
Principal strain4mm deflection
Principal strain6mm deflection
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Concrete strain limit
Principal strain6mm deflection
Strain limit 0.025 Strain limit 0.050
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Bond properties
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Fibre reinforced concrete in dapped-end beams E.V. Sarmiento et al.
> Results and discussionFinite Element Analysis
Bond properties
Embedded reinforcements Bond slip reinforcements
Principal strain3mm deflection
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Fibre reinforced concrete in dapped-end beams
Summary
E.V. Sarmiento et al.
In general, the maximum load is under a certain limit
well described
The model underestimates the loads at large
deflections
The crack pattern is poorly described
The bond slip properties have to be improved
Dependency on the mess alignment
Other material models for FRC need to be evaluated
Thank you for your attention
E.V. Sarmiento et al.Fibre reinforced concrete in dapped-end beams
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Fatig
ueAna
lysisof
BasculeBridgeDetail
Coenvan
derVliet/PeterKonijnenbe
lt
ArcadisNetherland
s
Im
aginetheresult
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C
ontents
Project
Fatigue
Appro
ach
FEModels&Results
FatigueVerification
RelatedTopics
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Deurganckdoksluis
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Length:
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Width:
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BridgeSpan:
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Fatiguegen
eralprinciple
Cyclicloadin
greducesstreng
th
Strengthred
uctionrelatedto
log(N)
Miner:6(ni/N
i)1
Stresspeaksatnotchesetc.
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Fatiguegen
eralprinciple
DianaUserMeeting|April25/2
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2013|ARCADIS2013
Dia13
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Fatigue-weld
s
Welds:locald
isturbancesof
stressdistrib
ution
Stresstrajec
toriesand
concentratio
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Stresspeak
dependsonweld
detail
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Dia14
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Fatiguewelds
Residualstressesequalyield
strength
Vmax=fy,Vmin=fy-'V
Stresslevel
notimportant
DianaUserMeeting|April25/2
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Fatiguewelddetails
DianaUserMeeting|April25/2
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Fatiguedeta
ilcat.strength
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Fatiguebasematerial
Stressreliev
ed:noresidual
stresses
Stresslevel
doesmatter
Fatiguestrengthdependson
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)
compone
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ompression,
shear)
DianaUserMeeting|April25/2
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'V
V
max
V
min
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Approa
ch
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Step1:globalloca
l
Translateglo
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Balancedloadcaseonlocal
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Supportstotakeunbalance
DianaUserMeeting|April25/2
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Step1:globalloca
l
Unitloadsatmodelboundaries
Memberforc
esfromglobal
modelloa
dfactorsinload
combinations
Fatigueverificationofwelds
aroundpivotpoint
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Step2:localdetail
Translateloc
alstructural
behaviourto
correctstress
stateindeta
ilmodelofcast
piece
Supportstotakeunbalance
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Step2:localdetail
Stressesatsectionsinlocal
modelloa
dsindetailmode
l
Fatigueverificationatfillets
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FiniteE
lemen
tModels&
Results
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Model
1:shells
Purposevsmodelspecs
Provideproperboundaryconditionsfordetailmodel
Geom
etry:globalshapesufficient
Mesh
:onlyfineeleme
ntsincastpiece
area
Enabled
etailedfatigueve
rificationofweldsaroundcastpie
ce
Geom
etry:accurate,u
ptomanandmo
useholes
Mesh
:fineelementsa
teverycriticalsp
ot
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Model
1:shells
Purposevsmodelspecs
Provideproperboundaryconditionsfordetailmodel
Geom
etry:globalshapesufficient
Mesh
:onlyfineeleme
ntsincastpiece
area
Enabled
etailedfatigueve
rificationofweldsaroundcastpie
ce
Geom
etry:accurate,u
ptomanandmo
useholes
Mesh
:fineelementsa
teverycriticalsp
ot
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Dia26
prima
ryscope
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Model
1:shells
Elementsize
andgradingoptimumbetween
modelsize
peakstre
ssaccuracy
Result
symmetricallineargrading2575foreveryedge
refineme
ntf
actor2
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Model
1:shells
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Model
1:shells
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Model
1:shells
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Model
1:shells
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Model
1:shells
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Model
1:shells
Modelverific
ation
SOLforinidividual(unity)
loadcases
DeformationscomparedtoSciamodel
Results
Firstimpressionbasedon
VonMisesstres
sesandprincipal
stresses
Fatigueverificationbased
onstressrange
alongsection
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Model
1:shells
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Model
1:shells
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Model
1:shells
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'V
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Model
2:solid
s
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Model
2:solid
s
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Model
2:solid
s
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Model
2:solid
s
DianaUserMeeting|April25/2
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Dia40
shellstresse
s
translatedin
to
lineloads
appliedto
beams
connectedto
shells
connectedto
solids
beams
shells
loadapplication
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Model
2:solid
s
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fatigue:allstress
co
mponentsin
re
levantelements
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FatigueVerific
ation
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Fatigueverific
ation
Hotspotstre
ss
realisticgeometry(3Dvolume)
extrapola
tionofstresstow
ardsweldtoe
Nominalstre
ss
Bernouillimodels
V=n/t+6m/
t2
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Shellm
odelvsreality
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realstresses
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Shellm
odelvsreality
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realstresses
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Shellm
odelvsreality
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shellstresses
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Shellm
odelvsreality
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whichsection?
1
2
3
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Shellm
odelvsreality
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whichsection?
1
2
3
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Shellm
odelvsreality
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whichstressc
omponents,
andwhere?
Vnn;top
Vns;mid/Wn;mid
Vnn;bot
2/3!
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Shellm
odelvsreality
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checkthes
e
stressesas
well!
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Fatiguestreng
th
N=C'V-m
Openingand
closingi.c.w.
windgoverning
n=310000
cycles
n/N1designmodification
checkconse
quences:update
model
iterativeprocess
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Wishfu
lthinking
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Thiswouldbe
nice
automatedd
eterminationofs
tressrange'V
cyclecounte
rbasedonsucce
ssiveloadcases
resultsinshiftedsection(e.g.fromcenterline
toweldtoe)
automatedfatigueverification
basematerial
VmaxandVmin
Stren
gthparsffatandm
Resu
lt:n/N
alongwe
lds
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Thiswouldbe
nice
automatedfatigueverification
alongwe
lds
weld
modelledasshe
ll-interface(alreadypresentinDIANA)
detailcategoryasmaterialparameter
stresscomponentsno
rmalandtangentialtoweld
result:n/N
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Imagine
theresult
Dia56DianaUserMeeting|April25/2
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Study of the behaviour of reinforced concrete
slabs subjected to concentrated loads near
supports
B. BELLETTI*, C. DAMONI*, M.A.N. HENDRIKS #
* University of Parma, Italy + Delft University of Technology,The Netherlands
#Norwegian University of Science and Technology,Norway
8th InternationalDIANA Users Meeting
25-26 April 2013
Chalmers University of TechnologyGothenburg - Sweden
OUTLINES
Background and aim of the research
Cases studies analyzed: experimental program
Finite element model
Evaluation of the carrying capacity of the RC slabs analyzed:
Final remarks
One way shear resistance
(Model Code 2010)
Punching resistance
(Eurocode2, Regans formulation, CSCT )
Bending resistance
(Yield line theory)
Nonlinear finite element analyses
-Sensitivity study
-Levels of Approximation Model Code 2010
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The Dutch Ministry of Infrastructure and the Environment initiated a
project to re-evaluate the carrying capacity of existing bridges andviaducts
- increased traffic in the last years- reallocation of emercency lanes to traffic lanes- need for additional traffic lanes
JoostWalraven Sal, 25 October 2010.
Why
For a certain amount of Dutch bridges andother infrastructures the safety verificationsare not satisfied if the usual analyticalprocedures are adopted
The Dutch Ministry of Infrastructure and theEnvironment proposed to make a structuralassessment ofexisting structures throughthe use of nonlinear finite elementanalyses
Final release of a document containing guidelines for nonlinear finiteelement (NLFE) analyses of reinforced and prestressed concrete
elements
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NLFEA represent a powerful instrument for structural assessment
The results of NLFEA strongly depend on the modelling choices
big scatter in the results for the same structure analyzed by several
analysts
Guidelines for NLFEA to be followed by all users in order to obtain
reliable and safe results is of big importance
The project well matches with the philosphy of the Model Code 2010:
Carrying capacity of concrete elements evaluated with different Levels of
Approximation adopting analytical calculations and NLFE analyses: the
accuracy of the results increases if NLFE analyses are adopted.
The carrying capacity of 3 RC slabs tested at TuDelft has been evaluated with:-NLFEA (following the Dutch guidelines)-anal tical calculations
LevelI
LevelII
LevelIII
LevelIV
complexity, effort, level of detail
precisio
nofevaluation
Analytical procedures for the evaluation of thedesign resistance
NLFE analyses for the structural behavior prediction
The design resistance is obtained byapplying Safety Format Methods
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2
[N/mm2]
[-]
Simple and continuous support
S1T1:10mmfeltP50-8mmplywood
S1T2:10mmfeltP50-8mmplyw ood
S4T1:15mmfeltN100-8mmplywood
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2
[N/mm2]
[-]
Support 3
S1T1:5mmfelt P50
S1T2:5mmfelt P50
S4T1:5mmfelt P50
Felt and plywood
5000
600
650
600
650
1250
1250
Simple support
Continuoussupport
Dywidag bars(Support 3)
Lantsoght, E., 2012. Shear tests ofReinforced Concrete SlabsExperimental data of Undamaged Slabs06-01-2012. Technical Report, Stevinlaboratory, Delft University ofTechnology.
18 slabs tested 2500 x 5000 x 300 mm 3 chosen as cases studies: S1T1, S1T2, S4T1
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S1T1
100
250
300
20/12010/240
10/240
10/240
20/12020/120
A-A
B-B
50
10/240 10/240
20/120
265300
20/120
20/120 10/240
265300
50
1 sheet 200 x 5 mm
felt P50
200 x 200 x10 mm
steel profile
P
3DYWIDAGBARS36300
600 2700 900 500
200 x 8 mmplywood
2 layers of 100 x 5 mmfelt P50
HEM 300
Bottom side
A-A B-B
5000
2500
200
200
F pre-stressed dywidag =3*15
kN
S1T2
100
250
300
20/12010/240
10/240
10/240
20/12020/120
A-A
B-B
50
10/240 10/240
20/120
265300
20/120
20/120 10/240
265300
50
P
3DYWIDAGBARS36300
2700 900 500600
1 sheet 200 x 5 mm
felt P50
200 x 200 x10 mm
steel profile
200 x 8 mmplywood
2 layers of 100 x 5 mmfelt P50
HEM 300
Bottom side
A-A B-B
5000
2500
200
200
F pre-stressed dywidag =3*15
kN
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S4T1Bottom sideA-A B-B
5000
2500
300
300
250300
20/12010/125
10/24010/25010/25010/125
20/12010/12510/240 10/25010/25010/125
125
A-A
B-B
10/240 10/250
20/120
20/120
20/120 10/125
300
265
50
265300
50
P
3DYWIDAGBARS36300
600 2700 900 500
1 sheet 200 x 5 mm
felt P50
200 x 200 x10 mm
steel profile
200 x 8 mmplywood
3 layers of 100 x 5 mmfelt N100
HEM 300
F pre-stressed dywidag =3*15
kN
CRACK PATTERN AT FAILURE, FAILURE MODE AND ULTIMATELOAD
S1T1 S1T2 S4T1
Ec: 30910 Mpa
fc: 29.7 Mpa
ft: 2.8 MPa
Failure: one-way shearPu,exp : 954 kN
Ec: 30910 Mpa
fc: 29.7 Mpa
ft: 2.8 MPa
Failure: one-way shearPu,exp : 1023 kN
Ec: 34930 Mpa
fc: 42.9 Mpa
ft: 3.8 MPa
Failure: one-way shearPu,exp : 1160 kN
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Analytical calculation
Numerical procedure
One-way shear
resistance
Model Code 2010Level I- II Approximation
Bending resistance Yield line method
Safety format methods for NLFEanalysesin order to reduce the peak load values toobtain the DESIGN SHEARRESISTANCE
Punching resistanceEurocode 2
Regans formulation
Critical Shear Crack Theory (Muttoni)
NLFE analyses Model Code 2010Level IV Approximation
Sensitivity study
-shell / brick model-parametric study on sensitiveparameters of the crack model
BEFORE STARTING WITH THE MODELLING IT IS IMPORTANT TO FEEL, THANK TO CIVIL
ENGINEERING KNOWLEDGE, WHICH SHOULD BE THE STRUCTURAL BEHAVIOUR
RC slabs treated as beams without shear reinforcement with an effective widthbeff
45 4
5
1500
45
1288
1500
S1T1 S1T2 S4T1
Analytical calculation: One-way shear resistance
Level I and II Approximation provided by Model Code 2010
eff
c
ck
vc,Rd zbf
kV
=
-
+
+=
+=
zk1000
1300
15001
4.0k
z25.11000
180k
dgx
IILevel,v
ILevel,v
+= Ed
l
Ed
ss
x Vz
M
AE2
1
Design shearresistance
75.0
d16
32k
gdg
+=
Model Code 2010
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Analytical calculation: Punching resistance
Eurocode 2 effRdcRdc duvV =
effd4b2a2u ++=
( ) 3/1ckc,RdRdc f100kCv =
cc,Rd /18.0C =
effd
2001k +=
tl =
Regan 2R1RR PPP +=
tt2
ll1
d5.1bd5.1u
d5.1ad5.1u
++=
++=
Eurocode 2a
b
1.5dl
1.5dt
Regan
1.5dt
1.5dl
4
lsl
d
500=
4
t
std
500=
3cklcl f10027.0v =
3cktct f10027.0v =
t1ctstl2clsl1R duv2duvP +=
l2clsl
v
l2R duv
a
d2P =
controlperimeter
Analytical calculation: Punching resistance
Critical Shear Crack Theory(CSCT)
dg
c
R
c
R
kd125.04.0
1
du
V
+=
=
Failure criterion
rotation of the slab chosen as controlparameter since the opening of the criticalshear crack reduces the strength of theinclined concrete compression strut thatcarries shear and eventually leads to thepunching shear failure
Muttoni A. (2008) Punching ShearStrength of Reinforced Concrete Slabswithout Transverse Reinforcement, ACIStructural Journal, V. 105, No. 4, 440-450.
S1T1
1. An linear elastic (LE) finite element analysis (mesh with shell elements) carried out to
determine the maximum shear force vmax,el and the control perimeter u;
2. a NLFE analysis (mesh with shell elements) carried out to determine the rotation ;
3. from the intersection between the results of NLFE analysis and the failure criterion the
failure load is determined.
MAIN STEPS FOLLOWED:
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XZ
Analytical calculation: Punching resistanceCSCT
S1T1
1. Calculation of maximum shear force vmax,el and control perimeteru
2D finite element model
(Software used: DIANA)
m257.0ddd yx ==
m/N3.759257.02950v elmax, ==
m32.1
3.759
1000
v
Qu
elmax,
===
Principal shear stress
detected from LE analysis:
Control perimeter u:
Applied load in LE analysis
Analytical calculation: Punching resistance CSCTS1T1
2. Evaluation of rotation
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0 1 2 3 4 5
Rotatio
ny
Distance [m]
P = 500 kN
P=750 kN
P=1000 kN
Point1
Point2
Point 1 Point 2
Rotation = difference between the rotations of
the slab at two points: Point 1 and Point 2.
Point 1: located at the centroid of the applied
load.
Point 2: chosen so that the maximal relative
rotation is obtained .
NLFLE analysis
is not the same at each load step
Arbitarly chosen max at P=750 kN
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Analytical calculation: Punching resistance CSCTS1T1
3. Determination of failure load
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20
/c
d kdg
Failure criterion
NLFEA results
Failure load P= 793 kN
)63.12571320(/P
)f3.0du(/P/ cc
=
=
)kd125.04.0(/1/ dgcR +=
Pfailure=793 kN
NLFE analysis
Failure criterion
Analytical calculation: Bending resistance Yield line method
a b
c
c
a b
c
c
a b
c
c
xl xr
y
y
Collapse mechanism 1
y
y
Collapse mechanism 2
xl xr
Collapse mechanism 3
xr
Collapse mechanism 1
Collapse mechanism 2
Collapse mechanism 3
==
++++= ++
1cve
yyyyxrxxrxxlxVi
PL
bm2am2c2mc2mc2mL
==
+++= +
2cve
yyyyxrxxrxVi
PL
bm2am2c2mc2mL
==
++= ++
3cve
xrxxrxxlxVi
PL
c2mc2mc2mL
Pc1=2198.22kN
Pc2=790.7 kN
Pc3=1970.5 kN
S1T1
Yield pattern of collapsemechanism 2 in agreement withexperimental crack patetrn
Different collapse mechanisms considered, according to the kinematic theorem of limit analysis
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Analytical results
Ultimate load P values [kN]
Minimum load value detected analytically: one-way shear
Measured mechanicalproperties used in calculations
(c=1, s=1)
Some remarks: it has been assumed a direct correspondance between minimum strength
(analytically obtained) and actual failure mode.
Fpe
FpeFpe
uz
Software used: DIANA 9.4
MESH
BOUNDARY CONDITIONS
CONVERGENCE
CRITERION:
displacement control
Newton Raphson based on
force (10-2) and energy (10-3)
Model with
brick elements
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Software used: DIANA 9.4
MESH
BOUNDARY CONDITIONS
CONVERGENCE
CRITERION:
displacement control
Newton Raphson based on
force (10-2) and energy (10-3)
Model with shell
elementsS1T1
4_NL
XYZ Fpe
Fpe
Fpe
( )( ) ( )( )
( )( ) ( )( )
nstt1ins
tt1i
211
1
211
211211
1
~
+
+
+
+
= ++++
Total strain crack models
Multi-axial stress state:
Reduction of fc due to lateral cracking-(Vecchio, F.J., Collins, M.P.: Compression response of
cracked reinforced concrete. Journal StructuralEngineering, 1993, 119, 3590^3610)
Constitutive laws
up
Rotating
Fixed
=
nssnns
s
snns
sns
snns
nsn
snns
n
G
EE
EE
D
00
011
011
=shear retention factor (variable)(linearly decreasing from 1 to 0 as a
function ofEand n
snns, =Poissons ratio
(variable)
GGns =
Gc=250Gf(Nakamura, H., Higai, T.,2001. CompressiveFracture Energy andFracture Zone Length ofConcrete. Modeling ofinelastic behaviour of RCstructures under seismicloads, P.Benson ShingTada-aki Tanabe (eds))
Gf=73fc0.18 (Model Code 2010)
For 3D modelling with brick elements total strain crack models implemented in standard software are
not powerful as in 2D modelling!
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Nonlinear finite element analyses 2D modelS1T1
0
200
400
600
800
1000
1200
1400
1600
1800
0 10 20 30 40
Load(kN)
deflection (mm)
Shell model
Experimental
Brick model
Yielding bottom f20
Yielding BOTF10T
Crushing of concrete
Punching (Regan)
One-way shear Model Code 2010 (Level II)
Yielding bottom 20 l
Punching (Eurocode 2)
Yield lineCSCT
S1T1
As expected the shellmodel is not able toproperly describe the shearfailure of the slab andsubstantiallyoverestimates thecapacity of the slab
(first) surfaceinonmodel set:.681E-2.518E-6
tsshown:edtonodes
.588E-
.8E-3
0
0. 5
1
1. 5
2
2. 5
3
0 0.0 0 0 5 0. 0 01 0 .0 0 1 5 0. 0 02 0 .0025
[N
/mm
2]
0
0 .5
1
1 .5
2
2 .5
3
0 0 .00 0 5 0.0 01 0 .0 0 1 5 0 .0 0 2 0 . 0 0 25
[
N/mm
2]
The other slabs (S1T2and S4T1) have been
analyzed only with 3Dmodels
Nonlinear finite element analyses
0
400
800
1200
1600
0 5 10 15 20 25 30
Load[kN]
Deflection [mm]
ANALYSIS B
ANALYSIS C
ANALYSIS D
ANALYSIS E
ANALYSIS F
Experimental
S1T1
0
400
800
1200
1600
0 5 10 15 20 25 30
Load[kN]
Deflection [mm]
ANALYSIS B
ANALYSIS C
ANALYSIS D
ANALYSIS E
ANALYSIS F
Experimental
S1T2
0
400
800
1200
1600
0 5 10 15 20 25 30
Load[kN]
Deflection [mm]
ANALYSIS B
ANALYSIS C
ANALYSIS E
Experimental
ANALYSIS A
S4T1
Parametric study: combined the main sensitive parameters of the crack model
ANALYSIS B =analysis that better fit with experiments for all slabsChosen as reference for the application of safety format methods
Model with brick elements
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0
0.5
1
1.5
2
2.5
0 .0 0 00 0 .0 0 05 0 .0 01 0 0 .0 0 15 0 .0 02 0
[N/mm2]
S4T1
0
400
800
1200
1600
0 5 10 15 20 25 30
Load[kN]
Deflection [mm]
ANALYSISB
Experimental
S4T1
Pmax=883 kN
0
0.5
1
1.5
2
2.5
3
0 0. 0005 0. 001 0. 0015 0. 002 0. 0025
[N/mm2]
S1T2
0
400
800
1200
1600
0 5 10 15 20 25
Load[kN]
Deflection[mm]
ANALYSISB
Experimental
S1T2 Pmax=1020 kN
Nonlinear finite element analyses
ANALYSIS B: crack pattern at failure
0
0.5
1
1.5
2
2.5
3
0 0 .0 00 5 0 .0 01 0 .0 01 5 0 .0 02 0 .0 02 5
[N/mm
2]
One-way shear failure(as detected in
experiments)
0
0.5
1
1.5
2
2.5
3
0 0 .0 00 5 0 .0 01 0 .0 01 5 0 .0 0 2 0 . 00 2 5
[N/mm2]
0
0.5
1
1.5
2
2.5
3
0 0 . 0 00 5 0 . 00 1 0 . 00 1 5 0 . 0 0 2 0 . 0 0 2 5
[N/mm
2]
S1T1
0
400
800
1200
1600
0 5 10 15 20 25 30
Load[kN]
Deflection [mm]
ANALYSISB
Experimental
S1T1
Pmax=907 kN
a b
c
c
a b
c
c
a b
c
c
xl xr
y
y
Collapse mechanism 1
y
y
Collapse mechanism 2
xl xr
Collapse mechanism 3
xr
0
0.5
1
1.5
2
2.5
3
0 0 .0 00 5 0 .0 01 0 .0 01 5 0 .0 02 0 .0 02 5
[N/mm2]
0
0.5
1
1.5
2
2.5
3
0 0 . 00 0 5 0 . 0 0 1 0 . 0 0 1 5 0 . 0 0 2 0 . 0 0 2 5
[N/mm
2]
S1T1 Strain values in the 10 transversal bars atthe bottom of the slab at peak load
The failure load strongly depends on boundary condition modelling (e.g. interface elements
stiffness, etc.). For real cases it could be quite difficult to have these data.
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Effective width beffused for the shear strength calculatiuon.
45 4
5
1500
45
1288
1500
S1T1 S1T2 S4T1
Effective width as a resul from NLFEA, as used in the analytical calculations and as
observed in the experiments
Overall results
Ultimate load P values [kN]
Minimum load value detected analytically: one-way shear
The failure mode detected analytically and from NLFE analyses is
consistent with the experimental failure mode
Measured mechanicalproperties used in calculations
(c=1, s=1)
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Design shear resistance: Levels of Approximation Model Code 2010
Evaluated the DESIGN SHEAR RESISTANCE of the slabs applying the Levels ofApproximation:
GRF
PF
ECOV
Mean mechanical properties as input data in NLFEA
Design mechanical properties as input data in NLFEA
Mean mechanical properties +Characteristic mechanical properties
as input data in NLFEA
3 SAFETY FORMAT METHODS proposed by MC2010 to reduce the peakload obtained from NLFEA in order to determine the design shear resistance
Analytically: Level I-IIApproximation
Design mechanical properties used incalculations(c=1.5, s=1.15)
From NLFE analysis: Level IV Approximation
1. Partial Factor Method (PF)2. Global Resistance Factor Method (GRF)
3. Estimation of Coefficient of Variation Method (ECOV)
( ),...fRR dd =
( ) ( ) ( )
27.1
,...fR
06.12.1
,...fR,...fRR mm
RdR
md =
=
=
Peak load obtained from NLFEA
Peak load obtained from NLFEA
( ) ( )
RdR
md
kkmm
RR
;,...fRR,,...fRR
=
== ( )
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=
km
RRR
RRln65.1
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Design shear resistance: Levels of Approximation: overall
results
Model Code
2010
LevelI Level II Level IV
PFLevelIV
GRFLevelIV
ECOVAnalysis B Exp
0
10
20
30
40
50
60
70
80
90
100
Pu/Pu,ex
p[%]
S1T1
Level I LevelII LevelIV
PF
Level IV
GRF
LevelIV
ECOVAnalysis B Exp
0
10
20
30
40
50
60
70
80
90
100
Pu/Pu,e
xp[%]
S1T2
LevelI Level II LevelIV
PF
LevelIV
GRFLevelIV
ECOVAnalysis B Exp
0
10
20
30
40
50
60
70
80
90
100
Pu/Pu
,exp[%]
S4T1
Level I- II Level IV (PF- GRF- ECOV) Analysis B (no safety format) Experimental (100%)
Pu/Pexp [%]
Good agreement with Model Code 2010 philosophy:
by increasing the Level of Approximation the design resistance
increases
From Level II to Level IV: Increase ranging from 69% to 87
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Three slabs subjected to concentrated loads near supports have been analyzed.The carrying capacity of each slab has been determined with NLFE analyses and
with analytical procedures.
For all slabs the lowest resistance value calculated analytically is the one-way shear
resistance, in accordance to experimental test observations.
However, S1T1 and S1T2 also showed a fully developed flexural cracking pattern at
failure. For S1T1 the critical collapse mechanism calculated with the yield line
method is in agreement with the crack pattern observed in experimental test at
failure.
The results ofNLFEA strongly depend on the modeling choices made by the analyst,
especially with regards of relatively simple crack models.
The availability ofguidelines on how to properly perform NLFE analyses is of big help
for analysts.
The results obtained well fit with the philosophy of the Model Code 2010: by
increasing the approximation level the shear resistance of the slabs increases.
Once the finite element model is properly validated, the structural assessment carried out
with multiple approximation levels can be of benefit for intervention plans on existing
structures (e.g. maintenance, repair, demolition etc.)
The authors acknowledge the Dutch Ministry of
Transport, Public Works and Water Management
for supporting this research.
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From learning outcomes:
Understanding of structural behaviour
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20
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40
50
60
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c
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Finite element analysis of concrete structures Restraint cracking and time-dependent deformations
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Use of FEA in different stages(from conceptual design to assessment)
To choose suitable element types, BC:s and loading
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Modeling on various levelsNon-linear FE analysisMaterial response in 3DFEA in practice
0
100
200
300
400
500
600
700
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Great preparation for master thesis!
The analysis of continuous beam:-Fits well within the course-Results hard to comprehend-Not full benefit of FE posibility-Continuum analysis would fitbetter in the MP progression
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How can we develop the project?How can we improve our education regarding FEA of concretestructures?
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600
700
800
900
0,0
E+00
5,0
E+05
1,0
E+06
1,5
E+06
2,0
E+06
2,5
E+06
3,0
E+06
3,5
E+06
4,0
E+06
4,5
E+06
5,0
E+06
spring stiffness in N/mm
ultimateloadinkN/m
total horizontal restrained
Finite lement model
total horizontal restrained
analytic solution
tth
Shear in reinforced concrete slabs
3UDFWLFDOH[DPSOH
160
10 - 15012 - 150
117
1200
fcu = 55 N/mm2fs = 350 N/mm2d = 117 mm
600
loaded area 600 x 350
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Shear in reinforced concrete slabs
7UDGLWLRQDOFDOFXODWLRQQR&0$
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3XQFKLQJVKHDUIDLOXUH N1
7KHZKHHOORDGFDSDFLW\SUHVFULEHGE\WKH'XWFK
FRGHLV[N1
7KHFRGHUHTXLUHPHQWLVQRWPHW
Shear in reinforced concrete slabs
&0$LQFOXGHG
%HQGLQJ N1
)LQLWHHOHPHQWPRGHO N1
3XQFKLQJVKHDUIDLOXUH N1
1RWHSXQFKLQJVKHDULVQRUPDOO\DOZD\VJRYHUQLQJEXWORDGHGDUHDLVUHODWLYHO\ODUJHFRPSDUHGWRVSDQ
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Shear in reinforced concrete slabs
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Shear in reinforced concrete slabs
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Non-linear finite element analysis of steel
fibre reinforced concrete in combination
with conventional reinforcement
David Fall and Karin Lundgren
Chalmers University of Technology
DIANA Users Meeting 2013 1/27
Modeling of SFRC-beams
Four point bending:
6
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ModelingofSFRC-beams
Fourpointbending:
6
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ModelingofSFRC-beams
Twodimensionalplain-stressmodel
Deformationcontrolledphasedanalysis
Reinforcementrepresentedbytrusselements
Interfaceelements
Smearedcrackapproach
Rotatingcracks
ModelingofSFRC-beamsDIANAUsersMeeting20134/27
ModelingofSFRC-beams
ModelingofSFRC-beamsDIANAUsersMeeting20135/27
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Materialinput
Concreteintension
012345Crackwidth,w[mm]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Stress[MPa]
Vf=0.50%
Vf=0.25%
Vf=0%
Reinforcement
0.000.020.040.060.080.100.120.140.160.18Straini[-]
0
100
200
300
400
500
600
700
800
900
Stressis
[MPa]
6
8
MaterialinputDIANAUsersMeeting20136/27
Materialinput
Bondstressvs.slip
sys4s3 36912Slip[mm]
f,pl
f
y
0
4
8
12
16
20
Bondstress[MPa]
Originalmodel
Engstrom
MaterialinputDIANAUsersMeeting20137/27
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Materialinput
Prioryielding:
OriginalModified
Vf=0.50%,applieddeformation2.7mm(prioryield.)
MaterialinputDIANAUsersMeeting20138/27
Materialinput
Prioryielding:
OriginalModified
Afteryielding:
Vf=0.50%,applieddeformation2.7mm(prioryield.)and14mm(afteryield.)
MaterialinputDIANAUsersMeeting20138/27
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Results:Generalbehavior
0510152025Deflection[mm]
0
5
10
15
20
25
30
35
40
Load[kN]
Experiment
FE
MC2010
Vf=0%
0510152025Deflection[mm]
0
5
10
15
20
25
30
35
40
Load[kN]
Experiment
FE
MC2010
Vf=0.50%
Load-deflection(mid-span)
ResultsDIANAUsersMeeting20139/27
Results:Vf=0.25%
ResultsDIANAUsersMeeting201310/27
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Results:Vf=0.25%
ResultsDIANAUsersMeeting201311/27
Results:Vf=0.25%
ResultsDIANAUsersMeeting201312/27
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Results:Vf=0.25%
ResultsDIANAUsersMeeting201313/27
Results:Vf=0.25%
ResultsDIANAUsersMeeting201314/27
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Results:Vf=0.25%
ResultsDIANAUsersMeeting201315/27
Results:Vf=0.25%
ResultsDIANAUsersMeeting201316/27
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Results:Vf=0.25%
ResultsDIANAUsersMeeting201317/27
Results:Vf=0.25%
ResultsDIANAUsersMeeting201318/27
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Results:Vf=0.25%
ResultsDIANAUsersMeeting201319/27
Results:Vf=0.25%
ResultsDIANAUsersMeeting201320/27
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Conclusions
TheeffectofSFRC,seeninexperiments,canbeestimatedwithFE-analysis.
ConclusionsDIANAUsersMeeting201321/27
Conclusions
TheeffectofSFRC,seeninexperiments,canbeestimatedwithFE-analysis.
CrackpatternsagreewhencomparingexperimentsandFE-analyses.
ConclusionsDIANAUsersMeeting201321/27
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Conclusions
TheeffectofSFRC,seeninexperiments,canbeestimatedwithFE-analysis.
CrackpatternsagreewhencomparingexperimentsandFE-analyses.
Utilizingabond-stressmodelwherethebondstressisreducedpostyielding,resultedinmorelocalizedcrackpatterns.
ConclusionsDIANAUsersMeeting201321/27
Conclusions
TheeffectofSFRC,seeninexperiments,canbeestimatedwithFE-analysis.
CrackpatternsagreewhencomparingexperimentsandFE-analyses.
Utilizingabond-stressmodelwherethebondstressisreducedpostyielding,resultedinmorelocalizedcrackpatterns.
MC2010underestimatesthebeneficialeffectsfromsteelfibresforthesebeams.Theunderestimationincreaseswithincreasedfibre content.
ConclusionsDIANAUsersMeeting201321/27
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Furtherwork
FurtherworkDIANAUsersMeeting201322/27
Furtherwork
Spanlength,l=2.2m.Thickness,t=80mm.Deflectionmeasuredin28
pointsontopsurfaceStraingaugesatsupportsfor
measuringreactionforcesUnsymmetricreinforcement
FurtherworkDIANAUsersMeeting201322/27
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Furtherwork
Spanlength,l=2.2m.Thickness,t=80mm.Deflectionmeasuredin28
pointsontopsurfaceStraingaugesatsupportsfor
measuringreactionforcesUnsymmetricreinforcement
#ReinforcementbarsSteelfibresTextile
TypeCR36--TypeCFR360.5%-TypeFR3-0.5%-TypeBTRC3--BasaltTypeGTRC3--AR-Glass
FurtherworkDIANAUsersMeeting201322/27
Furtherwork
FurtherworkDIANAUsersMeeting201323/27
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Furtherwork
050100150
0
20
40
60
80
100
Deflection[mm]
Load
[kN]
Conv.+SFRCConv.SFRC
FurtherworkDIANAUsersMeeting201324/27
Furtherwork
050100150
0
20
40
60
80
100
Deflection[mm]
Load
[kN]
Conv.+SFRCConv.SFRC
FurtherworkDIANAUsersMeeting201324/27
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Furtherwork:Materialtesting
Compressivetest
RILEM-beams
Uniaxialtensiontest
Tensiontestofreinforcementbars
FurtherworkDIANAUsersMeeting201325/27
Furtherwork:Modelling
Pre-testmodelsJiangpengShuandKamyabZandi
Detailednon-linearsolidmodellingJiangpengShu
ModellingoftextilereinforcedconcreteNatalieWilliamsPortalandKamyabZandi
Non-linearshellmodellingMasterThesis
PractitionersapproachMasterThesis
ModellingofRILEM-beamsDavidFall
FurtherworkDIANAUsersMeeting201326/27
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Projectpartners
david.fall@chalmers.se
ProjectpartnersDIANAUsersMeeting201327/27
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d
1
Structural appraisal existing box girders
8th International DIANA Users Meeting, Gothenburg, April 25-26, 2013 Henco Burggraaf,TNO, The Netherlands
Contents
Introduction
Linear 2.5D analysis
Linear 3D analysis
Non-linear 3D analysis
Conclusions
HencoBurggraaf Existing box girders
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d
Introduction
2007: recognition of risk that concrete structures, designed before
1974, may have insufficient shear capacity
Dutch building codes:
VB 74: reduction of shear strength due to higher steel qualities
VBC 1990 + VBC 1995: further reduction of shear strength
Lack of shear capacity may give a brittle failure mechanism, without
warning
HencoBurggraaf Existing box girders
3
Introduction
Bridges in the Netherlands
HencoBurggraaf Existing box girders
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d
Introduction
Assessment of each concrete structure would require too much time
How can the Dutch Ministry of Infrastructure and Environment
guarantee the structural safety of their concrete structures?
HencoBurggraaf Existing box girders
5
Approach
Corporation between Dutch Ministry of Infrastructure and
Environment, TU Delft, TNO and engineering companies
Risk controlled and phased approach
Quick Scans and qualitative classification
Advanced analyses
Fundamental approach
Looking for evidence of hidden reserves
Research outside the codes and on the edges of available knowledge
HencoBurggraaf Existing box girders
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