Earthquake Engineering by the beachthe beach - Reluis Engineering by the beachthe beach ......
Transcript of Earthquake Engineering by the beachthe beach - Reluis Engineering by the beachthe beach ......
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Earthquake Engineering by the beachthe beachCapri, July 2-4 2009
Nonlinear modelling of i f d t t treinforced concrete structures
Jesús Miguel Bairán GarcíaLecturer of Civil Engineering
Universitat Politecnica de CatalunyaDepartment of Construction Engineering
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Main research areas
• Nonlinear sectional analysis accounting for biaxial y gshear-bending-torsion and axial forces
• Seismic designSeismic design
• Prestressed concrete structures
• High-rise precast concrete and hybrid wind-towers
D t i ti d d bilit f t t t• Deterioration and durability of concrete structures
• D-regions
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Contents of the presentation
Sectional analysisPart 1: Beam regions
• Sectional analysis • Objectives for further steps• Problematic• TINSA: “Total interaction nonlinear sectional analysis”• Implementation• Applications• Further topics
Part 2: Disturbed regions• Problematic• Automatic generation of Strut & Tie models• Nonlinear assessment of D regions• Further topics
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Further topics
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PART 1
Beam regionsBeam regions
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Sectional analysisLevels of structural modeling
Solid Bars+Sections system
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Sectional analysis
• Easy and quick model construction
Advantages of frame modeling• Easy and quick model construction.
• Result interpretation in terms of generalized forces and deformations (directly used for ULS design and verification).
• Reduced degrees of freedom system.
• Computational cost.
• Excellent results in “B” regions governed by normal stresses• Excellent results in B regions governed by normal stresses.
• Possibilities of force-based or displacement based elements.
• Versatile geometric definition through fiber sectional discretization.
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Sectional analysis
Nonlinear analysis for normal stressesTraditional fiber element
( )y z z yε ε φ φ= + −• Define strain in each fiber.
• Evaluate material response
Traditional fiber element
0( , )x y zy z z yε ε φ φ= +• Evaluate material response.
• Integrate internal forces
“well solved”...
“versatile and aplicable to most load cases”...
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Sectional analysis
What does Navier-Bernoulli hypothesis imply?
• Bars are large.
• What happens in short directions is not important.
• Fibers only respond to normal stresses.
• Only axial force and bending can be considered.
• Only applicable to B regions
Can it be improved?
• Only applicable to B regions.
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What can be improved?
Main limitations of traditional frame element modelling
• Uniaxial σ-ε laws.
• Limited confinement modeling.
• Tangential forces (shear and torsion) usually neglected or considered in a• Tangential forces (shear and torsion) usually neglected or considered in a simplified manner.
• Interaction between normal and tangential forces is not considered
T
xN dAσ= ∫∫x
yM z dA
M dA
σ= −
∫∫∫∫
∫∫
Accuracy for tangential forces
Accuracy for normal forces<
φxzM y dAσ= ∫∫
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Should we try to improve sectional analysis?Non linear behavior of RC structures
• All engineering structures are subjected to a combination of normal and tangential forces. The matter is which is dominant.
• Most earthquake collapses of modern structures are related to shear forces.
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Objectives
• A sectional model for arbitrary geometry capable of reproducing the
non-linear response of reinforced concrete under fully 3D loading (6
internal forces) ( Nx, Vy, Vz, Tx, My, Mz )
• Reproduce other 3D phenomena taking place in RC sections.
(i.e. confinement, etc.)
• To extend the concept of fiber discretization to tangential forces (shear
and torsion) and achieved balanced accuracy in all 6 internal forcesand torsion) and achieved balanced accuracy in all 6 internal forces.
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Cracked concreteProblematic (1)B regions under combined normal and tangential forces:
• 6 internal forces
• Big difference between tensile and compression strength
• Inclined cracking
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Cracked concreteProblematic (1)B regions under combined normal and tangential forces:
• Cracked induced anisotropy
• Coupling of previously uncoupled forces i e V M• Coupling of previously uncoupled forces, i.e. V-M
⎟⎞
⎜⎛ ++ )(t)(( t)(t θηθVMT u ⎟
⎠⎜⎝
+−+= )(cot)(·(cot2
)(cot· αθηθ gggVz
T uu
u
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Cracked concrete
• In general with an inclined crack pattern all internal forces may be coupled
Problematic (1)
In general, with an inclined crack pattern all internal forces may be coupled.
Traditional sectional stiffness matrix (only vertical cracks):Sectional stiffness matrix after inclined cracking:
xNV
⎡ ⎤⎢ ⎥⎢ ⎥
0εγ
⎡ ⎤⎢ ⎥⎢ ⎥
11 15 160 0 00 0 0 0 0
K K KK
⎡ ⎤⎢ ⎥⎢ ⎥
11 12 13 14 15 16K K K K K KK K K K K K
⎡ ⎤⎢ ⎥⎢ ⎥
Traditional sectional stiffness matrix (only vertical cracks):Sectional stiffness matrix after inclined cracking:
y
z
VVT
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥
=
y
z
γγφ
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥
22
33
0 0 0 0 00 0 0 0 00 0 0 0 0
KK
K
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥
21 22 23 24 25 26
31 32 33 34 35 36
K K K K K KK K K K K KK K K K K K
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥x
y
TMM
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
x
y
φφφ
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
44
51 55 56
61 65 66
0 0 0 0 00 0 00 0 0
KK K KK K K
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 66
K K K K K KK K K K K KK K K K K K
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦zM⎢ ⎥⎣ ⎦ zφ⎢ ⎥⎣ ⎦61 65 660 0 0K K K⎢ ⎥⎣ ⎦
Shear and torsion are uncoupled
61 62 63 64 65 66K K K K K K⎢ ⎥⎣ ⎦
Totally coupled
14sectional response
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Cracked concrete
Experimental evidence:Problematic (1)
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Stress-strain distribution
Patterns of shear stress and strain are not constant along loading (state dependent):
Problematic (2)
•1D equilibrium among layers.
P d fi d h fl di i P l di i iStatically determined
problem
Aproaches:
• Predefined shear flow direction. Panel discretization. problem
Actual patterns depend on geometry, reinforcement, and concrete state.
3D problem is statically undetermined
Cracked induced anisotropy → 3D ilib i d tibilit i h fib
Jourawski like approachBiaxial bending and shear:
equilibrium and compatibility in each fiber
Shear flow predefined
and shear: Lateral reinforcement arrangement:
162D shear flowJ. M. Bairán
2009
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Stress-strain distribution
• The problem of fixed strain distribution patterns• Extensively used.
γ τ
y• Not good results in cracked RC sections...
γUncracked Cracked- small shear Cracked-large shear
ConstantConstant pattern
Parabolic pattern
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Stress-strain distribution
• The problem of fixed strain distribution patterns
Vecchio y
18
yCollins, 1988
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TOTAL INTERACTION SECTIONAL MODEL
Ideas:
TINSA: “Total Interaction Nonlinear Sectional Analysis”
• Any kinematical hypothesis implies an additional constraint in the solution space. Hence,
the model produces the “best” possible considering the new artificial constraint..
Sometimes Plain-Section kinematics is not good enough.
• PS solution can be improved “as much as necessary” by means of more
d d d f ti d i di t ti19
advanced deformation modes: warping + distortion.
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Section distortionWhy consider distortion?
In reinforced concrete:
•Stretching of lateral reinforcement.Stretching of lateral reinforcement.
• 2D shear flows.
• Wide sections.
• Shear-torsion resistance mechanisms.
• Confinement.
In composite laminates:
L l f il• Local failure
• Delamination
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TOTAL INTERACTION SECTIONAL MODEL
Hypotheses
1. Displacement decomposition
Plane Section (PS) Warping Distortion (w)
2. Small strains
Plane Section (PS) Warping-Distortion (w)
Strain decomposition
3. Stress decompositionp
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TOTAL INTERACTION SECTIONAL MODEL
• Full 3D equilibrium in fibers
Special weak for full 3D sectional analysis:
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TOTAL INTERACTION SECTIONAL MODEL
Dual system of equilibrium:
1. Structural level: Traditional beam theories
Solved by traditional frame elements (1D domain)
2. Sectional level: warping-distortion.
To be solved internally in the cross-section (2D domain)( ) ( )
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TOTAL INTERACTION SECTIONAL MODEL
Dual system of equilibrium:
1. Structural level: Traditional beam theories
Solved by traditional frame elements (1D domain)
2. Sectional level: warping-distortion.
To be solved internally in the cross-section (2D domain)
( )
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TOTAL INTERACTION SECTIONAL MODEL
Dual system of equilibrium:
1. Structural level: Traditional beam theories
Solved by traditional frame elements (1D domain)
2. Sectional level: warping-distortion.
To be solved internally in the cross-section (2D domain)( ) ( )
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Implementation
1. 2D FEM of the cross-sectionTwo approaches to warping-distortion definition:
2. Generalized coordinates
26γ γ1 γ2 γ3
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Implementation
2D FEM Generalized coordinates
• More accuracy for 3D effects (i.e. spalling, etc.)• Better distribution of stresses
• Less degrees of freedom.• More suitable for full structural level implementationAdvantages • Better distribution of stresses
and strains.• More versatile for arbitrary geometries.
implementation.• Accuracy may be improved by addition of more shape functions.
Disadvantages • Computational cost • Local errors may exist.
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Comparison with other methods for tangential forces
Description Characteristics
• Extended usedV i th
• Easy to implementFib ilib i t li itl id dFixed patterns • Various authors • Fiber equilibrium not explicitly considered.
• In general not correct distribution of strains or stresses.
Panel discretization• Extended used• Various authors
• Easy to implement• Fiber equilibrium not explicitly considered• In general not correct distribution of strains or stresses.
• Sectional program based on MCFT.• Requires analyzing two simultaneous sections under normal forces
• Fiber equilibrium considered through finite differences approach• Distortion not explicitly considered
RESPONSE –Dual sectional analysis
sections under normal forces• Constitutive model 2D
Distortion not explicitly considered• Only 2D in plane loading and vertically symmetric sections (N-V-M).• Solution depends on the distance between analysedsections.• Requires a specific frame element• Requires a specific frame element.
RESPONSE 2000 –Longitudinal stiffeness
th d
• Sectional program based on MCFT. • Analyzes a single section using differential equilibrium equation.•Constitutive model 2D
• Fiber equilibrium considered in a differential approach.• Distortion implicit• Only 2D in plane loading and vertically symmetric sections (N-V-M)method Constitutive model 2D sections (N V M).• Does not requires a specific frame element.
• Various constitutive models (3D)• Analyzes a single section using
• Fiber equilibrium considered in a differential approach.• Distortion explicitly considered
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TINSA
y g gdifferential equilibrium equation.•3D equilibrium equation• Any geometry and type of load
p y• Any type of load 3D• Reproduces confinement• Does not requires a specific frame element.
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MATERIALSConcrete: main aspects3D effects
• Current strength is the projection from the current stress state to a 3D failure surface, Willam & Warnke surface is used.
•Concrete in compression behaves non-linear with residual strains
Compression behaviour
• Collins & Porasz backbone σ-ε curve.Considers influence of concrete strength in curve’s shape.
Tension behaviour• Concrete in tension behaves non-linear with degrading modulusg g
• Damage is only active in tension and varies independently in each principal direction• Cervenka backbone σ-ε curve
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MATERIALSConcrete: cyclic response
Cyclic compression Cyclic tension
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Cyclic shear
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MATERIALSReinforcing steelBilinear elasto-plastic with kinematic hardening
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APLICATIONS
K i (1977)
Shear strengthPure shear. V-γ diagrams
Kani (1977)
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APLICATIONS
Moderate to high strength concrete with different reinforcing arrangementesCl d (2002)
Shear strength
Cladera (2002)• fc = 50 MPa
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APLICATIONS
Moderate to high strength concrete with different reinforcing arrangementesShear strength
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APLICATIONS
Location of strain gages
Crack patterns in H502 specimen
35V - εtransV - εlong
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APLICATIONSBending-shear interaction
M-ϕ and V-γ diagrams for different M/V ratios
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APLICATIONS
M-εlong and V- εtrans diagrams for different M/V ratios
Bending-shear interaction
ε o g a d εt a s d ag a s o d e e t / at os
M-εlong V- εtrans
• Effect of shear in longitudinal reinforcement • Effect of bending in transversal reinforcement
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APLICATIONSSlender cantilever
RC cantilever pier (L/h=4.92)
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APLICATIONSSlender cantilever
engt
h
Curvature distribution
plas
tic le
nsm
atio
n of
nd
rota
tion
Shear strain distributionstic
est
im an
Shear strain distribution
Rea
li
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APLICATIONSSlender cantilever
σz in stirrups at z=h/2 along length σx in concrete in critical section
Componente horizontal bielas
τxz in concrete in critical sectionσz distribution in stirrups in critical section
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APLICATIONSConfinement in RC sections
Centered loading
• Rectangular section L = 120 mm• Stirrups: 61 5 mm2 / 100 mm• Stirrups: 61.5 mm2 / 100 mm• Cover: 10 mm
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APLICATIONSConfinement in RC sections
Centered loading
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APLICATIONSConfinement in RC sections
In-plane and biaxial bending and compression
In-plane bending and compressionN=980 kN
Biaxial (45º) bending and compressionN=980 kN
Concrete: fc=38 Mpa
Steel: fy=480 Mpafs=648 MPa
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APLICATIONS
Momento vs. CurvaturaAxil= 980kN
Confinement in RC sectionsIn-plane and biaxial bending and compression
0.015; 231.4
0.023; 240.1
0.0927; 208.80.0296; 221.6 0.1616; 187.2200.0
250.0
300.0
Axil 980kN
M-ϕ diagrams
In-plane bending and 0.0125; 186.1
50 0
100.0
150.0
M kN‐m
TINSA
Fibras
p gcompressionN=980 kN
0.0
50.0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
φ 1/mMomento vs. CurvaturaAxil= 980kN
0.008; 204.70.0125; 221.0
0.035; 199.20.0122; 202.2
0.0714; 181.1
200.0
250.0
Biaxial (45º) bending and compression
0.0069; 165.3
100.0
150.0
M kN‐m
TINSA MC45
Flexion esviada 45º
pN=980 kN
440.0
50.0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
φ 1/m
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APLICATIONSConfinement in RC sections
Momento vs. CurvaturaAxil= 980kN
Experimental investigation on non-linear cyclic “P i ” t i
0.015; 231.4
0.023; 240.1
0.0927; 208.80.0296; 221.6 0.1616; 187.2200.0
250.0
300.0
Axil 980kN“Poisson” strains
0.0125; 186.1
50 0
100.0
150.0
M kN‐m
TINSA
Fibras
0.0
50.0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
φ 1/mMomento vs. CurvaturaAxil= 980kN
0.008; 204.70.0125; 221.0
0.035; 199.20.0122; 202.2
0.0714; 181.1
200.0
250.0
0.0069; 165.3
100.0
150.0
M kN‐m
TINSA MC45
Flexion esviada 45º
45J. M. Bairán2009
0.0
50.0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
φ 1/m
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APLICATIONSConfinement in RC sectionsExperimental investigation on non-linear cyclic “Poisson” strains
60
ensi
ón (M
Pa)
σ(M
Pa)
25 H60 - Muestra 8H60-Simulación
40
Teσ
15
20
- ε3 (
*10-3
)
2010
15
form
ació
n la
tera
l -tra
ns (1
E-3
)
0
5
Def εt
25 20 15 10 5 0Deformación lateral - ε3 (*10-3)
0 5Deformación axial - ε1(*10-3)
εtrans (1E-3) εlong(1E-3) 0 1 2 3 4 5Deformación axial - ε1(*10-3)
0
εlong(1E-3)
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APLICATIONSBending and shear cyclic loading
fc=37 MPa
f 414 MPfy=414 MPa
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APLICATIONS
Shear force history
25000
Shear historyBending moment history
12000
Bending moments history
5000
0
5000
10000
15000
20000
Vz [k
N] 1
2
3
4
6000
8000
10000
Mz
[kN
m]
1
2
3 6
7
8ed lo
ad
-25000
-20000
-15000
-10000
-5000
0 5000 10000 15000 20000
V
5
6
7
0
2000
4000
-15000 -10000 -5000 0 5000 10000 15000
M
4 5App
lie
3x 10-3 Shear strain history
7
8x 10-5 Curvature history
d ϕ
Vy [kN] My [kNm]
1
2
5
6
pons
e γ
an
2
-1
0γ z
2
3
4φ z
Res
p
0 1 2 3
x 10-3
-3
-2
γy
-4 -2 0 2 4
x 10-5
0
1
φy
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APLICATIONS
20
Vy - strain
20
Vz - strain
Bending and shear cyclic loading
10
15
y [kN]
5
10
15
20
V-γ diagrams
-5
0
5Vy
-10
-5
0
Vz [kN]
γ g
01
23
x 10-3-5
0
5
x 10-3
5
γy
γz0
12
3
x 10-3
-50
5
x 10-3
-20
-15
γyγz
15My - curvature
12Mz - curvature
5
10
8
10
M-ϕ diagrams
-5
0
My [kN-m
]
2
4
6
Mz [kN-m
]
-4 -2 0 2 4
x 10-5
-15
-10
φy
0 2 4 6 8
x 10-5
-2
0
φz
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APLICATIONS
Distribution of de σx
Distribution of σs in stirrups
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APLICATIONS
Di ib i f d iDistribution of damage in concrete
Distribution of damage h tshear component
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APLICATIONSPure torsion
Torsion stiffnessSh t flShear stress flow
φ
φ
φ
φφ
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APLICATIONS
Principal compression
Pure torsionTorsion stiffness
Principal compression
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APLICATIONS
Cracked stiffeness evaluated by Collins and Lampert (1972)
Torsion-axial strain coupling Torsion-bending couplingLongitudinal reinforcement stressTransversal reinforcement stress
Uncracked sectional stiffness matrix:
Cracked sectional stiffness matrix:
54J. M. Bairán2009
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APLICATIONSBending-torsion interaction
Bending-torsion interaction diagramsO (1978)Onsongo (1978)
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APLICATIONSBending-torsion interaction
Bending-torsion interaction diagrams
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APLICATIONSInfluence in the response of complete structures
Effect of tangential forces in the non-linear response of concrete structures
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APLICATIONS
Influence in the response of complete structuresEffects of tangential forces in the non linear response of concrete structuresEffects of tangential forces in the non-linear response of concrete structures
S1S1•Neglecting shear forces.•Navier-Bernoulli
l t
S2•Timoshenko elementelement.
• Traditional fiber discretization
element.• TINSA –Generalized coordinates
S3•Timoshenko element.• TINSA –Generalized
58
coordinates
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APLICATIONS
Influence in the response of complete structuresEffects of tangential forces in the non linear response of concrete structures
Load-displacement
Effects of tangential forces in the non-linear response of concrete structures
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APLICATIONS
Influence in the response of complete structuresEffects of tangential forces in the non linear response of concrete structures
Moment - Load
Effects of tangential forces in the non-linear response of concrete structures
InternalInternal Support
Mid-spanp
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APLICATIONS
Influence in the response of complete structuresEffects of tangential forces in the non linear response of concrete structures
Stresses in longitudinal reinforcements
Effects of tangential forces in the non-linear response of concrete structures
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APLICATIONS
Influence in the response of complete structuresEffects of tangential forces in the non linear response of concrete structures
Stresses in transversal reinforcements
Effects of tangential forces in the non-linear response of concrete structures
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APLICATIONS
Influence in the response of complete structuresEffects of tangential forces in the non linear response of concrete structures
S1
Effects of tangential forces in the non-linear response of concrete structures
Crack patterns
S2
S3
63q=43.8 kN/mJ. M. Bairán2009
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APLICATIONS
Influence in the response of complete structuresEffects of tangential forces in the non linear response of concrete structures
S1Crack patterns
Effects of tangential forces in the non-linear response of concrete structures
S2
S3
64q=127 kN/mJ. M. Bairán2009
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APLICATIONS
Influence in the response of complete structuresEffects of tangential forces in the non linear response of concrete structures
Left support
Distribution of stresses and strains in some sections q=127 kN/m
Mid-Span 1 Interior support
Effects of tangential forces in the non-linear response of concrete structures
Left support p
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Further topics
E t di li d di t f l ti
Cross-section modelling
• Extending generalized coordinates formulation.
• Dynamic and seismic response of structures sensible to shear forces and torsionand torsion.
• Stage construction.
• Evaluation of repaired and retrofitted structures.
• Computational cost .Material modelling
• Modelling lateral strains under cyclic loading.
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PART 2
Disturbed regionsDisturbed regions
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Disturbed regions
Geometric and load discontinuity
When a rod is not good eno ghWhen a rod is not good enough….
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Disturbed regions
Problematic
Design methodology: Strut and Tie
•Not uniqueness of Strut and Tie models for design.
• Sometimes it is difficult to find a plausible Strut and Tie scheme for a new elementSometimes it is difficult to find a plausible Strut and Tie scheme for a new element.
• Constructability of the resulting reinforcement arrangement.
• Strut and Tie models are a representation of the ultimate limit state.
• Lack of explicit rules for damage control and serviceability.
Assessment
• Real load carrying capacity.
• Damage assessment in different load levels.
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AUTOMATIC GENERATION OF STRUT & TIE MODELS
Idea
T l i l ti i ti th h d i i t ki it i b d th l i f• Topological optimization through decision taking criteria based on the analysis of energy density distribution in linear elastic analysis.
• Importance or efficiency of the each element is defined by means of a efficiency p y y yfactor.
• Element stiffness is modified according to its efficiency. Less important elements collaborate lesscollaborate less.
Implementation and applicability
• Several truss-and-tie schemes are generated according to the criteria used.
• Constructability can be considered through decision criteria and by orthotropic elastic behaviour
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AUTOMATIC GENERATION OF STRUT & TIE MODELS
Deep wall Linear elastic response
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AUTOMATIC GENERATION OF STRUT & TIE MODELS
Strut & Tie model from criterion 1 : no special constructability considerationsDeep wall
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AUTOMATIC GENERATION OF STRUT & TIE MODELS
Strut & Tie model from criterion 2 : constructability considerationsDeep wall
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EVALUATION OF “D” REGIONS
A t l f
Goal
• Actual performance
• Damage assessment
• Load carrying capacity
Approach
• Concrete: non-linear biaxial behaviour
• Softening induced by transversal tensile strains (according to MCFT)
• Smeared crack approach• Smeared crack approach
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EVALUATION OF “D” REGIONS
Crack patterns for strut & tie model 1Deep wall
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EVALUATION OF “D” REGIONS
Crack patterns for strut & tie model 2Deep wall
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EVALUATION OF “D” REGIONS
Force-displacement curves for models 1 and 2Deep wall
6000
7000
5000
6000
Criterion 1
3000
4000 Criterion 2P (kN)Pd=3000 kN
1000
2000
0 10 20 30 40 50 600
1000
77J. M. Bairán2009
d (mm)
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Further topics
• Performance based design – damage control
• Optimization - design
Possibilit of local fail re modes imperfect bond anchorage• Possibility of local failure modes: imperfect bond, anchorage failure
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Acknowlegments
Some of the works here presented have been conducted under the support of:
Spanish Ministry of Education and Science through the research programs:•SARCS: “Seismic Assesment of Reinforced Concrete Structures” (BIA-2006-05614)•SEDUREC: “Security and durability in Construction Structures” (CSD-2006-00060)
Institute for the Promotion of Certified Reinforcements (IPAC) Through the Research Agreement for the Study of Structural Advantages of Using Very High Ductility Reinforcement.
Spanish Lamination Company (CELSA) Research project to study effects of straightening of reinforcing steel coils in their mechanics and ductility characteristics.
The author wishes to acknowledge SARCS research team In particular to
y
The author wishes to acknowledge SARCS research team. In particular to Prof. Antonio MaríPh.D. students Steffen Mohr and Edison Osorio.
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Earthquake Engineering by the beachthe beachCapri, July 2-4 2009
Nonlinear modelling of i f d t t treinforced concrete structures
Jesús Miguel Bairán GarcíaLecturer of Civil Engineering
Universitat Politecnica de CatalunyaDepartment of Construction Engineering
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81J. M. Bairán2009