Upload
ashton-reilly
View
216
Download
3
Embed Size (px)
Citation preview
Dottorato di Ricerca in Ingegneria delle Strutturee del recupero edilizio e urbano - IX ciclo N. S.
Presentazione del lavoro di tesi
Analisi non lineare di pareti murarie sotto azioni orizzontali: modellazione a
telaio equivalente
Fisciano, 6 Maggio 2011
Dipartimento di Ingegneria Civile – Università degli Studi di Salerno
Dottorando: Ing. Riccardo Sabatino Tutor: Prof. Vincenzo PilusoCo-Tutor: Prof. Gianvittorio Rizzano
All exact science is dominated by the idea of All exact science is dominated by the idea of
approximationapproximation
Bertrand RussellBertrand Russell
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Science is organized knowledgeScience is organized knowledge
Herbert SpencerHerbert Spencer
Chapter 1: IntroductionChapter 1: Introduction
Chapter 2: FEM modellingChapter 2: FEM modelling
Chapter 3: Masonry Buildings Modelling StrategiesChapter 3: Masonry Buildings Modelling Strategies
Chapter 4: Mechanical Behaviour of masonry panelsChapter 4: Mechanical Behaviour of masonry panels
Chapter 5: Matrix Analysis of structuresChapter 5: Matrix Analysis of structures
Chapter 6: The FREMA codeChapter 6: The FREMA code
OutlineOutline
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Chapter 1: IntroductionChapter 1: Introduction
Chapter 2: FEM modellingChapter 2: FEM modelling
Chapter 3: Masonry Buildings Modelling StrategiesChapter 3: Masonry Buildings Modelling Strategies
Chapter 4: Mechanical Behaviour of masonry panelsChapter 4: Mechanical Behaviour of masonry panels
Chapter 5: Matrix Analysis of structuresChapter 5: Matrix Analysis of structures
Chapter 6: The FREMA codeChapter 6: The FREMA code
OutlineOutline
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
First Stone Dwellings (8350 b.C. – Jericho, First Stone Dwellings (8350 b.C. – Jericho,
Tell-es-Sultan)Tell-es-Sultan)
IntroductionIntroductionFresco found in Rekhamara’s Tomb (1500 b.C. – Egypt)Fresco found in Rekhamara’s Tomb (1500 b.C. – Egypt)
Djoser Pyramid (2600 b.C. – Egypt)Djoser Pyramid (2600 b.C. – Egypt)
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Performance-based Earthquake Engineering Performance-based Earthquake Engineering Non-linear static procedures (NLP) Non-linear static procedures (NLP)
IntroductionIntroduction
Non-linear Static AnalysisNon-linear Static Analysis
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Strategies for Modelling Masonry BuildingsStrategies for Modelling Masonry Buildings
IntroductionIntroduction
FEM modelsFEM models Simplified modelsSimplified modelsspandrel
pierrigid offest
√√ Very accurate predictionVery accurate prediction
√√ Any kind of structure may be analysedAny kind of structure may be analysed
XX Time-consuming Time-consuming
XX Amount of input data Amount of input data
XX High Analytical Skills requiredHigh Analytical Skills required
√√ Suitable for professional purposesSuitable for professional purposes
√√ Quick analysesQuick analyses
XX Regular geometry needed Regular geometry needed
XX Simplifications need to evaluated Simplifications need to evaluated
VSVS
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Chapter 1: IntroductionChapter 1: Introduction
Chapter 2: FEM modellingChapter 2: FEM modelling
Chapter 3: Masonry Buildings Modelling StrategiesChapter 3: Masonry Buildings Modelling Strategies
Chapter 4: Mechanical Behaviour of masonry panelsChapter 4: Mechanical Behaviour of masonry panels
Chapter 5: Matrix Analysis of structuresChapter 5: Matrix Analysis of structures
Chapter 6: The FREMA codeChapter 6: The FREMA code
OutlineOutline
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Accurate Modelling: mesoscale modelAccurate Modelling: mesoscale modelBlocks are modelled using continuum elements, while mortar and brick-mortar Blocks are modelled using continuum elements, while mortar and brick-mortar interfaces are modelled by means of nonlinear interface elements (Lourenço & interfaces are modelled by means of nonlinear interface elements (Lourenço & Rots, 1996).Rots, 1996).
Solid and interface elements account for large displacements, while only interface elements represent cracks in mortar and bricks.
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Material modelMaterial modelMulti-surfaceMulti-surface
nonassociated plasticity nonassociated plasticity
Elastic responseElastic response
0σ = k u
0
0
0
0 0
0 0
0 0
t
t
n
k
k
k
0kElastic stiffness
Mortar jointsMortar joints
0m
tj
Gk
h 0
mn
j
Ek
h
2 22 21 tan tan 0x y tF C C
2 22 22 tan tan 0x y cF D D
2 22 21 tan tan 0x y Q Q Q t QQ C C
Yield functions F1 - F2
Plastic potentials Q1 - Q2
A novel 2D nonlinear interface elementA novel 2D nonlinear interface elementPhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
A novel 2D nonlinear interface elementA novel 2D nonlinear interface elementMaterial modelMaterial model
Nonassociated plasticity Nonassociated plasticity Elastic responseElastic response
0σ = k u
0
0
0
0 0
0 0
0 0
t
t
n
k
k
k
0kElastic stiffness
0 0t nk k penalty factor
2 22 21 tan tan 0x y tF C C
2 22 21 tan tan 0x y Q Q Q t QQ C C
Brick interfaceBrick interface
Yield function F1
Plastic potential Q1
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
A novel 2D nonlinear interface elementA novel 2D nonlinear interface element
Material propertiesMaterial properties
t - tensile strength
C - cohesion
Gf,II - mode II fracture energy
C - compressive strength
Gf,I - mode I fracture energy
Gf,I
uz
t
- friction angle
<0
Gf,I
I ux(y)
c
tan
GC - crushing energy
c
uz
Gc
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
A novel 2D nonlinear interface elementA novel 2D nonlinear interface elementWork-softening plasticity Work-softening plasticity
0 0 rA A A A
** *
*
* *
11 cos 0
2
1
plpl f
f
pl f
WW G
G
W G
t cA C, ,tan ,D, ,tan
Evolution of the material parametersEvolution of the material parameters
with
Wpl1 - plastic work related to F1
Wpl2 - plastic work related to F2
Evolution of the surfacesEvolution of the surfaces
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
A novel 2D nonlinear interface elementA novel 2D nonlinear interface elementTraction deformation responseTraction deformation response
tension-compression cyclic behaviour
shear cyclic behaviour
tensionshear
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
In-plane behaviourIn-plane behaviourVermeltfoort AT, Raijmakers TMJ (1993)Vermeltfoort AT, Raijmakers TMJ (1993)
J4DJ4D J5DJ5D
pv=0.3 MPamortar mortar
interfaceinterface
mortar mortar interfaceinterface
brick brick interfaceinterface
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
In-plane behaviourIn-plane behaviourVermeltfoort AT, Raijmakers TMJ (1993)Vermeltfoort AT, Raijmakers TMJ (1993)
J4DJ4D J5DJ5D
Wpl1Wpl1Wpl1Wpl1
Wpl2
pv=0.3 MPa
pv=0.3 MPa
pv=2.12 MPa
dynamic analysisdynamic analysis
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
In-plane behaviourIn-plane behaviour
Mesh assessmentMesh assessment
• Mesh refinement
• Number of integration points over the interface
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
In-plane behaviourIn-plane behaviourVermeltfoort AT, Raijmakers TMJ (1993)Vermeltfoort AT, Raijmakers TMJ (1993)
Wpl1Wpl1
Wpl2Wpl2
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Retrofitting: Influence of spandrelsRetrofitting: Influence of spandrels
Numerical Modelling (STRAUS7): 144 panels
Panels have been obtained by assembling a
reference module whose geometry (piers,
spandrels) has been properly varied.
The parameter , ratio between the shear
stiffness of piers and spandrels, has been used to
take into account the panels geometry.
500
500
H=
400
B=500
30
30 bm
bf
hm
bm
hf
1-1 1-2 1-4
2-22-1 2-3 2-4
3-3 4-4
3
,3
3 12
12
f
em
f
f
m
m
f
m
EI
b
h
EI
k
k
f
ff h
b
m
mem b
h,
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Panels have been modelled by assuming two limit schemes:
infinite stiffness spandrels and “unreinforced” spandrels.
The parameter represents the expected
improvement of relative shear strength achievable by means of
spandrels retrofitting.
nc
nc
T
TT
Retrofitting: Influence of spandrelsRetrofitting: Influence of spandrels
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
The comparison shows a
significant improvement in
the field <1.5, i.e. for weak
spandrels.
In such field the average
strength improvement can
be estimated as:
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0
1-1 1-2 1-4
2-1 2-2 2-3
2-4 3-3 4-4
59.015.0 :5.1
0,20
0,30
0,40
0,50
0,60
0,70
0,50 0,75 1,00 1,25 1,50
1-1 1-2 1-4
2-1 2-2 2-3
2-4 3-3 4-4
Retrofitting: Influence of spandrelsRetrofitting: Influence of spandrels
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
RetrofittingRetrofitting
Then the panels 1-1 and 4-4 have been extensively investigated by considering
the retrofitting approach suggested in Italian Building Code.
For each panel, the weak spandrel (=0.70) and the strong spandrel (=5.35)
schemes have been analysed.
Three different kinds of reinforcements have been taken into account:
Injection Grouts;
Reinforced plasters;
Ring beams / Jack Arch.
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
RetrofittingRetrofitting
The shear resistance of the panels has been evaluated by means of a
non-linear static analysis. Both the unreinforced and the reinforced
wall have been analyzed.
The improvement deriving from the reinforcement has been
summarized into the parameter
where T is the reinforced wall resistance, Tnc the unreinforced wall
resistance.
nc
nc
T
TT
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
RetrofittingRetrofitting
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Retrofitting: Wall 1-1Retrofitting: Wall 1-1
0,024 0,031 0,042
0,718
1,015
0
0,2
0,4
0,6
0,8
1
1,2
Efficacia 0,024 0,031 0,042 0,718 1,015
CordoloCordolo +
piattabandaFascia rigida Iniezioni
Intonaco armato
Parete 1-1, =5,35
0,328
0,5260,582
0,749
1,052
0
0,2
0,4
0,6
0,8
1
1,2
Efficacia 0,328 0,526 0,582 0,749 1,052
CordoloCordolo +
piattabandaFascia rigida Iniezioni
Intonaco armato
Parete 1-1, =0,70
For weak spandrels walls, the spandrel improvement gives the same results of injection
grouts/reinforced plasters.
For strong spandrels walls, best improvements have been achieved with injection
grouts/reinforced plasters.
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Retrofitting: Wall 4-4Retrofitting: Wall 4-4
0,056
0,140 0,153
0,430 0,421
0
0,2
0,4
0,6
0,8
1
Efficacia 0,056 0,140 0,153 0,430 0,421
CordoloCordolo +
piattabandaFascia rigida
Iniezioni (1° piano)
Intonaco armato (1° piano)
Parete 4-4, =5,35
0,286
0,414
0,502
0,742 0,771
0
0,2
0,4
0,6
0,8
1
Efficacia 0,286 0,414 0,502 0,742 0,771
CordoloCordolo +
piattabandaFascia rigida
Iniezioni (1° piano)
Intonaco armato (1°
piano)
Parete 4-4, =0,70
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
RetrofittingRetrofitting
[Modena et al.][Modena et al.]
The expected improvement gets the same order of magnitude of data available in literatureThe expected improvement gets the same order of magnitude of data available in literature
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Retrofitting: Parete 4-4Retrofitting: Parete 4-4 For the wall 4-4, further numerical simulations have been performed, by assuming the
reinforcement (reinforced plaster/injection ) applied to 1 to 4 storeys.
Consolidamento con intonaco armato - Parete 4-4
0,00
1,00
2,00
3,00
4,00
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0
1 piano 2 piani
3 piani 4 piani
Consolidamento con iniezioni - Parete 4-4
0,00
1,00
2,00
3,00
4,00
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0
1 piano 2 piani
3 piani 4 piani
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Chapter 1: IntroductionChapter 1: Introduction
Chapter 2: FEM modellingChapter 2: FEM modelling
Chapter 3: Masonry Buildings Modelling StrategiesChapter 3: Masonry Buildings Modelling Strategies
Chapter 4: Mechanical Behaviour of masonry panelsChapter 4: Mechanical Behaviour of masonry panels
Chapter 5: Matrix Analysis of structuresChapter 5: Matrix Analysis of structures
Chapter 6: The FREMA codeChapter 6: The FREMA code
OutlineOutline
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Simplified ModelsSimplified Models
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Chapter 1: IntroductionChapter 1: Introduction
Chapter 2: FEM modellingChapter 2: FEM modelling
Chapter 3: Masonry Buildings Modelling StrategiesChapter 3: Masonry Buildings Modelling Strategies
Chapter 4: Mechanical Behaviour of masonry panelsChapter 4: Mechanical Behaviour of masonry panels
Chapter 5: Matrix Analysis of structuresChapter 5: Matrix Analysis of structures
Chapter 6: The FREMA codeChapter 6: The FREMA code
OutlineOutline
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Description of the modelDescription of the model
F2
F1
Main featuresMain features
1. Displacement Control approach 1. Displacement Control approach NLP NLP
2. Global and local equilibrium2. Global and local equilibrium
3. Spread plasticity approach3. Spread plasticity approach
4. Quick Analysis and Easy Post-processing4. Quick Analysis and Easy Post-processing
Piers (HPiers (Heffeff after Dolce, 1991) after Dolce, 1991)SpandrelsSpandrels
Rigid OffsetsRigid Offsets
Equivalent Frame ModelEquivalent Frame Model
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Piers - Constitutive Laws Piers - Constitutive Laws Generalized Uniaxial Compressive Stress-Strain RelationshipGeneralized Uniaxial Compressive Stress-Strain Relationship
C
u u u
A B
A=2, B=-1, C=2 A=2, B=-1, C=2 [Hendry, 1998][Hendry, 1998]
A=6.4, B=-5.4, C=1.17 A=6.4, B=-5.4, C=1.17 [Turnšek-Čačovič, 1980][Turnšek-Čačovič, 1980]
Accurate Moment-CurvatureAccurate Moment-Curvature
d
ud
[After Tomaževič, 1999]
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Piers - Flexural BehaviourPiers - Flexural Behaviour
N
M
D
t
M
D
yc
N
GG
yc
t
N
M
D
t
M
D
yc
N
GG
yc
t
normalised neutral axis
normalised axial force
normalised bending moment
u
M
Cross-section Equilibrium EquationsCross-section Equilibrium Equations
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Moment-Curvature relationship workflowMoment-Curvature relationship workflow
0
5
10
15
20
25
30
35
40
0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0
M [k
Nm
]
[mm-1 x 106]
D, t, ,
u
u
cr
M
YES
NOD [mm] 500t [mm] 250N [kN] 200
A 2B -1C 2
u 0,003
r 0,0045
u [MPa] 6,2
END
PhD Dissertation Talk – Fisciano, 6th May 2011
Piers - Shear BehaviourPiers - Shear Behaviour
[After Anthoine, Magenes, Magonette, 1994]
Experimental BehaviourExperimental Behaviour ModelModel
Ultimate drift Ultimate drift uu = 0.4% H = 0.4% Heffeff
[Italian Building Code][Italian Building Code]
u
V
Vu
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Piers - Shear BehaviourPiers - Shear Behaviour
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
i=Vi/Ki
min Vu
i
el
Ki+1=Ki *Vu/Vi
NO
YES
el=Vu/Kel
V
Ksec,i
Ksec,i+1
Vi
Vu
el
Ki+1=Kel
Shear-strain relationship workflowShear-strain relationship workflow
PhD Dissertation Talk – Fisciano, 6th May 2011
Collapse condition when the desired value of Collapse condition when the desired value of drift (set by the user) is attained drift (set by the user) is attained
(Italian Building Code suggets (Italian Building Code suggets = 0.004 for = 0.004 for shear collapse)shear collapse)
Shear-strain relationship workflowShear-strain relationship workflow
u
V
Vu
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Spandrels - Shear BehaviourSpandrels - Shear Behaviour
Experimental BehaviourExperimental Behaviour ModelModel
Residual Strength Residual Strength = 0.25= 0.25
[Magenes and Della Fontana, 1998][Magenes and Della Fontana, 1998]
u
V
Vu
Vu
0u vdV ht f
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Spandrels - Flexural BehaviourSpandrels - Flexural Behaviour
Experimental BehaviourExperimental Behaviour ModelModel
[After Calderoni et al., 2008]
u
M
Mu
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Spandrels - Flexural BehaviourSpandrels - Flexural Behaviour
Proposed formulations for MProposed formulations for Muu – – [Italian Building Code, 2008][Italian Building Code, 2008]
1.1. Stress-block approach (same equation of piers)Stress-block approach (same equation of piers)
2. If no tensile-resistant element is present 2. If no tensile-resistant element is present M Muu=0=0
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Spandrels - Flexural BehaviourSpandrels - Flexural BehaviourProposed formulations for MProposed formulations for Muu [Schubert & Weschke, 1986][Schubert & Weschke, 1986]
Take into account an “equivalent Take into account an “equivalent strut” provided with a tensile strut” provided with a tensile strength fstrength ftutu
fftutu is the minimum between two is the minimum between two collapse mechanisms:collapse mechanisms:
a) bricks failurea) bricks failure
b) bed joints failureb) bed joints failure
,
joint 22y bt
tu a bt
y
ff f
t
,
joint22
x xtu b
yy
f c p c pt
a)a)
b)b)
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Spandrels - Flexural BehaviourSpandrels - Flexural BehaviourSpandrels M-N Limit Domain Spandrels M-N Limit Domain [Cattari and Lagomarsino, 2008][Cattari and Lagomarsino, 2008]
= ratio between tensile strength f= ratio between tensile strength ftutu and compressive strength and compressive strength
fwc
/y-
c1
-
10.85
Constitutive LawConstitutive Law
Improvement of rocking Improvement of rocking resistance, also with low resistance, also with low
(or zero) values of N.(or zero) values of N.
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Chapter 1: IntroductionChapter 1: Introduction
Chapter 2: FEM modellingChapter 2: FEM modelling
Chapter 3: Masonry Buildings Modelling StrategiesChapter 3: Masonry Buildings Modelling Strategies
Chapter 4: Mechanical Behaviour of masonry panelsChapter 4: Mechanical Behaviour of masonry panels
Chapter 5: Matrix Analysis of structuresChapter 5: Matrix Analysis of structures
Chapter 6: The FREMA codeChapter 6: The FREMA code
OutlineOutline
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Masonry Panels – Anthoine, Magonette and Magenes (1998)Masonry Panels – Anthoine, Magonette and Magenes (1998)
Low PanelLow Panel High PanelHigh Panel
Cross-Section: 100 x 25 cmCross-Section: 100 x 25 cm22
Low panel high: 135 cmLow panel high: 135 cm
High panel high: 200 cmHigh panel high: 200 cm
Normal Load: 150 kNNormal Load: 150 kN
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Pavia Door Wall – Calvi and Magenes (1994)Pavia Door Wall – Calvi and Magenes (1994)
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Pavia Door Wall – Calvi and Magenes (1994)Pavia Door Wall – Calvi and Magenes (1994)
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Pavia Door Wall – Calvi and Magenes (1994)Pavia Door Wall – Calvi and Magenes (1994)
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Catania Project - Investigation on the seismic response of two masonry buildings (2000)Catania Project - Investigation on the seismic response of two masonry buildings (2000)
““Via Martoglio” 2D WallVia Martoglio” 2D Wall
Equivalent Frame model: 128 elements, 81 nodes, 219 DOF
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Model 1: Masonry, NO R.C. Ring BeamsModel 1: Masonry, NO R.C. Ring Beams
““Via Martoglio” 2D WallVia Martoglio” 2D Wall
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Model 2: Masonry, Elastic R.C. Ring Beams (E=20,000 MPa)Model 2: Masonry, Elastic R.C. Ring Beams (E=20,000 MPa)
““Via Martoglio” 2D WallVia Martoglio” 2D Wall
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Model 3: Masonry, Elastic R.C. Ring Beams (E=4,000 MPa)Model 3: Masonry, Elastic R.C. Ring Beams (E=4,000 MPa)
““Via Martoglio” 2D WallVia Martoglio” 2D Wall
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Catania Project - Investigation on the seismic response of two masonry buildings (2000)Catania Project - Investigation on the seismic response of two masonry buildings (2000)
Preliminary validation of the modelPreliminary validation of the model
““Via Verdi” BuildingVia Verdi” Building
Wall 1Wall 1Wall 2Wall 2
Wall 3Wall 3
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
““Via Verdi” – Wall 1Via Verdi” – Wall 1
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
““Via Verdi” – Wall 2Via Verdi” – Wall 2
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
““Via Verdi” – Wall 3Via Verdi” – Wall 3
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Mallardo et al. (2008) – Palazzo Renata di FranciaMallardo et al. (2008) – Palazzo Renata di Francia
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Mallardo et al. (2008)Mallardo et al. (2008)
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Salonikios et al. (2003)Salonikios et al. (2003)
Two-storey, 7-bay masonry wallTwo-storey, 7-bay masonry wall
Two lateral load distributions Two lateral load distributions considered:considered:
1.1. Uniform (ACC)Uniform (ACC)
F= {1.00; 0.59}F= {1.00; 0.59}
2.2. Inverse Triangular (LOAD)Inverse Triangular (LOAD)
F= {1.00; 1.19}F= {1.00; 1.19}
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Salonikios et al. (2003) – 7B_UniformSalonikios et al. (2003) – 7B_Uniform
0
200
400
600
800
1000
0 2 4 6 8 10 12 14 16
top displacement [mm]
Tota
l Bas
e Sh
ear [
kN]
Proposed Model
SAP 2000
Discrete FEM model
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Salonikios et al. (2003) – 7B_Inverse TriangularSalonikios et al. (2003) – 7B_Inverse Triangular
0
200
400
600
800
1000
0 2 4 6 8 10 12 14 16
top displacement [mm]
Tota
l Bas
e Sh
ear [
kN]
Proposed Model
SAP 2000
Discrete FEM model
The FREMA CodeThe FREMA Code
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Salonikios et al. (2003)Salonikios et al. (2003)
Mesh RefinementMesh Refinement
=Log(Nc/x)
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Salonikios et al. (2003) – 7B_Inverse TriangularSalonikios et al. (2003) – 7B_Inverse Triangular
Mesh RefinementMesh Refinement
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Salonikios et al. (2003) – 7B_UniformSalonikios et al. (2003) – 7B_Uniform
Mesh RefinementMesh Refinement
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Salonikios et al. (2003)Salonikios et al. (2003)
Time-cost AnalysisTime-cost Analysis
=Log(Nc/x)
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Time-cost AnalysisTime-cost Analysis
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
This dissertation deals with the seismic behaviour of masonry structures;This dissertation deals with the seismic behaviour of masonry structures;
The first part of the work is aimed at understanding the potentialities of The first part of the work is aimed at understanding the potentialities of very accurate FEM model very accurate FEM model in predicting masonry panels seismic response; the in predicting masonry panels seismic response; the panels simulated by means of ADAPTIC showed a very good prediction of the panels simulated by means of ADAPTIC showed a very good prediction of the experimental results, both in terms of force-displacement curve and in terms experimental results, both in terms of force-displacement curve and in terms of cracks path.of cracks path.
A further application of simplified (homogeneous) FEM models has been A further application of simplified (homogeneous) FEM models has been performed on masonry panels, aiming at evaluating the performed on masonry panels, aiming at evaluating the influence of influence of spandrels reinforcementspandrels reinforcement on the overall resistance; in the same application on the overall resistance; in the same application some some reinforcement techniques reinforcement techniques have been applied considering the Italian have been applied considering the Italian Building Code approach;Building Code approach;
ConclusionsConclusions
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
ConclusionsConclusions In the second part of the dissertation, a novel equivalent frame model has In the second part of the dissertation, a novel equivalent frame model has been developed. The main features of the model have been discussed, by been developed. The main features of the model have been discussed, by highlighting the main features of the proposed model (displacement control highlighting the main features of the proposed model (displacement control approach, accurate moment-curvature for piers behaviour, spandrels approach, accurate moment-curvature for piers behaviour, spandrels behaviour);behaviour);
A A validation and applicationvalidation and application of the model has been carried out of the model has been carried out comparison with experimental tests and accurate numerical simulationscomparison with experimental tests and accurate numerical simulations
The comparison showed a The comparison showed a good agreementgood agreement between the proposed model between the proposed model and both experimental and numerical results, showing that FREMA code is a and both experimental and numerical results, showing that FREMA code is a reliable tool for performing the non-linear static analysis of masonry panels.reliable tool for performing the non-linear static analysis of masonry panels.
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Thank you very much!Thank you very much!
PhD Dissertation Talk – Fisciano, 6th May 2011
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Dottorato di Ricerca in Ingegneria delle Strutturee del recupero edilizio e urbano - IX ciclo N. S.
Presentazione del lavoro di tesi
Analisi non lineare di pareti murarie sotto azioni orizzontali: modellazione a
telaio equivalente
Fisciano, 6 Maggio 2011
Dipartimento di Ingegneria Civile – Università degli Studi di Salerno
Dottorando: Ing. Riccardo Sabatino Tutor: Prof. Vincenzo PilusoCo-Tutor: Prof. Gianvittorio Rizzano