Dipartimento di Ingegneria Civile – Università degli Studi di Salerno
Dottorato di Ricerca in Ingegneria delle Strutture
e 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
Dottorando: Ing. Riccardo Sabatino
Tutor: Prof. Vincenzo Piluso
Co-Tutor: Prof. Gianvittorio Rizzano
PhD Dissertation Talk – Fisciano, 6th May 2011
All exact science is dominated by the idea of
approximation
Bertrand Russell
Science is organized knowledge
Herbert Spencer
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Outline
 Chapter 1: Introduction
 Chapter 2: FEM modelling
 Chapter 3: Masonry Buildings Modelling Strategies
 Chapter 4: Mechanical Behaviour of masonry panels
 Chapter 5: Matrix Analysis of structures
 Chapter 6: The FREMA code
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Outline
 Chapter 1: Introduction
 Chapter 2: FEM modelling
 Chapter 3: Masonry Buildings Modelling Strategies
 Chapter 4: Mechanical Behaviour of masonry panels
 Chapter 5: Matrix Analysis of structures
 Chapter 6: The FREMA code
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Introduction
Fresco found in Rekhamara’s Tomb (1500 b.C. – Egypt)
First Stone Dwellings (8350 b.C. – Jericho,
Tell-es-Sultan)
Djoser Pyramid (2600 b.C. – Egypt)
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Introduction
Performance-based Earthquake Engineering  Non-linear static procedures (NLP)
Non-linear Static Analysis
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Introduction
Strategies for Modelling Masonry Buildings
FEM models
VS
Simplified models
spandrel
rigid offest
pier
√ Very accurate prediction
√ Suitable for professional purposes
√ Any kind of structure may be analysed
√ Quick analyses
X Time-consuming
X Regular geometry needed
X Amount of input data
X Simplifications need to evaluated
X High Analytical Skills required
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Outline
 Chapter 1: Introduction
 Chapter 2: FEM modelling
 Chapter 3: Masonry Buildings Modelling Strategies
 Chapter 4: Mechanical Behaviour of masonry panels
 Chapter 5: Matrix Analysis of structures
 Chapter 6: The FREMA code
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Accurate Modelling: mesoscale model
Blocks are modelled using continuum elements, while mortar and brick-mortar
interfaces are modelled by means of nonlinear interface elements (Lourenço &
Rots, 1996).
Solid and interface elements account for large displacements, while
only interface elements represent cracks in mortar and bricks.
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
A novel 2D nonlinear interface element
Material model
Multi-surface
nonassociated plasticity
Elastic response
Yield functions F1 - F2
σ = k0 u
Elastic
stiffness
 kt 0
k0   0

 0
kt 0 
Gm
hj
0
kt 0
0
0
0

kn 0 
kn 0 
Em
hj
Plastic potentials Q1 - Q2
F1   x2   y2   C   tan     C   t tan    0
2
2
Q1   x2   y2   CQ   tan Q    CQ   t tan Q   0
2
Mortar joints
2
F2   x2   y2   D   tan     D   c tan    0
2
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
2
PhD Dissertation Talk – Fisciano, 6th May 2011
A novel 2D nonlinear interface element
Material model
Elastic response
σ = k0 u
Elastic
stiffness
 kt 0
k0   0

 0
Nonassociated plasticity
Yield function F1
0
kt 0
0
0
0

kn 0 
kt 0  kn0  penalty factor
Brick interface
Plastic potential Q1
F1   x2   y2   C   tan     C   t tan    0
2
2
Q1   x2   y2   CQ   tan Q    CQ   t tan Q   0
2
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
2
PhD Dissertation Talk – Fisciano, 6th May 2011
A novel 2D nonlinear interface element
Material properties
t - tensile strength

t
GC - crushing energy
Gf,I - mode I
fracture energy
Gf,I
uz

Gf,II - mode II
c
fracture energy
Gf,I
I


tan
ux(y)

c

<0
C - cohesion
 - friction angle
C - compressive strength



Gc
uz

R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

PhD Dissertation Talk – Fisciano, 6th May 2011
A novel 2D nonlinear interface element
Work-softening plasticity
Evolution of the material parameters
A  A0   A0  Ar 
Evolution of the surfaces
with A  C, t ,tan  ,D, c ,tan
1 
  W pl*  
 1  cos 
0  Wpl*  G f *
 G  
   2 
 f *  

Wpl*  G f *
 1
Wpl1 - plastic work related to F1
Wpl2 - plastic work related to F2
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
A novel 2D nonlinear interface element
Traction deformation response
shear
tension
shear cyclic
behaviour
tension-compression
cyclic behaviour
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
In-plane behaviour
Vermeltfoort AT, Raijmakers TMJ (1993)
mortar
interface
pv=0.3 MPa
brick
interface
mortar
interface
J4D
J5D
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
In-plane behaviour
Vermeltfoort AT, Raijmakers TMJ (1993)
Wpl1
Wpl1
Wpl1
Wpl1
=0.3 MPa
ppvv=2.12
MPa
Wpl2
J4D
J5D
pv=0.3 MPa
dynamic analysis
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
In-plane behaviour
Mesh assessment
• Mesh refinement
• Number of integration points
over the interface
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
In-plane behaviour
Vermeltfoort AT, Raijmakers TMJ (1993)
Wpl1
Wpl2
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Retrofitting: Influence of spandrels

500
Numerical Modelling (STRAUS7): 144 panels
B=500
30
reference
30
module whose geometry (piers,
spandrels) has been properly varied.

The parameter l, ratio between the shear
1-2
2-1
2-2
3-3
stiffness of piers and spandrels, has been used to
hm
bm
1-1
hf
H=400
Panels have been obtained by assembling a
500

bf
bm
1-4
2-3
2-4
4-4
take into account the panels geometry.
lf 
bf
hf
l m ,e
h
 m
bm
 l m ,e 
b 3f
k m 12  EI m


l



kf
12  EI  f  l f 
hm3
3
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Retrofitting: Influence of spandrels

Panels have been modelled by assuming two limit schemes:
infinite stiffness spandrels and “unreinforced” spandrels.

The parameter

T  Tnc
Tnc
represents the expected
improvement of relative shear strength achievable by means of
spandrels retrofitting.
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Retrofitting: Influence of spandrels

The comparison shows a
significant improvement in
0,70
0,70
0,60
0,60
0,50
the field l<1.5, i.e. for weak
1-1
1-2
1-4
2-11-1
2-21-2
1-4
2-3
2-42-1
3-32-2
2-3
4-4
2-4
3-3
4-4
0,50
0,40


0,30
0,40
spandrels.
0,20
0,30

In such field the average
strength improvement can be
estimated as:
0,10
0,20
0,00
0,50
0,0
0,5
1,0 0,75
1,5
2,0
l 1,00
2,5
3,0
l
3,5
4,0 1,25
4,5
5,0
l  1.5 :   0.15l  0.59
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
5,5 1,50
6,0
PhD Dissertation Talk – Fisciano, 6th May 2011
Retrofitting

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 (l=0.70) and the strong spandrel (l=5.35)
schemes have been analysed.

Three different kinds of reinforcements have been taken into account:

Injection Grouts;

Reinforced plasters;

Ring beams / Jack Arch.
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Retrofitting

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  
T  Tnc
Tnc
where T is the reinforced wall resistance, Tnc the unreinforced wall
resistance.
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Retrofitting
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Retrofitting: Wall 1-1
1,2
1,2
1,052
1
1
0,749
0,8

Parete 1-1, l=5,35
0,8
0,582

0,328
0,718
0,6
0,4
0,2
0,2
0
0
Efficacia

0,526
0,6
0,4
1,015
Parete 1-1, l=0,70
Cordolo
Cordolo +
piattabanda
Fascia rigida
Iniezioni
Intonaco
armato
0,328
0,526
0,582
0,749
1,052
Efficacia
0,024
0,031
0,042
Cordolo
Cordolo +
piattabanda
Fascia rigida
Iniezioni
Intonaco
armato
0,024
0,031
0,042
0,718
1,015
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.
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Retrofitting: Wall 4-4
1
1
0,8
Parete 4-4, l=0,70
Parete 4-4, l=5,35
0,742
0,8
0,6
0,6

0,430
0,421
0,4
0,771
0,502

0,414
0,4
0,286
0,140
0,153
Cordolo
Cordolo +
piattabanda
Fascia rigida
Iniezioni
(1° piano)
Intonaco armato
(1° piano)
0,056
0,140
0,153
0,430
0,421
0,2
0,2
0,056
0
Efficacia
0
Efficacia
Cordolo
Cordolo +
piattabanda
Fascia rigida
Iniezioni
(1° piano)
Intonaco
armato (1°
piano)
0,286
0,414
0,502
0,742
0,771
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Retrofitting
The expected improvement gets the same order of magnitude of data available in literature
[Modena et al.]
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Retrofitting: 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 iniezioni - Parete 4-4
Consolidamento con intonaco armato - Parete 4-4
4,00
1 piano
2 piani
3 piani
4 piani
4,00
2 piani
3 piani
4 piani
3,00
3,00

1 piano

2,00
1,00
2,00
1,00
0,00
0,00
0,0
0,5
1,0
1,5
2,0
2,5
3,0
l
3,5
4,0
4,5
5,0
5,5
6,0
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
4,5
5,0
l
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
5,5
6,0
PhD Dissertation Talk – Fisciano, 6th May 2011
Outline
 Chapter 1: Introduction
 Chapter 2: FEM modelling
 Chapter 3: Masonry Buildings Modelling Strategies
 Chapter 4: Mechanical Behaviour of masonry panels
 Chapter 5: Matrix Analysis of structures
 Chapter 6: The FREMA code
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Simplified Models
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Outline
 Chapter 1: Introduction
 Chapter 2: FEM modelling
 Chapter 3: Masonry Buildings Modelling Strategies
 Chapter 4: Mechanical Behaviour of masonry panels
 Chapter 5: Matrix Analysis of structures
 Chapter 6: The FREMA code
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Description of the model
Equivalent Frame Model
Spandrels
F2
Piers (Heff after Dolce, 1991)
Main features
F1
1. Displacement Control approach  NLP
2. Global and local equilibrium
3. Spread plasticity approach
Rigid Offsets
4. Quick Analysis and Easy Post-processing
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Piers - Constitutive Laws
Generalized Uniaxial Compressive Stress-Strain Relationship

 
 

 A   B  
u
 u 
 u 
d
C
A=2, B=-1, C=2 [Hendry, 1998]
A=6.4, B=-5.4, C=1.17 [Turnšek-Čačovič, 1980]
d
[After Tomaževič, 1999]
u

 Accurate Moment-Curvature
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Piers - Flexural Behaviour
Cross-section Equilibrium Equations
N
D
 
M
G
yc
yc


 

M
 normalised axial force
D
G
t
G
t
G
yc
D
D
x normalised neutral axis
N
M
M
t
M
t
N N




m normalised bending moment
yc

u
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

PhD Dissertation Talk – Fisciano, 6th May 2011
Moment-Curvature relationship workflow
D, t, , 
40
u
35
30
M [kNm]
25
20
15
10
5
D [mm]
t [mm]
N [kN]
500
250
200
A
B
C
u
2
-1
2
0,003
r
0,0045
u [MPa]
6,2
END
NO
 u
YES
cr
0
0,0
5,0
10,0
15,0
20,0
 [mm-1 x 106]
25,0
30,0
35,0
x
M
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Piers - Shear Behaviour
Model
Experimental Behaviour
V
Vu
u
[After Anthoine, Magenes, Magonette, 1994]

Ultimate drift u = 0.4% Heff
[Italian Building Code]
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Piers - Shear Behaviour
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Shear-strain relationship workflow
min Vu
V
gi=Vi/Ki
Vi
gel=Vu/Kel
Vu
YES
Ki+1=Kel
gi  gel
Ksec,i+1
NO
Ksec,i
gel
g
Ki+1=Ki *Vu/Vi
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Shear-strain relationship workflow
Collapse condition when the desired value of
drift (set by the user) is attained
(Italian Building Code suggets = 0.004 for
shear collapse)
V
Vu
u

R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Spandrels - Shear Behaviour
Model
Experimental Behaviour
V
Vu  ht  f vd 0
Vu
Vu
u

Residual Strength  = 0.25
[Magenes and Della Fontana, 1998]
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Spandrels - Flexural Behaviour
Model
Experimental Behaviour
M
Mu
u

[After Calderoni et al., 2008]
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Spandrels - Flexural Behaviour
Proposed formulations for Mu – [Italian Building Code, 2008]
1. Stress-block approach (same equation of piers)
2. If no tensile-resistant element is present  Mu=0
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Spandrels - Flexural Behaviour
Proposed formulations for Mu [Schubert & Weschke, 1986]
a)
b)

Take into account an “equivalent
strut” provided with a tensile
strength ftu

ftu is the minimum between two
collapse mechanisms:
a) bricks failure
ftu ,a  fbt
y
2   y  t joint 

fbt
2
b) bed joints failure
ftu ,b   c  m p 
x

 c  m p  x
2 y
2   y  t joint 
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Spandrels - Flexural Behaviour
Spandrels M-N Limit Domain [Cattari and Lagomarsino, 2008]
Constitutive Law
f wc
1
0.85

-
-

1
c
Improvement of rocking
resistance, also with low
(or zero) values of N.
/y
 = ratio between tensile strength ftu and compressive strength
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Outline
 Chapter 1: Introduction
 Chapter 2: FEM modelling
 Chapter 3: Masonry Buildings Modelling Strategies
 Chapter 4: Mechanical Behaviour of masonry panels
 Chapter 5: Matrix Analysis of structures
 Chapter 6: The FREMA code
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
Masonry Panels – Anthoine, Magonette and Magenes (1998)
Cross-Section: 100 x 25 cm2
Low panel high: 135 cm
High panel high: 200 cm
Normal Load: 150 kN
Low Panel
High Panel
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
Pavia Door Wall – Calvi and Magenes (1994)
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
Pavia Door Wall – Calvi and Magenes (1994)
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
Pavia Door Wall – Calvi and Magenes (1994)
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
Catania Project - Investigation on the seismic response of two masonry buildings (2000)
“Via Martoglio” 2D Wall
Equivalent Frame model: 128 elements, 81 nodes, 219 DOF
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
“Via Martoglio” 2D Wall
Model 1: Masonry, NO R.C. Ring Beams
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
“Via Martoglio” 2D Wall
Model 2: Masonry, Elastic R.C. Ring Beams (E=20,000 MPa)
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
“Via Martoglio” 2D Wall
Model 3: Masonry, Elastic R.C. Ring Beams (E=4,000 MPa)
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Preliminary validation of the model
Catania Project - Investigation on the seismic response of two masonry buildings (2000)
“Via Verdi” Building
Wall 1
Wall 2
Wall 3
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
“Via Verdi” – Wall 1
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
“Via Verdi” – Wall 2
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
“Via Verdi” – Wall 3
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
Mallardo et al. (2008) – Palazzo Renata di Francia
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
Mallardo et al. (2008)
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
Salonikios et al. (2003)

Two-storey, 7-bay masonry wall

Two lateral load distributions
considered:
1. Uniform (ACC)
F= {1.00; 0.59}
2. Inverse Triangular (LOAD)
F= {1.00; 1.19}
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
Salonikios et al. (2003) – 7B_Uniform
1000
Discrete FEM model
Proposed Model
800
Total Base Shear [kN]
SAP 2000
600
400
200
0
0
2
4
6
8
10
12
14
16
top displacement [mm]
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
The FREMA Code
Salonikios et al. (2003) – 7B_Inverse Triangular
1000
Discrete FEM model
Proposed Model
800
Total Base Shear [kN]
SAP 2000
600
400
200
0
0
2
4
6
8
10
12
14
16
top displacement [mm]
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Mesh Refinement
Salonikios et al. (2003)
b=Log(Nc/x)
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Mesh Refinement
Salonikios et al. (2003) – 7B_Inverse Triangular
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Mesh Refinement
Salonikios et al. (2003) – 7B_Uniform
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Time-cost Analysis
Salonikios et al. (2003)
b=Log(Nc/x)
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Time-cost Analysis
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Conclusions
 This dissertation deals with the seismic behaviour of masonry structures;
 The first part of the work is aimed at understanding the potentialities of
very accurate FEM model in predicting masonry panels seismic response; 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
of cracks path.
 A further application of simplified (homogeneous) FEM models has been
performed on masonry panels, aiming at evaluating the influence of
spandrels reinforcement on the overall resistance; in the same application
some reinforcement techniques have been applied considering the Italian
Building Code approach;
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Conclusions
 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
highlighting the main features of the proposed model (displacement control
approach, accurate moment-curvature for piers behaviour, spandrels
behaviour);
 A validation and application of the model has been carried out 
comparison with experimental tests and accurate numerical simulations
 The comparison showed a good agreement between the proposed model
and both experimental and numerical results, showing that FREMA code is a
reliable tool for performing the non-linear static analysis of masonry panels.
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
PhD Dissertation Talk – Fisciano, 6th May 2011
Thank you very much!
R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling
Dipartimento di Ingegneria Civile – Università degli Studi di Salerno
Dottorato di Ricerca in Ingegneria delle Strutture
e 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
Dottorando: Ing. Riccardo Sabatino
Tutor: Prof. Vincenzo Piluso
Co-Tutor: Prof. Gianvittorio Rizzano