The NOSA-ITACA code is a finite element software for nonlinear analysis of masonry structures. It was developed through the NOSA-ITACA project to model masonry as a nonlinear elastic material with limited tensile and compressive strength. The code has been used to analyze several historic masonry structures in Italy, including the Church of San Francesco in Lucca to evaluate seismic vulnerability and reinforcement needs. Modal, stress, and displacement results are presented from the analysis of the church with and without reinforcement.

1. The NOSA-ITACA code for modelling and assessing
the structural behaviour of ancient constructions
Maria Girardi
Cristina Padovani
Giuseppe Pasquinelli
Laboratory of Mechanics
of Materials and Structures
ISTI-CNR
Pisa
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
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2. funded by the Region of Tuscany (PAR-FAS 2007-2013)
The NOSA-ITACA project
2011-2013
Case study
ISTI-CNR
Pisa
DICEA
Firenze
NOSA -ITACABasic Research
CODE
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
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3. 3
The NOSA-ITACA project
NOSA-ITACA code
Case study: “Voltone”, Livorno
Municipalities
Monuments and Fine Arts Offices
Professional offices
NOSA CODE: f.e.m. nonlinear solver
SALOME: pre-post processor
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4. The NOSA-ITACA version will be freely downloadable by
http://www.nosaitaca.it/it/software/
•The NOSA-ITACA code is a finite element software for nonlinear analyses.
•Masonry is modelled by a nonlinear isotropic elastic material with zero
tensile strength and limited compressive strength (masonry-like or
no-tension material). [G. Del Piero, Meccanica 1989; S. Di Pasquale, Meccanica 1992; M.
Lucchesi, C. Padovani et al., Masonry Constructions and Numerical Applications, Springer 2008].
• Static analyses
• Dynamic analyses
• Thermo-mechanical analyses
• Modal analyses
• Stress fields
• Collapse loads
• Elastic, fracture and crushing strain fields
• Displacement fields
• Time- histories
• Eigenvalues and eigenvectors
• NOSA-ITACA library: beam, truss, shell, 2D, 3D elements (35 elements)
A previous version of the code (COMES-NOSA) is already downloadable.
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5. 55
the infinitesimal strain tensor,
the Cauchy stress tensor,
the elastic part of the strain,
the fracture strain,
the crushing strain,
the modulus of elasticity and the Poisson’s ratio,
the masonry maximum compressive stress.
T
c
E
E
f
E
e
E
E,
e
s0
s
0 0 
DE
ˆ ˆT = T(E), T(E)
Given E, find Ef, Ec, T such that

e f c
f c
E = E + E + E ,
E E = 0,
E
1+ 1-2
e e
T E tr( E )I ,

 
 
   
 f c
0T E T I E 0,    
0-T I 0, , c
T E 0,
f
E 0
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
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6. • 1995 Battistero del Duomo, Volterra
• 1996 Arsenale Mediceo, Pisa
• 1998 Teatro Goldoni, Livorno
• 1998 Chiesa Madre di S. Nicolò, Noto
• 2004 Chiesa di Santa Maria Maddalena, Morano Calabro
• 2005 Chiesa di San Ponziano, Lucca
• 2008 Chiesa Abbaziale di Santa Maria della Roccella, Roccella Ionica
• 2008 Torre “Rognosa” , San Gimignano
• 2010 Torre “delle Ore”, Lucca
• 2013 “Voltone” di Piazza della Repubblica, Livorno
• 2013 Chiesa Di San Francesco, Lucca
Some example applications
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7. The Church of San Francesco
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
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8. The Church of San Francesco: reinforcement operations
On masonry
On the roof
NPL 150X18 NPL 150X18
NPL 150X18 NPL 150X18 NPL 150X18
diagonali 20 diagonali 20
NPL 150X18 NPL 150X18
NPL 150X18 NPL 150X18
diagonali 20 diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20
NPL 150X18
diagonali 20diagonali 20
150X150x8
150X150x8
150X150x8
150X150x8
150X150x8
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150X150x8
On the cloister
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
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9. g1
g2
The Church of San Francesco: The finite element mesh
/2
11 11
/2
d ,
h
h
N T 

 
/2
22 22
/2
d
h
h
N T 

 
/2
11 11
/2
d ,
h
h
M T  

 
/2
22 22
/2
d .
h
h
M T  

 
11 1 1,T  g Tg 22 2 2 ,T  g Tg
{ ' | , , ( )},' ζ     p p p n p n n p
[ / 2, / 2].h h  
Stresses
Normal forces
Bending moments
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10. 0.5 1 1.5 2 2.5 3
T sec
1
2
3
4
a m sec 2
T1r=1,04 sT1=1,26 s
Without reinforcing With reinforcing
The Church of San Francesco: modal analyses
Elastic Response Spectrum
for the Lucca site
z
x
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11. Without reinforcing
With reinforcing
Stresses T22
SLV
The Church of San Francesco: evaluation of the seismic vulnerability
HU=6,5% Weigth
HU=4,1% Weigth
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
Maratea, 26-27 Settembre 2013

12. The Church of San Francesco: evolution of the maximum values of normal stresses
-2,5
-2
-1,5
-1
-0,5
0
-6,E+06 -5,E+06 -4,E+06 -3,E+06 -2,E+06 -1,E+06 0,E+00
T22[Mpa]
Total horizontal force H [N]
without reinforcement with reinforcement
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
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13. Eccentricities e22
SLV
Without reinforcing
With reinforcing
e22 = M22/N22
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
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14. Stresses T11
SLV
Without reinforcing
With reinforcing
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
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15. Displacements ux
SLV
Without reinforcing
With reinforcing
The Church of San Francesco: evaluation of the seismic vulnerability
HU=6,5% Weigth
Uxmax /h= 0,0078
Uxmax /h= 0,005
HU=4,1% Weigth
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
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16. Without reinforcing
Principal stresses
With reinforcing

17. 50
0.1
475
SI  
475
0.75
0.4
1.86
SLU
a
a
f
a
  
140
0.3
475
SI  
475
1.16
0.6
1.86
SLU
a
a
f
a
  
0.041SLUH
W
 0.065SLUH
W

Without reinforcing With reinforcing
Safety Indexes
(Direttiva 9 Febbraio 2011, “Valutazione e riduzione del rischio sismico del patrimonio
culturale”)
PGA
Reference periods
Maximum shear
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
Maratea, 26-27 Settembre 2013

18. The “Rognosa” tower in San Gimignano
x
z
SEZ. A-A
x
y
A
Side overlooking
the Cathedral Square
t
t
+0,00 (Square level)
+8,60 (Masonry vaults level)
+19,04 (Surrounding roofs level)
+43,34 (Top)
A A
x
z
SEZ. A-A
x
y
A
Side overlooking
the Cathedral Square
t
t
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
Maratea, 26-27 Settembre 2013

19. The “Rognosa” tower in San Gimignano:
- Static analysis The Tower is subjected to its own weight and to the
weight of the surrounding buildings
- Dynamic analysis The Tower subjected to the Nocera Umbra
earthquake in x - direction
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
Maratea, 26-27 Settembre 2013

20. The “Rognosa” tower in San Gimignano: dynamic analysis
+0,00 (Square level)
+8,60 (Masonry vaults level)
+19,04 (Surrounding roofs level)
+43,34 (Top)
A A
x
z
WONDERmasonry 2011, Facoltà di Ingegneria, Firenze
Numerical modelling of the dynamic behaviour of masonry constructions
+45,34

21. +0,00 (Square level)
+8,60 (Masonry vaults level)
+19,04 (Surrounding roofs level)
+43,34 (Top)
A A
x
z
The “Rognosa” Tower in San Gimignano: digital acquisition and structural analysis
CST 2010, The Tenth International Conference on Computational Structures Technology
14-17 September 2010, Valentia
Tower vertical section The bell chamber
+45,34

22. The “Rognosa” tower in San Gimignano: dynamic analysis
At time t=3,41 s: Minimum values reached
during the analysis :
Compressive stress Tzz
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
Maratea, 26-27 Settembre 2013

23. The “Rognosa” tower in San Gimignano: dynamic analysis
At time t=3,41 s: Maximum values reached
during the analysis :
Tangential fracture strain Ef
tt
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
Maratea, 26-27 Settembre 2013

24. The “Rognosa” tower in San Gimignano: dynamic analysis
At time t=3,41 s: Maximum values reached
during the analysis :
Fracture strain Ef
zz
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
Maratea, 26-27 Settembre 2013

25. Maximum values reached during the analysis:
Displacements ux
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
Maratea, 26-27 Settembre 2013

26. Conclusions
• The NOSA-ITACA project aimed to upgrade the NOSA code and
disseminate the use of numerical tools in the field of maintenance and
restoration of the architectural heritage.
• The NOSA - ITACA code is a finite element code for static and dynamic
nonlinear analyses of masonry structures. It will be freely downloadable by
the end of the year.
•Masonry is modelled by means of a masonry-like constitutive equation with
zero tensile strength and finite or infinite compressive strength.
•Some cases have been presented in which the seismic vulnerability of the
church of San Francesco in Lucca and of the “Rognosa” tower in San
Gimignano are assessed by means of a nonlinear static and dynamic
analyses conducted via the NOSA–ITACA code.
The financial support of the Region of Tuscany (project “Tools for modelling and assessing the
structural behaviour of ancient constructions: the NOSA-ITACA code”, PAR FAS 2007-2013) is
gratefully acknowledged.
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
Maratea, 26-27 Settembre 2013

27. The Church of San Francesco: evaluation of the seismic vulnerability
0
2
4
6
8
10
12
14
16
18
20
-0,50 -0,40 -0,30 -0,20 -0,10 0,00
load
increments
horizontal displacements [m]
without reinforcing
with reinforcing
The NOSA-ITACA code for modelling and assessing the structural behaviour of ancient constructions
PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE
Maratea, 26-27 Settembre 2013