girardi maratea

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 Maratea, 26-27 Settembre 2013

funded by the Region of Tuscany (PAR-FAS 2007-2013)

The NOSA-ITACA project 2011-2013

Case study

ISTI - CNR Pisa

DICEA

Firenze

NOSA - ITACA Basic Research

CODE



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


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.


5 5

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

cE

E

fE

eE

E,

e

s0

s

00

DE

ˆ ˆ T = 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 eT E tr( E )I ,

f c

0T E T I E 0,

0 -T I 0, ,

cT E 0,

fE 0



• 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


The Church of San Francesco



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

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NPL 150X18

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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

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On the cloister



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


0.5 1 1.5 2 2.5 3T sec

1

2

3

4

a m sec2

T1r=1,04 s T1=1,26 s

Without reinforcing With reinforcing

The Church of San Francesco: modal analyses

Elastic Response Spectrum for the Lucca site

z

x


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 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

T2

2 [

Mp

a]

Total horizontal force H [N]

without reinforcement with reinforcement



Eccentricities e22

SLV

Without reinforcing

With reinforcing

e22 = M22/N22



Stresses T11

SLV

Without reinforcing

With reinforcing



Displacements ux

SLV

Without reinforcing

With reinforcing


HU=6,5% Weigth

Uxmax /h= 0,0078

Uxmax /h= 0,005

HU=4,1% Weigth



Without reinforcing

Principal stresses

With reinforcing

500.1

475SI

475

0.750.4

1.86

SLUa

af

a

1400.3

475SI

475

1.160.6

1.86

SLUa

af

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 “Rognosa” tower in San Gimignano

+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




+43,34 (Top)

A A

x

z

SEZ. A-A

x

y

A

Side overlooking


t

t



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 “Rognosa” tower in San Gimignano: dynamic analysis




+43,34 (Top)

A A

x

z

SEZ. A-A

x

y

A

Side overlooking


t

t

WONDERmasonry 2011, Facoltà di Ingegneria, Firenze

Numerical modelling of the dynamic behaviour of masonry constructions

+45,34




+43,34 (Top)

A A

x

z

SEZ. A-A

x

y

A

Side overlooking


t

t

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


At time t=3,41 s: Minimum values reached during the analysis :

Compressive stress Tzz




At time t=3,41 s: Maximum values reached during the analysis :

Tangential fracture strain Eftt




At time t=3,41 s: Maximum values reached during the analysis :

Fracture strain Efzz



Maximum values reached during the analysis:

Displacements ux



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.




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



girardi maratea

Technology

e e e

e et e tr e i

tegiven e

f c0t e t i e

nosaitaca version

e s0 s

e f cf ce

masonry constructions