Numerical modelling of the static and seismic behaviour of historical buildings: the church of San Francesco in Lucca 1 The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013 Maria Girardi Cristina Padovani Giuseppe Pasquinelli Laboratory of Mechanics of Materials and Structures ISTI-CNR Pisa
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Numerical modelling of the static and seismic behaviour of historical buildings: the church of San Francesco in Lucca
1
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
Maria Girardi
Cristina Padovani
Giuseppe Pasquinelli
Laboratory of Mechanics of Materials and Structures
ISTI-CNR Pisa
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
The NOSA-ITACA version for static analyses will be freely downloadable by http://www.nosaitaca.it/it/software/
•The NOSA-ITACA code is a finite element solver 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)
3 3
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
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
The Church of San Francesco
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
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
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On the cloister
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
•Laboratory tests: mechanical characterization of materials and soil
Step 2
Numerical model of the existing structure: modal analyses, definition of the horizontal loads, static nonlinear analyses, definition of the collapse loads
Step 3
Numerical model of the reinforced structure: modal analyses, definition of the horizontal loads, static nonlinear analyses, definition of the collapse loads
Step 4
Existing and reinforced structure: comparison of numerical results
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
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 Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
The Church of San Francesco: modal analyses
Elastic Response Spectrum for the Lucca site
z
x
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
The Church of San Francesco: permanent loads
Stresses T22 Displacements ux
Without reinforcing
With reinforcing
Stresses T22
SLU
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
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
Eccentricities e22
SLU
Without reinforcing
With reinforcing
The Church of San Francesco: evaluation of the seismic vulnerability
e22 = M22/N22
Stresses T11
SLU
Without reinforcing
With reinforcing
Fracture strains
Without reinforcing
With reinforcing 11
fE
Without reinforcing
Stresses T22 With reinforcing
Normal force in the windbracing at the ultimate limit state
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
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
0.5 1 1.5 2 2.5 3T s
0.5
1
1.5
2
Sdm
s2
TR = 475 (reference)
TR = 140 (reinforced)
TR = 50 (not reinforced)
500.1
475SI
475
0.750.4
1.86SLU
a
af
a
1400.3
475SI
475
1.160.6
1.86
SLUa
af
a
0.041SLUH
W
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
0.065SLUH
W
Without reinforcing With reinforcing
20
The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
Conclusions •The NOSA - ITACA code is a finite element code for static and dynamic nonlinear analyses of masonry structures. The version for static analyses 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.
•A case study has been presented in which the seismic vulnerability of the church of San Francesco in Lucca is assessed by means of a nonlinear static analysis 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.