Numerical modelling of the static and seismic behaviour of
historical buildings: the church of San Francesco in Lucca
1
Th...
The Fourteenth International Conference on Civil, Structural and Environmental
Engineering Computing, Cagliari 3-6 Septemb...
33
the infinitesimal strain tensor,
the Cauchy stress tensor,
the elastic part of the strain,
the fracture strain,
the cru...
The Fourteenth International Conference on Civil, Structural and Environmental
Engineering Computing, Cagliari 3-6 Septemb...
The Fourteenth International Conference on Civil, Structural and Environmental
Engineering Computing, Cagliari 3-6 Septemb...
The Fourteenth International Conference on Civil, Structural and Environmental
Engineering Computing, Cagliari 3-6 Septemb...
The Fourteenth International Conference on Civil, Structural and Environmental
Engineering Computing, Cagliari 3-6 Septemb...
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 Fourteenth Internat...
The Fourteenth International Conference on Civil, Structural and Environmental
Engineering Computing, Cagliari 3-6 Septemb...
Without reinforcing
With reinforcing
Stresses T22
SLU
The Church of San Francesco: evaluation of the seismic vulnerability...
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,...
Displacements ux
SLU
Without reinforcing
With reinforcing
The Church of San Francesco: evaluation of the seismic vulnerabi...
Eccentricities e22
SLU
Without reinforcing
With reinforcing
The Church of San Francesco: evaluation of the seismic vulnera...
Stresses T11
SLU
Without reinforcing
With reinforcing
Fracture strains
Without reinforcing
With reinforcing
11
f
E
Without reinforcing
Stresses T22
With reinforcing
Normal force in the windbracing at the ultimate limit state
The Fourteenth International Conference on Civil, Structural a...
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 -...
0.5 1 1.5 2 2.5 3
T s
0.5
1
1.5
2
Sd
m
s2
TR = 475 (reference)
TR = 140 (reinforced)
TR = 50 (not reinforced)
50
0.1
475
S...
20
The Fourteenth International Conference on Civil, Structural and Environmental
Engineering Computing, Cagliari 3-6 Sept...
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Girardi presentation

  1. 1. 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
  2. 2. 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. 33 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 Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013
  4. 4. The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013 The Church of San Francesco
  5. 5. 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 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 150X150x8 On the cloister
  6. 6. The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013 Evaluation of the seismic vulnerability and the effectiveness of the reinforcement operations Step 1 •In situ tests: geometric survey, flat jacks tests, georadar scans •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
  7. 7. 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
  8. 8. 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 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
  9. 9. The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013 The Church of San Francesco: permanent loads Stresses T22Displacements ux
  10. 10. 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
  11. 11. 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
  12. 12. Displacements ux SLU 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
  13. 13. Eccentricities e22 SLU Without reinforcing With reinforcing The Church of San Francesco: evaluation of the seismic vulnerability e22 = M22/N22
  14. 14. Stresses T11 SLU Without reinforcing With reinforcing
  15. 15. Fracture strains Without reinforcing With reinforcing 11 f E
  16. 16. Without reinforcing Stresses T22 With reinforcing
  17. 17. 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
  18. 18. 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
  19. 19. 0.5 1 1.5 2 2.5 3 T s 0.5 1 1.5 2 Sd m s2 TR = 475 (reference) TR = 140 (reinforced) TR = 50 (not reinforced) 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  The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Cagliari 3-6 September 2013 0.065SLUH W  Without reinforcing With reinforcing
  20. 20. 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.

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