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

150X150x8

150X150x8

150X150x8

150X150x8

150X150x8

150X150x8

150X150x8

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150X150x8

150X150x8

150X150x8

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150X150x8

150X150x8

150X150x8

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On the cloister

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

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

-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

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

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.