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  • 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 Maratea, 26-27 Settembre 2013
  • 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 Maratea, 26-27 Settembre 2013
  • 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 PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE Maratea, 26-27 Settembre 2013
  • 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. PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE Maratea, 26-27 Settembre 2013
  • 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 PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE Maratea, 26-27 Settembre 2013
  • 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 PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE Maratea, 26-27 Settembre 2013
  • 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 Maratea, 26-27 Settembre 2013
  • 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 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 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
  • 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 PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE Maratea, 26-27 Settembre 2013
  • 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 PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE Maratea, 26-27 Settembre 2013
  • 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 PROBLEMI ATTUALI E PROSPETTIVE NELL’INGEGNERIA DELLE STRUTTURE Maratea, 26-27 Settembre 2013
  • 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 Maratea, 26-27 Settembre 2013
  • 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 Maratea, 26-27 Settembre 2013
  • 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 Maratea, 26-27 Settembre 2013
  • 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