Wondermasonry 2011 1

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Wondermasonry 2011 1

  1. 1. WONDERmasonry 2011, Facoltà di Ingegneria, FirenzeNumerical modelling of the dynamic behaviour of masonry constructions Laboratorio di Meccanica dei Materiali e delle Strutture Cristina Padovani Giuseppe Pasquinelli Maria Girardi Istituto di Scienza e Tecnologie dell’Informazione “A. Faedo” ISTI-CNR Pisa 1
  2. 2. WONDERmasonry 2011, Facoltà di Ingegneria, Firenze•The NOSA code is a finite element solver for nonlinear analyses.•Masonry is modelled by a nonlinear isotropic elastic material with zerotensile 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 • Stress fields • Collapse loads• Dynamic analyses • Elastic, fracture and crushing strain fields• Thermo-mechanical analyses • Displacement fields • Temperature fields • Time- histories• NOSA library: beam, shell, 2D, 3D elements (17 elements) The NOSA version for static analyses is freely downloadable by www.isti.cnr.it/research/unit.php?unit=MMS&section=software 22 Numerical modelling of the dynamic behaviour of masonry constructions
  3. 3. WONDERmasonry 2011, Facoltà di Ingegneria, Firenze The masonry-like constitutive equationE the infinitesimal strain tensor, sT the Cauchy stress tensor,Ee the elastic part of the strain,Ef the fracture strain, eEc the crushing strain,E,  the modulus of elasticity and the Poisson’s ratio, 0  0 the masonry maximum compressive stress. s0Given E, find Ef, Ec, T such thatE = Ee+ E f + Ec ,E f  E c = 0, E  e  T   E  tr( E e )I  , ˆ ˆ T  T(E), DET(E) 1+  1-2 T  E f  T   0 I   E c  0,T, E c  0, T- 0 I  0, E  0 f 33 Numerical modelling of the dynamic behaviour of masonry constructions
  4. 4. WONDERmasonry 2011, Facoltà di Ingegneria, Firenze Some example applications • 1995 Battistero del Duomo, Volterra • 1996 Arsenale Mediceo, PisaStatic Analyses • 1998 Teatro Goldoni, Livorno • 1998 Chiesa Madre di S. Nicolò, Noto • 2004 Chiesa di Santa Maria Maddalena, Morano Calabro • 2005 Chiesa di San Ponziano, LuccaDynamic Analyses • 2008 Chiesa Abbaziale di Santa Maria della Roccella, Roccella Ionica • 2008 Torre “Rognosa” , San Gimignano • 2010 Torre “delle Ore”, Lucca Numerical modelling of the dynamic behaviour of masonry constructions
  5. 5. WONDERmasonry 2011, Facoltà di Ingegneria, FirenzeThe “Rognosa” tower in San Gimignano (St@rt project) SEZ. A-A +45,34 (Top) +43,34 t SEZ. A-A y t A x t Side overlooking the Cathedral Square z +19,04 (Surrounding roofs level) y t A x Side overlooking +8,60 (Masonry vaults level) the Cathedral Square z A A +0,00 (Square level) x Numerical modelling of the dynamic behaviour of masonry constructions
  6. 6. WONDERmasonry 2011, Facoltà di Ingegneria, FirenzeThe “Rognosa” tower in San Gimignano: digital acquisition of the geometry (VC Lab – ISTI CNR) Merging resolution=1 cm
  7. 7. WONDERmasonry 2011, Facoltà di Ingegneria, FirenzeThe “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 Numerical modelling of the dynamic behaviour of masonry constructions
  8. 8. WONDERmasonry 2011, Facoltà di Ingegneria, Firenze +43,34 (Top)The “Rognosa” tower in San Gimignano: dynamic analysis Tower SEZ. A-A base section t +19,04 (Surrounding roofs level) y t A x Side overlooking +8,60 (Masonry vaults level) the Cathedral Square z A A +0,00 (Square level) x Numerical modelling of the dynamic behaviour of masonry constructions
  9. 9. WONDERmasonry 2011, Facoltà di Ingegneria, Firenze The “Rognosa” tower in San Gimignano: dynamic analysis +45,34 (Top) +43,34 +19,04 (Surrounding roofs level) +8,60 (Masonry vaults level)z A A +0,00 (Square level) x Numerical modelling of the dynamic behaviour of masonry constructions
  10. 10. CST 2010, The Tenth International Conference on Computational Structures Technology 14-17 September 2010, Valentia Tower vertical section The bell chamber +45,34 (Top) +43,34 +19,04 (Surrounding roofs level) +8,60 (Masonry vaults level)z A A +0,00 (Square level) xThe “Rognosa” Tower in San Gimignano: digital acquisition and structural analysis
  11. 11. WONDERmasonry 2011, Facoltà di Ingegneria, FirenzeThe “Rognosa” tower in San Gimignano: dynamic analysis Compressive stresses TzzAt time t=3,41 s: Minimum values reached during the analysis : Numerical modelling of the dynamic behaviour of masonry constructions
  12. 12. WONDERmasonry 2011, Facoltà di Ingegneria, FirenzeThe “Rognosa” tower in San Gimignano: dynamic analysis Crushing strain EczzAt time t=3,41 s: Minimum values reached during the analysis : Numerical modelling of the dynamic behaviour of masonry constructions
  13. 13. WONDERmasonry 2011, Facoltà di Ingegneria, FirenzeThe “Rognosa” tower in San Gimignano: dynamic analysis Tangential fracture strain EfttAt time t=3,41 s: Maximum values reached during the analysis : Numerical modelling of the dynamic behaviour of masonry constructions
  14. 14. WONDERmasonry 2011, Facoltà di Ingegneria, Firenze The “Rognosa” tower in San Gimignano: dynamic analysis Fracture strain EfzzAt time t=3,41 s: Maximum values reached during the analysis : Numerical modelling of the dynamic behaviour of masonry constructions
  15. 15. WONDERmasonry 2011, Facoltà di Ingegneria, FirenzeThe “Rognosa” tower in San Gimignano: dynamic analysis Displacements ux Maximum values reached during the analysis: Numerical modelling of the dynamic behaviour of masonry constructions
  16. 16. WONDERmasonry 2011, Facoltà di Ingegneria, Firenze The NOSA-ITACA project 2011-2013 funded by the Region of Tuscany (PAR-FAS 2007-2013) ISTI-CNR DCR Pisa Firenze ConsultingBasic Research NOSA -ITACA Case study Service CODE Numerical modelling of the dynamic behaviour of masonry constructions
  17. 17. WONDERmasonry 2011, Facoltà di Ingegneria, Firenze The NOSA-ITACA projectNOSA CODE: f.e.m. nonlinear solver SALOME: pre-post processor Case study: “Voltone”, Livorno NOSA-ITACA code CONSULTING SERVICE Municipalities Monuments and Fine Arts Offices 17 Professional offices
  18. 18. WONDERmasonry 2011, Facoltà di Ingegneria, FirenzeConclusions•The NOSA code is a finite element code for static and dynamic nonlinearanalyses of masonry structures. The version for static analyses is freelydownloadable.•Masonry is modelled by means of a masonry-like constitutive equation withzero tensile strength and finite or infinite compressive strength.•A case study has been presented in which the seismic vulnerability of theRognosa Tower in San Gimignano is assessed by means of a dynamicnumerical analysis conducted via NOSA code.• The NOSA-ITACA project aims to upgrade the NOSA code and disseminatethe use of numerical tools in the field of maintenance and restoration of thearchitectural heritage. Numerical modelling of the dynamic behaviour of masonry constructions

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