Skip to main content

Advertisement

SpringerLink
Log in

A fast and general upper-bound limit analysis approach for out-of-plane loaded masonry walls

  • New Trends in Mechanics of Masonry
  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

A new general approach for the limit analysis of out-of-plane loaded masonry walls based on an upper bound formulation is presented. A given masonry wall of generic form presenting openings of arbitrary shape is described through its Non-Uniform Rational B-Spline (NURBS) representation in the three-dimensional Euclidean space. A lattice of nodes is defined in the parameters space together with possible fracture lines. An initial set of rigid elements initially subdividing the original wall geometry is identified accordingly. A homogenized upper bound limit analysis formulation, which takes into account the main characteristics of masonry material such as very low resistance in traction and anisotropic behavior is deduced. Moreover the effect of vertical loads and membrane stresses is considered, assuming internal dissipation allowed exclusively along element edges. A number of technically meaningful examples prove that a good estimate of the collapse load multiplier is obtained, provided that the initial net of yield lines is suitably adjusted by means of a meta-heuristic approach (i.e. a Genetic Algorithm, GA) in order to enforce that element edges accurately represent the actual failure mechanism.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Giuffrè A (1993) Sicurezza e conservazione dei centri storici: il caso di Ortigia. Laterza, Bari

    Google Scholar 

  2. Spence R, Coburn A (1992) Strengthening buildings of stone masonry to resist earthquakes. Meccanica 27:213–221. doi:10.1007/BF00430046

  3. Chiozzi A, Simoni M, Tralli A (2016) Base isolation of heavy non-structural monolithic objects at the top of a masonry monumental construction. Mater Struct Constr. doi:10.1617/s11527-015-0637-z

    Google Scholar 

  4. De Felice G, Giannini R (2001) Out-of-plane seismic resistance of masonry walls. J Earthq Eng 5:253–271

    Google Scholar 

  5. Gazzola EA, Drysdale RG, Essawy AS (1985) Bending of concrete masonry walls at different angles to the bed joints. Proc Third North Am Mason Conf. doi:10.1520/STP34544S

    Google Scholar 

  6. Sinha BP (1978) A simplified ultimate load analysis of laterally loaded model orthotropic brickwork panels of low tensile strength. Struct Eng 56B:81–84

    Google Scholar 

  7. Losberg A, Johansson S (1969) Sideways pressure on masonry walls of brickwork. CIB Symp Bear, Walls

    Google Scholar 

  8. Haseltine BA, West HWH (1977) Design of walls to resist lateral loads. Struct Eng 55:422–430

    Google Scholar 

  9. Ministero delle infrastrutture—NTC2008 - Norme tecniche per le costruzioni—D.M. 14 Gennaio 2008 (D.M. 4/2/08)

  10. Circolare del Ministero dei Lavori Pubblici n. 617 del 2/2/2009 (2009) Istruzioni per l’applicazione delle “Nuove norme tecniche per le costruzioni” di cui al DM 14 gennaio 2008

  11. Heyman J (1966) The stone skeleton. Int J Solids Struct 2:249–279. doi:10.1016/0020-7683(66)90018-7

    Article  Google Scholar 

  12. Di Pasquale S (1984) Statica dei solidi murari: teoria ed esperienze. University of Firenze, Firenze

    Google Scholar 

  13. Angelillo M (1993) Constitutive relations for no-tension materials. Meccanica 28:195–202. doi:10.1007/BF00989121

    Article  MATH  Google Scholar 

  14. Del Piero G (1998) Limit analysis and no-tension materials. Int J Plast 14:259–271. doi:10.1016/S0749-6419(97)00055-7

    Article  MATH  Google Scholar 

  15. Como M (2013) Statics of historic masonry construction. Springer, Berlin Heidelberg

    Book  Google Scholar 

  16. Dhanasekar M, Page AW, Kleeman PW (1985) The failure of brick masonry under biaxial stresses. Proc Inst Civ Eng 79:295–313. doi:10.1680/iicep.1985.992

    Google Scholar 

  17. Heyman J (1995) The stone skeleton: structural engineering of masonry architecture. Cambridge University Press, Cambridge

    Book  Google Scholar 

  18. Vasconcelos G, Lourenço PB (2006) Assessment of the In-plane shear strength of stone masonry walls by simplified models. In: Proceedings of 5th international conference of structural analysis of historical constructions

  19. Radenkovic D (1961) Théorèmes limites pour un materiau de Coulomb a dilatation non standardise. C R Acad Sci Paris 252:4103–4104

    MathSciNet  MATH  Google Scholar 

  20. Salençon J (1977) Application of the theory of plasticity in soil mechanics. Wiley, New York

    Google Scholar 

  21. Orduña A, Lourenço PB (2005) Three-dimensional limit analysis of rigid blocks assemblages. Part I: torsion failure on frictional interfaces and limit analysis formulation. Int J Solids Struct 42:5140–5160. doi:10.1016/j.ijsolstr.2005.02.010

    Article  MATH  Google Scholar 

  22. Milani G, Zuccarello FA, Olivito RS, Tralli A (2007) Heterogeneous upper-bound finite element limit analysis of masonry walls out-of-plane loaded. Comput Mech 40:911–931. doi:10.1007/s00466-006-0151-9

    Article  MATH  Google Scholar 

  23. Milani G (2011) Simple lower bound limit analysis homogenization model for in- and out-of-plane loaded masonry walls. Constr Build Mater 25:4426–4443. doi:10.1016/j.conbuildmat.2011.01.012

    Article  Google Scholar 

  24. Casolo S (2000) Modelling the out-of-plane seismic behaviour of masonry walls by rigid elements. Earthq Eng Struct Dyn 29:1797–1813. doi:10.1002/1096-9845(200012)29:12<1797:AID-EQE987>3.0.CO;2-D

    Article  Google Scholar 

  25. Peña F, Lourenço PB, Lemos J V. (2006) Modeling the dynamic behavior of masonry walls as rigid blocks. In: III European conference on computational mechanics. Springer Netherlands, Dordrecht, pp 282–282

  26. Portioli F, Cascini L, Casapulla C, D’Aniello M (2013) Limit analysis of masonry walls by rigid block modelling with cracking units and cohesive joints using linear programming. Eng Struct 57:232–247. doi:10.1016/j.engstruct.2013.09.029

    Article  MATH  Google Scholar 

  27. Lemos JV (2007) Discrete element modeling of masonry structures. Int J Archit Herit 1:190–213. doi:10.1080/15583050601176868

    Article  Google Scholar 

  28. Sarhosis V, Bagi K, Lemos J V., Milani G (2016) Computational modeling of masonry structures using the discrete element method. doi: 10.4018/978-1-5225-0231-9

  29. Chetouane B, Dubois F, Vinches M, Bohatier C (2005) NSCD discrete element method for modelling masonry structures. Int J Numer Methods Eng 64:65–94. doi:10.1002/nme.1358

    Article  MathSciNet  MATH  Google Scholar 

  30. Lancioni G, Lenci S, Piattoni Q, Quagliarini E (2013) Dynamics and failure mechanisms of ancient masonry churches subjected to seismic actions by using the NSCD method: the case of the medieval church of S Maria in Portuno. Eng Struct 56:1527–1546. doi:10.1016/j.engstruct.2013.07.027

    Article  Google Scholar 

  31. Reccia E, Cazzani A, Cecchi A (2012) FEM-DEM modeling for out-of-plane loaded masonry panels: a limit analysis approach. Open Civ Eng J 6:231–238

    Article  Google Scholar 

  32. Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, New York

    Book  MATH  Google Scholar 

  33. Chiozzi A, Malagù M, Tralli A, Cazzani A (2016) ArchNURBS: NURBS-based tool for the structural safety assessment of masonry arches in MATLAB. J Comput Civ Eng. doi:10.1061/(ASCE)CP.1943-5487.0000481

    Google Scholar 

  34. Chiozzi A, Milani G, Tralli A (2016) Fast kinematic limit analysis of FRP masonry vaults through a new genetic algorithm NURBS-based approach. In Proceedings of 7th European congress on computational methods in applied sciences and engineering (ECCOMAS)

  35. Chiozzi A, Milani G, Tralli A (2017) A genetic algorithm NURBS-based new approach for fast kinematic limit analysis of masonry vaults. Comput Struct 182:187–204. doi:10.1016/j.compstruc.2016.11.003

    Article  Google Scholar 

  36. Chiozzi A, Milani G, Grillanda N, Tralli A (2016) An adaptive procedure for the limit analysis of FRP reinforced masonry vaults and applications. Am J Eng Appl Sci 9:735–745. doi:10.3844/ajeassp.2016.735.745

    Article  Google Scholar 

  37. Chiozzi A, Milani G, Tralli A (2017) Fast kinematic limit analysis of FRP-reinforced masonry vaults. I: a general genetic algorithm NURBS-based formulation. J Eng Mech ASCE. doi:10.1061/(ASCE)EM.1943-7889.0001267

  38. Chiozzi A, Milani G, Tralli A (2017) Fast kinematic limit analysis of FRP-reinforced masonry vaults. II: numerical simulations. J Eng Mech ASCE. doi:10.1061/(ASCE)EM.1943-7889.0001268

  39. Milani G (2015) Upper bound sequential linear programming mesh adaptation scheme for collapse analysis of masonry vaults. Adv Eng Softw 79:91–110. doi:10.1016/j.advengsoft.2014.09.004

    Article  Google Scholar 

  40. Milani G, Milani F (2008) Genetic algorithm for the optimization of rubber insulated high voltage power cables production lines. Comput Chem Eng 32:3198–3212. doi:10.1016/j.compchemeng.2008.05.010

    Article  Google Scholar 

  41. Mc4 Software (2011) Mc4Loc - L’analisi dei meccanismi locali

  42. McNeel R (2008) Rhinoceros: Nurbs modeling for windows. Robert McNeel & Associates, Seattle

    Google Scholar 

  43. USPRO (1996) Initial graphics exchange specification, IGES 5.3. US Product Data Association, Fairfax

    Google Scholar 

  44. Aboudi J (2013) Mechanics of composite materials: a unified micromechanical approach. Elsevier, Amsterdam

    MATH  Google Scholar 

  45. Taliercio A (2014) Closed-form expressions for the macroscopic in-plane elastic and creep coefficients of brick masonry. Int J Solids Struct 51:2949–2963. doi:10.1016/j.ijsolstr.2014.04.019

    Article  Google Scholar 

  46. Haupt RL, Haupt SE (2004) Practical genetic algorithms. Wiley, New York

    MATH  Google Scholar 

  47. Chong VL (1993) The behavior of laterally loaded masonry panels with openings. University of Plymouth, Plymouth

    Google Scholar 

  48. Milani G, Lourenço P, Tralli A (2006) Homogenization approach for the limit analysis of out-of-plane loaded masonry walls. J Struct Eng 132:1650–1663. doi:10.1061/(ASCE)0733-9445(2006)132:10(1650)

    Article  Google Scholar 

  49. Milani G (2009) Homogenized limit analysis of FRP-reinforced masonry walls out-of-plane loaded. Comput Mech 43:617–639. doi:10.1007/s00466-008-0334-7

    Article  Google Scholar 

  50. Boscato G, Pizzolato M, Russo S, Tralli A (2014) Seismic behavior of a complex historical church in L’Aquila. Int J Archit Herit 8:718–757. doi:10.1080/15583058.2012.736013

    Article  Google Scholar 

  51. Lourenço PB (1997) An anisotropic macro-model for masonry plates and shells: implementation and validation. Ph.D. Thesis, TU Delft

Download references

Author information

Authors and Affiliations

  1. Department of Engineering, University of Ferrara, Via Saragat 1, 44122, Ferrara, Italy

    Andrea Chiozzi, Nicola Grillanda & Antonio Tralli

  2. Department of Architecture, Built Environment and Construction Engineering (A.B.C.), Technical University of Milan, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Gabriele Milani

Authors
  1. Andrea Chiozzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gabriele Milani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicola Grillanda
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Antonio Tralli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrea Chiozzi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chiozzi, A., Milani, G., Grillanda, N. et al. A fast and general upper-bound limit analysis approach for out-of-plane loaded masonry walls. Meccanica 53, 1875–1898 (2018). https://doi.org/10.1007/s11012-017-0637-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-017-0637-x

Keywords

Search

Navigation