Advertisement

Archives of Computational Methods in Engineering

, Volume 17, Issue 3, pp 299–325 | Cite as

Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches

  • Pere Roca
  • Miguel Cervera
  • Giuseppe Gariup
  • Luca Pela’
Original Paper

Abstract

A review of methods applicable to the study of masonry historical construction, encompassing both classical and advanced ones, is presented. Firstly, the paper offers a discussion on the main challenges posed by historical structures and the desirable conditions that approaches oriented to the modeling and analysis of this type of structures should accomplish. Secondly, the main available methods which are actually used for study masonry historical structures are referred to and discussed.

The main available strategies, including limit analysis, simplified methods, FEM macro- or micro-modeling and discrete element methods (DEM) are considered with regard to their realism, computer efficiency, data availability and real applicability to large structures. A set of final considerations are offered on the real possibility of carrying out realistic analysis of complex historic masonry structures. In spite of the modern developments, the study of historical buildings is still facing significant difficulties linked to computational effort, possibility of input data acquisition and limited realism of methods.

Keywords

Limit Analysis Discrete Element Method Masonry Wall Masonry Building Masonry Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ali SS, Page AW (1988) Finite element model for masonry subjected to concentrated loads. J Struct Eng ASCE 114(8):1761–1784 CrossRefGoogle Scholar
  2. 2.
    Andreu A, Gil L, Roca P (2006) Limit analysis of masonry constructions by 3D funicular modeling. In: Structural analysis of historical constructions. MacMillan, New Deli, pp 1135–1142 Google Scholar
  3. 3.
    Andreu A, Gil L, Roca P (2007) Computational analysis of masonry structures with a funicular model. J Eng Mech ASCE 133(4):473–480 CrossRefGoogle Scholar
  4. 4.
    Anzani A, Binda L, Mirabella-Roberti G (2008) Experimental researches into long-term behavior of historical masonry. In: Binda L (ed) Learning from failure. Long term behaviour of heavy masonry structures. WIT Press, Southampton Google Scholar
  5. 5.
    Baggio C, Trovalusci P (1995) Stone assemblies under in-plane actions—comparison between nonlinear discrete approaches. Comput Methods Struct Mason 3:184–193 Google Scholar
  6. 6.
    Baggio C, Trovalusci P (1998) Limit analysis for no-tension and frictional three-dimensional discrete systems. Mech Struct Mach 26(3):287–304 CrossRefGoogle Scholar
  7. 7.
    Barthel R (1993) Rissbildung in gemauerten Kreutzgewölben. Structural preservation of the architectural heritage, IABSE, Zürich, Switzerland Google Scholar
  8. 8.
    Benedetti A, Pela’ L, Aprile A (2008) Masonry property determination via splitting tests on cores with a rotated mortar layer. In: Proceedings of the 8th international seminar on structural masonry ISSM 08, Istanbul, Turkey, 5–7 Novembre 2008, pp 647–655 Google Scholar
  9. 9.
    Berto L, Saetta A, Scotta R, Vitaliani R (2002) An orthotropic damage model for masonry structures. Int J Numer Methods Eng 55:127–157 zbMATHCrossRefGoogle Scholar
  10. 10.
    Bicanic N, Ponniah D, Robinson J (2001) Discontinuous deformation analysis of masonry bridges. Comput Model Mason 177–196 Google Scholar
  11. 11.
    Binda L, Gatti G, Mangano G, Poggi C, Sacchi Landriani G (1992) The collapse of the Civic Tower of Pavia: a survey of the materials and structure. Mason Int 6(1):11–20 Google Scholar
  12. 12.
    Binda L, Modena C, Baronio G, Abbaneo S (1997) Repair and investigation techniques for stone masonry walls. Constr Build Mater 11(3):133–142 CrossRefGoogle Scholar
  13. 13.
    Binda L, Saisi A, Messina S, Tringali S (2001) Mechanical damage due to long term behaviour of multiple leaf pillars in Sicilian Churches. In: III int seminar: historical constructions 2001. Possibilities of numerical and experimental techniques, Guimaraes, Portugal, pp 707–718 Google Scholar
  14. 14.
    Binda L, Anzani A, Saisi A (2003) Failure due to long term behaviour of heavy structures: the Pavia Civic Tower and the Noto Cathedral. In: 8th int conf on STREMAH 2003, Struct studies repairs and maintenance of heritage architecture, 7–9/5/2003, Halkidiki (Greece), pp 99–108 Google Scholar
  15. 15.
    Block P (2005) Equilibrium systems. Studies in masonry structure. MS dissertation, Department of Architecture, Massachusetts Institute of Technology Google Scholar
  16. 16.
    Block P, Ochserdorf J (2007) Thrust network analysis: a new methodology for three-dimensional equilibrium. J Int Assoc Shell Spat Struct IASS 48(3):155 Google Scholar
  17. 17.
    Block P, Ciblac T, Ochsendorf JA (2006) Real-time limit analysis of vaulted masonry buildings. Comput Struct 84:1841–1852 CrossRefGoogle Scholar
  18. 18.
    Brencich A, Gambarotta L, Lagomarsino S (1998) A macroelement approach to the three-dimensional seismic analysis of masonry buildings. In: Proc of the XI European conf on earthquake engineering, Paris, AA Balkema (Abstract Volume & CD-ROM), p 602 Google Scholar
  19. 19.
    Calderini C, Lagomarsino S (2006) A micromechanical inelastic model for historical masonry. J Earthq Eng 10(4):453–479 CrossRefGoogle Scholar
  20. 20.
    Calvi GM, Magenes M (1994) Experimental research on response of URM building system. In: Proc of US-Italy workshop on guidelines for seismic evaluation and rehabilitation of unreinforced masonry buildings. State University of New York at Bufalo, Pavķa, NCEER-94-0021, 3–41/57 Google Scholar
  21. 21.
    Casarin F (2006) Structural assessment and seismic vulnerability analysis of a complex historical building. PhD Thesis, Università degli Studi di Padova Google Scholar
  22. 22.
    Casarin C, Modena C (2008) Seismic assessment of complex historical buildings: Application to Reggio Emilia Cathedral, Italy. J Archit Heritage 2(3):304–327 CrossRefGoogle Scholar
  23. 23.
    Carocci CF (2001) Guidelines for the safety and preservation of historical centres in seismic areas. In: Historical constructions. University of Minhi, Guimaraes, pp 145–165 Google Scholar
  24. 24.
    Casapulla C, D’Ayala D (2001) Lower bound approach to the limit analysis of 3D vaulted block masonry structures. In: Proceedings of the 5th international symposium on computer methods in structural masonry, STRUMAS V Rome, pp 28–36 Google Scholar
  25. 25.
    Casolo S, Sanjust CA (2009) Seismic analysis and strengthening design of a masonry monument by a rigid body spring model: the “Maniace Castle” of Syracussa. Eng Struct 31:1447–1459 CrossRefGoogle Scholar
  26. 26.
    Casolo S, Peña F (2007) Rigid element model for in-plane dynamics of masonry walls considering hysteretic behaviour and damage. Earthq Eng Struct Dyn 36:1029–1048 CrossRefGoogle Scholar
  27. 27.
    Cauvin A, Stagnitto G (1993) Problems concerning strength assessment and repair of Historical Vaulted Structures. In: Public assembly structures from antiquity to the present, IASS, Istanbul, Turkey Google Scholar
  28. 28.
    Cauvin A, Stagnitto G (1995) Criteria of design and methods of structural analysis of Gothic ribbed vaults using traditional and computer methods. In: Spatial structures: heritage, present and future. SGE Editoriali, Padova, Italy Google Scholar
  29. 29.
    Chen SY, Moon FL, Yi T (2008) A macroelement for the nonlinear analysis of in-plane unreinforced masonry piers. Eng Struct 30:2242–2252 CrossRefGoogle Scholar
  30. 30.
    Chiarugi A, Fanelli A, Giuseppetti G (1993) Diagnosis and strengthening of the Brunelleschi Dome. In: IABSE Symposium 1993, IABSE, Zürich Google Scholar
  31. 31.
    Clemente R (2006) Structural analysis of historical buildings by localized cracking models (in Spanish). PhD dissertation, Universitat Politècnica de Catalunya, Barcelona, Spain Google Scholar
  32. 32.
    Clemente R, Roca P, Cervera M (2006) Damage model with crack localization—application to historical buildings: structural analysis of historical constructions. New Delhi, pp 1125–1135 Google Scholar
  33. 33.
    Coulomb CA (1773) Essai sur une application des regles des maximis et minimis à quelques problémes de statique relativs a l’arquitecture. In: Mémoires de mathematique et de physique présentés à l’académie royal des sciences per divers savants et lus dans ses assemblées, 1, París, pp 343–382 Google Scholar
  34. 34.
    Croci G (1995) The Colosseum: safety evaluation and preliminary criteria of intervention. Structural Analysis of Historical Constructions, Barcelona Google Scholar
  35. 35.
    Croci G (1998) The Basilica of St Francis of Assisi after the September 1997 earthquake. Struct Eng Int 8(1):56–58 CrossRefGoogle Scholar
  36. 36.
    Croci G, Viscovik A (1993) Causes of failures of Colosseum over the centuries and evaluation of the safety levels. In: Public assembly structures. From antiquity to the present. IASS-Mimar Sinan University, Istanbul, Turkey, pp 29–52 Google Scholar
  37. 37.
    Croci C, Cerone M, Viskovic A (1997) Analysis from a historical and structural point of view of the domes of Pantheon. In: Hagia Sophia and St Peter studies in ancient structures. YTU Faculty of Architecture Publication, Istanbul, Turkey Google Scholar
  38. 38.
    Croci G, Carluccio G, Viskovic A (1998) Análisis estructural de la Catedral de Santa María Vieja de Vitoria. In: Primer congreso Europeo sobre catedrales góticas, Diputación Foral de Alava, Vitoria, Spain Google Scholar
  39. 39.
    Croci G, Taupin JL, Viskovic A (1998) Análisis matemático del derrumbamiento de bóvedas en la catedral de San Pedro de Beauvais. In: Primer congreso Europeo sobre catedrales góticas, Diputación Foral de Alava, Vitoria, Spain Google Scholar
  40. 40.
    Cundall PA, Hart P (1971) A computer model for simulating progressive large scale movements in blocky rock systems. In: Proc of the symposium of the int society of rock mechanics. Nancy, France, vol 1, paper No II-8 Google Scholar
  41. 41.
    D’Ayala D, Speranza E (2002) An integrated procedure for the assessment of the seismic vulnerability of historic buildings. In: 12th European conference on earthquake engineering. Paper n 561, London Google Scholar
  42. 42.
    De Luca A, Giordano A, Mele E (2004) A simplified procedure for assessing the seismic capacity of masonry arches. Eng Struct 26:1915–1929 CrossRefGoogle Scholar
  43. 43.
    Fajfar P (1999) Capacity spectrum method based on inelastic demand spectra. Earthq Eng Struct Dyn 28:979–993 CrossRefGoogle Scholar
  44. 44.
    Fanelli M (1993) Information systems for monuments and historical buildings. In: IABSE symposium, structural preservation of the architectural heritage, Rome, pp 65–72 Google Scholar
  45. 45.
    Ferris M, Tin-Loi F (2001) Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints. Int J Mech Sci 43:209–224 zbMATHCrossRefGoogle Scholar
  46. 46.
    Gambarotta L, Lagomarsino S (1997) Damage models for the seismic response of brick masonry shear walls Part I & Part II. Earthq Eng Struct Dyn 26 Google Scholar
  47. 47.
    Ghaboussi J, Barbosa R (1990) Three-dimensional discrete element method for granular materials. Int J Numer Anal Methods Geomech 14:451–472 CrossRefGoogle Scholar
  48. 48.
    Gilbert M (2007) Limit analysis applied to masonry arch bridges: state-of-the-art and recent developments. In: Arch bridges ‘07, Funchal, Madeira, pp 13–28 Google Scholar
  49. 49.
    Gilbert M, Melbourne C (1994) Rigid-block analysis of masonry structures. Struct Eng 72(21):356–361 Google Scholar
  50. 50.
    Gilbert M, Casapulla C, Ahmed HM (2006) Limit analysis of masonry block structures with non-associative frictional joints using linear programming. Comput Struct 84:873–887 CrossRefGoogle Scholar
  51. 51.
    Giuffrè A (1990) Letture sulla meccanica delle murature storiche. Kappa, Rome Google Scholar
  52. 52.
    Giuffrè A (1995) Vulnerability of historical cities in seismic areas and conservation criteria. In: Congress “Terremoti e civiltà abitative”, Annali di Geofisica, Bologna Google Scholar
  53. 53.
    Giuffrè A, Carocci C (1993) Statica e dinamica delle costruzioni murarie storiche. In: Atti del Convegno internazionale CNR “Le pietre da costruzione: il tufo calcareo e la pietra leccese”. Mario Adda Editore, Bari, pp 539–598 Google Scholar
  54. 54.
    Gonzalez A, Casals A, Roca P, Gonzalez JL (1993) Studies of Gaudi’s Cripta de la Colonia Güell. IABSE Symposium, Structural Preservation of the Architectural Heritage, Rome, pp 457–464 Google Scholar
  55. 55.
    Hanganu DA (1997) Análisis no lineal estático y dinámico de estructuras de hormigón armado mediante modelos de Daño. PhD Thesis, UPC, Barcelona Google Scholar
  56. 56.
    Heyman J (1966) The stone skeleton. Int J Solids Struct 2:270–279 Google Scholar
  57. 57.
    Heyman J (1976) Couplet’s engineering memoirs 1726-33. Hist Technol 1:21–44 Google Scholar
  58. 58.
    Heyman J (1989) Hooke’s cubico-parabolical conoid. Notes Rec R Soc 52(1):39–50 CrossRefMathSciNetGoogle Scholar
  59. 59.
    Huerta S (2001) Mechanics of masonry vaults: the equilibrium approach. In: Historical Constructions. University of Minho, Guimaraes, pp 47–69 Google Scholar
  60. 60.
    ICOMOS/ISCARSAH Committee (2005) Recommendations for the analysis, conservation and structural restoration of architectural heritage. See www.icomos.org
  61. 61.
    Karantoni FV, Fardis MN (1992) Effectiveness of seismic strengthening techniques for masonry buildings. J Struct Eng ASCE 118(7):1884–1902 CrossRefGoogle Scholar
  62. 62.
    Kwan AKH (1991) Analysis of coupled wall/frame structures by frame method with shear deformation allowed. Proc Inst Civ Eng 91:273–297 Google Scholar
  63. 63.
    Lagomarsino S (2006) On the vulnerability assessment of monumental buildings. Bull Earthq Eng 4:445–463. European Comission, Brussels CrossRefGoogle Scholar
  64. 64.
    Lagomarsino S, Giovinazzi S, Podestà S, Resemini S (2003) RISK-UE-EVK4-CT-2000-00014 An advanced approach to earthquake risk scenarios with application to different European Towns. WP5: Vulnerability assessment of historical and monumenttal buildings Google Scholar
  65. 65.
    Lemos JV (1995) Assesment of the ultimate load of a masonry arch using discrete elements. Comput Methods Struct Mason 294–302 Google Scholar
  66. 66.
    Lemos JV (1998) Discrete element modeling of the seismic behavior of stone masonry arches. In: Pande G et al. (eds) Computer methods in structural masonry, 4. E& FN Spon, London, pp 220–227 Google Scholar
  67. 67.
    Livesley RK (1978) Limit analysis of structures formed from rigid blocks. Int J Numer Methods Eng 12:1853–1871 zbMATHCrossRefGoogle Scholar
  68. 68.
    Lopez J, Oller S, Oñate E, Lubliner J (1999) A homogeneous constitutive model for masonry. Int J Numer Methods Eng 46:1651–1671 zbMATHCrossRefGoogle Scholar
  69. 69.
    Lotfi HR, Shing PB (1994) Interface model applied to fracture of masonry structures. J Struct Eng ASCE 120(1):63–80 CrossRefGoogle Scholar
  70. 70.
    Lourenço PB (1996) Computational strategies for masonry structures. PhD Thesis. Delft University of Technology, Delft, The Netherlands Google Scholar
  71. 71.
    Lourenço PB (1997) An anisotropic plasticity model for quasi-brittle composite shells. In: Computational plasticity: fundamentals and applications. Pinteridge Press, London Google Scholar
  72. 72.
    Lourenço PB, Mourão S (2001) Safety assessment of Monastery of Jerónimos. In: Historical constructions 2001. Guimarães, pp 697–706 Google Scholar
  73. 73.
    Lourenço PB, Pina-Henriques J (2008) Collapse prediction and creep effects. In: Binda L (ed) Learning from failure. Long term behaviour of heavy masonry structures. WIT Press, Southampton Google Scholar
  74. 74.
    Lourenço PB, Rots JG (1997) A multi-surface interface model for the analysis of masonry structures. J Eng Mech ASCE 123(7):660–668 CrossRefGoogle Scholar
  75. 75.
    Lourenço PB, Rots JG, Blaauwendraad J (1998) Continuum model for masonry: parameter estimation and validation. J Struct Eng ASCE 1(6):642–652 CrossRefGoogle Scholar
  76. 76.
    Lourenço PB, Milani G, Tralli A, Zucchini A (2007) Analysis of masonry structures: review of and recent trends of homogenisation techniques. Can J Civil Eng 34:1443–1457 CrossRefGoogle Scholar
  77. 77.
    Lucchesi M, Padovani C, Pasquinelli G, Zani N (2007) Statics of masonry vaults, constitutive model and numerical analysis. J Mech Mater Struct 2(2):221–244 CrossRefGoogle Scholar
  78. 78.
    Ma MY, Pan AD, Luan M, Gebara JM (1996) Seismic analysis of stone arch bridges using discontinuous deformation analysis. In: Proceedings of the 11th world conference on earthquake engineering. Elsevier, Amsterdam, paper no 1551 Google Scholar
  79. 79.
    Macchi G, Ruggeri M, Eusebio M, Moncecchi M (1993) Structural assessment of the leaning tower of Pisa. In: Structural preservation of the architectural heritage, IABSE, Zürich, Switzerland, pp 401–408 Google Scholar
  80. 80.
    Mallardo V, Malvezzi R, Milani E, Milani G (2008) Seismic vulnerability of historical masonry buildings: a case study in Ferrara. Eng Struct 30:2223–2241 CrossRefGoogle Scholar
  81. 81.
    Mamaghani IHP, Aydan O, Kajikawa Y (1999) Analysis of masonry structures under static and dynamic loading by discrete finite element method. Struct Eng/Earthq Eng JSCE 16(2):75–86 Google Scholar
  82. 82.
    Mark R, Çakmak AS, Erdik M (1993) Modelling and monitoring the structure of Hagia Sophia in Istambul structural. In: Preservation of the architectural Heritage, Zürich, Switzerland, pp 179–186 Google Scholar
  83. 83.
    Mark R, Çakmak AS, Hill K, Davison R (1993) Structural analysis of Hagia Sophia: a historical perspective. In: Structural Repair and Maintenace of Historical Builsings III. Computational Mechanics Publications, UK Google Scholar
  84. 84.
    Martínez G, Roca P, Caselles O, Clapés J (2006) Characterization of the dynamic response for the structure of Mallorca Cathedral. In: Lourenço PB, Roca P, Modena C, Agrawal S (eds) Structural analysis of historical constructions, New Delhi, India Google Scholar
  85. 85.
    Massart TJ, Peerlings RHJ, Geers MGD (2004) Mesoscopic modeling of failure and damageinduced anisotropy in brick masonry. Eur J Mech A/Solids 23:719–735 zbMATHCrossRefGoogle Scholar
  86. 86.
    Melbourne C, Gilbert M (1994) The application of limit analysis techniques to masonry arch bridges. In: Barr BIG, Evans HR, Harding JE (eds) Bridges assessment, management and design. Elsevier, Amsterdam, pp 193–198 Google Scholar
  87. 87.
    Meli R, Peña F (2004) On elastic models for evaluation of the seismic vulnerability of masonry churches. In: Structural analysis of historical constructions. Balkema, Leiden, pp 1121–1131 Google Scholar
  88. 88.
    Meli R, Sánchez-Ramírez AR (1995) Structural aspects of the rehabilitation of the Mexico City Cathedral. In: Structural analysis of historical constructions I, CIMNE, Barcelona, Spain, pp 123–140 Google Scholar
  89. 89.
    Milani G, Lourenço PB, Tralli A (2006) Homogenised limit analysis of masonry walls. Part I: Failure surfaces. Comput Struct 84(3–4):166–180 CrossRefGoogle Scholar
  90. 90.
    Milani G, Lourenço PB, Tralli A (2006) Homogenised limit analysis of masonry walls. Part II: Structural applications. Comput Struct 84(3–4):181–195 CrossRefGoogle Scholar
  91. 91.
    Milani G, Lourenço PB, Tralli A (2006) A homogenization approach for the limit analysis of out-of-plane loaded masonry walls. J Struct Eng ASCE 132:1650–1663 CrossRefGoogle Scholar
  92. 92.
    Milani G, Lourenço PB, Tralli A (2007) 3D Homogenized limit analysis of masonry buildings under horizontal loads. Eng Struct 29(11):3134–3148 CrossRefGoogle Scholar
  93. 93.
    Mola F, Vitaliani R (1995) Analysis, diagnosis and preservation of ancient monuments: the St. Mark’s Basilica in Venice. In: Structural analysis of historical constructions I. CIMNE, Barcelona, Spain, pp 166–188 Google Scholar
  94. 94.
    Molins C, Roca P (1998) Capacity of masonry arches and spatial frames. J Struct Eng ASCE 124(6):653–663 CrossRefGoogle Scholar
  95. 95.
    Munjiza A, Owen DRJ, Bicanic N (1995) A combined finite-discrete element method in transient dynamics of fracturing solids. Eng Comput 12:145–174 zbMATHCrossRefGoogle Scholar
  96. 96.
    Murcia-Delso J, Das AK, Roca M, Cervera M (2009) Seismic safety analysis of historical masonry structures using a damage constitutive model. In: Thematic conference on computational methods in structural dynamics and earthquake engineering Google Scholar
  97. 97.
    Ngo D, Scordelis AC (1964) Finite element analysis of reinforced concrete beam. J Am Concr Inst 64:152 Google Scholar
  98. 98.
    Ochsendorf JA (2002) Collapse of masonry structures. PhD thesis. Department of Engineering, Univ of Cambridge, Cambridge, UK Google Scholar
  99. 99.
    O’Dwyer D (1999) Funicular analysis of masonry vaults. Comput Struct 73:187–197 zbMATHCrossRefGoogle Scholar
  100. 100.
    Oñate E, Hanganu A, Barbat A, Oller S, Vitaliani R, Saetta A, Scotta R (1995) Structural analysis and durability assessment of historical constructions using a finite element damage model. In: Structural analysis of historical constructions. CIMNE, pp 189–224 Google Scholar
  101. 101.
    Ordinanza OPCM 3274, 2003 Modified according to OPM 3431, 2005. Allegato 2, Norme tecniche per il progetto, la valutazione e l’adeguamento sismico degli edifici. Consiglio dei Ministri, Rome Google Scholar
  102. 102.
    Orduña A, Lourenço P (2003) Cap model for limit analysis and strengthening of masonry structures. J Struct Eng 129(10):1367–1375 CrossRefGoogle Scholar
  103. 103.
    Orduña A, Lourenço PB (2005) Three-dimensional limit analysis of rigid block assemblages. Part I: Torsion failure on frictional interfaces and limit analysis formulation. Int J Solids Struct 42(18–19):5140–5160 zbMATHCrossRefGoogle Scholar
  104. 104.
    Orduña A, Lourenço PB (2005) Three-dimensional limit analysis of rigid blocks assemblages. Part II: Load-path following solution procedure and validation. Int J Solids Struct 42(18–19):5161–5180 zbMATHCrossRefGoogle Scholar
  105. 105.
    Pagnoni T (1994) Seismic analysis of masonry and block structures with the discrete element method. In: Proc 10th European conference on earthquake engineering, vol 3, pp 1674–1694 Google Scholar
  106. 106.
    Pagnoni T, Vanzi I (1995) Experimental and numerical study of the seismic response of block structures. In: Computer methods in structural masonry, pp 213–222 Google Scholar
  107. 107.
    Papa EA (1996) Unilateral damage model for masonry based on a homogenization procedure. Mech Cohes-Frict Mater 1:349–366 CrossRefGoogle Scholar
  108. 108.
    Papa E, Taliercio A (2000) Prediction of the evolution of damage in ancient masonry towers. In: Proc int symposium ‘bridging large spans from antiquity to the present’. Istanbul, pp 135–144 Google Scholar
  109. 109.
    Papastamatiou D, Psycharis I (1993) Seismic response of classical manuments—a numerical perspective developed at the Temple of Apollo Bassae, Greece. Terra Nova 5:591–601 CrossRefGoogle Scholar
  110. 110.
    Pegon P, Pinto AV, Anthoine A (1995) Numerical simulation of historical buildings subjected to earthquake loading. In: Structural Studies of Historical Buildings IV, 2. Computational Mechanics Publications, Southampton, pp 29–36 Google Scholar
  111. 111.
    Pegon P, Pinto AV, Géradin M (2001) Numerical modelling of Stone-block monumental structures. Comput Struct 79:2165–2181 CrossRefGoogle Scholar
  112. 112.
    Pela’ L (2009) Continuum damage model for nonlinear analysis of masonry structures. PhD dissertation. University of Ferrara, Ferrara Google Scholar
  113. 113.
    Pela’ L, Cervera M, Roca P, Benedetti A (2008) An orthrotropic damate model for the analysis of masonry structures. In: 8th International seminar on structural masonry ISSM 08, pp 175–178 Google Scholar
  114. 114.
    Pela’ L, Aprile A, Benedetti A (2009) Seismic assessment of masonry arch bridges. Eng Struct 31:1777–1788 CrossRefGoogle Scholar
  115. 115.
    Peña F, Prieto F, Lourenço PB, Campos Costa A, Lemos JV (2007) On the dynamics of rocking motion of single rigid–block structures. In: Earthquake engineering and structural dynamics Google Scholar
  116. 116.
    Poleni G (1743) Memorie istoriche della gran cupola del tempio Vaticano. Stamperia del Seminario, Padova Google Scholar
  117. 117.
    Psycharis I, Lemos JV, Papastamatiou D, Zambas C, Papantonopoulos C (2003) Numerical study of the seismic behaviour of a part of the Partenón Pronaos. Earthq Eng Struct Dyn 32:2063–2084 CrossRefGoogle Scholar
  118. 118.
    Ràfols JF (1929) Gaudí. Canosa, Barcelona Google Scholar
  119. 119.
    Roca P (1998) Studies of Gaudi’s Cripta de la Colonia Güell. In: Structural analysis of historical constructions II. CIMNE, Barcelona, pp 377–393 Google Scholar
  120. 120.
    Roca P (2001) Studies on the structure of Gothic Cathedrals. In: Lourenço PB, Roca P (eds) Historical constructions. University of Guimaraesr, Guimaraes Google Scholar
  121. 121.
    Roca P (2004) Considerations on the significance of history for the structural analysis of ancient constructions. In: Structural analysis of historical constructions IV. Balkema, Amsterdam, pp 63–73 Google Scholar
  122. 122.
    Roca P, Pellegrini L, Oñate E, Hanganu A (1998) Analysis of Gothic constructions. In: Structural analysis of historical constructions II. CIMNE, Barcelona Google Scholar
  123. 123.
    Roca P, Massanas M, Cervera M, Arun G (2004) Structural analysis of Küçük Ayasofya Mosque in Ístanbul. In: Structural analysis of historical constructions IV. Balkema, Amsterdam, pp 679–686 Google Scholar
  124. 124.
    Roca P, Molins C, Marí AR (2005) Strength capacity of masonry wall structures by the equivalent frame method. J Struct Eng ASCE 131(10):1601–1610 CrossRefGoogle Scholar
  125. 125.
    Roca P, López-Almansa F, Miquel J, Hanganu A (2007) Limit analysis of reinforced masonry vaults. Eng Struct 29:431–439 CrossRefGoogle Scholar
  126. 126.
    Roca P, Vacas A, Cuzzilla R, Murica-Delso J, Das AK (2009) Structural features and response of Gothic churches in moderate seismic regions. In: ISCARSAH symposium on Assessment and strengthening of historical stone masonry constructions subjected to seismic action. Interproject, Mostar Google Scholar
  127. 127.
    Rubió J (1912) Lecture on the organic, mechanical and construction concepts of Mallorca Cathedral (in Catalan). Anuario de la Asociación de Arquitectos de Cataluña, Barcelona Google Scholar
  128. 128.
    Schlegel R, Rautenstrauch K (2004) Failure analysis of masonry shear walls. Numer Model Discrete Mater 15–18 Google Scholar
  129. 129.
    Shi G-H, Goodman RE (1988) Discontinuous deformation analysis—a new method for computing stress, strain and sliding of block systems. In: Cundall PA, Sterling R, Starfield A (eds) Key questions in rock mechanics. Balkema, Rotterdam, pp 381–393 Google Scholar
  130. 130.
    Shieh-Beygi B, Pietruszczak S (2008) Numerical analysis of structural masonry: mesoscale approach. Comput Struct 86:1958–1973 CrossRefGoogle Scholar
  131. 131.
    Sincraian GE (2001) Seismic behaviour of blocky masonry structures. A discrete element method approach. PhD Dissertation, IST, Lisbon, Portugal Google Scholar
  132. 132.
    Sutcliffe DJ, Yu HS, Page AW (2001) Lower bound limit analysis of unreinforced masonry shear walls. Comput Struct 79(14):1295–1312 CrossRefGoogle Scholar
  133. 133.
    Taliercio A, Papa E (2008) Modelling of the long-term behavior of historical towers. In: Binda L (ed) Learning from failure. Long term behaviour of heavy masonry structures. WIT Press, Southampton Google Scholar
  134. 134.
    Tzamtzis AD (1994) Dynamic finite element analysis of complex discontinuous and jointed structural systems using interface elements. PhD Thesis, Department of Civil Engineering, QMWC, University of London Google Scholar
  135. 135.
    van der Pluijm R (1999) Out of plane bending of masonry: Behaviour and strength. PhD Dissertation. Eindhoven University of Technology: The Netherlands Google Scholar
  136. 136.
    Zienkiewicz OC, Taylor RL (1991) The finite element method. McGraw Hill, New York Google Scholar
  137. 137.
    Zucchini A, Lourenço PB (2002) A micro-mechanical model for the homogenization of masonry. Int J Solids Struct 39:3233–3255 zbMATHCrossRefGoogle Scholar
  138. 138.
    Zucchini A, Lourenço PB (2004) A coupled homogenisation-damage model for masonry cracking. Comput Struct 82:917–929 CrossRefGoogle Scholar
  139. 139.
    Zucchini A, Lourenço PB (2007) Mechanics of masonry in compression: results from a homogenisation approach. Comput Struct 85:193–204 CrossRefGoogle Scholar
  140. 140.
    Zucchini A, Lourenco PB (2009) A micro-mechanical homogenisation model for masonry: application to shear walls. Int J Solids Struct 46(3–4):871–886 CrossRefGoogle Scholar

Copyright information

© CIMNE, Barcelona, Spain 2010

Authors and Affiliations

  • Pere Roca
    • 1
  • Miguel Cervera
    • 1
  • Giuseppe Gariup
    • 1
  • Luca Pela’
    • 2
  1. 1.Technical University of CataloniaBarcelonaSpain
  2. 2.University of BolognaBolognaItaly

Personalised recommendations