Numerical-vector succession for the graphic structural analysis of masonry historic buildings with arches and symmetrical systems
Abstract
Many historic buildings have symmetry in their geometric configuration. The objective of this research is to denote the application of numerical-vector succession in the structural analysis of historical masonry buildings, with arches and symmetrical systems, including mathematical processes in ancient graphic analysis, emphasizing the importance of loads in the structural stability. We based the analysis on three fundamental stages: recognition of the construction system of the heritage object, geometric discretization of the system and vector analysis under different physical considerations. Hence, the thrust lines are affected by the loads, boundary conditions and history of structural behaviour. Numerical and computational tools offer faster and more accurate graphic analysis processes.
Many historic buildings have symmetry in their geometric configuration. The objective of this research is to denote the application of numerical-vector succession in the structural analysis of historical masonry buildings, with arches and symmetrical systems, including mathematical processes in ancient graphic analysis, emphasizing the importance of loads in the structural stability. We based the analysis on three fundamental stages: recognition of the construction system of the heritage object, geometric discretization of the system and vector analysis under different physical considerations. Hence, the thrust lines are affected by the loads, boundary conditions and history of structural behaviour. Numerical and computational tools offer faster and more accurate graphic analysis processes.
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References
Angelillo M., et al., (2014), “Mechanics of Mansory Structures”, Editado por Maurizio Angelillo. Springer. Università di Salerno, Fisciano, Italy.
Biblioteca Tomás Navarro Tomás, (19/10/2023), “Escuela de Santa Catarina, Atotonilco El Grande en Hidalgo (México)”, https://www.pinterest.com.mx/pin/334533078561349371/
Barlow, William Henry (1846). "On the Existence (practically) of the line of equal Horizontal Thrust in Arches, and the mode of determining it by Geometrical Construction “, Minutes and Proceedings of the Institution of Civil Engineers, Vol. 5, pp. 179-180. DOI: https://doi.org/10.1680/imotp.1846.24301
Block, P., DeJong, M., Ochsendorf, J. A. (2006), "As Hangs the Flexible Line: Equilibrium of Masonry Arches". Nexus Network Journal - Vol 8, No. 2. https://doi.org/10.1007/s00004-006-0015-9. DOI: https://doi.org/10.1007/s00004-006-0015-9
Chávez, Mauricio M., (2010), “Validación Experimental De Modelos Analíticos Para El Estudio Del Comportamiento Sísmico De Estructuras Históricas”, México, UNAM, p. 24.
Chávez, M. (2005), “Estudio experimental de las propiedades mecánicas de mamposterías de piedra natural”, publicado por el Instituto de ingeniería UNAM. Ciudad Universitaria, CP 04510, Ciudad de México.
Chávez, M. (2010), “Validación experimental de modelos analíticos para el estudio del comportamiento sísmico de estructuras históricas”, publicado por el Instituto de Ingeniería UNAM. Ciudad Universitaria, CP 04510, Ciudad de México.
Circolare, (2019), Código italiano DM 14.1. Il Ministro: Toninelli
Durán, D., Chávez m. M. (2022), "Mechanical properties of masonry stone samples extracted from Mexican colonial churches", Elsevier, coordinación de ingeniería estructural, instituto de ingeniería, universidad nacional autónoma de México, México, E01295, https://doi.org/10.1016/j.cscm.2022.e01295 DOI: https://doi.org/10.1016/j.cscm.2022.e01295
Goodno, B. J., Gere, J. M., (2013), “Mechanics of Materials (Ninth Edition)”, Cengage Learning, U.S., pp. 26-27.
Mas-Guindal, A. J. (2021). “Mecánica de las estructuras antiguas o cuando las estructuras no se
calculaban”. Munilla-Lería, España-Madrid.
Heyman, J. (1969), “Teoría, Historia Y Restauración De Estructuras De Fábrica”, Inst. Juan de Herrera, México, pp. 1-1
Heyman, J. (1995), “The Stone Skeleton Structural engineering of masonry architecture (First Publish)”, Cambridge University Press, United Kingdom, pp. 5-49. DOI: https://doi.org/10.1017/CBO9781107050310
Hibbeler, R.C. (2016), “Ingeniería mecánica estática (decimosegunda edición)”, Prentice Hall, Pearson Educación, México, pp. 447-456, 599.
Huerta, S. (2004), “Arcos, bóvedas y cúpulas. Geometría y equilibrio en el cálculo tradicional de estructuras de fábrica”, Inst. Juan de Herrera, Madrid, pp. 11-34.
Huerta, S. (2006). “Galileo was wrong: The Geometrical Design of Masonry Arches”, E.T.S. de Arquitectura Universidad Politécnica de Madrid, Inst. Juan de Herrera, Nexus Network Journal 8 (2006), p. 26. DOI: https://doi.org/10.1007/s00004-006-0016-8
ICOMOS Internacional Council of Monument and Cities. (2003). “Principles for the analysis, conservation, and restoration of architectural heritage structures”. Victoria Falls, Zambia. Retrieved from http://www.icomos.org
ISCARSAH. (2003). “Recommendations for the analysis conservation, and structural restoration of architectural heritage”. Course on Architectural Heritage Intervention of the College of Architects of Catalonia. Catalonia: ICOMOS.
Markou, A. A., Ruan, G. (2022), “Graphic statics: projective funicular polygon”, ELSEVIER, Department of Civil Engineering, Aalto University, Rakentajanaukio 4A, Espoo FI-00076, Finland, pp. 1394-1395. DOI: https://doi.org/10.1016/j.istruc.2022.05.049
Mas-Guindal, A. J. (2021). “Mecánica de las estructuras antiguas o cuando las estructuras no se calculaban”. Munilla-Lería, España-Madrid, pp. 34-73.
Mc Cormac, J. C., Brown, R. H. (2017), “Diseño de Concreto Reforzado (décima edición)”, Alfaomega Grupo Editor, México, p. 355.
Meli, R. (1998), “Ingeniería estructural de los edificios históricos”, ICA, México, p. 10
Meli, R. (2011), “Diseño Estructural (segunda edición)”, Limusa Noriega Editores, México, p. p. 544, 552.
Minke, G. (1994), “Manual de construcción en tierra, La tierra como material de construcción y su aplicación en la arquitectura actual”, Editorial Fin de Siglo, Alemania, p. 25.
Popov, E. P., Toader, A. B. (1999),” Mecánica de Sólidos (Segunda Edición) Prentice Hall”, Pearson Educación, México, p. 4.
Computers and Structures, Inc. (2023), “SAP2000: Integrated Software for Structural Analysis and Design” (Version 23.1.0).
Segovia, M. A. (2022), “Análisis constructivo - estructural para determinar el comportamiento de un inmueble de mampostería del siglo XVI, Santa Catarina, Atotonilco del grande”, Tesis del IPN, México, pp. 49, 77.
Spiegel, M. R. (1970), “Análisis vectorial, Teoría y 480 Problemas Resueltos”, Serie SCHAUM, U.S.A., pp. 1-4
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