Graphic Statics for Continuous Beams and Frames: A Review of the Fixed-points Method

References

• Allen, E., and W. Zalewski. 2009. Form and forces: Designing efficient, expressive structures. Hoboken, New Jersey & Canada: John Wiley & Sons.
   Google Scholar
• Bill, M. 1955. Robert Maillart. 2d ed. Zürich: Girsberger.
   Google Scholar
• Billington, D. P. 1979. Robert Maillart’s bridges: The art of engineering. Reprinted edition. Princeton, N.J: Princeton University Press.
   Google Scholar
• Block, P., and L. Lachauer. 2014. Three-dimensional (3D) equilibrium analysis of gothic masonry vaults. International Journal of Architectural Heritage 8 (3):312–35.
   Web of Science ®Google Scholar
• Boothby, T. E. 2015. Engineering iron and Stone: Understanding structural analysis and design methods of the Late 19th Century.
   Google Scholar
• Capecchi, D. 2012. Historical roots of the rule of composition of forces. Meccanica 47 (8):1887–901.
   Web of Science ®Google Scholar
• Chalmers, J. B. 1881. Graphical determination of forces in engineering structures. London: Macmillan & Co.
   Google Scholar
• Charlton, T. M. 1982. A history of theory of structures in the nineteenth century. Cambridge, London, New York, New Rochelle, Melbourne, Sydney: Cambridge University Press.
   Google Scholar
• Costa-Jover, A., J. Lluis i Ginovart, and S. Coll-Pla. 2017. Limit analysis and the study of building stages in masonry structures. Experiences with the gothic apse of tortosa cathedral (1345–1441). International Journal of Architectural Heritage 11 (4):475–89.
   Web of Science ®Google Scholar
• Cross, H. 1932. Analysis of continuous frames by distributing fixed-end moments. Transactions of the American Society of Civil Engineers 96 (1):1–10.
   Google Scholar
• Culmann, C. 1866. Die graphische Statik. 1st ed. Zürich: Verlag von Meyer und Zeller.
   Google Scholar
• Culmann, C. 1875. Die graphische Statik. Vol. 1, 2nd ed. Zürich: Verlag Von Meyer und Zeller.
   Google Scholar
• Cusano, C., A. Montanino, C. Cennamo, G. Zuccaro, and M. Angelillo. 2023. Geometry and stability of a double-shell dome in four building phases: The case study of Santa Maria Alla Sanità in Naples. International Journal of Architectural Heritage 17 (2):362–88.
   Web of Science ®Google Scholar
• D’acunto, P., J.-P. Jasienski, P. Ole Ohlbrock, C. Fivet, J. Schwartz, and D. Zastavni. 2019. Vector-based 3D graphic statics: A framework for the design of spatial structures based on the relation between form and forces. International Journal of Solids and Structures 167:58–70.
   Web of Science ®Google Scholar
• Du Bois, A. J. 1875. The elements of graphical statics and their application to framed structures. New York: John Wiley and Son.
   Google Scholar
• ETH-Archiv. 2018. Biographisches Dossier Ernst Suter (1884-) von Basel; PD für Methode der Festpunkte an der ETH. https://eth.swisscovery.slsp.ch/permalink/41SLSP_ETH/lshl64/alma99117435336605503.
   Google Scholar
• Fang, D. L., R. K. Napolitano, T. L. Michiels, and S. M. Adriaenssens. 2019. Assessing the stability of unreinforced masonry arches and vaults: A comparison of analytical and numerical strategies. International Journal of Architectural Heritage 13 (5):648–662. doi:10.1080/15583058.2018.1463413.
   Web of Science ®Google Scholar
• Fivet, C., and D. Zastavni. 2012. Robert Maillart’s key methods from the salginatobel bridge design process (1928). Journal of the International Association for Shell and Spatial Structures 53 (1):39–47.
   Google Scholar
• Fivet, C., and D. Zastavni. 2015. A fully geometric approach for interactive constraint-based structural equilibrium design. Computer-Aided Design 61:42–57.
   Web of Science ®Google Scholar
• Guldan, R. 1943. Rahmentragwerke und Durchlaufträger. 2nd ed. Vienna: Springer-Verlag Wien GmbH.
   Google Scholar
• Han, S., and D. Zastavni. 2022. A historical graphical analysis method for rigid frames. IASS/APCS 2022 Beijing Symposium: Next Generation Parametric Design, Beijing, China, September 19-22. https://www.ingentaconnect.com/contentone/iass/piass/2022/00002022/00000008/art00025.
   Google Scholar
• Han S., and D. Zastavni. 2023. Fixed-Points Method in Robert Maillart’s Analysis of Rigid Frame Bridges. In the International Conference on Structural Analysis of Historical Constructions (SAHC 2023), Kyoto, eds. Y. Endo and T. Hanazato, 68–77. Cham: Springer. doi:10.1007/978-3-031-39603-8_6.
   Google Scholar
• Hartz, C., M. M. Arek Mazurek, T. M. Tomás Zegard, and W. F. Baker. 2018. The application of 2D and 3D graphic statics in design. Journal of the International Association for Shell and Spatial Structures 59 (4):235–42.
   Google Scholar
• Henn. 1951. Ernst Suter, Die Methode der Festpunkte. ZAMM - Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 31 (8–9):299. doi:10.1002/zamm.19510310862
   Google Scholar
• Hirschfeld, K. 1959. Berechnung statisch unbestimmter systeme. In Baustatik: theorie und beispiele, ed. K. Hirschfeld, 171–684. Berlin: Springer. doi:10.1007/978-3-662-30166-1_5.
   Google Scholar
• Huerta, S. 2006. Structural design in the work of Gaudi. Architectural Science Review 49 (4):324–39.
   Google Scholar
• Karanikoloudis, G., P. B. Lourenço, L. E. Alejo, and N. Mendes. 2021. Lessons from structural analysis of a great gothic cathedral: Canterbury cathedral as a case study. International Journal of Architectural Heritage 15 (12):1765–94.
   Web of Science ®Google Scholar
• Kavanaugh, C., I. Mae Morris, R. Napolitano, and J. Jose Jorquera-Lucerga. 2017. Validating the use of graphical thrust line analysis for pier buttresses: The case study of amiens cathedral. International Journal of Architectural Heritage 11 (6):859–70.
   Web of Science ®Google Scholar
• Koechlin, M. 1889. Applications de la statique graphique. Vol. 1. Paris: Baudry et Cie, libraires-éditeurs.
   Google Scholar
• Kurrer, K.-E. 2018. The history of the theory of structures: Searching for equilibrium. Berlin: John Wiley & Sons.
   Google Scholar
• Levy, M. M. 1886. La statique graphique et ses applications aux constructions, Vol. 2, 2nd ed. Paris: Gauthier-Villars.
   Google Scholar
• Mohr, C. O. 1868. Beitrag zur theorie der holz-und eisenkonstruktionen. Zeitschrift des Architekten- und Ingenieurvereins zu Hannover 14 (19–51):397–400.
   Google Scholar
• Müller-Breslau, H. F. B. 1892. Die graphische Statik der Baukonstruktionen 2. vollständig umgearbeitete und wesentlich vermehrte Aufl. ed. Vol. 2.Leipzig: Baumgärtner’s Buchhandlung.
   Google Scholar
• Muttoni, A., J. Schwartz, and B. Thürlimann. 1996. Design of concrete structures with stress fields. Basel, Boston, Berlin: Birkhauser.
   Google Scholar
• Navier, C. L. M. H. 1833. Resume des lecons sur l’ application de la mecanique…ect. Paris: NP.
   Google Scholar
• Pillet, J. 1895. Traité de stabilité des constructions : Leçons professées au Conservatoire national des arts et métiers et a l’Ecole spéciale d’architecture, Cours techniques de l’architecte et du constructeur. Paris: En vente au dépot des cours techniques.
   Google Scholar
• Ramos, L. F., and T. Sturm. 2014. Seismic safety analysis of the old Portuguese cathedral in Safi, Morocco. International Journal of Architectural Heritage 8 (4):475–97.
   Web of Science ®Google Scholar
• Rankine, W. J. M., and V. L. Roberts. 1858. A manual of applied mechanics. 1st. ed. Encyclopaedia Metropolitana; or, System of Universal Knowledge: on a methodical plan/projected by Samuel Taylor Coleridge London: R. Griffin.
   Google Scholar
• Ritter, K. W. 1871. Die elastische Linie und ihre Anwendung auf den kontinierlichen Balken: ein Beitrag zur graphischen Statik. Zürich: Meyer und Zeller.
   Google Scholar
• Ritter, W. 1883. Die elastische linie und ihre anwendung auf den continuirlichen balken: Ein beitrag zur graphischen statik. Mit 12 textfiguren und 1 lithographirten tafel. Zürich: Meyer & Zeller (H. Reimmann).
   Google Scholar
• Ritter, W., and K. Culmann. 1900. Anwendungen der graphischen Statik. Dritter Teil. Der Kontinuierliche Balken 4 vols. Vol. 3. Zurich: Meyer & Zeller.
   Google Scholar
• Robin, R. C. 1933. A graphical solution of statcally indetermiant frames. Journal of the Institution of Engineers, Australia 5 (No. 5):145–60.
   Google Scholar
• Rondeaux, J.-F., and D. Zastavni. 2018. A fully graphical approach for limit state analysis of existing structures: Application to plane elastic-plastic bended structures and to plane masonry arches. International Journal of Architectural Heritage 12 (3):409–31.
   Web of Science ®Google Scholar
• Saliklis, E. 2019. Structures: A geometric approach. Cham, Switzerland: Springer.
   Google Scholar
• Sattler, K. 1969. Statisch unbestimmte Systeme. Festpunktmethode. In Lehrbuch der Statik: Theorie und ihre Anwendungen. Erster Band: Grundlagen und fundamentale Berechnungsverfahren, ed. K. Sattler, 357–87. Berlin, Heidelberg: Springer Berlin Heidelberg.
   Google Scholar
• Suter, E. 1916. Berechnung des kontinuierlichen Balkens mit veränderlichem Trägheitsmoment auf elastisch drehbaren Pfeilern sowie Berechnung des mehrfachen Rahmens mit geradem Balken nach der Methode der Fixpunkte. Berlin: Springer.
   Google Scholar
• Suter, E. 1923. Die Methode der Festpunkte. 1st ed. Berlin: Springer-Verlag.
   Google Scholar
• Suter, E., O. Baumann, and F. Häusler. 1932. Die Methode der Festpunkte zur Berechnung der statisch unbestimmten Konstruktionen mit zahlreichen Beispielen aus der Praxis insbesondere ausgeführten Eisenbetontragwerken. Berlin: Springer-Verlag.
   Google Scholar
• Suter, E., and E. Traub. 1951. Die Methode der Festpunkte. 3 ed. Berlin/Göttingen/Heidelberg: Springer Berlin, Heidelberg.
   Google Scholar
• Varignon, P. 1725. Nouvelle mecanique ou statique: dont le projet fut donné en MDCLXXXVII Vol. 2. chez Claude Jombert.
   Google Scholar
• Wolfe, W. S. 1921. Graphical analysis; a text book on graphic statics. 1st ed. New York, etc.: McGraw-Hill book company, inc.
   Google Scholar
• Zastavni, D. 2008. The structural design of Maillart’s chiasso shed (1924): A graphic procedure. Structural Engineering International 18 (3):247–52.
   Google Scholar