Graphical methods for continuous beams and frames : historical, pedagogical, and design approaches
(2025)
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- (en) This dissertation revisits and redevelops historical graphical methods for the elastic analysis of continuous beams and frames—currently a neglected branch of graphic statics. While graphic statics is renowned for its clarity and intuitive treatment of axial-force systems, its application to flexural, statically indeterminate structures has been largely overlooked in contemporary scholarship. Yet historical records reveal that between the late 19th and mid-20th centuries, several graphical methods were developed for analysing continuous beams and frames, most notably the fixed-points method and a group of trial-and-error-based methods collectively termed in this dissertation as the trial-closing-string methods. Despite their past prominence, these methods have largely faded from both practice and scholarship, leaving only fragmented accounts in contemporary literature. Furthermore, their potential for contemporary teaching and design remains largely unexplored. This research first reviews the historical development and rationale of these methods, with particular attention to the fixed-points method and the characteristic-points method within the trial-closing-string family. Building on this foundation, two graphical methods are proposed: Method I, an enhanced characteristic-points method, and Method II, a synthesis of the fixed-points method and Method I, both designed to provide a more intuitive, bidirectional representation of the relationship between stiffness and bending moments. Furthermore, they are accessible to architects and sufficiently versatile to handle complex frame structures. Implemented within interactive parametric environments, the pedagogical and design potential of the proposed methods is further explored. In teaching, Method I provides a dynamic graphical interpretation of classical displacement-based analysis methods, while Method II facilitates the development of intuition for stiffness–moment relationship. In design, both methods support parametric feasibility assessment, offering greater transparency, real-time bidirectional control, and clearer geometric constraints than conventional finite element method–based tools.
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Han, S. (2025). Graphical methods for continuous beams and frames : historical, pedagogical, and design approaches. https://hdl.handle.net/2078.5/276395