Constructing and adjusting bending moment diagrams and elastic curves with graphic statics

Han, Shuyuan;Zastavni, Denis
(2019) RESEARCH SEMINAR UCLOUVAIN-ETH-EPFL-SOM — Location: VIERVES-SUR-VIROIN, BELGIUM (28.August.2019)

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This paper reviews the historical methods of constructing bending moment diagrams and deflection curves with graphic statics. A design-oriented development is then suggested to enable users to directly adjust these diagrams. The current mainstream of studies on graphic statics pays limited attention to bent or hyperstatic structures. However, explorations of these issues played an important part in the history of graphic statics. Dating back to Die graphische Statik, Carl Culmann proposed a wholly graphical method for constructing bending moment diagrams with funicular polygons. It was developed by Christian Mohr and other researchers to construct deflection curves. these methods clearly present the entire analysis process and the relation between diagrams and design variables in the same drawing, which has a cognitive value. Nevertheless, these methods were devised only to analyze and verify pre-set structures rather than reset them. the paper develops this method to make the constructed moment diagrams and deflection curves adjustable. The original methods thereby obtain the capacity to redistribute loads and vary moments of inertia of cross-sections according to the adjustment.
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Han, S., & Zastavni, D. (2019). Constructing and adjusting bending moment diagrams and elastic curves with graphic statics. RESEARCH SEMINAR UCLOUVAIN-ETH-EPFL-SOM, VIERVES-SUR-VIROIN, BELGIUM. https://hdl.handle.net/2078.5/108420