Fixed-Points Method in Robert Maillart's Analysis of Rigid Frame Bridges

Han, Shuyuan [UCL] Zastavni, Denis [UCL]

This paper explains Robert Maillart’s analysis approach – using the fixed-points method – for the Weissensteinstrasse Overpass that he designed in 1938. A brief history and a technical explanation of this method are also presented as back-ground information. The structure of this reinforced-concrete bridge consists of two identical rigid frames each with five degrees of static indeterminacy. This bridge was one of the few continuous bridges designed by Maillart. Its long-forgotten analysis method, the fixed-points method, is a geometrical method for the elastic analysis of continuous beams and frames, which addresses the static indeterminacy by means of geometric constraint of fixed points on bending moment diagrams. This method was invented by Christian Otto Mohr for analysing continuous beams [1], which was based on the work of Carl Culmann [2], and then refined and extended by Karl Wilhelm Ritter [3] for the analysis of frames. Ernst Suter then generalized and analytically formulated this method for complex cases [4]. In view of the historical context, this method is of special significance for the his-tory of graphic statics. The history and core techniques of this method, including fixed points, crossing-lines, distribution factor, and virtual lateral constrain, are all outlined. The techniques are illustrated with Maillart’s analysis of Weissensteinstrasse Overpass. REFERENCES [1] Mohr, C. "Beiträge zur Theorie der Holz- und Eisenkonstruktionen", Beiträge aus der Plasmaphysik, vol. 14, pp. 20-52, 397-400, 1868. [2] Culmann, K. (1875). Die graphische statik (Vol. 1). Meyer & Zeller (A. Reimann). [3] Ritter, W. Die elastische Linie und ihre Anwendung auf den kontinierlichen Balken: ein Beitrag zur graphischen Statik. Meyer und Zeller. (1871) [4] Suter, Ernst. Der Methode Der Fixpunkte. 1st ed. Springer-Verlag Berlin Heidelberg GmbH, (1923).