Pure geometrical consideration for bridge design in the early 20th century

By reviewing some of the reinforced-concrete structures built in the early 20th century, this paper questions the geometrical aspects surrounding their design. It is well established that in the case of Robert Maillart’s designs, he relied on the logic of thrust lines, as was the case for masonry bridges that were provided by funicular polygons and graphic statics. Maillart also relied on trial sketches to define the mechanical features of successive sections of the bridge and on geometrical considerations to define the line of his bridges. In the case of his stiffened arch bridges, geometrical considerations were confined to following with almost regular thickness the trajectory of the thrust line. However, for some of them and for the whole family of three-hinged arch bridges, formal and geometrical considerations applied, for which some rules are presented here, and their evolution can be seen over time. The challenge in the geometrical organization of concrete around the thrust line is to equilibrate the stresses and manage the group of possible thrust lines depending on various loading cases. A well-designed concrete geometry avoids tensile stresses, which guarantees relatively long-lasting structures. With Maillart’s approach, an almost completely geometrical approach to design is encountered, since forces are also managed by geometry within the scope of graphic statics. Regular geometries and isostatic and symmetrical structures guarantee the possibility of undertaking a complete analysis using graphical approaches. However, when hyperstaticity or lateral forces are taken into account, the analysis is not as straightforward. This paper examines the extent to which the geometrical approach provides answers to these issues, with various hypotheses such as elastic analysis or a plastic lower-bound approach. The paper concludes by questioning this approach to the design of concrete structures in the early 20th century and its relative interest for structural design today.