Illustrative Example of the Shape of Arch in Tied-Arch Bridges

Finding the shape of a structure has evolved into a good design practice when alternative solutions are considered in the early stages of design. Form-finding of the moment-less tied arch can be based on initial main dimensions, loads and forces. The cross-sections are not needed, as this is not yet the final design phase. The burden of unnecessary variables consumes only the time of the designer. This study shows the power of graphical static calculation to iterate the anti-funicular tied-arch bridge. An example calculations of a light traffic tied-arch bridge, with a variable deck weight, is presented. The steel arch is placed on the center line of the bridge. The constant stress shape of the arch and material quantities of the arch, hanger cables and tie tendons are calculated. The assumed preliminary geometry of the bridge, the weight of the deck and the selected stress values of the arch, tie tendons and hangers are given as input variables. Stability of the arch has not been studied. It has been expected that the selection of the stress value used for the arch covers the problem of the stability. The results, when comparing the iterated constant stress arch to the respective parabolic arch, reveal the importance of the shape of the arch.