The importance of the shape of arches in arch bridges

The aim of the article is to show the importance of the anti-funicular geometry of the arch in tied-arch bridges. The concrete tied-arch resembles a prestressed unbonded structure when tie tendons and adjustable hanger cables are used. In the study the hanger cables are assumed vertical.
The form of the arches has been of interest to Architects and Engineers through the ages. The mathematical solution to the catenary curve was successfully solved in the late 17th century. Interest in arch bridge constructions has increased recently. The traditional arch forms of circle and parabola do not represent optimal geometry of bridge arches. The comparative calculations of a concrete tied-arch footbridge with a span length of 100 m by using different arch forms awakes the reader to notice the importance of the geometric shape of the arch.
This paper presents the formulae of circle, parabola, catenary and constant stress arch. The visual difference of the arches is demonstrated in the article by exact drawings.
An iterative application of graphical statics and vector algebra quickly results in the momentless and also constant stress shape of the arch for the permanent loads. The final arch geometry can be fine-tuned by the weights of the dimensioned cross-sections of the arch rib and stiffening girder.
Based on the study circle shape leads to the most uneconomical solution. The parabolic arch shape, and also the pure catenary arch shape, result in significant bending moments because of combined effect of weights of arch rib and stiffening girder. The final arch geometry and cross-sections are obtained as momentless arch by using the final weights.