Optimal arch shape for tied-arch bridges

Thesis event information

Date and time of the thesis defence

Place of the thesis defence

Remote connection: https://oulu.zoom.us/j/61675276755

Topic of the dissertation

Optimal arch shape for tied-arch bridges

Doctoral candidate

Lic.Sc., (Tech), M.Sc., (Tech) Esko Järvenpää

Faculty and unit

University of Oulu Graduate School, Faculty of Technology, Structures and Construction Technology Research Unit

Subject of study

Civil Engineering


Professor Anssi Laaksonen, University of Tampere


Professor Antti Niemi, University Of Oulu

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Optimal arch shape of tied arch-bridges substantially improves the economy of the bridge

The results of the dissertation on the optimal shape of the arch for tied-arch bridges show that the momentless form of the arch and its cost-optimal height leads to significant cost savings for arch structures.

Known in history are the variations of the circular shapes of the bridge arches of the Roman Empire. The scientific basis for the shape of arches was obtained with the development of differential and integral calculus in the mid-17th century, when the analytic formula for the catenary arch based on the hyperbolic cosine function was derived.

In this study, new key figures have been solved for the parabolic, catenary and constant-stress arch. The theoretical maxima of the span lengths of the arches for the self-weight of the arch are obtained by using constant-stress arch. The extreme span lengths of the constant-stress arch are significantly longer than the span lengths of the parabolic and catenary arches. The study does not address the circular arch, as it has been found to be an almost inefficient shape of the bridge arch, despite its good aesthetic properties.

The parabolic arch has generally been considered the best bridge arch shape. Research shows that the optimal shape of an arch is determined by the load carried by the arch. In tied-arch bridges, the optimal shape of the arch is obtained by calculating the momentless shape of the arch using the permanent load of the bridge. An iterative algorithm for calculating the shape and the material quantities of the arch has been developed in the study.

The cost of bridge arch structures has been calculated by considering the effect of arch height as a cost-increasing factor. The results show that the momentless constant-stress form of the arch is decisively more efficient than the shape of the parabola or the catenary.

The study shows that the cost-optimal heights of bridge arches are higher than the heights normally used. According to the study, the optimal height ratio l/h of the arch changes from 2.8 to 4.4 as the span of the bridge lengthens from 100 meters to 700 meters. Conventionally, the values of 5–7 are used as the rise ratios. The research results are based on steel-structure arches with vertical hanger cables.

The results of the study can be used in the design and construction of arch bridges to improve the economy, aesthetics and environmental sustainability of arch bridges.
Last updated: 22.4.2021