In these cases, the so-called spatial arch bridges, their structural behaviour extends from the original vertical plane to a three-dimensional configuration. For single arch bridges with only one deck, this spatial behaviour emerges, mainly, in the following cases:

• when arch springing and deck abutment are not at the same location.
• if the arch (or deck) is curved in plan.
• if the arch is out of the vertical plane of symmetry of a straight deck.
• in the case where the arch plane is leaning away from the vertical plane or rotated around a vertical axis.
• if the arch axis is an out-of-plane curve.

This paper presents a new iterative method that has been developed in order to find antifunicular out-of-plane shapes of arches [1]. These three-dimensional compression-only shapes appear when out-of-plane loads act upon the arch, for example, when the deck is curved in plan.

The method solves the most general case, where clamped ends and non-linear behaviour can be considered. Detailed formulation for this case is presented. The method can be used both for upper and lower deck arch bridges.

An alternative uncoupled formulation is also justified and shown. If this formulation is used, antifunicular shapes can be obtained for one bending direction, and, if desired, any other geometrical restriction may be imposed on the other direction. It can be very helpful to minimize internal forces in plane arches, both vertical and inclined.

The antifunicular forms obtained depend heavily on the arch-deck transversal relative position. The effect of the relative transversal position over the form is shown.

Since the method presented generalizes methods previously developed for plane arches, the vertical plane arch (i.e. the "classical" arch bridge) can be considered as a particular case of spatial arch bridge.

Compression-only shapes returned by the algorithm are not only highly efficient from the structural point of view, but also aesthetically challenging.

It can also be easily adapted for finding out-of-plane shapes of tension elements or cables when uniform and/or point loads act upon them.

1

J.J Jorquera Lucerga, "A study on Structural Behaviour of Spatial Arch Bridges", (In Spanish), PhD Thesis, Polytechnic University of Madrid, 2007. http://oa.upm.es/812/

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