# Improving the Structural Behavior of Tied-Arch Bridges by Doubling the Set of Hangers
## 6 The Forked Arch  
As described in Sections 4 and 5, in V2 and N2 bridges, under the \(q_{2}\) load, the axial forces at the hangers attached at the same location of the arch are different. As has been shown, the orientation of the horizontal components of the axial forces makes the arch move towards the loaded side whereas the deck separates from it. As discussed in Section 5, the deck behaves as a beam with the same span as that of the arch subjected to vertical-axis bending, whereas the arch acts as a curved member in which torsion appears by coupling. However, the arch and the deck are rigidly connected at their ends, and, therefore, bending moments are developed at those intersections because the deck and the arch prevent each other from rotating. In the V2 bridge, the hangers are contained in vertical planes parallel to the \(Y\)-axis. That is, the hangers are not able to support part of the moment appearing in the arch-deck intersection, which is fully supported by the arch and by the deck. However, in the N2 bridge, the hangers, which are contained within diagonal planes with respect to the X-axis, do have some capacity to develop a force couple and support part of the moment. Therefore, it may happen that, in the N2 bridge, the hangers closest to the ends of the arch go into compression.  
To confirm this, Figure 26 shows, for the V2 and N2 bridges and for the \(q_{2}\) load, the axial forces \(P\) of the hangers, where \(P_{a}\) corresponds to the hangers closer to the loaded side and \(P_{b}\) to the nonloaded side of the deck. As can be seen, the axial forces \(P_{a}\) are, in general terms, higher. However, the most important aspect is that in the N2 bridge, the axial forces of two hangers near the ends go in compression, which indicates that, at each end of the bridge, the vertical-axis moment is partially resisted by the force couple generated by the hangers.  
This can be avoided by forking the arch (Figure 27) so that the bending moment shown in Figure 26 can be supported by a force couple, composed of a compressive and a tensile force, each one acting at each leg of the arch. An example of this Nielsen-type solution is the Montigny-Les-Cormeilles footbridge (Figure 28), designed by [PERSON]. In this footbridge, in addition, the deck section is made up of two longitudinal beams placed at the edges of the deck, tying the springing points of each leg of the arch (see [PERSON] et al. [22]).  
Although the problem of the hangers entering into compression is something inherent to N2-type bridges, there are also bridges with vertical cable arrangements where the arch has been forked, such as the Wittenberg Bridge, shown in Figure 4. In the Third Millennium Bridge (Figure 29b), in Saragossa (Spain), the forked tied-arch is made up of concrete and is attached to both edges of the deck ([PERSON] et al. [23]), whereas in the Barqueta Bridge (Figure 29a), the arch is made up of steel and attached to the axis of the deck ([PERSON] and [PERSON] [24]). However, in this case, beyond structural considerations, the intention of the designer, [PERSON], was to create a \"gate effect\" under the arch for the pedestrians entering the 1992 Seville Exhibition. Secondarily, when the arch is forked, its buckling length is reduced, as will be discussed in the next section.  
Figure 25: Axial forces at the hangers of a V2 bridge for a load on the edge of the deck as a function of the transversal stiffness of the arch: (**a**) \(I_{A,z}\approx 0\); (**b**) \(I_{A,z}\approx\infty\); (**c**) actual \(I_{A,z}\).  
Figure 27: Forked arch for vertical cable arrangement (**a**) and for Nielsen cable arrangement (**b**).  
Figure 26: Axial loads at hangers located at both sides for bridges N2 and V2 under \(q_{2}\) loading.