# Improving the Structural Behavior of Tied-Arch Bridges by Doubling the Set of Hangers
## 4 Structural Behavior of the Tied-Arch Bridge with Two Sets of Lateral Hangers  
In this section, two bridges, V2 and N2 (Figure 11), are analyzed, which differ from V1 and N1 respectively, in that they have two sets of hangers, each one attached to an edge of the deck. Obviously, the geometry of the cable arrangement must not interfere with the deck clearance in order to allow both pedestrian and vehicular traffic. Sometimes, this restriction may lead to the introduction of additional width in the deck. In this research, it has been assumed that the geometries shown in Figure 11 meet this requirement. The dimensions of the cross-sections and the hangers are the same as already defined in Table 1.  
Figure 12 compares the deflections for bridges V2 and N2 with those of bridges V1 and N1, already shown in Figure 8. For the asymmetric longitudinal load \(q_{3}\) (Figure 12), the deflections are virtually identical for models V1 and V2 and very similar for models N1 and N2. The difference can be attributed to the slight increase in the vertical rigidity of N2 with respect to N1 provided by the additional set of hangers. It should be noted that the Nielsen-type cable arrangement keeps the efficiency that has already been shown for the N1 when reducing deflections. However, regarding the deflections at the edge of the deck due to a live load on the half of the deck distributed over the entire span, such as \(q_{2}\), it is shown in Figure 13a that the deflections for bridges V2 and N2 are much smaller (about 50% for the bridges studied) than for the bridges N1 and V1 with central hangers, previously shown in Figure 9a. In fact, even if the torsional inertia of the deck is reduced to a mere 10% of its original value (Figure 13b), the deflections at the edge of the deck of bridges N2 and V2 are only moderately higher than those obtained for the original stiffness. This happens because, in the bridges with two sets of hangers, the torsion due to the eccentricity of \(q_{2}\) is not only supported by the deck, as it is the case in bridges V1 and N1, but also by the axial forces of the hangers attached to the edges of the V2 and N2 decks. The structural systems involved in this structural behavior are detailed in Section 5. Figure 14b shows how the torsion in the deck is lower in bridges N2 and V2 than in bridges V1 and N1. This is consistent with the mentioned fact that, in bridges N2 and V2, the deck resists only a fraction of the torsion under \(q_{2}\). Figure 11: (**a**) Model V2; (**b**) model N2; (**c**) cross-section. Figure 12: Deflections at the deck axis (and edges) for \(q_{3}\). Figure 13: Deflections at the axis and edge of the deck for \(q_{2}\). Deck torsional stiffness factored by (**a**) 1.0 and (**b**) 0.1. Since, under \(q_{2}\), the axial forces of the hangers attached to the same location of the arch are different, in bridges with two sets of hangers, the torsion in the deck causes out-of-plane bending in the arch (Figure 15a) and vertical-axis bending moments at the deck (Figure 15b). Note that this bending does not appear in bridges N1 and V1 neither at the arch nor at the deck (Figure 15). Similarly, in bridges V1 and N1, where the hangers are attached to the center of the deck, there is no reduction in torsion (Figure 14b). Torsion appears in the arch for \(q_{2}\) (Figure 14a) by coupling with the out-of-plane bending, as in any curved member. It appears when it is loaded by the out-of-its-plane components of the hangers. The transversal behavior of both the arch and the deck becomes evident when their transversal displacements are analyzed (Figure 16). In both N2 and V2 bridges, the arch gets closer to the loaded  
Figure 14: Torsion at the arch (**a**) and the deck (**b**) for \(q_{2}\). Figure 15: Bending under \(q_{2}\). (**a**) Out-of-plane bending at the arch. (**b**) Vertical-axis bending at the deck. area while the deck separates from it. It should be noted that for V1 and N1 there is no transversal displacement neither of the arch nor of the deck.