# Improving the Structural Behavior of Tied-Arch Bridges by Doubling the Set of Hangers
## 2 Reference Bridges and Considered Load Cases  
The bridges shown in this paper are based on the reference bridges shown in Figure 5. As mentioned above, not only has a vertical center cable arrangement been considered but also a Nielsen-type layout (with inclined V-shaped hangers, such as the diagonal members of a curved-upper-chord truss, Figure 5b) because of its known effectiveness in reducing deflections and forces in classical vertical planar tied-arch bridges with one central set of hangers. The reference models have a span \(L=100\) m and a rise \(f=20\) m. The spacing between anchorages of the hangers in the deck is \(s=5\) m and \(s=10\) m for V1 and N1, respectively. The loaded width of the deck is \(b=8\) m. The bridge is assumed to have a relatively common configuration and, therefore, the cross-section of the arch is assumed to be an all-steel hollow-box section, whereas the cross-section of the deck is assumed to be a composite steel-concrete section composed of a steel box section and a reinforced concrete slab. Each end of the arch is fully fixed to the deck. The box has also transversal ribs, although they have no influence on  
Figure 4: Wittenberg Bridge over the Elbe River. Left: Forked railway tied-arch bridge with two sets of lateral hangers. Right: Road bridge with single central set of hangers. Photo: [PERSON]. Wikimedia Commons. the global structural behavior. The self-weight of the concrete slab has been considered as part of the permanent loads, and the mechanical properties of the cross-section of the deck are, in a simplified way, assumed to be those of the hollow all-steel box cross-section described in Table 1. These dimensions are inspired by real arch bridges and are relatively common (see for example Leonhardt [14] or Lebet and Hirt [15]). All the bridges studied have been preliminarily designed according to Eurocode 3-2 [16]. The dimensions are shown in Table 1.  
In the studied bridges, the stiffness of the cross-section of the hangers is a more restrictive criterion than the failure and serviceability checking. Therefore, the same cross-section has been used for all the hangers. A sensitivity study has been carried out for the V1 model to obtain the minimum diameter of the hangers from which it can be considered that the ratio between the arch and the deck deflections is close enough to one. When this situation occurs (the so-called \"curtain effect\"), the loads are effectively transferred from the deck to the arch without increasing the deck forces and deflections too much. Details of a similar study can be found in [13]. With the objective of illustrating the studied structural behavior, the following load cases have been considered in this study:  
* The self-weight (\(SW\)) of the bridge, evaluated for a specific weight of 78.5 kN/m\({}^{3}\), and a dead load (\(DL\)), with a value of 3.75 kN/m\({}^{2}\). * Three downward pedestrian live loads distributions, \(q_{1}\), \(q_{2}\), and \(q_{3}\), which correspond to the LM-4 load model defined in Eurocode 1-2 [17] (Figure 6a). * The wind load (\(W\)) (Figure 6b) has been considered in a simplified way, as an equivalent static transversal loading (parallel to the Y-axis) of 2 kN/m, acting both at the centroids of the cross-sections of the arch and the deck. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structural Element** & **Cross-Sections** & **Size 1** & **Young’s Modulus (N/mm2)** \\ \hline Arch & Square hollow-box & \(1250\times 1250\) mm, & \(2.0\times 10^{5}\) \\ Hangers & Solid circular & \(\mathcal{O}\) 80 mm & \(1.6\times 10^{5}\) \\ Deck & Rectangular hollow-box & \(5000\times 1000\) mm, & \(2.0\times 10^{5}\) \\  & & \(t_{f}=t_{w}=20\) mm & \(2.0\times 10^{5}\) \\ \hline \hline \end{tabular}  
* \(t_{f}\), \(t_{w}\): thickness, respectively, of flanges and webs.  
\end{table} 
Table 1: Definition of reference models. Figure 5: Reference models for a central set of hangers attached to the centerline of the deck: (**a**) vertical hangers; (**b**) Nielsen-type hangers; (**c**) cross-section.