# The Diagonal Arch Bridge, a Particular Case of Spatial Arch Bridges
## 4 Structural Behavior  
One of the main features of SABs is that there are certain structural systems that remain inactive in a CAB but are activated for spatial configurations. In the particular case of DABs, the two bridges shown in Figure 28 have been compared to illustrate this fact. The main difference between the two bridges is that in the CAB (Figure 28a) the arch is aligned parallel to the centerline of the straight deck, whereas in the DAB (Figure 28b) the arch spans diagonally over the deck. Besides, in the DAB, due to the above-mentioned clearance restrictions, the hangers have been attached to one edge of the deck. Of the two possible hangers attached to the same point of the arch, the steeper one has been selected at each point, which causes the antisymmetrical distribution shown in the figure. Both bridges 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. The loaded width of the deck is \(b=8\) m. 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. It has also been assumed that the box has transverse ribs, although they have no influence on the overall 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, [PERSON] [17] or [PERSON] and Hirt [19]). Their dimensions are shown in Table 1.  
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 \(3\) 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 [20] (Figure 29). Figure 28: Reference bridges: (**a**) classical arch bridge (CABs) and (**b**) diagonal arch bridge DABs. The response of the bridges has been determined by applying the finite-element method. For this purpose, linear elastic analyses have been carried out under static loads. The models are three-dimensional, with six degrees of freedom per node, and are composed of linear members (\"frame elements\" in SAP2000 [21]). With respect to the in-plane bending moments' longitudinal bending (Figure 30), the behavior of bridges such as the CAB is well known, and the most adverse load case corresponds to \(q_{1}\) (Figure 29). The in-plane bending moments in this bridge have the well-known S-shape both at the arch (Figure 30a) and the deck (Figure 30b). The longitudinal bending in this bridge is defined by the projection of the axial forces of the hangers on the plane of the arch, i.e., in this case, their vertical components. The same occurs in the DAB, and the distribution of bending moments in the DAB in this case is very similar to that of the CAB. \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, \(t_{f}=t_{w}=30\) & \(2.0\times 10^{5}\) \\ Hangers & Solid circular & \(\O\) 80 mm & \(1.6\times 10^{5}\) \\ Deck & Rectangular hollow-box & \(5000\times 1000\) mm, \(t_{f}=t_{w}=20\) & \(2.0\times 10^{5}\) \\ \hline \hline \end{tabular} \({}^{1}\)\(t_{f}\), \(t_{a}\): thickness, respectively, of flanges and webs.  
\end{table} 
Table 1: Definition of reference bridges. Figure 30: In-plane bending moments under \(q_{1}\) load, for the arch (**a**) and the deck (**b**).