# Influence of Multiple-Support Excitation on Seismic Response of Reinforced Concrete Arch Bridges
## 2 Prototype Bridges  
### Bridge Prototypes Description  
Numerical models represent bridges of layout, material properties and cross-sections dimensions that are verified for persistent design situations [35]. Analyzed bridges were of arch spans L = 100 m, 200 m, 300 m and 400 m with the rise to span ratio of 0.2 (Figure 3) and shaped as catenary with constant springing to crown load ratio. Deck spans were between 28 m and 33.5 m for all bridges. Three different sets of bridge layouts were analyzed in order to investigate the influence of dynamic properties of the structural system on the seismic response to multiple-support excitation. In the first set, the connection between spandrel columns and the superstructure is hinged (provided by fixed bearings), the connection is fixed in the second set, while in the third one it is also monolithic but the arch is additionally stiffened (using large cross section) in order to analyze the influence of the arch stiffness on bridge response. It was assumed that superstructure is connected to abutments by longitudinally movable bearings. Bridges are founded on a good-quality rock (corresponding to  
Figure 2: Relative arch displacements due to the uniform and multiple-support excitation [10].  
ground type A according to Eurocode 8 [36]). It is important to mention that bridges with different site conditions were not studied and local site effect was not accounted for.  
Figure 4 presents cross sections of the bridge. The superstructure, spandrel columns, portal columns and arches are of cell-box type cross sections with constant dimensions given in Table 1. The designed concrete grade for the arch and superstructure is C45/55 and C35/45 for the columns [37]. Diaphrags are placed inside the arch under spandrel columns. Their width is equal to the width of spandrel columns that they support. The arch is connected to arch abutments by a diaphragm.  
Figure 4: Cross sections of the bridges: (**a**) Spans L = 100 and 200 m; (**b**) Spans L = 300 and 400 m.  
Figure 3: Layout of analyzed bridges.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **Arch Outer** & **Arch Outer** & **Arch inner Web** & **Arch Chord** & **Column Outer** & **Thickness of** & **Portal Outer** & **Portal Chords** \\
**Span L [m]** & **Dimensions d** & **Web Thickness** & **Thickness c\({}_{\text{q}}\)** & **Thicknesse\({}_{\text{q}}\)** & **Dimensionsd\({}_{\text{q}}\)** & **the Column** & **Dimensionsd\({}_{\text{p}}\)** & **Thickness c\({}_{\text{p}}\)** \\  & \(\times\) h [m] & **b\({}_{\text{b}}\) [m]** & **[m]** & **[m]** & \(\times\) h [m] & **Chords c\({}_{\text{c}}\) [m]** & \(\times\) h [m] & **[m]** \\ \hline
100 & 10 \(\times\) 2 & 0.30 & 0.30 & 0.45 & \(3.0\times 1.5\) & 0.30 & \(4.0\times 2.0\) & 0.50 \\
200 & 10 \(\times\) 3 & 0.50 & 0.30 & 0.50 & \(5.0\times 2.5\) & 0.30 & \(6.5\times 3.5\) & 0.50 \\
300 & 11 \(\times\) 5 & 0.50 & 0.50 & 0.50 & \(5.0\times 2.5\) & 0.30 & \(6.5\times 3.5\) & 0.50 \\
400 & 12 \(\times\) 7 & 0.60 & 0.60 & 0.60 & \(5.0\times 2.5\) & 0.30 & \(6.5\times 3.5\) & 0.50 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Cross-section dimensions of arches and columns.