# Influence of Multiple-Support Excitation on Seismic Response of Reinforced Concrete Arch Bridges
## 1 Introduction
The authors concluded that the multiple-support excitation significantly increases the longitudinal force in the arch, even exceeding its load-bearing capacity. The similar conclusion was reached by authors of [30] in which the response of several smaller-span reinforced concrete arch bridges was investigated and in [33] where authors considered only the wave-passage effect on the response of a reinforced concrete arch bridge of long span. It may  
Figure 1: Principal forms of spatial variability of ground motion [12]. be observed that no systematic study of the response of reinforced concrete arch bridges of large spans to multiple-support excitation may be found in literature. It is common knowledge that the response to multiple-support excitation differs from uniformly excited response. Due to relative displacements of the supports, a quasi-static component of the response is induced, while dynamic component of the response also changes because different eigen-modes are excited to modes excited by uniform excitation. For instance, in symmetrical arch bridges, uniform excitation in the longitudinal direction of the bridge excites only the antisymmetric vibration modes, while in the case of multiple-support excitation, both symmetric and antisymmetric modes are activated (Figure 2), including the higher modes, which should not be neglected in the analysis. It is interesting to mention studies presented in [19; 34], despite the fact that a cable-stayed bridge (not an arch one) was studied. On the basis of monitoring a real structure (free-field and on-structure recordings) it was revealed that the asynchronous excitation of a bridge excited higher modes of vibration while suppressing the oscillation in its fundamental frequency. To summarize, in the research community there is still no consensus whether the multiple-support excitation phenomenon is favorable or detrimental for seismic response of structures, because it depends on many parameters, including the excitation features, soil characteristics and dynamic characteristics of excited structure. Therefore, the objective of this paper is to study its effect on seismic response of long-span reinforced concrete deck arch bridges, the structural system which has not yet been investigated in detail regarding this effect. This study contributes to better understanding of seismic behavior of these structures and it aims to give guidelines whether the multiple-support excitation should be considered for seismic analysis of bridges of similar structural systems and spans. Analyses were conducted using state-of-the art methodologies and tools on bridge prototype numerical models of different spans. The methodology for conducted research is described in detail in [12], but for the legibility and clarity of the paper, the most important features will be repeated herein. Detailed analysis results presented in this paper showed that multiple-support excitation had an unfavorable effect on the seismic behavior of analyzed bridges. Hence, this phenomenon should be considered in the design of bridges of similar layouts.