## 1 Introduction  
Nonlinear dynamic analysis is widely used for predicting the seismic response of structures and it is typically performed using either 2D or 3D structural models. Different methods for applying ground motion records are observed for performing 2D and 3D analysis. This research is intended to investigate and compare the results obtained using different methods currently used in research and practice. Some issues are not very well addressed in seismic codes, including the effects of directivity of records in 2D and 3D analysis, the use of different combination rules for prediction of inelastic displacements and the methods for predicting the mean response of structures subjected to a number of records at different incident angles. In design, it is often assumed that the seismic response of straight bridges is independent in the two orthogonal directions and therefore the seismic responses in the two principal directions can be predicted using 2D analysis with the application of horizontal components of the ground motion records applied separately in the transverse and in the longitudinal directions (e.g., [1]). In addition, different methods are available to predict the mean values of seismic demands when structural models are subjected to seven or more records. The use of different averaging methods for the prediction of the mean response of bridges (i.e., averaging the maximum absolute value displacements and averaging the displacements in different directions) is investigated in this study and the predictions from different methods are compared. Seismic analysis results, including the maximum responses, are typically obtained only for the two perpendicular principal directions of a structure. As a result, the actual maximum vectorial displacement, referred to as the \"radial displacement\" in this paper, for each record is not predicted during the analysis. The radial displacement, \(\Delta_{i}\), at each time interval \(i\), is calculated according to \(\Delta_{i}=\sqrt{\Delta_{ix}^{2}+\Delta_{iy}^{2}}\), where \(\Delta_{ix}\) and \(\Delta_{iy}\) are the displacements in the \(x\) and \(y\) directions, respectively. Therefore the maximum overall displacements are often estimated using the 30% rule (i.e., the combination of 100% response in one direction with 30% of response in the perpendicular direction) or the square root of the sum of the squares (SRSS) combination of the results from the two principal axes of the structure (e.g., [2; 3]). The use of such combination rules is an attempt to account for the fact that the maximum displacements in the two principal directions do not occur at the same time. In this study the radial displacements of the bridge columns are determined by post processing the analysis results at each time step (small time steps were considered for this purpose). As a result, the maximum radial displacements (i.e., actual seismic demands) are determined for each record and the results are compared to the predictions obtained using the simplified methods such as the 30% combination rule. It is noted that only the horizontal displacements of columns are considered in this paper, since the vertical displacements are negligible. It is customary to apply the ground motion records in the principal axes of the structure with no attempt to investigate the variation of the seismic responses as the direction of the applied records changes. This issue is particularly important for bridges, because the seismic responses of the bridges in the transverse and longitudinal directions are typically significantly different. One of the important parameters that should be considered in seismic analysis and design of bridges is the direction of the input ground motions. [PERSON] and [PERSON] [4] demonstrated that since the location of the epicenter of an earthquake is unknown, the direction of the applied earthquake excitations cannot be predicted.