## 1 Introduction
[17] in 2011 demonstrated that the significance of orthogonal effects in bridge structures depends on the structural properties as well as the number of ground motion records used in the analysis. The directionality effects on the probability of exceeding different damage states and fragility curves have also been studied by some researchers. [PERSON] and [PERSON] [18] in 2011 concluded that the critical angle of seismic excitation does not coincide the principal orthogonal axes of bridges and ground motion directionality is an important parameter in predicting the probability of damage. [PERSON] and [PERSON] [19; 20] in 2012 and 2014 demonstrated that ground motion directionality effects can influence the median fragility values by 66%. A study by [PERSON] and [PERSON] [21] in 2015 demonstrated that the orthogonal effects have a more significant influence on the fragility curves of individual components of the bridge compared to the fragility of the bridge system. A study by [PERSON] and [PERSON] [22] in 2015 on regular buildings demonstrated that the maximum engineering demand parameter (EDP) values were increased up to 39% when both the effects of ground motion directionality and spatial distribution of EDPs were considered simultaneously. In recent years more researchers studied the influence of incident angle of ground motion records on fragility analysis of different types of bridges using different modelling assumptions (e.g., [21; 23; 24; 25; 26; 27; 28; 29]). The results from these studies indicate that the incident angle of the ground motion records may have a significant influence on the seismic demands in critical components of the bridge, especially in irregular, skewed or horizontally curved bridges and therefore, the seismic fragility of a bridge may be underestimated when the directionality effects are ignored. While fragility analysis of bridges provides valuable information regarding the probability of damage expected due to directionality effects for existing bridges, more research should be focused on the methods currently used for analysis and design of bridges by codes to properly address the directionality effects in predicting mean seismic demandsfor seismic design of different types of bridges. One of the key points that is missing in the literature is the fact that the maximum displacement of columns does not necessarily occur in the direction of the principal axes of the bridge, while in most analyses performed in practice and research only displacements along the principal axes of the structures are reported and used for evaluations. This is because current available programs for structural analysis typically report the results only for such principal axes (i.e., X and Y directions). In this research in addition to the displacements in the principal axes of the bridges, the actual maximum displacement of the columns during the time history analysis is predicted by determining the vectorial combination of the displacements in X and Y direction for each time step in the analysis (referred to as the radial displacement) to evaluate different methods. In addition, an advanced averaging technique based on the recommendations by [PERSON] et al. [1] is used to predict the responses of columns in different directions from 0 to 360\({}^{\circ}\). It is noted that the resulting radial displacement differs from the incident angle for the application of earthquake records (i.e., incident angles from 0 to 180\({}^{\circ}\)). In fact, both directivity effects due to application of records in different directions and effects of maximum displacement of columns occurring in different directions for different records are considered in this research to predict the mean seismic response. The combination of these effects have not been considered in the past.