## 1 Introduction
In recent years, the directional and orthogonal effects in seismic response of structures have been studied by some researchers to predict the critical angle of excitation for seismic analysis. To account for directivity effects some studies recommend applying the ground motion records in two perpendicular directions and combining the results using a combination rule (e.g., 100-30 percentage rule, 100-40 percentage rule and Square Root of the Sum of the Squares (SRSS) method) to somehow account for the uncertainty due to directionality effects. Such combination rules are often based on experience and have no theoretical basis. Therefore, the use of such rules may result in an underestimation of the seismic response for different structures. [PERSON] and [PERSON] [5] in 1997 proposed a simple method to determine the critical angle of seismic incidence and the corresponding peak response of structures subjected to two horizontal components applied along any arbitrary directions for elastic response spectrum analyses. [PERSON] and [PERSON] [6] in 1998 developed a new general combination rule for the multi-component excitation called complete quadratic combination with three components (CQC3) and showed that the use of this rule results in improved predictions. [PERSON] et al. [7] in 2000 developed a formula, using the CQC3 method, to predict the maximum response of structures in a multi-component response spectrum analysis. [PERSON] et al. [8] in 2002 proposed a design procedure for predicting the critical direction and maximum responses under bi-directional seismic excitations. [PERSON] [9] in 2005 showed that imposing ground motions with various incident angles may increase the maximum response of structure up to 80%. [PERSON] and [PERSON] [10] in 2007 concluded that applying ground motion records with different angles can result in up to 60% difference in prediction of the engineering demand parameters (EDPs) in asymmetrical buildings. [PERSON] and [PERSON] [11] in 2006 investigated the orthogonal effects in linear seismic analyses of skewed bridges using three ground motion records and compared the predictions of different combination rules. They concluded that the use of 100-40% rule was satisfactory only for the response spectrum analysis, while for the linear time history analyses none of the combination rules were able to predict the maximum response obtained using three records. All studies mentioned so far investigated the directivity effects using elastic analyses. [PERSON] and [PERSON] [12] in 2010 evaluated the importance of orthogonal effects in nonlinear time history analyses of single-span straight bridges using three ground motion records and demonstrated that nonlinear analyses are more sensitive to the directivity effects than are linear analyses. Similar results for the use of nonlinear analyses were observed in a study by [PERSON] and [PERSON] [13] in 2013. In a study by [PERSON] and [PERSON] [14] in 2011 the use of different combination rules such as the 30% rule, the 40% rule and the SRSS rule for the prediction of maximum response was investigated. The result of that study indicated that the use of these combination rules with nonlinear analyses performed using pairs of records tends to overestimate the predicted maximum response. The use of combination rules was recommended for 2D analyses performed using the horizontal component of ground motion (the component with the larger PGA) in each principal direction of the bridges [14]. [PERSON] et al. [15; 16] in 2011 investigated the use of combination rules for the seismic evaluation of two span bridges, located in different cities with different seismicity levels, and concluded that different combination rules may be appropriate for different locations (i.e., the use of 100-20% and 100-40% for bridges in different regions were recommended, rather than using 100-30% rule for all structures). [PERSON] et al.