Contents lists available at ScienceDirect Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn Estimating seismic response under bi-directional shaking per uni-directional analysis: Identification of preferred angle of incidence Aparna Roy a , Atanu Santra b , Rana Roy c, ⁎ a Research Scholar, Department of Civil Engineering, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India b Research Scholar, Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India c Professor, Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India ARTICLE INFO Keywords: Bi-directional Reinforced concrete Near-fault Far-fault Energetic length scale Characteristic intensity Combination rule ABSTRACT Implications of incidence angle of ground motions on inelastic demand of bridge piers under bi-directional seismic excitation have been studied against the corresponding uni-directional counterparts. Recognizing that the bi-directional analysis is complex and computationally intensive, to improve the use of less-rigorous uni- directional analysis, present study identifies the most and the least preferred orientations for a given pair of horizontal ground motion. We define the most and least preferred orientations, where the difference between bi- directional and uni-directional response is respectively minimized and maximized. These orientations can be uniquely identified for both peak and cumulative demand in terms of appropriate ground motion parameters (energetic length and characteristic intensity respectively for peak and cumulative demand) independent of structural properties. It has been shown that the improved estimate of bi-directional response may be obtained from simplified uni-directional analysis by utilizing these preferred incidence angles in conjunction with ap- propriate combination rules (30% for peak and 40% for cumulative demand). 1. Introduction In the event of an earthquake, bridge piers are excited pre- dominantly by a pair of orthogonal components in the horizontal plane, while vertical (and rotational) component of motion may not be sig- nificant. Stronger vulnerability of structures under bi-directional shaking relative to that under uni-directional excitation has been de- monstrated in numerous studies [e.g., 1–4]. The phenomenon of bi- axial bending, its practical implications and the associated difficulties in the mathematical simulation are apparent from the excellent works of Sfakianakis and Fardis [5,6]. Consequence of this interaction in re- inforced concrete (RC) bridge piers has recently been studied by Sen- gupta et al. [7] under near-fault motions. This study, likewise majority of the related earlier works, has applied the as-recorded horizontal components of motions along two principal axes of pier. It is important to note that in strong-motion database, horizontal components of motions are generally available along orientations of recording which are often arbitrary. Such recorded horizontal compo- nents are usually applied along two principal axes of the structure. Thus it is often presumed that the arbitrarily placed recording sensors (often oriented in north-south, i.e., N-S and east-west, i.e., E-W directions) are aligned with the principal axes of the structures. The limitations of this simplification are apparent from the seminal contributions of Penzien and Watbe [8], Boore et al. [9] and have been restated by Kalkan and Kwong [10]. The issue of angle of incidence by rotating ground motion pairs has been investigated in different contexts by many researchers using re- sponse spectrum method [e.g., 11–14] as well as response history analysis in linear [e.g., 14–20] and nonlinear range [e.g., 10,18–27]. Critical earthquake direction has been established by Anastassiadis and Avramidis [11], Lopez and Torres [12] and Anastassiadis et al. [13] using response spectrum method; while Lopez et al. [28] investigated the critical response of structures to multicomponent earthquake ex- citation. Kostinakis et al. [26] observed that the critical angle de- termined elsewhere [15] in the linear range may also result in some improvement of responses in nonlinear range. Extensive studies [18,19] on post-elastic range response of symmetric and asymmetric buildings have recommended, especially when M w > 7.0, to adopt the maximum response computed by rotating near-fault motions (within 15 km) to fault-normal/fault-parallel as well as maximum direction [29]. Detailed investigation [30,31] per nonlinear response history analysis have broadly concluded that the incidence angle resulting in maximum https://doi.org/10.1016/j.soildyn.2017.12.022 Received 4 September 2017; Received in revised form 15 December 2017; Accepted 15 December 2017 ⁎ Corresponding author. E-mail addresses: aparnauit@gmail.com (A. Roy), atanu.juce@gmail.com (A. Santra), rroybec@yahoo.com (R. Roy). Soil Dynamics and Earthquake Engineering 106 (2018) 163–181 0267-7261/ © 2017 Elsevier Ltd. All rights reserved. T