Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct Effect of incidence angle on the seismic performance of skewed bridges retrofitted with buckling-restrained braces Yuandong Wang a, ⁎ , Luis Ibarra b , Chris Pantelides b a BHB Consulting Engineers, Salt Lake City, UT 84115, USA b Department of Civil and Environmental Engineering, University of Utah, Salt Lake City, UT 84112, USA ARTICLE INFO Keywords: Incidence angle Retrofit Skewed bridge Buckling-restrained brace Far-field and near-field earthquake Maximum response ABSTRACT This study examines the effect of ground motion (GM) incidence angles on the seismic response of skewed bridges retrofitted with buckling-restrained braces (BRBs) under far-field and near-field ground motions (FFGMs and NFGMs). Bridge models for a three-span reinforced concrete bridge with skew angles of 0°, 18°, 36°, and 54° are used as a case study. Three-dimensional nonlinear dynamic analyses are performed with scaled GMs under 11 incidence angles (from 0° to 180°) to obtain the maximum bridge response parameters on the maximum considered earthquake hazard level. This study demonstrates the effectiveness of a BRB retrofit to reduce the influence of GM incidence angle. The results indicate that skewed bridges are less sensitive to the GM incidence angle and BRBs further decrease the incidence effect. Also, the seismic response under different GM incidence angles is more predictable when the bridge is subjected to FFGMs. In general, the maximum response of skewed bridges could be estimated by applying the scaled principal GMs along the bridge’s longitudinal axis and its orthogonal direction (i.e., 0° and 90°), regardless of GM characteristics, skewed angle, and BRB retrofit. 1. Introduction Skewed bridges are more vulnerable during seismic events due to the lack of orthogonality in the longitudinal and transverse bridge di- rections, and because deck rotation may lead to higher demand on the bridge bents and abutments [1]. The bents and shear keys of a skewed bridge might experience loads that exceed their yield capacity, and develop nonlinear behavior under the design basis earthquakes (DBEs). The abutment backwall of skewed bridges could generate asymmetric passive soil resistance that causes deck ends to “bounce” off the abut- ment seat in the skew direction of a bridge. In a seismic analysis, the orthogonal horizontal accelerations are usually applied in the major axes of the investigated structure, if these axes are orthogonal. The principal ground motion (GM) directions are commonly recommended because they are uncorrelated [2], but they are rarely recorded, because the instrumentation is often aligned with geographic coordinates or the structure’s orientation. In response spectrum analysis, combination results for orthogonal earthquake ef- fects are used to assess the structural response, such as the 100-30-30 and the 100-40-40 percent rule, the square root of the sum of squares (SRSS) method, the complete quadratic combination (CQC) method, and response envelopes [3–5]. The 100-30-30 and 100-40-40 rules are simple methods in which 100 percent of the maximum seismic force is applied in one direction, whereas only 30 or 40 percent of the corre- sponding maximum seismic forces are applied in the other two ortho- gonal directions [6,7]. Although the SRSS and CQC methods are derived from random vibration theory, they are still approximations that should provide more conservative results than time history analyses (THAs), because the maximum responses in each orthogonal direction occur at different times [8,9]. For THAs of skewed bridges, previous studies show discrepant re- sults on the effect of GM incidence angle on bridges. Maleki and Bisadi [8] recommended applying each set of GM horizontal accelerations in at least three incidence angles of 0°, 60°, and 120° to capture the maximum seismic response. Similar studies also concluded that even though GMs applied in the skew direction do not necessarily predict the maximum responses of skewed bridges by using fault-normal and fault- parallel GMs [10,11], the critical incidence angle depends on GM characteristics [e.g., far-field ground motion (FFGM) or near-field ground motion (NFGM)], skew angles, and pier support modeling as- sumptions [9,12–14]. Furthermore, De Bortoli and Zareian [15] de- monstrated that bridge ductility demand is determined by the GM in- cidence angle. On the contrary, Mackie et al. [16] indicated that varying the incidence angle with principal GM records from 0° to 180° has negligible effects on bridge response parameters, and analysis with rotating GMs is not necessary. Similarly, the critical GM incidence angle https://doi.org/10.1016/j.engstruct.2020.110411 Received 2 September 2019; Received in revised form 18 February 2020; Accepted 19 February 2020 ⁎ Corresponding author. E-mail addresses: matt.wang@utah.edu, matt.wang@bhbengineers.com (Y. Wang), luis.ibarra@utah.edu (L. Ibarra), c.pantelides@utah.edu (C. Pantelides). Engineering Structures 211 (2020) 110411 0141-0296/ © 2020 Elsevier Ltd. All rights reserved. T