Hysteretic Model for Shear-Critical Reinforced Concrete Columns Bo Yu, M.ASCE 1 ; Chao-lie Ning 2 ; and Bing Li, M.ASCE 3 Abstract: A continuous and smooth hysteretic model for shear-critical reinforced concrete (RC) columns was identified and calibrated based on an efficient stochastic search technique and an experimental database consisting of 30 shear-critical RC columns. The inelastic restoring force of shear-critical columns was described by the Bouc-Wen-Baber-Noori (BWBN) model to produce the requisite strength and stiffness degradation as well as pinching effect. Meanwhile, the backward Euler and Newton-Raphson schemes were adopted to determine the inelastic restoring force by solving the ordinary differential equations. Then a differential evolution (DE) algorithm was utilized to identify the control parameters of the BWBN hysteretic model based on an experimental database consisting of 30 shear-critical rectangular columns under cyclic loading. Finally, prediction equations for the BWBN model parameters were developed in terms of four structural physical parameters. The capability and accuracy of the calibrated hysteretic model were demonstrated by comparison with the available experimental data. DOI: 10.1061/(ASCE)ST.1943-541X.0001519. © 2016 American Society of Civil Engineers. Author keywords: Reinforced concrete; Shear-critical RC column; Parameter identification; Stiffness degradation; Strength deterioration; Pinching effect; Analysis and computation. Introduction In RC building structures, gravity and lateral loads are mainly carried by the RC columns. Hence, failure of RC columns is considered one of the primary causes of the collapse of RC building structures. However, in a large number of existing buildings built prior to the 1970s, the RC columns were often designed with widely spaced and poorly anchored transverse reinforcements. These columns are gen- erally referred to as nonseismically detailed RC columns (Pan and Li 2013). Recent investigations indicate that nonseismically detailed RC columns are vulnerable to shear failure (i.e., shear-critical col- umns) when subjected to lateral displacement reversals caused by strong ground motions (Elwood 2004; Tran 2010). Subjected to excitations generated by strong ground motions, the restoring force of a RC column becomes highly nonlinear and exhibits significant hysteresis (Ismail et al. 2009; Song and Dyke 2014). Meanwhile, there is a significant reduction in the flexural strength after the bending moment exceeds the peak flexu- ral capacities of shear-critical RC columns (Elwood and Moehle 2005). Furthermore, shear-critical RC columns often exhibit an ob- vious stiffness degradation and pinching characteristics owing to concrete cracking as well as bond slip between reinforcing steel and concrete. Therefore, two typical types of finite-element (FE) models have been developed for modeling the nonlinear seismic behavior of shear-critical RC columns. The first type of FE model is the microscopic model (Chung and Ahmad 1995; Petrangeli et al. 1999; Mostafaei and Kabeyasawa 2007), which incorporates the shear mechanism into the axial-flexure interaction behavior from the concrete and reinforcement stress–strain relationship. Currently, they are capable of rationally describing strength and stiffness degradation, but they still have a hard time capturing the pinching effect owing to the bond-slip mechanism between con- crete and reinforcing steel. The second type of FE model is the macroscopic model (Ricles et al. 1998; D’Ambrisi and Filippou 1999; Lee and Elnashai 2001; Elwood 2004; Xu and Zhang 2011; LeBorgne and Ghannoum 2014), which simplifies RC col- umns as an assembly of interconnected springs or subelements with lumped or distributed nonlinearity. Thus such models have greater flexibility and versatility, and they are capable of rationally describ- ing strength and stiffness degradation as well as pinching effects, but their accuracy and efficiency are largely dependent on the appropriate hysteretic models for each spring or subelement. Several typical hysteretic models have been developed over the last several decades for springs or subelements, such as the elasto- plastic model (Veletsos et al. 1965), bilinear degrading stiffness model (Clough and Johnston 1966), Bouc–Wen–Baber–Noori (BWBN) model (Bouc 1967, 1971), Takeda degrading stiffness model (Takeda et al. 1970), peak-oriented degrading bilinear model (Imbeault and Nielsen 1973), trilinear degrading stiffness model (Otani and Sozen 1974), Q-hysteresis model (Saiidi and Sozen 1979), Otani bilinear model (Otani 1980), hysteresis shear model (Ozcebe and Saatcioglu 1989), Pivot hysteresis model (Dowell et al. 1998), energy-based hysteretic model (Sucuo ˇ glu and Erberik 2004), Ibarra pinching hysteresis model (Ibarra et al. 2005), and hysteretic model including shear and axial load failure (Sezen and Chowdhury 2009). Of these, the BWBN type of hysteretic model has been widely used due to its versatility (Chung and Loh 2002; Skalomenos et al. 2014). The BWBN model was origi- nally developed by Bouc (1967, 1971) and then extended by Wen (1976), Baber and Wen (1981), and Baber and Noori (1985). During the past few years, the BWBN model has been applied 1 Associate Professor, Key Laboratory of Disaster Prevention and Struc- tural Safety of Ministry of Education of P. R. China, School of Civil Engineering and Architecture, Guangxi Univ., Nanning 530004, China. E-mail: gxuyubo@gxu.edu.cn 2 Research Fellow, Institute of Catastrophe Risk Management (ICRM) in Singapore, Nanyang Technological Univ., 50 Nanyang Ave., Singapore 639798. E-mail: clning@ntu.edu.sg 3 Associate Professor, School of Civil and Environmental Engineering, Nanyang Technological Univ., 50 Nanyang Ave., Singapore 639798 (corresponding author). E-mail: cbli@ntu.edu.sg Note. This manuscript was submitted on January 31, 2015; approved on January 24, 2016; published online on April 6, 2016. Discussion period open until September 6, 2016; separate discussions must be submitted for individual papers. This paper is part of the Journal of Structural En- gineering, © ASCE, ISSN 0733-9445. © ASCE 04016056-1 J. Struct. Eng. J. Struct. Eng., 2016, 142(9): 04016056