Damping-Ductility Relationship for Performance Based Seismic Design of Shape Memory Alloy Reinforced Concrete Bridge Pier

In performance based seismic design of structures, estimating the equivalent viscous damping (EVD) using a damping-ductility relationship is a major step. The seismic response of Shape Memory Alloy (SMA) reinforced concrete (RC) bridge pier is different from its traditional steel reinforced or post-tensioned counterparts. Due to its significantly different hysteretic response and material properties, it is necessary to estimate the EVD of SMA-RC pier and establish the damping-ductility relationship. An error in the estimation of equivalent viscous damping can lead to significant errors in the ductility demand of the designed pier. This study aims to develop expressions for equivalent viscous damping and damping-ductility relationship for SMA reinforced bridge pier when SMA rebars are used in the plastic hinge region of the bridge pier. New equivalent damping relations for five different bridge piers reinforced with five different types of SMAs have been developed. Nonlinear dynamic time history analyses were conducted on five different SMA-RC bridge piers using 100 ground motions. The accuracy of the new equivalent damping relation was assessed to ensure the applicability of the proposed relationships. Finally, a general expression was developed that can assist in estimating equivalent viscous damping for performance based seismic design of SMA reinforced bridge pier.