SummaryShaking table tests are performed on a one‐bay one‐story steel frame with superelastic Cu–Al–Mn shape memory alloy (SMA) tension braces. The frame is subjected to a series of scaled ground motions recorded during the 1995 Kobe earthquake, Japan. The test results demonstrate that the SMA braces are effective to prevent residual deformations and pinching. It is also shown that the time history responses observed from the shaking table tests agree well with the numerical predictions using a rate‐independent piecewise‐linear constitutive model calibrated to the quasi‐static component tests of the SMA braces. This suggests that the loading rate dependence of Cu–Al–Mn SMAs as well as the modeling error due to the piecewise linear approximation can be neglected in capturing the global response of the steel frame. Numerical simulations under a suite of near‐fault ground motion records are further performed using the calibrated analytical models to demonstrate the effectiveness of the SMA braces when the variability of near‐fault ground motions is taken into account. A stopper, or a deformation restraining device, is also proposed to prevent premature fracture of SMA bars in unexpectedly large ground motions while keeping the self‐centering capability in moderate to large ground motions. The effectiveness of the stopper is also demonstrated in the quasi‐static component and shaking table tests. Copyright © 2015 John Wiley & Sons, Ltd.