Bridge structures adapt to movement through the addition of joint systems that accommodate anticipated movement due to temperature variations or earthquakes, thereby relieving stress on the bridge structure. Shape memory alloys (SMAs) have been proposed to limit joint displacements because of their ability to dissipate seismic energy and restore their original shape. A parametric study is conducted in this study using computer simulations of some advanced MATLAB programs to show the effects of all hysteretic parameters of SMA retrofit devices on seismic joint openings. The results show that SMA hysteretic parameters have a huge effect on SMA efficiency as a restrainer, which is compatible with energy dissipation philosophy, but there are some reversible impacts of some hysteretic parameters in some cases due to the resonance problem and their dependence on other parameters such as natural time period, period ratio, mass ratio, and seismic records. As a result, some design charts are created in this study after more than 200 million trials, taking into account the variation of all key parameters of the structure and the SMA under a suite of historical ground motion records. Moreover, bridge designers can choose optimal SMA hysteresis for a desired opening width, a desired time period, and desired period/mass ratios between adjacent frames with the help of these charts to overcome the two bridge problems of pounding and unseating of bridge decks.