In this work, an application of damping using shape memory alloy bracings on a simple frame is analyzed using a modified form of a popular shape memory alloy constitutive model. The popular model is first modified to remove inherent inconsistencies and is then further improved to also simulate hysteresis / subloop response that are essential for damping applications. Simple static and dynamic cases of loading are simulated to demonstrate its effectiveness. The results are discussed in the light of suitability to damping under earthquake excitations.