Among the earthquake induced engineering demand parameters, the peak floor acceleration (PFA) is closely relevant to the function of the nonstructural components in structures. Self-centering frames (SCFs) emerge as one of advanced seismic resilient structures, primarily because they have better recentering capacity than conventional frames. However, SCFs often experience larger PFAs than conventional frames. This unfavorable performance partially impedes the applications of SCFs in seismic prone areas. Towards understanding and controlling PFAs, this paper paid particular efforts on evaluating the effects of varying the 'post-yield' stiffness ratio (alpha) which is a hysteretic parameter frequently ignored by peer studies. In the first part, to have a basic understanding, this paper defined various two-degree-of-freedom (2DOF) systems characterized by flag-shaped hysteresis, and analyzed their responses during free vibration processes. In the second part, this paper designed two multi-story frames with alpha of 0.01, and then conducted nonlinear time history analysis to observe the magnitudes and height-wise distributions of PFAs when alpha is increased to 0.05, 0.1 and 0.2. The seismic analysis results indicated that the increase of alpha not only reduced the magnitudes of PFAs except for the roof level, but also, it realized a more uniform heigh-wise PFAs.