Code-based procedures rely on a simplified sub-structure approach for analyzing soil structure interaction (SSI) effects. This simplified approach separates the site response analysis (SRA) from the SSI problem. Such separation prohibits a holistic view of the entire soil-structure system under seismic loading. Specifically, perspective is lost on the concurrent period migration of the structure and soil column. In both structure and soil column period lengthening we can observe a decrease in stiffness and corresponding increase in damping with increased dynamic shear strain. Indeed, period shifting may increase or decrease seismic demand depending if building period shifts towards or away from soil column fundamental period. This study presents the results of a statistical analysis on the response of a generic building underlain by a suite of hypothetical soil profiles. Each soil profile is excited by a large database of ground motions from past earthquakes recorded at rock sites. We investigated the soil period shift, the building period shift, and the resulting building seismic demands. The free field site amplification factors are shown to have a strong dependence on the strain-compatible first and second fundamental periods of the soil columns. For four soil profiles, the mean building seismic demands remain unchanged under SSI effects, when the building period is shifting towards soil column fundamental period. For two soil profiles, we found a net mean reduction of up to 9% in building seismic demands under SSI effects, when the building period shifts away from the first or second fundamental period of soil column. Despite the relatively low mean impact of SSI on seismic demand, the record-to-record variability of seismic demands is significant. These findings illustrate the critical role of period migration on seismic demand and reinforce the need to evaluate SSI in the broader context of site response analysis.