Although the M (w) = 6.1 Kovancilar-Turkey earthquake of March 8, 2010 had a moderate intensity with a recorded PGA of 0.07g, it caused heavy damages in 2870 residential buildings having traditional or masonry structural systems and 42 human loss. Damage has been reported to be particularly concentrated at Kovancilar and Palu counties of Elazig province. Five hours after this earthquake, an aftershock of M (L) = 5.6 with a PGA of 0.08g struck the same region, developing the existing damages in the structures. In order to investigate this significant amount of reported damages under the effect of such low ground shakings, our reconnaissance team arrived at the region and unexpectedly came across a two-story RC building settled on a slope in Yukari Demirci village, which suffered moderate damage during the shakes. The outline of this paper can be summarized as the presentation of the results of the investigations in the order of describing the overall observed damages within the region; evaluation of the recorded motions; the details of the field-work carried out for the two story RC building and the analytical estimation of the site-assessed damages by means of nonlinear dynamic analysis. Employing the gathered data, the building is analytically modeled as plane frames and analyses are performed under the effects of the processed earthquake records, which are applied to the structure one after another in the consistent directions due to the building location. It is shown herein that the structural elements remain in the elastic range subjected to the processed recorded motions; henceforth acceleration time histories are scaled step by step up to 0.40g and computations are repeated for each acceleration level. Comparison with the observed and the analytically obtained damages confirmed that approximately 0.30g of peak ground acceleration should have to be exposed during the earthquakes.