In most Seismic design codes, expected objectives and performance of buildings under an earthquake are expressed, then it is claimed that if some proposed criteria are satisfied, buildings meet these objectives and performance. Although for more precise and obvious seismic design objective definition along with more appropriate proposed criteria the results are more reliable, the experience of previous earthquakes demonstrates that the proposed criteria should be based on actual building behavior during an earthquake. The purpose of this study is investigating the damage index of ordinary concrete moment frames with different height and vibrational properties under artificial earthquake of north fault of Tabriz. To this aim, damage index of three frames with 4, 7 and 10 stories designed based on Iranian 2800 seismic design code are investigated under artificial earthquake of Tabriz’s north fault. Since in the considered scenario the closest rupture distance to site was considered among all possible scenarios, the earthquake is categorized as a near-fault earthquake in which it is expected its high-frequency content make short-period structures (short buildings) more vulnerable than long-period structures (tall buildings). As it can be concluded from the results, by increasing of the structure’s height, the total damage to the structure decreases; In other words, the destructive effect of such records in tall structures are less than in short structures.