Assessing the effects of near-field ground motions shows that the directivity effects in velocity histories of these ground motions leads to one or more impact pulses with large amplitudes that yield in increased ductility demand of rigid structures placed in near source areas. In this study, the cumulative Park-Ang DAMAGE INDEX has been used for comparing the DAMAGE potential brought about by the two acceleration components of ground motions that are normal to the fault direction or parallel to it. Two-dimensional steel moment frames with 4, 7, 10, 15 and 20 stories have been nonlinearly modeled and analyzed using the Opensees software. The investigations have been performed in different performance levels corresponding to target ductility values equal to 2, 3 and 4. The utilized ground motion records include 40 records divided equally to the normal and parallel sets regarding the fault direction. The scaling of the record sets have been performed so that the studied frames have met the considered target ductility values. The results show that the lower stories are more frequently affected by the normal records, therefore, more intense DAMAGEs are attributed to these records. That is while, the parallel records have been found to affect mostly intermediate and especially upper stories. The results also show that increasing the target ductility values leads to an increased DAMAGE potential for the studied structures.