•Seismic pounding between multistory structures is likely to introduce a torsional behavior.•The inter – story pounding problem has not been studied effectively yet.•Asymmetric pounding between an 8-storey RC building and an adjacent shorter one is investigated.•The column that suffers the hit of the adjacent structure proved to be the key issue in the inter – story pounding problem.•In asymmetric pounding neglecting its effects leads to non-conservative building design or even to critical situation. Collisions between structures due to seismic oscillations have been reported many times in literature as a common case of damage. Further it is quite usual seismically induced oscillations of a structure in a city center block of buildings to be partly restrained in lateral displacements and therefore torsional behavior to be introduced in the structure. Two different types of structural interaction may be defined: (a) Diaphragm-to-diaphragm collisions (Type A). (b) The floor levels of the two structures are different. Consequently during the seismic oscillations the diaphragms of the first one impact the columns of the other (Τype B or interstory pounding). In this work the cases of an 8-story reinforced concrete building that suffers pounding with an adjacent structure that has 1, 2, 3, 4, 5, 6, 7 or 8 stories are studied. Pounding occurs only in one (Case 1) or in two (Case 2) columns of the structures and since the other columns are free to move without restrictions a torsional behavior is introduced (asymmetric pounding). Moreover in Type B interaction these columns of the 8-story frame structure undergo impacts at a height equal to 2/3 of their deformable length from the diaphragms of the other structure. The influence of an initial distance between the two interacting structures on the torsion effect is investigated too. Nonlinear seismic step-by-step analyses are performed. More than two hundred pounding cases with torsional effect each one for three natural seismic excitations are studied. Results in terms of shear and ductility demands of the columns are presented and commented. Both types A and B yielded high torsional structural rotation. In interaction Type B it can be deduced from the cases under examination that the column that is endured the impact from the top floor of the other structure develops high shear demands that exceed the available capacity many times during the step-by-step seismic analysis. Moreover high ductility demands have been observed for this column. Finally it is concluded that for buildings that may undergo asymmetric pounding not taking it into account may lead under certain conditions to non-secure design or even critical situations.