The present work provides expressions about the Inter-storey Drift Ratios at the damage state of the first yield (IDRy). The proposed expressions are compatible with i) composite (steel/concrete) moment resisting frames (MRFs), ii) steel MRFs, iii) steel eccentrically braced frames (EBFs) and iv) steel buckling restrained braced frames (BRBFs) for soil types B and D. These expressions have been derived by means of statistical and regression analysis incorporating a large databank composed by numerous IDR values that correspond to the first yield of the aforementioned under-study frames. The databank has been produced after extensive dynamic analyses, considering a plethora of seismic recordings compatible with different soil types. The validity of these expressions is proved through an indicative number of numerical examples. Most importantly, the proposed expressions may constitute a very useful tool towards the direct displacement based design (DDBD), where the existing equations for the calculation of the IDRy are crude and oversimplified, leading to unreliable results. The superiority of the proposed expressions over those stipulated in the DDBD code is verifying through an additional numerical example.