During the 2012 Emilia earthquake, several precast RC industrial buildings were damaged or collapsed due to a strong rotational response triggered by the presence of a single or few eccentric walls within the regular mesh of columns. The objective of this work is to analyse the torsional effects induced by an eccentric wall in one-storey frame structures, and to provide formulas for a quick estimation of the displacement of the flexible side. Starting from the typical structural scheme of industrial one-storey structures consisting of a regular grid of uniformly spaced columns, a stiff lateral shear wall has been added to make the structure asymmetric. A response parameter (displacement amplification factor), defined as the ratio between the translational displacement of the irregular structure over the translational displacement of the corresponding equivalent regular structure without the added wall/s, is introduced to evaluate the torsional response of the system. An analytical formula is derived by means of a linear static analysis. The results indicate that the presence of a shear wall, albeit significantly stiffer than the columns (or even infinitely rigid) with respect to lateral action, does not always lead to a reduction of the seismic displacement demand in the columns.