This work aims at presenting and discussing Generalised Beam Theory (GBT) numerical results concerning the elastic geometrically non-linear behaviour of simply supported lipped channel (LC) beams under uniform major-axis bending and experiencing distortional-global (D-G) interaction, making it possible to shed fresh light on the mechanics underlying this coupling phenomenon. Two LC beams geometries are considered, each exhibiting a different type of D-G interaction, namely (i) "true D-G interaction" (close global, McrG, and distortional, McrD, critical buckling moments), containing three critical-mode initial geometrical imperfection shapes (two global, due to the lack of symmetry, and one distortional) and (ii) "secondary global-bifurcation interaction -SGI" (McrD<