Through revisiting the classic problems of elastic and elastic-plastic buckling of frames, elastic-plastic stability of beam-columns, buckling of column braced at midspan by a horizontal brace and the buckling of dual structural system, it was proposed the concept of residual stiffness, i.e.the residual part of the total stiffness after deducting the stiffness depleted by horizontal forces and bending moments in the members.Check for stability of members and structures in real steel structures is to assure a minimum residual stiffness of the members and structures to resist against the destabilizing effect of gravity loads.Through analysis of the instability of beam-columns and dual structural systems, it was revealed that in the limit state, the stiffness was linearly or more than linearly decreased due to the horizontal load(bending moment).