Nowadays various soft wares are used to design steel structures. The theory of steel structures design, however, is still the base for different soft wares. Studying the stability of columns as important parts of a structure is very important. Usually geometric imperfection in the process of installation, (i.e., out of plumb, decentralization, column curvature) and also the effect of shear deformations in computational relations, all lead to some deviations in the design accuracy. Therefore in this article, by considering the effects of shear deformations, the stability of columns with semi-rigid connections including initial imperfection have been studied and the related slope-deflection equations have been extracted and proposed. And thereafter, by means of ABAQUS software and modelling the three models of column, one-story frame and three-story frame, the accuracy and validity of the proposed relations were confirmed.