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Stepped columns are adopted extensively as supporting members of single-storey industrial buildings. In order toensure the stability of this type of structure, the carrying capacity of single compressed member must be analyzed, which is represented by the concept of member’s effective length. Therefore the effective length value directly affect the carrying capability of compressed members, and it is necessary and important to make full use of the material’s mechanical property.Now, when considering the stability of the stepped columns, only two theories are adopted: One supposes that the top of the column can move and rotate freely, and the other thinks the top of the column can only move and can’t rotate. With the development of the light steel structure, the single-storey industial building will inevitablely become lighter. Moreover, the new light roofing material, such as color pattern plate, laminate composite board, sunlight panel and BAP coloring zinc aluminized steel plate (which weight is only 5%~10% of the normal conrete structure), make contributions to reducing the roof load. Therefore, when designing the roof system, the roof structure form will turn from heavy truss to light roof beam. In this case, the linear stiffness of crossbeam of the framework maybe smaller than that of the top of the stepped column, and the linear stiffness of crossbeam can not be considered as infinity. Thus, the effective lenghth detemined by the theory which considers the linear stiffness of crossbeam is infinite is unsafe.In this papper, elastic stabilty theory is adopted. The elastic stability critical force equations of the single stepped column, double stepped column and three stepped column are builded considering the relationship between r1 and r2 which are the bending restraint constants of the two ends of axial compression column with side sway. When caculating the effective length of the stepped column, the following factors are taken into consideration, such as the restraints of the top of the column, the stiffness ratio of all parts of the stepped column, the change of the axial pressure of all parts of the column, and the change of the linear stiffness of crossbeam of the framework. Critical force equations are worked out by using numerical method and the values of the effective length factor of the single stepped column, double stepped column and three stepped column are obtained when linear stiffness of crossbeam is taken into consideration. What is more, the effective length factors are made into table as a reference. At the same time, it can be used as a reference for the amendment of the steel structure design code.
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