This paper deals with the collapse mechanisms of steel columns with variable cross-section subjected to the cyclic bending under alternating axial force. The second order rigid plastic and elasto-plastic analyses of columns with rotational restraint at both ends are carried out by using the rigid body - rotational spring models. Numerical results demonstrate that the collapse mechanisms in columns might vary every half cycle due mainly to the plastic deformation in the middle of columns and corresponding PΔ effect. Then the instability region S of collapse mechanisms develops severely by the variation of axial force. A conventional method on the basis of rigid plastic approach is proposed to predict the instability transition region S in columns with variable cross-section.
