A second-order flexibility-based model for steel frames of tapered members

The paper presents a new computer method for nonlinear inelastic analysis of steel frames consisting with members with non-uniform cross-sections. A novel second-order flexibility-based element has been developed. The behaviour model accounts for material inelasticity due to combined bending and axial force, element geometrical nonlinear effects in conjunction with initial geometric imperfections using only one element per structural member. The proposed element formulation combines the power series approach to obtain the general solution of the second-order bending moments with the Maxwell-Mohr method to compute the force-displacement relationship of the general continuously non-prismatic Timoshenko-Euler beam-column element. The method ensures also that the plastic strength interaction requirements are always satisfied in the plastic hinges developed at the ends of the member or within the member length. The second-order elasto-plastic tangent stiffness matrix and equivalent nodal loads vector of non-uniform 2D steel members with semi-rigid connections is developed and the proposed nonlinear analysis formulation has been implemented in a computer program. In order to verify the efficiency and accuracy of the proposed approach, several benchmark problems have been studied and the results prove the performance of the proposed method.