AbstractThe beam–column element analysis method has been extensively adopted in practice, relying on the robustness of its element formulation. Steel members with open sections are commonly used; their cross-sectional shapes are usually nonsymmetric to improve material efficiency. Nevertheless, an offset exists between the shear center and the centroid of a nonsymmetric section. If the applied loads do not act at the shear center, torsion can be induced; this is sometimes unavoidable. When a member is subject to torsion, the inclined angle between the local axes of the cross section and the element is varied along the element length, complicating the summating of the cross section’s stiffness to form an element stiffness matrix. This study developed a new beam–column element formulation based on the nonsymmetric section assumption and a Gaussian quadrature procedure to formulate the element stiffness matrix of being concise in expressing formulation. The updated Lagrangian method was modified to consider large deflections. This method permitted the use of fewer elements to simulate a member under torsion, leading to a significant improvement in numerical efficiency. Detailed derivations and verification examples are given in the paper.