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Tapered members produced by robotic fabrication techniques offer architectural and structural advantages and have the potential to become more prevalent than prismatic members. However, the conventional analysis and design methods based on simplified assumptions such as equivalent stiffness cannot be used to accurately evaluate a member's performance. To provide a reliable and practicable stability design method, a direct analysis method of tapered I sections is proposed. A mixed-field tapered beam-column element is derived for use within the modeling of structural frames. The effects of initial geometric imperfection and additional shear stress are directly considered in the element formulation. A polynomial describing the member's critical initial out-of-plumbness is adopted, and an arbitrarily located internal hinge is incorporated in the element to enhance the element's deformation capacity and capture …