Direct analysis of tapered-I-section columns by one-element-per-member models with the appropriate geometric-imperfections

•New initial imperfection shape function is proposed for non-prismatic members.•Formulations for non-prismatic elements are derived based on analytical expressions.•Direct analysis method for non-prismatic members is investigated.•Extensive verifications are conducted for the proposed formulations. In the structural stability design using direct analysis method (DM), the member initial geometric imperfections should be explicitly simulated. In current design practices, the imperfection shape is usually assumed as a half-sinusoidal curve. For the design of tapered columns, however, the use of this initial configuration may overestimate the buckling strength. Therefore, a generalized imperfection shape function is proposed for the practical design of tapered I-section columns. A new beam-column element by incorporating this imperfection shape-function, named the Tapered-Compound-Curved (TCC) element, is developed for tapered symmetric-I sections. The analytical expressions of the flexural stiffness are adopted in the element derivation. The one-element-per-member modeling method with the TTC element is proposed for practical applications. Examples verifying the proposed equations are provided, and the influences of different imperfection shapes are assessed.