Timoshenko line-element for stability analysis of tapered I-section steel members considering warping effects

Tapered I-section steel members can achieve efficient material utilization, and are economical alternatives to traditional prismatic ones. Current line-element formulations for tapered I-section members may not accurately capture buckling behavior because they typically ignore shear and warping deformations. The research refines the existing line-element formulation for tapered I-section members by directly considering warping deformation. The tapered member's flexural rigidity is analytically expressed in a stiffness matrix via utilizing a series of tapering factors, which can produce more accurate analysis than those by the conventional stepped-element or the approximate distribution (e.g., linear, parabolic, or cubic) methods. The element formulation is established based upon the Updated-Lagrangian method that permits moderate deformation. The numerical procedure for tracing the solution path is illustrated in detail with a flowchart. Finally, performances of the proposed method, particularly the accuracy of the new element stiffness matrices, are thoroughly assessed by presenting several examples.