Generalized line-element formulations for geometrically nonlinear analysis of nonsymmetric tapered steel members with warping and Wagner effects

Abstract

With advancements in manufacturing technology, steel members can be innovatively fabricated in nonsymmetric section shapes and tapered along the length to bring certain benefits in material utilization and aesthetic appearance. The frame analysis of the steel structures with these members is quite challenging because of lacking the suitable line-element formulations to robustly and efficiently consider tapered section characteristics together with the Warping and Wagner effects resulting from nonsymmetric section shapes. This research proposes generalized line-element formulations for geometrically nonlinear analysis of tapered steel members with nonsymmetric cross-sections, adequately assessing the member buckling behaviors. The element stiffness matrix is derived via the total potential energy, considering the axial and transverse elastic strains, the Warping deformations, and the Wagner effects. Parametric studies have been conducted to generate approximate equations for the geometric parameters of common shapes of nonsymmetric cross-sections, thereby reflecting the variable cross-section properties along the length. Afterwards, the generalized line-element tangent stiffness matrix is obtained, compatible with the existing frame analysis frameworks for easy programming. The element formulation is validated through several examples with the benchmark results generated by shell finite-elements. This work could be helpful for the sustainable development of modern steel structures with efficient material utilization and futuristic geometry.