Geometric Nonlinear Analysis of Steel Members with Imperfections

Abstract

Steel members inherently possess Initial Out-of-Straightness (IOS) and residual stresses, both of which are known to reduce their lateral-torsional buckling (LTB) resistance. Despite this, current Canadian and American design standards evaluate the LTB resistance of long-span, laterally unbraced members (expected to fail by elastic LTB) based on the critical moment of perfectly straight members, thereby neglecting the adverse effects of IOS. This approach stands in contrast to Eurocode and Australian standards, which explicitly account for IOS in their design provisions. Within this context, the present study investigates the impact of imperfections on LTB capacity of long-span, laterally unbraced steel members and advances the existing body of knowledge through three key contributions.

In the first contribution, a novel finite element formulation is developed for the geometrically nonlinear analysis of doubly symmetric I-shaped steel members. The formulation is grounded in the kinematics of thin-walled beam theory, thus capturing warping effects, and incorporates an algorithm to account for initial out-of-straightness (IOS) in the form of sweep, camber, twist, or combinations thereof. The model's ability to predict displacements and stresses is validated through comparisons with benchmark problems based on shell models and other thin-walled beam solutions. The model is subsequently employed in conjunction with a first-yield criterion to evaluate the buckling resistance of flexural members associated with various IOS patterns.

In the second contribution, the developed finite element is employed to conduct a parametric study involving 504 simulations of long-span, laterally unbraced flexural members with hot-rolled wide flange cross-sections. The investigation focuses on members whose capacities are governed by elastic LTB, aiming to quantify the influence of IOS on their buckling resistance. The analyses account for geometric nonlinearity, IOS, and residual stress effects. The study investigates the influence of various IOS characteristics, including pattern (symmetric vs. asymmetric), type (lateral, twist, and lateral-torsional), amplitude, member span, cross-sectional geometry, and loading conditions, on the LTB resistance of long-span steel members. Based on the parametric results, regression equations are developed to characterize the LTB resistance for members with different IOS types and amplitudes. The practical application of these equations is demonstrated through a design example.

The third contribution builds upon the capabilities of the finite element formulation developed in the first contribution by introducing three key enhancements: (a) incorporation of cross-sectional monosymmetric, thus enabling the analysis of I beams with a reduced flange; (b) inclusion of the destabilizing effect associated with load height; and (c) integration of residual stresses into the constitutive model as initial stresses. The enhanced model's capabilities are demonstrated through illustrative examples, and its accuracy is validated through comparisons with shell finite element models.