Modeling Elastic and Inelastic, Critical- and Post-buckling Behavior of Bracing Members

An efficient beam element, the modified elastofiber (MEF) element, has been developed to capture the overall features of the elastic and inelastic response of slender columns and braces under axial cyclic loading without unduly heavy discretization. It consists of three fiber segments, two at the member ends and one at mid-span, with two elastic segments sandwiched in between. The segments are demarcated by two exterior nodes and four interior nodes. The fiber segments are divided into 20 fibers in the cross-section that run the length of the segment. The fibers exhibit nonlinear axial stress-strain behavior akin to that observed in a standard tension test of a rod in the laboratory, with a linear elastic portion, a yield plateau, and a strain hardening portion consisting of a segment of an ellipse. All the control points on the stress-strain law are user-defined. The elastic buckling of a member is tracked by continuously updating both exterior and interior nodal coordinates, and checking force equilibrium in the updated configuration. Inelastic post-buckling response is captured by fiber yielding, fracturing, and/or rupturing in the nonlinear segments. Key features of the element include the ability to model each member using a single element, and easy incorporation of geometric imperfection, partial fixity support conditions, member susceptibility to fracture defined in a probabilistic manner, and fiber rupture leading to complete severing of the member. The element is calibrated to accurately predict the Euler critical buckling load of box and I-sections with varying slenderness ratios and support conditions. Elastic post-buckling of the Koiter-Roorda L-frame with varying member slenderness is simulated and shown to compare well against second-order analytical approximations to the solution, even when using a single MEF element to model each leg of the frame. The inelastic behavior of struts under cyclic loading observed in the Black et al., Fell et al., and Tremblay et al. experiments is accurately captured by single MEF element models. A FRAME3D model (using MEF elements for braces) of a fullscale 6-story braced frame structure that was pseudodynamically tested under the US-Japan cooperative research program, subjected to the 1978 Miyagi-Ken-Oki earthquake record, is analyzed and shown to closely mimic the experimentally observed behavior.