Modified Elastofiber Element for Steel Slender Column and Brace Modeling

An efficient beam element, the modified elastofiber MEF element, has been developed to capture the overall features of the elastic and inelastic responses 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 midspan, 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 updating both exterior and interior nodal coordinates at each iteration of a time step and checking force equilibrium in the updated configuration. Inelastic postbuckling response is captured by fiber yielding, fracturing, and/or rupturing in the nonlinear segments. The key features of the element include the ability to model each member using a single element, 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 a wide range of slenderness ratios L /r=40, 80, 120, 160, and 200 and support conditions pinned-pinned, pinned-fixed, and fixed-fixed . Elastic postbuckling of the Koiter-Roorda L frame tubes and I sections with various member slenderness ratios L /r=40, 80, 120, 160, and 200 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 experiments of Black et al., Fell et al., and Tremblay et al. is accurately captured by single-MEF-element models. A FRAME3D model using MEF elements for braces of a full-scale six-story braced frame structure that was pseudodynamically tested at the Building Research Institute of Japan subjected to the 1978 Miyagi-Ken-Oki earthquake record is analyzed and shown to closely mimic the experimentally observed behavior. DOI: 10.1061/ ASCE ST.1943-541X.0000238 CE Database subject headings: Elasticity; Inelasticity; Buckling; Steel columns; Beam columns; Bracing; Cracking; Failures; Cyclic tests; Plastic hinges. Author keywords: Elastic and inelastic buckling; Beam-column modeling; Brace modeling; Fracture; Instability; Collapse simulation; Cyclic tests on struts; Plastic hinge element; Fiber element; Material and geometric nonlinearity. Background and Motivation A cyclically axially loaded slender element has a tendency to buckle laterally under compression, straighten out, and possibly yield in the ensuing tensile excursion. Subsequent loading cycles may result in localization of the buckled region at the midlength of the member followed possibly by cracking and/or rupturing, ultimately severing the element completely. The buckling instability is greatly sensitive to end-fixity conditions and initial geometric imperfection. While the initial buckling may be a purely elastic phenomenon, subsequent compression excursions may result in significant inelastic buckling accompanied with a gradual or rapid degradation of the buckling strength. Thus, what starts Assistant Professor of Structural Engineering and Geophysics, California Institute of Technology, MS104-44, Pasadena, CA 91125. E-mail: [email protected] Note. This manuscript was submitted on June 22, 2009; approved on April 23, 2010; published online on October 15, 2010. Discussion period open until April 1, 2011; separate discussions must be submitted for individual papers. This paper is part of the Journal of Structural Engineering, Vol. 136, No. 11, November 1, 2010. ©ASCE, ISSN 0733-9445/ 2010/11-1350–1366/$25.00. 1350 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / NOVEMBER Downloaded 28 Jun 2011 to 131.215.127.56. Redistribu out as a purely geometric nonlinearity evolves into a complex interplay between material and geometric nonlinearities, with the ductility of the material playing an important role in determining the low-cycle fatigue degradation and ultimate failure of the member. Accurately modeling such a multifaceted phenomenon using a single element to represent the entire member is highly challenging, given the uncertainties associated with the member geometry including boundary conditions and the sensitivity of buckling response to the geometry. In addition, the ill conditioning of the element stiffness matrix close to buckling and/or the stiffening of an imperfect or a buckled member due to a tensile excursion might make the solution difficult to converge numerically when using the tangent stiffness matrix for the NewtonRaphson iterations. The objective of this study is to develop a beam-column element that can overcome these challenges and incorporate it into a previously developed three-dimensional 3D analysis framework, FRAME3D Krishnan 2003, 2009a; Krishnan and Hall 2006a,b . The end goal is to be able to perform efficient and accurate 3D collapse analysis of tall braced steel structures under strong earthquake ground motion. Early studies on braced structures e.g., Jain and Goel 1978; Ikeda and Mahin 1984; Tang and Goel 1989; Hassan and Goel