Modeling steel moment frame and braced frame buildings in three dimensions using FRAME3D

Abstract

A procedure for the efficient three-dimensional nonlinear time-history analysis of steel framed buildings is derived. It incorporates three types of nonlinear beam elements - the plastic hinge type, the elastofiber type, and the 5-segment modified elastofiber type – and nonlinear panel zone elements to model yielding and strain-hardening in moment frames, and buckling in braced frames. Floors and roofs of buildings are modeled using 4-node elastic diaphragm elements. The procedure utilizes an iteration strategy applied to an implicit time-integration scheme to solve the nonlinear equations of motion at each time-step. Geometric nonlinearity is included. The plastic hinge beam element consists of two nodes at which biaxial flexural yielding is permitted, leading to the formation of plastic hinges. Elastic rotational springs are connected across the plastic hinge locations to model strain-hardening. Axial yielding is also permitted. A normalized PMM interaction surface is calculated for one of the model sections, and used to characterize the axial force-biaxial moment interaction for all model sections. The panel zone element consists of two orthogonal panels forming a cruciform section. Each panel may yield and strain-harden in shear. The elastofiber beam element is divided into three segments - two end nonlinear segments and an interior elastic segment. The cross-sections of the end segments are subdivided into fibers. Associated with each fiber is a nonlinear hysteretic stress-strain law for axial stress and strain. This accounts for coupling of nonlinear material behavior between bending about the major and minor axes of the cross-section and axial deformation. While beams and columns in moment-frames can be modeled using the elastofiber beam element, braces and columns susceptible to buckling may be modeled using a modified elastofiber beam element with the elastic segment in the standard elastofiber beam element subdivided into two elastic segments and a central nonlinear segment. First mode buckling in the element is simulated through yielding of the central nonlinear segment. All these elements are integrated into a building analysis program, FRAME3D. The various elements and the program are validated against analytical solutions of simple problems, as well as scaled and full-scale tests of beam-column assemblies and 4-6 story structures.

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