Reduced-order Models for Simulating Coupled Geometric Instabilities in Steel Beam-columns Under Inelastic Cyclic Straining

Numerical models that can simulate coupled geometric instabilities in steel beam-columns are required for the seismic assessment of certain steel moment-resisting frames. Reliably simulating coupled instabilities requires that the steel material is precisely characterized under inelastic cyclic straining. Full continuum finite element (CFE) models can be used in this context, however, reduced order models are preferred for building-level simulations because of their lower computational cost. Concentrated plasticity models are a typical reduced order approach, although findings from recent full-scale experiments conducted on steel beam-columns have highlighted their limitations in simulating component behavior.

The aim of this thesis is to propose accurate reduced-order simulation models for steel beam-column components to simulate coupled buckling at a diminished computational expense compared to full CFE approaches. This goal is achieved by using component macro models that couple CFEs in critical regions with beam-column elements elsewhere. The specific objectives related to the aim of this thesis are to: (i) advance the state-of-the-art in constitutive modeling for structural steels subjected to earthquake-induced inelastic straining; (ii) develop an efficient method of coupling beam-column and CFE domains that incorporates torsion-warping; and (iii) develop general recommendations for modeling wide flange beam-column components subjected to inelastic cyclic straining using the macro model.

This thesis developed a constitutive model for mild structural steels to improve upon the initial yield behavior of a classic metal plasticity model by accounting for the discontinuous yielding phenomenon. Constitutive model calibration methodologies were developed using constrained optimization for the cases when the material's cyclic behavior is known and when it is unknown. Simulated geometric instabilities were shown to be sensitive to the constitutive model's input parameters in steel beam-columns of particular geometries subjected to multiaxis loading. Coupling methods that included torsion-warping were developed using multipoint constraint equations. Findings indicate that including torsion-warping in the coupling formulation is critical for steel beam-columns that are susceptible to coupled local and lateral-torsional instabilities. The proposed macro model is efficient for the investigated range of steel beam-columns: it reduces computational cost metrics in benchmark CFE analyses by around 50 %. It is also accurate, as the average error between benchmark CFE and macro model analyses is only 3 %.

The advances in material modeling made by this thesis can be used to reduce the uncertainty in steel component simulations. This enables analysts to better comprehend component behavior through simulations and improves simulation-assisted design. Component models that explicitly simulate geometric instabilities and material inelastic behavior at lower computational costs are important in probabilistic assessments and uncertainty quantification. They may be especially useful, for example, in benchmarking concentrated plasticity models and in the process of developing new structural systems.