A Softening Constitutive Law and Gradient-Inelastic Fiber-Based Element for 3-Dimensional Frame Simulations Under Seismic Excitations

Steel frame structures are essential components of modern infrastructure. Understanding their behavior under seismic loading is critical for ensuring public safety and minimizing damage that occurs during earthquakes. To accurately predict the response of steel frame structures during an earthquake, model representations should capture a complex range of deteriorating phenomena that are typically associated with nonlinear geometric instabilities, such as local and lateral torsional buckling.

While numerical models of high fidelity may be suitable to explicitly simulate nonlinear geometric instabilities that compromise the load-carrying capacity of a member and subsequently a structure, the associated computational cost of these models currently prohibits large-scale parametric studies to benchmark a targeted collapse and generally seismic risk of large building inventories. Given this constraint, reduced-order simulation models are promising alternatives. Current approaches, however, face various limitations.

To advance the state of knowledge on 3-dimensional earthquake-induced collapse simulation of steel structures, this doctoral thesis attempts to develop innovative modeling methods that ensure a viable computational cost when analyzing frame structures under earthquake shaking. These approaches aim to accurately capture the inelastic behavior of steel beam-columns subjected to seismic loading while maintaining computational efficiency. The research conducted focuses on two primary contributions: (i) the development of a multiaxial effective material law formulation with softening for accurately modeling inelastic local buckling in steel beam-columns, and (ii) the development of a modified gradient-inelastic fiber-based beam-column element to address strain localization issues in structural simulations where softening is a key behavioral characteristic of steel members, which in turn triggers structural collapse.

The developed multiaxial material law formulation can accurately model both the pre- and post-peak responses of steel beam-column members subjected to monotonic and cyclic loading. This includes capturing cyclic hardening and nonlinear local geometric instabilities, such as inelastic cyclic local buckling. The modified gradient-inelastic beam-column element formulation enhances traditional fiber-based beam-column element approaches by selectively applying gradient averaging only during the softening phases, thereby ensuring mesh-convergent results. System-level validation studies are also conducted to provide valuable insights into the behavior of steel frame structures during an earthquake and highlight the practical benefits of the developed models and methods.