Seismic Collapse Analysis of Reinforced Concrete Framed Structures Using the Gradient Inelastic Force-Based Frame Element

Abstract eng:
This study assesses the capability of a novel force-based (FB) frame element – termed gradient inelastic (GI) FB element – to simulate the softening response and eventual collapse of a reinforced concrete (RC) framed structure. Although FB elements have been proven to be very efficient in predicting the hardening (pre-peak) response of framed structures, robust predictions of their softening response using FB elements have been hindered by strain softening phenomena that result in: (i) strain localization and loss of objectivity, and (ii) instabilities and failure of the numerical solution. The GI element has been formulated on the basis of a gradient inelastic beam theory and eliminates strain localization phenomena providing objective (mesh convergent) response and stability of the numerical solution. The GI element along with two other types of FB elements are employed to model a three-bay two-story RC moment frame. The other two FB elements incorporate end plastic hinge lengths through a plastic hinge integration method and are termed beam-with-hinges (BwH) elements herein. Both BwH elements use the so-called modified Gauss-Radau integration method. However, in the first BwH element, plasticity is solely introduced at the end sections (at the plastic hinge lengths), while, in the second BwH element, spread of plasticity is allowed by considering inelastic material response at all sections. Frame models generated with each modeling approach are analyzed using static pushover and Incremental Dynamic Analysis (IDA) and the predicted responses are compared in terms of pushover curves, IDA curves, and fragility curves for various limit states, including collapse. Although the models developed using the BwH elements predict pushover curves close to those obtained from the models generated with GI elements, BwH elements always underestimate damage (controlled by the peak strains), because the predicted peak strains by the BwH elements represent an average strain over the plastic hinge length. As a result, BwH elements predict systematically larger collapse capacities. On the contrary, the GI elements provide a deformation distribution over the entire member length, including the damage zones; hence, more accurately predicting peak responses. The GI elements were also found to provide stability of the numerical solution compared to all considered BwH elements.

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