Abstract
In the presence of softening section constitutive relations, classical beam theories predict erroneous strain singularities, and the corresponding force/flexibility-based (FB) beam-column element formulations result in strain localization and loss of response objectivity, i.e., divergence, rather than convergence, with progressive mesh refinements. To address this challenge, various FB element formulations have been proposed in the literature. One of these formulations is the so-called “gradient inelastic” (GI) FB formulation, which is a two-node element formulation that eliminates the strain localization and achieves response objectivity through strain gradient nonlocality relations. Although a single two-node GI element can effectively simulate an entire beam or column, simulating such a member via multiple two-node GI elements in series (e.g., to apply intermediate point loads, to more accurately capture geometric nonlinearities, or to represent cross-section variation) would not lead to accurate response predictions. This is because, in a model with multiple two-node GI elements in series, the nonlocality relations are not enforced at the intermediate/connection nodes between adjacent elements. Instead, end member boundary conditions (BCs) are enforced at those connection nodes because the two-node GI formulation has been designed to simulate an entire member. To tackle this shortcoming, this paper proposes an innovative multinode GI FB element formulation. To enforce the nonlocality relations at the connection nodes, two different sets of mathematically admissible section strain compatibility conditions (CCs) are adopted. The multinode formulations using both sets of CCs are evaluated through several simulation examples, including beams and columns subjected to various loads. The evaluations demonstrate the ability of both element formulations to produce objective softening responses, while one set of CCs is found to more closely predict the responses of previously tested RC beams under midspan loading.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
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Journal of Structural Engineering
Volume 150 • Issue 2 • February 2024
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© 2023 American Society of Civil Engineers.
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Received: Mar 6, 2023
Accepted: Sep 26, 2023
Published online: Dec 12, 2023
Published in print: Feb 1, 2024
Discussion open until: May 12, 2024
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Cited by
- M. Aghajani Delavar, M. Salehi, P. Sideris, Shear-Enhanced Gradient Inelastic Force-Based Frame Element Formulation for Analysis of Shear-Critical Reinforced Concrete Members, Journal of Structural Engineering, 10.1061/JSENDH.STENG-13165, 150, 11, (2024).