A Force‐Based Beam‐Column Element With Selective Gradient‐Inelasticity for Softening Materials in 3‐Dimensional Nonlinear Analysis

ABSTRACT Fiber‐based beam‐column elements featuring an effective material constitutive law with softening can capture the degrading response of structural members under extreme loading. However, these elements exhibit strain localization and mesh divergence, which impedes their accuracy. To tackle these issues, this paper proposes a gradient‐inelastic formulation that selectively applies gradient averaging during softening, whereas the local formulation is only employed in the elastic and the post‐yield response regimes. It is shown that the developed element formulation, which extends the conventional force‐based beam‐column element, mitigates the mesh dependence in the presence of a material constitutive formulation with softening. The proposed formulation is suitable for both 2‐ and 3‐dimensional force‐based beam‐ column elements. Validation studies with physical experiments from steel columns featuring both wide flange and hollow square sections under multiaxial monotonic and cyclic loading histories demonstrate the ability of the proposed formulation in providing mesh‐convergent moment‐chord rotation and axial shortening‐chord rotation relations even when structural members exhibit softening. The efficacy of the proposed formulation is demonstrated through 3‐dimensional nonlinear response history analysis of a 4‐story steel frame building.