The use of empirically calibrated moment-rotation models that account for strength and stiffness deterioration of steel frame members is paramount in evaluating the performance of steel structures prone to collapse under seismic loading. These deterioration models are typically used as zero-length springs in a concentrated plasticity formulation; however, a calibration procedure is required when they are used to represent the moment-curvature (M−χ) behavior in distributed plasticity formulations because the resulting moment-rotation (M−θ) response depends on the element integration method. A plastic hinge integration method for using deterioration models in force-based elements is developed and validated using flexural stiffness modifications parameters to recover the exact solution for linear problems while ensuring objective softening response. To guarantee accurate results in both the linear and nonlinear range of response, the flexural stiffness modification parameters are computed at the beginning of the analysis as a function of the user-specified plastic hinge length. With this approach, moment-rotation models that account for strength and stiffness deterioration can be applied in conjunction with force-based plastic hinge beam-column elements to support collapse prediction without increased modeling complexity.
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