The variability in the seismic demand and capacity of a steel frame having beam hinges with uncertain properties is investigated through Incremental Dynamic Analysis (IDA) using both Monte Carlo simulation and approximating techniques. The 9-story steel moment-resisting frame is modeled using parameterized moment-rotation relationships with quadrilinear backbones for the beam plastic-hinges. The uncertain properties of the backbones include the yield moment, the post-yield hardening ratio, the end-of-hardening rotation, the slope of the descending branch, the residual moment capacity and the ultimate rotation reached. IDA is employed to accurately assess the seismic performance of the model for any combination of the parameters by performing multiple nonlinear time history analyses for a suite of ground motion records. IDA sensitivity analysis reveals the yield moment and the two rotational-ductility parameters to be the most influential for the frame behavior. To propagate the parametric uncertainty to the actual seismic performance we employ a) Monte Carlo simulation with latin hypercube sampling, b) point-estimate and c) first-order second-moment techniques, thus offering competing methodologies that represent different compromises between speed and accuracy. The final results provide firm ground for challenging current assumptions in seismic guidelines on using a mean-parameter model to estimate the mean seismic performance and employing the well-known square-root-sum-of-squares rule to combine aleatory randomness and epistemic uncertainty.
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