Uncertainty quantification for seismic responses of bilinear SDOF systems: A semi-closed-form estimation

The ability to accurately quantify uncertainty in structural system seismic responses is a critical component of performance based earthquake engineering (PBEE). Currently, for nonlinear systems, this is achieved empirically using a large number of simulations with different excitation inputs (ground motion suites) and numerically randomized structural model samples. This study focused on one of the simplest nonlinear hysteretic systems, the bilinear single-degree-of-freedom (SDOF) oscillator, to develop a semi-closed-form solution for seismic response uncertainty as a function of 1) intensity-independent ground motion characteristics, 2) structural parameters, and 3) ground motion intensity level. This approach included the development of a parametric model for bilinear system IDA curves with intensity independent ground motion parameters and structural parameters. The accuracy of the proposed model was validated through nonlinear time history analysis (NLTHA) simulations.