Yielding oscillator subjected to simple pulse waveforms: Numerical analysis & closed-form solutions

Numerical and analytical solutions are presented for the elastic and inelastic response of single-degree-of-freedom yielding oscillators to idealized ground acceleration pulses. These motions are typical of near-fault earthquake recordings generated by forward rupture directivity and may inflict damage in the absence of substantial structural strength and ductility capacity. Four basic pulse waveforms are examined: (1) triangular; (2) sinusoidal; (3) exponential; and (4) rectangular. In the first part of the article, a numerical study is presented of the effect of oscillator period, strength, damping, post-yielding stiffness and number of excitation cycles, on inelastic response. Results are presented in the form of dimensionless graphs and regression formulas that elucidate the salient features of the problem. It is shown that conventional R-μ relations may significantly underestimate ductility demand imposed by near-fault motions. The second part of the article concentrates on elastic-perfectly plastic oscillators. Closed-form solutions are derived for post-yielding response and associated ductility demand. It is shown that all three ground motion histories (i.e. acceleration, velocity, and displacement) control oscillator response - contrary to the widespread view that ground velocity alone is of leading importance. The derived solutions provide insight on the physics of inelastic response, which is often obscured by the complexity of numerical algorithms and actual earthquake motions. The model is evaluated against numerical results from near-field recordings. A case study is presented.