Yielding oscillator under triangular ground acceleration pulse

An analytical solution is presented for the response of a bilinear inelastic simple oscillator to a symmetric triangular ground acceleration pulse. This type of motion is typical of near-fault recordings generated by source-directivity effects that may generate severe damage. Explicit closed-form expressions are derived for: (i) the inelastic response of the oscillator during the rising and decaying phases of the excitation as well as the ensuing free oscillations; (ii) the time of structural yielding; (iii) the time of peak response; (iv) the associated ductility demand. It is shown that when the duration of the pulse is long relative to the elastic period of the structure and its amplitude is of the same order as the yielding seismic coefficient, serious damage may occur if significant ductility cannot be supplied. The effect of post-yielding structural stiffness on ductility demand is also examined. Contrary to presently-used numerical algorithms, the proposed analytical solution allows many key response parameters to be evaluated in closed-form expressions and insight to be gained on the response of inelastic structures to such motions. The model is evaluated against numerical results from actual near-field recorded motions. Illustrative examples are also presented.