A better rigid-plastic estimate for earthquake-induced plastic displacements

The earthquake ductility demand on structures may be predicted by means of a rigid-plastic method, which derives the maximum plastic response of elastic-plastic oscillators from that of a simpler rigid-plastic model. The maximum response of the latter is a purely plastic one and may be obtained from the earthquake rigid-plastic pseudo-spectrum, as a function of the oscillator yield acceleration. The results of a wide investigation presented in this paper show that such a method generally leads to a conservative and reliable enough estimate of the maximum plastic displacements. Small mean errors are in fact found for both comparatively short-period and long-period oscillators. In the medium-period range, however, the rigid-plastic prediction is found to be less satisfactory. This is due to the appliance in that range of an empirical formula, which estimates the discrepancy between the elastic-plastic and the rigid-plastic peak response. To improve the rigid-plastic prediction in the medium-period range, a new semi-empirical formula is derived in the paper which is shown to halve, on average, the error in estimating the earthquake ductility demand on medium-period oscillators. Thanks to the new formula, the mean relative errors are always kept below 15%, whatever the earthquake and the oscillator. This makes the rigid-plastic method competitive with respect to other approximate methods, as discussed in the paper.