Direct scaling of residual displacements for bilinear and pinching oscillators

The estimation of residual displacements in a structure due to an anticipated earthquake event has increasingly become an important component of performance-based earthquake engineering because controlling these displacements plays an important role in ensuring cost-feasible or cost-effective repairs in a damaged structure after the event.An attempt is made in this study to obtain statistical estimates of constant-ductility residual displacement spectra for bilinear and pinching oscillators with 5%initial damping,directly in terms of easily available seismological,site,and model parameters.None of the available models for the bilinear and pinching oscillators are useful when design spectra for a seismic hazard at a site are not available.The statistical estimates of a residual displacement spectrum are proposed in terms of earthquake magnitude,epicentral distance,site geology parameter,and three model parameters for a given set of ductility demand and a hysteretic energy capacity coefficient in the case of bilinear and pinching models,as well as for a given set of pinching parameters for displacement and strength at the breakpoint in the case of pinching model alone.The proposed scaling model is applicable to horizontal ground motions in the western U.S.for earthquake magnitudes less than 7 or epicentral distances greater than 20 km.

Scaling of residual displacements in terms of elastic and inelastic spectral displacements for existing SDOF systems

Structures undergoing inelastic displacements during earthquake ground motions are known to sustain some amount of residual displacements, which may make them unusable or unsafe. In this study an attempt is made to estimate residual displacements for elastic-perfectly-plastic single-degree-of-freedom oscillators with a given lateral strength ratio. It is observed in the case of a class of ground motions that there are no trends in the dependence of residual displacement on the temporal features of the ground motion, and thus any estimation of residual displacements should be carried out only in the statistical sense. Statistical estimation of residual displacement spectrum via normalization with respect to inelastic or elastic spectral displacements is considered, and it is found that normalization with respect to inelastic spectral displacements is preferable. Expressions for residual displacement spectra are proposed for both types of normalizations and for the givenlateral-strength-ratio type oscillators.

Study on inelastic displacement ratio spectra for near-fault pulse-type ground motions

In displacement-based seismic design, inelastic displacement ratio spectra （IDRS） are particularly useful for estimating the maximum lateral inelastic displacement demand of a nonlinear SDOF system from the maximum elastic displacement demand of its counterpart linear elastic SDOF system. In this study, the characteristics of IDRS for near-fault pulse-type ground motions are investigated based on a great number of earthquake ground motions. The influence of site conditions, ratio of peak ground velocity （PGV） to peak ground acceleration （PGA）, the PGV, and the maximum incremental velocity （MIV） on IDRS are also evaluated. The results indicate that the effect of near-fault ground motions on IDRS are significant only at periods between 0.2 s - 1.5 s, where the amplification can approach 20%. The PGV/PGA ratio has the most significant influence on IDRS among the parameters considered. It is also found that site conditions only slightly affect the IDRS.

Optimal vector-valued intensity measure for seismic collapse assessment of structures

The present study is aimed to investigate the ability of different intensity measures （IMs）, including response spectral acceleration at the fundamental period of the structure, Sa（T1）, as a common scalar IM and twelve vector-valued IMs for seismic collapse assessment of structures. The vector-valued IMs consist of two components, with S（T1） as the first component and different parameters that are ratios of scalar IMs, as well as the spectral shape proxies εSa and N, as the second component. After investigating the properties of an optimal IM, a new vector-valued IM that includes the ratio of Sa（T1） to the displacement spectrum intensity （DSI） as the second component is proposed. The new IM is more efficient than other IMs for predicting the collapse capacity of structures. It is also sufficient with respect to magnitude, source-to-site distance, and scale factor for collapse capacity prediction of structures. To satisfy the predictability criterion, a ground motion prediction equation （GMPE） is determined for Sa（T1）/DSI by using the existing GMPEs. Furthermore, an empirical equation is proposed for obtaining the correlation between the components of the proposed IM. The results of this study show that using the new vector-valued IM leads to a more reliable seismic collapse assessment of structures.