Estimate of Peak Relative Velocity from Conventional Spectral Velocity for Response Spectrum Based Force Evaluation in Damping Devices

Structural control by passive devices is reliable and well-accepted means for earthquake resistance. In absence of peak relative velocity (SV), conventional spectral velocity (PSV) obtained by undamped natural frequency times spectral displacement, is recommended by prevailing seismic standards to estimate damping forces in velocity-dependent devices in response spectrum method of analysis. For structures using velocity dependent energy dissipation devices peak relative velocity across the ends of these devices is essential to capture damping forces fairly accurately. In general, SV is not available in spectrum based procedures in codes, which requires approximation or estimation. A new methodology of estimating SV values from PSV by using Bi-functional regression model is proposed in this study. An ensemble of 108 strong ground motions with wide variations in their characteristics is used to derive the proposed model by regression analysis. Accuracy of estimation of the suggested model is verified and validated by comparing it with exact SV and other available models. Numerical results show that proposed Bi-functional model performs reliably well for all damping values and periods and able to capture SV values more accurately in selected period range with root mean square (r.m.s.) error smaller than other similar approximations considered.