Apparent translational component for rotational ground motions

Even though the rotational ground motion may contribute significantly to the response of certain structures, their effects are generally ignored in seismic design, because of non-availability of appropriate instruments for direct recording of the rotational components. Like many others, a simplified framework was proposed by the authors elsewhere (Rodda and Basu in Int J Earthq Impact Eng 1(3):253–288, 2016) to extract the rotational motion as a temporal derivative of an apparent translational component (ATC) followed by scaling with an apparent velocity. ATC was defined such that its time derivative is closely correlated with the respective rotational motion. But the a priori knowledge of rotational motion is required in estimating the ATC for rocking component. An empirical procedure has been proposed here to bypass the requirement of rotational motion a priori. This paper also assesses the definition of ATC through examining the similitude between the time derivative of ATC and the respective rotational motion (benchmark) quantitatively. Similitude is assessed on smoothened response spectra (by Hamming window) of the time derivative of ATC and that of rotational motion. A new definition of spectral contrast angle (SCA) based on distance correlation has been proposed to assess the spectral similitude. To differentiate the similar from non-similar spectra, SCA corresponding to an acceptable degree of similarity is proposed by studying a large ensemble of ground motions from the PEER database. This similitude study is further extended using relative energy build up and energy spectra.