Free‐field rotations during earthquakes: Relevance on buildings

Abstract

Soil rotations around horizontal axes, during an earthquake, are studied through records collected by closely spaced arrays of strong motion accelerometers. The cross power spectrum of accelerations at nearby stations has been generally utilized to describe the spatial distribution of the motion. A number of cross spectra have been obtained during the training of these arrays. To take profit of these elaborations, a mathematical relation is established between the cross power spectrum and the power spectrum of the rotation.\ud Rotation data presented by Liu et al, concerning 52 earthquake records collected at a single station in Taiwan, are compared with rotation data computed according to our procedure. The two series of data are suitably normalized to the peak horizontal acceleration. The data are shown in function of the distance from epicentre. The same ratio, computed according to our procedure, is in good agreement with the average value of these data.\ud Direct measurements and the present approach have lead to evaluations of rotation higher than those predicted by mathematical investigations on the basis of the wave propagation theory, for comparable circumstances.\ud The relevance of this input motion for relatively tall structures is examined, with reference to the structural effects that the horizontal motion concurrently provides. Meaningful will be ranked those effects of the order of magnitude of 20% or higher than those implied by the horizontal excitation.\ud For understanding the relevance on building structures, the procedure has two areas of concern: 1) the coherence implicit in the cross power spectra, which depends on the interpolation process of the original records, collected in the arrays of instruments, and 2) the relative importance of the vertical to the horizontal input motion.\ud As to the second item, the relevance of the rotation component on structures largely depends on the relative importance of the vertical to the horizontal input motion. When the records in an area a few km from the epicenter are considered, the response spectrum of vertical motion is comparable and in some records even higher, than that of horizontal motion, over the entire range of frequencies. This has been observed as well for the 2009 earthquake event of L’Aquila, Italy, and that at the Christchurch (New Zealand) 2011. When the response spectrum of vertical motion is comparable to that of horizontal motion, the effects of rotational motions on most engineering structures can be meaningful

The Torsional Response of Civil Engineering Structures during Earthquake from an Observational Point of View

“…Newmark’s study paved the way for more sophisticated solutions (examples among others: [ 18 , 76 , 85 , 86 , 87 ]), from horizontal motion recorded in a free field to the generation of products (such as synthetic seismograms and response spectra) for designing structures. Numerical studies, whether based on the analysis of equivalent static lateral forces (force applied at a distance—eccentricity—from the centre of stiffness) or dynamic analysis, conclude that design forces increase due to accidental eccentricity [ 60 ].…”

“…In asymmetric structures, when Ty increases and Ω decreases, the influence of static eccentricity increases, and the effect of torsional ground motion can be ignored for tall asymmetric buildings. Castellani et al [ 87 ] concluded that the contribution of the rotational component on the response of the structure is more significant for a high-rise building (based on a numerical comparison between a low-rise building Ty=0.48s and a flexible building Ty = 1.56 s), which is a difference that can exceed 20%. They also showed that the higher modes could be neglected and that only the low-frequency portion of the response spectra induces significant rotational excitation.…”

Engineering analysis of measured rotational ground motions at GVDA

“…Extending the response spectrum to rotational ground motion adds a similarly useful tool when considering rotational ground motions in seismic design. Similarly to the translational response spectrum, the rotational response spectrum represents the peak rotational acceleration of a single degree of freedom rotational oscillator as a function of natural period and damping ratio, excited by a prescribed rotational ground acceleration [46].…”

Investigation of Topographic Site Effects using 3D Waveform Modelling: Amplification, Polarization and Torsional Motions in the Case Study of Arquata del Tronto (Italy)

“…On the other hand, ground motion rotations are rarely considered in site effects studies, due to difficulties involved in measuring rotational motions and strains and because of a widespread preconception in the seismological community that rotational motions are insignificant (Lee et al 2009). In the earthquake engineering community instead, the ground rotational motion gained interest (Lee and Trifunac 1985;Castellani et al 2012), since the travelling wave effect was recognized by Newmark (1969) and it is today accounted for in building codes under the term accidental eccentricity (Anagnostopoulos et al 2015). While the research regarding the relevance of ground motion rotations is still undergoing (Guidotti et al 2018), in the present work we investigate the possibility of topography-induced rotations around the vertical axis (torsional motion).…”