Response Spectra for Differential Motion of Columns

Abstract

SUMMARYThe validity of the response spectrum concept for determining loads in structures excited by differential earthquake ground motion is examined. It is shown that the common definition of response spectrum for synchronous ground motion can be reconciled to remain valid in cases when the columns of extended structures experience different motions. Then, a relative displacement response spectrum for design of first-storey columns, SDC(¹, , , ), is defined. In addition to natural period, ¹, and fraction of critical damping, , this spectrum depends also on the 'travel time', (of the waves in the soil over distances about one half width, or length of the structure), and on a factor, , specifying the relative displacement of the first floor. It is shown how this spectrum can be determined using existing empirical scaling equations for relative displacement spectra SD(¹, ) and for peak velocity and peak acceleration of strong ground motion. These new spectra are illustrated for a horizontal component of a record in the near field of the 1994 Northridge earthquake. The results show that differential motions are more important for short period (stiff ) than for longer period (flexible) structures, and for structures founded on softer ground (small shear wave velocity).

Energy dissipation by nonlinear soil strains during soil–structure interaction excited by SH pulse

“…Near and beyond these large, strong motion amplitudes, the soil may begin to break into blocks, moving independently on the liquefied substratum. The structures will then begin to be damaged and destroyed by large differential displacements [44] and rotations of their foundation, due to deformations and forces larger than those resulting from shaking.…”

Response spectra for differential motion of columns paper II: Out-of-plane response

“…For propagation along the longitudinal axis of the building, SH and Love waves will excite the OP motion and torsion, while the body P, SV, and surface Rayleigh waves will cause IP horizontal, vertical, and rocking motions. Trifunac and Todorovska [3] have studied horizontal differential motions of column foundations for IP excitation (Fig. 1b) and for long wavelengths of incident waves for which lbL.…”

“…The IP motion can further be separated into horizontal (longitudinal), vertical, and rocking components, while OP motion consists of horizontal motion in the transverse direction and torsion along the vertical axis. Trifunac and Todorovska [3] analyzed the effects of the horizontal IP components of differential motion for buildings with models that are analogous to the sketch in Fig. 1b, and they showed how the response spectrum method could be modified to include the first-order effects of differential motion.…”

Anti-symmetric mode excitation and seismic response of base-isolated bridges under asynchronous input motion

“…For instance, random vibration analysis has been used to estimate the response of highway [30,31], suspension [32,33] and cable-stayed bridges [34][35][36]. The impact of multi-support excitation on the seismic behavior of bridges has also been investigated in the frequency (using response spectrum-based methods [1,[37][38][39][40][41][42][43]) and the time domain. In the second case, numerous studies investigated both the linear and/or the non-linear response of different types of bridges, namely: (a) straight bridges on uniform [44][45][46][47] or varying soil profiles, ignoring [45,47,48] or accounting for the soil-structure interaction (SSI) effects [49,50], (b) curved bridges [47,51,52], (c) skewed bridges [45,53], and (d) isolated bridges [54][55][56][57].…”