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

It is shown that the common response spectrum method for synchronous ground motion can be extended to make it applicable for earthquake response analyses of extended structures experiencing differential out-of-plane ground motion. A relative displacementspectrum for design of first-story columns SDC (T, TT, z, zT, t, d) is defined. In addition to the natural period of the out-of-plane response, T, and the corresponding fraction of critical damping, z, this spectrum also depends on the fundamental period of torsional vibrations, TT, and the corresponding fraction of critical damping, zT, on the ‘‘travel time,’’ t (of the waves in the soil over a distance of about one-half the length of the structure), and on a dimensionless factor d, describing the relative response of the first floor. The new spectrum, SDC, can be estimated by using the empirical scaling equations for relative displacement spectra, SD, and for peak ground velocity, vmax. For recorded strong-motion acceleration, and for symmetric buildings, the new spectrum can be computed from Duhamel’s integrals of two uncoupled equations for dynamics equilibrium describing translation and rotation of a two-degree-offreedom system. This representation is accurate when the energy of the strong-motion is carried by waves in the ground the wavelengths of which are one order of magnitude or more longer than the characteristic length of the structure

Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artificial and historic records

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals’ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice

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

It is shown that the common response spectrum method for synchronous ground motion can be extended to make it applicable for earthquake response analyses of extended structures experiencing differential out-of-plane ground motion. A relative displacementspectrum for design of first-story columns SDC (T, TT, z, zT, t, d) is defined. In addition to the natural period of the out-of-plane response, T, and the corresponding fraction of critical damping, z, this spectrum also depends on the fundamental period of torsional vibrations, TT, and the corresponding fraction of critical damping, zT, on the ‘‘travel time,’’ t (of the waves in the soil over a distance of about one-half the length of the structure), and on a dimensionless factor d, describing the relative response of the first floor. The new spectrum, SDC, can be estimated by using the empirical scaling equations for relative displacement spectra, SD, and for peak ground velocity, vmax. For recorded strong-motion acceleration, and for symmetric buildings, the new spectrum can be computed from Duhamel’s integrals of two uncoupled equations for dynamics equilibrium describing translation and rotation of a two-degree-offreedom system. This representation is accurate when the energy of the strong-motion is carried by waves in the ground the wavelengths of which are one order of magnitude or more longer than the characteristic length of the structure