Comparing Hysteretic Energy and Ductility Uniform Annual Failure Rate Spectra for Traditional and a Spectral Shape-Based Intensity Measure

In this study, with the objective to develop a reliability-based seismic design tool, ductility and dissipated hysteretic energy uniform annual failure rate (UAFR) spectra are obtained and compared using the spectral acceleration at first mode of vibration of the structure Sa(T1) and the well-known spectral shape-based intensity measure INp. Notice that this is the first time in the literature that UAFR spectra are obtained for the advanced spectral shape intensity measure INp. For this aim, 110 simulated ground motions recorded from the soft soil of Mexico City were selected due to their large energy amount demanded to the structures; moreover, four elastoplastic hysteretic behavior models are considered for the dynamic analyses with post-yielding stiffness of 0, 3, 5, and 10%. It is observed that the use of elasto-perfectly plastic models provided similar UAFR spectra in comparison with hysteretic models with different post-yielding stiffness. This conclusion is valid for the two selected intensity measures. In addition, the lateral resistance required to achieve similar structural reliability levels is larger when the INp intensity measure is used, especially for buildings with vibration periods equal or larger than the soil period, in such a way that the traditional use of Sa(T1) could provide structures with less structural reliability levels.

Hysteretic Energy Demand under Superposition of Bidirectional Ground Motions

To address the irrationality of making a structure subjected to bidirectional ground motions equivalent to an SDOF system, a new approach method is presented in this paper. The ratio between modal participation factors of the two components of the structure is expressed as γ, and the superposition of bidirectional ground motions is regarded as one-directional earthquake excitation for the equivalent SDOF system. Based on this, an energy balance equation is established, and a method used to estimate normalized hysteretic energy (NHE) is proposed. Analysis of the ratio between NHE (γ ≠ 0) and NHE (γ = 0) is suggested in order to analyze the influence of bidirectional ground motions on hysteretic energy demand, and then, “α1 = NHE (γ ≠ 0)/NHE (γ = 0)” is defined, and bidirectional ground motion records for different soil sites are selected for establishing superimposed excitations. In addition, the period range of 0–5 s for the energy spectrum is divided into 6 ranges. In each period range, the means of α1 are defined as α. The curves of α of constant ductility factors for different soil sites are established, in which α is the vertical coordinate and γ is the horizontal coordinate. Through nonlinear response history analysis, the influence of soil types at different sites, the ductility factor, the ratio of modal participation factors, and the period on the values of α are analyzed. According to the analytical results, correction coefficient αs (the simplified value of α) is obtained so that the hysteretic energy demand under bidirectional ground motions can be determined.

A Nonstationary Mathematical Model for Acceleration Time Series

The choice of nonstationary stochastic models for the study is fully justified by the limitation of acceleration time series number. The three acceleration time series under consideration are used to generate a new, artificial series of ten per historical one using autoregressive moving average model. Subsequently, the average of nonlinear is utilized for the ten acceleration time series in order to obtain the spectral response of a system with single degree of freedom. Modeling of acceleration time series involves critical estimation of metrics that characterize nonstationary acceleration time series. Thus, for the stiffness degrading systems and bilinear systems, the metrics of hysteretic energy demand and displacement ductility demand during displacement are used. The applicability of artificially generated acceleration time series for the qualitative description of information was shown. More specifically, ARMA (2,2) showed the best results in the study for three accelerated time series through nonlinear response analysis. In addition, as a result, normalized hysteretic energy demand, empirically valid displacement ductility relationships, and model parameters were proposed.

Seismic Energy Response of SDOF Systems Subjected to Long-Period Ground Motion Records

To provide an important reference for the energy-based seismic design of long-period structures, the elastoplastic dynamic analysis program is employed to study the seismic energy response of single-degree-of-freedom (SDOF) systems under two types of typical long-period ground motions. Then, the influencing relationships of external and internal factors on the energy response spectra under near-fault pulse-like and far-field harmonic ground motions are analyzed one by one. Study results are obtained as follows: within the whole period, all the input energy, hysteretic energy and damping energy spectra of SDOF systems under near-fault pulse-like and far-field harmonic ground motions, are larger than those under common ground motions, even the seismic energy response under far-field harmonic ground motions is larger than that under near-fault pulse-like ground motions. From the aspect of energy concept, the energy response spectra and energy distribution rule of SDOF systems are evaluated based on the intensity and spectral distribution under near-fault pulse-like and far-field harmonic ground motions. If the ratio of hysteretic energy to input energy (RHEIE) is determined, the hysteretic energy which must be dissipated by a structure would be derived by the method of energy-based design. The input energy and hysteretic energy are mainly influenced by damping ratio and ductility coefficient, while the yield stiffness ratio exerts minor effects. It indicates that reasonable structural design parameters would contribute to the hysteretic energy of a structure itself.