ALBERT

Description: The task of selecting and scaling an appropriate set of ground motion records is one of the most important challenges facing practitioners in conducting dynamic response history analyses for seismic design and risk assessment. This paper describes an integrated experimental and analytical evaluation of selected ground motion scaling methods for linear-elastic building frame structures. The experimental study is based on the shake table testing of small-scale frame models with four different fundamental periods under ground motion sets that have been scaled using different methods. The test results are then analytically extended to a wider range of structural properties to assess the effectiveness of the scaling methods in reducing the dispersion and increasing the accuracy in the seismic displacement demands of linear-elastic structures, also considering biased selection of ground motion subsets. For scaling methods that are based on a design estimate of the fundamental period of the structure, effects of possible errors in the estimated period are investigated. The results show that a significant reduction in the effectiveness of these scaling methods can occur if the fundamental period is not estimated with reasonable certainty. © 2012 John Wiley & Sons, Ltd.

Description: An analytical approximation for the calculation of the stationary reliability of linear dynamic systems with higher-dimensional output under Gaussian excitation is presented. For systems with certain parameters theoretical and computational issues are discussed for two topics: (1) the correlation of failure events at different parts of the failure boundary and (2) the approximation of the conditional out-crossing rate across the failure boundary by the unconditional one. The correlation in the first topic is approximated by a multivariate integral, which is evaluated numerically by an efficient algorithm. For the second topic some existing semi-empirical approximations are discussed and a new one is introduced. The extension to systems with uncertain parameters requires the calculation of a multi-dimensional reliability integral over the space of the uncertain parameters. An existing asymptotic approximation is used for this task and an efficient scheme for numerical calculation of the first-and second-order derivatives of the integrand is presented. Stochastic simulation using an importance sampling approach is also considered as an alternative method, especially for cases where the dimension of the uncertain parameters is moderately large. Comparisons between the proposed approximations and Monte Carlo simulation for some examples related to earthquake excitation are made. It is suggested that the proposed analytical approximations are appropriate for problems that require a large number of consistent error estimates of the probability of failure, as occurs in reliability-based design optimization. Numerical problems regarding computational efficiency may arise when the dimension of both the output and the uncertain parameters is large. Copyright © 2006 John Wiley & Sons, Ltd.

Description: Inerter-based vibration absorbers (IVAs), such as the tuned-mass-damper-inerter (TMDI), have become popular in recent years for the earthquake protection of building structures. Previous studies using linear structural models have shown that IVAs can achieve enhanced vibration suppression, but at the expense of increased control forces exerted from the IVA to the host building structure. The authors recently developed a bi-objective IVA design framework for linearly behaving buildings to balance between structural performance (drift/acceleration suppression) and IVA forces. This paper extends the framework to multi-storey hysteretic/yielding structures under seismic excitation. Though the proposed design framework can accommodate any type of IVA, the focus is herein on TMDI applications, with tuned-mass-damper (TMD) and tuned-inerter-damper (TID) treated as special cases of the TMDI. Earthquake hazard is modeled through representative, design-level acceleration time-histories and response of the IVA-equipped structure is evaluated through nonlinear response-history analysis. A high-fidelity finite element model (FEM) is established to accurately describe hysteretic structural behavior. To reduce the computational burden, a reduced order model (ROM) is based on the original FEM, using the framework proposed recently by the first and second authors. The ROM maintains the accuracy of the original FEM while enabling for a computationally efficient solution to the optimization problem. As an illustrative example, the bi-objective design for different IVA placements along the height of a non-linear benchmark 9-storey steel frame structure is examined. The accuracy of the ROM-based design is evaluated by comparing performance to the FEM-based response predictions across the entire Pareto front resulting from the bi-objective optimization. Then, the designs and associated performance predicted by using a linear or a nonlinear structural model are compared to evaluate how the explicit consideration of nonlinearities, as well as the degree of nonlinear behavior, impact the IVA design and efficiency.