Estimation of peak relative velocity and peak absolute acceleration of linear SDOF systems

In the seismic analysis and design of structures, the true velocity and absolute acceleration are usually approximated by their corresponding pseudo-values. This approach is simple and works well for structures with small damping (say, less than 15%). When the damping of a structure is enhanced for the purpose of response reduction, it may result in large analysis and design errors. Based on theory of random vibration and the established mechanism of seismic response spectra analysis, a method is developed (1) to predict the relative velocity spectra with any damping ratio level directly from the 5% standard pseudo-acceleration spectrum; and (2) to estimate the peak absolute acceleration. The accuracy of both is validated by using two selected ensembles of ground motion records.     

Nonlinear aspects of energy dissipation in wood-panel joints

The joints connecting vertical and horizontal elements are the "weak link" in structural systems assembled from wood panels. If they are too weak, local failures may occur, resulting in performance that is significantly below expectations. If they are too resistant, the joints may be unable to dissipate energy during vibrations, thus possibly initiating a fast progressive failure. This paper re-processes and re-elaborates the results of shaking table tests previously carried out by the author and other co-workers. The goal is to assess the feasibility of a joint which is able to dissipate energy during vibration, without degrading the connection performance.     

Analytical investigations of seismic responses for reinforced concrete bridge columns subjected to strong near-fault ground motion

Strong near-fault ground motion, usually caused by the fault-rupture and characterized by a pulse-like velocity- wave form, often causes dramatic instantaneous seismic energy (Jadhav and Jangid 2006). Some reinforced concrete (RC) bridge columns, even those built according to ductile design principles, were damaged in the 1999 Chi-Chi earthquake. Thus, it is very important to evaluate the seismic response of a RC bridge column to improve its seismic design and prevent future damage. Nonlinear time history analysis using step-by-step integration is capable of tracing the dynamic response of a structure during the entire vibration period and is able to accommodate the pulsing wave form. However, the accuracy of the numerical results is very sensitive to the modeling of the nonlinear load-deformation relationship of the structural member. FEMA 273 and ATC-40 provide the modeling parameters for structural nonlinear analyses of RC beams and RC columns. They use three parameters to define the plastic rotation angles and a residual strength ratio to describe the nonlinear load- deformation relationship of an RC member. Structural nonlinear analyses are performed based on these parameters. This method provides a convenient way to obtain the nonlinear seismic responses of RC structures. However, the accuracy of the numerical solutions might be further improved. For this purpose, results from a previous study on modeling of the static pushover analyses for RC bridge columns (Sung et al. 2005) is adopted for the nonlinear time history analysis presented herein to evaluate the structural responses excited by a near-fault ground motion. To ensure the reliability of this approach, the numerical results were compared to experimental results. The results confirm that the proposed approach is valid.     

A new spatial coherence model and analytical coefficients for multi-support response spectrum combination

In this paper, a new spatial coherence model of seismic ground motions is proposed by a fi tting procedure. The analytical expressions of modal combination (correlation) coeffi cients of structural response are developed for multi-support seismic excitations. The coeffi cients from both the numerical integration and analytical solutions are compared to verify the accuracy of the solutions. It is shown that the analytical expressions of numerical modal combination coeffi cients are of high accuracy. The results of random responses of an example bridge show that the analytical modal combination coeff icients developed in this paper are accurate enough to meet the requirements needed in practice. In addition, the computational effi ciency of the analytical solutions of the modal combination coeff icients is demonstrated by the response computation of the example bridge. It is found that the time required for the structural response analysis by using the analytical modal combination coeffi cients is less than 1/20 of that using numerical integral methods.     

Damping characteristics of friction damped braced frame and its effectiveness in the mega-sub controlled structure system

Based on energy dissipation and structural control principle, a new structural configuration, called the mega- sub controlled structure (MSCS) with friction damped braces (FDBs), is first presented. Meanwhile, to calculate the damping coefficient in the slipping state a new analytical method is proposed. The damping characteristics of one-storey friction damped braced frame (FDBF) are investigated, and the influence of the structural parameters on the energy dissipation and the practical engineering design are discussed. The nonlinear dynamic equations and the analytical model of the MSCS with FDBs are established. Three building structures with different structural configurations, which were designed with reference to the conventional mega-sub structures such as used in Tokyo City Hall, are comparatively investigated. The results illustrate that the structure presented in the paper has excellent dynamic properties and satisfactory control effectiveness.     

Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.     

Reconstruction of earthquake hazard in regions of sparse seismic monitoring

Studying strong motion records and the spatial distribution of ground shaking is of great importance in understanding the underlying causes of damage in earthquakes. Many regions in the world are either not instrumented or are sparsely instrumented. As such, significant opportunities for motion-damage correlations are lost. Two recent and damaging earthquakes belong to the class of lost opportunities, namely the Kashmir (Pakistan) earthquake of October 2005 and the Yogyakarta (Indonesia) earthquake of May 2006. In this paper, an overview of the importance of supply and demand studies in earthquake-stricken regions is given, followed by two examples of investigative engineering seismology aimed at reconstructing the hazard from sparse data. The paper closes with a plea for responsible authorities to invest in seismic monitoring networks in the very near future.     

Minimal cut-based recursive decomposition algorithm for seismic reliability evaluation of lifeline networks

In this paper, a new probabilistic analytical approach, the minimal cut-based recursive decomposition algorithm (MCRDA), is presented to evaluate the seismic reliability of large-scale lifeline systems. Based on the minimal cut searching algorithm, the approach calculates the disjoint minimal cuts one by one using the basic procedure of the recursive decomposition method. At the same time, the process obtains the disjoint minimal paths of the system. In order to improve the computation efficiency, probabilistic inequality is used to calculate a solution that satisfies the prescribed error bound. A series of case studies show that MCRDA converges rapidly when the edges of the systems have low reliabilities. Therefore, the approach can be used to evaluate large-scale lifeline systems subjected to strong seismic wave excitation.     

Semi-active model predictive control for 3rd generation benchmark problem using smart dampers

A semi-active strategy for model predictive control (MPC), in which magneto-rheological dampers are used as an actuator, is presented for use in reducing the nonlinear seismic response of high-rise buildings. A multi-step predictive model is developed to estimate the seismic performance of high-rise buildings, taking into account of the effects of nonlinearity, time-variability, model mismatching, and disturbances and uncertainty of controlled system parameters by the predicted error feedback in the multi-step predictive model. Based on the predictive model, a Kalman-Bucy observer suitable for semi-active strategy is proposed to estimate the state vector from the acceleration and semi-active control force feedback. The main advantage of the proposed strategy is its inherent stability, simplicity, on-line real-time operation, and the ability to handle nonlinearity, uncertainty, and time-variability properties of structures. Numerical simulation of the nonlinear seismic responses of a controlled 20-story benchmark building is carried out, and the simulation results are compared to those of other control systems. The results show that the developed semi-active strategy can efficiently reduce the nonlinear seismic response of high-rise buildings.     

Application of saddlepoint approximation in reliability analysis of dynamic systems

The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function (CDF) of the performance variable. The failure probability is obtained as the value of the complement CDF at a specif ied threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function (CGF) of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and effi ciency of the proposed methodology.