Frequency domain modal analysis of earthquake input energy to highly damped passive control structures

A new complex modal analysis‐based method is developed in the frequency domain for efficient computation of the earthquake input energy to a highly damped linear elastic passive control structure. The input energy to the structure during an earthquake is an important measure of seismic demand. Because of generality and applicability to non‐linear structures, the earthquake input energy has usually been computed in the time domain. It is shown here that the formulation of the earthquake input energy in the frequency domain is essential for deriving a bound on the earthquake input energy for a class of ground motions and for understanding the robustness of passively controlled structures to disturbances with various frequency contents. From the viewpoint of computational efficiency, a modal analysis‐based method is developed. The importance of overdamped modes in the energy computation of specific non‐proportionally damped models is demonstrated by comparing the energy transfer functions and the displacement transfer functions. Through numerical examinations for four recorded ground motions, it is shown that the modal analysis‐based method in the frequency domain is very efficient in the computation of the earthquake input energy. Copyright © 2004 John Wiley & Sons, Ltd.     

Efficient analysis of pile-group effect on seismic stiffness and strength design of buildings

A new efficient method is developed for the analysis of pile-group effects on the seismic stiffness and strength design of buildings with pile foundations. An efficient continuum model consisting of a dynamic Winkler-type soil element and a pile is used to express the dynamic behavior of the structure-pile-soil system with only a small numerical error. The pile-group effect is taken into account through the influence coefficients among piles which are defined for interstory drifts and pile-head bending moments. It is shown that, while the pile-group effect reduces the interstory drift of buildings in general, it may increase the bending moment of piles at the head. This means that the treatment without the pile-group effect results in the conservative design for super-structures and requires a revised member design for piles.     

Deterministic and probabilistic representation of near-field pulse-like ground motion

The response and damage assessment of engineering structures under near-field ground motions is currently of great interest. Near-field ground motion with directivity focusing or fling effects produces pulse-like ground motion that has characteristics different from those of ordinary records. This paper develops simple deterministic and probabilistic models for near-field pulse-like ground motions. These models belong to the class of engineering models that aim to replicate some of the gross features observed in near-field records. The ground velocity is expressed as a steady-state function or a stationary random process modulated by an envelope function. Both models account for the non-stationarity and the multiple pulses in the ground velocity. While the deterministic model is similar to some of the models developed earlier, the probabilistic model facilitates handling uncertainties in the ground motion and variability in the structure's properties. For instance, this model combined with structural reliability methods can be used for reliability assessment of structures under near-field random ground motion. The reduction of the structural response by adding supplemental dampers is also investigated.     

Seismic frame design via inverse mode design of frame-ground systems

A two-step stiffness design procedure is developed for a moment-resisting planar frame supported by a prescribed two-dimensional finite-element ground-pile system. In the first step, a hybrid inverse eigenmode problem is formulated and its solution is derived in an analytical form. A difficulty resulting from the existence of multiple interface nodes is overcome by incorporating a deformation constraint into a set of linear equations for finding the lowest-mode displacements at the interface nodes and in the ground. In the second step, the fundamental natural frequency of the combined system and the lowest mode-strain ratios in the frame specified in the first step are regarded as the parameters for adjusting the mean peak seismic member-end strains to their specified values. If the fundamental natural frequency of the frame with a fixed-base happens to be close to that of the ground, a difficulty arises in the two-step stiffness design procedure because of an irregular response amplification and of the non-predominance of the lowest-mode components. A new practical design procedure of rapid convergence is proposed such that an initial design is found for a stiff ground and that a sequence of stiffness designs is generated with respect to a ground stiffness parameter without any differential coefficient of series expansion. The accuracy of the model utilized in this paper and the validity of the present stiffness design procedure are verified through time-history response analysis.     

Remarkable response amplification of building frames due to resonance with the surface ground

Seismic response of a building structure is influenced greatly by soil-structure interaction. This fact has been demonstrated in the past earthquakes. It is shown that tuning of the natural period of a building structure with that of a surface ground causes remarkable response amplification of the building structure. Introduction of an overall system as a building-pile-soil system is inevitable to investigate such a tuning effect. It is demonstrated to be essential to define a design earthquake at a bedrock level in order to guarantee the structural safety of building structures under seismic disturbances. Comparison of the response due to input of double the upward-propagating wave (an outcropping motion) into the bedrock without any viscous boundary with that due to input of an within motion into the bedrock without any viscous boundary is also shown in order to investigate the effect of input motions on the response of the superstructure.     

Scaling of tropical rainfall as observed by TRMM precipitation radar

We used a three-year (1998–2000) dataset of TRMM Precipitation Radar observations to investigate the scaling properties of spatial rainfall fields. This dataset allows consideration of spatial scales ranging from about 4.3 km to 138 km and short temporal scales corresponding to the sensor overpasses. The focus is on the marginal spatial moment scaling, which allows estimation of the scaling parameters from a single scene of data. Here we present a global perspective of the scaling properties of tropical rainfall in terms of its spatial variability, atmospheric forcing, predictability, and applicability. Our results reveal the following: 1) the scaling parameters exhibit strong variability associated with land/ocean contrast and mean precipitation at the synoptic scale; 2) there exists a one-to-one relationship between the scaling parameters and the large-scale spatial average rain rate of a universal functional form; 3) the majority of the scenes are consistent with the hypothesis of scale invariance at the moment orders of 0 and 2; 4) relatively there are more scale-invariant rain scenes over land than over ocean; and 5) for the scenes that are non-scale-invariant, deviation from scale-invariance mainly arises from the increasingly intermittent behavior of rainfall as spatial scale decreases. These results have important implications for the development and calibration of downscaling procedures designed to reproduce rainfall properties at different spatial scales and lead to a better understanding of the nature of tropical rainfall at various spatial resolutions.     

A unified earthquake-resistant design method for steel frames using arma models

The objective of this paper is to develop a unified earthquake-resistant design method for moment-resisting steel frames, including the design earthquake via a dynamic ARMA model. Important features of this design method are: (i) to make it possible to incorporate inherent uncertain features of design earthquakes into the design process itself through the dynamic ARMA model, (ii) to provide a simplified design formula for a preliminary design of moment-resisting steel frames based upon the concept of stiffness-oriented design and (iii) to facilitate the formulation of a new probabilistic multi-objective optimal design problem aimed at finding the design with the minimum level of designer's dissatisfaction. In this optimal design problem, constraints and objectives are handled in a unified manner after a feasible design is obtained. A design example is presented to demonstrate the validity of this unified design method and to examine the convergence of response statistics. Finally, the generality and practicality of this design method are assessed.     

Probabilistic critical excitation for MDOF elastic–plastic structures on compliant ground

Earthquake ground motions and their effects on structural responses are very uncertain even with the present knowledge. It is therefore desirable to develop a robust structural design method taking into account these uncertainties. Critical excitation approaches are promising and a new random critical excitation method is proposed for MDOF elastic–plastic shear‐building structures on compliant ground. The power (area of power spectral density (PSD) function) and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. In contrast to linear elastic structures, transfer functions and simple expressions for response evaluation cannot be defined in elastic–plastic structures and difficulties arise in describing the peak responses except by laborious elastic–plastic time‐history response analysis. Statistical equivalent linearization is used to estimate the elastic–plastic stochastic peak responses approximately. The critical excitation responses are obtained for several examples and compared with those of the corresponding recorded earthquake ground motion. Copyright © 2001 John Wiley & Sons, Ltd.     

Resonance and criticality measure of ground motions via probabilistic critical excitation method

Resonant characteristics of recorded ground motions are investigated and a new measure of criticality of ground motions is proposed. Four classes of recorded ground motions, i.e., (i) near fault motions (rock records), (ii) near fault motions (soil records), (iii) long duration motions (rock records) and (iv) long duration motions (soil records), are taken from Abrahamson N, Ashford S, Elgamal A, Kramer S, Seible F, Somerville P, Proc of First PEER Workshop on Characterization of Special Source Effects, 1998. It is shown that resonant characteristics of recorded ground motions can be captured appropriately by means of the probabilistic critical excitation method due to the present author regardless of the type of ground motions and the distance between the critical response and the actual one can be a new measure of criticality of ground motions. The time-averaged approximate treatment of nonstationary ground motions as stationary ones is shown to be adequate for structures with shorter natural periods subjected to long duration ground motions.