Bijan Mohraz

A METHOD OF ESTIMATING THE PARAMETERS OF TUNED MASS DAMPERS FOR SEISMIC APPLICATIONS

The optimum parameters of tuned mass dampers (TMD) that result in considerable reduction in the response of structures to seismic loading are presented. The criterion used to obtain the optimum parameters is to select, for a given mass ratio, the frequency (tuning) and damping ratios that would result in equal and large modal damping in the first two modes of vibration. The parameters are used to compute the response of several single and multi-degree-of-freedom structures with TMDs to different earthquake excitations. The results indicate that the use of the proposed parameters reduces the displacement and acceleration responses significantly. The method can also be used in vibration control of tall buildings using the so-called ‘mega-substructure configuration’, where substructures serve as vibration absorbers for the main structure. It is shown that by selecting the optimum TMD parameters as proposed in this paper, significant reduction in the response of tall buildings can be achieved.

Single‐ and multiple‐tuned liquid column dampers for seismic applications

Design parameters for single- and multiple-tuned liquid column dampers for reducing the response of structures to seismic excitations are presented. A deterministic analysis is carried out using 72 earthquake ground motion records to determine the tuning ratio, tube width to liquid length ratio, and head loss coefficient corresponding to a given mass ratio for single-tuned liquid column dampers. A similar analysis is performed to determine the central tuning ratio, tuning bandwidth, and grouping of dampers for multiple-tuned liquid column dampers. The study indicates that by properly selecting the design parameters, single- and multiple-tuned liquid column dampers can reduce the response of structures to seismic excitation by up to 45 per cent. Design examples using single- and multiple-tuned liquid column dampers in a bridge and a ten-storey building are presented to illustrate how the parameters are selected and to demonstrate the performance of the devices under different ground excitations. The response of several structures with tuned liquid column dampers is compared with that using tuned mass dampers where it is shown that both devices result in comparable reductions in the response.

Distribution of earthquake input energy in structures

In developing an energy-based design approach and assessing the damage potential of structures, one must know the distribution of earthquake input energy among energy components: kinetic, elastic strain, hysteretic, and damping. This report examines the influences of the ground motion characteristics: intensity, frequency content, and duration of strong motion and the structural properties: ductility, damping, and hysteretic behavior on the distribution of input energy for a oneand a five-story building using 20 accelerograms, ten with short and ten with long duration of strong motion. Results indicate that for certain damping ratios, ductility has a significant influence on input energy and its distribution among energy components in a structure. For a given ductility ratio, small damping ratio (less than 5%) has a minor effect on input energy, but a major influence on the energy distribution. Damping ratios larger than 5% have a significant influence on the input energy and its distribution. Three energy ratios that relate to hysteretic energy were computed: the maximum ratio of hysteretic to input energy (Eh/Eir)m, the ratio of the maximum hysteretic energy to the maximum input energy Ehm/Eirm, and the equivalent number of yield excursions Neq=Ehm/(Fy.up) where Fy is the yield strength, and up is the plastic deformation. It is found that (Eh/Eir)m generally reflects the energy demand for the largest yield excursion, and Ehm/Eirm and Neq reflect the energy demand for the entire duration of accelerogram. The study shows that (Eh/Eir)m is independent of the duration of strong motion and period of structure; however, Ehm/Eirm is independent of both only for periods less than 1 s. Results indicate that as the duration becomes longer the equivalent number of yield excursions Neq increases indicating more structural damage. The influence of ground motion characteristics and structural properties on the distribution of energy parameters for a five-story building with fixed-base, base-isolation, supplemental damping, and semi-active control are examined using the 20 accelerograms. The results show that: 1) the distribution of energy through the height of the building is mostly independent of the frequency content and the duration of strong motion, 2) baseisolation, supplemental damping, and semi-active control reduce the damage potential by reducing the input and hysteretic energy demands and have significant influences on the distribution of energy through the height of the building.

Earthquake Ground Motion and Response Spectra

This chapter surveys the state-of-the-art work in strong motion seismology and ground motion characterization. Methods of ground motion recording and correction are first presented, followed by a discussion of ground motion characteristics including peak ground motion, duration of strong motion, and frequency content. Factors that influence earthquake ground motion such as source distance, site geology, earthquake magnitude, source characteristics, and directivity are examined. The chapter presents probabilistic methods for evaluating seismic risk at a site and development of seismic maps used in codes and provisions. Earthquake response spectra and factors that influence their characteristics such as soil condition, magnitude, distance, and source characteristics are also presented and discussed. Earthquake design spectra proposed by several investigators and those recommended by various codes and provisions through the years to compute seismic base shears are described. The latter part of the chapter discusses inelastic earthquake spectra and response modification factors used in seismic codes to reduce the elastic design forces and account for energy absorbing capacity of structures due to inelastic action. Earthquake energy content and energy spectra are also briefly introduced. Finally, the chapter presents a brief discussion of artificially generated ground motion.

A Simplified Procedure for Constructing Probabilistic Response Spectra

This paper provides a simplified procedure for computing the probabilistic maximum response of a linear single-degree-of-freedom system subjected to earthquake ground motion. The formulation uses the root-mean-square (rms) response of the system and a probabilistic peak factor which is modified to account for the wide-band characteristics. The modification uses a set of damping-dependent coefficients obtained from correlating the peak factor with the ratio of the maximum response to the rms response from accelerograms recorded on alluvium and rock. The procedure incorporates the influence of soil condition and the strong motion duration as parameters in computing response spectra.

Comments on earthquake response spectra

Abstract Statistical summaries have been carried out on a large number of earthquake records to examine the influences of geological conditions, duration of strong motion, and peak ground acceleration on ground motion and response spectra. The results indicate that the peak ground velocity-acceleration ratio is substantially lower for records on rock deposits than those on alluvium, and it is lower for records with a peak ground acceleration greater than 0.20 g than those with acceleration less than 0.20 g . For each influence the spectral bounds defined as the product of mean ground motion and mean plus one standard deviation amplifications are computed for five damping coefficients and compared to those for alluvium deposits without consideration of duration and acceleration level.

Proceedings of a workshop on developing and adopting seismic design and construction standards for lifelines

These recommendations for developing and adopting seismic design and construction standards for lifelines describe the properties intended for lifeline systems, equipment, and materials. They provide both the mechanism for communication between buyers and sellers of lifeline products and services and the basis for regulations protecting the public health, safety, and welfare.

MODAL ANALYSIS OF NONLINEAR SYSTEMS WITH NONCLASSICAL DAMPING

This paper presents a mode-superposition pro- cedure for the analysis of nonlinear problems in structural dynamics where damping cannot be assumed proportional. The procedure consists of treating the nonlinearity as a pseudo force and using a complex eigenvalue solution to decouple the equations of motion. The response time history of a twenty-degree-of-freedom system with nonpropor- tional damping to a base excitation is obtained using the proposed procedure and compared with that from a direct integration of the equations of motion. The comparison indicates excellent agree- ment.