Showing papers in "Earthquake Engineering & Structural Dynamics in 1992"

Development of real‐time pseudo dynamic testing

Abstract: This paper presents a study for the development of a system capable of performing real-time pseudo dynamic testing. The system combines the basics of the pseudo dynamic test with a dynamic actuator, a digital displacement transducer and a digital servo-mechanism. The digital servo-mechanism has been introduced to ensure accurate displacement and velocity control, in which digital feedback control with a time interval of 2 msec has been performed continuously during actuator motion. Using the system, pseudo dynamic tests under sinusoidal and earthquake ground motion are carried out for a structure having a viscous damper, demonstrating that a perfectly real-time pseudo dynamic test can be achieved by incorporating the modified central difference method into an extra buffer operation of the digital servo-mechanism. The responses solved by the pseudo dynamic tests are compared with the responses of the test structure as well as those obtained from post-numerical analysis, and it is found that the real-time pseudo dynamic test conducted in this study is accurate.

Response spectrum method for multi‐support seismic excitations

Abstract: A new response spectrum method is developed for seismic analysis of linear multi-degree-of-freedom, multiply supported structures subjected to spatially varying ground motions. Variations of the ground motion due to wave passage, loss of coherency with distance and variation of local soil conditions are included. The method is based on fundamental principles of random vibration theory and properly accounts for the effects of correlation between the support motions as well as between the modes of vibration of the structure.

Dynamic pile‐soil‐pile interaction. Part II: Lateral and seismic response

Abstract: SUMMARY A simplified three-step procedure is proposed for estimating the dynamic interaction between two vertical piles, subjected either to lateral pile-head loading or to vertically-propagating seismic S-waves. The starting point is the determination of the deflection profile of a solitary pile using any of the established methods available. Physically-motivated approximations are then introduced for the wave field radiating from an oscillating pile and for the effect of this field on an adjacent pile. The procedure is applied in this paper to a flexible pile embedded in a homogeneous stratum. To obtain analytical closed-form results for both pile-head and seismic-type loading pile-soil and soil-pile interaction are accounted for through a single dynamic Winkler model, with realistic frequency-dependent ‘springs’ and ‘dashpots’. Final- and intermediate-step results of the procedure compare favourably with those obtained using rigorous formulations for several pile group configurations. It is shown that, for a homogeneous stratum, pile-to-pile interaction effects are far more significant under head loading than under seismic excitation.

Dynamic characteristics of multiple substructures with closely spaced frequencies

Abstract: This paper considers a main structure supporting a large number of substructures. The substructures have closely spaced natural frequencies, and the combined main structure/multiple substructures system is subjected to harmonic or wide-band forces. The goal is to characterize the effects of the substructures on the response of the main structure. A special, fundamental case is studied in detail, where the substructures are oscillators with equal stiffnesses and equally spaced natural frequencies. The exact response expressions for the combined system are in terms of a complicated rational polynomial. However, by taking the limit where the number of substructures becomes large, the response expressions reduce to simple, physically meaningful results. It is found that the multiple substrutures are equivalent to a single viscous damping which is added to the damping of the main structure. An example illustrates how the results can be applied to passive vibration control of large structures.

An investigation of earthquake induced pounding between adjacent buildings

Abstract: The response of adjacent buildings in city blocks to several strong earthquakes is analysed, taking into account the mutual collisions, or pounding, resulting from insufficient or non-existing separation distances. The buildings are idealized as lumped-mass, shear beam type, multi-degree-of-freedom (MDOF) systems with bilinear force-deformation characteristics and with bases supported on translational and rocking spring-dashpots. Collisions between adjacent masses can occur at any level and are simulated by means of viscoelastic impact elements. Using five real earthquake motions the effects of the following factors are investigated: building configuration and relative size, seismic separation distance and impact element properties. It is found that pounding can cause high overstresses, mainly when the colliding buildings have significantly different heights, periods or masses. This suggests a possibility for introducing a set of conditions into the codes, combined with some special measures, as an alternative to the seismic separation requirement.

Equivalent ductility factors, taking into account low‐cycle fatigue

Abstract: During strong earthquakes, the deformation capacity of structures is reduced due to the cumulative damage caused by cyclic load reversals. In the paper, equivalent (reduced) ductility factors have been proposed, which take into account this effect. They are based on different failure hypotheses. Ductility reduction due to low-cycle fatigue is controlled by a dimensionless parameter γ, which is a function of dissipated hysteretic energy, maximum displacement and the natural frequency of the structural system, and which has been proved to be a relatively stable quantity in the whole period range. If approximate values for γ are used, the determination of equivalent ductility is very simple, and thus appropriate for design purposes. The formulae for equivalent ductility factors include damage indices, and permit the designer to choose acceptable level of structural damage explicitly. As an example, equivalent ductility factors have been used to construct inelastic acceleration spectra, which are proportional to strength demand, for the El Centro 1940 SOOE record. The results have been compared with the ‘exact’ spectra obtained by non-linear dynamic analysis.

Dynamics of pounding when two buildings collide

Abstract: A formulation and solution of the multiple-degree-of-freedom equations of motion for pounding between two multistorey buildings are presented. Pounding occurs at rigid horizontal diaphragms in each building. The theory is implemented into a microcomputer program and sample earthquake analyses involving pounding between 15-storey and 8-storey buildings are performed. The influence of building separation, relative mass, and contact location properties are assessed. Conclusions are drawn regarding response behaviour trends that are relevant to other actual pounding situations.

A new passive confinement model for the analysis of concrete structures subjected to cyclic and transient dynamic loading

Abstract: SUMMARY The paper describes an analytical model for reinforced concrete members subjected to cyclic or transient dynamic loading. Model characterization is given in the context of a pseudo-spatial description of the stress state. This comprises a procedure for calculating and continuously updating the transverse confinement stress for a given applied axial strain, thus accounting for the passive confinement which an element of concrete is subjected to within a structural member. Comparison with existing uniaxial models shows that the new formulation takes note of previously neglected effects, such as non-coincident peaks of the steel and concrete stress-strain curves, and Poisson's ratio variation during loading. Moreover, comparison with 3D concrete constitutive relationships indicates that the level of accuracy is comparable, whilst significant computing time saving is achieved by the new model. Model validation is confirmed by comparison with cyclic loading laboratory test results. Finally, two frames with the same overall strength enhancement factor are analysed under earthquake loading; the difference in the response clearly demonstrates that the model accounts for important behavioural characteristics which are hitherto neglected in comparable existing models.

Pounding of buildings modelled by an impact oscillator

Abstract: Pounding of adjacent buildings is modelled by an impact oscillator subjected to harmonic excitation. Non-linear impact stiffness is represented by a Hertz-type relationship. Spectra of impact velocity are presented for a range of model parameters. These spectra are characterized by a strong peak near a period equal to one half the natural period of a similar non-impacting oscillator. Bands of response are found in which periodic multiple impacts and non-periodic or chaotic impacts occur.

Effects of ground motion spatial variability on the response of cable‐stayed bridges

Abstract: In order to extend our knowledge of the performance of long-span bridges under earthquake loading the effects of spatial variability of ground motion on the structural response of cable-stayed bridges are studied; the result can be useful to practising bridge engineers. The multiple-support excitation analysis is described, and two three-dimensional models representing the modern and future trends in cable-stayed bridge design are utilized to shed some light on salient features of the seismic response characteristics of these modern bridges. In addition, models of steel- and concrete-design alternates of an existing bridge are considered. Differential ground motion records (obtained from dense instrument arrays) are used as synchronous and non-synchronous support motions; in addition, non-dispersive seismic waves travelling along the bridge are considered. The bridge response to non-uniform ground motion is compared to its response to uniform input. An overview of the unique dynamic characteristics of these cable-supported bridges is also presented. Finally, the study, which was used in the seismic design of several existing cable-stayed bridges in U.S. and Canada, indicates that the response quantities may increase substantially from the non-uniform input ground motion, especially for more rigid bridges and for bridges having different dynamic properties of the local soils at the supporting points, but the degree of increase depends upon the specific problem, in particular upon the aspects of span length, rigidity and structural redundancy. Thus, the response to non-uniform input ground motion should be examined for these bridges.

Ambient vibration survey of the fatih sultan mehmet (second Bosporus) suspension bridge

Abstract: Ambient accelerations due to dynamic excitation by wind and traffic were measured on the deck, towers, cables and hangers of the Fatih suspension bridge. From these measurements it was possible to obtain natural frequencies, mode shapes and damping ratios for vertical, lateral, torsional and associated modes in the deck and tower up to a maximum of 2 Hz. The objective of the test was to validate the mathematical modelling used in seismic analyses of the bridge. The agreement between the experimental and theoretical modes was acceptable for vertical modes below 1 Hz, and for torsional modes, but it was difficult to identify the lateral modes due to low levels of response. The dynamic behaviour of this bridge and two other major European suspension bridges is discussed in relation to the differences in loading and structural design.

Spring‐viscous damper systems for combined seismic and vibration isolation

Abstract: SUMMARY The coupled lateral-vertical-rocking dynamic response of spring-viscous damper isolated structures is considered. The force-displacement relation of the viscous dampers is described by an experimentally calibrated fractional derivative viscoelasticity model. The equations of motion are derived and reduced to a form for direct solution by the discrete Fourier transform method. The validity and accuracy of the derived solution are demonstrated by comparison with shake table test results. The developed analysis procedure is employed in the seismic analysis of a recently constructed isolated structure. The analytical and experimental results demonstrate that spring-viscous damper isolation systems are capable of providing both effective seismic and vibration isolation.

Scattering of plane sh waves by a semi‐cylindrical hill

Abstract: A new analytical method is presented to study the problem of scattering of plane SH waves by a semi-cylindrical hill in an otherwise homogeneous, isotropic and elastic two-dimensional half-space, using the series of wave functions and a new expansion technique. The results obtained show that (1) the hill has quite considerable effects on ground motions for both the points on the hill and its environs, (2) these effects depend mainly on the frequency, the angle of wave incidence and the ratio of radius of hill to one-half the wave length of incident waves, and (3) prominent and depression topographies having equal form and radius for the same incident waves would cause quite different mechanisms of wave propagation in both response performance and magnitude. The results, doubtless, would be useful for further deepening knowledge of the effects of prominent topography on seismic ground motion and for testing the accuracy of various approximate methods so far available.

The masonry arch as a four‐link mechanism under base motion

Abstract: The dynamic response of an unreinforced masonry arch is examined, modelling the rigid body motions of arch segments under the influence of gravitational and inertial forces. This extends earlier studies of single rocking blocks, stacked blocks, and portal mechanisms of blocks; the masonry arch is analysed as another kinematic form of such a system. In this first effort a part-circular planar arch ring is studied and excitation is restricted to horizontal ground acceleration of the base. The mechanism kinematics are presented and the governing equation of motion is derived in non-linear form. The instantaneous form is determined for small rotations about the initial geometry and is used to study the conditions for the onset of mechanism motion. Possible failure conditions are posed and bounding principles are stated. One possible failure condition, direct overturning as a four-link mechanism, is studied for one simplified base motion. The results show that an arch geometry establishes good resistance to earthquake excitation in that ground acceleration must exceed a rather high threshold before any mechanism motion would develop; however, once that threshold has been passed the arch has relatively modest resistance before failure. Other possible failure conditions are discussed; one emerges from pounding effects between segments at impact, and another develops from sliding of blocks over one another as the internal forces (normal and tangential to the masonry joint) vary with the inertial forces.

Seismic ground motion simulations from a class of spatial variability models

Abstract: An improved version of the spectral representation method (References 12-14) for the generation of simulations of random processes and random fields by means of the Fast Fourier Transform algorithm is developed. The new formulation produces simulations that are ergodic in the mean without any restricting assumptions at the origin of the spectra and leads to a faster convergence rate of the stochastic characteristics of the simulations to those of the random fields. As an example of the methodology, simulations in space and time based on a spatial variability model for the seismic ground motions are generated.

Design of torsionally unbalanced structural systems based on code provisions I: Ductility demand

Abstract: Using a three element single mass model, this paper presents the ductility demands on the elements of torsionally unbalanced systems when subjected to strong earthquake shaking. Torsionally unbalanced systems based on nine structural configurations are considered, ranging from torsionally stiff systems with the centre of rigidity (CR) centrally located to torsionally flexible systems with CR eccentrically located. The strength of the elements is designed based on the Canadian and New Zealand codes, and the Uniform Building Code (UBC) of the United States. It is shown that all three codes can limit the ductility demands on the elements to that of a similar but torsionally balanced system when the system is torsionally stiff. However, substantial additional ductility demands on the element at the stiff edge of the system exist for torsionally flexible systems when the New Zealand code or UBC is used. The large ductility demand is caused by the low strength of the stiff-edge element permitted by these codes.

Response spectrum analysis of structures subjected to spatially varying motions

Abstract: An important aspect of earthquake loads exerted on extended structures, or structures founded on several foundations, is the spatial variability of the seismic motion. Hence, a rigorous earthquake resistant design of lifeline structures should account for the spatial character of the seismic input, at least in an approximate way. A procedure is proposed which enables addressing the problem of multiply supported structures, subjected to imperfectly correlated seismic excitations, by means of an extension to the response spectrum method. A modified response spectrum model is developed for the design of extended facilities subjected to single and multicomponent ground motion. The modification procedure is based on adjusting each spectral value of the given design response spectrum by means of a correction factor, which depends on the structural properties and on the characteristics of the wave propagation phenomenon. Finally, the theoretical model is validated through digital simulation of seismic ground motion, whereby model predictions are found to be in good agreement with exact results.

A Posteriori Local Error Estimation and Adaptive Time-stepping for Newmark Integration in Dynamic Analysis

Abstract: A simple a posteriori local error estimate for Newmark time integration schemes in dynamic analysis is presented, based on the concept of a so called post-processing technique. In conjunction with the error estimate, an adaptive time-stepping algorithm is described, which adjusts the time step size so that the local error of each time step is within a prescribed error tolerance. Numerical examples given in the paper indicate that the error estimate is asymptotically convergent, computationally efficient and convenient, and the adaptive time-stepping scheme can predict a nearly optimal step size from time to time, thus making the numerical solution reliable in an efficient manner

Some aspects of testing small-scale masonry building models on simple earthquake simulators

Abstract: The basic aspects of testing small-scale masonry building models on simple earthquake simulators are discussed. Since the scale effects represent a difficult problem to solve, the overall seismic behaviour of structural systems, and not the behaviour of structulal details, has been studied by testing the reduced-sized models on a simple earthquake simulator. Accurate results regarding the dynamic behaviour and failure mechanism of the tested structures have been obtained by means of testing the relatively simple, adequately designed small-scale masonry building models. A simple earthquake simulator capable of simulating the uni-directional earthquake ground motion has been developed to study the seismic behaviour of masonry building models. Although a multipurpose programmable actuator was used to drive the shaking table, the comparison of the dynamic characteristics of the generated shaking-table motion and the earthquake acceleration records used for the simulation of seismic loads showed an acceptable degree of correlation between the input and output seismic motion.

The system damping, the system frequency and the system response peak amplitudes during in‐plane building‐soil interaction

Abstract: The system damping, the system frequency, the relative building response and the base rocking response peak amplitudes are studied, as those depend on the building mass and height, the flexibility of the soil, the structural damping, the type of incident waves and their angle of incidence. A linear two-dimensional model is used, which assumes the soil to be a homogeneous isotropic half-space, the foundation supporting the building to be a rigid embedded cylinder, and in which the building model is an equivalent single-degree-of-freedom oscillator. The system frequency and the system damping ratio are determined by measuring the width and the frequency of the peak in the transfer function of the oscillator relative response, using the analogy with the half-power method for a single-degree-of-freedom fixed-base oscillator. Previous similar studies are for dynamic soil-structure interaction only, and for simplified models in which the stiffness of the soil and the damping due to radiation are represented by springs and dashpots. The study in this paper differs from the previous studies in that the wave passage effects (or the kinematic interaction) are also included, and that no additional simplifications of the model are made. Results are shown for excitation by plane P- and SV-waves.

Attenuation of modified mercalli intensity in New Zealand earthquakes

Abstract: This paper describes a comprehensive study of the attenuation of Modified Mercalli intensity in New Zealand earthquakes, which has resulted in significantly different and new findings when compared with those of earlier work. The current study used recently revised magnitudes for the 30 events in the carefully selected data set. Magnitudes ranged from ML = 5.0 to Ms = 7.8. Special effort was also put into establishing the depths of the events, which ranged from very shallow to 65 km. An expression of a form also used in peak ground acceleration attenuation studies was adopted, I = a + bM + cr + dlog10r with r being taken as the mean distance from the centre of the fault rupture surface to each isoseismal. A two-step stratified regression analysis was used because it results in more realistic estimates of standard errors, although its mean curves were virtually the same as those derived from the standard one-step method. It was found possible to model accurately the attenuation of the deepest events from regressions of the data of the shallowest events, but the inverse was not true. In a study of the influence of source mechanisms it was found that the attenuation was the same for events with normal and strike-slip faulting. In contrast, events with reverse fault mechanisms were found to have higher intensities (for the same M and r) than normal and strike-slip events, by a factor corresponding to that found by Campbell in a study of peak ground accelerations, although the statistical test was narrowly short of the conventional significance level.

Groundborne vibrations due to trains in tunnels

Abstract: An analytical procedure is presented for determining groundborne vibrations in buildings due to subway trains. The procedure involves a finite element idealization of the subway-soil-structure interaction problem, using an analytical model for the train loading spectrum at the tunnel invert. Both direct fixation and floating slab track support systems are considered. The train model is verified using the measurements of rail velocities. The proposed procedure is applied to the case of a four-storey podium block enclosing twin double-box subways within the confines of its ribbed wall foundations. The severity of velocity response levels of the building, in relation to vibration standards, is also considered.

Response of pile foundations to rayleigh waves and obliquely incident body waves

Abstract: The paper presents results of a study on the harmonic response of piles and pile groups embedded in a halfspace to various forms of seismic waves. These include the Rayleigh wave as well as obliquely incident P, SV and SH waves. The pertinent mixed boundary value problems of pile-soil-pile interaction are solved by a numerical model of the boundary integral nature. All modes of foundation vibrations, i.e. translational, rocking and torsional, are included in the model. The results presented are used to highlight the salient features of the seismic response of piles. In addition, the influence of certain pile-soil parameters, such as pile rigidity and pile spacing, on the seismic behaviour of pile foundations is investigated.

Lumped‐parameter model for a rigid cylindrical foundation embedded in a soil layer on rigid rock

Abstract: Note: [149] Reference LCH-ARTICLE-1992-009View record in Web of Science Record created on 2007-04-24, modified on 2016-08-08

Seismic response of rotating machines

Abstract: The equations of motion of a rotor finite element subjected to six components of base excitation are developed by applying variational principles. The equations contain speed dependent gyroscopic terms, base rotation dependent parametric terms and several forcing function terms which depend upon the linear accelerations, rotational accelerations and a combination of linear and rotational velocities. To evaluate the importance of various terms, seismic response characteristics of a rotating machine subjected to simulated base excitations are studied. It is observed that even for strong rotational inputs the parametric terms in the equation of motion can be ignored without affecting the response. The rotational input terms in the forcing function, however, are quite important and can be ignored only when they are not very strong. Since the problematic parametric terms can be ignored, one can use a generalied modal analysis approach.

Design of torsionally unbalanced structural systems based on code provisions II: Strength distribution

Abstract: This paper presents the results of an analytical study of the strength distribution of lateral load resisting elements in torsionally unbalanced systems designed based on codified torsional provisions. It is shown that the element strength can be expressed conveniently as the element strength of a similar but torsionally balanced system multiplied by a strength factor. This strength factor depends on three system parameters, namely, the location of the element relative to the centre of rigidity, and the torsional stiffness and eccentricity of the structure. In addition, it depends on the design coefficients of the code specified design eccentricity expressions. The influence of each of these factors on the element strength distribution is discussed. A new set of values for the design coefficients is proposed. By means of examples, it is shown that the proposed torsional provision is an improvement over those suggested in the National Building Code of Canada and the New Zealand code.

Predictive control of base‐isolated structures

Abstract: A control design for absolute motion reduction of base-isolated structures subjected to earthquake excitation is presented herein. The control objective is to provide a vibration-free environment for sensitive equipment protection. Predictive control theory is used for the control design. This theory allows the designer to handle time delays generated by the dynamics of actuators. The study reported herein demonstrates, by numerical simulation, the efficacy of this controller in reducing acceleration response in the superstructure in the presence of delays. Stability analysis, frequency response and response to ground motion excitation are developed to assess the characteristics of the controller.

Seismic analysis of the fatih sultan mehmet (second Bosporus) suspension bridge

Abstract: Theoretical dynamic characteristics of the Fatih Bridge in terms of natural frequencies and mode shapes of free vibration were obtained using a range of finite element models. Based on this free-vibration data, separate analyses of the asynchronous response of the bridge to earthquake excitation in three orthogonal axes with different speeds of wave propagation, and of stochastic response to vertical excitation were used to estimate levels of dynamic response due to seismic loading. Fatih is the third of three modern European long-span box-girder suspension bridges that have been investigated and the relationship of the different design features and the dynamic responses of this type of bridge is reviewed. The main conclusion is that where seismic response is an important consideration, the effects of asynchronous excitation can be significant and must be considered.

Behaviour of near‐source vertical and horizontal response spectra at smart‐1 array, Taiwan

Abstract: SUMMARY Over 700 accelerograms recorded from 12 earthquakes in northeast Taiwan have been analysed for investigating the behaviour of the vertical and horizontal peak and spectral ground motion in the near-source region. Pseudo-relative spectral velocities (PSV), at 5 per cent critical damping for 23 frequencies in the range of engineering interest have been subjected to non-linear regression procedures in terms of magnitude and hypocentral distance. Predicted response spectra for several discrete distances and magnitudes are presented. The results show that the shape of response spectra for both vertical and horizontal components of ground motion is magnitude- as well as distance-dependent. The 2/3 ratio of vertical to horizontal ground motion, commonly used in engineering applications, appears unconsei-uatioe in the very near field for high frequency ground motion. However, it falls below 1/2 at distances greater than 50 km. The same ratio for peak ground velocity (FGV) and peak ground displacement (PGD) tends to increase with distance-the latter at a faster rate.

An identification methodology for a class of hysteretic structures

Abstract: This paper presents a method of identification for determining non-linear dynamic models for certain hysteretic structures. Particular attention is given to modelling and identifying the hysteretic behaviour of structures from strong-motion earthquake data. In this method, the response is separated into mode-like components which are analogous to those of a linear system. Based on modelling of the generalized restoring force of each mode-like component, both non-hysteretic and hysteretic non-linear models are incorporated into the general methodology. A non-hysteretic model provides an initial estimate for a final hysteretic model. The approach is applicable even when data are available from only a small number of locations in the structure. The structural model identified from this method provides a means to predict the response to future events and, ultimately, to examine the damage to a structure as a result of an earthquake.