Showing papers in "Earthquake Engineering & Structural Dynamics in 1973"

Simulation of artificial earthquakes

Abstract: A procedure is developed for the simulation of artificial earthquake accelerograms, The time variation of amplitude and frequency content is preserved in the simulation procedure. Sixteen artificial earthquake accelerograms are simulated and compared with a target accelerogram. The time variation of amplitude and frequency content for 26 historical earthquake accelerograms is characterized.

Vibration of viscoelastic foundations

Abstract: Simple approximate solutions are presented for the steady-state response of rigid, circular foundations which are supported at the surface of a linear viscoelastic half space and are excited by a harmonically varying torque. The half space is idealized either as a standard Voigt solid or as a constant hysteretic solid. Comprehensive data are presented and their significance analyzed. It is shown that the principal effects of material damping are to increase the damping capacity of the system and to reduce its natural frequency. The increase in damping and the associated reduction in response may be of considerable practical consequence. Some attention is also given to the response of foundations subjected to transient excitations, and a procedure is recommended for interrelating the responses of systems for the two models of viscoelastic action investigated. It is shown that, provided the parameters of the two viscoelastic models are selected as recommended, the maximum transietn responses of the two models are for most practical purposes equal. /ASCE/

Minimal structural response under random excitation using the vibration absorber

Abstract: The equations of motion are derived for the first mode response of a linear multistorey structure having a linear vibration absorber attached to the roof. Furthermore, the variance of the first mode response to a gaussian white noise lateral base acceleration (as a model of earthquake excitation) is determined. Smallest possible values of the variance of the response along with corresponding absorber parameters are established using an optimization program. It is demonstrated that the absorber is quite effective in reducing first mode response for 5- and 10-storey structures even with relatively small values of the absorber mass. Moreover, minimal responses for the randomly excited single-degree-of-freedom system have been determined, and a design example is presented. The absorber system has potential application not only in earthquake engineering but also in aerospace and terrestrial vehicle design.

The Seismic Response of a Reinforced Concrete Bridge Pier Designed to Step

Abstract: A new technique to enhance the earthquake resistance of tall reinforced-concrete bridges is introduced whereby the tall piers are allowed to ‘step’ during a severe seismic attack. This means that each pier is free to rock from side to side with vertical separation of parts of the pier from the supporting foundations. This stepping action limits stresses in the reinforced-concrete piers to values below the yield levels and this should lead to a substantial reduction in the cost of providing earthquake resistance As part of a feasibility study, a 200 feet-high stepping pier is defined and its displacements are calculated for the ground accelerations of the 1940 El Centre earthquake, N-S component. With no damping present the computations give many ‘stepping’ separations of rather large extent. When the effects of internal structural damping are included in the analysis, there is little reduction in the stepping motions at the level of damping expected in the pier. However, when the computations include the effects of some energy-absorbing devices of a recently-developed type, installed between the pier and its foundations, the amplitude and number of the stepping cycles are considerably reduced.

Earthquake analysis of gravity dams including hydrodynamic interaction

Abstract: A general procedure for analysis of the response of gravity dams, including hydrodynamic interaction and compressibility of water, to the transverse horizontal and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions considering the transverse vibration of a monolith of a dam, and the material behaviour is assumed to be linearly elastic The complete system is considered as composed of two substructures—the dam, represented as a finite element system, and the reservoir, as a continuum of infinite length in the upstream direction governed by the wave equation. The structural displacements of the dam (including effects of water) are expressed as a linear combination of the modes of vibration of the dam with the reservoir empty. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only the first few modes. The complex frequency response for the modal displacements are obtained first. The responses to arbitrary ground motion are subsequently obtained with the aid of the Fast Fourier Transform algorithm An example analysis is presented to illustrate results obtained from this method. It is concluded that the method is very effective and efficient and is capable of producing results to any desired degree of accuracy by including the necessary number of modes of vibration of the dam.

Time and amplitude dependent response of structures

Abstract: SUMMARY An understanding of the precise nature of the non -linear response of structures is essential for future improvement of earthquake resistant design procedures. This paper presents a summary of observations of dynamic behaviour which were made on two typical modern buildings during a period of about ten years. These structures underwent numerous tests and experienced three strong earthquake ground motions . The data presented should prove useful for calibration of parameters in theoretical non-linear models. For buildings having an apparent soft -spring-type non -linearity, a partial or complete recovery of the structural stiffness appears to occur following the large strains created by strong ground shaking . The rate and extent of this recovery appear to depend strongly on the strain levels throughout the excitation.

Torsional and coupled vibrations of embedded footings

Abstract: An approximate analytical solution is presented for torsional vibrations of footings partially embedded into a semi-infinite medium or a stratum. Simple formulas derived for pure torsional motion make it possible to apply a correction for the effect of embedment to the known solutions of surface footings. The solution completes an approach to the analysis of all modes of footing vibrations, including the coupled modes. The approach to coupled modes is illustrated by the solution of coupled response involving horizontal translation, rocking and torsion. Formulas are presented for stiffness and damping coefficients that can be used in the analysis of embedded footings or structures supported by such footings Field experiments were conducted with concrete footings featuring circular, square and rectangular bases and variable embedment depths. The experimental results were compared with theoretical predictions of pure torsional vibrations.

Dynamic Response by Large Step Integration

Abstract: A family of unconditionally stable algorithms for the economical computation of large linear dynamic systems is described and applied. Possible application to divergent systems is considered and some of the difficulties of extending the use of the algorithms to non-linear systems are discussed. In an Appendix a previously developed conditionally stable algorithm is applied to the non-linear gust response of a prestressed cable roof structure over the Munich Olympic Stadium. The idealisation involves 1164 degrees of freedom.

Damped vibration mode superposition method for dynamic response analysis

Abstract: In the dynamic response analysis of extremely complex structural systems in which the damping characteristics of each element are independent, the damping matrix is not always diagonalized by the use of undamped free vibration mode shapes In the present paper, a mode-superposition method by the use of damped free vibration mode shapes is developed for such structural systems It is also shown that the Fast Fourier Transform (FFT) procedures, that are available for the dynamic response analysis of linear structural systems, are used effectively in this mode-superposition method with good accuracy

Seismic analysis of skewed highway bridges with intermediate supports

Abstract: DUE TO THE DAMAGE SUFFERED BY MANY SKEWED HIGHWAY BRIDGES DURING THE SAN FERNANDO EARTHQUAKE, 1971, A STUDY IS MADE ON THE DYNAMIC RESPONSE OF THIS TYPE OF BRIDGE. USING A BEAM MODEL CAPABLE OF FLEXURAL AND TORSIONAL DEFORMATIONS, THE MODE SHAPES AND FREQUENCY EQUATIONS ARE PRESENTED. DUE TO THE SKEWNESS OF THE SUPPORTS, COUPLED FLEXURAL AND TORSIONAL VIBRATION WILL BE INDUCED ON SKEWED HIGHWAY BRIDGES. THE NATURAL FREQUENCIES OF THESE VIBRATIONS ARE GENERALLY FAIRLY HIGH (ABOVE 4 CPS) AS A RESULT OF THE TYPICAL DIMENSIONS OF THIS TYPE OF BRIDGE. HOWEVER, IF THE BRIDGE IS LOCATED CLOSE TO THE FAULT, THERE WILL BE SUFFICIENTLY STRONG HIGH FREQUENCY COMPONENT IN THE VERTICAL GROUND MOTION TO EXCITE THE COUPLED FLEXURAL AND TORSIONAL VIBRATIONS IN THE BRIDGE. /AUTHOR/

Analysis of strong earthquake ground motion for prediction of response spectra

Abstract: SUMMARY Prediction of response spectra for earthquake engineering purposes is considered from a new point of view based on the dislocation theory of earthquakes. It is shown that the traditional scaling of response spectra by the predicted peak acceleration should be limited to the high-frequency end of the spectrum, and that the peak acceleration in the near field is not strongly correlated with earthquake magnitude. The amplitude of the long-period end of response spectrum at source to station distances greater than about 10 source dimensions should be scaled with seismic moment, while for distances less than about one source dimension this amplitude should be proportional to the permanent ground displacement. To reconcile the existing extensive data on seismicity of active regions based on magnitude scale, it is shown that magnitude can be used to determine approximately the seismic moment.

Earth dam-foundation interaction during earthquakes

Abstract: Several significant parameters that could affect interaction in a dam-foundation system are discussed. These parameters are: (1) Fundamental periods of the dam and the foundation layer. (2) Lateral extent of the dam. (3) The material properties of the dam and the foundation layer. Five cases are analysed to illustrate the influence of these parameters on interaction. An interaction ratio, R1, relating the response of the dam-foundation system at the base of the dam to the free field response is introduced and interaction effects are expressed in terms of this ratio; the smaller this ratio, the less are the interaction effects. For very small values of R1, it is shown that the dam-foundation system could be decoupled The results of the studies presented in the paper suggest that the interaction effects cannot be uniquely related to either the ratio of the period of the dam to the period of the foundation layer, or to the material properties of the dam and foundation layer. However, for the limited number of cases investigated, the interaction effects were found to be uniquely related to the ratio D/B, where D is the depth of the foundation layer and B is the width of the dam section. For values of D/B less than unity, strong interaction effects were obtained and the dam-foundation system could only be analysed as a coupled system. For values of D/B greater than unity, the interaction appeared negligible and the dam and its foundation layer could be decoupled. It should be noted, however, that for very small values of D/B the interaction effects would decrease becaase as D approaches zero, there would be no interaction The use of the interaction ratio, R1, and the parameter D/B should aid in assessing the need for analysing the response of the dam-foundation as a coupled or as a decoupled system.

Overturning of top profile of the Koyna Dam during severe ground motion

Abstract: The Koyna Dam in India was subjected to a severe earthquake on 11 December 1967 with its epicentre very close to the dam site. During this earthquake, higher non-overflow monoliths of the dam suffered significant damage. In the highest non-overflow monolith, a horizontal crack occurred at the level where there was an abrupt change in the downstream slope. The dynamic behaviour of the top profile of this monolith of the dam above the crack has been investigated treating it as a rigid body. The study shows that the overturning of the cracked portion of the dam will not occur due to the severest anticipated ground motion at the site. However, to prevent the seepage of water and as a permanent remedial measure, strengthening of the dam is necessary but no emergency measures need be taken.

Effects of stiffness degradation on ductility requirements for multistorey buildings

Abstract: The effect of stiffness degradation in reinforced concrete structural members on the inelastic response of multistorey buildings to earthquakes is investigated. In particular, the following question is examined. How do the ductility requirements for multistorey systems with degrading stiffness behaviour compare with those for structures with ordinary bilinear hysteretic property? Inelastic dynamic responses of two idealized multistorey buildings, one having a long and the other a relatively short fundamental period, to an ensemble of twenty simulated earthquakes representative of moderately intense ground motions in California at moderate epicentral distances on firm ground, are analysed for ordinary bilinear hysteretic behaviour and for bilinear hysteretic behaviour with stiffness degradation property. The conclusions deduced from the results of this investigation include the following (1) It is, in general, not possible to predict the maximum response of a degrading stiffness system from results for the corresponding ordinary bilinear system (2) The differences in ductility requirements due to stiffness degradation are generally smaller than those associated with probabilistic variability from one ground motion to another (3) Stiffness degradation has little influence on the ductility requirements for flexible buildings, but it leads to increased ductility requirements for stiff buildings.

Approximate analysis of natural vibrations of coupled shear walls

Abstract: The continuous connection technique is used to analyse the free vibrations of a system of coupled shear walls. The dynamic equation is expressed in integro-differential form, and the natural modes and frequencies are determined by the Galerkin method. Theoretical results are compared with published experimental data.

Prediction of buckling strengths of cylindrical shells from their natural frequencies

Abstract: The instability of thin elastic shells still remains the most challenging of all the classical problems of the theory of elasticity It is the aim of this investigation to verify a rational experimental technique for predicting the buckling loads of cylindrical tubes under axial load as well as under external radial pressure, by measuring their natural frequencies under different loadings Cylindrical tubes made of Hostaphan (thickness 0·254 mm and radius 100 mm) were tested under axial load and under external radial pressure in the German Air and Space Research Laboratory (Deutsche Forschungsanstalt fur Luft und Raumfahrt) at Braunschweig, West Germany, and the results compared with an actual buckling test The tests revealed that the buckling load can be predicted satisfactorily by the proposed non-destructive vibration method of testing

On the choice of the acceptable seismic risk

Abstract: The proper choice of the acceptable seismic risk requires an accurate cost-benefit analysis. As is well known these analyses present considerable difficulties if one wishes to face the problem in a general way from the technical point of view. Besides, there are no generally accepted criteria for formulating a quantitative evaluation of the intangibles, among which the most important is the risk to human life. However, it appears indispensable that research should be started in the field which leads to some numerical results In this paper a simplified analytical model is proposed and the problem of intangibles is discussed. The basic idea is that the comparison with other risks is the most realistic instrument for the choice of an acceptable level of the specific considered risk. The conclusion reached is that a fundamental index for comparison and decision is the incremental cost of investment necessary to save, on average, one human life a year. An evaluation of such an index, valid as a first approximation, is given for this simplified model.

Inelastic dynamic analysis of tall buildings

Abstract: The importance of inelastic action of frame structures subjected to strong ground motions has been recognized by engineers for many years. However, the dynamic analysis of buildings undergoing inelastic deformations requires the solution of many theoretical problems, as well as the development of computer software which makes such analyses economically feasible in a design office–in spite of the extraordinary amount of computation involved. In this paper, some of the principal theoretical problems are briefly described. These are the load-deformation relationship, yield capacity reduction, ductility, P– δ effect, viscous damping, panel zone distortions, numerical integration techniques, energy analysis and the effect of non-structural elements. Special consideration is given to questions associated with the practical implementation of this theory. These questions arose during the development of a computer program, called NLDYN, capable of analysing the non-linear dynamic behaviour of tall buildings in an engineering office environment. The capabilities of this computer program are illustrated with the results of the analysis of a 60 storey office building currently under construction in downtown Los Angeles.

Response of rectangular orthotropic plates to random excitations

Abstract: The paper describes the application of the finite strip method, a modification of the finite element method, to determine the random response of rectangular plates. An example problem of a rectangular orthotropic plate, simply supported on two opposite edges and clamped on the other two, under acoustic white noise excitation is solved.

Structural response to random acoustic excitation

Abstract: The design of aerospace structures necessitates the study of their behaviour in intense acoustic environments. This is more so in recent times due to an increase in power of the vehicles. The present paper deals with an investigation of the response of structures such as flat, stiffened plates to such environments. A peaked type of power spectral density of excitation is assumed, which is more realistic and representative of actual random acoustic excitations than the conventionally assumed white noise type excitations, either ideal or band-limited. The space correlation of the excitation field is assumed to be unity over the plate surface. Generalized harmonic analysis is used to obtain responses such as auto-correlation functions and mean square values of both accelerations and stresses. To obtain the response quantities of stiffened plates the approximate method of analysis suggested by Lin12 is used.

Accuracy of finite difference representations for the transient response analysis of shells

Abstract: The frequency versus wave number characteristics of four O(ΔS2) finite difference formulations for one-dimensional linear shell (ring and axisymmetric) equations are investigated and compared with the exact continuum characteristics. It is found that three of the formulations give virtually identical results. These are half-spacing techniques with equilibrium in terms of displacements or resultants and whole-spacing with equilibrium in terms of displacements. The formulation based on whole-spacing with equilibrium in terms of resultants produces some dramatically different results. These discrepancies partially explain some late time instability problems and critical time step behaviour that have been reported by other investigators.

Calculation of selected ordinates of fourier spectra

Abstract: A method is presented for calculating single or, by repeated use, selected ordinates of Fourier spectra rapidly and efficiently. The approach differs from standard methods in that any frequency consistent with the interval of digitization may be chosen and records of arbitrary length may be analysed. The method is based on the relation between Fourier spectra of an accelerogram and the final response of an undamped oscillator to the same accelerogram. This relation is reviewed and extended to aid the development of the computing method and to assist in the interpretation of Fourier spectrum techniques in earthquake engineering. Because only the terminal values of the response of an undamped oscillator are required to define the Fourier spectra, repeated application of superposition is used to form equivalent excitations with durations of only one-quarter of the period of the oscillator.

Earthquake interaction forces between two structures of different rigidities

Abstract: A combined structure is assumed to be composed of a rigid part and a flexible part. Each component structure would have a different period of natural vibration if it were built independently. When they are combined in one structure and subjected to an earthquake, there must be generated some interaction forces so that the component structures will have a common vibration. In this paper is an analytical method described to evaluate such interaction forces The general principle is as follows. For each of the component structures, equations of motion taking account of the unknown interaction forces are derived first. Then by eliminating the interaction forces, equations of motion of the combined structure are obtained. After solving these equations and substituting the solution into the equations of motion of the component structures, the unknown interaction forces are obtained directly In the present paper, two structures corresponding to two-degree elastic systems are considered; numerical examples also are included.