Vertical Earthquake Excitation Research Articles

SHAKING TABLE TESTS AND NUMERICAL ANALYSIS FOR VERTICAL SEISMIC RESPONSE OF QUAYSIDE CONTAINER CRANES

Vertical seismic performance is an important issue for the seismic design of large-scale engineering structures. The structure, which is relatively flexible and unrestricted vertically, may resonate and its response is obviously magnified under vertical earthquake excitations. The main objective of this study is to investigate the earthquake-resistance performance of a quayside container crane under vertical seismic excitations. To this end, a geometric-scaled model of 1:50 was firstly constructed according to the similitude law. Then using this model, a hammering modal test and a series of shaking table tests were successively conducted to obtain the dynamic characteristics and vertical seismic responses. Furthermore, the experimental results were compared with the computed results of prototype obtained from numerical analysis and agreed fairly well. From dynamic response results, it is found that the large-scale structure has relatively high vertical earthquake-resistance capacity and could satisfy the seismic design requirement. The findings reported in this paper are expected to provide some valuable information for studying other similar structures in the future.

Random vibration of a train traversing a bridge subjected to traveling seismic waves

Non-stationary random vibration of 3D time-dependent train–bridge systems subjected to multi-point earthquake excitations, including wave passage effect, is investigated using the pseudo-excitation method (PEM). The motion equation of such a system is established by coupling the train and bridge through wheel–rail contact relationships and accounting for the phase-lags between pier excitations. The horizontal and vertical earthquake excitations are both assumed to be uniformly modulated, fully coherent random excitations with different phases, while the excitation due to track irregularities is assumed to be a 3D, fully coherent random excitation with velocity-dependent time lags. PEM is first proven to be applicable to such time-dependent systems, and is then used to transform the random excitations into a series of deterministic pseudo excitations. By solving for the corresponding deterministic pseudo responses, various non-stationary random responses, including the time-dependent power spectral density functions (PSD) and standard deviations (SD), can be obtained easily. A case study is then presented in which the China-Star high-speed train traverses a seven-span continuous bridge that is being excited by an earthquake. The results show the effectiveness and accuracy of the proposed method by comparison with a Monte Carlo simulation. Additionally, the influences of seismic apparent wave velocity and train speed on the system random responses are discussed.

Equivalent mechanical model for seismic forces in combined tanks subjected to vertical earthquake excitation

Liquid-storage tanks with circular cross sections are commonly built with a combined vessel consisting of a truncated cone and a superimposed top cylindrical cap. Unlike cylindrical tanks, combined tanks are characterized by the inclination of the walls of the conical segment. As a result, compressive meridional stresses are induced in the shell by the hydrostatic pressure of the contained fluid and the hydrodynamic pressure associated with vertical ground excitation. The current paper aims at identifying the dynamic characteristics of liquid-filled combined tanks subjected to vertical ground excitation. Numerical analysis is conducted based on a coupled finite-boundary element formulation that accounts for the associated fluid–structure interaction. An equivalent model is developed to duplicate forces induced in liquid-filled combined vessels subjected to vertical base excitation. The proposed model accounts for the flexibility of the vessel walls. Meanwhile, the contained fluid is idealized as rigid and flexible components. The proposed equivalent model provides a simplified tool to predict seismically-induced forces in liquid-filled vessels subjected to vertical earthquake excitation.

Vertical Earthquake Loads on Seismic Isolation Systems in Bridges

An important consideration for the design of seismic isolation systems composed of elastomeric and lead–rubber bearings is the safety of individual bearings for maximum considered earthquake shaking. One assessment of bearing safety involves the calculation of the vertical (or axial) earthquake load on the individual seismic isolation bearings. This paper investigates the influence of vertical earthquake excitation on the response of a bridge isolated with low-damping rubber and lead–rubber bearings through earthquake simulation testing. Response data collected from the experimental program are used to determine the vertical load on the isolation system due to the vertical component of excitation. A comparison of the normalized vertical load data to the vertical base acceleration showed significant amplification of the vertical response for each simulation and configuration. Disaggregation of the axial load history showed the summation of maximum values from the vertical earthquake load and overturning moment overestimates the maximum axial load because these maximum values are unlikely to occur simultaneously. Additionally, a spectral analysis procedure using the unreduced vertical stiffness of the bearings was shown to provide a reasonable estimate of the vertical earthquake load.

Seismic response of large underground structures in liquefiable soils subjected to horizontal and vertical earthquake excitations

The seismic performance of large underground structures in soils, e.g., subway and highway tunnels, has been an important topic followed the damages of such structures in recent large earthquakes. The dynamic behavior of a subway station in saturated sandy deposit was investigated using the fully coupled dynamic Finite Element code DYNA Swandyne-II. A generalized plasticity model that can simulate both cyclic liquefaction and pressure dependency of soils was incorporated in the program to model the sandy deposit. A Mindlin beam element was also included and used to model the underground structure. The effects of vertical earthquake motions and the buried depth of the underground structure were analyzed. It is found that the effects of vertical motions depended on the characteristics of the excitations. It is also found that the increase in buried depth improved the safety of the underground structure against earthquake damage. A mitigation method against the floatation of underground structures using injection grouting was also studied and it was proved to be effective.

Dynamic characteristics of single-layer cylindrical lattice shells

This investigation is concerned with the free vibration and seismic response of single-layer cylindrical lattice shells. The effects of basic structural parameters such as the ratio of rise to span, mass, damping, the ratio of length to span and the rigidity of supports, on the dynamic behaviour of single-layer cylindrical lattice shells are investigated in detail. In this paper the finite-element method is used, in which three-dimensional beam elements are employed. Both the natural frequencies and their associated modes of vibration are obtained with a subspace iteration technique, and the direct dynamic analysis method is adopted to analyse the dynamic responses of single-layer lattice shells under vertical and horizontal earthquake excitations. The objective of this study is to achieve a better understanding of the dynamic characteristics and seismic behaviour of single-layer lattice shells. The results are valuable for the earthquake-resistant design of such structures.

Dynamic characteristics of single-layer cylindrical lattice shells

This investigation is concerned with the free vibration and seismic response of single-layer cylindrical lattice shells. The effects of basic structural parameters such as the ratio of rise to span, mass, damping, the ratio of length to span and the rigidity of supports, on the dynamic behaviour of single-layer cylindrical lattice shells are investigated in detail. In this paper the finite-element method is used, in which three-dimensional beam elements are employed. Both the natural frequencies and their associated modes of vibration are obtained with a subspace iteration technique, and the direct dynamic analysis method is adopted to analyse the dynamic responses of single-layer lattice shells under vertical and horizontal earthquake excitations. The objective of this study is to achieve a better understanding of the dynamic characteristics and seismic behaviour of single-layer lattice shells. The results are valuable for the earthquake-resistant design of such structures.

Effects of column axial force – bending moment interaction on inelastic seismic response of steel frames

AbstractIt is well known that axial force – bending moment interaction (N–M interaction) affects to a large extent the cyclic inelastic behaviour of structural elements, especially columns in framed structures, with reduction in bending capacity and loss of available ductility. A few studies have also shown that significant inelastic axial shortening affects the response of column elements subjected to medium–high levels of axial loads and cyclic bending.This paper is primarily aimed at evaluating the effects of column N–M interaction on the inelastic seismic response of steel frames. By considering the contemporaneous action of vertical loads, due to gravity, and of horizontal seismic excitation, it is shown that the progressive axial shortening of adjacent columns may differ substantially, thus inducing significant relative settlements at the ends of the connecting beams and, then, remarkable amplifications in beam plastic rotations. An evaluation of additional beam plastic rotations induced by column N–M interaction is carried out for real structures by investigating the inelastic response of steel frames designed according to European standards under horizontal and vertical earthquake excitations. Copyright © 2003 John Wiley & Sons, Ltd.

Analytical study of saturation effects on seismic vertical amplification of a soil layer

An analysis is presented of saturation effects on the amplification of a single soil layer to vertical earthquake excitation. Rigorous solutions for various responses are derived based on Biot's theory and the concept of homogeneous pore fluid. The transfer function of the layer is described as a function of degree of saturation, soil properties, layer thickness and loading frequency. Numerical examples are given to illustrate the influence of saturation on the motion amplification. The present study indicates that partial saturation of soils may always lead to a larger amplification compared with a full saturation model, and consequently provides a physical insight into an array observation on vertical site amplification during the Kobe earthquake of 1995.

Analytical study of saturation effects on seismic vertical amplification of a soil layer

An analysis is presented of saturation effects on the amplification of a single soil layer to vertical earthquake excitation. Rigorous solutions for various responses are derived based on Biot's theory and the concept of homogeneous pore fluid. The transfer function of the layer is described as a function of degree of saturation, soil properties, layer thickness and loading frequency. Numerical examples are given to illustrate the influence of saturation on the motion amplification. The present study indicates that partial saturation of soils may always lead to a larger amplification compared with a full saturation model, and consequently provides a physical insight into an array observation on vertical site amplification during the Kobe earthquake of 1995.

A simplified method for seismic analysis of lattice telecommunication towers

A simplified static method for estimating the member forces in self-supporting lattice telecommunication towers due to both horizontal and vertical earthquake excitations is presented in this paper. The method is based on the modal superposition technique and the response spectrum approach, which are widely used for seismic analysis of linear structures. It is assumed that the lowest three flexural modes of vibration are sufficient to correctly estimate the tower's response to horizontal excitation, while only the lowest axial mode is sufficient to capture the response to vertical excitation. An acceleration profile along the height of the tower is defined using estimates of the lowest three flexural modes or the lowest axial mode, as appropriate, together with the spectral acceleration values corresponding to the associated natural periods. After the mass of the tower is calculated and lumped at the leg joints, a set of equivalent static lateral or vertical loads can be determined by simply multiplying the mass profile by the acceleration profile. The tower is then analyzed statically under the effect of these loads to evaluate the member forces. This procedure was developed on the basis of detailed dynamic analysis of ten existing three-legged self-supporting telecommunication towers with height range of 30-120 m. The maximum differences in member forces obtained with the proposed method and the detailed seismic analysis are of the order of ±25% in the extreme cases, with an average difference of ±7%. The results obtained for two towers with heights of 66 and 83 m are presented in this paper to demonstrate the accuracy and practicality of the proposed method.Key words: self-supporting tower, earthquake, vertical excitation, dynamic analysis.

A simplified method for seismic analysis of lattice telecommunication towers

A simplified static method for estimating the member forces in self-supporting lattice telecommunication towers due to both horizontal and vertical earthquake excitations is presented in this paper. The method is based on the modal superposition technique and the response spectrum approach, which are widely used for seismic analysis of linear structures. It is assumed that the lowest three flexural modes of vibration are sufficient to correctly estimate the tower's response to horizontal excitation, while only the lowest axial mode is sufficient to capture the response to vertical excitation. An acceleration profile along the height of the tower is defined using estimates of the lowest three flexural modes or the lowest axial mode, as appropriate, together with the spectral acceleration values corresponding to the associated natural periods. After the mass of the tower is calculated and lumped at the leg joints, a set of equivalent static lateral or vertical loads can be determined by simply multiplying the mass profile by the acceleration profile. The tower is then analyzed statically under the effect of these loads to evaluate the member forces. This procedure was developed on the basis of detailed dynamic analysis of ten existing three-legged self-supporting telecommunication towers with height range of 30-120 m. The maximum differences in member forces obtained with the proposed method and the detailed seismic analysis are of the order of ±25% in the extreme cases, with an average difference of ±7%. The results obtained for two towers with heights of 66 and 83 m are presented in this paper to demonstrate the accuracy and practicality of the proposed method.Key words: self-supporting tower, earthquake, vertical excitation, dynamic analysis.

Analysis of Northridge Damaged Thirteen-Story WSMF Building

The case study building experienced moment connection fractures and has instructure recorded response. Correlative analyses are performed using a probability approach to describe the connection rotational capacities. The Northridge calibrated model is then subjected to other scenario earthquake records. The main points include: -Northridge connection damage can be reasonably simulated using models that idealize the rotation capacities as random variables, -Many of the connection fractures occurred from beam moment demands that were less than the beam yield moments, -Vertical earthquake excitation and gravity loads did not play a major role in the connection fractures, -The damaged building can withstand another Northridge intensity quake, -Near-source ground motions from great quakes have the potential to collapse the building with pre-Northridge type connection details, and -Connection rotation capacity can make the difference between building survival or collapse during severe quakes.

Behavior of Beam-Column Connections under Axial Column Tension

Recent analytical studies have shown that reduced column compression and even tension may be experienced by intermediate stories of medium to high-rise reinforced concrete (RC) structures. This is a consequence of high overturning moments coexisting with vertical ground motion. In recognition of such observations, the present study was initiated to investigate the seismic performance of interior beam-column subassemblages under reduced column compression or net tension. A state-of-the-art synchronized shake-table facility was used to test a total of six ordinary and marginal high-strength RC interior subassemblages. A nonconventional design approach was adopted to ensure pure panel-zone (PZ) shear failure, hence a realistic estimate of joint shear strength will ensue. Results indicated loss of shear capacity and increase in deformability when compression column load is markedly reduced or tension is experienced. Findings of this investigation are most useful in providing necessary information about the effect of axial tension on the PZ shear capacity, the joint confinement efficiency, and the overall structural stability in areas of potential high vertical earthquake excitations.

Effects of Soil on the Dynamic Response of Liquid-Tank Systems

Abstract A procedure is presented for the subsystem approach of a liquid-tank-soil system subjected to horizontal and vertical earthquake excitations by the Rayleigh-Ritz method. The dynamic interaction forces between the tank and soil are represented by the impedance functions obtained from the boundary element method. The tank is modeled as an elastic shell and the base of the tank is considered as a surface rigid disk resting on an elastic half-space or a layered elastic medium. A shaking table test of a liquid-elastic tank on an elastic soil model was carried out to verify experimentally the dynamic interaction. The numerical results show that the elastic response of the tank decreases due to the effect of radiation damping in the foundation. Furthermore, the experimental results show that the response of the tank decreases due to stiffness of the soil.

Analysis of a Three-Dimensional Tank-Liquid-Soil Interaction Problem

A three-dimensional analysis of the dynamic behavior of liquid-filled elastic cylindrical tanks based on flexible grounds, undergoing horizontal and vertical earthquake excitation is presented. The interaction of the ideal fluid with the elastic shell and with the flexible ground yields a problem of linear potential theory which must be solved together with the equations of motion of the shell and of the ground. With the unknown modal shapes of vibration developed in Fourier and in Fourier-Bessel series, the partial differential equations are transformed into coupled generalized equations of vibration by a weighted residual approach. The results show the strong influence of the flexible ground characterized by a remarkable shifting of natural frequencies, by the existence of additional natural frequencies, and by high damping ratios.

Response of structures subjected to horizontal-vertical random earthquake excitations

A single-degree-of-freedom column subjected to horizontal and vertical earthquake excitations is considered. The earthquake ground accelerations are modelled by segments of stationary and nonstationary Gaussian white noise processes. The Fokker-Planck equation governing the transition probability density of the response is described and the associated second moment equations are derived. The transient and nonstationary response statistics for a range of values of parameters are obtained. A Monte-Carlo digital simulation study is also performed. The results are compared with the theoretical findings and good agreement is observed. Particular attention is given to the amplification effect of the vertical ground acceleration. It is shown that the effect of the vertical ground motion is significant when the load ratio is relatively large. Based on the presented statistical analysis, peak velocity responses for a range of natural periods are estimated. The results are compared with the combined horizontal-vertical response spectra of El Centro 1940 earthquake and reasonable agreement is obtained.

Vibration Analysis of Hyperbolic Cooling Towers due to Earthquake Excitations

The hyperbolidal shells of revolution supported on columns have been used effectively as natural draft cooling towers of reinforced concrete. The purpose of this paper is to analyze the dynamic response of hyperbolic cooling towers to earthquake excitations. Taking the propagating velocity of earthquake excitations into account, the author shows that hyperbolic cooling towers oscillate not only in beam vibration modes but also in such higher vibration modes as ovalization of their cross sections. When the value αR/V is considerably large, where α and V are circular frequency and propagating velocity of the earthquake excitation, respectively, and R is the radius of hyperbolic cooling towers on the foundation level, numerical example shows that owing to horizontal earthquake excitations an hyperbolic cooling tower oscillates mainly in an ovalization mode and that owing to vertical earthquake excitations it oscillates mainly in a rocking mode.

Design of Columns for Seismic Loads

An analytical solution for the column safety problem is presented herein with earthquake engineering applications. The probabilities of failure are computed for 25 columns subjected to design loads as well as certain earthquake excitations. Results indicate that the vertical earthquake excitation of earthquake motions should not be ignored in the seismic design of building structures.