Multiple Support Excitation Research Articles

Vibration control of cable-stayed bridges—part 1: modeling issues

The objective of the research presented here is to increase the understanding of how the complexities associated with modeling cable-stayed bridges, such as non-linear behaviour and the participation of highly coupled, high-order vibration modes in the overall dynamic response, affect the overall effectiveness of active control schemes. The 316-degree-of-freedom analytical model studied here is based on the Jindo Bridge located in South Korea. Computational considerations associated with control analyses require the size of the model to be significantly reduced, without loss of the important vibration characteristics and complexities. Three separate reduced-order modelling techniques for creating effective control models are studied here: the IRS method, the internal balancing method, and a modal reduction method. These methods are studied and compared on their ability to capture the complex dynamic response of cable-stayed bridges subjected to multiple-support excitation and their ability to create viable and computationally sound state-space models for control analyses. Results show that the modal reduction technique, because of the ability to select only those modes causing the largest force and displacement response, is most effective for control applications. © 1998 John Wiley & Sons, Ltd. Language: en

Modal superposition method for dynamic analysis of structures excited by prescribed support displacements

The conventional method for dynamic analysis of structures subjected to support excitation requires support acceleration as input. In this paper, a modal superposition method using support displacement as input is proposed and its accuracy is investigated. To determine an accurate structural response, a static correction term representing the contribution of neglected high-frequency vibration modes must be added to the modal superposition result. The proposed method is suitable for both uniform support excitation and multiple support excitation. Associated numerical integration schemes to compute the Duhamel integral for displacement input functions are also studied. The structural response is shown to be the same if calculated using either the proposed method for displacement input or the conventional method.

Seismic Retrofit of Vincent Thomas Suspension Bridge

The Vincent Thomas Bridge in Los Angeles, California, is a major suspension bridge with a total length of 1848 m (6,060 ft), including approaches, and a main span bridge 766 m (2,513 ft) long, whose center span is 458 m (1,500 ft). The bridge, built in the 1960s, used the seismic codes of the time. The site conditions and tall, slender towers and bents have resulted in vulnerabilities that are particular to suspended bridges. This paper focuses on the suspended spans. The bridge is located within the Port of Los Angeles in a vicinity that has a legacy of earthworks associated with such projects as dock expansion, fuel lines, and rail lines. Geotechnical conditions include an active fault running between the main towers with a potential for liquefaction, fault rupture, and lateral spreading. A nonlinear time history analysis of the main suspended bridge was performed, using ADINA. The model included the effects of geometric stiffness of the cables and of multiple-support excitation of the bridge. The critical vulnerabilities detected in this study, arising from large predicted longitudinal motions, indicated distress in the towers, in the cable bents near the anchorages, in the short midspan suspenders, and in the stiffening trusses. During the retrofit study the nonlinear behavior was further developed, including tower rocking and uplift, the postyield deformations of the tower, and the optimization of the damper properties. Retrofit measures include releasing of the side-span trusses at the cable bents, creating fused hinges in the stiffening trusses, the installation of dampers at these locations and between the stiffening trusses and the towers of the bridge, stiffening of the bridge towers to prevent plate buckling, and cable and suspender modifications.

Stability of Simple Beam Subjected to Multiple Seismic Excitations

This technical note analyzes the stability of a simple beam subjected to spatially varying random seismic excitations. It uses the stochastic average method to calculate the stability boundaries of a beam under various earthquake excitations. The structural responses are modeled as a two-dimensional (2D) Markov process representing the response amplitude and phase angle. The parametric random excitation is induced by the spatially varying multiple seismic excitations at the two supports. Only the second-order moment stability is considered in this study. Based on the average properties of highway bridges and an empirical ground motion coherency loss function, the stability boundaries of a simple beam subjected to multiple support excitations are calculated. It is found that the stability strongly depends on the beam properties such as the span length, vibration frequency, and damping ratio. It also depends on ground excitation intensity, propagation velocity, and the coherency loss between the multiple excitations.

Response of transmission lines to multiple support excitation

The effect of multiple support excitation on the response of overhead power transmission lines is analysed. The transmission towers are modelled by space truss elements, while the cable is modelled by straight two node elements that account for the nonlinear geometry of the cable. The structure is subjected to spatially incoherent seismic ground motions. The effects of wave propagation velocity, wave travel and the coherency of the seismic input waves are evaluated. The results indicate that the assumption of uniform ground motions at all supports of a transmission line does not provide the most critical case for the response calculations. It was found that the wave propagation velocity has a substantial effect on the system response. In order to obtain a representative analysis of transmission lines, an accurate estimation of wave velocity is required.

Site effects on the seismic response of a suspension bridge: M. Rassem, A. Ghobarah & A. C. Heidebrecht, Engineering Structures, 18(5), 1996, pp 363–370

Abstract The free-field surface motions in a hypothetical sedimentary valley are calculated and applied to the supports of the Humber suspension bridge in the UK. The purpose is to analyse the dynamic response of the bridge to spatially varying.longitudinal excitations at its supports. The support motions differ in amplitude and frequency due to variations in soil patterns of amplification at different valley sites. Two soil categories with soft and stiff profiles are used. Five cases of excitation are considered by moving the bridge supports to different locations in the valley. The SAP IV computer program is modified to perform a multiple-support dynamic analysis on the bridge using mode superposition. It is concluded that the inclusion of the multiple-support excitation case in the analysis is significant, when soil conditions and topography cause noticeable variations in the intensity of support motions in the period range of interest for the bridge response. Soil type, site topography and the location of the bridge supports in a valley must be considered for more realistic evaluation of the ground motions affecting the bridge.

Site effects on the seismic response of a suspension bridge

The free-field surface motions in a hypothetical sedimentary valley are calculated and applied to the supports of the Humber suspension bridge in the UK. The purpose is to analyse the dynamic response of the bridge to spatially varying.longitudinal excitations at its supports. The support motions differ in amplitude and frequency due to variations in soil patterns of amplification at different valley sites. Two soil categories with soft and stiff profiles are used. Five cases of excitation are considered by moving the bridge supports to different locations in the valley. The SAP IV computer program is modified to perform a multiple-support dynamic analysis on the bridge using mode superposition. It is concluded that the inclusion of the multiple-support excitation case in the analysis is significant, when soil conditions and topography cause noticeable variations in the intensity of support motions in the period range of interest for the bridge response. Soil type, site topography and the location of the bridge supports in a valley must be considered for more realistic evaluation of the ground motions affecting the bridge.

Dynamics of structures: theory and applications to earthquake engineering

Dynamics of structures: theory and applications to earthquake engineering

Active tendon control systems for structures subjected to multiple support excitation

This paper analyzes the feasibility and efficiency of active tendon control systems for the vibration control of structures subjected to multiple support excitation. This type of external excitation can be used to represent, for example, earthquake-induced spatially varying ground motion. The structured response is decomposed into a dynamic component and a quasistatic component. While the active tendon control system is quite effective in reducing the dynamic response, the quasistatic component of the structural response can be controlled by such a system only in particular structural conditions.

Nonlinear seismic response of antenna-supporting structures

In the event of a severe seismic excitation, preservation of essential infrastructures, such as telecommunication facilities, is of high priority. The objective of this paper is to investigate the geometrically nonlinear response of antenna-supporting guyed towers under earthquake loading. Two guyed towers are analysed: a 350 ft (107 m) tower with six stay levels and an 80 ft (24m) mast with only two stay levels. Two horizontal accelerograms are used, El Centro and Parkfield, with each record being scaled to match the elastic design spectra of the 1990 National Building Code of Canada. Elements of response analysed are: guy tensions, horizontal shears, and displacements and rotations at the tip of the mast. Results indicate that although the absolute values of the dynamic amplifications are well below the limit strength and serviceability criteria for such towers, dynamic interactions between the guywires and the mast are important, especially in the vertical direction. Multiple support excitation of the tallest tower also causes additional dynamic effects that are not present when only synchronous ground motion is studied.

Nonstationary response analysis of suspension bridges for multiple support excitations

A method for the nonstationary response analysis of suspension bridges subjected to earthquake ground excitations at multiple supports is developed. The equation of motion is formulated for the vertical motion of the bridge girder using a continuous co-ordinate system. The nonstationarity of the earthquake excitation is modeled by utilizing a time-varying envelope function. The correlation effects between ground excitations at different supports are investigated, for various cases of traveling seismic waves with different wave propagation velocities. The non-stationary responses are obtained in terms of time-dependent variance functions. Expected peak responses are also evaluated, thereafter. Numerical results from the example analysis indicate that the correlation effects between different support excitations are very significant on the response of the suspension bridge.

A Test and Analysis of the Multiple Support Piping Systems

Abstract One of the current topics in the seismic design of piping systems is the overall reliability of them in earthquake events. Actual piping systems are generally supported by independent structures such as vessels and steel structures. So, it is very important to clarify the behavior of actual piping systems during the seismic events. For this purpose, the analytical method of multiple excitation problems is a preferable approach to not only evaluate the actual behavior of the piping systems, but also improve the reliability of piping systems. To clarify the dynamic characteristics of the piping systems and to assess the computational methods in the linear system subjected to multiple support excitations, an experimental study using a realistic large-scale piping model has been conducted. The equations for the multiple excitation problem have been validated and the adequacy of the multiple response spectra method has been confirmed by the comparison of the test results with the analytical one. This paper reports the results focusing on the analytical methods of the multiple support piping system. It is noted that the multiple response spectrum method is efficient for the multiple excitation problems.

A Load Combination Method for Aseismic Design of Multiple Supported Piping Systems

Abstract A new load combination scheme for seismic response calculation of piping systems subjected to multiple support excitations is presented. This scheme has an advantage, such that the cross-correlation among support excitations are properly taken into account by use of a stationary random vibration approach. The authors also present the idea of generating a “multi-excitation floor response spectrum.” First, using a simple analytical SDOF piping system to two support excitations and a simple Z-shaped piping model for shaking test, the combination law is supplied to various correlation cases of two support excitations and the maximum responses of piping in a fundamental mode is calculated. Second, nonlinear characteristics such as gap and friction appearing between piping itself and supports are specifically investigated. The response effect due to these nonlinearities is evaluated by the results through the shaking test with a piping-support structural model, and the amount of response reduction effect is represented by “a response reduction factor β.”

RMS Response of Cascaded MDOF Subsystem to Multiple Support Excitation

The RMS response of a general multiple degrees of freedom (MDOF) cascaded secondary system attached at several points to a primary system is obtained using time domain random vibration formulation. The primary system is excited by ground motion at multiple support points. This in turn excites the subsystem at the attachment points. To analyze a primary system, filter parameters are chosen to represent the spectral shapes of earthquakes. The output of the filter, i.e., the time histories of RMS ground excitation at support points and their cross‐correlation, is directly prescribed. Fictitious piecewise linear strength envelopes, which represent the corresponding input of the filter, are generated accordingly before engaging the filter to the system. The time history of the RMS modal coordinates of the supporting system and their cross‐correlation are evaluated and stored as input to its subsystems. To analyze a subsystem, filter parameters are chosen to represent the spectral shapes of the modal coordinates of the supporting system, with a predominant frequency equal to the corresponding natural frequency of the primary system. Piecewise linear strength envelopes are generated as the diagonal terms to match the RMS time histories of modal coordinates and the cross‐terms to match the time histories of cross‐correlation between corresponding modal coordinates. This formulation enables one to independently analyze and design various multiply supported cascaded subsystems attached to a primary system.

APPROXIMATE SPECTRAL MULTIPLE SUPPORT SEISMIC ANALYSIS: TRAVELLING WAVE APPROACH.

Keywords ISRAEL INSTITUTE OF TECHNOLOGY HAIFA., MCMASTER UNIVERSITY HAMILTON, ONTARIO. BRIDGES, STRUCTURES, EARTHQUAKES, GROUND, MOTION, SUPPORTS, SEISMIC, ANALYSIS, TRAVELLING, WAVES, TECHNIQUES, FORCES... Show All

The SMART I Accelerograph Array (1980-1987): A Review

SMART 1 is the first large digital array of strong-motion seismographs specially designed for engineering and seismological studies of the generation and near-field properties of earthquakes. Since the array began operation in September 1980, it has recorded over 3000 accelerogram traces from 48 earthquakes ranging in local magnitude ( ML) from 3.6 to 7.0. Peak ground accelerations have been recorded up to 0.33g and 0.34g on the horizontal and vertical components, respectively. Epicentral distances have ranged from 3 km 200 km from the array center, and focal depths have ranged from shallow to 100 km. The recorded earthquakes had both reverse and strike-slip focal mechanisms associated with the subduction zone and transform faults. These high quality, digital, ground motions provide a varied resource for earthquake engineering research. Earthquake engineering studies of the SMART 1 ground motion data have led to advances in knowledge in several cases: for example, on frequency-dependent incoherency of free-surface ground motions over short distances, on response of linear systems to multiple support excitations, on attenuation of peak ground-motion parameters and response spectra, on site torsion and phasing effects, and on the identification of wave types. Accelerograms from individual strong-motion seismographs do not, in general, provide such information. This review describes the SMART 1 array and the recorded earthquakes with special engineering applications. Also, it tabulates the unfiltered peak array accelerations, displays some of the recorded ground motion time histories, and summarizes the main engineering research that has made use of SMART 1 data.

A study on a load combination method for multi-supported piping systems. Fundamental investigation using piping system with two inputs.

This paper is an extended study of the practical combination method of dynamic loads proposed in the previous paper, in which problems of the maximum response calculation of piping systems to multiple-support excitations were discussed. In this paper, experimental and numerical investigations are carried out in order to confirm the validity and feasibility of the proposed method. Using a simple Z-beam-shaped piping model for shaking tests, the maximum response of the piping in the fundamental mode is measured, and the combination law is applied to various correlation cases among two-vibrational loads. From the experimental results, it has been made clear that the proposed method is reasonable in comparison with other combination laws, like the square root of the sum of the squares (SRSS) method.

A study on a load combination method considering the correlation among dynamic loads. (3rd Report, Response analysis for multi-supported piping system, Part 1)

A dynamic load combination method proposed in previous papers for seismic analysis of a liquid storage tank has been developed for response calculations of piping systems subjected to multiple support excitations. This method has an advantage in which cross·correlation among support excitations are properly taken into account. The correlation factor can be semi-automatically evaluated by using a stationary random vibration approach. Investigation is mainly devoted to a maximum acceleration response calculation of a simple piping model to two-input excitation. Results for the system corresponded fairly well with the exact numerical results through analytical simulation. On the other hand, the SRSS procedure and the absolute value summation which neglect cross-correlation among excitations can lead to large errors. Finally, the authors have also proposed the idea of generating a multi-excitation floor response spectrum using the results.

A study on a load combination method considering the correlation among dynamic loads. (4th report Response analysis for multi-supported piping system, experimental investigation)

This paper is an extended study of a practical combination method of dynamic loads proposed in the previous paper in which problems of the maximum response calculation of piping systems to multiple support excitations were discussed. In this paper, experimental and numerical investigations are carried out in order to confirm the validity and feasibility of the proposed method. Using a simple Z-beam shaped piping model for a shaking test, the maximum response of piping in the fundamental mode is measured and the combination law is applied to various correlation cases among two vibrational loads. From the experimental results, it has been made clear that the proposed method could be reasonable by comparison with other combination laws, like the square root of the sum of the square (SRSS) method.

Spatial variation of ground motion determined from accelerograms recorded on a highway bridge

AbstractA set of time-synchronized strong-motion accelerograms, obtained on the San Juan Bautista 156/101 Separation Bridge in California during the 6 August 1979 Coyote Lake earthquake (ML = 5.9), are used to study the spatial variation of ground motion at the bridge site, including traveling wave effects and the influence of multiple-support excitation. Analysis of the ground motion recorded at the base of two of the bridge supports (32.6 m apart) revealed the presence of a differential support excitation having a period of ≈ 3 sec, much longer than any structural periods of the bridge. This signal also appeared as a noticeable long-period component in the superstructure displacements. Analysis of the vertical and radial components of the 3-sec ground motion indicated that ground displacements were retrograde for the duration of strong shaking, with several cycles exhibiting elliptical particle motions. These findings suggest that long-period differential support motions were induced by phase delays in a Rayleigh wave traveling across the bridge site. Further support to this premise is given by the location of the bridge site near a maxima of the Rayleigh wave radiation pattern for the Coyote Lake earthquake (based on published focal mechanism data). Traveling wave effects were also detected for compressional body waves by a correlation analysis which indicated a time delay of ≈ 7 msec between P-wave arrivals at two of the bridge supports.