Torsional Ground Motion Research Articles

Characteristics of torsional ground motions obtained for Turkey and their appraisal against Eurocode 8

In current engineering practice, the torsional effects of ground motions are only considered implicitly through “accidental eccentricity coefficients". In seismic design codes, these coefficients account for not only the unintended (or uncertain) asymmetric distributions of structural mass and stiffness in the plan but also the torsional components of ground motions. The torsional effects may develop due to wave passage effects or the incoherency of translational ground motions along the foundation systems. While it is possible to obtain torsional components of ground motions directly from seismic records with modern instruments, such sensors are uncommon. Therefore, several numerical procedures have been proposed in the literature for estimating torsional components of ground motions from translational measurements. In this study, the Single Station Procedure (SSP)—based on the deconstruction of translational ground motions into body waves and the subsequent reconstruction of rotational ground motions—is employed to obtain torsional ground motions for seven different seismic events in Turkey. Additionally, the corresponding accidental eccentricity coefficients that can cause the same response modification with torsional ground motions are determined. First, a conventional procedure is utilized to obtain the corresponding accidental eccentricity coefficients. Various drawbacks of the conventional procedure, such as negative eccentricity coefficients, are addressed. Then, a relatively obscure definition of accidental eccentricity is revived to propose a novel procedure for determining accidental eccentricity coefficients. It is observed that the proposed procedure yields higher values for the accidental eccentricity coefficients than the conventional procedure. It also observed that the torsional spectrum provided in Eurocode 8 provisions requires higher eccentricity values than those implied by the recorded ground motions from Turkey.

Optimum torsion axis in multistory buildings under earthquake excitation: A new criterion based on axis of twist

The elastic axis is essential for the definition of structural eccentricity, which significantly affects the torsional behavior of buildings. However, it can be determined straight-forwardly in single-story and some special cases of multi-story buildings. Therefore, for the majority of multi-story buildings, the notion of optimum torsion axis has been introduced, according to which, the torsion of the building is considered optimum when the sum of squares of the floor torsional angles is minimum under horizontal forces passing through this axis. The existing determination procedures refer to the application of static horizontal forces and static torsional moments at each story. The present study proposes a new criterion, which approaches the optimum torsion axis by the prism of axis of twist and requires the sum of floor translational displacements of the axis to be minimal. The criterion can be applied under: i) static torsional moments imposed at each story or ii) torsional ground motion excitation. In the latter case, the term of dynamic optimum torsion axis is introduced. Mathematical formulae are provided for the application of the new criterion as well as for the determination of the location of the optimum torsion axis, static or dynamic. It is mathematically proved that the coordinates of the static optimum torsion axis depend on the distribution of torsional moments along the building’s height. However, the coordinates of the dynamic optimum torsion axis are independent of the torsional base excitation and depend only on the mass moments of inertia at each floor level. The proposed method can be easily implemented, as it is based on data given by any structural program, either in terms of structural characteristics or in terms of response.

Assessment of Seismic Demand Due to Torsional Ground Motions on Symmetric Skew Bridges

ABSTRACT Potential effects of torsional components of ground motions (TGM) on the overall seismic response of symmetric skew highway bridges have been investigated. Analyses were conducted for various skew angles, plan dimensions, deck-abutment gap sizes, dynamic properties, and soil types (B and D). The models included nonlinear impact between deck-abutment explicitly. It was demonstrated that seismic response of symmetric highway bridges are amplified consistently due to TGM components for all considered parameters. It is further suggested that a systematic definition of “accidental eccentricity” in terms of system dynamics, geometry, and associated design spectral response may be used in lieu of analysis.

Inelastic seismic response of box-girder bridges due to torsional ground motions

The torsional components of strong ground motions (TGMs) may result in unanticipated displacement and force demand particularly in highway bridges due to their complex dynamic characteristics. For this purpose, the present study investigates the effects of TGMs on the inelastic seismic response of continuous concrete box-girder highway bridges with seat type abutments. Three-dimensional finite element (3D FE) models of bridges with varying skew angles, number of bent columns, and column height-to-diameter ratios were developed using OpenSees, and a series of nonlinear response history analyses were conducted. Comparison of seismic response of bridges subjected to only translational and both translational and TGMs revealed that TGMs may result in uneven and asymmetric failure of the shear keys. Therefore, deck rotations are significantly amplified due to induced instantaneous eccentricity when deck comes in contact with shear key(s). The amplified impact forces due to TGMs further amplify the deck rotations, which in return result in higher inelastic displacement and force demand. Last but not the least, the induced torsion due to TGM combined with axial-flexure-shear interactions may result in complex failure modes, higher shear stresses, and reduction in lateral deformation and flexural capacity of the bridge columns.

Effect of Torsional Ground Motions on Floor Acceleration Response in Flexible SMRF Buildings

ABSTRACT This study investigates the effect of torsional components of the ground motions (TGM) on the floor acceleration response of flexible special moment-resisting frame (SMRF) buildings. For this purpose, computational models of three SMRF buildings were subjected to far-field ground motions with and without TGMs. Accordingly, the effect of TGM on the floor acceleration of structures with relatively short torsional period of vibration may be significant. Furthermore, TGMs may have adverse impact on rigid nonstructural components as it can be inferred from the amplifications in floor acceleration spectra, regardless of the flexibility of the parent structure.

Effect of torsional ground motion on the seismic response of highway bridges

Seismological aspects of rotational ground motions can be found in published research, however, studies on implications for the seismic response of structural systems are rare. This preliminary study investigates the effects of torsional component of the ground motions (TGM) on the overall seismic response of bridges and interactions among their components. For this purpose, a series of computational models of bridges were developed. The models assume linear-elastic substructure with continuous rigid deck, sliding supports and rigid abutments, and vary key parameters including skew angle (β), normalized stiffness eccentricity between the center of mass and rigidity (ex/r), gap size between deck and abutments, dominant frequency ratios. However, inelastic impact between the superstructure and abutments is modeled explicitly to ensure that consequential in-plane deck rotations are accounted for. It was shown that larger deck rotations due to TGM lead to larger impact forces, which further amplifies deck rotations. The adverse effects may be more pronounced in symmetric bridges and in bridges with significant skew. All response quantities; deformations and substructure forces, are amplified significantly due to TGMs which suggests that current design codes may underestimate seismic deformation and force demand.

Numerical study on the effects of seismic torsional component on multistory buildings

In this paper, the influence of the rotational component, about a vertical axis, of earthquake ground motion on the response of building structures subjected to seismic action is considered. The torsional component of ground motion is generated from the records of translational components. Torsional component of ground motion is then, together with translational components, applied in numerical linear dynamic analysis of different reinforced concrete framed structure of three stories buildings. In total, more than 40 numerical models were created and analyzed. The obtained results show clearly the dependence of the effects of the torsional seismic component on structural system and soil properties. Thus, the current approach in seismic codes of accounting for the effects of accidental torsion due to the torsional ground motion, by shifting the center of mass, should be reevaluated.

Accidental eccentricity in multistory buildings due to torsional ground motion

Accidental eccentricity is aimed to account for any unforeseen factor that may attribute to the torsional response. These sources can be broadly classified into two components, namely, uncertainty in geometry and material properties, and torsional ground motion. Recently, conventional approach of shifting the center of mass was reported to be inappropriate when accidental torsion is contributed from the torsional ground motion and an alternative approach was proposed for the single story buildings subjected to unidirectional ground motion. The alternative approach is further investigated in this paper so as to include the multistory buildings under bidirectional ground motions, given the accidental eccentricity. Also developed is a framework for evaluating the minimum required accidental eccentricity due to torsional ground motion that can be used in developing the seismic code recommendations. Even though the number of response candidates based on which accidental eccentricity can be assessed is many for a multistory building, this paper presents a simple recommendation for the vertically regular buildings.

An equivalent accidental eccentricity to account for the effects of torsional ground motion on structures

The seismic design of buildings and other structures should include provisions for inherent and accidental torsion effects. Procedures developed decades ago for use with equivalent lateral force (static) analysis have been often used for response-history analysis with no investigation of whether the procedures achieve the desired result; namely, robust framing systems with limited susceptibility to excessive torsional displacement. The utility of procedures presented in ASCE 7 for treating accidental eccentricity as means for accounting for the effects of torsional ground motion is examined by analysis of simple linear and nonlinear systems. Results indicate that these standards-based procedures do not achieve the desired trends when torsional ground motion effects are considered, namely, increased component demands with increasing accidental eccentricity. An alternate approach for using accidental eccentricity concepts in accounting for torsional ground effects is then proposed and verified in representative examples for simple linear and nonlinear systems. In each case, component demand increases monotonically as the accidental eccentricity increases.

The Effect of Torsional Ground Motion on Structural Response: Code Recommendation for Accidental Eccentricity

In this article, data were collected from the Chiba dense array, which consists of 44 accelerometers with interstation spacing in the range of 5-300 m that are employed to estimate the torsional ground motion. The geodetic method was used to estimate torsional motions from the translational records in the Chiba dense array. The translational and computed torsional motions were then applied to the building models with different structural characteristics to evaluate the effectiveness of the accidental eccentricity levels proposed in various design codes. The results of analy- sis suggest that the 5% accidental eccentricity is on the safe side for most periods of interest in engineering practice. However, in the case of stiff structures (with periods shorter than 0.3 sec), an increase of up to four times in building displacement is ob- served by including the torsional excitation. Furthermore, we found that the acciden- tal eccentricity coefficient increased up to 0.6 at periods shorter than 0.3 sec, which is 12 times larger than what is proposed by the codes.

On the characteristics of ground motion rotational components using Chiba dense array data

AbstractAn effort is made to examine the properties of rotational (torsional and rocking) ground motions using Chiba dense array data. The Chiba array system, located 30 km east of Tokyo, Japan, is composed of 15 boreholes with separation distances varying from 5 to 320 m. This provides a unique opportunity to examine the characteristics of rotational components. For this purpose, 17 events are considered and rotational ground motions are evaluated using spatial derivatives of translational ones. The effects of seismological parameters and separation distances between stations on properties of rotational motions are examined, showing a sudden increase in rotational motions for the earthquakes with large magnitude or PGA and decrease of these motions with increasing separation distance. While the duration of torsional motion is found to be larger than translational ones, there is no significant difference between durations of rocking and vertical motions. The effects of separation distance and earthquake magnitude on rotational response spectra are also investigated. The normalized rotational response spectra are found to be strongly affected by separation distance. The spectral ratios of rotational and translational motions are not linearly proportional to period as suggested by the previous studies. Finally, the torsional motion is predicted from translation ones for different separation distances at the site. The comparison of the predicted and the calculated torsional motions reveals a weak estimation in close separation distances (<30m) and satisfactory predictions in other cases. Copyright © 2007 John Wiley & Sons, Ltd.

Stochastic model of seismic torsional ground motion: Application to Lotung soft site

The purpose of this paper is to present a stochastical approach, which analyse the torsional ground motion, induced by the spatial variability of seismic motions. For this purpose, a torsional ground motion analytical model is proposed and a normalised differential motion parameter is introduced. The approach regards the seismic motion as the combination of a travelling wave on the site (coherent component) and a zero mean randomizing factor that introduces a loss of correlation effect. The soil parameters as fundamental frequency and damping coefficient are integrating by modeling the coherent component with the commonly used Kanai-Tajimi power spectral density. The parametric analysis of the model shows an increase of the induced torsion with both the soil frequency and the motion scattering parameter, and a decrease with the separation distance, the apparent wave velocity and the correlation length. Finally, in order to test the proposed torsional ground motion model prediction, it is compared to the experimental results recorded by the EPRI LSST array in Lotung, Taiwan (Laouami and Labbe, 2002). The comparison leads to the identification of the model parameters for the Lotung soft site.

The effects of torsion and motion coupling in site response estimation

AbstractSoil amplification characteristics are investigated using data from the Chibaken‐Toho‐Oki earthquake and its aftershocks recorded at Chiba dense array in Japan. The frequency‐dependent amplification function of soil is calculated using uphole‐to‐downhole spectral ratio analysis, considering the horizontal components of shear wave. The identified spectral ratios consistently demonstrate the splitting of peaks in their resonance frequencies and low amplification values in comparison with a 1D model. The torsional behaviour and horizontal ground motion coupling are clarified as the reasons for these phenomena at the site. To prove the hypothesis, the torsional motion is directly evaluated using the data of the horizontal dense array in different depths at the site. The comparison between Fourier spectra of torsional motion and identified transfer functions reveals the peaks at the same frequencies. The wave equation including torsion and horizontal motion coupling is introduced and solved for the layered media by applying wave propagation theory. Using the developed model, the effects of torsional motion with horizontal motion coupling on soil transfer function are numerically examined. Splitting and low amplification at resonance frequencies are confirmed by the results of numerical analysis. Furthermore, the ground motion in two horizontal directions at the site is simulated using site geotechnical specification and optimizing the model parameters. The simulated and recorded motions demonstrate good agreement that is used to validate the hypothesis. In addition, the spectral density of torsional ground motions are compared with the calculated one and found to be well predicted by the model. Finally, the results are used to explain the overestimation of damping in back‐calculation of dynamic soil properties using vertical array data in small strain level. Copyright © 2003 John Wiley & Sons, Ltd.

Experimental analysis of seismic torsional ground motion recorded by the LSST‐Lotung array

AbstractThe purpose of this study was to perform an experimental analysis of the amplitude of full‐scale spatial variability of seismic motions with regard to earthquake engineering. The LSST‐Lotung array in Taiwan provides a good set of records for this type of study. Of interest are the free‐field torsional seismic components induced by the spatial variability of seismic motions. In this study, three events have been considered: LSST‐06, LSST‐07 and LSST‐16. In time domain analysis, the experimental results obtained show that when the separation distance increases, the induced torsion decreases, and the normalized differential motion parameter increases. Also, the results show that the stronger the event, in terms of maximum PGA, the larger the induced torsional amplitude and the smaller the induced normalized differential motion parameter. Copyright © 2002 John Wiley & Sons, Ltd.

CHARACTERISTICS OF TORSIONAL GROUND MOTIONS

Due to the inherent difficulty in directly recording the rotational ground motions, torsional ground motions have to be estimated from the recorded spatially varying translational motions. In this paper, an empirical coherency function, which is based on the recorded motions at the SMART-1 array, is suggested to model the spatial variation of translational motions. Then, the torsional ground motion power spectral density function is derived. It depends on the translational motion power spectral density function and the coherency function. Both the empirical coherency function and the torsional motion power spectral density function are verified by the recorded motions at the SMART-1 array. The response spectra of the torsional motions are also estimated. Discussion on the relations between the torsional motion response spectrum and the corresponding translational motion response spectrum is made. Numerical results presented can be used to estimate the torsional ground motion power spectral density function and response spectrum.

The effects of torsional ground motion on thin cylindric shell structures

The effects of torsional component of earthquake ground motion on thin cylindric shell structures were investigated qualitatively and quantitatively. The results show that the contributions of torsional component to structural response are related to the height, the radius-to-height ratio, and the stiffness of the structure. The structural response caused by torsional component can not be neglected for the containment structure of nuclear power plant and the industrial oil tank.

ねじり地動ピックアップの試作

This paper is mainly concerned with the cross-talk of a torsional vibration pickup, which was developed to measure the torsional ground motion with a minimum of cross-talk. The causes of the cross-talk considered in this paper are : (1) the static intrinsic errors of cross-spring pivot and (2) the unbalance of the mass element of seismic system. The cross-talk generation due to these causes is investigated in detail. Description of a balancing method utilising a rectilinear vibration table, which was devised to minimize the unbalance of the mass element under actual operating condition of the pickup, is included, together with the construction and performance characteristics of the pickup.

Rotational ground motion and seismic codes

The primary purpose of this paper is to discuss the separation of travelling wave effects from the mass center to resistance center eccentricity effects, and to propose means by which the torsional spectrum (or a torsional seismic factor) could be incorporated in the seismic provisions of the National Building Code of Canada. The paper begins the treatment of the subject matter by presenting a detailed review of previous work on the effects of torsional ground motion, emphasizing the methods which have been proposed to develop torsional response spectra. The travelling wave assumption is critically reviewed and the effective phase velocities applicable for design purposes are discussed. This is followed by a simple analysis showing how the torsional spectra can be derived directly from the corresponding translational response spectra. Formulae separating the torsional input effects from the accidental eccentricity effects are presented and discussed. Finally, it is shown how the torsional spectrum can be incorporated within the framework of the response spectrum procedure of the 1985 edition of the National Building Code of Canada. Key words: seismic, earthquake, structure, dynamic, rotation, code, torsion, foundation, eccentricity, response spectrum, acceleration, velocity, design.

Torsional Earthquake Response of Suspension Bridges

The earthquake‐induced torsional response of suspension bridges when subjected to multiple support excitations is analyzed in the frequency domain by means of random vibration theory. Appropriate rocking and torsional ground motion inputs are defined from finite Fourier transforms of recorded translational motions by using a simplified approach based upon wave propagation theory. An example is presented in which the torsional response of the Golden Gate Bridge to earthquake ground motions (the 1979 Imperial Valley earthquake) with characteristics significantly different at each support point is investigated. It is observed that the participation of higher modes in the total response is essential to assess the torsional seismic behavior of such structures. It is also observed that both the vibrational displacement and vibrational cable tension induced by torsional vibration are very small but the flexural stresses induced by the torsional vibration are relatively large as live loads.

Seismic torsional effects on buildings

This paper gives the background to the seismic torsional provisions of the New Zealand Loadings Code. These provisions attempt to deal with three effects: accidental eccentricity, torsional ground motion, and coupling between torsional and translational modes. The first two effects lead to an effective eccentricity of one-tenth of the width of a building, while the third leads to a parabolic function of the calculated eccentricity: this was obtained by applying existing results for torsional amplification to a number of typical building structures.