Effect of transverse load-resisting elements on inelastic earthquake response of eccentric-plan buildings

The accurate evaluation of code torsional provisions for plan-eccentric structures exhibiting inelastic response relies on the adoption of appropriate systems defining both the torsionally balanced (reference) and torsionally unbalanced cases. Whilst a considerable number of analytical studies of this problem have been presented in the literature, inconsistencies have arisen in their conclusions. It is evident from a review of previous studies that one factor contributing significantly to these discrepancies arises in the definition of the structural layout. An issue of particular importance is whether the transverse load-resisting elements oriented perpendicular to the assumed (lateral) direction of earthquake loading should, for purposes of realism, be included in model definitions. Given the diverse approaches in the existing literature, clarification of this issue is required in order to advance the understanding of inelastic torsional response behaviour and to assist the interpretation and comparison of previous studies. This paper aims to provide such clarification, based on analyses of a series of models defined rigorously according to code design provisions. Such models have been subjected to both uni- and bi-directional ground motion input. It is concluded that for the flexible-edge element, accurate estimates of additional ductility demand arising from torsional effects may be obtained from uni-directional models (in which both the transverse elements and the corresponding earthquake component are neglected) only for medium-period to long-period systems. Such estimates may be over-conservative for short-period systems, which constitute a large proportion of systems for which code static torsional provisions are utilized. It is further concluded that models incorporating the transverse elements but analysed under uni-directional lateral loading may underestimate by up to 100% the torsional effects in such systems, but are reasonably accurate for medium- and long-period structures.     

Empirical models for estimating liquefaction-induced lateral spread displacement

Existing empirical models for estimating liquefaction-induced lateral spread displacement (D_LL) have been derived from a dataset poorly distributed with respect to earthquake magnitude and source distance, and also produced from different tectonic source types and faulting mechanisms. Both the poor distribution and mixed tectonic source types and faulting mechanisms of the data have an adverse impact on the reliability of the empirical models. To overcome these problems in the development of empirical models, we replace the direct use of magnitude and source distance with pseudo-displacement derived from spectral acceleration attenuation models that are well supported by earthquake data, and use a modification factor to account for effects of the non-linear soil response. Attenuation models derived from very large and reasonably well-balanced datasets have been selected, one being a Japanese attenuation model and other being a combination of the Sadigh et al. model and the Youngs et al. model. These models are capable of accounting for the effects of earthquake tectonic source type and faulting mechanism. We determined the model coefficients by selecting the pseudo-displacements calculated for a number of spectral periods to achieve an unbiased distribution of residuals with respect to earthquake magnitude and source distance. Sensitivity analyses have been carried out based on the new and existing models, and show that the new model is more robust than the existing models. Comparison with a limited number of data from the 1997 Kocaeli, Turkey earthquake suggests our model provides comparable liquefaction-induced lateral displacement D_LL estimates.     

Shaking table tests on a high‐rise RC building model having torsional eccentricity in soft lower storeys

A series of shaking table tests on a 1:12‐scale model using scaled TaftN21E earthquake records were conducted to investigate the seismic performance of a 17‐storey high‐rise reinforced concrete structure with a high degree of torsional eccentricity and soft‐storey irregularities in the bottom two storeys. Based on the analysis of test results, the following conclusions were drawn: (1) the model responded mainly in the coupled mode of translation and torsion or in the torsional mode. Under severe table shaking, the flexible side underwent large inelastic deformation, and the predominant mode of the model changed from the coupled mode to the torsional mode, resulting in greatly increased torsional stiffness, thereby limiting damage in the flexible frame; (2) the shear force and deformation of the flexible side were governed by the torsional behaviour, whereas those of the stiff side were affected mainly by the overturning deformation. The lateral stiffness of the shear wall in the torsional mode was about four times that in the coupled mode because the warping deformation due to torsion counteracted the flexural deformation due to overturning moment in the torsional mode; and (3) the reversed cyclic overturning moments predicted by linear elastic dynamic analysis in the direction transverse to the table excitations contradicted unilateral overturning moments of the serviceability‐level test results, which showed a bias towards tension or compression in the columns. Copyright © 2006 John Wiley & Sons, Ltd.     

Torsional response of nonductile structures with soft‐first‐storey

In this paper, torsional response of nonductile structures with soft‐first‐storey subjected to bidirectional ground motions is studied using a simplified two‐storey model with two‐way eccentricities. The stiffness ratio of second storey to first storey is varied to create different levels of soft‐first‐storey effect, while the stiffness eccentricity is varied to create torsional effects. Different overstrength ratios are used in the simplified models to study the response of structure with different structural capacity. Hysteretic model with strength deterioration and stiffness degradation properties is used to capture the deterioration of element stiffness and strength. Ductility capacity of 2.0 is used as the models are for nonductile structures. In general, displacement amplification of irregular model with respect to regular model increases as stiffness ratio increases, while no consistent trend of changes in displacement amplification is found with increase in stiffness eccentricity. It is found that the displacement amplification due to only soft‐first‐storey effect can be conservatively taken as 1.5. Coupling of torsional and soft‐first‐storey effects is more significant in affecting the displacement amplification of elements at flexible side. The trend of changes in displacement amplification of elastic system is similar to that of inelastic system. The displacement amplification of elements at the flexible side is larger than that at the stiff side. The elements at the flexible side in the direction of shorter uncoupled lateral period have larger displacement response than those in the orthogonal direction. Ductility demand–capacity curves subsequently constructed can be used to approximately assess the seismic performance of existing structures and as guidelines for designing structures in Singapore to withstand the maximum credible earthquake considering the coupling of torsional and soft‐first‐storey effects. Copyright © 2014 John Wiley & Sons, Ltd.     

1D System identification of a 54‐story steel frame building by seismic interferometry

A 54‐story steel, perimeter‐frame building in downtown Los Angeles, California, is identified by a wave method using records of the Northridge earthquake of 1994 (M_L = 6.4, R = 32 km). The building is represented as a layered shear beam and a torsional shaft, characterized by the corresponding velocities of vertically propagating waves through the structure. The previously introduced waveform inversion algorithm is applied, which fits in the least squares sense pulses in low‐pass filtered impulse response functions computed at different stories. This paper demonstrates that layered shear beam and torsional shaft models are valid for this building, within bands that include the first five modes of vibration for each of the North–South (NS), East–West (EW), and torsional responses (0–1.7 Hz for NS and EW, and 0–3.5 Hz for the torsional response). The observed pulse travel time from ground floor to penthouse level is τ ≈1.5 s for NS and EW and τ ≈ 0.9 s for the torsional responses. The identified equivalent uniform shear beam wave velocities are β_eq ≈ 140 m/s for NS and EW responses, and 260 m/s for torsion, and the apparent Q ≈ 25 for the NS and torsional, and ≈14 for the EW response. Across the layers, the wave velocity varied 90–170 m/s for the NS, 80–180 m/s for the EW, and 170–350 m/s for the torsional responses. The identification method is intended for use in structural health monitoring. Copyright © 2013 John Wiley & Sons, Ltd.     

The dynamic foundation interaction of multistorey frames

This paper discusses the extent to which foundation properties influence the response of some framed structures to earthquakes. Three stages can be isolated, the first of which checks the validity of a theoretical method by means of model studies. Five models were made, a five-storey plane frame rigidly fixed at its feet, two models of the same frame but now in association with a linearly elastic isotropic foundation, Adiprene L-100 and L-167, which had E-values of 4.4 and 39.7 N/mm², respectively. A five-storey, asymmetric space frame was also made, with fixed feet and with a foundation of modulus 4.4 N/mm². In this first stage, resonance tests were made, using the MAMA,² to obtain frequencies, mode shapes and damping values. Corresponding frequencies and mode shapes were calculated using a finite element idealization. The second stage uses a proven computer program for a parametric study to obtain a large number of results, which give a good indication of the effect of different foundation conditions on this type of structure. Some calculations are also made in which the foundation is represented by equivalent springs⁸ instead of finite elements. In the third stage dynamic response was considered. A shaking table was built on which the models were subjected to a number of actual earthquake records, which had been suitably scaled and recorded on magnetic tape. The structural response was measured, and compared with calculated values obtained by step-by-step methods and, alternatively, the modal addition approach. For the asymmetric space-frame, particular attention was paid to the torsional effect.     

Inelastic torsional response of buildings to the 1985 Mexican earthquake: a parametric study

This study aims to determine the influence of torsional coupling on the inelastic response of a series of models representing typical structural configurations in real buildings. The lake bed (SCT) east-west component of the 1985 Mexico City earthquake was employed in the analysis, and is representative of a severe ground motion known to have induced large inelastic structural deformations in a high proportion of those buildings having asymmetrical distributions of stiffness and/or strength. Material non-linearity in lateral load-resisting elements has been defined using a hysteretic Ramberg-Osgood model. Structural eccentricities have been introduced into the building models by (i) asymmetrical distributions of stiffness and/or strength, (ii) asymmetrical configuration of lateral load-resisting elements, or (iii) varying post-elastic material behaviour in the resisting elements. The dynamic inelastic response of these models has been obtained by a numerical integration of the relevant equations of motion, expressed in a non-dimensional incremental form.

In the elastic range, the results correlate well with those of previous studies. In the inelastic range, it is concluded that the peak ductility demand of the worst-affected element increases with the ground excitation level across the range of building periods considered, and that the influence of torsional coupling on the key response parameters is model dependent. Most significantly, the strength eccentricity relative to the centre of mass has been shown to influence the peak edge displacement response more than conventionally employed stiffness eccentricity.     

Effect of irregular structural configuration on floor acceleration demand in hill‐side buildings

A suite of reinforced‐concrete frame buildings located on hill sides, with 2 different structural configurations, viz step‐back and split‐foundation, are analyzed to study their floor response. Both step‐back and split‐foundation structural configurations lead to torsional effects in the direction across the slope due to the presence of shorter columns on the uphill side. Peak floor acceleration and floor response spectra are obtained at each storey's center of rigidity and at both its stiff and flexible edges. As reported in previous studies as well, it is observed that the floor response spectra are better correlated with the ground response spectrum. Therefore, the floor spectral amplification functions are obtained as the ratio of spectral ordinates at different floor levels to the one at the ground level. Peaks are observed in the spectral amplification functions corresponding to the first 2 modes in the upper portion of the hill‐side buildings, whereas a single peak corresponding to a specific kth mode of vibration is observed on the floors below the uppermost foundation level. Based on the numerical study for the step‐back and split‐foundation hill‐side buildings, simple floor spectral amplification functions are proposed and validated. The proposed spectral amplification functions take into account both the buildings' plan and elevation irregularities and can be used for seismic design of acceleration‐sensitive nonstructural components, given that the supporting structure's dynamic characteristics, torsional rotation, ground‐motion response spectrum, and location of the nonstructural components within the supporting structure are known, because current code models are actually not applicable to hill‐side buildings.     

Evaluation of code torsional provisions by a time history approach

Presented in this paper is a detailed parametric study of the coupled lateral and torsional response of single-storey building models subjected to earthquake base loadings. The aim is to assess the influence of torsional coupling on the elastic responses of buildings subjected to transient ground motion records, and to make comparisons with current code provisions which make allowance for coupling effects by means of empirical design procedures. The study of building responses to selected earthquake excitations shows that the qualitative effects of the controlling parameters on the maximum translational and torsional responses of the coupled system are similar to those observed in analyses using idealized response spectra to represent the input ground motion. It is also demonstrated that for particular ranges of the key parameters defining the structural system, typical of the properties of many actual buildings, torsional coupling induces significant amplification of earthquake forces. This amplification is shown to be inadequately accounted for in the current design provisions of major building codes. Recommendations for improving existing design practice for asymmetric structures are outlined.     

Effect of orthogonal inplane structural elements on inelastic torsional response

The elastic torsional stiffness of a structure has important influence on the seismic response of an asymmetric structure, both in the elastic and inelastic range. For elastic structures it is immaterial whether the stiffness is provided solely by structural elements in planes parallel to the direction of earthquake or by a combination of such elements in parallel and orthogonal planes. The issue of how the relative contribution of structural elements in orthogonal planes affects the torsional response of inelastic structures has been the subject of continuing study. Several researchers have noted that structural elements in orthogonal planes reduce the ductility demands in both the flexible and stiff edge elements parallel to the earthquake. Some have noted that the beneficial effect of structural elements in orthogonal planes is more pronounced when such elements remain elastic. These issues are further examined in this paper through analytical studies on the torsional response of single-storey building models. It is shown that, contrary to the findings of some previous studies, the torsional response of inelastic structures is affected primarily by the total torsional stiffness in the elastic range, and not so much by whether such stiffness is contributed solely by structural elements in parallel planes or by such elements in both parallel and orthogonal planes. Copyright © 1999 John Wiley & Sons, Ltd.     

Experimental evidence for flexibility of a building foundation supported by concrete friction piles

This article explores the possibility to measure deformations of building foundations from measurements of ambient noise and strong motion recordings. The case under study is a seven-storey hotel building in Van Nuys, California. It has been instrumented by strong motion accelerographs, and has recorded several earthquakes, including the 1971 San Fernando (M_L=6.6, R=22 km), 1987 Whittier–Narrows (M_L=5.9, R=41 km), 1992 Landers (M_L=7.5, R=186 km), 1992 Big Bear (M_L=6.5, R=149 km), and 1994 Northridge (M_L=6.4, R=1.5 km) earthquake and its aftershocks (20 March: M_L=5.2, R=1.2 km; 6 December, 1994: M_L=4.3, R=11 km). It suffered minor structural damage in 1971 earthquake and extensive damage in 1994. Two detailed ambient vibration tests were performed following the Northridge earthquake, one before and the other one after the 20 March aftershock. These included measurements at a grid of points on the ground floor and in the parking lot surrounding the building, presented and analyzed in this article. The analysis shows that the foundation system, consisting of grade beams on friction piles, does not act as a “rigid body” but deforms during the passage of microtremor and therefore earthquake waves. For this geometrically and by design essentially symmetric building, the center of stiffness of the foundation system appears to have large eccentricity (this is seen both from the microtremor measurements and from the earthquake recordings). This eccentricity may have contributed to strong coupling of transverse and torsional responses, and to larger than expected torsional response, contributing to damage during the 1994 Northridge, earthquake.     

双向偏心结构扭转耦联地震反应的序列最优控制

本文分析了不对称建筑结构平移-扭转耦联振动的动力特性及地震作用下的响应;根据地震动输入结构的过程,推导出一种更为一般的最优控制算法,所获得的控制力表达式同时包括地震响应和地震激励。通过对一非规则四层框架结构的扭转耦联地震反应控制分析表明,该算法不仅能有效地控制结构的平移地震反应,而且更有效地抑制结构的扭转耦联地震反应。     

Influence of structural parameters on dynamic characteristics and wind-induced buffeting responses of a super-long-span cable-stayed bridge

A 3D finite element (FE) model for the Sutong cable-stayed bridge (SCB) is established based on ANSYS. The dynamic characteristics of the bridge are analyzed using a subspace iteration method. Based on recorded wind data, the measured spectra expression is presented using the nonlinear least-squares regression method. Turbulent winds at the bridge site are simulated based on the spectral representation method and the FFT technique. The influence of some key structural parameters and measures on the dynamic characteristics of the bridge are investigated. These parameters include dead load intensity, as well as vertical, lateral and torsional stiffness of the steel box girder. In addition, the influence of elastic stiffness of the connection device employed between the towers and the girder on the vibration mode of the steel box girder is investigated. The analysis shows that all of the vertical, lateral and torsional buffeting displacement responses reduce gradually as the dead load intensity increases. The dynamic characteristics and the structural buffeting displacement response of the SCB are only slightly affected by the vertical and torsional stiffness of the steel box girder, and the lateral and torsional buffeting displacement responses reduce gradually as the lateral stiffness increases. These results provide a reference for dynamic analysis and design of super-long-span cable-stayed bridges.     

An experimental and numerical investigation into the seismic performance of a multi-storey concentrically braced plan irregular structure

In this investigation, the seismic torsional response of a multi-storey concentrically braced frame (CBF) plan irregular structure is evaluated numerically and experimentally through a series of hybrid tests. CBF structures have become popular in seismic design because they are one of the most efficient types of steel structures to resist earthquake loading. However, their response under plan irregular conditions has received little focus mostly in part due to their complex behaviour under seismic loading conditions. The majority of research on the seismic response of plan irregular structures is based purely on numerical investigations. This paper provides much needed experimental investigation of the seismic response of a CBF plan irregular structure with the aim of characterising the response of this class of structure. The effectiveness of the Eurocode 8 torsional effects provision as a method of designing for low levels of mass eccentricity is evaluated. Results indicate that some of the observations made by purely numerical models are valid in that; torsionally stiff structures perform well and the stiff side of the structure is subjected to a greater ductility demand compared to the flexible side of the structure. The Eurocode 8 torsional effects provision is shown to be adequate in terms of ductility and interstorey drift however the structure performs poorly in terms of floor rotation. Importantly, stiffness eccentricity occurs when the provision is applied to the structure when no mass eccentricity exists and results in a significant increase in floor rotations.     

Seismic vulnerability assessment to slight damage based on experimental modal parameters

The aim of this paper is to adjust behaviour models for each class of structure for vulnerability assessment by using ambient vibration. A simple model based on frequencies, mode shapes and damping, taken from ambient vibrations, allows computation of the response of the structures and comparison of inter‐storey drifts with the limits found in the literature for the slight damage grade, considered here as the limit of elastic behaviour. Two complete methodologies for building fragility curves are proposed: (1) using a multi‐degree of freedom system including higher modes and full seismic ground‐motion and (2) using a single‐degree of freedom model considering the fundamental mode f₀ of the structure and ground‐motion displacement response spectra S_D(f₀). These two methods were applied to the city of Grenoble, where 60 buildings were studied. Fragility curves for slight damage were derived for the various masonry and reinforced concrete classes of buildings. A site‐specific earthquake scenario, taking into account local site conditions, was considered, corresponding to an M_L = 5.5 earthquake at a distance of 15 km. The results show the benefits of using experimental models to reduce variability of the slight damage fragility curve. Moreover, by introducing the experimental modal model of the buildings, it is possible to improve seismic risk assessment at an overall scale (the city) or a local scale (the building) for the first damage grade (slight damage). This level of damage, of great interest for moderate seismic‐prone regions, may contribute to the seismic loss assessment. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical study of a full‐scale six‐story reinforced concrete wall‐frame structure tested at E‐Defense

A full‐scale shake table test on a six‐story reinforced concrete wall frame structure was carried out at E‐Defense, the world's largest three‐dimensional earthquake simulation facility, in January 2006. Story collapse induced from shear failure of shear critical members (e.g., short columns and shear walls) was successfully produced in the test. Insights gained into the seismic behavior of a full‐scale specimen subjected to severe earthquake loads are presented in this paper. To reproduce the collapse process of the specimen and evaluate the ability of analytical tools to predict post‐peak behavior, numerical simulation was also conducted, modeling the seismic behavior of each member with different kinds of models, which differ primarily in their ability to simulate strength decay. Simulated results showed good agreement with the strength‐degrading features observed in post‐peak regions where shear failure of members and concentrated deformation occurred in the first story. The simulated results tended to underestimate observed values such as maximum base shear and maximum displacement. The effects of member model characteristics, torsional response, and earthquake load dimensions (i.e., three‐dimensional effects) on the collapse process of the specimen were also investigated through comprehensive dynamic analyses, which highlighted the following seismic characteristics of the full‐scale specimen: (i) a model that is incapable of simulating a specimen's strength deterioration is inadequate to simulate the post‐peak behavior of the specimen; (ii) the torsional response generated from uniaxial eccentricity in the longitudinal direction was more significant in the elastic range than in the inelastic range; and (iii) three‐dimensional earthquake loads (X–Y–Z axes) generated larger maximum displacement than any other loading cases such as two‐dimensional (X–Y or Y–Z axes) or one‐dimensional (Y axis only) excitation. Copyright © 2011 John Wiley & Sons, Ltd.     

Influence of lateral-load-resisting system on the earthquake response of structures—a system identification study

Analysis and comparison of the dynamic responses of three well instrumented (with accelerographs) high-rise buildings shaken during the 1984 Morgan Hill earthquake are presented. The buildings examined in the present work are (i) the Town Park Towers Apartment building, a 10-storey, concrete shear wall building; (ii) the Great Western Savings and Loan building, a 10-storey building with concrete frames and shear walls; and (iii) the Santa Clara County Office building, a 13-storey, moment-resistant steel frame building. The structures are located within 2 km of each other and, as may be confirmed by visual inspection of the recorded seismograms, experienced similar ground motions. One-dimensional and three-dimensional linear structural models are fitted to the observations using the modal minimization method' for structural identification, in order to determine optimal estimates of the parameters of the dominant modes of the buildings. The time-varying character of these parameters over the duration of the response is also investigated. Comparison of the recorded earthquake response of the structures reveals that the type of lateral-load-resisting system has an important effect on the dynamic behaviour of the structures because it controls the spacing of the characteristic modes on the frequency axis. The Santa Clara County Office building has closely spaced natural frequencies and exhibits strong torsional response and modal coupling. Its dynamic behaviour is contrasted with that of the Great Western Savings and Loan building which has well separated natural frequencies and exhibits small torsional response and no modal coupling. Strong modal coupling causes a beating-type phenomenon and makes earthquake response of structures different from that envisioned by codes.     

EFFECT OF MODELLING ASSUMPTIONS AND INPUT MOTION CHARACTERISTICS ON SEISMIC DESIGN PARAMETERS OF RC BRIDGE PIERS

Modelling assumptions, boundary and loading conditions have a significant effect on analytical assessment of ductility supply and demand measures for RC bridges, a structural form which had suffered extensively in recent earthquakes. In recognition of the important role played by analysis in advancing seismic design of bridges, this paper is concerned with assessing the effect of model characteristics and earthquake strong-motion selection on analytical action and deformation seismic design parameters. This is of particular significance when viewed in the light of the large capital investment and problems with the satisfaction of dynamic similitude encountered in physical testing of piers and pier-deck assemblies. The models studied range between simple fixed-base cantilever and inclusion of both soil and deck effects, represented by assemblies of springs in translational and rotational degrees of freedom. Moreover, two sets of earthquake records are used in dynamic analysis, each comprising six records covering low, intermediate and high a/v, where a and v are the peak ground acceleration and velocity, respectively. The two sets differ in the scaling procedure employed to bring them to a common level of severity; the first set is obtained by direct acceleration scaling whilst the second utilizes the concept of velocity spectral intensity. The results from static and dynamic analysis, using advanced material characterization and solution procedures, are assessed and discussed. Subject to the limitations of the study, outlined in the paper, the results indicate that the inclusion of deck stiffness and/or soil representation is essential to avail of accurate seismic response parameters. However, the effect of variations in soil stiffness and/or deck torsional rigidity applied in the analysis is rather small, compared to the inclusion/exclusion of the model feature. Moreover, it is also observed that using acceleration scaling leads to much larger scatter in the results than when velocity spectral intensity scaling is used. Finally, the results from two particular earthquakes, Friuli and El Centro, highlight the peril of using a small number of records selected without due consideration to the relationship between their wave form, predominant periods and spectral shapes on the one hand and the response periods of the structure on the other.     

Optimum strength ratio of hysteretic damper

This paper deals with steel moment frames combined with hysteretic dampers. Specifically, it examines the strength of dampers required to minimize damage to moment frames under earthquake loading. The important structural variables are the ratio of the dampers' shear strength to the maximum resistance, termed β in this study, and the relative stiffness between the damper and the main frame, termed k. The equivalent viscous damping ratio of the entire structural system is affected by the quantities β and k and the ductility ratio of the main frame. The optimum dampers' strength ratio (β_opt), which maximizes the equivalent viscous damping ratio, was formulated as a function of k, and it was found that β_opt is independent of the ductility ratio of the main frame. Earthquake response analysis confirmed that damage to the main frame can be significantly reduced by hysteretic dampers and minimized at the value of β_opt. © 1998 John Wiley & Sons, Ltd.     

A new approach to earthquake prediction: The Load/Unload Response Ratio (LURR) theory

The response to loading is different from that to unloading when the focal media is approaching instability. The ratio of the response rate during loading to that during unloading, called Load/Unload Response RatioY (LURR), could be a measure of the closeness degree to instability and is used in a new approach to earthquake prediction. Retrospective examination of some one hundred earthquake cases (fromM 4 toM 8.6) indicates that for more than 80% of the examined ones, the value ofY is much higher than 1 for a period before the main shock, but theY value always fluctuates slightly about 1 during two decades for seven stable regions, so that the parameterY value always fluctuates slightly degree of an impending earthquake. Several earthquakes occurring on the Chinese mainland in recent years as well as the Northridge California, U.S.A. earthquake (Jan. 17, 1994,M _w 6.7) have been predicted beforehand with this method.