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.     

On the inelastic torsional response of single‐storey structures under bi‐axial excitation

An attempt has been made to explore the general trends in the seismic response of plan‐asymmetric structures without any restrictions imposed by a particular code. Systems with structural elements in both orthogonal directions under bi‐directional excitation were studied. Idealized single‐storey models with bi‐axial eccentricity were employed. The systems were torsionally stiff and, in the majority of cases, mass‐eccentric. The main findings are: in general, inelastic torsional response is qualitatively similar to elastic torsional response. Quantitatively, the torsional effect on the flexible side, expressed as an increase of displacements due to torsion, decreases slightly with increasing plastic deformation, unless the plastic deformations are small. The response on the stiff side generally strongly depends on the effect of several modes of vibration and on the influence of the ground motion in the transverse direction. These influences depend on the structural and ground motion characteristics in both directions. Reduction of displacements due to torsion, typical for elastic torsionally stiff structures, usually decreases with increasing plastic deformations. As an additional effect of large plastic deformations, a flattening of the displacement envelopes in the horizontal plane usually occurs, indicating that torsional effects in the inelastic range are generally smaller than in the elastic range. The dispersion of the results of inelastic torsional response analysis is generally larger than that of elastic analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Torsional balance of plan‐asymmetric structures with frictional dampers: experimental results

This investigation deals with the measured seismic response of a six‐storey asymmetric structural model with frictional dampers. Its main objective is to experimentally prove the concept of weak torsional balance for mass‐ and stiffness‐eccentric model configurations. The goal is to control the torsional response of these asymmetric structures and to achieve, if possible, a weak form of torsional balance by placing the so‐called empirical centre of balance (ECB) of the structure at equal distance from the edges of the building plan. The control of the dynamic response of asymmetric structures is investigated herein by using steel–teflon frictional dampers. As expected from theory, experimental results show that the mean‐square and peak displacement demand at the flexible and stiff edges of the plan may be similar in magnitude if the dampers are optimally placed. Frictional dampers have proven equally effective in controlling lateral‐torsional coupling of torsionally flexible as well as stiff structures. On the other hand, it is shown that impulsive ground motions require larger frictional capacities to achieve weak torsional balance. Copyright © 2006 John Wiley & Sons, Ltd.     

Pseudodynamic response of torsionally unbalanced two‐storey test structure

Two one‐way eccentric, two‐storey, one‐by‐one‐bay reinforced concrete (RC) structures are pseudodynamically tested under unidirectional ground motions. Theoretical considerations about the effect of torsional coupling on modal periods and shapes agree with modal results of the test structure, considering member stiffness is equal to the secant stiffness to yielding in skew‐symmetric bending. Modal periods of such an elastic structure are in fair agreement with effective periods inferred from the measured response at the beginning of a test of a thoroughly cracked structure and at the end of the test. A time‐varying stiffness matrix and a non‐proportional damping matrix fitted to the test results may be used to reproduce the measured response approximately by modal superposition and identify the role of the four time‐varying modes. Flexible side columns sustained very large drift demands simultaneously in the two transverse directions and suffered significant but not heavy, damage at lap‐splices. RC‐jacketing of the flexible side columns practically eliminated the static eccentricity between the floor centres of twist and mass as well as the torsional response. Inelastic time‐history analysis with point‐hinge member models, using as elastic stiffness the secant stiffness to yielding and neglecting post‐ultimate‐strength cyclic degradation of resistance in members with plain bars and poor detailing, predicted fairly well the response until the peak displacements and member deformations occurred. After that, it underestimated displacement peaks and the lengthening of the apparent period and missed the gradual drifting of the response towards a permanent offset. Copyright © 2007 John Wiley & Sons, Ltd.     

Predicting torsion‐induced lateral displacements for pushover analysis: Influence of torsional system characteristics

The increasing popularity of simplified nonlinear methods in seismic design has recently led to many proposals for procedures aimed at extending pushover analysis to plan asymmetric structures. In terms of practical applications, one particularly promising approach is based on combining pushover analysis of a 3D structural model with the results of linear (modal) dynamic analysis. The effectiveness of such procedure, however, is contingent on one fundamental requirement: the elastic prediction of the envelope of lateral displacements must be conservative with respect to the actual inelastic one. This paper aims at verifying the above assumption through an extensive parametric analysis conducted with simplified single‐storey models. The main structural parameters influencing torsional response in the elastic and inelastic range of behaviour are varied, while devoting special attention to the system stiffness eccentricity and radius. The analysis clarifies the main features of inelastic torsional response of different types of building structures; in this manner, it is found that the above‐mentioned method is generally suitable for structures characterized by moderate to large torsional stiffness, whereas it cannot be recommended for extremely torsionally stiff structures, as their inelastic torsional response almost always exceeds the elastic one. Copyright © 2010 John Wiley & Sons, Ltd.     

On the inelastic seismic response of asymmetric buildings under bi‐axial excitation

The elastic and inelastic seismic response of plan‐asymmetric regular multi‐storey steel‐frame buildings has been investigated under bi‐directional horizontal ground motions. Symmetric variants of these buildings were designed according to Eurocodes 3 and 8. Asymmetric buildings were created by assuming a mass eccentricity in each of the two principal directions. The torsional response in the elastic and inelastic range is qualitatively similar with the exception of the stiff edge in the strong direction of torsionally stiff buildings and the stiff edge in the weak direction of torsionally flexible buildings. The response is influenced by the intensity of ground motion, i.e. by the magnitude of plastic deformation. In the limiting case of very strong ground motion, the behaviour of initially torsionally stiff and initially torsionally flexible buildings may become qualitatively similar. A decrease in stiffness due to plastic deformations in one direction may substantially influence the behaviour in the orthogonal direction. The response strongly depends on the detailed characteristics of the ground motion. On average, torsional effects are reduced with increasing plastic deformations, unless the plastic deformations are small. Taking into account also the dispersion of results which is generally larger in the inelastic range than in the elastic one, it can be concluded that (a) the amplification of displacements determined by the elastic analysis can be used as a rough estimate also in the inelastic range and (b) any favourable torsional effect on the stiff side of torsionally stiff buildings, which may arise from elastic analysis, may disappear in the inelastic range. The conclusions are limited to fairly regular buildings and subject to further investigations. Copyright © 2005 John Wiley & Sons, Ltd.     

Torsional response of symmetric buildings to incoherent and phase‐delayed earthquake ground motion

This paper studies the effect of coherency loss and wave passage on the seismic torsional response of three‐dimensional, multi‐storey, multi‐span, symmetric, linear elastic buildings. A model calibrated against statistical analyses of ground motion records in Mexico City is used for the coherency function. The structural response is assessed in terms of shear forces in structural elements. Incoherence and wave passage effects are found to be significant only for columns in the ground level of stiff systems. The increase of column shears in the ground level is much higher for soft than for firm soil conditions. For the torsionally stiff systems considered, it is found that incoherent and phase‐delayed ground motions do not induce a significant rotational response of the structure. The use of a code eccentricity to account for torsion due to ground motion spatial variation is assessed. On firm soil, the use of a base shear along with an accidental eccentricity results in highly overestimated shear forces; however, for soft soil conditions, code formulations may result in underestimated shear forces. Copyright © 2003 John Wiley & Sons, Ltd.     

单轴平扭耦联基础隔震结构动力简化分析

为了建立单轴平扭耦联基础隔震结构的动力简化分析方法,探讨了影响结构扭转反应的参数取值规律,首先基于层单元模型,通过假定上部结构楼层回转半径、偏心距、弹力半径相等,推导了单轴平扭耦联基础隔震结构线性化的动力计算方程;其次,运用该简化分析方程,通过一算例进行了动力响应的参数分析。结果表明:调整隔震层刚心使其与上部结构质心位置接近,可显著降低偏心隔震结构扭转反应;增大隔震层刚度半径及阻尼半径可有效减少或抑制结构扭转反应;所建简化分析方程能有效模拟偏心隔震结构动力响应。     

Out‐of‐plane seismic response of vertically spanning URM walls connected to flexible diaphragms

A simplified numerical model was used to investigate the out‐of‐plane seismic response of vertically spanning unreinforced masonry (URM) wall strips. The URM wall strips were assumed to span between two flexible diaphragms and to develop a horizontal crack above the wall mid‐height. Three degrees of freedom were used to accommodate the wall displacement at the crack height and at the diaphragm connections, and the wall dynamic stability was studied. The equations of dynamic motion were obtained using principles of rocking mechanics of rigid bodies, and the formulae were modified to include semi‐rigid wall behaviour. Parametric studies were conducted that included calculation of the wall response for different values of diaphragm stiffness, wall properties, applied overburden, wall geometry and earthquake ground motions. The results of the study suggest that stiffening the horizontal diaphragms of typical low‐rise URM buildings will amplify the out‐of‐plane acceleration demand imposed on the wall and especially on the wall–diaphragm connections. It was found that upper‐storey walls connected to two flexible diaphragms had reduced stability for applied earthquake accelerograms having dominant frequency content that was comparable with the frequency of the diaphragms. It was also found that the applied overburden reduced wall stability by reducing the allowable wall rotations. The results of this study suggest that the existing American Society of Civil Engineers recommendations for assessment of vertically spanning walls overestimate the stability of top‐storey walls in multi‐storey buildings in high‐seismic regions or for walls connected to larger period (less stiff) diaphragms. Copyright © 2015 John Wiley & Sons, Ltd.     

Effects of torsion on the behavior of peripheral steel‐braced frame systems

In this study, the torsional response of buildings with peripheral steel‐braced frame lateral systems is evaluated. A three‐dimensional model of a three story braced frame with various levels of eccentricity is created and the effects of torsion on the seismic response is assessed for four hazard levels. The response history analysis results indicate that, unlike frame structures, the torsional amplifications in the inelastic systems exceed those of corresponding elastic systems and tend to increase with an increase in the level of inelasticity. The ability of two simplified procedures, elastic response spectrum analysis and pushover analysis, to capture the torsional amplifications in steel‐braced frames is evaluated. Copyright © 2010 John Wiley & Sons, Ltd.     

The applicability of the N2 method to the estimation of torsional effects in asymmetric base‐isolated buildings

The paper deals with the applicability of the extended N2 method to base‐isolated plan‐asymmetric building structures. The results obtained by the usual pushover analysis of a 3D structural model are further combined with the aid of linear dynamic (spectral) analysis to account for the dynamic effects caused by structural asymmetry. In the paper, the method has been applied to the seismic analysis of a mass‐eccentric four‐storeyed RC frame building isolated with lead rubber bearings. Three different positions of the center of isolation system (CI) with respect to the center of mass (CM) and the center of stiffness of the superstructure (CS) were considered. The response was analyzed for three different eccentricities, three different torsional to lateral frequency ratios of the superstructure, and two ground motion intensities. The stiffness of the isolators was selected for three different protection levels, which resulted in elastic as well as moderately to excessively damaged superstructure performance levels. The results are presented in terms of the top, base and relative displacements, as well as the stiff/flexible side amplification factors. A more detailed insight into the nonlinear behavior of the superstructure is given in a form of ductility factors for the flexible and stiff side frames. The results of the extended N2 method for selected lateral load distributions are compared with the average results of nonlinear dynamic analyses. It was concluded that the extended N2 method could, with certain limitations, provide a reasonable prediction of the torsional influences in minor to moderately asymmetric base‐isolated structures. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic response of a case study soft story frame retrofitted using a GIB system

This paper presents results from a numerical investigation into the seismic retrofit of a soft story frame using a novel gapped‐inclined brace (GIB) system. The GIB system consists of a pinned brace and a gap element that is added to the first story columns of the frame. The inclusion of GIB elements in addition to increasing the lateral capacity of columns at the first story increases the post‐yield stiffness ratio of the system and reduces the P‐delta effects on the columns, while not increasing the first story lateral resistance or stiffness. This allows for the isolating benefits of the soft story to protect the upper floors of the structure from damage while avoiding excessive deformations and reducing the propensity for collapse. A six‐story RC frame with masonry infills on all floors except for the first floor is studied. The dynamic response of the retrofitted building using the GIB system is investigated numerically and is compared with the response of the original un‐retrofitted building and the same building in which masonry infills are added to the first story to mitigate the soft story response. Results from the nonlinear time‐history analyses indicate that the GIB system could provide a reliable seismic retrofit mechanism for soft story buildings, which greatly reduces the likelihood of collapse by increasing the displacement capacity of the soft storey and by reducing P‐delta effects, while minimizing the overall damage and losses in the building by taking advantages of the isolation that is provided by the soft story to the rest of the structure located above. Copyright © 2014 John Wiley & Sons, Ltd.     

A displacement‐based seismic design procedure for RC buildings and comparison with EC8

A procedure for displacement‐based seismic design (DBD) of reinforced concrete buildings is described and applied to a 4‐storey test structure. The essential elements of the design procedure are: (a) proportioning of members for gravity loads; (b) estimation of peak inelastic member deformation demands in the so‐designed structure due to the design (‘life‐safety’) earthquake; (c) revision of reinforcement and final detailing of members to meet these inelastic deformation demands; (d) capacity design of members and joints in shear. Additional but non‐essential steps between (a) and (b) are: (i) proportioning of members for the ULS against lateral loads, such as wind or a serviceability (‘immediate occupancy’) earthquake; and (ii) capacity design of columns in flexure at joints. Inelastic deformation demands in step (b) are estimated from an elastic analysis using secant‐to‐yield member stiffnesses. Empirical expressions for the deformation capacity of RC elements are used for the final proportioning of elements to meet the inelastic deformation demands. The procedure is applied to one side of a 4‐storey test structure that includes a coupled wall and a two‐bay frame. The other side is designed and detailed according to Eurocode 8. Major differences result in the reinforcement of the two sides, with significant savings on the DBD‐side. Pre‐test calculations show no major difference in the seismic performance of the two sides of the test structure. Copyright © 2001 John Wiley & Sons, Ltd.     

Test on full‐scale three‐storey steel moment frame and assessment of ability of numerical simulation to trace cyclic inelastic behaviour

A test on a full‐scale model of a three‐storey steel moment frame was conducted, with the objectives of acquiring real information about the damage and serious strength deterioration of a steel moment frame under cyclic loading, studying the interaction between the structural frame and non‐structural elements, and examining the capacity of numerical analyses commonly used in seismic design to trace the real cyclic behaviour. The outline of the test structure and test program is presented, results on the overall behaviour are given, and correlation between the experimental results and the results of pre‐test and post‐test numerical analyses is discussed. Pushover analyses conducted prior to the test predicted the elastic stiffness and yield strength very reasonably. With proper adjustment of strain hardening after yielding and composite action, numerical analyses were able to accurately duplicate the cyclic behaviour of the test structure up to a drift angle of 1/25. The analyses could not trace the cyclic behaviour involving larger drifts in which serious strength deterioration occurred due to fracture of beams and anchor bolts and progress of column local buckling. Copyright © 2005 John Wiley & Sons, Ltd.     

Additional seismic inelastic deformation caused by structural asymmetry

Using a single mass monosymmetric model, this paper examines the additional seismic inelastic deformations and displacement caused by structural asymmetry of the model. Stiffness eccentricity and resistance eccentricity are used as measures of asymmetry in the elastic and inelastic range respectively. Seven ways of specifying strength distribution among resisting elements are considered, including code provisions from Canada, Mexico, New Zealand and the United States. These specifications are related t o the model resistance eccentricity. It is shown that when torsional shears are included in the strength design of the elements, the structure in general will have small resistance eccentricity, even if it has large stiffness eccentricity in the elastic range. For structures which are designed with allowance for torsional shears, the ductility demands on the elements are similar to those when the structure is symmetrical. However, the edge displacements can be up to three times that if the system is symmetrical. This finding has significant implications in evaluating adequate separation between buildings to avoid the pounding problem during earthquakes.     

Torsional balance of plan‐asymmetric structures with frictional dampers: analytical results

This investigation deals with the torsional balance of the earthquake response and design of elastic asymmetric structures with frictional dampers. Plan asymmetry leads to an uneven lateral deformation demand among structural members and to unbalanced designs with larger capacities in some resisting planes. Frictional dampers are capable of controlling lateral‐torsional coupling by placing the so‐called empirical center of balance (ECB) of the structure at equal distance from all edges of the building. This rule is developed for single‐story systems with linear and inelastic behavior. However, recently obtained theoretical and experimental results demonstrate that this rule carries over to multistory structures. Results show that the peak displacement demand at the building edges and that of resisting planes equidistant from the geometric center may be similar if the damper is optimally placed. It is also shown that torsional amplification of the edge displacements of arbitrary asymmetric structures relative to the displacement of the symmetric counterparts are approximately bound by a factor of 2. Furthermore, frictional dampers are equally effective in controlling lateral‐torsional coupling of torsionally flexible as well as stiff structures. Copyright © 2005 John Wiley & Sons, Ltd.     

Earthquake resistance of buildings with a ‘soft’ first storey

The dynamic, bi-linear response behaviour of a series of eight storey shear buildings subjected to simulated earthquake excitation is studied. The specific objective of the investigation is to determine under what conditions a yielding first storey can adequately protect the upper storeys from significant yielding. Two classes of buildings are considered: stiff (0.5 sec period) and flexible (2.0 sec period), and the basic parameters considered in the yielding first storey are the yield force level and the bi-linear stiffness. The results demonstrate that a very low yield force level and an essentially perfectly plastic yielding mechanism are required in the first storey to provide effective protection to the superstructure. Moreover, the required displacement capacity of such an effective first storey mechanism is found to be very large.     

Inelastic earthquake response of single‐story asymmetric buildings: an assessment of simplified shear‐beam models

The inelastic seismic torsional response of simple structures is examined by means of shear‐beam type models as well as with plastic hinge idealization of one‐story buildings. Using mean values of ductility factors, obtained for groups of ten earthquake motions, as the basic index of post‐elastic response, the following topics are examined with the shear‐beam type model: mass eccentric versus stiffness eccentric systems, effects of different types of motions and effects of double eccentricities. Subsequently, comparisons are made with results obtained using a more realistic, plastic hinge type model of single‐story reinforced concrete frame buildings designed according to a modern Code. The consequences of designing for different levels of accidental eccentricity are also examined for the aforementioned frame buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Shake table tests on a mass eccentric model with base isolation

A mass eccentric structure is usually more seismically vulnerable than its concentric counterpart because of the coupled torsional–translational response of such structures. In this work, dynamic characteristics and response of a five‐storey benchmark model with moderate mass eccentricity were investigated using a shake table, simulating four different ground motions. The effectiveness of laminated rubber bearings (LRB) and lead‐core rubber bearings (LCRB) in protecting eccentric structures was examined and evaluated in relation to translational and torsional responses of the benchmark model. It was observed that both translational and torsional responses were significantly reduced with the addition of either a LRB or LCRB isolated system regardless of the nature of ground motion input. The LRB were identified to be more effective than LCRB in reducing model relative displacements, the relative torsional angle as well as accelerations, and therefore provided a better protection of the superstructure and its contents. On the other hand, LCRB rendered a smaller torsional angle and absolute displacement of the base isolation system, hence a more stable structural system. Copyright © 2003 John Wiley & Sons, Ltd.