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.     

Torsional balance as new design criterion for asymmetric structures with energy dissipation devices

Lateral–torsional coupling in asymmetric‐plan buildings leads to correlated translations and rotations of the building plan, which generate uneven distributions of deformation demand among resisting planes. The deformation demand of a resisting plane depends on the relative magnitude of the plan translation and rotation and on the correlation between the two signals. Thus, small rotations highly correlated with building translation may lead to significantly different deformations of the resisting planes at the building edges. Consequently, the use of supplemental dampers is intended not only to reduce the magnitude of the plan translation and rotation, but also the correlation between these motions. For the sake of simplicity, linear viscous dampers are used in this investigation, which properly located in plan lead to a minimum response of the geometric center, thus achieving the same mean‐square value of the displacements at the building edges. Mathematically, this condition may be understood as creating zero correlation between the translations and rotation at the geometric center of the plan, which represents an uncoupling in the mean‐square sense. Results show that the optimal damper location depends on the static eccentricity and frequency ratio of the bare structure, the total amount of supplemental damping considered, and the frequency content of the excitation. Through a final 6‐story model example, the torsional balance concept is demonstrated to work on multistory buildings subjected to bidirectional ground motions. Copyright © 2009 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.     

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.     

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.     

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.     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Simplified analysis and supplemental damping system design

Investigated is the accuracy in estimating the response of asymmetric one‐storey systems with non‐linear viscoelastic (VE) dampers by analysing the corresponding linear viscous system wherein all non‐linear VE dampers are replaced by their energy‐equivalent linear viscous dampers. The response of the corresponding linear viscous system is determined by response history analysis (RHA) and by response spectrum analysis (RSA) extended for non‐classically damped systems. The flexible and stiff edge deformations and plan rotation of the corresponding linear viscous system determined by the extended RSA procedure is shown to be sufficiently accurate for design applications with errors generally between 10 and 20%. Although similar accuracy is also shown for the ‘pseudo‐velocity’ of non‐linear VE dampers, the peak force of the non‐linear VE damper cannot be estimated directly from the peak damper force of the corresponding linear viscous system. A simple correction for damper force is proposed and shown to be accurate (with errors not exceeding 15%). For practical applications, an iterative linear analysis procedure is developed for determining the amplitude‐ and frequency‐dependent supplemental damping properties of the corresponding linear viscous system and for estimating the response of asymmetric one‐storey systems with non‐linear VE dampers from the earthquake design (or response) spectrum. Finally, a procedure is developed for designing non‐linear supplemental damping systems that satisfy given design criteria for a given design spectrum. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

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.     

Estimation of inelastic seismic deformations in asymmetric multistorey RC buildings

Four real buildings with three to six stories, strong irregularities in plan and little engineered earthquake resistance are subjected to inelastic response‐history analyses under 56 bidirectional EC8‐spectra‐compatible motions. The average chord rotation demand at each member end over the 56 response‐history analyses is compared to the chord rotation from elastic static analysis with inverted triangular lateral forces or modal response spectrum analysis. The storey‐average inelastic‐to‐elastic‐chord‐rotation‐ratio was found fairly constant in all stories, except when static elastic analysis is applied to buildings with large higher mode effects. Except for such buildings, static elastic analysis gives more uniform ratios of inelastic chord rotations to elastic ones within and among stories than modal response spectrum analysis, but generally lower than 1.0. With increasing EPA the building‐average inelastic‐to‐elastic‐chord‐rotation‐ratio decreases but scatter in the results increases. Static elastic analysis tends to overestimate the inelastic torsional effects at the flexible or central part of the torsionally flexible buildings and underestimate them at their stiff side. Modal response spectrum analysis tends to overestimate the inelastic torsional effects at the stiff or central part of the torsionally stiff buildings and underestimate them at the flexible side. Overall, for multistorey RC buildings that typically have fundamental periods in the velocity‐sensitive part of the spectrum, elastic modal response spectrum analysis with 5% damping gives on average unbiased and fairly accurate estimates of member inelastic chord rotations. If higher modes are not significant, elastic static analysis in general overestimates inelastic chord rotations of such buildings, even when torsional effects are present. Copyright © 2007 John Wiley & Sons, Ltd.     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Earthquake response

Investigated are earthquake responses of one‐way symmetric‐plan, one‐storey systems with non‐linear fluid viscous dampers (FVDs) attached in series to a linear brace (i.e. Chevron or inverted V‐shape braces).Thus, the non‐linear damper is viscous when the brace is considered rigid or viscoelastic (VE) when the brace is flexible. The energy dissipation capacity of a non‐linear FVD is characterized by an amplitude‐dependent damping ratio for an energy‐equivalent linear FVD, which is determined assuming the damper undergoes harmonic motion. Although this formulation is shown to be advantageous for single‐degree‐of‐freedom (SDF) systems, it is difficult to extend its application to multi‐degree‐of‐freedom (MDF) systems for two reasons: (1) the assumption that dampers undergo harmonic motion in parameterizing the non‐linear damper is not valid for its earthquake‐induced motion of an MDF system; and (2) ensuring simultaneous convergence of all unknown amplitudes of dampers is difficult in an iterative solution of the non‐linear system. To date, these limitations have precluded the parametric study of the dynamics of MDF systems with non‐linear viscous or VE dampers. However, they are overcome in this investigation using concepts of modal analysis because the system is weakly non‐linear due to supplemental damping. It is found that structural response is only weakly affected by damper non‐linearity and is increased by a small amount due to bracing flexibility. Thus, the effectiveness of supplemental damping in reducing structural responses and its dependence on the planwise distribution of non‐linear VE dampers were found to be similar to that of linear FVDs documented elsewhere. As expected, non‐linear viscous and VE dampers achieve essentially the same reduction in response but with much smaller damper force compared to linear dampers. Finally, the findings in this investigation indicate that the earthquake response of the asymmetric systems with non‐linear viscous or VE dampers can be estimated with sufficient accuracy for design applications by analysing the same asymmetric systems with all non‐linear dampers replaced by energy‐equivalent linear viscous dampers. Copyright © 2003 John Wiley & Sons, Ltd.     

The role of overstrength on the seismic performance of asymmetric-plan structures

Uneven distribution of seismic demand in asymmetric-plan structures is a critical concern in earthquake-resistant design. Contemporary seismic design strategies that are based on linear elastic response, single load reduction factor, and uniform ductility demand throughout an asymmetric system generally lead to unsatisfactory performance in terms of realized ductilities and nonuniform damage distribution due to strong torsional coupling associated with asymmetric-plan systems. In many cases, actual nonlinear behavior of the structure displays significant deviation from what is estimated by a linear elastic, force-based seismic design approach. This study investigates the prediction of seismic demand distribution among structural members of a single-story, torsionally stiff asymmetric-plan system. The focus is on the effect of inherent unbalanced overstrength, resulting from current force-based design practices, on the seismic response of code-designed single-story asymmetric structures. The results obtained are utilized to compile unsymmetrical response spectra and uniform ductility spectra, which are proposed as assessment and preliminary design tools for estimating the seismic performance of multistory asymmetric structures. A simple design strategy is further suggested for improving the inelastic torsional performance of asymmetric systems. Providing additional strength to stiff edge members over their nominal design strength demands leads to a more balanced ductility distribution. Finally, seismic responses of several asymmetric case study structures designed with the aid of the proposed strategy are assessed for validating their improved performance.     

Bi‐directional coupled tuned mass dampers for the seismic response control of two‐way asymmetric‐plan buildings

This paper proposes bi‐directional coupled tuned mass dampers (BiCTMDs) for the seismic response control of two‐way asymmetric‐plan buildings subjected to bi‐directional ground motions. The proposed BiCTMD was developed from the three‐degree‐of‐freedom modal system, which represents the vibration mode of a two‐way asymmetric‐plan building. The performance of the proposed BiCTMD for the seismic response control of elastic two‐way asymmetric‐plan buildings was verified by investigating the reductions of the amplitudes of the associated frequency response functions. In addition, the investigation showed that the proposed BiCTMD is effective in reducing the seismic damage of inelastic asymmetric‐plan buildings. Therefore, the BiCTMD is an effective approach for the seismic response control of both elastic and inelastic two‐way asymmetric‐plan buildings. Copyright © 2010 John Wiley & Sons, Ltd.     

Multiple‐tuned liquid column dampers for torsional vibration control of structures: theoretical investigation

This paper presents a theoretical investigation on the performance of multiple‐tuned liquid column dampers (MTLCD) for reducing torsional vibration of structures in comparison with single‐tuned liquid column dampers (STLCD). The analytical model is first developed for torsional vibration of a structure with an MTLCD under either harmonic excitation or white noise excitation. The experimental results are then used to verify the analytical model for coupled MTLCD‐structure systems under harmonic excitation. The performance of an MTLCD and its beneficial parameters for achieving the maximum torsional response reduction to white noise excitation are finally investigated through an extensive parametric study in terms of the distance from the centre line of the MTLCD to the rotational axis of the structure, the ratio of the horizontal length to the total length of liquid column, frequency bandwidth, head‐loss coefficient, the number of TLCD units in an MTLCD, frequency‐turning ratio and the spectral level of excitation moment. The results show that there is an optimal head‐loss coefficient and an optimal frequency bandwidth for an MTLCD to achieve the maximum torsional response reduction. It is also demonstrated that the sensitivity of an optimized MTLCD to the frequency‐tuning ratio is less than that of an optimized STLCD, and it can be further improved by increasing the bandwidth but at the cost of less torsional vibration reduction. Copyright © 2002 John Wiley & Sons, Ltd.     

Accidental torsion due to overturning in nominally symmetric structures isolated with the FPS

Overturning of a structure causes variations in the normal loads of the isolators supporting that structure. For frictional isolators, such variation leads to changes in the frictional forces developed and, hence, in the strength distribution in plan. For frictional pendulum system (FPS) isolators, it also causes changes in the pendular action, i.e. in the stiffness distribution of the isolation interface. Therefore, although the structure is nominally symmetric it develops lateral–torsional coupling when it is subjected to two horizontal components of ground motion. This coupling is denoted herein as accidental torsion due to overturning, and its effect in the earthquake response of nominally symmetric structures is evaluated. Several parameters are identified to control this coupling, but the most important are the slenderness of the structure and the aspect ratio of the building plan. Results are presented in terms of the torsional amplification of the deformations of the isolation base and the interstorey deformations of the superstructure. The FPS system is modelled accurately by including true large deformations and the potential uplift and impact of the isolators. Impulsive as well as subduction‐type ground motions are considered in the analysis, but results show small differences between them. An upper bound for the mean‐plus‐one standard deviation values of the torsional amplifications for the base due to this accidental torsion is 5%. This implies that for design purposes of the isolation system such increase in deformations could probably be neglected. However, the same amplification for the interstorey deformations may be as large as 50%, depending on the torsional stiffness and slenderness of the superstructure, and should be considered in design. In general, such amplification of deformations decreases for torsionally stiffer structures and smaller height‐to‐base aspect ratios. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic performance and damage evaluation of a waffle‐flat plate structure with hysteretic dampers through shake‐table tests

Reinforced concrete waffle‐flat plate (WFP) structures present 2 important drawbacks for use as a main seismic resisting system: low lateral stiffness and limited ductility. Yet the former can serve a positive purpose when, in parallel, the flexible WFP structure is combined with a stiff system lending high‐energy dissipation capacity, to form a “flexible‐stiff mixed structure.” This paper experimentally investigates the seismic performance of WFP structures (flexible system) equipped with hysteretic dampers (stiff system) through shake‐table tests conducted on a 2/5‐scale test specimen. The WFP structure was designed only for gravitational loads. The lateral strength and stiffness provided by the dampers at each story were, respectively, about 3 and 7 times greater than those of the bare WFP structure. The mixed system was subjected to a sequence of seismic simulations representing frequent to very rare ground motions. Under the seismic simulations associated with earthquakes having return periods ranging from 93 to 1894 years, the WFP structure performed in the level of “immediate occupancy,” with maximum interstory drifts up to about 1%. The dampers dissipated most (75%) of the energy input by the earthquake.     

Earthquake response of asymmetric building with MR damper

Plan asymmetric buildings are very susceptible to earthquake induced damage due to lateral torsional coupling, and the corners of these systems suffer heavy damage during earthquakes. Therefore, it is important to investigate the seismic behavior of an asymmetric plan building with MR dampers. In this study, the effectiveness of MR damper-based control systems has been investigated for seismic hazard mitigation of a plan asymmetric building. Furthermore, the infl uence of the building parameters and damper command voltage on the control performance is examined through parametric study. The building parameters chosen are eccentricity ratio and frequency ratio. The results show that the MR damper-based control systems are effective for plan asymmetric systems.     

三种阻尼减振结构抗震性能的对比分析

对设置两种新型摩擦阻尼器(T形芯板摩擦阻尼器和拟粘滞摩擦阻尼器)和粘滞阻尼器的单自由度结构及多层实际工程结构进行了时程分析研究。结果表明，一方面三种阻尼器都能有效地控制结构的反应，另一方面T形芯板摩擦阻尼器的位移控制效果略好于拟粘滞摩擦阻尼器，但是后者的加速度控制效果好于前者。     

Optimal design of viscoelastic dampers using eigenvalue assignment

In this study a procedure for determining the optimum size and location of viscoelastic dampers is proposed using the eigenvalue assignment technique. Natural frequencies and modal damping ratios, required to realize a given target response, are determined first by the convex model. Then the desired dynamic structural properties are realized by optimally distributing the damping and stiffness coefficients of viscoelastic dampers using non‐linear programming based on the gradient of eigenvalues. This optimization method provides information on the optimal location as well as the magnitude of the damper parameters. The proposed procedure is applied to the retrofit of a 10‐story shear frame, and to a three‐dimensional structure with an asymmetric plan. The analysis results confirm that the responses of model structures retrofitted by the proposed method correspond well with the given target response. Copyright © 2003 John Wiley & Sons, Ltd.     

Amplification system for concentrated and distributed energy dissipation devices

Recent analytic, experimental, and practical studies are developing energy dissipation devices combined with amplifying mechanisms (AM) to enhance structural behavior. This research presents the theoretical and experimental development of the eccentric lever‐arm system (ELAS), a new system generically called amplified added damping (AAD), which is a combination of an AM with one or more dampers capable of supporting large deformations. The proposed AM device is a variant of the well‐known lever‐arm system. This work is divided in four parts: (1) kinematics of the ELAS and definition of an equivalent AAD; (2) parametric analysis of a linear single‐story structure with ELAS; (3) numerical analysis of a multi‐degree‐of‐freedom structure with frictional damping with and without AM; and (4) pseudo‐dynamic tests of a full scale asymmetric one story steel structure with and without frictional AAD. Parametric analyses demonstrate that using high‐amplification ratios and low supplemental damping could be a good practice. On the other hand, similar to systems without AMs, dissipation efficiency increases conformably with the stiffness of the secondary structure. As expected, it was observed that deformation was highly concentrated in the flexible edge of the asymmetric test model without damper. Conversely, the structure with frictional AAD clearly showed uniform plane deformation. The implemented AM, which has a large amplifying ratio of α≈11, performed with close accordance with numerical simulations and a high mechanical efficiency (≈95%) using a frictional damper with a very low force capacity. Copyright © 2016 John Wiley & Sons, Ltd.