Seismic Design of Symmetric Structures for Accidental Torsion

The paper presents an analytical estimation of the dynamic effects, caused by the shifting of the centre of mass with accidental eccentricity in symmetric structures. The approximate analytical solution proves, that even under small accidental eccentricities the symmetric structures exhibit “irregular behaviour” and the accidental torsional effects cannot be described properly by static application of torsional moments. The prescribed application rule by Eurocode 8 for multimodal analysis underestimates the accidental torsional effects up to 21% for 5% eccentricity for the structures considered in the paper. An expression for the correction of member responses is derived. It is proved by numerical simulations of the dynamic response of three-dimensional models of symmetric structures, that the proposed correction coefficient gives accurate results in cases of single-storey and multi-storey structures. It gives a convenient way for the design practice to estimate accurately the accidental torsional effects on planar and 3-D models of symmetric structures. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamic response of bilinear asymmetric structures

The inelastic behaviour of eccentric single-storey building structures subjected to sinusoidal ground excitation is examined. The Kryloff-Bogoliuboff method is employed to provide approximate solutions in the amplitude-frequency domain. Structural resisting elements are assumed to exhibit bilinear hysteretic behaviour and coupled response is investigated in terms of both system response as well as individual element ductility requirements. In addition to demonstrating the well-known softening property inherent in yielding systems, the importance of the principal parameters governing coupled response is evaluated in a consistent parametric fashion. Within the context of earthquake resistant building design, the results indicate the absence of amplified response when torsional and translational frequencies are close, in contrast to the much emphasized observation of internal resonance for linear elastic structures. Equally important, structural elements located on the stiff edge of eccentric buildings are found to be only marginally affected by the magnitude of the eccentricity, thus indicating that seismic building codes which reduce design requirements for these elements underestimate actual behaviour substantially.     

建筑物偏心结构对其抗震性能的影响

偏心对建筑物的抗震效果有很大的影响。在对三种常见建筑物框架结构在偏心扭矩作用下的受震反应进行数值模拟时,采用6层建筑物模型,通过三维非线性模拟偏心结构对建筑物抗震性能影响的分析,采用最大层间位移作为衡量标准,绘制易损曲线来进行结果分析。结果显示:若忽略意外扭矩的影响,可能会高估钢结构体系的抗震性能,而影响安全评估结果;如果采用全层5%质量偏心来考虑意外偏心扭矩的话,会低估钢结构建筑物的抗震性能。     

结构偏心对基础隔震结构地震反应的影响

本文对基础隔震偏心结构在不同场地上的地震动作用下的反应进行了深入研究，探讨了上部结构偏心、隔震层偏心、场地条件等因素对于基础隔震结构地震反应的影响，选取了能反映结构偏心特性的参数，以便将分析各因素对隔震结构地震反应的影响转化为分析参数的影响。通过大量的数值计算与分析，得到了一些对实际工程有意义的结论。     

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.     

使用偏心支撑减小不规则高层建筑的扭转振动效应

文章对比分析了一个不规则高层钢筋混凝土框-剪结构和在原结构基础上增设偏心支撑后的新结构的抗震性能,比较了它们的自振特性以及层间位移等地震作用效应。针对不规则高层建筑在地震作用下不可避免的扭转振动问题,提出在结构中适当地增设偏心支撑来减小结构的扭转振动效应及其它结构地震反应这种简单可行、经济适用的方法。     

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.     

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.     

Effective strength eccentricity concept for inelastic analysis of asymmetric structures

A large number of parameters affect the inelastic response of an eccentric system. The centre of resistance no longer remains constant due to continuous loading and unloading of various elements of the system in and out of the inelastic region. The objective of this study is to develop the concept of strength eccentricity for asymmetrical structures excited well into the inelastic region in the event of a severe earthquake. A single mass monosymmetric three-element system is selected. The torsional flexibility parameter is varied so as to obtain nine eccentric configurations covering the entire spectrum of such systems. These models were subjected to S00E component of the El Centro earthquake of 1940 which is considered to be a very severe earthquake. The concept of effective strength eccentricity is introduced which is defined as strength eccentricity at the point of intersection of ductility ratio curves of REE and FEE. It is proposed to provide additional strength in the elements of a torsionally unbalanced system independent of the design eccentricity. Empirical equations are proposed to account for design eccentricity and additional strength as well as distribution of the design strength. The proposed formulation is compared with the torsional provisions of UBC 1991, NBCC 1990 and NZC 1992. It is concluded that additional ductility demand on the REE and FEE designed based on the proposed formulation is almost nil as compared to that given by the three codes. The NZC and UBC require maximum ductility on the REE. The increase in overall strength of the system is least for the proposed formulation as compared to that given by the three codes. NBCC consistently requires the maximum total strength ratio.     

Inelastic seismic response of code-designed multistorey frame buildings with regular asymmetry

Based on an asymmetric multistorey frame building model, this paper investigates the influence of a building's higher vibration modes on its inelastic torsional response and evaluates the adequacy of the provisions of current seismic building codes and the modal analysis procedure in accounting for increased ductility demand in frames situated at or near the stiff edge of such buildings. It is concluded that the influence of higher vibration modes on the response of the upper-storey columns of stiff-edge frames increases significantly with the building's fundamental uncoupled lateral period and the magnitude of the stiffness eccentricity. The application of the equivalent static torsional provisions of certain building codes may lead to non-conservative estimates of the peak ductility demand, particularly for structures with large stiffness eccentricity. In these cases, the critical elements are vulnerable to excessive additional ductility demand and, hence, may be subject to significantly more severe structural damage than in corresponding symmetric buildings. It is found that regularly asymmetric buildings excited well into the inelastic range may not be conservatively designed using linear elastic modal analysis theory. Particular caution is required when applying this method to the design of stiff-edge frame elements in highly asymmetric structures.     

Seismic response of torsionally coupled base isolated structures

An analytical study of the seismic response of typical base isolated structures mounted on rubber bearings is presented. Isolated buildings are liable to have closely spaced lower modes of vibration with small eccentricity between centres of mass and rigidity. The isolated structure is modelled as a rigid deck with lumped masses supported on axially inextensible elastomeric rubber bearings. This simplified system has three degrees of freedom (dof), two translations and one rotation in the horizontal plane. The Green's functions for the displacement response of the 3 dof system are derived for both undamped and damped cases with small and large eccentricities. The small eccentricity case is taken from a specific isolated building, while the large eccentricity case arises from the 5 per cent accidental eccentricity which is required by various seismic codes. An interaction equation for normalized displacements is established for an idealized flat velocity spectrum or hyperbolic acceleration spectrum. An isolated building on rubber bearings would have its fundamental period fall into this range of a design spectrum. Numerical results for the specific building subjected to the El Centro earthquake of 1940 are presented. Both the time history and the response spectrum modal superposition analysis were performed. In the response spectrum analysis, the Complete Quadratic Combination (CQC) showed superiority over the Square Root of the Sum of Squares (SRSS) in estimating maximum responses. It is concluded that the effect of torsional coupling on the transient response of base isolated structures is insignificant, due to the combined effect of the time lag between the maximum translational and torsional responses and the influence of damping in the isolation system which for elastomeric bearings can be as high as 8 to 10 per cent.     

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。     

Seismic torsional provisions for dynamic eccentricity

A study is made of the dynamic torsional response of a single mass partially symmetric system to ground excitation. Using the response spectrum technique, the torsional response and dynamic eccentricity are determined as functions of the eccentricity of the system and its uncoupled frequency ratio. It is shown that the dynamic eccentricity can best be expressed as a bilinear function of eccentricity. For the critical condition which occurs when the uncoupled frequency ratio is unity, a comparison is made with the torsional provisions of five seismic codes (Canada, Mexico, New Zealand, ATC3 and Germany). It is shown that the first four codes underestimate the torsional moment, and also the edge displacement of the system, significantly when the eccentricity is small and the uncouped torsional and lateral frequencies are close.     

ON ECCENTRIC SEISMIC POUNDING OF SYMMETRIC BUILDINGS

Results of a parameter study on eccentric pounding of two symmetric single storey systems under seismic excitation are presented. Linear behaviour is assumed, and pounding effect is considered using the restitution coefficient approach. The effect of impact eccentricity is studied on two sets of symmetric models symmetrically and asymmetrically aligned with respect to each other for several gap widths, period dependent gaps and three values of the torsional-to-lateral frequency ratio. Two time histories are used for input. On the whole it was found that impact eccentricity amplifies the response relative to symmetric impact but the effect is not proportional to first impact eccentricity. Also, increasing gap width is likely to be effective when the separation is sufficiently wide practically to eliminate contact. Larger torsional rigidity tends to lower response amplification. SRSS code-type gaps appear to be adequate, or even excessive, when the design spectrum is compatible with the expected earthquake record at the site.     

Torsionally coupled dynamic performance analysis of asymmetric offshore platforms subjected to wave and earthquake loadings

The dynamic equations of motion of asymmetric offshore platforms under three different environmental conditions:seismic action,wave action and their combination are established in this paper. In establishing these motion equations,three typical eccentricity types including mass eccentricity,rigidity eccentricity and their combination were considered,as are eccentricities that occur un-idirectionally and bi-directionally. The effects of the eccentricity type,the dynamic characteristics and the environmental conditions on the torsional coupling response of platforms are investigated and compared. An effort has also been made to analyze the inffluence of accidental eccentricity on asymmetric platforms with different eccentricity in two horizontally orthogonal directions. The results are given in terms of non-dimensional parameters,accounting for the uncoupled torsional to lateral frequency ratio. Numerical results reveal that the eccentricity type has a great inffluence on the torsionally coupled response under different environmental conditions. Therefore,it is necessary to consider the combination of earthquake and wave action in the seismic response analysis of some offshore platforms.     

Improving the seismic torsional behavior of plan-asymmetric,single-storey,concrete moment resisting buildings with fluid viscous dampers

The optimal distribution of fluid viscous dampers(FVD)in controlling the seismic response of eccentric,single-storey,moment resisting concrete structures is investigated using the previously defined center of damping constant(CDC).For this purpose,a number of structural models with different one-way stiffness and strength eccentricities are considered.Extensive nonlinear time history analyses are carried out for various arrangements of FVDs.It is shown that the arrangement of FVDs for controlling the torsional behavior due to asymmetry in the concrete structures is very dependent on the intensity of the peak ground acceleration(PGA)and the extent of the structural stiffness and strength eccentricities.The results indicate that,in the linear range of structural behavior the stiffness eccentricity es which is the main parameter in determining the location of optimal CDC,is found to be less or smaller than the optimal damping constant eccentricity e*d,i.e.,|e*d| |es|.But,in the nonlinear range of structural behavior where the strength eccentricity er is the dominant factor in determining the location of optimal CDC,|e*d| |er|.It is also concluded that for the majority of the plan-asymmetric,concrete structures considered in this study with er ≠ 0,the optimal CDC approaches the center of mass as er decreases.     

Seismic behavior of asymmetric RC wall buildings: principles and new deformation‐based design method

The seismic design of multi‐story buildings asymmetric in plan yet regular in elevation and stiffened with ductile RC structural walls is addressed. A realistic modeling of the non‐linear ductile behavior of the RC walls is considered in combination with the characteristics of the dynamic torsional response of asymmetric buildings. Design criteria such as the determination of the system ductility, taking into account the location and ductility demand of the RC walls, the story‐drift demand at the softer (most displaced) edge of the building under the design earthquake, the allowable ductility (ultimate limit state) and the allowable story‐drift (performance goals) are discussed. The definition of an eccentricity of the earthquake‐equivalent lateral force is proposed and used to determine the effective displacement profile of the building yet not the strength distribution under the design earthquake. Furthermore, an appropriate procedure is proposed to calculate the fundamental frequency and the earthquake‐equivalent lateral force. A new deformation‐based seismic design method taking into account the characteristics of the dynamic torsional response, the ductility of the RC walls, the system ductility and the story‐drift at the softer (most displaced) edge of the building is presented and illustrated with an example of seismic design of a multi‐story asymmetric RC wall building. Copyright © 2005 John Wiley & Sons, Ltd.     

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。     

Nonlinear seismic analysis of unsymmetric-plan structures retrofitted by hysteretic damped braces

A displacement-based design procedure using hysteretic damped braces (HYDBs) is proposed for the seismic retrofitting of unsymmetric-plan structures. An expression of the viscous damping equivalent to the hysteretic energy dissipated by the damped braced frame is proposed under bidirectional seismic loads, where corrective factors are assumed as a function of design parameters of the HYDBs. To this end, the nonlinear dynamic analysis of an equivalent two degree of freedom system is firstly carried out on seven pairs of real ground motions whose displacement response spectra match, on average, the design spectrum proposed by the Italian seismic code for a high-risk seismic zone and a medium subsoil class. Then, the extended N2 method considered by the European seismic code, which combines the nonlinear static analysis along the in-plan principal directions of the structure with elastic modal analysis, is adopted to evaluate the higher mode torsional effects. The town hall of Spilinga (Italy), a reinforced concrete (r.c.) framed building with an L-shaped plan, is supposed to be retrofitted with HYDBs. Six structural solutions are compared considering two alternative in-plan distributions of the HYDBs, to eliminate (elastic) torsional effects, and three design values of the frame ductility combined with a constant design value of the damper ductility. To check the effectiveness and reliability of the DBD procedure, the nonlinear static analysis of the test structures is carried out, by evaluating the vulnerability index of r.c. frame members and the ductility demand of HYDBs for different in-plan directions of the seismic loads.     

Accidental eccentricity in symmetric buildings due to wave passage effects arising from near‐fault pulse‐like ground motions

This article investigates the characteristics of the accidental eccentricity in symmetric buildings due to torsional response arising from wave passage effects in the near‐fault region. The soil–foundation–structure system is modeled as a symmetric cylinder placed on a rigid circular foundation supported on an elastic halfspace and subjected to obliquely incident plane SH waves simulating the action of near‐fault pulse‐like ground motions. The translational response is computed assuming that the superstructure behaves as a shear beam under the action of translational and rocking base excitations, whereas the torsional response is calculated using the mathematical formulation proposed in a previous study. A broad range of properties of the soil–foundation–structure system and ground motion input are considered in the analysis, thus facilitating a detailed parametric investigation of the structural response. It is demonstrated that the normalized accidental eccentricity is most sensitive to the pulse period (T_P) of the near‐fault ground motions and to the uncoupled torsional‐to‐translational fundamental frequency ratio (Ω) of the structure. Furthermore, the normalized accidental eccentricities due to simplified pulse‐like and broadband ground motions in the near‐fault region are computed and compared against each other. The results show that the normalized accidental eccentricity due to the broadband ground motion is well approximated by the simplified pulse for longer period buildings, while it is underestimated for shorter period buildings. For symmetric buildings with values of Ω commonly used in design practice, the normalized accidental eccentricity due to wave passage effects is less than the typical code‐prescribed value of 5%, except for buildings with very large foundation radius. Copyright © 2017 John Wiley & Sons, Ltd.