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.     

Estimation of inelastic deformation demands in multistorey RC frame buildings

Estimation of peak inelastic deformation demands is a key component of any displacement-based procedure for earthquake-resistant design of new structures or for seismic evaluation of existing structures. On the basis of the results of over a thousand non-linear dynamic analyses, rules are developed for the estimation of mean and upper-characteristic peak inelastic interstorey drifts and member chord rotations in multistorey RC frame buildings, either bare or infilled in all storeys but the first. For bare frame structures, mean inelastic deformation demands can be estimated from a linear, equivalent static, or preferably multimodal response spectrum analysis with 5 per cent damping and with the RC members considered with their secant stiffness at yielding. 95 per cent characteristic values can be estimated as multiples of the mean deformations. For open-first-storey buildings, the linear analysis can be equivalent static, with the infills modelled as rigid bidiagonal struts and all RC members considered with their secant stiffness to yielding. Copyright © 1999 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.     

An answer to an important controversy and the need for caution when using simple models to predict inelastic earthquake response of buildings with torsion

This paper presents evidence that the extension of conclusions based on the widely used simplified, one story, eccentric systems of the shear‐beam type, to actual, nonsymmetric buildings and consequent assessments of the pertinent code provisions, can be quite erroneous, unless special care is taken to match the basic properties of the simplified models to those of the real buildings. The evidence comes from comparisons of results obtained using three variants of simplified models, with results from the inelastic dynamic response of three‐ and five‐story eccentric buildings computed with detailed MDOF systems, where the members are idealized with the well‐known plastic hinge model. In addition, a convincing answer is provided on a pertinent hanging controversy: For frame‐type buildings, designed in accordance with the dynamic provisions of modern codes (such as EC8 or IBC2000), which allow reduced shears at the stiff edge due to torsion, the frames at the flexible sides are the critical elements in terms of ductility demands. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

平面不规则结构非弹性扭转地震反应研究进展

不规则建筑结构在侧向地震荷载作用下由于质量中心和刚度中心的不重合导致平扭耦联反应的发生,使得结构构件的变形需求分布在结构平面内并不一致,从而产生附加的强度和变形需求。尽管不规则建筑结构在地震作用下的扭转问题一直受到研究学者的关注和研究,并取得了很多显著的成果,但仍然存在着一些争议,有待于继续深入研究。本文从结构的分析模型、影响参数及地震动输入等方面回顾总结了平面不规则建筑结构在地震作用下非弹性扭转的研究进展,结合当前的研究工作指出今后研究的发展方向。     

Inelastic response of one-storey asymmetric-plan systems subjected to bi-directional earthquake motions

The inelastic response of one-storey systems with one axis of asymmetry subjected to bi-directional base motion is studied in this paper. The effect of the system parameters on response is also evaluated: uncoupled torsional-to-lateral frequency ratio, stiffness eccentricity, and yield strength of the lateral resisting elements. The ensemble of earthquake records used consists of 15 two-component strong ground motions. The response to uni-directional excitation is considered first to examine the influence of the system parameters and to serve as a basis to examine the results of the bi-directional case, which are presented in terms of average spectra for bi- over uni-directional lateral-deformation ratios. It is shown that the effect of inelastic behaviour is, on the average, noteworthy for stiff structures, in turn, the same structures are the most affected by the action of bi-directional ground motions. The effect of the relative intensity of the two orthogonal ground motion components is also studied. Copyright © 1999 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.     

空间钢筋混凝土框架结构的非弹性地震反应

对两个缩比为十五分之一的三层、双跨、两开间的钢筋混凝土框架模型进行了振动台试验,一个模型模拟质量中心与刚度中心不一致的偏心结构,另一个模型模拟承受双向地面运动的结构。研究了结构的空间非弹性地震反应。计算结果表明,理论分析与实测结果有较好的吻合性。     

Inelastic spectra to predict period elongation of structures under earthquake loading

Period lengthening, exhibited by structures when subjected to strong ground motions, constitutes an implicit proxy of structural inelasticity and associated damage. However, the reliable prediction of the inelastic period is tedious and a multi‐parametric task, which is related to both epistemic and aleatory uncertainty. Along these lines, the objective of this paper is to investigate and quantify the elongated fundamental period of reinforced concrete structures using inelastic response spectra defined on the basis of the period shift ratio (T_in/T_el). Nonlinear oscillators of varying yield strength (expressed by the force reduction factor, R_y), post‐yield stiffness (a_y) and hysteretic laws are examined for a large number of strong motions. Constant‐strength, inelastic spectra in terms of T_in/T_el are calculated to assess the extent of period elongation for various levels of structural inelasticity. Moreover, the influence that structural characteristics (R_y, a_y and degrading level) and strong‐motion parameters (epicentral distance, frequency content and duration) exert on period lengthening are studied. Determined by regression analyses of the data obtained, simplified equations are proposed for period lengthening as a function of R_y and T_el. These equations may be used in the framework of the earthquake record selection and scaling. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic behaviour of asymmetric buildings with supplemental damping

This paper investigates the response of asymmetric‐plan buildings with supplemental viscous damping to harmonic ground motion using modal analysis techniques. It is shown that most modal parameters, except dynamic amplification factors (DAFs), are affected very little by the plan‐wise distribution of supplemental damping in the practical range of system parameters. Plan‐wise distribution of supplemental damping significantly influences the DAFs, which, in turn, influence the modal deformations. These trends are directly related to the apparent modal damping ratios; the first modal damping ratio increases while the second decreases as CSD moves from right to left of the system plan, and their values increase with larger plan‐wise spread of the supplemental damping. The largest reduction in the flexible edge deformation occurs when damping in the first mode is maximized by distributing the supplemental damping such that the damping eccentricity takes on the largest value with algebraic sign opposite to the structural eccentricity. Copyright © 2000 John Wiley & Sons, Ltd.     

Simulation of the response of base-isolated buildings under earthquake excitations considering soil flexibility

The accurate analysis of the seismic response of isolated structures requires incorporation of the flexibility of supporting soil.However,it is often customary to idealize the soil as rigid during the analysis of such structures.In this paper,seismic response time history analyses of base-isolated buildings modelled as linear single degree-of-freedom(SDOF) and multi degree-of-freedom(MDOF) systems with linear and nonlinear base models considering and ignoring the flexibility of supporting soil are conducted.The flexibility of supporting soil is modelled through a lumped parameter model consisting of swaying and rocking spring-dashpots.In the analysis,a large number of parametric studies for different earthquake excitations with three different peak ground acceleration(PGA) levels,different natural periods of the building models,and different shear wave velocities in the soil are considered.For the isolation system,laminated rubber bearings(LRBs) as well as high damping rubber bearings(HDRBs) are used.Responses of the isolated buildings with and without SSI are compared under different ground motions leading to the following conclusions:(1) soil flexibility may considerably influence the stiff superstructure response and may only slightly influence the response of the flexible structures;(2) the use of HDRBs for the isolation system induces higher structural peak responses with SSI compared to the system with LRBs;(3) although the peak response is affected by the incorporation of soil flexibility,it appears insensitive to the variation of shear wave velocity in the soil;(4) the response amplifications of the SDOF system become closer to unit with the increase in the natural period of the building,indicating an inverse relationship between SSI effects and natural periods for all the considered ground motions,base isolations and shear wave velocities;(5) the incorporation of SSI increases the number of significant cycles of large amplitude accelerations for all the stories,especially for earthquakes with low and moderate PGA levels;and(6) buildings with a linear LRB base-isolation system exhibit larger differences in displacement and acceleration amplifications,especially at the level of the lower stories.     

Seismic code analysis of multi-storey asymmetric buildings

Static torsional provisions in most seismic codes require that the lateral force at each floor level be applied at some distance from the reference centre at that floor. However, codes do not specify how to determine the locations of these centres. As a result, several different definitions of the reference centres are being used to implement the code analysis. This investigation examined how the results using various reference centres differ and which of these centres would lead to results that are in agreement with those of dynamic analysis. For this purpose three different buildings ranging form torsionally stiff to torsionally flexible were analysed. It was shown that for the class of buildings studied in this investigation that although the locations of the reference centres were quite different, the results were very similar and nearly independent of the reference centre. Comparison of results calculated from static code equivalent lateral force procedures and results from dynamic response spectrum analyses showed that the static code procedures led to design forces very close (flexible wall) or slightly conservative (stiff wall) when compared to the dynamic analysis for the torsionally stiff building. However, the static code procedures significantly underestimated the design forces of the stiff walls and significantly overestimated the design forces of the flexible walls for the torsionally flexible buildings. © 1998 John Wiley & Sons, Ltd.     

Dynamic responses of two buildings connected by viscoelastic dampers under bidirectional earthquake excitations

In this study,dynamic responses of two buildings connected by viscoelastic dampers under bidirectional excitations are extensively investigated.The two buildings are a 10-story building and a 16-story building,with the shorter building on the left.Viscoelastic dampers are installed at all fl oors of the shorter building.Equations of motion are formulated using a fractional derivative model to represent the viscoelastic dampers.Three cases are considered with mass eccentricities at 0,10% and-10% with respect to the dimensions of the buildings.The responses of the buildings are numerically predicted at different damper properties.The simulation results indicated that the maximum horizontal responses of the buildings without eccentricities are signifi cantly mitigated.However,torsional effects are adversely increased.For asymmetric buildings,the effectiveness of the connecting dampers is affected by building eccentricities.As a result,mass eccentricities must be taken into account in damper selection.When compared with vibrations induced by unidirectional excitations,bidirectional excitations can increase the responses of coupled asymmetric buildings.In addition,installing dampers only at the top fl oor of the shorter building may cause a sudden change in lateral stiffness of the taller building.Consequently,the story shear envelopes of the taller building are changed.     

Inelastic response of RC frame buildings with seismic isolation

A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (F_y/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.     

Alternative method to locate centre of rigidity in asymmetric buildings

Response of asymmetric buildup under earthquake excitation often involves lateral vibration coupled with torsional vibration. Floor slab is, in general, assumed as rigid along the in‐plane direction. Building code provisions to account for the torsional effect in static force procedure are based on centre of rigidity or shear centre of the building. A convenient procedure is developed here to locate the centre of rigidity or shear centre, which can be implemented, using any standard building analysis software. The procedure is applicable for orthogonal as well as non‐orthogonal building systems and accounts for all possible definitions of static eccentricity to compute the design response. An irregular building is analysed to illustrate the proposed methodology. Significant variation in member force resultants is observed due to different definitions of static eccentricity. Finally, a mathematical proof is presented to substantiate the applicability of the proposed procedure to a non‐orthogonal building. Copyright © 2006 John Wiley & Sons, Ltd.     

Parametric investigation of the stability of classical columns under harmonic and earthquake excitations

The seismic response of free‐standing classical columns is analysed numerically through implementation of the distinct element method. Typical sections of two ancient temples are modelled and studied parametrically, in order to identify the main factors affecting the stability and to improve our understanding of the earthquake behaviour of such structures. The models were first subjected to harmonic base motions. The analysis showed that, for frequencies usually encountered in earthquake motions, intact multi‐drum free‐standing columns can withstand large amplitude harmonic excitations without collapse. The dynamic resistance decreases rapidly as the period of the harmonic excitation increases. Imperfections, such as initial tilt of the column or loss of contact area due to edge damage, also reduce the stability of the system significantly. The effects of such imperfections could be additive and the cumulative effect of many imperfections may render deteriorating abandoned monuments vulnerable to earthquakes. The response of more complete sections of the temple, such as two columns coupled with an architrave, did not deviate systematically from that of the single multi‐drum column or indeed of the equivalent single block. Therefore, a much simpler single block analysis can be used to size‐up the seismic threat to the monument. The model of the column of the Temple of Apollo at Bassae was also tested under recorded earthquake motions by scaling‐up the acceleration amplitude progressively until collapse of the column. It was found that the columns are particularly vulnerable to long‐period impulsive earthquake motions. A comparison of the instability thresholds associated with harmonic excitations and earthquake motions throws more light onto the dynamic response: it appears that around three cycles of monochromatic excitation at the predominant period of the expected earthquake motions lead to a gross prediction of the stability of a classical column during an earthquake. Copyright © 2000 John Wiley & Sons, Ltd.     

Effects of structural walls on the elastic–plastic earthquake responses of frame–wall buildings

Effects of structural walls on the elastic–plastic earthquake response of short- to medium-height reinforced concrete buildings were investigated. The analytical model consists of independent lumped mass systems representing walls and frames connected at each floor. The wall structure undergoes flexural as well as shear deformation and fails in shear at relatively small story drifts, the frames deforming only in shear. As a measure of structural damage, the ductility factor responses of frame structures were calculated for different combinations of base shear coefficients for the frames and walls. In buildings with relatively weak frames, the installation of structural walls did not improve the large plastic response of the frames up to the point where the walls were unfailed in shear and the ductility factors of the frame structure were suddenly reduced to a very small number. For relatively strong frames, however, the response displacements decreased gradually as the number of walls increased, whether or not the walls failed. Empirical formulas for the required base shear coefficients of the walls and frames which gave a target ductility factor response also were derived for two particular groups of accelerograms. These equations should be of practical use in designing frame-wall type buildings and in retrofitting damaged buildings. Copyright © 1999 John Wiley & Sons, Ltd.     

Use of collision shear walls to minimize seismic separation and to protect adjacent buildings from collapse due to earthquake‐induced pounding

The use of collision shear walls (bumper‐type), acting transversely to the side subject to pounding, as a measure to minimize damage of reinforced concrete buildings in contact, is investigated using 5‐story building models. The buildings were designed according to the Greek anti‐seismic and reinforced concrete design codes. Owing to story height differences potential pounding in case of an earthquake will occur between floor slabs, a case specifically chosen because this is when pounding can turn out to be catastrophic. The investigation is carried out using nonlinear dynamic analyses for a real earthquake motion and also a simplified solution for a triangular dynamic force of short duration, comparable to the forces caused by pounding. For such analyses, nonlinear, prismatic beam–column elements are used and the effects of pounding are expressed in terms of changes in rotational ductility factors of the building elements. The local effects of pounding on the collision shear walls are investigated using a detailed nonlinear finite element model of the shear walls and results are expressed in terms of induced stresses. It is found that pounding will cause instantaneous acceleration pulses in the colliding buildings and will somewhat increase ductility demands in the members of the top floor, but all within tolerable limits. At the same time the collision walls will suffer repairable local damage at the points of contact, but will effectively protect both buildings from collapse, which could occur if columns were in the place of the walls. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal placement of DVFC controllers on buildings subjected to earthquake loading

The dynamic responses of tall civil structures due to earthquakes are very important to the civil engineer. These dynamic responses can produce situations that can range from uncomfortable to unsafe for the building occupants. In recent years classical control theory has been used in civil engineering to reduce the dynamic responses of tall civil structures. Most optimal control algorithms for civil structures involve full state feedback control which requires good estimates of the velocity and displacements throughout the structure. However, there are several important advantages of output feedback control: it takes less computational effort and it has the robustness of passive systems. In this paper, optimal control algorithms are formulated for the optimization of feedback gains and controller placement for building structures. The fundamental basis for these algorithms is the calculation of the gradient of the performance function with respect to the gain matrix. The effectiveness of the algorithm is demonstrated for deterministic earthquake loads in the time domain. Copyright © 1999 John Wiley & Sons, Ltd.