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.     

Seismic behaviour of girder bridges for horizontally propagating waves

The results obtained from a parametric study on the influence of horizontally propagating waves for the earthquake behaviour of continuous girder bridges are presented. The investigation is performed for floating-supported bridges excited by an earthquake acting in their vertical planes. The shallow foundations are assumed to be supported on the surface of either a visco-elastic halfspace or a visco-elastic layer resting on an elastic halfspace. Steady-state response for harmonic excitation and transient response for an artificial time history are investigated. Approximate equations describing the influence of horizontally propagating waves are presented and criteria are derived indicating when an increase of the internal forces and of the relative motion between the girder and the abutments can be expected.     

A simple boundary element formulation and its application to wavefield excited soil-structure interaction

A simple boundary element formulation which is based directly on the point load solutions for an elastic full-space is presented. It is integrated in a finite element program to calculate dynamic soil-structure interaction problems. The combined boundary and finite element method is applied to structures which are excited by horizontally propagating waves in the soil. For three different types of flexible structure-elastic beams, low and high (square) shear walls-and the corresponding rigid structures the vibration modes and the soil-structure transfer functions have been investigated. The flexible foundations display the same wave pattern as the exciting free-field of the soil, but the amplitudes are reduced with increasing frequency, depending on the stiffness or wave resistance of the structure. Rigid structures show, in part, quite different behaviour, giving free-field reductions caused by kinematic and inertial soil-structure interaction.     

Response of a nuclear power plant on aseismic bearings to horizontally propagating waves

The nuclear island of Koeberg with a large basemat, a non-linear base isolation effective in the horizontal direction only, founded on rock, is analysed for inclined body waves and for a combination of surface and body waves associated with prescribed horizontal and vertical components of the control motion. When compared to vertical incidence, an additional rocking component arises, generated by the horizontally propagating vertical component. As the aseismic bearings do not isolate against this rocking component, the corresponding horizontal response bears comparison with that of a conventional structure. The ratio of the response for horizontally propagating waves and that for vertically incident waves is thus considerably larger for the base-isolated structure than for a conventional one. However, the actual design incorporating other loading cases is affected much less.     

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.     

Soil–structure interaction in yielding systems

The effects of soil–structure interaction in yielding systems are evaluated, including both kinematic and inertial interaction. The concepts developed previously for interacting elastic systems are extended to include the non‐linear behavior of the structure. A simple soil–structure system representative of code‐ designed buildings is investigated. The replacement oscillator approach used in practice to account for the elastic interaction effects is adjusted to consider the inelastic interaction effects. This is done by means of a non‐linear replacement oscillator defined by an effective ductility together with the known effective period and damping of the system for the elastic condition. To demonstrate the efficiency of this simplified approach, extensive numerical evaluations are conducted for elastoplastic structures with embedded foundation in a soil layer over elastic bedrock, excited by vertically propagating shear waves. Both strength and displacement demands are computed with and without regard to the effect of foundation flexibility, taking as control motion the great 1985 Michoacan earthquake recorded at a site representative of the soft zone in Mexico City. Results are properly interpreted to show the relative effects of interaction for elastic and yielding systems. Finally, it is demonstrated how to implement this information in the context of code design of buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Dynamics of elastic–plastic shear frames with secondary structures: shake table and numerical studies

Results from experimental and numerical studies of earthquake‐excited small‐scale primary–secondary structures are presented. The primary structure considered is a plane three‐storey shear frame with a fundamental frequency of 5.5 Hz. The columns of the first floor are built with soft aluminium and they are stressed beyond its linear range of behaviour. After each test the elastic–plastic columns are replaced by a new set of undeformed virgin aluminium bars. The elastic–plastic shear frame is tested with and without an attached secondary structure. The secondary structure is modelled as an elastic SDOF oscillator, and its natural frequency is tuned to the fundamental frequency of the shear frame. Alternatively, the oscillator is mounted on the horizontal beam of the second and third floor. The base excitation of the structural model is characterized by a broad band random process with constant spectral density in a frequency range between 3 and 30 Hz. In the numerical study, the digital recorded acceleration of the base excites the mechanical model of the investigated structures. Numerical outcomes assuming fictitious unlimited elastic material behaviour of the shear frame are set in contrast to results from experiments and computational simulations where the measured non‐linear force displacement relation of the elastic–plastic floor is approximated by a piecewise linear curve. The effect of elastic–plastic materials on the dynamic interaction between primary and secondary structure is shown and the difference to unlimited elastic material behaviour is worked out in detail. Copyright © 2001 John Wiley & Sons, Ltd.     

Estimating kinematic interaction of raft foundations from earthquake records and its effects on structural response

A practical method for estimating kinematic interaction from earthquake records is presented. The kinematic interaction is characterized by a two-parameter model and these parameters can be estimated by using a frequency-domain systems identification method. The simple model can be used to model both wave passage effects and the effects of incoherent wave fields. Numerical simulation tests show that kinematic interaction parameters can be estimated to their best accuracy by using building base responses and the free-field excitation and can also be estimated by using building responses, base responses and the free-field excitation. The method was applied to two buildings with raft foundations and it was found that kinematic interaction was significant during earthquakes. Published theoretical models (wave passage effect) for vertically incident SH waves can be used to estimate the transfer functions up to 4–5 Hz and the models for horizontally propagating waves under-predict the estimated transfer functions by a significant amount at frequencies beyond about 1–2 Hz. Theoretical models for a massless rigid foundation under the excitation of an incoherent wave field predict the general trend of the estimated transfer function reasonably well over a large frequency range. The results of numerical examples show that the recorded response spectral attenuation of basement records at high frequencies with respect to the free-field is mainly caused by kinematic interaction, while the changes in storey shear and overturning moment in a structure due to soil flexibility are mainly the results of inertial interaction.     

Active control of the seismic response of structures by combined use of base isolation and absorbing boundaries

The relative advantages of several control strategies to reduce the seismic response of multi-storey structures are studied. The strategies involve the separate or combined use of passive base isolation mechanisms and active control forces. The base isolation mechanism is modelled as an equivalent linear soft storey with high damping. The active control forces are selected so that an absorbing boundary is obtained at the top of the structure and non-reflecting or reflecting boundaries are obtained at the base of the building. It is found that the best results are obtained when a passive base isolation system is combined with an active absorbing boundary placed at the top of the building. However, the incremental gains resulting from adding a base isolation system to a structure already controlled by a roof-top active absorbing boundary are significant only for relatively soft base isolation systems. Also, the incremental gains appear to decrease as the number of storeys of the structure increases.     

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.     

Controlling seismic response of eccentric structures by friction dampers

Previous studies have demonstrated the good performance of friction dampers in symmetric frame structures subjected to earthquake excitation. This paper examines their effectiveness in asymmetric structures where lateral-torsional coupling characterizes the behaviour. A parametric study is first performed employing an idealized single-storey structure; this is followed by the example of a three-dimensional 5-storey prototype structure equipped with friction dampers. The parametric results show that it is necessary to tune the friction damped braces with respect to both the stiffness of the braces and the slip load of the devices. For properly tuned structures, maximum response for all magnitudes of eccentricity between the centres of stiffness and mass is reduced to levels equal to or less than that of the corresponding symmetric structure. Compared to this prediction, the prototype structure with friction damped bracing exhibits the desired improvement in performance; namely, the devices slip at all storey levels while the frames remain elastic.     

Effects of source and cavity depths on wave fields in homogeneous half spaces

In homogeneous half spaces excited by small buried, spherically symmetric P-wave sources, Rayleigh waves (R-waves) could be generated. The effects of the source depth on the induced wave pattern and propagation behavior of R-waves are analyzed using the thin layer method. When a cavity is present in a homogeneous half space, R-waves could be formed in the scattered wave field. It is found that the energy of R-waves in the incident (direct) surface wave-field is related to the ratio of the source depth to the wavelength of R-waves; R-waves have relatively strong energy when the ratio is less than 1; the buried source induced R-waves approximately travel at the velocity of the planar R-waves in the range of the offset beyond about one wavelength; the energy of R-waves in the back-scattered surface wave-field depends on the ratio of the depth of cavity to the wavelength of R-waves; and for the case of the cavity presented at depths less than one wavelength, R-waves can be clearly observed in the back-scattered wave field. The results are helpful for selecting the source depth and the frequency component in seismic surveys and interpreting both the incident wave and the scattered wave patterns.     

Midbroken reinforced concrete shear frames due to earthquakes. A hysteretic model to quantify damage at the storey level

A nonlinear hysteretic model for the response and local damage analyses of reinforced concrete shear frames subject to earthquake excitation is proposed, and, the model is applied to analyse midbroken reinforced concrete (RC) structures due to earthquake loads. Each storey of the shear frame is represented by a Clough and Johnston hysteretic oscillator with degrading elastic fraction of the restoring force. The local damage is numerically quantified in the domain [0,1] using the maximum softening damage indicators which are defined in closed form based on the variation of the eigenfrequency of the local oscillators due to the local stiffness and strength deterioration. The proposed method of response and damage analyses is illustrated using a sample 5 storey shear frame with a weak third storey in stiffness and/or strength subject to sinusoidal and simulated earthquake excitations for which the horizontal component of the ground motion is modeled as a stationary Gaussian stochastic process with Kanai-Tajimi spectrum, multiplied by an envelope function.     

Low‐frequency normal wave propagation in a periodically layered medium with weak contrast in elastic properties

We derive the phase velocity dispersion and the scattering for wave vertically propagating in a periodically weak‐contrast horizontally layered medium with arbitrary number of layers in a period. Phase velocity dispersion is defined as the frequency dependence of vertical travel time, and scattering is defined as a reflection coefficient at the interface between the multilayered system and the corresponding Backus medium. Low‐frequency approximation is used to define a dynamic effective medium with frequency‐dependent phase velocity. The results are compared with those obtained earlier for a gradient medium. We show that the low‐frequency weak‐contrast approximation is valid for models with realistic contrasts in elastic properties.     

Estimation of seismic drift demands for frame structures

A process is outlined and evaluated for the estimation of seismic roof and storey drift demands for frame structures from the spectral displacement demand at the first mode period of the structure. The spectral displacement demand is related to the roof drift demand for the multi‐degree‐of‐freedom (MDOF) structure using three modification factors, accounting for MDOF effects, inelasticity effects, and P‐delta effects. Median values and measures of dispersion for the factors are obtained from elastic and inelastic time history analyses of nine steel moment resisting frame structures subjected to sets of ground motions representative of different hazard levels. The roof drift demand is related to the storey drift demands, with the results being strongly dependent on the number of stories and the ground motion characteristics. The relationships proposed in this paper should prove useful in the conceptual design phase, in estimating deformation demands for performance assessment, and in improving basic understanding of seismic behaviour. Copyright © 2000 John Wiley & Sons, Ltd.     

近断层地震作用下基础隔震层组合限位振动台实验研究

近断层脉冲型地震作用下,基础隔震结构隔震层会产生过大变形,导致隔震支座侧倾失稳,隔震体系破坏。设计制作了3层基础隔震钢框架实验模型和11种U型钢板I型铅棒组合限位器,进行了U型钢板静力加载实验和近断层脉冲型地震作用下基础隔震层软碰撞限位振动台模型实验。实验表明：①静力加载时,U型钢板具有很好的弹性性能;②动力作用下,组合限位器残余变形较小,仍具有良好限位复位能力;③近断层地震作用下,基础隔震层软限位效果良好,同时控制上部结构层间变形在允许范围内。     

The effect of coulomb damping on multidegree of freedom elastic structures

This paper is based on the premise that the damping mechanism of a multidegree of freedom structure can be represented by viscous and coulomb dampers. A closed form solution for the structure subjected to a sinusoidal forcing function is presented. The solution is used as the basis of a method for determining relative amounts of viscous and coulomb damping from vibration tests. The method was applied to the results of a series of vibration tests on a five storey reinforced concrete structure and approximate values of viscous and coulomb damping obtained. A comparison of the effect of various combined damping values on the earthquake response of the structure was made. It was concluded that the use of the equivalent viscous damping concept to approximate the combined effect of viscous and coulomb damping results in a low estimate of the elastic response of the structure.     

An experimental study of a midbroken 2-bay, 6-storey reinforced concrete frame subject to earthquakes

A 2-bay, 6-storey model test reinforced concrete frame (scale l:5) subjected to sequential earthquakes of increasing magnitude is considered in this paper. The frame was designed with a weak storey, in which the columns are weakened by using thinner and weaker reinforcement bars. The aim of the work is to study the global response to a damaging strong motion earthquake event of such buildings. Special emphasis is put on examining to what extent damage in the weak storey can be identified from global response measurements during an earthquake where the structure survives, and what level of excitation is necessary in order to identify the weak storey. Furthermore, emphasis is put on examining how and where damage develops in the structure and especially how the weak storey accumulates damage. Besides the damage in each storey the structure is identified by a static load at the top storey while measuring the horizontal displacement of the stories and also visual inspection is performed. From the investigations it is found that the reason for failure in the weak storey is that the absolute value of the stiffness deteriorates to a critical value where large plastic deformations occur and the storey is not capable of transferring the shear forces from the storeys above so failure is unavoidable.     

复合隔震结构模型振动台试验研究

作者对一个二层复合隔震结构钢框架模型进行了振动台试验,该模型采用夹层橡胶支座与摩擦滑移支座并联组合作为隔震层,既能提供足够的弹性恢复力,又具有良好的结构耗能能力。试验测得结构各项动力响应,并将软件计算数据与试验数据进行了比较,结果表明复合隔震结构的加速度反应小,楼层层间位移也较小,上部结构基本为平动,结构耗能能力显著,而且软件可以很好地模拟结构的地震反应规律。     

Influence of the soil–structure interaction on the fundamental period of buildings

This paper includes an investigation of the influence of the soil–structure interaction (SSI) on the fundamental period of buildings. The behaviour of both the soil and the structure is assumed to be elastic. The soil‐foundation system is modelled using translational and rotational discrete springs. Analysis is first conducted for one‐storey buildings. It shows that the influence of the SSI on the fundamental frequency of building depends on the soil–structure relative rigidity K_ss. Analysis is then extended for multi‐storey buildings. It allows the generalization of the soil–structure relative rigidity K_s to such complex structures. Charts are proposed for taking into account the influence of the SSI in the calculation of the fundamental frequency of a wide range of buildings. Copyright © 2007 John Wiley & Sons, Ltd.