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.     

A new methodology for energy-based seismic design of steel moment frames

A procedure is proposed whereby input and hysteretic energy spectra developed for single-degree-of-freedom (SDOF) systems are applied to multi-degree-of-freedom (MDOF) steel moment resisting frames. The proposed procedure is verified using four frames, viz., frame with three-, five-, seven- and nine-stories, each of which is subjected to the fault-normal and fault-parallel components of three actual earthquakes. A very good estimate for the three- and five-story frames, and a reasonably acceptable estimate for the seven-, and nine-story frames, have been obtained. A method for distributing the hysteretic energy over the frame height is also proposed. This distribution scheme allows for the determination of the energy demand component of a proposed energy-based seismic design (EBSD) procedure for each story. To address the capacity component of EBSD, a story-wise optimization design procedure is developed by utilizing the energy dissipating capacity from plastic hinge formation/rotation for these moment frames. The proposed EBSD procedure is demonstrated in the design of a three-story one-bay steel moment frame.     

基础非线性对桥墩地震反应的影响

在桩基础桥墩滞回特性的模型试验基础上,提出了用Clough模型模拟基础(地基)的恢复力特性。桥墩采用Takeda恢复力模型。用强震记录与人工合成地震动作为输入对铁路简支梁桥进行了非线性地震反应分析,讨论了不同地震动输入及不同地震强度时基础非线性对桥梁地震反应的影响。研究结果表明,考虑基础的非线性一般会使墩顶位移增大,而墩底的曲率明显减小,且随着地震动强度的增加,基础的非线性影响更加明显。     

Modified capacity design rule for columns in tall steel MRFs with linear viscous dampers within the framework of Eurocode 8

Seismic design codes enforce a set of capacity design rules for steel moment-resisting frames (MRFs) to promote a ductile sway plastic mechanism that involves plastic hinges in beams and column bases. Previous research showed that these capacity design rules may not be effective for tall steel MRFs with viscous dampers under strong earthquakes due to high axial forces in columns. To address this issue, steel MRFs with linear viscous dampers of different stories are designed according to Eurocode 8 along with using a slightly modified conservative capacity design rule. According to this rule, the axial force for the capacity design of a column in the force path of viscous dampers is calculated as the envelope of the axial force from the peak drift state, and, the axial force from the peak velocity state times a scale factor. This envelope axial force value along with the bending moment and shear force from the peak drift state are used to carry out the capacity design of the column by using the formulae of Eurocode 8, i.e. in the same way with a column of a steel MRF without dampers. Incremental dynamic analyses for 44 earthquake ground motions show that the modified conservative capacity design rule results in steel MRFs with viscous dampers that have plastic mechanisms similar to those of steel MRFs without dampers. Moreover, the proposed capacity design rule becomes stricter for buildings with more than 10 stories to address that available analysis methods for structures with dampers underestimate the peak damper forces in the lower stories of yielding tall steel MRFs. More work is needed to extend the findings of this work to the case of steel MRFs with nonlinear viscous dampers.     

Numerical evaluation of seismic response of soft-story RC frames retrofitted with passive devices

This study presents a nonlinear modelling technique for reinforced concrete (RC) frames retrofitted with metallic yielding devices to predict the seismic response using a computer software OpenSees. The numerical model considers the axial–flexure interaction, shear force–displacement response and the bond-slip characteristics of the frame members. The predicted hysteretic response has been compared with the results of slow-cyclic testing. The validated numerical model is then used to predict the seismic response of a five-story RC frame with soft-story. Nonlinear cyclic pushover and dynamic analyses are conducted to investigate the effectiveness of the proposed retrofitting scheme in enhancing the lateral strength and energy dissipation potential and in controlling the premature failure of the study frame. Analysis results showed significant improvement in the seismic response of RC frames with soft-story using the proposed retrofitting technique.     

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.     

隔震减震主次结构体系非线性随机地震反应分析

为研究隔震、减震装置非线性恢复力特性对2自由度主次结构体系均方根位移反应的影响规律,以隔震、减震装置微分型恢复力模式的滞回参数为变量,地震地面运动模拟成高斯白噪声过程,利用等效线性化方法得到主体结构和二次结构均方根位移反应的表达式.分析表明,主体结构隔震装置非线性恢复力特征对主、次结构的均方根位移反应的影响占主导地位;隔震、减震装置的恢复力特征产生适度非线性有利于减小主、次结构的均方根位移反应.     

Low cyclic fatigue and hysteretic behavior of U‐shaped steel dampers for seismically isolated buildings under dynamic cyclic loadings

Energy dissipation devices are necessary for base‐isolated buildings to control the deformation in the isolation system and to dissipate the earthquake‐induced energy. U‐shaped steel dampers (also known as U‐dampers) dissipate energy through plastic deformation of specially designed U‐shaped steel elements. This type of device can be installed at several locations in the isolation system. U‐dampers have been widely used in Japan for different types of isolated structures, such as hospitals, plants and residential buildings, since the 1995 Kobe Earthquake. Previous research has used static tests to estimate the performance of U‐dampers. However, the ultimate plastic deformation capacities and hysteretic behaviors of full‐scale U‐dampers under dynamic excitations still remain unclear. In addition, it is unclear whether the initial temperature has an effect on the hysteretic behavior and plastic deformation capacity of U‐dampers. In this paper, two series of dynamic loading tests of U‐dampers were conducted to evaluate the issues described earlier. The major findings of the study are (i) the loading speed has little effect on the plastic deformation capacity of U‐dampers; (ii) method to evaluate the ultimate plastic deformation capacities of U‐shaped steel dampers of different sizes is established using a Manson–Coffin relation‐based equation that is based on the peak‐to‐peak horizontal shear angle γ_t, which is defined as the lateral deformation amplitude (peak‐to‐peak amplitude) divided by the height of the dampers; (iii) the loading rate and the initial temperature have a minimal effect on the hysteretic behavior of the U‐dampers; and (iv) a bilinear model is proposed to simulate the force‐deformation relationships of the U‐dampers. Copyright © 2014 John Wiley & Sons, Ltd.     

带可替换腹板连接型耗能梁段的恢复力模型研究

带可替换耗能梁段的偏心支撑钢框架具有震后修复方便、经济等优点,但目前国内外学者对该类型的研究很少。为此,设计16组与偏心支撑钢框架采用螺栓连接的腹板连接型耗能梁段,并对16组试件进行数值模拟分析,讨论截面尺寸、耗能长度、加劲肋间距、加劲肋布置以及综合参数等变化参数对腹板连接型耗能梁段在低周往复荷载作用下的滞回性能、骨架曲线的影响,建立腹板连接型耗能梁段简化的恢复力模型。结果表明,影响腹板连接型耗能梁段耗能的主要参数是截面尺寸,建立的恢复力模型与模拟的骨架曲线对比吻合较好,可以为此类耗能梁段弹塑性分析作为参考。     

单自由度自复位体系设计能量谱研究

本文对具有旗帜型滞回模型的单自由度自复位体系提出了设计能量谱的构造方法,包括设计输入能量谱和设计滞回耗能比谱。首先按中国规范场地类别选取360条实际强震记录进行时程分析,对影响单自由度自复位体系输入能量谱和滞回耗能比谱的参数,包括地震波类型、滞回模型、阻尼比、延性系数等进行研究。在此基础上分别建议了设计输入能量谱和设计滞回耗能比谱及其曲线参数的确定方法,并与实际强震记录计算结果进行比较。结果表明结构滞回模型对能量谱影响明显;阻尼比和延性系数对输入能量谱的影响在整个周期范围内有显著差异,但均有明显的削峰作用。建议的两种设计能量谱综合考虑了结构参数、地震波参数和中国场地类别的影响,可以较好的拟合实际情况,并对弹塑性单自由度自复位体系在地震作用下的耗能需求做出较准确的估计。     

具有滞迟耗能装置的高层建筑结构的随机响应分析

本文提出了一个近似分析具有滞迟耗能装置的高层建筑的方法。结果被模拟为一个有滞迟非线性支座的悬壁梁。其控制方程由Ｒｉｔｚ法导出，用等效线性化方法分析。     

滞变—摩擦基底隔震支座的试验和模型

本提出了一种滞变－摩擦基底隔震支座。这种支座由钢棒和摩擦元件组成，钢棒容许摩擦元件水平滑动，同时又限制这种滑动；摩擦元件承受结构的竖向荷载，作完成了钢棒滞变恢复力特性的试验，并给出了钢棒的滞变恢复力模型的模型参数的计算公式，该模型与常用的折线模型有所不同，它仅用一个非线性微分方程来描述滞变恢复力，而不需要复杂的规则。     

公路简支梁桥的地震能量响应分析

利用有限元软件SAP2000建立了某公路简支梁桥的有限元模型,以7条典型强震记录为输入,研究了公路简支梁桥的地震能量响应及其分配规律。结果表明:①地基柔性效应对公路简支梁桥的地震能量响应及其分配规律的影响较小;②当场地土质变软时,地震总输入能、结构阻尼耗能和结构阻尼耗能比均呈递增趋势,而结构滞回耗能和结构滞回耗能比则不断减小,即地基土体作为桥梁动力系统的一部分,增大了系统阻尼,并分担了部分非弹性变形;③随着PGA增大,输入结构的地震能量也增加,导致塑性铰的非弹性变形增加,即结构滞回耗能和结构阻尼耗能增大。     

半刚性连接钢框架抗震性能的模型试验研究

通过两榀1／2比例的一跨两层半刚性连接钢框架模型的低周反复荷载试验,研究了框架模型的破坏机制、、出饺顺序、滞回特性、耗能能力等抗震性能。从而得出结论：具有腹板双角钢的顶底角钢连接的钢框架由于节点连接刚度较小,因此框架在侧向力作用下变形较大,但同时此连接也改善了梁柱的内力分布,提高了框架的耗能能力,增加了结构抗震性能。     

Using centrifuge tests data to identify the dynamic soil properties: Application to Fontainebleau sand

Knowledge of the dynamic properties of the soil is of great importance as the dynamic shear modulus and damping ratio are necessary input data in finite element modeling programs. This paper presents a post-processing strategy to identify the shear modulus and damping ratio vs. shear strain curves using the experimental results of a dynamic centrifuge program. Application is presented for the Fontainebleau sand. The proposed methodology is fast, robust and able to capture the nonlinear hysteretic behavior of the material. Based on the results, specific parameters for the Fontainebleau sand are identified for the empirical equation of shear modulus and damping ratio proposed by Ishibashi and Zhang [1]. It is found that confining pressure has an important influence on both shear modulus evolution and damping ratio.     

Inelastic response analysis of reinforced concrete structures using modified force analogy method

A modified force analogy method (MFAM) is developed to simulate the nonlinear inelastic response of reinforced concrete (RC) structures. Beam–column elements with three different plastic mechanisms are utilized to simulate inelastic response caused by moment and shear force. A multi‐linear hysteretic model is implemented to simulate the nonlinear inelastic response of RC member. The P‐Δ effect of the structure is also addressed in MFAM. Static and dynamic inelastic response of structure, damage condition and failure type for structural element, structural limit state and collapse time can also be simulated using MFAM. Compared with the general algorithm, the MFAM provides less computational time especially in the case of large structural system. It is also easier to be written as computer program. Three test data groups, which include cyclic loading test data of a non‐ductile RC bridge column, a two‐storey RC frame, and dynamic collapse test data of a non‐ductile RC portal frame, are selected to confirm the effectiveness of applying MFAM to simulate the inelastic behaviour of structures. Copyright © 2007 John Wiley & Sons, Ltd.     

Influence of connection typology on seismic response of MR‐Frames with and without ‘set‐backs’

The work presented is aimed at the investigation of the influence of beam‐to‐column connections on the seismic response of MR‐Frames, with and without ‘set‐backs’, designed according to the Theory of Plastic Mechanism Control. The investigated connection typologies are four partial strength connections whose structural details have been designed to obtain the same flexural resistance. The first three joints are designed by means of hierarchy criteria based on the component approach and are characterized by different location of the weakest joint component, leading to different values of joint rotational stiffness and plastic rotation supply and affecting the shape of the hysteresis loops governing the dissipative capacity. The last typology is a beam‐to‐column connection equipped with friction pads devoted to the dissipation of the earthquake input energy, thus preventing the connection damage. An appropriate modelling is needed to accurately represent both strength and deformation characteristics, especially with reference to partial‐strength connections where the dissipation of the earthquake input energy occurs. To this aim, beam‐to‐column joints are modelled by means of rotational inelastic springs located at the ends of the beams whose moment‐rotation curve is characterized by a cyclic behaviour which accounts for stiffness and strength degradation and pinching phenomena. The parameters characterizing the cyclic hysteretic behaviour have been calibrated on the base of experimental results aiming to the best fitting. Successively, the prediction of the structural response of MR‐Frames, both regular frames and frames with set‐backs, equipped with such connections has been carried out by means of both push‐over and Incremental Dynamic Analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

Mechanical formulations for bilinear and trilinear hysteretic models used in base isolators

The best known model for numerically simulating the hysteretic behavior of various structural components is the bilinear hysteretic system. There are two possible mechanical formulations that correspond to the same bilinear model from a mathematical viewpoint. The first one consists of a linear elastic spring connected in series with a parallel system comprising a plastic slider and a linear elastic spring, while the second one comprises a linear elastic spring connected in parallel with an elastic-perfectly plastic system. However, the bilinear hysteretic model is unable to describe either softening or hardening effects in these components. In order to account for this, the bilinear model is extended to a trilinear one. Thus, two trilinear hysteretic models are developed and numerically tested, and the analysis shows that both exhibit three plastic phases. More specifically, the first system exhibits one elastic phase, while the second one exhibits two elastic phases according to the level of strain amplitude. Next, the change of slope between the plastic phases in unloading does not occur at the same displacement level in the two models. Furthermore, the dissipated energy per cycle in the first trilinear model, as proven mathematically and explained physically, decreases in the case of hardening and increases in the case of softening, while in the second trilinear model the dissipated energy per cycle remains unchanged, as is the case with the bilinear model. Numerical examples are presented to quantify the aforementioned observations made in reference to the mechanical behavior of the two trilinear hysteretic models. Finally, a set of cyclic shear tests over a wide range of strain amplitudes on a high damping rubber bearing is used in the parameter identification of the two different systems, namely (a) trilinear hysteretic models of the first type connected in parallel, and (b) trilinear hysteretic models of the second type also connected in parallel. The results show that the complex nonlinear shear behavior of high damping rubber bearings can be correctly simulated by a parallel system which consists of only one component, namely the trilinear hysteretic system of the first type. The second parallel system was not able to describe the enlargement of the dissipated hysteresis area for large strain amplitudes.     

Efficiency of base isolation systems in structural seismic protection and energetic assessment

This paper concerns the seismic response of structures isolated at the base by means of High Damping Rubber Bearings (HDRB). The analysis is performed by using a stochastic approach, and a Gaussian zero mean filtered non‐stationary stochastic process is used in order to model the seismic acceleration acting at the base of the structure. More precisely, the generalized Kanai–Tajimi model is adopted to describe the non‐stationary amplitude and frequency characteristics of the seismic motion. The hysteretic differential Bouc–Wen model (BWM) is adopted in order to take into account the non‐linear constitutive behaviour both of the base isolation device and of the structure. Moreover, the stochastic linearization method in the time domain is adopted to estimate the statistical moments of the non‐linear system response in the state space. The non‐linear differential equation of the response covariance matrix is then solved by using an iterative procedure which updates the coefficients of the equivalent linear system at each step and searches for the solution of the response covariance matrix equation. After the system response variance is estimated, a sensitivity analysis is carried out. The final aim of the research is to assess the real capacity of base isolation devices in order to protect the structures from seismic actions, by avoiding a non‐linear response, with associated large plastic displacements and, therefore, by limiting related damage phenomena in structural and non‐structural elements. In order to attain this objective the stochastic response of a non‐linear n‐dof shear‐type base‐isolated building is analysed; the constitutive law both of the structure and of the base devices is described, as previously reported, by adopting the BWM and by using appropriate parameters for this model, able to suitably characterize an ordinary building and the base isolators considered in the study. The protection level offered to the structure by the base isolators is then assessed by evaluating the reduction both of the displacement response and the hysteretic dissipated energy. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic performance and damage evaluation of a reinforced concrete frame with hysteretic dampers through shake‐table tests

Passive energy dissipation devices are increasingly implemented in frame structures to improve their performance under seismic loading. Most guidelines for designing this type of system retain the requirements applicable to frames without dampers, and this hinders taking full advantage of the benefits of implementing dampers. Further, assessing the extent of damage suffered by the frame and by the dampers for different levels of seismic hazard is of paramount importance in the framework of performance‐based design. This paper presents an experimental investigation whose objectives are to provide empirical data on the response of reinforced concrete (RC) frames equipped with hysteretic dampers (dynamic response and damage) and to evaluate the need for the frame to form a strong column‐weak beam mechanism and dissipate large amounts of plastic strain energy. To this end, shake‐table tests were conducted on a 2/5‐scale RC frame with hysteretic dampers. The frame was designed only for gravitational loads. The dampers provided lateral strength and stiffness, respectively, three and 12 times greater than those of the frame. The test structure was subjected to a sequence of seismic simulations that represented different levels of seismic hazard. The RC frame showed a performance level of ‘immediate occupancy’, with maximum rotation demands below 20% of the ultimate capacity. The dampers dissipated most of the energy input by the earthquake. It is shown that combining hysteretic dampers with flexible reinforced concrete frames leads to structures with improved seismic performance and that requirements of conventional RC frames (without dampers) can be relieved. Copyright © 2014 John Wiley & Sons, Ltd.