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。     

框架结构地震输入能量影响因素研究

通过对框架结构弹塑性地震输入能量反应的分析,采用基于等效单自由度体系的振型分解能量求解方法,输入多条真实地震波,综合分析了地震动三要素对地震总输入能量的影响规律,通过实例计算表明:框架结构体系的输入能量与地震波的峰值平方成正比,地震波的卓越周期越大、持时越长,总输入能量也越大.     

基于等效单自由度体系的结构地震输入能量的研究

通过对多自由度体系结构在地震作用下的能量分析,考虑地震动因素和结构自身特性,提出一种框架结构地震总输入能量的简化求解方法.实例计算结果表明:基于等效单自由度体系来估计多自由度体系的地震总输入能,是一种计算简便且较为准确的方法.     

基于小波方法的多自由度体系地震动输入能量研究

对多自由度体系应用小波分解的地震激励,将地震动总输入能量表示为不同频段地震动输入能量的叠加.与单自由度体系相比,多自由度体系应用小波分解会产生较大的误差,这并不影响研究小波分解后各频段对单一固有振型输入能量的贡献.这样可以从频率的角度分析多自由度体系的地震动输入能量.     

基于能量被动耗能结构抗震设计方法的研究

将结构前两阶振型各自等效为单自由度,采用模态pushover分析确定各等效单自由度的屈服强度系数和延性系数,然后由反应谱计算各阶振型耗散能量需求,利用各振型能量分布曲线,求得各层耗散能量需求,叠加得到各层地震总能量需求,据此确定耗能装置的类型及设计参数.运用该方法对9层钢框架进行了设计,并通过非线性动力分析进行了验证,结果表明该方法精确度符合实际工程需求.     

剪切型多自由度体系瞬时输入能量的分布

通过对剪切型多自由度体系的地震能量反应分析,提出了描述多自由度体系整体脉冲能量反应的参数,瞬时输入能量等效平均速度,并在此基础上建立了瞬时输入能量分布系数的概念,提出了估计瞬时输入能量分布的方法。     

抗震结构的滞回耗能谱

本文在分析不同类型地面运动引起抗震结构不同类型破坏的基础上，指出结构滞回耗能总量是累积破坏的重要参数，以1735条实际地震记录作为输入计算了不同动力参数单自由度体系弹性及弹塑性总输入能量及滞回耗能量，得出计算弹塑性体系滞回耗能谱的简化公式。     

钢筋混凝土框架抗震结构地震能量分布及耗散研究

基于能量平衡原理,对多层钢筋混凝土框架结构的地震输入能量的分布及耗散规律进行了研究。选用8条天然地震波和2条人工波,运用Perform-3D软件,对多层钢筋混凝土框架结构模型在7度罕遇地震作用下的弹塑性能量进行数值仿真计算。计算了钢混框架结构在不同地震波下的地震总输入能量、滞回耗能、阻尼耗能以及滞回耗能占总耗能的比例时程,分析了地震能量在各分量中的分布及分配规律;分析了阻尼比和延性比对地震输入能量的影响,确定了滞回耗能随阻尼比和延性比的变化规律;研究了钢筋混凝土框架结构梁柱构造和竖向侧移刚度变化对地震输入能及其分量的影响,确定了多层钢筋混凝土框架结构滞回耗能沿竖向的分布规律及沿横向在框架构件中的分配,研究了框架结构存在薄弱层情况下的滞回耗能的分布规律。揭示了多自由度钢筋混凝土框架结构地震输入能量及其分布规律,可为基于能量平衡原理的抗震设计理论在工程实际中的运用提供有益的参考。     

地震动持续时间和结构弹塑性耗能的关系

本文将不同持续时间的八条天然地震记录及大量人工地震波,分别输入不同周期的11个个单自由度体系及三座遭受实际震害的多自由度结构中,进行直接动力积分计算,从计算出的累积变形能,能量反应指数和延性反应的结果中,分析它们与地震动持续时间的关系。其结果表明,我们所定义的能量指数对持续时间最为敏感。     

基于小波方法的无限自由度体系地震动输入能量研究

将小波分解的地震激励应用于无限自由度体系,得到地震动对结构的相对输入能量可以表示为各个频段地震动输入能量的叠加。相比单自由度与多自由度而言,无限自由度体系应用小波分解会产生较大的误差,但这并不影响研究小波分解后各个频段对单一固有振型输入能量贡献的大小,我们可以分析不同地震波的不同频段对不同振型的反应,这将比较有意义。     

Non-linear seismic behavior of structures with limited hysteretic energy dissipation capacity

This paper investigates the non-linear seismic behavior of structures such as slender unreinforced masonry shear walls or precast post-tensioned reinforced concrete elements, which have little hysteretic energy dissipation capacity. Even if this type of seismic response may be associated with significant deformation capacity, it is usually not considered as an efficient mechanism to withstand strong earthquakes. The objective of the investigations is to propose values of strength reduction factors for seismic analysis of such structures. The first part of the study is focused on non-linear single-degree-of-freedom (SDOF) systems. A parametric study is performed by computing the displacement ductility demand of non-linear SDOF systems for a set of 164 recorded ground motions selected from the European Strong Motion Database. The parameters investigated are the natural frequency, the strength reduction factor, the post-yield stiffness ratio, the hysteretic energy dissipation capacity and the hysteretic behavior model (four different hysteretic models: bilinear self-centring, with limited or without energy dissipation capacity, modified Takeda and Elastoplastic). Results confirm that the natural frequency has little influence on the displacement ductility demand if it is below a frequency limit and vice versa. The frequency limit is found to be around 2 Hz for all hysteretic models. Moreover, they show that the other parameters, especially the hysteretic behavior model, have little influence on the displacement ductility demand. New relationships between the displacement ductility demand and the strength reduction factor for structures having little hysteretic energy dissipation capacity are proposed. These relationships are an improvement of the equal displacement rule for the considered hysteretic models. In the second part of the investigation, the parametric study is extended to multi-degree-of-freedom (MDOF) systems. The investigation shows that the results obtained for SDOF systems are also valid for MDOF systems. However, the SDOF system overestimates the displacement ductility demand in comparison to the corresponding MDOF system by approximately 15%.     

A nonlinear SDOF model for the simplified evaluation of the displacement demand of low-rise URM buildings

The determination of displacement demands for masonry buildings subjected to seismic action is a key issue in the performance-based assessment and design of such structures. A technique for the definition of single-degree-of-freedom (SDOF) nonlinear systems that approximates the global behaviour of multi-degree-of-freedom (MDOF) 3D structural models has been developed in order to provide useful information on the dependency of displacement demand on different seismic intensity measures. The definition of SDOF system properties is based on the dynamic equivalence of the elastic properties (vibration period and viscous damping) and on the comparability with nonlinear hysteretic behaviour obtained by cyclic pushover analysis on MDOF models. The MDOF systems are based on a nonlinear macroelement model that is able to reproduce the in-plane shear and flexural cyclic behaviour of pier and spandrel elements. For the complete MDOF models an equivalent frame modelling technique was used. The equivalent SDOF system was modelled using a suitable nonlinear spring comprised of two macroelements in parallel. This allows for a simple calibration of the hysteretic response of the SDOF by suitably proportioning the contributions of flexure-dominated and shear-dominated responses. The comparison of results in terms of maximum displacements obtained for the SDOF and MDOF systems demonstrates the feasibility and reliability of the proposed approach. The comparisons between MDOF and equivalent SDOF systems, carried out for several building prototypes, were based on the results of time-history analyses performed with a large database of natural records covering a wide range of magnitude, distance and local soil conditions. The use of unscaled natural accelerograms allowed the displacement demand to be expressed as a function of different ground motion parameters allowing for the study of their relative influence on the displacement demand for masonry structures.     

Simplified analysis of frame structures with viscoelastic dampers considering the effect of soil-structure interaction

In this study, simplified numerical models are developed to analyze the soil-structure interaction (SSI) effect on frame structures equipped with viscoelastic dampers (VEDs) based on pile group foundation. First, a single degree-of-freedom (SDOF) oscillator is successfully utilized to replace the SDOF energy dissipated structure considering the SSI effect. The equivalent period and damping ratio of the system are obtained through analogical analysis using the frequency transfer function with adoption of the modal strain energy (MSE) technique. A parametric analysis is carried out to study the SSI effect on the performance of VEDs. Then the equilibrium equations of the multi degree-of-freedom (MDOF) structure with VEDs considering SSI effect are established in the frequency domain. Based on the assumption that the superstructure of the coupled system possesses the classical normal mode, the MDOF superstructure is decoupled to a set of individual SDOF systems resting on a rigid foundation with adoption of the MSE technique through formula derivation. Numerical results demonstrate that the proposed methods have the advantage of reducing computational cost, however, retaining the satisfactory accuracy. The numerical method proposed herein can provide a fast evaluation of the efficiency of VEDs considering the SSI effect.     

Performance spectra based method for the seismic design of structures equipped with passive supplemental damping systems

A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd.     

ENERGY INPUT AND DISSIPATION BEHAVIOUR OF STRUCTURES WITH HYSTERETIC DAMPERS

This paper presents qualitative investigations on the energy behaviour of structures into which hysteretic dampers are incorporated. Emphasis was given to the ratio of the structural stiffness after the yielding of hysteretic dampers to the initial elastic stiffness, with a premise that this ratio, termed α in this study, tends to be large for structures with hysteretic dampers. Structures concerned were represented by discrete spring–mass systems having bilinear restoring force behaviour, in which the second stiffness relative to the initial stiffness is α. It was found that with the increase of α the total input energy tends to increase, but the increase is confined to a narrow range of natural periods. Both the total input energy and hysteretic energy were found to become less sensitive to the yield strength with the increase of α. A simple formula was also proposed to estimate the maximum deformation given the knowledge of the hysteretic energy. Analysis of MDOF systems revealed that, even when α is large, the total input energy and hysteretic energy for MDOF systems are approximately the same as those of the equivalent SDOF system, and the hysteretic energy can be distributed uniformly over the stories if α is large.     

延性需求谱在基于性能的抗震设计中的应用

基于性能的抗震设计理论涉及如何简便而合理地确定结构在指定强度地震下的弹塑性位移需求。本文给出了利用延性需求谱求解结构位移需求的一般步骤:借助模态Pushover分析将多自由度体系分解为几个非线性单自由度体系,以考虑各阶振型的影响;利用延性需求谱计算对应模态的等效单自由度体系的延性及位移需求,并以一定方式组合转化为多自由度体系位移需求。最后,通过算例分析表明:利用延性需求谱求解结构位移需求是一种具有一定精度可为工程接受的简便方法,在基于性能的抗震设计中具有较好的应用前景。     

基于位移的RC框架结构与附加消能减震装置一体化设计

消能减震结构中主体结构和附加消能减震装置通常是单独设计的,由于主体结构和附加消能减震装置之间的耦合特性,为实现期望的性能目标需要进行迭代计算。本文提出一种基于位移的主体结构与附加消能减震装置一体化设计方法,首先,基于所选地震动记录和预期性能目标,得出结构阻尼比需求曲面;其次,推导了阻尼器-支撑部件参数计算公式,在已知主体结构基本信息及预期性能目标时,根据阻尼比需求曲面及所提出公式即可获得所需附加消能减震装置的支撑刚度及粘滞系数;再次,引入无量纲成本指数,以成本指数最小为目标函数,在可实现目标性能的附加消能减震装置参数中识别最优设计参数;最后,基于所提出的设计方法,分别以等效SDOF体系、MDOF体系及SAP2000设计的6层RC框架结构为例,对所提出的设计方法的有效性进行了验证,结果表明:经一体化设计的结构体系均可实现性能目标。     

框架结构基于能量地震反应分析及设计方法的理论研究

通过对多自由度体系结构在地震作用下的能量分析,考虑地震动因素和结构自身特性,提出基于能量概念的二阶段设计方法,取得了较有意义的研究成果,对于基于能量的抗震设计方法走向实用化,提供一条思路。     

Estimation of hysteretic energy demand using concepts of modal pushover analysis

Hysteretic energy dissipation in a structure during an earthquake is the key factor, besides maximum displacement, related to the amount of damage in it. This energy demand can be accurately computed only through a nonlinear time‐history analysis of the structure subjected to a specific earthquake ground acceleration. However, for multi‐story structures, which are usually modeled as multi‐degree of freedom (MDOF) systems, this analysis becomes computation intensive and time consuming and is not suitable for adopting in seismic design guidelines. An alternative method of estimating hysteretic energy demand on MDOF systems is presented here. The proposed method uses multiple ‘generalized’ or ‘equivalent’ single degree of freedom (ESDOF) systems to estimate hysteretic energy demand on an MDOF system within the context of a ‘modal pushover analysis’. This is a modified version of a previous procedure using a single ESDOF system. Efficiency of the proposed procedure is tested by comparing energy demands based on this method with results from nonlinear dynamic analyses of MDOF systems, as well as estimates based on the previous method, for several ground motion scenarios. Three steel moment frame structures, of 3‐, 9‐, and 20‐story configurations, are selected for this comparison. Bias statistics that show the effectiveness of the proposed method are presented. In addition to being less demanding on the computation time and complexity, the proposed method is also suitable for adopting in design guidelines, as it can use response spectra for hysteretic energy demand estimation. Copyright © 2008 John Wiley & Sons, Ltd.