An energy-based methodology for the assessment of seismic demand

A methodology for the assessment of the seismic energy demands imposed on structures is proposed. The research was carried out through two consecutive phases. Inelastic design input energy spectra for systems with a prescribed displacement ductility ratio were first developed. The study of the inelastic behavior of energy factors and the evaluation of the response modification in comparison with the elastic case were performed by introducing two new parameters, namely: (1) the Response Modification Factor of the earthquake input energy (R_E), representing the ratio of the elastic to inelastic input energy spectral values and (2) the ratio α of the area enclosed by the inelastic input energy spectrum in the range of periods between 0.05 and 4.0 s to the corresponding elastic value. The proposed design inelastic energy spectra, resulting from the study of a large set of strong motion records, were obtained as a function of ductility, soil type, source-to-site distance and magnitude.Subsequently, with reference to single degree of freedom systems, the spectra of the hysteretic to input energy ratio were evaluated, for different soil types and target ductility ratios. These spectra, defined to evaluate the hysteretic energy demand of structures, were described by a piecewise linear idealization that allows to distinguish three distinct regions as a function of the vibration period. In this manner, once the inelastic design input energy spectra were determined, the definition of the energy dissipated by means of inelastic deformations followed directly from the knowledge of hysteretic to input energy ratio.The design spectra of both input energy and hysteretic to input energy ratio were defined considering an elasto-plastic behavior. Nevertheless, other constitutive models were taken into account for comparison purposes.     

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%.     

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。     

配置自复位耗能跨低多层钢框架体系的能量系数

利用超弹性SMA螺栓梁柱节点的耗能能力和自复位特性,将其引入到耗能跨而构建"自复位耗能跨",基于既有的节点试验研究结果对结构体系的滞回性能进行了探讨。在此基础上,以具有旗形滞回特征的单自由度体系为工具,对配置自复位耗能跨低多层钢框架体系的能量系数进行推导。能量系数可以合理量化具有旗形滞回规则结构的峰值响应需求,能量系数越低,表明地震动下结构的峰值响应越低。为了阐明滞回参数对能量系数的影响,对具有不同滞回参数组合可代表低多层结构的等效SDOF体系进行了非线性动力分析,参数组合包括周期、屈服后刚度比、延性系数及能量比。同时对能量系数的离散性也进行了分析。结果表明:能量系数及能量系数的离散性受结构周期、屈服后刚度比及延性系数影响较大,受能量比的影响较小。     

Consistent inelastic design spectra: Hysteretic and input energy

This is the second of two companion papers on inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor. All the spectra are consistent (interrelated and based on the same assumptions). This paper deals with two quantities related to cumulative damage: hysteretic and input energy. The input data for the procedure are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum and the time integral of the square of the ground acceleration ∫a² dt. Simple, approximate expressions for two dimensionless parameters (the parameter γ and the hysteretic to input energy ratio E_HE_I) have been proposed. The parameter 7, which controls the reduction of the deformation capacity of structures due to low-cycle fatigue, depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour and the ground motion characteristics. The ratio E_H/E_I is influenced by damping, the ductility factor and the hysteretic behaviour. Very good approximations to the inelastic spectra for hysteretic and input energy can be derived from the elastic spectrum using the spectra for the reduction factor R, proposed in the companion paper, and the proposed values for γ and E_H/E_I     

Statistical analysis of the inelastic response of shear structures subjected to earthquakes

Inelastic deformations of structures subjected to strong earthquakes are commonly accepted by Aseismic Codes; some discrepancies exist in the different procedures proposed to design a structure for which the ductility demand is to be limited within acceptable values. To have a better insight into the seismic behaviour of multi-degree-of-freedom structures beyond the elastic range, the dynamic elasto-plastic response of a ten-storey shear system under two sets of artificial and recorded accelerograms is studied considering different stiffness-strength distributions and constitutive laws. Statistics of the results are presented, demonstrating the dependence of the overall and storey ductility values and of their ratio on the characteristics of the structure and excitation.     

地震动滞回能量谱衰减规律研究

本文选用美国西部California州15次较大地震中的266条强地震动记录,利用衰减关系建立了滞回能量谱,分析了场地条件、延性系数、震级及距离等参数对滞回能量谱的影响。研究发现,场地条件对滞回能量谱影响很大,随着场地变软,滞回能量谱变大,与A B类场地相比,C类场地的滞回能量谱平均要高出70％左右,D类场地则要高出170％左右。随着延性系数的增大,滞回能量谱有增大的趋势,尤其是当延性系数由2变到4或6时更为明显,但当延性系数增加到一定程度时,滞回能量谱的差别不大,延性系数为4和6时的滞回能量谱差别不大,甚至在周期较大时,延性系数为6的滞回能量谱反而小于延性系数为4时的滞回能量谱。另外,研究结果表明,大的震级和小的距离对结构产生比较大的滞回能量需求。利用本文结果,可以估计未来地震中结构物所遭受滞回能量的大小。     

Seismic damage assessment based on different hysteretic rules

The inelastic response of a single-degree-of-freedom (SDOF) system to different sets of earthquake records was analysed to study the significance of ground motion characteristics on structural damage. Six non-linear models were used. The ductility ratio and hysteretic energy index were chosen as two important damage indices to measure the structural damage. The dispersion phenomenon exhibited by yield spectra due to input ground motion was reduced by incorporating the ground motion a/v ratio into the two damage indices. Finally, empirical formulae for estimating two measures of structural damage were developed for each hysteretic model.     

不同再生骨料取代率再生混凝土柱抗震试验研究

进行了1根普通混凝土柱和3根不同再生骨料取代率的再生混凝土柱模型的低周反复荷载试验研究,模型按1/2缩尺。在试验基础上,分析了其承载力、刚度及其退化过程、滞回特性、延性、耗能能力、破坏形态等,提出了基于混凝土强度折减的承载力实用计算方法。研究表明:随着再生骨料取代率的增加,其混凝土的弹性模量明显减小,试件初始刚度明显下降、承载力呈下降趋势、耗能值下降,抗震能力呈下降趋势。再生混凝土柱可用于多层结构轴压比较小的柱的抗震设计。     

Seismic response of self‐centring hysteretic SDOF systems

The seismic response of single‐degree‐of‐freedom (SDOF) systems incorporating flag‐shaped hysteretic structural behaviour, with self‐centring capability, is investigated numerically. For a SDOF system with a given initial period and strength level, the flag‐shaped hysteretic behaviour is fully defined by a post‐yielding stiffness parameter and an energy‐dissipation parameter. A comprehensive parametric study was conducted to determine the influence of these parameters on SDOF structural response, in terms of displacement ductility, absolute acceleration and absorbed energy. This parametric study was conducted using an ensemble of 20 historical earthquake records corresponding to ordinary ground motions having a probability of exceedence of 10% in 50 years, in California. The responses of the flag‐shaped hysteretic SDOF systems are compared against the responses of similar bilinear elasto‐plastic hysteretic SDOF systems. In this study the elasto‐plastic hysteretic SDOF systems are assigned parameters representative of steel moment resisting frames (MRFs) with post‐Northridge welded beam‐to‐column connections. In turn, the flag‐shaped hysteretic SDOF systems are representative of steel MRFs with newly proposed post‐tensioned energy‐dissipating connections. Building structures with initial periods ranging from 0.1 to 2.0s and having various strength levels are considered. It is shown that a flag‐shaped hysteretic SDOF system of equal or lesser strength can always be found to match or better the response of an elasto‐plastic hysteretic SDOF system in terms of displacement ductility and without incurring any residual drift from the seismic event. Copyright © 2002 John Wiley & Sons, Ltd.     

Consistent inelastic design spectra: Strength and displacement

A procedure for the determination of inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor has been developed. All the spectra are consistent (interrelated and based on the same assumptions). This is the first of two companion papers which deals with the ‘classical’ structural parameters: strength and displacement. The input data are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum. Simple, approximate expressions for the strength reduction factor R are proposed. The value of R depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour, damping and ground motion. Fairly accurate approximations to the inelastic spectra for strength and displacement can be derived from the elastic spectrum using the proposed values for R.     

耗能减振结构的抗震设计方法

本文基于国内外耗能减振装置的性能试验和耗能减振结构的计算研究并结合我国正在修订的建筑结构抗震规范。提出了耗能减震结构抗震设计的统一方法。首先,提出了速度相关型线性耗能器和滞变型耗能器等效阻尼和刚度的计算方法;其次,通过大量的计算比较,研究了耗能减振结构非交阻尼阵强行解耦的精度和实际应用的可行性,提出了在结构地震反应分析了振型分解反应谱法中耗能器可统一归结为结构附加振型阻尼比的方法;第三,通过耗能减     

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。     

震后混凝土缺陷加固修复构件性能实验分析

为避免震后建筑工程加固不合理导致再次受损,并为加固修复工程提供合理化建议,促进震后救灾工作顺利开展,提出震后建筑工程混凝土缺陷加固修复方法的研究。首先,对混凝土梁试件和混凝土柱试件进行设置,研究基于碳纤维布或外包钢套加固方法对混凝土梁和混凝土柱试件展开循环荷载试验;其次,通过混凝土梁试件滞回曲线、骨架曲线、延性及耗能情况,分析不同加固修复方法的混凝土梁试件抗震性能;最后,通过混凝土柱试件延性及耗能、刚度退化和承载力退化情况,分析采用不同加固方法修复的混凝土柱试件抗震性能。试验结果显示：高配筋率可提升混凝土梁试件滞回特性,外包钢套加固混凝土梁试件滞回饱满程度较高、耗能较少,碳纤维布加固梁试件可将加载位移由10 mm延缓至30 mm,提升延性;碳纤维布加固可提升混凝土柱延性,外包钢套加固重度缺陷混凝土柱可以良好抑制其刚度和承载力退化。试验结果验证了碳纤维加固可提升震后建筑工程混凝土结构延性,外包钢套加固可抑制混凝土结构刚度、承载力退化。     

Evaluation of the structural response under seismic actions using non‐linear static methods

The paper investigates the degree of accuracy achievable when some non‐linear static procedures based on a pushover analysis are used to evaluate the seismic performance. In order to assess the significance of different sources of errors, three types of structural systems are analysed: (i) single‐degree‐of‐freedom (SDOF) systems with different hysteretic behaviour; (ii) shear‐type multi‐degree‐of‐freedom (MDOF) systems with elastic–perfect plastic (EPP) shear force–interstorey drift relationships; (iii) a steel moment‐resisting frame with rigid joints and EPP moment–curvature relationship. In SDOF systems, the source of approximation comes only from the calibration of the demand spectrum, while in MDOF systems some further errors are introduced by the schematization with an equivalent SDOF system. The non‐linear static procedures are compared with rigorous time‐history analyses carried out by considering ten generated earthquake ground motions compatible with the Eurocode 8 elastic spectra. It was found that SDOF systems with longer periods satisfy the equal displacement approximation regardless of the hysteretic model, while hysteresis loops with smaller energy dissipated indicate lower response for shorter periods. This is the opposite of what predicted by the ATC‐40 capacity spectrum method, which underestimates and overestimates, respectively, the actual response of low‐ and high‐ductility systems. Conversely, the inelastic spectrum method proposed by Vidic, Fajfar and Fischinger leads to the most accurate results for all types of structural systems. The analyses carried out on EPP shear‐type frames point out a large concentration of the ductility demand on some storeys. However, such a concentration markedly reduces when some hardening is accounted for. Copyright © 2006 John Wiley & Sons, Ltd.     

不同配筋率的再生混凝土柱抗震性能试验研究

本文对1根普通混凝土柱和4根全再生混凝土柱模型进行了低周反复荷载试验研究,模型按1/2缩尺。在试验基础上,分析了其承载力、刚度及其退化过程、滞回特性、延性、耗能能力、破坏形态等。研究表明:随着配筋率的增加,再生混凝土柱的承载力、刚度、耗能能力均有提高;同时,建立了基于再生混凝土强度折减的承载力实用计算方法,其计算结果与试验结果符合较好。     

Hysteretic model development and seismic response of unbonded post‐tensioned precast CFT segmental bridge columns

The study investigated the cyclic behavior of unbonded, post‐tensioned, precast concrete‐filled tube segmental bridge columns by loading each specimen twice. Moreover, a stiffness‐degrading flag‐shaped (SDFS) hysteretic model was developed based on self‐centering and stiffness‐degrading behaviors. The proposed model overcomes the deficiency of cyclic behavior prediction using a FS model, which self‐centers with fixed elastic and inelastic stiffnesses. Experimental and analytical results showed that (1) deformation capabilities of the column under the first and second cyclic tests were similar; however, energy dissipation capacities significantly differed from each other, and (2) the SDFS model predicted the cyclic response of the column better than the FS model. Inelastic time‐history analyses were performed to demonstrate the dynamic response variability of a single‐degree‐of‐freedom (SDOF) system using both models. A parametric study, performed on SDOF systems subjected to eight historical earthquakes, showed that increased displacement ductility demand was significant for structures with a low period and low‐to‐medium yield strength ratio and reduced displacement ductility demand in these systems was effectively attained by increasing energy dissipation capacity. Copyright © 2008 John Wiley & Sons, Ltd.     

Influence of different mechanical column-foundation connection devices on the seismic behaviour of precast structures

Dry-assembled precast concrete frame structures are typically made with dowel beam-to-column connections, which allow relative rotation along the beam direction. In the orthogonal direction the rotation of the beam is prevented but again the connections of the superimposed floor elements allow for relative rotation. All the ductility and energy dissipation demand in case of seismic action is therefore concentrated at the base of cantilever columns. Hence, the column-to-foundation connection plays a key role on the seismic performance of such structures. Mechanical connection devices, even if correctly designed for what concerns resistance, may affect the behaviour of the whole joint modifying the ductility capacity of the columns and their energy dissipation properties. An experimental campaign on different mechanical connection devices has been performed at Politecnico di Milano within the Safecast project (European programme FP7-SME-2007-2, Grant agreement No. 218417, 2009). The results of cyclic tests on full scale structural sub-assembly specimens are presented. Design rules are suggested for each of the tested connections on the basis of the experimental observations, and numerical analyses have been performed with hysteretic parameters calibrated on the experimental loops. The seismic performance of structures provided with those connections is investigated through a case study on a multi-storey precast building prototype, which has also been subject to full-scale pseudo-dynamic testing within the same research project at the European Laboratory of Structural Assessment of the Joint Research Centre of the European Commission. The comparison of the results from the structure provided with the different studied connections clearly highlights how some solutions may lead to both reduction of ductility capacity and dissipation of energy, increasing the expected structural damage and the seismic risk.     

Effect of hysteretic smoothness on inelastic response spectra with constant‐ductility

This paper presents an efficient methodology for computing constant‐ductility inelastic response spectra. The computation of constant‐ductility spectra involves numerical root‐finding algorithms to find the strongest structure providing a desired ductility response. Smooth inelastic structural behavior is modeled using a first‐order nonlinear differential equation and the transient structural response is solved using an implicit algorithm requiring Newton iterations at each time step. For structural models with smooth hysteretic behavior (not piece‐wise linear), a simple root‐finding method involving a combination of hyperbolic fits, linear interpolation, and Newton's method converges upon the highest strength (conservative) solution with a small number of iterations. The effect of the hysteretic smoothness on the occurrence of multiple roots is examined for two near‐fault and two far‐fault earthquake records, and for two measures of ductility and for normalized hysteretic energy. The results indicate how the smoothness of the hysteretic behavior affects ductility demand and constant‐ductility response spectra. Copyright © 2010 John Wiley & Sons, Ltd.     

Shaking table tests on reinforced concrete frames without and with passive control systems

An extensive experimental program of shaking table tests on reduced‐scale structural models was carried out within the activities of the MANSIDE project, for the development of new seismic isolation and energy dissipation devices based on shape memory alloys (SMAs). The aim of the experimental program was to compare the behaviour of structures endowed with innovative SMA‐based devices to the behaviour of conventional structures and of structures endowed with currently used passive control systems. This paper presents a comprehensive overview of the main results of the shaking table tests carried out on the models with and without special braces. Two different types of energy dissipating and re‐centring braces have been considered to enhance the seismic performances of the tested model. They are based on the hysteretic properties of steel elements and on the superelastic properties of SMAs, respectively. The addition of passive control braces in the reinforced concrete frame resulted in significant benefits on the overall seismic behaviour. The seismic intensity producing structural collapse was considerably raised, interstorey drifts and shear forces in columns were drastically reduced. Copyright © 2005 John Wiley & Sons, Ltd.