Effect of ground motion duration on inelastic displacement ratio of SDOF systems

In this paper,the influence of ground motion duration on the inelastic displacement ratio,C_(1),of highly damped SDOF systems is studied.For this purpose,two sets of spectrally equivalent long and short duration ground motion records were used in an analysis to isolate the effects of ground motion duration on.The effect of duration was evaluated for observed values of C_(1) by considering six ductility levels,and different damping and post-yield stiffness ratios.A new predictive equation of C_(1) also was developed for long and short duration records.Results of non-linear regression analysis of the current study provide an expression with which to quantify the duration effect.Based on the average values of estimated C_(1) ratios for long duration records divided by C_(1) for a short duration set,it is concluded that the maximum difference between long and short duration records occurs when the damping ratio is 0.3 and the post-yield stiffness ratio is equal to zero.

Self-centering seismic retrofit scheme for reinforced concrete frame structures:SDOF system study

This paper presents the results of a parametric study of self-centering seismic retrofit schemes for reinforced concrete (RC) frame buildings. The self-centering retrofit system features flag-shaped hysteresis and minimal residual deformation. For comparison purpose,an alternate seismic retrofit scheme that uses a bilinear-hysteresis retrofit system such as buckling-restrained braces (BRB) is also considered in this paper. The parametric study was carried out in a single-degree-of-freedom (SDOF) system framework since a multi-story building structure may be idealized as an equivalent SDOF system and investigation of the performance of this equivalent SDOF system can provide insight into the seismic response of the multi-story building. A peak-oriented hysteresis model which can consider the strength and stiffness degradation is used to describe the hysteretic behavior of RC structures. The parametric study involves two key parameters -the strength ratio and elastic stiffness ratio between the seismic retrofit system and the original RC frame. An ensemble of 172 earthquake ground motion records scaled to the design basis earthquake in California with a probability of exceedance of 10% in 50 years was constructed for the simulation-based parametric study. The effectiveness of the two seismic retrofit schemes considered in this study is evaluated in terms of peak displacement ratio,peak acceleration ratio,energy dissipation demand ratio and residual displacement ratio between the SDOF systems with and without retrofit. It is found from this parametric study that RC structures retrofitted with the self-centering retrofit scheme (SCRS) can achieve a seismic performance level comparable to the bilinear-hysteresis retrofit scheme (BHRS) in terms of peak displacement and energy dissipation demand ratio while having negligible residual displacement after earthquake.

Hilbert spectrum and intrinsic oscillation mode of dynamic response of a bilinear SDOF system: influence of harmonic excitation amplitude

Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.

Seismic Reliability Assessment of Inelastic SDOF Systems Subjected to Near-Fault Ground Motions Considering Pulse Occurrence

The ground motions in the orientation corresponding to the strongest pulse energy impose more serious demand on structures than that of ordinary ground motions.Moreover,not all near-fault ground motion records present distinct pulses in the velocity time histories.In this paper,the parameterized stochastic model of near-fault ground motion with the strongest energy and pulse occurrence probability is suggested,and the Monte Carlo simulation(MSC)and subset simulation are utilized to calculate the first excursion probability of inelastic single-degree-of-freedom(SDOF)systems subjected to these types of near-fault ground motion models,respectively.Firstly,the influences of variation of stochastic pulse model parameters on structural dynamic reliability with different fundamental periods are explored.It is demonstrated that the variation of pulse period,peak ground velocity and pulse waveform number have significant effects on structural reliability and should not be ignored in reliability analysis.Then,subset simulation is verified to be unbiased and more efficient for computing small reliable probabilities of structures compared to MCS.Finally,the reliable probabilities of the SDOF systems with different fundamental periods subjected to impulsive,non-pulse ground motions and the ground motions with pulse occurrence probability are performed,separately.It is indicated that the ground motion model with the pulse occurrence probability can give a rational estimate on structural reliability.The impulsive and ordinary ground motion models may overestimate and underestimate the reliability of structures with fundamental period much less than the mean pulse period of earthquake ground motions.

Estimation of peak relative velocity and peak absolute acceleration of linear SDOF systems

We have found some mistakes in the article by Jianwei Song et al. （2007）. The revisions are given below：

Effect of the spectral shape of ground motion records on the collapse fragility assessment of degrading SDOF systems

The main purpose of this paper is to study the collapse capacity of single degree of freedom(SDOF)systems and to produce fragility curves as well as collapse capacity spectra while considering a broad range of structural parameters,including system degradation,the P-Δeffect,ductility capacity and the post-capping stiffness ratio.The modified Ibarra-Krawinkler deterioration model was used to consider hysteretic behavior.A comprehensive study was conducted to extract the collapse capacity spectrum of SDOF systems with a wide range of periods,varying from 0.05 to 4 s,to cover short,intermediate and long periods.Incremental dynamic analysis(IDA)was performed for SDOF systems to identify the condition in which the collapse capacity of the system is determined.The IDAs were performed using different sets of seismic ground motions.The ground motion records were categorized into different sets based on three spectral shape parameters,including the epsilon,SaRatio and N_(p).The collapse fragility curves of SDOF systems with different periods were extracted to illustrate the collapse capacity at different probability levels.The results show that structural degradation and ductility as well as the spectral shape parameters significantly affect the collapse capacity of SDOF systems.On the other hand,the post-capping stiffness ratio and small levels of the P-Δeffect do not remarkably change collapse capacity.Also,the collapse capacity of SDOF systems is more sensitive to the records categorized based on SaRatio and N_(p)than those classified based on epsilon.

Modification of SDOF model for reinforced concrete beams under close-in explosion

In this paper,a modified single-degree-of-freedom(SDOF)model of reinforced concrete(RC)beams under close-in explosion is proposed by developing the specific impulse equivalent method and flexural resistance calculation method.The equivalent uniform specific impulse was obtained based on the local conservation of momentum and global conservation of kinetic energy.Additionally,the influence of load uniformity,boundary condition and complex material behaviors(e.g.strain rate effect,hardening/softening and hoop-confined effect)was considered in the resistance calculation process by establishing a novel relationship between external force,bending moment,curvature and deflection successively.The accuracy of the proposed model was verified by carrying out field explosion tests on four RC beams with the scaled distances of 0.5 m/kg~(1/3)and 0.75 m/kg~(1/3).The test data in other literatures were also used for validation.As a result,the equivalent load implies that the blast load near the mid-span of beams would contribute more to the maximum displacement,which was also observed in the tests.Moreover,both the resistance model and test results declare that when the blast load becomes more concentrated,the ultimate resistance would become lower,and the compressive concrete would be more prone to softening and crushing.Finally,based on the modified SDOF model,the calculated maximum displacements agreed well with the test data in this paper and other literatures.This work fully proves the rationality of the modified SDOF method,which will contribute to a more accurate damage assessment of RC structures under close-in explosion.

Prediction of damage potential in mainshock–aftershock sequences using machine learning algorithms

Assessing the potential damage caused by earthquakes is crucial for a community’s emergency response.In this study,four machine learning(ML)methods—random forest,extremely randomized trees,AdaBoost(AB),and gradient boosting(GB)—were employed to develop prediction models for the damage potential of the mainshock(DIMS)and mainshock–aftershock sequences(DIMA).Building structures were modeled using eight single-degree-of-freedom(SDOF)systems with different hysteretic rules.A set of 662 recorded mainshock–aftershock(MS-AS)ground motions was selected from the PEER database.Seven intensity measures(IMs)were chosen to represent the characteristics of the mainshock and aftershock.The results revealed that the selected ML methods can well predict the structural damage potential of the SDOF systems,except for the AB method.The GB model exhibited the best performance,making it the recommended choice for predicting DIMS and DIMA among the four ML models.Additionally,the impact of input variables in the prediction was investigated using the shapley additive explanations(SHAP)method.The high-correlation variables were sensitive to the structural period(T).At T=1.0 s,the mainshock peak ground velocity(PGVM)and aftershock peak ground displacement(PGDA)significantly influenced the prediction of DIMA.When T increased to 5.0 s,the primary high-correlation factor of the mainshock IMs changed from PGVM to the mainshock peak ground displacement(PGDM);however,the highcorrelation variable of the aftershock IMs remained PGDA.The high-correlation factors for DIMS showed trends similar to those of DIMA.Finally,a table summarizing the first and second high-correlation variables for predicting DIMS and DIMA were provided,offering a valuable reference for parameter selection in seismic damage prediction for mainshock–aftershock sequences.

计算思维培养的教学探索——以简谐型脉冲动力响应为例

目前,计算思维已成为信息技术教育中的研究热点。土木工程属于相对比较传统的专业,主干课程为数学、力学和结构类课程,在教学中开展计算思维培养的教学探索,强调所学知识的综合运用,对于提高课程教学质量具有重要意义。文章以单自由度体系的简谐型脉冲动力响应为研究对象,分析了单自由度体系动力响应峰值出现的时刻,讨论了单自由度体系的周期与脉冲周期的对比分析与结构响应的关系,帮助学生正确认识脉冲周期在结构动力响应中的影响,将计算思维融入学生的知识学习和问题解决中,适当拔高学习目标,以达到培养学生计算思维的目的。

基于加速度反应谱与地震动持时的地震输入能量谱研究

建立具有设计意义的地震动总输入能量谱是实现结构能量设计的基础。根据中长周期段修正的加速度反应谱及地震动有效持时,提出了一种生成地震动输入能量谱的方法。统计270组人工波的时程分析结果,得到了以等效速度表征的四段式弹性单自由度(single degree of freedom,SDOF)体系总输入能量谱,并给出了不同场地类型、抗震设防烈度等设计条件下归一化等效速度谱的参数取值。在考虑延性系数及刚度折减系数的影响后,提出了弹塑性SDOF体系修正输入能量谱的等效速度谱,估算了引起结构损伤的滞回耗能占总能量的比值。该能量谱可为基于能量的结构设计及研究提供参考。

SDOF体系残余变形响应与地震强度指标相关性分析

结构震后可修复性在现代抗震设计中扮演越来越重要的角色,残余变形作为可修复性的一个主要指标受到广泛的重视。弹塑性时程分析法是研究结构震后残余变形的主要方法,传统通过调整输入波PGA指标得到的计算结果离散性很大,因此需要选择一个合适的地震动强度指标控制输入波的选择。计算60条地震动作用下不同强度折减系数和屈服后刚度系数的双线性SDOF体系残余变形,研究以PGA,PGV,PGD为代表的18个地震动强度指标与残余变形之间的相关系数随SDOF体系周期变化规律。结果表明,不同强度指标与残余变形之间的相关系数受强度折减系数影响很大,基本不受屈服后刚度系数的影响,其中以PGV为代表的速度型强度指标与残余变形之间的整体相关性较好,并且考虑到PGV指标的工程特性,建议进行残余变形计算时,以PGV作为输入波主要控制指标。

基于等效线性化方法弹塑性SDOF系统能量谱的研究

选择了被认为精度较高或者有关规范中建议的8种等效线性化方法,以4种场地土条件下40条强震记录为输入,通过时程分析方法对各种等效线性化方法计算弹塑性SDOF系统能量谱的精度进行了分析。分析结果表明,现有等效线性化方法的等效周期和等效阻尼比之间存在较大差异,且用于预测弹塑性SDOF系统的能量谱时存在较大误差。根据能量谱分析结果的统计计算,建议了一种新的适用于弹塑性SDOF系统能量谱计算的等效线性化方法。

基于汶川地震记录的地震动强度指标与SDOF体系响应的相关性

选择2008年5月12日汶川地震四川台站中峰值加速度值大于200Gal的18组水平地震动记录,对周期为1.0s、阻尼比为5%的双线性SDOF体系,利用时程分析方法分别计算其有代表性的地震响应指标,如加速度、速度和位移,利用统计分析方法研究不同地震动强度指标,如峰值加速度、累积绝对速度、Arias强度、速度谱强度、加速度谱强度、均方根加速度、特征强度及Housner强度等与线性、非线性响应最大值的相关性。结果表明,不同地震动强度指标与SDOF体系最大响应的相关性差别很大,其中速度谱强度、Housner强度与SDOF体系最大响应的相关性较好,而加速度谱强度、峰值加速度与SDOF体系最大响应的相关性较差。另外,速度谱强度和Housner强度对SDOF体系非线性最大响应的相关性明显好于其对于线性体系最大响应的相关性。因此,对传统的基于峰值加速度选择和调整时程分析输入地震动记录的合理性及可靠性需进一步探讨。

罕遇地震作用下SDOF结构位移响应的统计特性分析

基于大量非线性时程算例分析结果和显著性分析 ,建立了多波输入下 SDOF结构平均最大位移响应与输入地震动拟位移谱、结构基本周期和屈服强度系数间的关系式 ,可为 DBD法中设计位移谱的确定提供参考。

基于瞬时输入能量的SDOF弹塑性结构最大位移反应分析

分析了不同周期的SDOF弹塑性模型在强震作用下的能量反应和位移反应,通过对二者相关性的探讨,提出了由瞬时输入能量推算结构最大位移反应的近似方法。

SDOF体系地震输入能量谱的简化问题研究

从美国加州大学地震动数据库选取40条强震记录并按我国场地类型进行了分类;基于能量平衡原理,采用归一化方法,分析了不同地震动作用和结构自身质量对弹性、弹塑性SDOF体系地震输入能量谱的影响;并根据能量谱特征提出了一种更为简便且可直接用于我国场地类型的三段式能量谱,并给出了相关参数取值。分析结果表明：SDOF体系质量对三段式能量谱曲线的分界周期无明显影响;在场地土类型和结构自身质量相同的情况下,弹性SDOF体系地震输入能量是弹塑性SDOF体系的1.1倍~1.4倍。

弹塑性SDOF系统累积滞回耗能谱

本文对弹塑性SDOF系统累积滞回耗能谱进行了分析研究。以4种场地土条件下40条强震记录为输入,分析了结构和地面运动参数对弹塑性SDOF系统累积滞回耗能谱与输入能量谱比值的影响。结果表明:阻尼比、延性系数、初始周期有很大的影响,而地面运动参数影响不大。结合现有的10种累积滞回耗能谱的计算模型和影响参数分析,建议了一个新的累积滞回耗能谱的计算方法。计算结果表明,本文建议的方法较好地反映了累积滞回耗能谱的影响参数和变化趋势,与现有计算模型有较好的一致性,且满足边界条件、便于计算。

近断层地震动强度参数与双线型SDOF体系地震反应的回归分析

针对已有研究的不足,引入函数拟合的局部精度评价指标,采用不受重视的多项式回归模型,分析评价了近断层地震动强度参数与双线型单自由度(SDOF)体系地震反应的回归关系和拟合优度。综合比较回归分析的整体精度和局部误差表明,二者之间的拟合效果和地震动有、无速度脉冲以及选择的强度参数有关,也与体系自振周期和采用的回归模型有关。根据拟合结果可识别较佳的近断层地震动强度参数。而且,二次多项式可以满足结构抗震回归分析的拟合精度要求。研究结果可为地震动选择和结构易损性分析提供参考。

弹塑性SDOF体系地震输入归一化等效速度谱

为了确定弹塑性单自由度(single degree of freedom,SDOF)体系地震输入能,分析了中美场地土剪切波速转换关系,将从美国PEER地震记录数据库选取的220条强震记录按中国场地土类型进行分类,基于能量平衡原理,采用归一化方法,建议了一种基于复合强度指标的弹性SDOF体系三段式等效速度谱.分析了5类场地土条件下SDOF体系系统参数对地震输入等效速度谱的影响.研究结果表明:刚度折减系数对等效速度谱无明显影响;延性系数和阻尼比增大均对等效速度谱峰值和下降段衰减速度有削弱作用.综合考虑各类影响因素,通过参数多次拟合,得出弹性SDOF体系归一化等效速度谱峰值段及下降段修正系数,提出了一种适用于我国场地土类型、可直接供设计使用的弹塑性SDOF体系归一化等效速度谱确定方法,并验证了其有效性.

基于多尺度线调频基稀疏信号分解的线性时变SDOF系统参数识别

对于参数时变的SDOF系统,提出一种基于多尺度线调频基稀疏信号分解的参数识别方法。该方法能将SDOF系统的强迫振动响应自适应地分解为稳态响应和瞬态响应。从系统的稳态响应可得到外部激振力的频率估计;对系统的瞬态响应用多尺度线调频基稀疏信号分解方法进一步分解,可得到系统的瞬时频率估计,进而可得到系统的刚度和阻尼,从而实现对SDOF系统的参数识别。刚度线性变化、刚度突变与刚度周期缓变3种情况下的参数识别仿真算例表明,本文方法能有效识别线性时变SDOF系统参数,具有重要的工程应用价值。