Energy evaluation of inelastic structures subjected to random earthquake excitations

The modified force analogy method combined with static condensation is applied to study the seismic behaviour of inelastic structures, while energy transfer and dissipation in the structure during an earthquake hazard are investigated through energy formulation based on the equation of motion. The earthquake ground motion is modelled as a non‐stationary Gaussian random process. Rigid‐end offsets of the plastic hinges forming on the members, as well as the ability for panel zones to deform, are included in the structural analysis model. Monte Carlo simulation method is performed on a six‐story real moment‐resisting frame to determine the mean and the standard deviation of seismic energy dissipation time histories. Based on this combination of the force analogy method and energy formulation in the equation of motion with the stochastic earthquake model, the feasibility of the analysis procedure for studying the dynamics of inelastic structures is demonstrated through varying the rigidity of panel zones. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic analysis of inelastic moment‐resisting frames Part II: Energy dissipation in deformable panel zones

The simple analytical method developed in the companion paper is applied to study the dynamic behavior and energy dissipation of inelastic structures with panel zone deformation using rotational springs. Both shear deformation and inelastic behaviors of the panel zone are modeled using rotational springs to capture the actual vibration characteristics of the overall structural responses. The modified force analogy method with static condensation proposed in the companion paper is employed to study the effects of panel zone deformation on the dynamic behavior of inelastic structures, while rigid end offsets are also included to give a more accurate structural model. Based on this proposed analytical method, numerical simulation is first performed to study the responses of a one‐story one‐bay moment‐resisting frame. Results show that rigidity of panel zones plays a major role in the overall structural responses during earthquake excitations. Numerical simulations are then performed on a multi‐degree of freedom structure to demonstrate the use of the proposed method. Comparison of results between modeling structures with various panel zone rigidities and yield moments in the rotational springs shows that significant differences in both structural responses and energy dissipations exist between the models, and therefore the effects of panel zone deformation should be considered in dynamic analysis. Copyright © 2007 John Wiley & Sons, Ltd.     

Nonlinear dynamic analysis of frames with plastic hinges at arbitrary locations

This paper presents a method for nonlinear dynamic analysis of frames subjected to distributed loads, which is based on the semi‐rigid technique and moving node strategy. The plastic hinge is modelled as a pseudo‐semi‐rigid connection with nonlinear hysteretic moment–curvature characteristics at element ends. The stiffness matrix with material and geometric nonlinearities is expressed as a sum of products of the standard and geometric stiffness matrices with their corresponding correction matrices based on the plasticity‐factors developed from the section flexural stiffness at the plastic hinge locations. Each beam member is modelled by two elements. The moving node strategy is applied to the intermediate node to track the exact location of any intermediate plastic hinge that may be formed. Equilibrium iterations and geometry updating are carried out in every time step. Stiffness degradation is adopted to describe the deterioration of plastic hinges, and the effects of various parameters in the degradation model are evaluated. Examples are used to illustrate the applicability and excellent performance of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Implications of using refined plastic hinge analysis for load and resistance factor design

A plastic hinge analysis based on a two-surface stiffness degradation model is outlined for second-order inelastic analysis of steel structures. The analysis approach is based on refinements to the elastic-plastic hinge method and allows for a smooth transition from initial yielding to the full yielding of cross-sections in a beam-column element. This analysis method shows a good representation of the inelastic structural response compared to the conventional elastic-plastic hinge analysis, and it is efficient for use in the analysis design of large-scale structures. Design implications, recommendations and case studies for use of refined plastic hinge analysis for direct frame design considering semirigid connection effects are presented.     

Energy‐based damage assessment on structures during earthquakes

Several seismic damage indices have been developed using the energy concept in attempt to compensate for the inadequacy of ductility criteria. However, these indices are either based on implicitly defined energy as a cumulative effect on ductility or are unable to consider energy in a quantitative manner. In this paper, a method of assessing the structural performance during earthquakes based on both explicitly computed plastic rotation and plastic energy at every hinge of a moment‐resisting frame is proposed. This method uses the force analogy method to evaluate the structural response and energy in the inelastic domain. Inelastic deformation is expected to occur during major earthquakes, and active control based on an instantaneous optimal control algorithm is used to improve the structural performance. Comparisons are made between uncontrolled response and instantaneous optimal control response based on a single‐degree‐of‐freedom system to demonstrate the computation of plastic energy. Damage analysis of a six‐storey moment‐resisting steel frame is then presented to evaluate the performance and applicability of the proposed damage measure. Results show that the proposed damage assessment criteria are feasible and that active control can reduce plastic rotation and plastic energy, thereby reducing damage to a certain acceptable limit. Copyright © 2001 John Wiley & Sons, Ltd.     

基于拟力法的纤维梁有限元非线性分析方法

以拟力法中的弹塑性分解思路和纤维梁理论为基础,将梁单元的截面变形分解为弹性变形和塑性变形,并引入塑性自由度,在材料层面建立了基于拟力法的纤维梁有限元非线性分析方法。该方法可以保持结构整体刚度矩阵不变,其非线性状态通过局部塑性矩阵加以体现,在迭代计算时避免了结构整体刚度矩阵的实时更新与分解,且塑性矩阵相比于结构整体刚度矩阵规模小,提高了计算效率。通过数值算例,将文中方法与采用有限元软件ABAQUS的分析结果进行对比,两者吻合较好,证明了该方法的有效性。     

Probabilistic structural damage assessment and control based on energy approach

This paper proposes a probabilistic method for assessing the seismic damage to structures based on both plastic rotation and plastic energy. Four basic features of this method are: (1) the incorporation of the state space method and force analogy method in inelastic dynamic analysis; (2) the exact quantification of the overall plastic energy and individual plastic energy dissipated at each plastic hinge; (3) the definition of damage model with both the monotonic and cyclic damage extremes; and (4) the probabilistic expression of the structural damage indices. An example of a ten‐storey moment‐resisting steel frame is presented to demonstrate the practical application of the proposed procedure. Optimal linear control is applied to improve the structural performance. Responses and energies at selected plastic hinges arising from 28 earthquake ground motions are compared, and statistical characteristic values of these variables are computed. Finally, comparisons are made between the drift ratio and failure probability of the proposed local damage index. Results show that active control can reduce plastic rotation and plastic energy, therefore reducing the damage. In addition, this study shows that using the drift ratio alone is inadequate to predict damage on certain occasions, and the proposed damage index is a more rational measure. Copyright © 2001 John Wiley & Sons, Ltd.     

大跨度连续刚构桥的弹塑性动力时程分析

采用刚度退化三线性模型对某大跨度连续刚构桥实体工程进行了弹塑性动力时程分析,确定了桥墩塑性铰对结构抗震性能的影响,算例分析结果可为同类桥梁工程的抗震设计提供指导。     

鱼骨形模型对钢框架二阶弹塑性动力分析

多质点系剪切模型在多层平面框架的抗震分析中已得到了广泛的应用 ,但这种模型不能考虑梁柱的强度比和刚度比、节点域变形、附加轴力和梁塑性铰对地震响应的影响。本文介绍的鱼骨形模型既能考虑以上所有因素 ,又对平面框架进行了有效的简化 ,非常适合于钢框架的二阶弹塑性动力分析     

基于刚体准则的空间框架弹塑性非线性分析方法

基于刚体准则,采用二阶改进塑性铰模型,构建了空间弹塑性梁单元及其弹塑性刚度矩阵,建立了高效简洁的非线性增量迭代方法,可有效分析截面屈服产生的有限转动、二阶效应等柔性空间钢框架结构材料与几何非线性耦合效应。对于受初始力平衡的单元,随着单元的刚体转动与移动,其初始平衡力在当前状态下应保持大小不变,仅方向随单元做刚体转动,而实际结构的变形可以视为较大的刚体位移与较小的自然变形(弹性或非弹性)的组合。将此刚体准则植入增量迭代法,在预测阶段采用通过了刚体运动检验的弹塑性矩阵,从而合理确定迭代初始方向;在修正阶段使用刚体准则计算单元结点力,保证了计算精度。对三个典型柔性框架结构所做分析表明,本文方法能够准确预测结构的极限承载力值与塑性铰发展过程。对于空间框架结构,每根杆件仅需划分一个单元,极大提高了计算效率、降低了计算成本。与塑性区法、纤维元法以及考虑截面翘曲的修正切线刚度法等相比,本文提出的方法具有物理概念明确、单元划分少、刚度矩阵简单、分析过程简洁、计算精度与效率高等显著特点,适于工程应用。     

基于拟力法的框架结构静力弹塑性分析

针对拟力法仅在刚性连接钢框架中应用的现状,根据钢筋混凝土框架以及半刚性连接钢框架的受力特点,并基于拟力法的基本假定与思路,得出了钢筋混凝土结构中塑性铰和半刚性连接钢框架中连接的弯矩-相对转角关系,从而推导并获得了拟力法在框架结构静力弹塑性分析中的通用公式。通过与有限元理论计算结果的比较,表明基于拟力法的框架结构静力弹塑性分析方法在应用于各类框架结构时都有着较高的精度,从而为将基于拟力法的动力弹塑性分析包括地震能量分析拓展到钢筋混凝土框架结构以及半刚性连接钢框架结构中奠定了基础。     

Nonlinear hysteretic behavior simulation of reinforced concrete shear walls using the force analogy method

Reinforced concrete (RC) shear walls that provide high strength and stiffness are widely used in buildings to resist lateral loads. It often exhibits complex and multiple hysteretic behaviors, including shear behavior, flexural behavior, strength softening, and deterioration, which are often influenced by the reinforcement and concrete material characteristics, vertical loads, and so on. Significant effort has gone toward developing accurate and efficient models, and these models fall into two categories: macroscopic and microscopic models. The microscopic models are accurate but computationally expensive and need more material information and experimental results for calibration. The present research is to implement an existing macroscopic model for use in the force analogy method, which is an accurate, efficient, and stable algorithm for conducting dynamic analysis when coupled with the state space formulation. The RC shear wall model with two vertical sliding hinges and one horizontal sliding hinge assigned to capture the relationship of the lateral deflection or rotation versus the RC shear wall force is validated against prior experimental results. The proposed model is also implemented in a frame, in which inelastic response occurs in both the frame and the RC shear wall members, to demonstrate the application of the model and the potential for simulating complex inelastic dynamic RC frame‐wall structural behavior with the force analogy method. Copyright © 2014 John Wiley & Sons, Ltd.     

钢筋混凝土框架结构地震易损性分析

本文以一榀7层的钢筋混凝土框架结构为分析对象,采用SAP2000建立有限元模型,选取非线性Nlink单元来模拟梁和柱两端的塑性角,其中柱铰单元采用纤维PMM铰,梁铰单元设置弯矩铰。分别指定最大层间位移角和最大顶点位移角作为结构地震需求参数,并定义了相应的破坏状态。输入8条地震动记录进行结构地震易损性分析,得到了相应的易损性曲线。该方法可为结构的抗震性能评价提供参考。     

高强钢焊接箱形柱力学性能研究(Ⅱ)：二阶非弹性分析

高强钢的焊接残余应力分布和普通钢材的有较大差异,现有的切线模量和刚度退化函数不适合用于高强钢焊接箱形截面的二阶非弹性分析。而精炼塑性铰模型通过切线模量和刚度退化函数可合理考虑残余应力的影响和塑性渐进发展,达到与塑性区模型相近的精度。基于此,提出适合高强钢焊接箱形截面的二阶非弹性分析方法。通过稳定函数考虑单元二阶效应,基于杆端部转动引起的构件弯曲及其导致的轴向应变,考虑弯曲效应。在精炼塑性铰模型中,采用高强钢焊接箱形截面的残余应力统一分布模型,通过截面分析法构建不同强度等级的焊接箱形截面切线模量计算公式。同时,分析轴力和弯矩共同作用下的渐进屈服对箱形截面刚度退化的影响,从而建立可模拟截面塑性发展的刚度退化函数。结合塑性铰的产生与发展对平衡微分方程解的影响,建立梁柱单元的弹塑性刚度矩阵。结果表明,所提出的二阶非弹性分析方法可准确分析高强钢焊接箱形截面轴压构件的力学性能,可应用于高强钢框架结构设计,为二阶非弹性分析方法的工程应用提供参考。     

附加节点斜筋对梁柱节点区域粘结机制的影响

梁柱节点在非弹性阶段的表现同钢筋和混凝土之间的相互作用有极大的关系。不仅因为梁纵筋的粘结 -滑移效应 ,尤其是发生在柱面处的滑移是使整个结构试件刚度下降的重要原因 ,也因为纵筋的粘结应力分布直接影响到节点内的抗剪机制。梁柱内节点在反复循环荷载下通常面临最不利的粘结条件 ,提出的一种新的附加斜钢筋的节点构造方式 ,被证明能有效地提高梁柱内节点的性能 ,而又避免了其内部钢筋拥挤的情形。附加斜筋的出现抑制了节点裂缝和梁柱界面裂缝的发展 ,这对保持节点的刚度是至为重要的。由于梁塑性铰出现在柱面以外一段距离 ,节点核心混凝土可避免来自钢筋的屈服渗透 ,而加强混凝土斜压杆的作用。降低了的梁内纵筋的应力能在反复循环荷载下获得较为有利的粘结条件 ,特别是在缺少柱上轴向压力的时候。     

国家游泳中心子结构模型抗震能力分析

国家游泳中心子结构模型分析结果与试验对比表明,焊接空心球(半球)节点对子结构模型整体刚度有较大贡献,用带刚域的集中塑性铰杆单元建立的分析模型能较好地模拟子结构模型的弹塑性性能.采用该分析模型,分别用能力谱法和弹塑性时程分析法对子结构模型进行罕遇地震反应分析.结果表明,两种方法的计算结果很接近;罕遇地震作用下子结构模型仅少量杆件屈服,整体上处于弹性,具有很强的抗震能力.     

A numerical study based on sequential procedure for optimally placing active controllers

A sequential procedure based on the concept of degree of controllability is developed for optimally placing active controllers in structures. The optimal locations are selected to be located where the largest structural response occurs. This sequential procedure uses time history analysis to determine these optimal locations, and the effect of each additional controller on the next optimal location is considered in every step of the analysis procedure. Force analogy method (FAM) is used to take into consideration any possible structural inelasticity during earthquakes. Different from conventional methods of inelastic analysis using changing stiffness, FAM varies the structural displacement field, and therefore greatly simplifies the computation. Since only initial stiffness is used in the inelastic analysis, it can be easily incorporated into the optimal linear control algorithm using the state space method. Numerical simulation of a six‐storey frame is performed to demonstrate the simplicity of optimal placement procedure while considering structural inelasticity. Results show that optimal locations determined by the proposed sequential procedure have advantages over other locations in terms of control efficiency, where placement of the controllers in these locations reduces the desired overall structural and energy response most effectively. Copyright © 2005 John Wiley & Sons, Ltd.     

单向壁式框架对剪力墙结构体系抗震性能影响的研究

在框架-剪力墙结构内力变形分析方法的基础上,推导了壁式框架-剪力墙结构的刚度特征值计算公式,理论分析了剪力墙结构变形特征随壁式框架比例和房屋高度的变化规律,并采用弹性反应谱法进行了计算验证。采用静力弹塑性分析法,以层位移和层间位移角分布,以及结构塑性铰发展过程为指标,研究了壁式框架比例和房屋高度对结构抗震性能的影响。研究结果表明,壁式框架对剪力墙结构体系抗震性能带来不利影响,应根据其底部承担的倾覆力矩比例分别执行局部构件加强、控制结构高度等的设计规定。     

国家体育场大跨度钢结构罕遇地震性能分析

采用杆端塑性铰模型、动力弹塑性分析法和静力弹塑性分析法对国家体育场大跨度钢结构罕遇地震作用下的性能进行了分析。三维动力弹塑性分析的输入包括4组地震记录和1组人工地震波;静力弹塑性分析包括单向、双向和三向推覆共12种工况。结果表明,罕遇地震作用下,国家体育场大跨度钢结构最大位移小于其限值;主结构的塑性铰主要出现在桁架柱,数量很少,且屈服程度较轻;次结构的塑性铰数量少,极少数铰的强度下降至残余强度;结构的整体刚度没有下降,承载能力未达到最大。国家体育场大跨度钢结构设计达到了预定的抗震设防性能目标。对静力和动力弹塑性分析两种方法的结果进行了比较,探讨了静力弹塑性分析合适的加载模式,为大跨度钢结构的静力弹塑性分析提供了参考。     

钢筋混凝土框架全过程分析的非线性简化单元及其应用

本文根据框架结构在加载过程中表现出来的塑性铰形成机理，介绍了一种用于钢筋混凝土框架非线性分析的简化单元模式。它考虑了轴力的二阶效应、横截面自开裂后的塑化和塑性区长度等非线性因素对结构的影响。此外，在分析中也考虑了钢筋锚固滑移和节点刚域的影响。经与试验结果比较，说明用本文模式对钢筋混凝土试验框架进行非线性有限元分析所得的计算结果是正确的。