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.     

Seismic damage analysis including inelastic shear–flexure interaction

The paper focusses on seismic damage analysis of reinforced concrete (R/C) members, accounting for shear–flexure interaction in the inelastic range. A finite element of the beam-column type recently proposed by the writers for the seismic analysis of R/C structures is first briefly described. The analytical model consists of two distributed flexibility sub-elements which interact throughout the analysis to simulate inelastic flexural and shear response. The finite element accounts for shear strength degradation with inelastic curvature demand, as well as coupling between inelastic flexural and shear deformations after flexural yielding. Based on this model, a seismic damage index is proposed taking into account both inelastic flexural and shear deformations, as well as their interaction. The finite element and the seismic damage index are used to analyse the response of R/C columns tested under cyclic loading and failing either in shear or in flexure. It is shown that the analytical model and damage index can predict and describe well the hysteretic response of R/C columns with different types of failure.     

Seismic response analysis of reinforced concrete frames using inelasticity‐separated fiber beam‐column model

Evaluating the inelastic seismic response of structures accurately is of great importance in earthquake engineering and generally requires refined simulation, which is a time‐consuming process. Because the material nonlinearity generally occurs in a small part of the whole structure, many researches focus on taking advantage of this characteristic to improve the computational efficiency and the inelasticity‐separated finite element method (IS‐FEM) proposed recently provide a generic finite element formulation for solving this kind of problems efficiently. Although the fiber beam‐column element is widely used for the simulation of reinforced concrete (RC) framed structures, the inelastic deformation is often detected in a large part of the numerical model under earthquake excitation so that it is hard to achieve high efficient computation when applying the IS‐FEM to the inelastic response analysis of RC fiber models directly. In this paper, a new numerical scheme for seismic response analysis of RC framed structures model by fiber beam‐column element is proposed based on the IS‐FEM. To implement the RC fiber model for use in IS‐FEM and improve the computational performance of proposed scheme, a method of identifying the local domains with severe section inelasticity level is proposed and a modified Kent‐Park concrete material model is developed. Because the Woodbury formula is adopted as the solver, the global stiffness matrix can keep unchanged throughout the analysis and the main computational effort is only invested on a small matrix representing local inelastic behavior. The numerical examples demonstrate the validity and efficiency of the proposed scheme.     

Accuracy of nonlinear static procedures for the seismic assessment of shear critical structures

The nonlinear behavior of reinforced concrete (RC) members represents a key issue in the seismic performance assessment of structures. Many structures constructed in the 1980s or earlier were designed based on force limits; thus they often exhibit brittle failure modes, strength and stiffness degradation, and severe pinching effects. Field surveys and experimental evidence have demonstrated that such inelastic responses affect the global behavior of RC structural systems. Efforts have been made to consider the degrading stiffness and strength in the simplified nonlinear static procedures commonly adopted by practitioners. This paper investigates the accuracy of such procedures for the seismic performance assessment of RC structural systems. Refined finite element models of a shear critical bridge bent and a flexure‐critical bridge pier are used as reference models. The numerical models are validated against experimental results and used to evaluate the inelastic dynamic response of the structures subjected to earthquake ground motions with increasing amplitude. The maximum response from the refined numerical models is compared against the results from the simplified static procedures, namely modified capacity spectrum method and coefficient method in FEMA‐440. The accuracy of the static procedures in estimating the displacement demand of a flexure‐critical system and shear‐critical system is discussed in detail. Copyright © 2015 John Wiley & Sons, Ltd.     

梁铰型屈服RC框架结构地震弹塑性位移增大系数研究

本文通过弹性和弹塑性时程分析,研究了水平地震作用下梁铰型屈服RC框架模型结构的楼层屈服剪力系数、基本自振周期、楼层数3个因素对弹塑性位移增大系数的影响,通过非线性回归分析给出了弹塑性层间位移增大系数经验公式;通过分析滞回耗能沿楼层高度的分布,初步确定了梁铰型屈服RC框架结构的薄弱楼层位置;基于结构损伤分析,讨论了抗震规范中RC框架结构弹塑性层间位移角限值的水准。     

Cyclic tests of four two‐story narrow steel plate shear walls. Part 2: experimental results and design implications

This paper is the second part of a two‐part paper presenting the cyclic tests of four two‐story narrow steel plate shear walls (SPSWs). The first paper introduces the analytical studies and the specimen designs. This paper describes the test results. Some design implications including the capacity design for the first story column and the width‐to‐thickness ratio check for the beam web are discussed based on key observations from the tests. Test results confirm that the simplified strip model can accurately predict the inelastic responses of the specimens. Test results also confirm that the proposed capacity design method is effective in ensuring the plastic hinge formation at the bottom end of the first story column for SPSW with or without restrainers. Test results also show that the horizontal restrainers are effective in reducing the member forces in the boundary beam and column elements. Comparing the test results of the typical SPSW with those of the restrained SPSW (R‐SPSW) specimens, it is found that the R‐SPSW possesses an improved cyclic performance and reduced material weight. Analytical results predict the compressed column moments at the onset of the column plastic hinge formation well. The analytical hysteretic energy distribution in the first story column agrees very well with the observed inelastic actions developed in the four specimens. The detailed frame response analyses and the test results confirm that the assumptions made in developing the proposed column capacity design method are reasonable. Copyright © 2009 John Wiley & Sons, Ltd.     

Elastk-plastic dynamic analysis of structures using known elastic solutions

A numerical method is shown to analyse the dynamic elastic-plastic responses of those structures with known elastic solutions. The displacement at one point at time t caused by a unit load applied at another point at zero time, called dynamic influence coefficient, is calculated from the known elastic solutions. Incremental plastic strain is accounted for by a set of additional incremental loads, so the stiffness matrix and the eigenvectors do not vary with time. From the incremental load including that caused by the incremental plastic strain, the displacement vs. time of the structure is obtained. This method is applied to simply supported beams with bilinear stress-strain relations with different strain-hardening rates and to a simply supported elastic-ideally plastic rectangular plate. This procedure can be extended to structures with no available known analytical elastic solutions. For these structures, the elastic solutions can be obtained by the finite element method.     

Static inelastic analysis of RC shear walls

A macro-model of a reinforced concrete (RC) shear wall is developed for static inelastic analysis. The model is composed of RC column elements and RC membrane elements. The column elements are used to model the boundary zone and the membrane elements are used to model the wall panel. Various types of constitutive relationships of concrete could be adopted for the two kinds of elements. To perform analysis, the wall is divided into layers along its height. Two adjacent layers are connected with a rigid beam. There are only three unknown displacement components for each layer. A method called single degree of freedom compensation is adopted to solve the peak value of the capacity curve. The post-peak stage analysis is performed using a forced iteration approach. The macro-model developed in the study and the complete process analysis methodology are verified by the experimental and static inelastic analytical results of four RC shear wall specimens. Supported by: National Natural Science Foundation of China, Grant number 59895410     

Convergence and stability of step-by-step integration for model with negative-stiffness

The convergence and stability of step-by-step integration schemes used in the inelastic dynamic analysis of structures and their corresponding criteria were studied for a restoring force model with negative-stiffness. Convergence conditions and stability conditions 1, 2 or 3 were established. The numerical stability of the integration under negative-stiffness belongs to the category of relative stability; consequently, the concepts and the conclusions concerning numerical stability in the case of positive-stiffness (which belongs to absolute stability) cannot be used. Research into several step-by-step integration methods usually employed in inelastic dynamic analysis has shown great differences in numerical stability for models with negative-stiffness as compared with positive-stiffness models. The central difference method is convergent and unconditionally stable in the case of negative-stiffness, though it is only conditionally stable in the case of positive-stiffness. The Houbolt method satisfies the requirement for convergence; its stability, however, depends not only on the integration step size Δt but also on the stiffness ratio β for the model with negative-stiffness, unlike the unconditional stability for the model with positive-stiffness. The Newmark constant acceleration method is convergent and unconditionally stable in the case of negative-stiffness just like it is in the case of positive-stiffness.     

Estimation of inelastic deformation demands in multistorey RC frame buildings

Estimation of peak inelastic deformation demands is a key component of any displacement-based procedure for earthquake-resistant design of new structures or for seismic evaluation of existing structures. On the basis of the results of over a thousand non-linear dynamic analyses, rules are developed for the estimation of mean and upper-characteristic peak inelastic interstorey drifts and member chord rotations in multistorey RC frame buildings, either bare or infilled in all storeys but the first. For bare frame structures, mean inelastic deformation demands can be estimated from a linear, equivalent static, or preferably multimodal response spectrum analysis with 5 per cent damping and with the RC members considered with their secant stiffness at yielding. 95 per cent characteristic values can be estimated as multiples of the mean deformations. For open-first-storey buildings, the linear analysis can be equivalent static, with the infills modelled as rigid bidiagonal struts and all RC members considered with their secant stiffness to yielding. Copyright © 1999 John Wiley & Sons, Ltd.     

Biaxial effects in modelling earthquake response of R/C structures

Recent studies reveal that R/C structural members subjected to biaxial flexure due to two-dimensional earthquake excitation can deform much more than would be predicted by conventional one-dimensional response analysis. The biaxial flexure may therefore have a significant effect on the dynamic collapse process of structures subjected to intense ground motions. The present paper is intended to develop a new formulation of the two-dimensional restoring force model of R/C columns acted upon by biaxial bending moments, and to discuss the dynamic response properties of R/C structures. The model considered is a two-dimensional extension of various non-linear models for one-dimensional response analysis, including the degrading trilinear stiffness model which is one of the simpler idealizations of the restoring force characteristics of flexural-failure-type R/C structures. The modelling validity is then examined by comparison with experimental data on the biaxial bending behaviour of R/C columns. Calculations are made to study the role of different system properties on the influence of inelastic biaxial bending on the dynamic structural response. It is shown that the inelastic biaxial effect is generally significant and, in some cases, critical in the case of R/C structures with stiffness-degrading properties, while the effect is not so important for the non-degrading inelastic cases.     

Non-linear seismic analysis of base-isolated RC frame structures

In this paper, seismic analysis of plane RC frame structures with High Damping Rubber Bearings (HDRBs) base-isolation systems is performed in the non linear range. For RC members, a modified version of hysteretic Park model is used. For HDRB isolators, a new hysteretic model is presented, which is able to accurately predict the mechanical response in the large strain range. The dynamic equilibrium equations are solved making use, at each time step, of a block iterative Newton–Raphson scheme: the frame is divided into superelements (beams and columns) with master nodes at the extremities and internal local nodes for the computation of relations between end moments and relative rotations at superelement extremities. The effectiveness of HDRB base-isolation systems to reduce inelastic deformations in the RC superstructures is investigated through some numerical examples. Copyright © 1999 John Wiley & Sons, Ltd.     

Normalized residual displacement spectra for post-mainshock assessment of structures subjected to aftershocks

Residual displacement, as a significant measure of structural inelasticity, is effectively used in post-earthquake seismic assessment of structures. This demand can be considered for seismic evaluation of structures under multiple earthquakes. This study introduces a simple and novel index to predict the residual displacement of mainshock-damaged structures against subsequent aftershock. The proposed index is defined as a ratio between residual displacement of damaged structures against aftershock and peak inelastic displacement of intact structures under mainshock. In this study, constantstrength spectra based on the index are developed considering the effects of important structural characteristics and also significant seismic parameters. Moreover, analytical equations are presented to predict the proposed index for bi-linear single-degree-of-freedom(SDOF) systems considering both the effects of positive and negative polarities of aftershock. Furthermore, an equation is suggested to estimate the peak inelastic displacement of intact systems under mainshock, which is required to compute the index.     

Floor response spectra in RC frame structures designed according to Eurocode 8

Nonstructural components (NSCs) should be subjected to a careful and rational seismic design, in order to reduce the economic loss and to avoid threats to the life safety, as well as what concerns structural elements. The design of NSCs is based on the evaluation of the maximum inertia force, which is related to the floor spectral accelerations. The question arises as to whether Eurocode 8 is able to predict actual floor response spectral accelerations occurring in structures designed according to Eurocode 8. A parametric study is conducted on five RC frame structures in order to evaluate the floor response spectra. The structures, designed according to Eurocode 8, are subjected to a set of earthquakes, compatible with the design response spectrum. Time-history analyses are performed both on elastic and inelastic models of the considered structures. Eurocode formulation for the evaluation of the seismic demand on NSCs does not well fit the numerical results. Some comments on the target spectrum provided by AC 156 for the seismic qualification of NSC are also included.     

基于向量式有限元的黏滞阻尼减震结构抗竖向连续倒塌动力反应分析

向量式有限元是以向量力学为基础的一种新的结构分析方法,在处理结构大变形等复杂行为时具有较大的优势。基于向量式有限元理论建立了黏滞阻尼单元,对附加黏滞阻尼器的平面钢框架结构进行了抗竖向连续倒塌动力分析,结合拆除构件法,采用MATLAB编制可以考虑初始变形的瞬时卸载法程序,实现结构在构件拆除前的静力分析和构件拆除后动力分析的全过程统一。研究了阻尼器布置位置和参数在结构抗竖向连续倒塌中的性能需求,以失效点竖向位移时程曲线、梁端转角、动力放大系数和结构塑性铰分布为参考指标,对比分析布置阻尼器前后钢框架结构的抗连续倒塌能力。结果表明向量式有限元是一种研究结构竖向连续倒塌动力响应的有效方法,合理布置阻尼器能够有效控制剩余结构的变形和振动,降低构件内力,减少塑性铰个数,较大地提高结构的抗竖向连续倒塌能力。     

基于OpenSees的防屈曲支撑加固钢筋混凝土框架数值模拟

提出了一种既有钢筋混凝土框架结构的抗震加固方法,该法采用防屈曲支撑提高框架结构体系的水平承载力和耗能能力,利用外包钢进一步提高柱子的抗弯和抗剪承载力。采用开源有限元程序OpenSees,分别建立空钢筋混凝土框架和防屈曲支撑加固钢筋混凝土框架的分析模型,对2榀钢筋混凝土框架的抗震性能进行模拟。防屈曲支撑采用了弹塑性桁架单元模型,加固框架柱混凝土考虑了外包钢的约束作用。将分析结果与拟静力试验结果进行比较,以检验分析模型的准确性,以及研究防屈曲支撑和外包钢对混凝土框架抗震性能的影响。分析结果表明,数值模拟与试验结果吻合较好,验证了基于OpenSees建立的数值模型的准确性;外包钢有效改善了框架柱的抗弯承载力和变形能力;防屈曲支撑显著提高了加固框架体系的水平刚度、水平承载力和耗能能力。     

An efficient fiber beam-column element considering flexure–shear interaction and anchorage bond-slip effect for cyclic analysis of RC structures

In this paper, a fiber beam-column element considering flexure–shear interaction and bond-slip effect is developed for cyclic analysis of reinforced concrete (RC) structures. The element is based on conventional displacement-based Timoshenko beam theory, where the transverse shear deformation is included, and adopts the fiber model to describe the section force–deformation behavior. In the fiber model, shear deformation is assumed to be uniformly distributed along the section and is only resisted by concrete, thus the multi-dimensional concrete damage model is used for concrete fibers and therefore flexure–shear interaction is reflected naturally at the material level. Meanwhile, to account for the significant bond-slip effect at critical regions, the anchorage slip of bars at these regions is analytically derived. Then it is used to modify the uniaxial stress–strain model for steel fibers by assuming that the total strain can be treated as the sum of the bar deformation and anchorage slip, therefore the bond-slip effect is implicitly but simply represented. To validate the proposed element, a series of RC member and structure tests under cyclic loading are simulated. The results indicate that the proposed element can predict cyclic responses of RC structures, and can be used as a reliable tool for analysis of RC structures.     

Seismic performance evaluation of steel arch bridges against major earthquakes. Part 1: dynamic analysis approach

In this study the inelastic behavior of steel arch bridges subjected to strong ground motions from major earthquakes is investigated by dynamic analyses of a typical steel arch bridge using a three‐dimensional (3D) analytical model, since checking seismic performance against severe earthquakes is not usually performed when designing such kinds of bridge. The bridge considered is an upper‐deck steel arch bridge having a reinforced concrete (RC) deck, steel I‐section girders and steel arch ribs. The input ground motions are accelerograms which are modified ground motions based on the records from the 1995 Hyogoken‐Nanbu earthquake. Both the longitudinal and transverse dynamic characteristics of the bridge are studied by investigation of time‐history responses of the main parameters. It is found that seismic responses are small when subjected to the longitudinal excitation, but significantly large under the transverse ground motion due to plasticization formed in some segments such as arch rib ends and side pier bases where axial force levels are very high. Finally, a seismic performance evaluation method based on the response strain index is proposed for such steel bridge structures. Copyright © 2004 John Wiley & Sons, Ltd.     

Generalized force vectors for multi‐mode pushover analysis

A generalized pushover analysis (GPA) procedure is developed for estimating the inelastic seismic response of structures under earthquake ground excitations. The procedure comprises applying different generalized force vectors separately to the structure in an incremental form with increasing amplitude until a prescribed seismic demand is attained for each generalized force vector. A generalized force vector is expressed as a combination of modal forces, and simulates the instantaneous force distribution acting on the system when a given response parameter reaches its maximum value during dynamic response to a seismic excitation. While any response parameter can be selected arbitrarily, generalized force vectors in the presented study are derived for maximum interstory drift parameters. The maximum value of any other response parameter is then obtained from the envelope of GPAs results. Each nonlinear static analysis under a generalized force vector activates the entire multi‐degree of freedom effects simultaneously. Accordingly, inelastic actions develop in members with the contribution of all ‘instantaneous modes’ in the nonlinear response range. Target seismic demands for interstory drifts at the selected stories are calculated from the associated drift expressions. The implementation of the proposed GPA is simpler compared with nonlinear response history analysis, whereas it is less demanding in computational effort when compared with several multi‐mode adaptive nonlinear static procedures. Moreover, it does not suffer from the statistical combination of inelastic modal responses obtained separately. The results obtained from building frames have demonstrated that GPA is successful in estimating maximum member deformations and member forces with reference to the response history analysis. When the response is linear elastic, GPA and response spectrum analysis produce identical results. Copyright © 2010 John Wiley & Sons, Ltd.