Inelastic displacement demand of bridge columns considering shear–flexure interaction

Reinforced concrete bridge columns exhibit complex hysteretic behavior owing to combined action of shear, bending moment, and axial force under multi‐directional seismic shakings. The inelastic displacement of columns can be increased by shear–flexure interaction (SFI). This paper develops a simple yet reliable demand model for estimating the inelastic displacement and ductility based on the nonlinear time history analyses of 24 full‐size columns subject to a suite of near‐fault ground motions. A coupled hysteretic model is used to simulate the shear‐flexure interactive (SFI) behavior of columns and the accumulated material damage during loading reversals, including pinching, strength deterioration, and stiffness softening. Guided by rigorous dimensional analysis, the inelastic displacement responses of bridge columns are presented in dimensionless form showing remarkable order. A dimensionless nonlinearity index is derived taking into account of the column strength, ground motion amplitude, and softening or hardening post‐yield behavior. Strong correlation is revealed between the normalized inelastic displacement and the dimensionless structure‐to‐pulse frequency, the dimensionless nonlinearity index as well as the aspect ratio. Two regressive equations for displacement and ductility demands are proposed and validated against the simulation results. The SFI effects are discussed and included explicitly through the aspect ratio in the proposed model. This study offers a new way to realistically predict the inelastic displacement of columns directly from structural and ground motion characteristics. Copyright © 2010 John Wiley & Sons, Ltd.     

Composed analytical models for seismic assessment of reinforced concrete bridge columns

This paper presents general composed analytical models to predict the behavior of reinforced concrete (RC) bridge columns. The analytical models were developed in OpenSees to represent the common hysteretic behavior of RC bridge columns. The proposed composed models can accommodate flexure failure, flexure‐shear failure, and pure shear failure, which are observed in existing RC bridge piers. The accuracy of the models was verified using data from the static cyclic‐loading experiments of 16 single columns and one multi‐column bent and dynamical experiment from two pseudo‐dynamic tests. The results showed that the analytical models could simulate the nonlinear behavior until the post‐failure behavior, including the strength degradation, the buckling of the reinforcement, and the pinching effect. Therefore, a global view of the behavior of reinforcement concrete is prescribed as simply as possible from the academic perspective, and these models are expected to provide sufficient accuracy when applied in engineering practice. Copyright © 2014 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.     

Implications of seismic pounding on the longitudinal response of multi-span bridges-an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach, Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is essential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

Experimental research and finite element analysis of bridge piers failed in flexure-shear modes

In recent earthquakes, a large number of reinforced concrete （RC） bridges were severely damaged due to mixed flexure-shear failure modes of the bridge piers. An integrated experimental and finite element （FE） analysis study is described in this paper to study the seismic performance of the bridge piers that failed in flexure-shear modes. In the first part, a nonlinear cyclic loading test on six RC bridge piers with circular cross sections is carried out experimentally. The damage states, ductility and energy dissipation parameters, stiffness degradation and shear strength of the piers are studied and compared with each other. The experimental results suggest that all the piers exhibit stable flexural response at displacement ductilities up to four before exhibiting brittle shear failure. The ultimate performance of the piers is dominated by shear capacity due to significant shear cracking, and in some cases, rupturing of spiral bars. In the second part, modeling approaches describing the hysteretic behavior of the piers are investigated by using ANSYS software. A set of models with different parameters is selected and evaluated through comparison with experimental results. The influences of the shear retention coefficients between concrete cracks, the Bauschinger effect in longitudinal reinforcement, the bond-slip relationship between the longitudinal reinforcement and the concrete and the concrete failure surface on the simulated hysteretic curves are discussed. Then, a modified analysis model is presented and its accuracy is verified by comparing the simulated results with experimental ones. This research uses models available in commercial FE codes and is intended for researchers and engineers interested in using ANSYS software to predict the hysteretic behavior of reinforced concrete structures.     

CFRP布约束增强高强混凝土柱抗震性能数值分析

采用地震工程开源模拟软件OpenSees（Open System for Earthquake Engineering Simulation）对CFRP（Carbon Fiber Reinforced Polymer,碳纤维增强复合材料）布加固高强钢筋混凝土方柱的抗震性能进行了数值分析。采用Steel02Material和Concrete02Material材料本构模型模拟了CFRP布加固高强混凝土方柱的抗震性能;在此基础上,进一步研究了轴压比和剪跨比这2个因素对试件抗震性能的影响。将所得数值分析结果与相同条件下的试验结果对比后发现：基于Steel02 Material和Concrete02 Material材料本构,利用OpenSees,可以较好地模拟CFRP布加固高强混凝土方柱的抗震性能,并且与试验结果（滞回曲线、骨架曲线、水平承载力和位移延性系数）能够较好地吻合,从而说明该数值分析方法还可以准确地反映出轴压比和剪跨比对高强混凝土柱抗震性能的影响规律。     

A distributed shear and flexural flexibility model with shear–flexure interaction for R/C members subjected to seismic loading

A beam–column‐type finite element for seismic assessment of reinforced concrete (R/C) frame structures is presented. This finite element consists of two interacting, distributed flexibility sub‐elements representing inelastic flexural and shear response. Following this formulation, the proposed model is able to capture spread of flexural yielding, as well as spread of shear cracking, in R/C members. The model accounts for shear strength degradation with inelastic curvature demand, as well as coupling between inelastic flexural and shear deformations after flexural yielding, observed in many experimental studies. An empirical relationship is proposed for evaluating the average shear distortion of R/C columns at the onset of stirrup yielding. The proposed numerical model is validated against experimental results involving R/C columns subjected to cyclic loading. It is shown that the model can predict well the hysteretic response of R/C columns with different failure modes, i.e. flexure‐critical elements, elements failing in shear after flexural yielding, and shear‐critical R/C members. Copyright © 2008 John Wiley & Sons, Ltd.     

Effect of abutment modeling on the seismic response of bridge structures

Abutment behavior significantly influences the seismic response of certain bridge structures. Specifically in the case of short bridges with relatively stiff superstructures typical of highway overpasses, embankment mobilization and inelastic behavior of the soil material under high shear deformation levels dominate the response of the bridge and its column bents. This paper investigates the sensitivity of bridge seismic response with respect to three different abutment modeling approaches. The abutment modeling approaches are based on three increasing levels of complexity that attempt to capture the critical components and modes of abutment response without the need to generate continuum models of the embankment, approach, and abutment foundations. Six existing reinforced concrete bridge structures, typical of Ordinary Bridges in California, are selected for the analysis. Nonlinear models of the bridges are developed in OpenSees. Three abutment model types of increasing complexity are developed for each bridge, denoted as roller, simplified, and spring abutments. The roller model contains only single-point constraints. The spring model contains discrete representations of backfill, bearing pad, shear key, and back wall behavior. The simplified model is a compromise between the efficient roller model and the comprehensive spring model. Modal, pushover, and nonlinear dynamic time history analyses are conducted for the six bridges using the three abutment models for each bridge. Comparisons of the analysis results show major differences in mode shapes and periods, ultimate base shear strength, as well as peak displacements of the column top obtained due to dynamic excitation. The adequacy of the three abutment models used in the study to realistically represent all major resistance mechanisms and components of the abutments, including an accurate estimation of their mass, stiffness, and nonlinear hysteretic behavior, is evaluated. Recommendations for abutment modeling are made.     

基于OpenSees的钢筋混凝土桥墩拟静力试验数值分析

以4个呈弯曲破坏形态的圆形钢筋混凝土桥墩的拟静力试验结果为依据,基于OpenSees中的Beamwith Hinges Element单元,建立了相应的桥墩滞回分析纤维单元模型。由模拟结果与试验结果对比可知,所建立的纤维单元模型对桥墩的骨架曲线及滞回曲线都有良好的模拟效果,且能体现桥墩在反复加载过程中刚度、强度退化现象,表明了模型的有效性。     

Implications of seismic pounding on the longitudinal response of multi-span bridges - an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach. Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is cssential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

A rate‐dependent constitutive model of high damping rubber bearings: modeling and experimental verification

In this study, a constitutive model of high damping rubber bearings (HDRBs) is developed that allows the accurate representation of the force–displacement relationship including rate‐dependence for shear deformation. The proposed constitutive model consists of two hyperelastic springs and a nonlinear dashpot element and expresses the finite deformation viscoelasticity laws based on the classical Zener model. The Fletcher–Gent effect, manifested as high horizontal stiffness at small strains and caused by the carbon fillers in HDRBs, is accurately expressed through an additional stiffness correction factor α in the novel strain energy function. Several material parameters are used to simulate the responses of high damping rubber at various strain levels, and a nonlinear viscosity coefficient η is introduced to characterize the rate‐dependent property. A parameter identification scheme is applied to the results of the multi‐step relaxation tests and the cyclic shear tests, and a three‐dimensional function of the nonlinear viscosity coefficient η with respect to the strain, and strain rate is thus obtained. Finally, to investigate the accuracy and feasibility of the proposed model for application to the seismic response assessment of bridges equipped with HDRBs, an improved real‐time hybrid simulation (RTHS) test system based on the velocity loading method is developed. A single‐column bridge was used as a test bed and HDRBs was physically tested. Comparing the numerical and RTHS results, advantage of the proposed model in the accuracy of the predicted seismic response over comparable hysteretic models is demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.     

Shake-table tests and numerical simulation of an innovative isolation system for highway bridges

Damage investigation of small to medium-span highway bridges in Wenchuan earthquake revealed that typical damage of these bridges included: sliding between laminated-rubber bearings and bridge girders, concrete shear keys failure, excessive girder displacements and even span collapse. However, the bearing sliding could actually act as a seismic isolation for piers, and hence, damage to piers for these bridges was minor during the earthquake. Based on this concept, an innovative solation system for highway bridges with laminated-rubber bearings is developed. The system is comprised of typical laminated-rubber bearings and steel dampers. Bearing sliding is allowed during an earthquake to limit the seismic forces transmitting to piers, and steel dampers are applied to restrict the bearing displacements through hysteretic energy dissipation. As a major part of this research, a quarter-scale, two-span bridge model was constructed and tested on the shake tables to evaluate the performance of this isolation system. The bridge model was subjected to a Northridge and an artificial ground motion in transverse direction. Moreover, numerical analyses were conducted to investigate the seismic performance of the bridge model. Besides the test bridge model, a benchmark model with the superstructure fixed to the substructure in transverse direction was also included in the numerical analyses. Both the experimental and the numerical results showed high effectiveness of this proposed isolation system in the bridge model. The system was found to effectively control the pier-girder relative displacements, and simultaneously, protect the piers from severe damage. Numerical analyses also validated that the existing finite element methods are adequate to estimate the seismic response of bridges with this isolation system.     

Modelling of R/C members accounting for shear failure localisation: Hysteretic shear model

Reinforced concrete (R/C) frame buildings designed according to older seismic codes represent a large part of the existing building stock worldwide. Their structural elements are often vulnerable to shear or flexure‐shear failure, which can eventually lead to loss of axial load resistance of vertical elements and initiate vertical progressive collapse of a building. In this study, a hysteretic model capturing the local shear response of shear‐deficient R/C elements is described in detail, with emphasis on post‐peak behaviour; it differs from existing models in that it considers the localisation of shear strains after the onset of shear failure in a critical length defined by the diagonal failure planes. Additionally, an effort is made to improve the state of the art in post‐peak shear response modelling, by compiling the largest database of experimental results for shear and flexure‐shear critical R/C columns cycled well beyond the onset of shear failure and/or up to the onset of axial failure, and developing empirical relationships for the key parameters defining the local backbone post‐peak shear response of such elements. The implementation of the derived local hysteretic shear model in a computationally efficient beam‐column finite element model with distributed shear flexibility, which accounts for all deformation types, will be presented in a companion paper.     

A simplified analytical model for U-shaped steel dampers considering horizontal bidirectional deformation

Hysteresis steel dampers are widely used in earthquake-resistant structures, where some of them are anisotropic and capable of sustaining earthquake-induced bidirectional deformation. In this paper, a simplified analytical model is proposed for simulating the hysteretic behavior of U-shaped steel dampers with horizontal bidirectional deformation. The proposed model is composed of a series of shear springs with different nonlinear characteristics in a radial configuration, and the Menegotto–Pinto hysteresis model is employed to represent the hysteretic characteristics of the springs. The mechanical and shape-related parameters of the hysteresis model are set according to the multi-directional deformation characteristics of steel dampers. With the aim of validating the effectiveness and applicability of the analytical model, a U-shaped steel damper was used as an example. The pseudo-static hysteretic characteristics of the steel damping element were analyzed and the elasto-plastic seismic response of a curved bridge featuring a steel hysteresis device was investigated. The results showed that the proposed model is sufficiently accurate to simulate the hysteretic behavior of U-shaped steel dampers, and thus provides a practical method to assess U-shaped steel dampers through seismic response analysis.     

采用板式橡胶支座的连续斜梁桥横向抗震行为研究

为了提高采用板式橡胶支座的斜梁桥横向抗震能力,揭示其在不同设计参数下的横向抗震行为,考虑板式橡胶支座的滑移、钢筋混凝土挡块的滞回力学性能、桥台-背土效应等非线性因素,采用OpenSEES建立某连续斜梁桥的三维分析模型,提出支座位移评价指标、主梁平面转角指标、墩柱曲率延性指标和抗剪指标,研究不同挡块强度和间隙组合下桥梁的横向抗震性能。研究表明:同时增大挡块强度和间隙,总体上会降低支座的横向变形,但会增加其纵向变形;挡块强度越高,主梁的横向位移有所下降,但平面转角越大,对两侧桥台处的支座抗剪越不利;挡块强度越高,间隙越小,墩柱越有可能进入弹塑性状态。在本文桥例中,当挡块强度取40%支反力,间隙取0.08m时,所有抗震指标都可满足规范要求。     

不同加载路径对钢筋混凝土L形柱抗震性能的影响

为了进一步探讨复杂加载路径下钢筋混凝土L形柱的受力性能,采用基于有限单元柔度法纤维模型梁柱单元,对忽略剪切和扭转影响的钢筋混凝土L形柱在不同加载路径下的抗震性能进行了计算机模拟分析,研究了不同加载路径对钢筋混凝土L形柱承载力、延性、累积滞回耗能等的影响。结果表明,现有钢筋混凝土L形柱抗震性能评定方法应作适当调整,以考虑加载路径对评定结果的影响。     

密肋壁板结构宏观模型及非线性时程反应分析

采用SAP程序中的Link单元进行了密肋壁板结构非线性时程反应分析。推导了Link单元的刚度矩阵,确定了相对转动中心高度。并结合钢筋混凝土柱轴向恢复力模型和密肋复合墙体水平抗侧恢复力模型,给出了Link单元竖向和水平连接弹簧非线性力-位移关系的计算公式。采用Link单元建立了密肋壁板结构宏观有限元分析模型,并对1/10比例振动台模型试验进行了非线性时程反应分析。结果表明:计算结果与试验结果吻合良好,这说明采用Link单元可以较好的模拟密肋壁板结构的动力非线性行为。     

多维地震下考虑桩-土相互作用的曲线桥地震响应分析

为研究曲线桥梁在多维地震激励下考虑桩-土动力相互作用的地震响应特性,本文建立了空间桩-土脱离、摩阻和土体压缩非线性理论分析模型。为简化计算将该非线性弹簧模型进行线性化处理,结合有限元ANSYS分析平台建立了黄土场地的曲线桥仿真分析模型,对考虑桩-土相互作用的曲线桥进行了多维多工况数值分析,对比研究了曲线主梁跨中弯矩、墩底剪力和弯矩及桥墩顶位移的地震响应。结果表明:考虑桩-土相互作用的曲线桥梁主梁跨中内力与地震波输入方向密切相关,三维地震作用下主梁内力最大;各工况地震荷载作用下桥墩底部径向剪力响应比切向剪力响应大很多,而桥墩径向弯矩比切向弯矩略小;同一工况下不同桥墩顶切向位移响应大小相当,而径向位移差异较大。在进行非规则曲线桥梁抗震设计时,应充分考虑多维和单维地震激励输入工况。     

Evaluation of code criteria for bridges with unequal pier heights

One of the challenges associated with Eurocode 8 and AASHTO-LRFD is predicting the failure of irregular bridges supported by piers of unequal heights. EC8 currently uses “moment demand-to-moment capacity” ratios to somewhat guarantee simultaneous failure of piers on bridges, while AASHTO-LRFD relies on the relative effective stiffness of the piers. These conditions are not entirely valid, in particular for piers with a relative height of 0.5 or less, where a possible combination of flexure and shear failure mode may occur. In this case, the shorter piers often result in brittle shear failure, while the longer piers are most likely to fail due to flexure, creating a combination of different failure modes experienced by the bridge. To evaluate the adequacy of EC8 design procedures for regular seismic behavior, various irregular bridges are simulated through a non-linear pushover analysis using shear-critical fiber-based beam-column elements. The paper investigates the behavior of irregular monolithic and bearing-type bridges experiencing different failure modes, and proposes different methods for regularizing the bridge performance to balance damage. The ultimate aim is to obtain a simultaneous or near-simultaneous failure of all piers irrespective of the different heights and failure mode experienced.     

Optimum hysteretic damper design for multi-story timber structures represented by an improved pinching model

Timber structures are characterized by a pinching phenomenon that leads to reduced dissipative capability. A few hysteretic models have been proposed to simulate the mechanical behavior of timber structures, among which the one composed of a bilinear element and a slip element in parallel has been popular in practice. Based on this model, this paper expands on the existing seismic control design methodology to determine the capacity of hysteretic dampers for multi-story timber structures. The equivalent linearization method for a single-degree-of-freedom timber structure with added hysteretic damper is established and is verified through nonlinear timber history analysis over a wide range of structural parameters. The design formulas for determining the damper capacity for a multi-degree-of-freedom system are derived, based on the concept of adjusting the distribution of equivalent stiffness of structure. The seismic control design is applied to many buildings with randomly generated parameters and the effectiveness is confirmed through a nonlinear time history analysis with four sets of seismic excitations. An extended study has shown that the shear force pattern plays an important role in the seismic control design results and thus the performance of structures. The effectiveness of the control of residual deformations by adding dampers is also studied.