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 of long curved bridge structures: Experimental model studies

This paper presents the results of a shaking table study conducted on the seismic behaviour of curved reinforced concrete bridge structures of the type used in highway interchanges. A series of representational 1/30th scale models was constructed in microconcrete to study the effects of both linear and non-linear dynamic behaviour, the non-linearity including sliding and impacting at the expansion joints and ductility in the columns. Each model was subjected to a series of increasingly severe simulated earthquakes in the longitudinal and transverse directions, both with and without the vertical component. Response data were recorded in the form of selected displacement time-histories which were subsequently used as control data in a companion theoretical study. Each model was eventually taken to failure which consisted primarily of extensive damage at the expansion joints. The paper concludes with general observations on the seismic behaviour of long-span long-period curved bridges, and emphasizes the sensitivity of this behaviour to the location and design of the joints.     

INELASTIC SEISMIC RESISTANCE OF REINFORCED CONCRETE STACK-LIKE STRUCTURES

A method is presented to quantify the inelastic seismic resistance of reinforced concrete stack-like structures by non-linear earthquake analysis. The deformed configuration of stack is idealized as an assemblage of beam elements and actual stress–strain relationships of concrete and reinforcing steel are used to evaluate element matrices. Repeated non-linear analyses are performed by gradually increasing the intensity of acceleration time histories to a level where collapse of the stack is observed in primary stresses. The set of time histories thus obtained are then used to define the ultimate intensity of ground motion that the stack can sustain if inelastic deformations are permitted. A procedure is presented to quantify the difference between inelastic seismic resistance and elastic seismic resistance in terms of displacement ductility capacity factors. For seismic design using available inelastic resistance, values of curvature ductility factor demand for the cross-sections of stacks are also presented. © 1997 by John Wiley & Sons, Ltd.     

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.     

Cyclic behaviour of interior beam–column joints reinforced with plain bars

The seismic damages commonly observed on beam–column joints of old reinforced concrete structures, built with plain bars and without proper detailing, justifies the need to further study the behaviour of this type of structures. The response of these structures when loaded cyclically, as occurs during the earthquakes, is partially controlled by the bond properties between the reinforcing bars and the surrounding concrete. This paper presents the results of an experimental campaign of unidirectional cyclic tests carried out on six full‐scale beam–column joints built with plain bars. These joint specimens are representative of existing reinforced concrete structures, that is, built without adequate reinforcement detailing for seismic demands. For comparison, an additional specimen is built with deformed bars and tested. The seven specimens are designed and detailed to allow the investigation of the influence of bond properties, lapping of the longitudinal bars in columns and beams, bent‐up bars in the beams, slab contribution and concrete strength. The lateral force–drift relationships, global dissipated energy evolution, contribution of the joint, beams and columns to the global dissipated energy, ductility, equivalent damping, final damage observed, homogenized reinforced concrete damage index, displacement components, curvature evolutions and Eurocode requirements are presented and discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

CFRP加固高强混凝土柱改善延性的试验研究

通过对九根高强混凝土柱在低周反复荷载作用下受力性能的试验研究，探讨了碳纤维布对高强混凝土柱延性的改善作用，包括加固后柱的破坏形态、滞回曲线、骨架曲线、延性系数等性能特点。试验结果表明，采用碳纤维布横向缠绕高强混凝土柱可显著提高柱的延性，改善柱的抗震性能。     

A displacement‐based seismic design procedure for RC buildings and comparison with EC8

A procedure for displacement‐based seismic design (DBD) of reinforced concrete buildings is described and applied to a 4‐storey test structure. The essential elements of the design procedure are: (a) proportioning of members for gravity loads; (b) estimation of peak inelastic member deformation demands in the so‐designed structure due to the design (‘life‐safety’) earthquake; (c) revision of reinforcement and final detailing of members to meet these inelastic deformation demands; (d) capacity design of members and joints in shear. Additional but non‐essential steps between (a) and (b) are: (i) proportioning of members for the ULS against lateral loads, such as wind or a serviceability (‘immediate occupancy’) earthquake; and (ii) capacity design of columns in flexure at joints. Inelastic deformation demands in step (b) are estimated from an elastic analysis using secant‐to‐yield member stiffnesses. Empirical expressions for the deformation capacity of RC elements are used for the final proportioning of elements to meet the inelastic deformation demands. The procedure is applied to one side of a 4‐storey test structure that includes a coupled wall and a two‐bay frame. The other side is designed and detailed according to Eurocode 8. Major differences result in the reinforcement of the two sides, with significant savings on the DBD‐side. Pre‐test calculations show no major difference in the seismic performance of the two sides of the test structure. Copyright © 2001 John Wiley & Sons, Ltd.     

Seismic performance of a 3D full‐scale high‐ductile steel–concrete composite moment‐resisting frame—Part II: Test results and analytical validation

This paper presents the results of a multi‐level pseudo‐dynamic seismic test program that was performed to assess the performance of a full‐scale three‐bay, two‐storey steel–concrete composite moment‐resisting frame built with partially encased composite columns and partial‐strength beam‐to‐column joints. The system was designed to develop a ductile response in the joint components of beam‐to‐column joints including flexural yielding of beam end plates and shear yielding of the column web panel zone. The ground motion producing the damageability limit state interstorey drift caused minor damage while the ultimate limit state ground motion level entailed column web panel yielding, connection yielding and plastic hinging at the column base connections. The earthquake level chosen to approach the collapse limit state induced more damage and was accompanied by further column web panel yielding, connection yielding and inelastic phenomena at column base connections without local buckling. During the final quasi‐static cyclic test with stepwise increasing displacement–amplitudes up to an interstorey drift angle of 4.6%, the behaviour was ductile although cracking of beam‐to‐end‐plate welds was observed. Correlations with numerical simulations taking into account the inelastic cyclic response of beam‐to‐column and column base joints are also presented in the paper together. Inelastic static pushover and time history analysis procedures are used to estimate the structural behaviour and overstrength factors of the structural system under study. Copyright © 2008 John Wiley & Sons, Ltd.     

地震作用下纤维编织网增强钢筋混凝土柱的抗震性能分析

为了解地震作用下纤维编织网增强钢筋混凝土柱的抗震性能,采用钢筋、混凝土、纤维编织网浇筑纤维编织网增强钢筋混凝土柱,编织网主材为碳、玻璃纤维束;利用电液伺服加载系统为试件加载地震作用,监测相关数据,部分试件置入氯化钠溶液进行多次干湿循环。不同环境下的实验结果显示:纤维编织网层数越多,纤维编织网增强钢筋混凝土柱承载能力越强,抗震性能越好;配箍间距较大时,纤维编织网增强钢筋混凝土柱的抗震性能仅在地震作用的后期呈现较差状态;干湿循环次数越多,纤维编织网增强钢筋混凝土柱承载力越弱,抗震性能越差。对于氯盐环境而言,可增加纤维编织网增强钢筋混凝土柱的抗腐蚀措施改善抗震性能。适当增加纤维编织网的数量、降低配箍间距有利于提升纤维编织网增强钢筋混凝土柱的抗震性能。     

Shaking table tests on a high‐rise RC building model having torsional eccentricity in soft lower storeys

A series of shaking table tests on a 1:12‐scale model using scaled TaftN21E earthquake records were conducted to investigate the seismic performance of a 17‐storey high‐rise reinforced concrete structure with a high degree of torsional eccentricity and soft‐storey irregularities in the bottom two storeys. Based on the analysis of test results, the following conclusions were drawn: (1) the model responded mainly in the coupled mode of translation and torsion or in the torsional mode. Under severe table shaking, the flexible side underwent large inelastic deformation, and the predominant mode of the model changed from the coupled mode to the torsional mode, resulting in greatly increased torsional stiffness, thereby limiting damage in the flexible frame; (2) the shear force and deformation of the flexible side were governed by the torsional behaviour, whereas those of the stiff side were affected mainly by the overturning deformation. The lateral stiffness of the shear wall in the torsional mode was about four times that in the coupled mode because the warping deformation due to torsion counteracted the flexural deformation due to overturning moment in the torsional mode; and (3) the reversed cyclic overturning moments predicted by linear elastic dynamic analysis in the direction transverse to the table excitations contradicted unilateral overturning moments of the serviceability‐level test results, which showed a bias towards tension or compression in the columns. Copyright © 2006 John Wiley & Sons, Ltd.     

反复荷载下混凝土框架柱塑性铰区基于延性的抗剪承载力机理分析

在试验研究的基础上,以框架结构延性设计为目的采用桁架＋拱模型研究了框架柱塑性铰区域抗剪受力机理,分析了,位移延性系数、加载循环次数等因素对框架柱构件塑性铰区域剪切受力性能的影响,并结合试验结果提出了混凝土框架柱塑性铰区域剪切承载力抗震延性设计实用公式,可有效实现结构的延性破坏机制。主要为配合GBJ10-89的修订,该成果已被《混凝土结构设计规范》（GB50010—2003）吸收。     

Experimental and analytical studies on earthquake resisting behaviour of confined concrete block masonry structures

To improve the seismic performance of masonry structures, confined masonry that improves the seismic resistance of masonry structures by the confining effect of surrounding bond beams and tie columns is constructed. This study investigated the earthquake resisting behaviour of confined masonry structures that are being studied and constructed in China. The structural system consists of unreinforced block masonry walls with surrounding reinforced concrete bond beams and tie columns. The characteristics of the structure include: (1) damage to blocks is reduced and brittle failure is avoided by the comparatively lower strength of the joint mortar than that of the blocks, (2) the masonry walls and surrounding reinforced concrete bond beams and tie columns are securely jointed by the shear keys of the tie columns. In this study, wall specimens made of concrete blocks were tested under a cyclic lateral load and simulated by a rigid body spring model that models non‐linear behaviour by rigid bodies and boundary springs. The results of studies outline the resisting mechanism, indicating that a rigid body spring model is considered appropriate for analysing this type of structure. Copyright © 2006 John Wiley & Sons, Ltd.     

型钢高强混凝土柱抗震性能的试验研究

通过14根型钢高强混凝土柱的低周反复加载试验，得到了型钢高强混凝土柱在压、弯、剪共同作用下的主要破坏形态，并探讨了剪跨比、配箍率、混凝土强度对型钢高强混凝土柱滞回曲线、耗能能力以及延性的影响。试验结果表明，型钢高强混凝土柱具有抵御二次地震作用的能力，其抗震性能优于钢筋混凝土柱。     

核心型钢混凝土柱的轴压比限值试验研究

基于界限破坏时的内力平衡条件,推导了核心型钢混凝土柱轴压比限值的理论计算公式,计算分析了配钢率、混凝土强度等级、柱截面尺寸等因素对核心型钢混凝土柱轴压比限值的影响。进行了5个1/2比例模型柱试件的低周反复加载试验,验证了配置核心型钢对提高混凝土柱的抗震性能和轴压比限值的有效性。计算和试验结果表明,在混凝土柱中配置一定数量的核心型钢,可以有效提高轴压比限值。本文建议的方法可以较为合理地确定核心型钢混凝土柱的轴压比限值,供工程实践参考。     

Seismic behavior of outrigger truss-wall shear connections using multiple steel angles

An experimental investigation on the seismic behavior of a type of outrigger truss-reinforced concrete wall shear connection using multiple steel angles is presented. Six large-scale shear connection models, which involved a portion of reinforced concrete wall and a shear tab welded onto a steel endplate with three steel angles, were constructed and tested under combined actions of cyclic axial load and eccentric shear. The effects of embedment lengths of steel angles, wall boundary elements, types of anchor plates, and thicknesses of endplates were investigated. The test results indicate that properly detailed connections exhibit desirable seismic behavior and fail due to the ductile fracture of steel angles. Wall boundary elements provide beneficial confinement to the concrete surrounding steel angles and thus increase the strength and stiffness of connections. Connections using whole anchor plates are prone to suffer concrete pry-out failure while connections with thin endplates have a relatively low strength and fail due to large inelastic deformations of the endplates. The current design equations proposed by Chinese Standard 04G362 and Code GB50011 significantly underestimate the capacities of the connection models. A revised design method to account for the influence of previously mentioned test parameters was developed.     

RC框架结构地震塑性损伤分析

基于经典塑性模型与连续损伤模型,根据广义应力空间塑性力学确定了塑性变形的演化法则,文中发展了一种地震塑性损伤分析方法。用来进行混凝土框架结构的抗震分析,将塑性损伤的本构关系运用于两端具有塑性铰的梁模型,模拟框架结构的梁柱。同时该方法的损伤指数可以确定结构各单元和整体的地震时性能,确定结构极限荷载,算例表明该方法具有可靠的精度。     

Earthquake response analysis of the olive view hospital psychiatric day clinic

The collapse of the Olive View Hospital Psychiatric Day Clinic is studied using three biaxial force-deflection models to represent the columns of the building. These models are: shear collapse, elastic and inelastic. The biaxial models for shear and inelastic behaviour are new developments and are useful for non-linear structural dynamic studies. In the present study, the shear collapse model is intended to represent the actual prototype behaviour. The inelastic model, which is based on a hardening rule of plasticity, is used to study the performance of a hypothetical structure with the same storey shear capacity as the prototype but which exhibits ductile behaviour. The prototype structure had a base storey shear capacity of 25 per cent, and actually failed by shearing of all of the first floor columns. In the present study, the shear collapse model predicted this behaviour even with the El Centro accelerogram as input. This result may have far-reaching significance because many low-rise reinforced concrete buildings which were designed according to recent codes have similar storey shear capacity coefficients and column properties. According to this study, such buildings may collapse even in a moderate earthquake. In the inelastic representation, the structure was found to have a base storey shear capacity of 80 per cent when moment hinging was assumed to occur at the top and bottom of the columns. Even with this high strength capacity, the permanent offset computed from the inelastic model corresponded to a ductility factor of 5 when the Pacoima Dam accelerogram was used as input. On the basis of damage to other structures observed on the site, it seems likely that ground motion of about the Pacoima Dam intensity occurred at Olive View. From this it is concluded that a low-rise ductile frame concrete building, even with this high shear force capacity, may not prove satisfactory for hospital use when subjected to strong ground motion.     

SIMPLE PUSH-OVER ANALYSIS OF ASYMMETRIC BUILDINGS

A simple method for the non-linear static analysis of complex building structures subjected to monotonically increasing horizontal loading (push-over analysis) is presented. The method is designed to be a part of new methodologies for the seismic design and evaluation of structures. It is based on the extension of a pseudo-three-dimensional mathematical model of a building structure into the non-linear range. The structure consists of planar macroelements. For each planar macroelement, a simple bilinear or multilinear base shear–top displacement relationship is assumed. By a step-by-step analysis an approximate relationship between the global base shear and top displacement is computed. During the analysis the development of plastic hinges throughout the building can be monitored. The method has been implemented into a prototype computer program. In the paper the mathematical model, the base shear–top displacement relationships for different types of macroelements, and the step-by-step computational procedure are described. The method has been applied for the analysis of a symmetric and an asymmetric variant of a seven-storey reinforced concrete frame–wall building, as well as for the analysis of a complex asymmetric 21-storey reinforced concrete wall building. The influence of torsion on structural behaviour is discussed. © 1997 by John Wiley & Sons, Ltd.     

Effects of column axial force – bending moment interaction on inelastic seismic response of steel frames

It is well known that axial force – bending moment interaction (N–M interaction) affects to a large extent the cyclic inelastic behaviour of structural elements, especially columns in framed structures, with reduction in bending capacity and loss of available ductility. A few studies have also shown that significant inelastic axial shortening affects the response of column elements subjected to medium–high levels of axial loads and cyclic bending. This paper is primarily aimed at evaluating the effects of column N–M interaction on the inelastic seismic response of steel frames. By considering the contemporaneous action of vertical loads, due to gravity, and of horizontal seismic excitation, it is shown that the progressive axial shortening of adjacent columns may differ substantially, thus inducing significant relative settlements at the ends of the connecting beams and, then, remarkable amplifications in beam plastic rotations. An evaluation of additional beam plastic rotations induced by column N–M interaction is carried out for real structures by investigating the inelastic response of steel frames designed according to European standards under horizontal and vertical earthquake excitations. Copyright © 2003 John Wiley & Sons, Ltd.