基于等效框架模型的砌体结构抗震模拟及验证

等效框架模型采用宏观模型来模拟砌体墙在平面内的抗震性能。砌体墙的墙柱和墙梁采用同时考虑轴向弯曲和剪切变形的基于力法的纤维截面进行模拟,且两者的连接视为刚性区域。轴向压缩及弯曲效应在截面纤维模型中考虑,而剪切效应由V-γ剪切恢复力模型表达,弯曲和剪切在单元层面进行耦合。通过统计和分析,确定骨架曲线的计算方法,并基于Ibarra-Krawinkler模型提出剪切恢复力模型。通过算例得出:该模型在单调加载和循环加载下的数值计算结果与试验结果均吻合较好。     

Modelling of R/C members accounting for shear failure localisation: Finite element model and verification

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 computationally efficient member‐type finite element model for the hysteretic response of shear critical R/C frame elements up to the onset of axial failure is presented; it accounts for shear‐flexure interaction and considers, for the first time, the localisation of shear strains, after the onset of shear failure, in a critical length defined by the diagonal failure plane. Its predictive capabilities are verified against experimental results of column and frame specimens and are shown to be accurate not only in terms of total response, but also with regard to individual deformation components. The accuracy, versatility, and simplicity of this finite element model make it a valuable tool in seismic analysis of complex R/C buildings with shear deficient structural elements.     

A nonlinear macroelement model for the seismic analysis of masonry buildings

The macroelement technique for modelling the nonlinear response of masonry panels is particularly efficient and suitable for the analysis of the seismic behaviour of complex walls and buildings. The paper presents a macroelement model specifically developed for simulating the cyclic in‐plane response of masonry walls, with possible applications in nonlinear static and dynamic analysis of masonry structures. The model, starting from a previously developed macroelement model, has been refined in the representation of flexural–rocking and shear damage modes, and it is capable of fairly simulating the experimental response of cyclic tests performed on masonry piers. By means of two internal degrees of freedom, the two‐node macroelement permits to represent the coupling of axial and flexural response as well as the interaction of shear and flexural damage. Copyright © 2013 John Wiley & Sons, Ltd.     

A regularized fiber element model for reinforced concrete shear walls

Reinforced concrete shear walls are used because they provide high lateral stiffness and resistance to extreme seismic loads. However, with the increase in building height, these walls have become slenderer and hence responsible of carrying larger axial and shear loads. Because 2D/3D finite element inelastic models for walls are still complex and computationally demanding, simplified but accurate and efficient fiber element models are necessary to quickly assess the expected seismic performance of these buildings. A classic fiber element model is modified herein to produce objective results under particular loading conditions of the walls, that is, high axial loads, low axial loads, and nearly constant bending moment. To make it more widely applicable, a shear model based on the modified compression field theory was added to this fiber element. Consequently, this paper shows the formulation of the proposed element and its validation with different experimental results of cyclic tests reported in the literature. It was found that in order to get objective responses in the element, the regularization techniques based on fracture energy had to be modified, and nonlinearities because of buckling and fracture of steel bars, concrete crushing, and strain penetration effects were needed to replicate the experimental cyclic behavior. Thus, even under the assumption of plane sections, which makes the element simple and computationally efficient, the proposed element was able to reproduce the experimental data, and therefore, it can be used to estimate the seismic performance of walls in reinforced concrete buildings. Copyright © 2016 John Wiley & Sons, Ltd.     

Coupled shear‐bending formulation for seismic analysis of stacked wood shear wall systems

A summary of the development of a new coupled shear‐bending model for analysis of stacked wood shear walls and multi‐story wood‐frame buildings is presented in this paper. The model focuses on dynamic response of light‐frame wood structures under seismic excitation. The formulation is intended to provide a more versatile option than present pure shear models in that the new model is capable of accurately capturing the overall lateral response of each story diaphragm and separates the inter‐story shear deformation and the deformation associated with rotation of the diaphragm due to rod elongation, which is an analogue to the bending deformation in an Euler–Bernoulli beam model. Modeling the coupling of bending and shear deformation is shown to provide more accurate representation of stacked shear wall system behavior than a pure shear model, particularly for the upper stories in the assembly. The formulation is coupled with the newly developed evolutionary parameter hysteretic model for wood shear walls. Existing data from a shake table test of an isolated three‐story wood shear wall were used to verify the accuracy of the model prediction. The numerical results agreed very well with shake table test measurements. The influence of a continuous rod hold‐down system on the dynamic behavior of the three‐story stacked wood shear wall was also successfully simulated. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Shake table testing of un‐reinforced brick masonry building test model isolated by U‐FREI

This paper presents a detailed study on feasibility of un‐bonded fiber reinforced elastomeric isolator (U‐FREI) as an alternative to steel reinforced elastomeric isolator (SREI) for seismic isolation of un‐reinforced masonry buildings. Un‐reinforced masonry buildings are inherently vulnerable under seismic excitation, and U‐FREIs are used for seismic isolation of such buildings in the present study. Shake table testing of a base isolated two storey un‐reinforced masonry building model subjected to four prescribed input excitations is carried out to ascertain its effectiveness in controlling seismic response. To compare the performance of U‐FREI, same building is placed directly on the shake table without isolator, and fixed base (FB) condition is simulated by restraining the base of the building with the shake table. Dynamic response characteristic of base isolated (BI) masonry building subjected to different intensities of input earthquakes is compared with the response of the same building without base isolation system. Acceleration response amplification and peak response values of test model with and without base isolation system are compared for different intensities of table acceleration. Distribution of shear forces and moment along the height of the structure and response time histories indicates significant reduction of dynamic responses of the structure with U‐FREI system. This study clearly demonstrates the improved seismic performance of un‐reinforced masonry building model supported on U‐FREIs under the action of considered ground motions. Copyright © 2015 John Wiley & Sons, Ltd.     

Simplified macro‐model for infill masonry walls considering the out‐of‐plane behaviour

One of the main challenges in earthquake risk mitigation is the assessment of existing buildings not designed according to modern codes and the development of effective techniques to strengthen these structures. Particular attention should be given to RC frame structures with masonry infill panels, as demonstrated by their poor performance in recent earthquakes in Europe. Understanding the seismic behaviour of masonry‐infilled RC frames presents one of the most difficult problems in structural engineering. Analytical tools to evaluate infill–frame interaction and the failure mechanisms need to be further studied. This research intends to develop a simplified macro‐model that takes into account the out‐of‐plane behaviour of the infill panels and the corresponding in‐plane and out‐of‐plane interaction when subjected to seismic loadings. Finally, a vulnerability assessment of an RC building will be performed in order to evaluate the influence of the out‐of‐plane consideration in the building response. Copyright © 2015 John Wiley & Sons, Ltd.     

A macro‐model with nonlinear springs for seismic analysis of URM buildings

Seismic assessment of existing unreinforced masonry buildings represents a current challenge in structural engineering. Many historical masonry buildings in earthquake regions were not designed to withstand seismic loading; thus, these structures often do not meet the basic safety requirements recommended by current seismic codes and need to be strengthened considering the results from realistic structural analysis. This paper presents an efficient modelling strategy for representing the nonlinear response of unreinforced masonry components under in‐plane cyclic loading, which can be used for practical and accurate seismic assessment of masonry buildings. According to the proposed strategy, generic masonry perforated walls are modelled using an equivalent frame approach, where each masonry component is described utilising multi‐spring nonlinear elements connected by rigid links. When modelling piers and spandrels, nonlinear springs are placed at the two ends of the masonry element for describing the flexural behaviour and in the middle for representing the response in shear. Specific hysteretic rules allowing for degradation of stiffness and strength are then used for modelling the member response under cyclic loading. The accuracy and the significant potential of the proposed modelling approach are shown in several numerical examples, including comparisons against experimental results and the nonlinear dynamic analysis of a building structure. Copyright © 2016 John Wiley & Sons, Ltd.     

多层错层砖砌体房屋抗震分析

本文根据典型的东西和南北错层单元模型,按不同的错层高度、不同收层情况和不同理置深度的实际房屋情况,分析建立了错层房层和相应的等效规整房屋模型,采用板壳单元,用有限元方法计算了这些模型的动力特征和在地震作用下的墙肢剪应力分布,经过对比分析得到了一些错层房屋墙应力的分布规律。根据错层房屋的受力特点,文中提出了相应的加强构造措施,结构布置要求和错层房屋的抗震计算模型等具体建议。     

轴向压力对配筋砌体短肢剪力墙抗剪性能的影响

通过对6片足尺290mm厚全灌芯配筋砌块砌体短肢剪力墙拟静力试验结果的分析,利用非线性有限元方法,模拟了此种墙体在压弯剪共同作用下的抗剪特性,研究了轴向压力对配筋砌块砌体短肢剪力墙抗剪性能的影响。研究表明,在不同高宽比的墙体中,轴向压力均对墙体的抗剪能力有较大影响,随着轴向压力增大,墙体抗剪能力先增大后减小（轴压比n从0.1增长到0.4时,墙体抗剪能力逐渐增大,而n从0.4增长到0.6时,墙体抗剪能力却逐渐减小）;随着轴向压力的增大,墙体延性在逐渐减小。提出当轴压比等于0.3时,墙体抗剪能力和延性均较好,建议在建筑抗震设计规范中采用此值。     

R/C frame–infill interaction model and its application to Indonesian buildings

This paper proposes a new analytical model for masonry‐infilled R/C frames to evaluate the seismic performance considering R/C frame–infill interactions. The proposed analytical model replaces masonry infill with a diagonal compression strut, which represents distributed compression transferred between frame and infill interfaces. The equivalent strut width is presented as a function of the frame–infill contact length, which can be evaluated by static equilibriums related to compression balance and lateral displacement compatibility at the frame–infill interfaces. The proposed analytical model was verified through comparisons with experimental results obtained for several brick masonry‐infilled R/C frames representing a typical R/C building with nonstructural masonry infill in Indonesia. As a result, good agreements were observed between the experimental and analytical values of the lateral strength and ductility of the infilled frames. The seismic performances of two earthquake‐damaged R/C buildings with different damage conditions were evaluated considering infill effects by applying the proposed analytical model. Consequently, the nonstructural brick masonry infill significantly affected the seismic resistances of the buildings, which seemed to lead to differing levels of damage for each building. These results indicate that the proposed analytical model can be an effective tool for more precisely screening earthquake‐vulnerable existing R/C buildings in Indonesia. Copyright © 2016 The Authors. Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.     

A simplified methodology for the seismic assessment of masonry buildings with RC slabs

The present paper aims to contribute to the knowledge concerning the seismic assessment of load bearing masonry buildings with reinforced concrete slabs. The final goal of the present research was to propose a simple, yet accurate, methodology to assess the seismic safety of existing masonry buildings. The methodology here presented was based on the so-called ICIST/ACSS methodology with major improvements such as the extension to load bearing masonry wall buildings and the consideration of the effects of one of the most common strengthening solutions for masonry walls, here referred to as reinforced plastering mortar, as well as the possibility of considering four levels of increasing refinement: global, by alignment, by wall panel and by wall element. An extended research was performed on the existing methodologies to evaluate the seismic structural risk of load bearing masonry buildings, briefly describing methodologies similar to the one proposed, namely all of those that have in common the fact that they are based in the physical comparison between the resisting and acting shear forces at all storeys and along the two orthogonal horizontal directions. A case study is presented to check the applicability of the proposed methodology. The case study showed that the proposed methodology is relatively simple to apply and has a sufficiently good accuracy when compared with alternative methodologies. The degree of refinement of the analysis (global, by alignment, by wall panel and by wall element) must be taken into consideration and successively more complex analyses may be required when the results of simpler analyses are inconclusive.     

Seismic collapse simulation of existing masonry buildings with different retrofitting techniques

Masonry buildings are primarily constructed out of bricks and mortar which become discrete pieces and cannot sustain horizontal forces created by a strong earthquake.The collapse of masonry walls may cause significant human casualties and economic losses.To maintain their integrity,several methods have been developed to retrofit existing masonry buildings,such as the constructional RC frame which has been extensively used in China.In this study,a new method using precast steel reinforced concrete(PSRC)panels is developed.To demonstrate its effectiveness,numerical studies are conducted to investigate and compare the collapse behavior of a structure without retrofitting,retrofitted with a constructional RC frame,and retrofitted with external PSRC walls(PSRCW).Sophisticated finite element models(FEM)were developed and nonlinear time history analyses were carried out.The results show that the existing masonry building is severely damaged under occasional earthquakes,and totally collapsed under rare earthquakes.Both retrofitting techniques improve the seismic performance of existing masonry buildings.However,it is found that several occasional earthquakes caused collapse or partial collapse of the building retrofitted with the constructional RC frame,while the one retrofitted by the proposed PSRC wall system survives even under rare earthquakes.The effectiveness of the proposed retrofitting method on existing masonry buildings is thus fully demonstrated.     

Seismic response of three‐dimensional r/c multi‐storey frame building under uni‐ and bi‐directional input ground motion

This paper deals with seismic analysis of plan‐asymmetric r/c frame multi‐storey buildings. Non‐linear numerical analyses are carried out by using a lumped plasticity model for beams and a multi‐spring model for columns, the latter one introduced to account for axial force–biaxial bending moment interaction. A comparison between numerical analyses and experimental test results is reported in order to calibrate the numerical model, showing that the adopted model is very suitable. In order to study the effects of the earthquake orthogonal component, the seismic response of the modelled structure under uni‐directional excitation is compared to the one under bi‐directional excitation. Such comparison shows that the maximum base shear and the top displacement are not very sensitive to the presence of the orthogonal component, which, conversely, leads to large increase in the column plastic excursions. Copyright © 2007 John Wiley & Sons, Ltd.     

Non-linear static analysis of masonry buildings based on a strut-and-tie modeling

This paper presents an analytical method for evaluating the capacity curve of masonry buildings according to non-linear static analysis. This method splits the building into stories, and the vertical structures of each story into masonry panels, which are analyzed individually by a new push-over analysis. The behavior of each panel is reproduced with an evolutive strut-and-tie model, which simulates the uncracked and cracked behavior of the panel subjected to a vertical constant force and a lateral force that increases up to the complete development of the failure mechanism. The strut-and-tie model provides the capacity curve of the panel. The composition of the capacity curves of all the panels of a story provides the capacity curve of this story. The capacity curves of all the stories of the building can be used to obtain either the maximum drift that the building can withstand or the behavior factor of the structure. Either outcome allows the specific dissipation capacity and overstrength of the masonry building to be considered in the seismic analyses, which provides ultimate limit state verifications with more reliability.The proposed method is applied to a school building. The comparison between seismic safety assessed with this method and with a linear dynamic analysis, all other parameters being equal, shows that the latter approach is overly-conservative and misleading. In fact, the specific inelastic capacity, which only the former approach can consider, influences greatly the seismic behavior of the case study.     

Effects of vertical irregularity and thickness of unreinforced masonry infill on the robustness of RC framed buildings

Presence of irregularities in reinforced concrete (RC) buildings increases seismic vulnerability. During severe seismic shaking, such buildings may suffer disproportionate damage or even collapse that can be minimized by increasing robustness. Robustness is a desirable property of structural systems that can mitigate susceptible buildings to disproportionate collapse. In this paper, the effects of vertical irregularity and thickness of unreinforced masonry infill on the robustness of a six‐story three‐bay RC frame are quantified. Nonlinear static analysis of the frame is performed, and parametric study is undertaken by considering two parameters: absence of masonry infill at different floors (i.e., vertical irregularities) and infill thickness. Robustness has been quantified in terms of stiffness, base shear, ductility, and energy dissipation capacity of the frame. It was observed that the infill thickness and vertical irregularity have significant influence on the response of RC frame. The response surface method is used to develop a predictive equation for robustness as a function of the two parameters. The predictive equation is validated further using 12 randomly selected computer simulations. Copyright © 2013 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.