Damage index based on stiffness degradation of low‐rise RC walls

Widely used damage indices, such as ductility and drift ratios, do not account for the influences of the duration of strong shaking, the cumulative inelastic deformation or energy dissipation in structures. In addition, the formulation and application of most damage indices have until now been based primarily on flexural modes of failure. However, evidence from earthquakes suggests that shear failure or combined shear‐flexure behavior is responsible for a large proportion of failures. Empirical considerations have been made in this paper for evaluating structural damage of low‐rise RC walls under earthquake ground motions by means of a new energy‐based low‐cycle fatigue damage index. The proposed empirical damage index is based on the results of an experimental program that comprised six shake table tests of RC solid walls and walls with openings; results of six companion walls tested under QS‐cyclic loading were used for comparison purposes. Variables studied were the wall geometry, type of concrete, web shear steel ratio, type of web shear reinforcement, and testing method. The index correlates the stiffness degradation and the destructiveness of the earthquake in terms of the duration and intensity of the ground motions. The stiffness degradation model considers simultaneously the increment of damage associated to the low‐cycle fatigue, energy dissipation, and the cumulative cyclic parameters, such as displacement demand and hysteretic energy dissipated. Copyright © 2014 John Wiley & Sons, Ltd.     

Strength and stiffness reduction factors for infilled frames with openings

Framed structures are usually infilled with masonry walls. They may cause a significant increase in both stiffness and strength, reducing the deformation demand and increasing the energy dissipation capacity of the system. On the other hand, irregular arrangements of the masonry panels may lead to the concentration of damage in some regions, with negative effects; for example soft story mechanisms and shear failures in short columns. Therefore, the presence of infill walls should not be neglected, especially in regions of moderate and high seismicity. To this aim, simple models are available for solid infills walls, such as the diagonal no-tension strut model, while infilled frames with openings have not been adequately investigated. In this study, the effect of openings on the strength and stiffness of infilled frames is investigated by means of about 150 experimental and numerical tests. The main parameters involved are identified and a simple model to take into account the openings in the infills is developed and compared with other models proposed by different researchers. The model, which is based on the use of strength and stiffness reduction factors, takes into account the opening dimensions and presence of reinforcing elements around the opening. An example of an application of the proposed reduction factors is also presented.     

Nonlinear seismic analysis of reinforced concrete frames using the force analogy method

A method of nonlinear seismic analysis for RC framed structures considering full‐range factors, including stiffness and strength degradation, geometric nonlinearity, and structural member failure, is established based on the fundamental concept of the force analogy method. The strong material nonlinearity, large geometric deformation, and internal forces redistribution due to the member failure can be depicted by the proposed local plastic mechanisms, the rotation hinges at the member ends and the slide hinges assigned to the columns, of which the measurement relationships are moment versus plastic rotation and shear force versus shear plastic deformation, respectively. They are capable of evaluating the exact response of RC structures. Because only unchanging initial stiffness matrices are used through the whole computation process, the state‐space formulation was used for solving the equations of motion. The advantages of the force analogy method, such as high efficiency and stability, are still retained. The exactness of the proposed local plastic mechanisms is verified against a group of tests data, and the application of the proposed procedure is performed to an RC framed structure to simulate the full‐range nonlinear response by increasing the excitation step by step until failure of partial structural members appear. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental assessment of low-aspect-ratio,reinforced concrete shear wall stiffness

Low-aspect-ratio, reinforced concrete shear walls are the primary lateral-load-carrying element in many structures designed for protective purposes. A review of the technical literature shows that considerable uncertainty exists regarding the elastic stiffness these structures will exhibit during seismic excitation. Because of this uncertainty, current design practice often employs a stiffness reduction factor. In an attempt to develop accurate information regarding the stiffness of these structures, 13 shear wall elements were tested statically; dynamically, with simulated seismic base excitations on a shake table; and with experimental modal analysis procedures. Results of these tests show that the shear wall's stiffness can be accurately estimated with a mechanics-of-materials analysis that accounts for shear deformation.     

In‐plane and out‐of‐plane behavior of confined masonry walls for various toothing and openings details and prediction of their strength and stiffness

Eight half‐scale brick masonry walls were tested to study two important aspects of confined masonry (CM) walls related to its seismic behavior under in‐plane and out‐of‐plane loads. Four solid wall specimens tested to investigate the role of type of interface between the masonry and tie‐columns, such as toothing varying from none to every course. The other four specimens with openings were tested to study the effectiveness of various strengthening options around opening to mitigate their negative influence. In the set of four walls, one wall was infilled frame while the other three were CM walls of different configurations. The experimental results were further used to determine the accuracy of various existing models in predicting the in‐plane response quantities of CM walls. Confined masonry walls maintained structural integrity even when severely damaged and performed much better than infill frames. No significant effect of toothing details was noticed although toothing at every brick course was preferred for better post‐peak response. For perforated walls, provision of vertical elements along with continuous horizontal bands around openings was more effective in improving the overall response. Several empirical and semi‐empirical equations are available to estimate the lateral strength and stiffness of CM walls, but those including the contribution of longitudinal reinforcement in tie‐columns provided better predictions. The available equations along with reduction factors proposed for infills could not provide good estimates of strength and stiffness for perforated CM walls. However, recently proposed relations correlating strength/stiffness with the degree of confinement provided reasonable predictions for all wall specimens. Copyright © 2016 John Wiley & Sons, Ltd.     

Topology optimization of shear wall structures under seismic loading

A topology optimization formulation is developed to find the stiffest structure with desirable material distribution subjected to seismic loads. Finite element models of the structures are generated and the optimality criteria method is modified using a simple penalty approach and introducing fictitious strain energy to simultaneously consider both material volume and displacement constraints. Different types of shear walls with/without opening are investigated. Additionally, the effects of shear wall-frame interaction for single and coupled shear walls are studied. Gravity and seismic loads are applied to the shear walls so that the definitions provide a practical approach for locating the critical parts of these structures. The results suggest new viewpoints for architectural and structural engineering for placement of openings.     

Analysis of shear‐dominated RC columns using the nonlinear truss analogy

This paper uses nonlinear truss models for the analysis of shear‐dominated reinforced concrete (RC) columns subjected to cyclic loading. A previously established method, aimed to the analysis of RC walls, is enhanced to allow simulations of column members. The concrete constitutive equations are modified to account for the contribution of the aggregate interlock to the shear resistance. Additionally, an equation is proposed to determine the inclination angle of the diagonal members in the truss models. The modeling approach is validated using the results of quasi‐static and dynamic tests on shear‐dominated RC columns. The combination of predictive capabilities and conceptual simplicity establishes truss‐based models as an attractive approach for the systematic analysis of shear‐dominated RC frame construction. Copyright © 2014 John Wiley & Sons, Ltd.     

The effective stiffness of modern unreinforced masonry walls

Code design of unreinforced masonry (URM) buildings is based on elastic analysis, which requires as input parameter the effective stiffness of URM walls. Eurocode estimates the effective stiffness as 50% of the gross sectional elastic stiffness, but comparisons with experimental results have shown that this may not yield accurate predictions. In this paper, 79 shear‐compression tests of modern URM walls of different masonry typologies from the literature are investigated. It shows that both the initial and the effective stiffness increase with increasing axial load ratio and that the effective‐to‐initial stiffness ratios are approximately 75% rather than the stipulated 50%. An empirical relationship that estimates the E‐modulus as a function of the axial load and the masonry compressive strength is proposed, yielding better estimates of the elastic modulus than the provision in Eurocode 6, which calculates the E‐modulus as a multiple of the compressive strength. For computing the ratio of the effective to initial stiffness, a mechanics‐based formulation is built on a recently developed analytical model for the force‐displacement response of URM walls. The model attributes the loss in stiffness to diagonal cracking and brick crushing, both of which are taken into account using mechanical considerations. The obtained results of the effective‐to‐initial stiffness ratio agree well with the test data. A sensitivity analysis using the validated model shows that the ratio of effective‐to‐initial stiffness is for most axial load ratios and wall geometries around 75%. Therefore, a modification of the fixed ratio of effective‐to‐initial stiffness from 50% to 75% is suggested.     

改善混凝土剪力墙抗震性能的研究

混凝土剪力墙被广泛运用于各类结构体系中。它作为主要的抗侧力单元,其刚度大、承载力高,但当剪力墙以受剪破坏为主时,其抗震性能较差。为此,不少学者提出了各种改善混凝土剪力墙抗震性能的措施。本文对几种采用不同构造措施的剪力墙作了简要介绍,特别是介绍一种新型双重组合剪力墙。     

Nonlinear hysteresis curve derived by direct numerical investigation of acceleration data

Acceleration measurements often provide engineers with a means by which to determine the forces within dynamic structural systems; however, for certain problems, information about the structural motion and the displacement-time history may also be of interest. One such application deals with the evaluation of stiffness in reinforced concrete structures during seismic events. Scaled model test of these events suggest that the stiffness of these structures often degrades drastically. The displacement response of these seismic events is required both for the hysteresis curve (load vs displacement) and evaluation of postulated structural stiffness models. By applying data processing techniques to acceleration data obtained from scaled model tests, displacement-time histories were obtained for low aspect shear walls subjected to simulated seismic loadings. Procedures, difficulties, and results of this work are discussed herein.     

Seismic retrofi tting of RC columns with RC jackets and wing walls with different structural details

An original reinforced concrete(RC) column and four strengthened specimens, two with RC jackets and two with wing walls, were tested in this study. The original column specimen was designed to comply with older(pre-1999) design standards so that the usual detailing defi ciencies in existing school buildings in Taiwan could be simulated. Two different structural details were chosen to fabricate the full-scale specimens for each retrofi tting technique. The study confi rmed that either RC jacketing or the installation of wing walls with two different structural details can effectively improve the stiffness and strength of an existing column. RC jacketing shows a better improvement in energy dissipation and ductility when compared to the columns with wing walls installed. This is because the two RC jacketed columns experienced a fl exural failure, while a shear failure was found in the two columns with the wing walls installed, and thus led to a drastic decrease of the maximum lateral strengths and ductility. Since many factors may affect the installation of a post-installed anchor, it is better to use standard hooks to replace post-installed anchors in some specifi c points when using RC jacketing or installing wing walls.     

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.     

Seismic retroftting of RC columns with RC jackets and wing walls with different structural details

An original reinforced concrete(RC) column and four strengthened specimens, two with RC jackets and two with wing walls, were tested in this study. The original column specimen was designed to comply with older(pre-1999) design standards so that the usual detailing defi ciencies in existing school buildings in Taiwan could be simulated. Two different structural details were chosen to fabricate the full-scale specimens for each retrofi tting technique. The study confi rmed that either RC jacketing or the installation of wing walls with two different structural details can effectively improve the stiffness and strength of an existing column. RC jacketing shows a better improvement in energy dissipation and ductility when compared to the columns with wing walls installed. This is because the two RC jacketed columns experienced a fl exural failure, while a shear failure was found in the two columns with the wing walls installed, and thus led to a drastic decrease of the maximum lateral strengths and ductility. Since many factors may affect the installation of a post-installed anchor, it is better to use standard hooks to replace post-installed anchors in some specifi c points when using RC jacketing or installing wing walls.     

A capacity curve model for confined clay brick infills

Experimental studies have proven that clay brick infills, confined with carbon-fiber-reinforced polymers (CFRP) in reinforced concrete (RC) frames, have some advantages in terms of stiffness, strength, energy dissipation capability and damage intensity. Owing to these advantages, existing infill walls in RC frames may be retrofitted with CFRP strips, especially in low-rise buildings in earthquake-prone areas. There is a gap in the literature concerning their behavior model, for use in structural analysis. A piecewise linear capacity curve model called “DUVAR” is proposed here, which estimates the envelope of force-vs.-displacement hysteresis, depending on the data compiled from the literature and the completed experimental studies. A nonlinear shear spring element is utilized in the model to represent the bare and retrofitted infills. The ultimate shear strength and the corresponding displacement, the ratio of cracking stiffness to initial stiffness, the ratio of ultimate strength to cracking strength, and the ductility ratio are the five key parameters of the model. The model is validated against the experimental results of two sovereign studies. Finally, the model is employed in the performance evaluation of an existing three-story RC building to exemplify its straightforward application.     

Strength,stiffness and cyclic deformation capacity of RC frames converted into walls by infilling with RC

In seismic retrofitting of concrete buildings, frame bays are converted into reinforced concrete (RC) walls by infilling the space between the frame members with RC of a thickness of not more than their width. The cyclic behavior of the resulting wall depends on the connection between the RC infill and the surrounding RC members. The paper uses the results from 56 cyclic tests on such composite walls to express their properties in terms of the geometry, the reinforcement and the connection. Properties addressed are: (a) the yield moment at the story base; (b) the secant-to-yield-point stiffness over the shear span of the wall in a story; (c) the deflection at flexural failure in cyclic loading; (d) the cyclic shear resistance, including a sliding shear failure mode. Separate models are given for squat walls failing in shear and for those where the top of the column shears-off. The proposals are modifications of models developed in the past for monolithic RC walls from several hundred cyclic tests; blind application of these latter models as though the walls were monolithic gives, in general, unsafe predictions. By contrast, the diagonal compression strut approach in ASCE41-06 is safe-sided, but gives unacceptably large prediction scatter.     

Linear‐elastic lateral load analysis and seismic design of pin‐supported wall‐frame structures with yielding dampers

This paper describes an analytical investigation on a reinforced concrete lateral load resisting structural system comprising a pin‐supported (base‐rocking) shear wall coupled with a moment frame on 1 or both sides of the wall. Yielding dampers are used to provide supplemental energy dissipation through the relative displacements at the vertical connections between the wall and the frames. The study extends a previous linear‐elastic model for pin‐supported wall‐frame structures by including the effects of the dampers. A closed‐form solution of the lateral load behavior of the structure is derived by approximating the discrete wall‐frame‐damper interactions with distributed (ie, continuous) properties. The validity of the model is verified by comparing the closed‐form results with computational models using OpenSees program. Then, a parametric analysis is conducted to investigate the effects of the wall, frame, and damper stiffness on the behavior of the structure. It is found that the damper stiffness significantly affects the distribution of shear forces and bending moments over the wall height. Finally, the performance‐based plastic design approach extended to the wall‐frame‐damper system is proposed. Case studies are carried out to design 2 damped pin‐supported wall‐frame structures using the proposed approach. Nonlinear dynamic time‐history analyses are conducted to verify the effectiveness of this method. Results indicate that the designed structures can achieve the performance level with the story drift ratios less than target values, and weak‐story failure mechanism is not observed. The approach can be used in engineering applications.     

Test and analysis of reinforced concrete (RC) precast shear wall assembled using steel shear key (SSK)

Reinforced concrete (RC) precast shear walls are extensively applied in practical engineering, owing to their fast construction speed. However, because of the transport conditions, RC precast shear walls have to be separated into small wall segments during the factory prefabrication procedure before being assembled on site. Typically, wet-type jointing methods are adopted to link the segments, which is time-consuming and results in unreliable post-pouring area strength. To overcome this problem, the novel scheme of the steel shear key (SSK) featuring steel shear panels and combined fillet and plug welding is proposed. Three RC precast shear wall specimens with different linking strength, termed as weakened SSK wall, standard SSK wall, and strengthened SSK wall, respectively, and an integrated shear wall specimen were designed. Quasi-static cyclic loading was applied to investigate the specimens' dynamic properties. The test results suggest the prefabricated wall segments equipped with SSKs showed reliable stiffness and bearing capacity and were improved in energy dissipation ability, compared with conventional shear walls. As the shear stiffness and number of equipped SSKs increased, the specimens exhibited higher strength, but their ductility and energy dissipation were slightly decreased. Most importantly, the standard SSK wall specimen could achieve satisfactory bearing capacity and deformability and is thus recommended for precast building structures. Finite element method (FEM) models were established to validate the test results, and parametric study analysis was conducted based on the coupling ratio of the SSK walls. Finally, an appropriate coupling ratio range is recommended for practical engineering applications.     

Multi‐scale modelling approach for the pushover analysis of existing RC shear walls—Part I: Model formulation

This work focuses on the modelling issues related to the adoption of the pushover analysis for the seismic assessment of existing reinforced concrete (RC) structures. To this purpose a prototype reference structure, one of the RC shear walls designed according to the multi‐fuse concept and tested on shaking table for the CAMUS project, is modelled at different levels of refinement. The meso‐scale of a stiffness‐based fibre element and the micro‐scale of the finite element (FE) method are herein adopted; in the latter separate elements are adopted for the concrete, the steel and the steel–concrete interface. This first of the two companion papers presents in detail the wall under study, illustrating the design philosophy, the geometry of the wall, the instrumentation set‐up and the test programme. The two modelling approaches are then described; the most important points in terms of element formulation and constitutive relations for materials are presented and discussed for each approach, in the light of the particular design of the wall and of its experimental behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental study on a new type of earthquake resilient shear wall

Reinforced concrete (RC) shear walls have been extensively used as lateral load resisting structural members in tall buildings. However, in the past, strong earthquake events RC structural walls in some buildings suffered severe damage, which concentrated at the bottom and was very difficult to be repaired. The installation of the replaceable corner components (RCCs) at the bottom of the structural wall is a new method to form an earthquake resilient structural wall whose function can be quickly restored by replacing the RCCs after the strong earthquake because of the damage concentrating on RCCs. In this study, a new kind of replaceable energy‐dissipation component installed at the bottom corner of RC structural walls was proposed. To study the seismic performance of the new structural wall with RCCs, the cyclic loading tests on three new structural wall specimens and one conventional RC structural wall specimen were conducted. One of the new structural wall specimens experienced replacement and reloading process to verify the feasibility of replacement. The results show that the structural behavior of all specimens was flexure dominating. The damage in the new shear specimens mainly concentrated on RCCs. The replacement of RCCs can be implemented conveniently after the residual deformation occurred in the structure. Compared with the conventional structural wall specimen, the seismic performance of new structural wall specimens was improved significantly. Copyright © 2017 John Wiley & Sons, Ltd.     

An improvement to linear‐elastic procedures for seismic performance assessment

An improved linear‐elastic analysis procedure is developed in this paper as a simple approximate method for displacement‐based seismic assessment of the existing buildings. The procedure is mainly based on reducing the stiffness of structural members that are expected to respond in the inelastic range in a single global iteration step. Modal spectral displacement demands are determined from the equal displacement rule. Response predictions obtained from the proposed procedure are evaluated comparatively by using the results of benchmark nonlinear response history analysis, and both the conventional and the multi‐mode pushover analyses. In comparative evaluations, a twelve‐story RC plane frame and a six‐story unsymmetrical‐plan RC frame are employed by using 91 ground motion components. It is observed that the proposed procedure estimates the flexural deformation demands in deformation‐controlled members and the shear forces in force‐controlled members with reasonable accuracy. Copyright © 2010 John Wiley & Sons, Ltd.