Analytical and empirical models for predicting the drift capacity of modern unreinforced masonry walls

Displacement‐based seismic assessment of buildings containing unreinforced masonry (URM) walls requires as input, among others, estimates of the in‐plane drift capacity at the considered limit states. Current codes assess the drift capacity of URM walls by means of empirical models with most codes relating the drift capacity to the failure mode and wall slenderness. Comparisons with experimental results show that such relationships result in large scatter and usually do not provide satisfactory predictions. The objective of this paper is to determine trends in drift capacities of modern URM walls from 61 experimental tests and to investigate whether analytical models could lead to more reliable estimates of the displacement capacity than the currently used empirical models. A recently developed analytical model for the prediction of the ultimate drift capacity for both shear and flexure controlled URM walls is introduced and simplified into an equation that is suitable for code implementation. The approach follows the idea of plastic hinge models for reinforced concrete or steel structures. It explicitly considers the influence of crushing due to flexural or shear failure in URM walls and takes into account the effect of kinematic and static boundary conditions on the drift capacity. Finally, the performance of the analytical model is benchmarked against the test data and other empirical formulations. It shows that it yields significantly better estimates than empirical models in current codes. The paper concludes with an investigation of the sensitivity of the ultimate drift capacity to the wall geometry, static, and kinematic boundary conditions.     

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.     

Hysteretic energy dissipation capacity and the cyclic to monotonic drift ratio for rectangular RC columns in flexure

Predictions of energy dissipation capacity and of the deterioration of deformation capacity due to cumulative damage have been made by means of a non‐parametric empirical approach, called the conditional average estimator method, using empirical data on rectangular reinforced concrete columns that failed in flexure. Five input parameters were used: axial load index, index related to confinement, shear span index, concrete compressive strength, and longitudinal reinforcement index. The energy capacity was expressed in three different normalized forms and the deterioration of deformation capacity was defined as the ratio of the cyclic to the monotonic ultimate drift. The longitudinal reinforcement index, the index related to confinement, and the axial load index are the most influential input parameters in the case of energy capacity, whereas the latter two indices exhibit the most significant influence in the case of the drift ratio. Energy capacity decreases with an increasing axial load index, whereas it increases with increasing longitudinal reinforcement and with better confinement. In the case of the shear span index, the trend is more complex. Normal concrete has a higher energy dissipation capacity than high‐strength concrete. Similar trends are observed for the drift ratio, with the exception of the influence of the axial load index, where the trend is opposite. The dispersion of the results is high. Copyright © 2008 John Wiley & Sons, Ltd.     

Flexural deformation capacity of rectangular RC columns determined by the CAE method

A non‐parametric empirical approach, called the conditional average estimator (CAE) method, has been implemented for the estimation of the flexural deformation capacity of reinforced concrete rectangular columns expressed in terms of the ultimate (‘near collapse’) drift. Two databases (PEER and Fardis), which represent subsets of the original databases, were used. Four input parameters were employed in the basic model: axial load index, index related to confinement, shear span index, and concrete compressive strength. The results of analyses suggest that, in general, ultimate drift decreases with increasing axial load index, and increases with better confinement. An increase in the shear span‐to‐depth ratio has a beneficial effect until a turning point is reached. After that the opposite trend can be observed, i.e. a decrease in the ultimate drift with further increasing of the shear span‐to‐depth ratio. No clear trend is observed in the case of concrete compressive strength. The predictions, obtained by using the Fardis database are in general somewhat larger than the predictions from the PEER database, due to the difference in the definition of ultimate drift. The scatter of results is large. The local coefficient of variation, which is a measure for dispersion, amounts to about 0.2–0.5. The ultimate drifts obtained by using the two databases, were compared with the values predicted by the Eurocode 8 empirical formula. Copyright © 2006 John Wiley & Sons, Ltd.     

Prediction of the force–drift envelope for RC columns in flexure by the CAE method

A non‐parametric empirical approach, called the conditional average estimator (CAE) method, has been applied for the prediction of the normalized lateral force–drift envelope of reinforced concrete (RC) rectangular columns, as well as their characteristic drifts (effective yield drift, capping drift and ultimate drift), and drift‐related parameters (the ratio between the effective yield drift and elastic drift, and two ductility measures). A subset of the PEER RC column database was used. Five input parameters were employed: axial load index, index related to confinement, shear span index, concrete compressive strength, and longitudinal reinforcement index. The results suggest that the relations between the input and output parameters are complex, and that it is difficult to isolate the influence of a single parameter. Nevertheless, some trends were observed. The axial load index is the most influential input parameter. All the results decrease with an increasing axial load index, whereas they increase with an increasing longitudinal reinforcement index. An increase in the index related to confinement results in increases in the ultimate drift and in ductility. The influence of the shear span index is the most complex. The influence of the concrete strength is small with the exception of two output parameters related to elastic drift, which substantially decrease with increasing strength. The dispersion of the results is relatively large. The results of the predictions can be used for mathematical modelling of moment–rotation backbone curves for plastic hinges, and for the estimation of the deformation capacity of columns in seismic performance assessments. Copyright © 2007 John Wiley & Sons, Ltd.     

Out‐of‐plane strength reduction of unreinforced masonry walls because of in‐plane damages

There are numerous studies on the behavior of Unreinforced Masonry (URM) walls in both in‐plane (IP) and out‐of‐plane (OP) directions; however, few aimed at understanding the simultaneous contribution of these intrinsic responses during earthquakes. Undoubtedly, even a strong URM wall shows weakened capacity in the OP direction because of minor cracks and other damages in the IP direction, and this capacity reduction has not yet been accounted for in seismic codes. In this study, performance of three URM walls is evaluated by several numerical analyses in terms of the OP capacity reduction because of IP displacements and failure modes. Several parameters influencing the OP capacity have been studied including aspect ratio, roof boundary condition, IP displacement and IP loading patterns. The results indicate that reduction in the OP capacity of URM walls varies from negligible to very high depending on boundary conditions, IP failure mode and IP damage severity. Moreover, IP loading pattern is more important in walls with higher aspect ratios because of their IP failure modes. Copyright © 2015 John Wiley & Sons, Ltd.     

底部放置聚苯板的预制剪力墙抗震性能试验研究

为研究底部放置聚苯乙烯硬泡沫板的抗震性能,对3个剪跨比2.0的两端设置后浇段、底部放置聚苯乙烯硬泡沫板的预制剪力墙试件以及1个相同剪跨比的现浇剪力墙试件进行了拟静力试验。试验结果表明:预制剪力墙底部放置硬聚苯乙烯泡沫板的试件,破坏形态为后浇段与预制剪力墙脱开、后浇段受压破坏;底部放置聚苯板的预制剪力墙试件承载力小于现浇剪力墙试件,耗能能力接近或大于现浇剪力墙试件;各试件的极限位移角为1/98~1/81;预制剪力墙试件的屈服刚度及峰值刚度均比现浇剪力墙试件降低27%~75%,水平分布钢筋未伸入后浇段的试件比伸入后浇段的试件刚度降低更多,后浇段短的试件比后浇段长的试件刚度降低更多。预制试件轴压力主要由后浇段承担,名义屈服及峰值水平力时,钢筋应变分布不符合平截面假定。     

内置钢板钢筋混凝土组合剪力墙数值模拟

内置钢板钢筋混凝土组合剪力墙具有良好的抗震性能,目前已在超高层建筑中得到越来越多的应用。采用OpenSees程序对普通钢筋混凝土剪力墙和钢板组合剪力墙试验构件进行模拟分析,验证了建模与分析方法的合理性与准确性,分析结果表明,该方法能够较好地模拟组合剪力墙的弹塑性行为。分析了轴压比和配钢率这两个关键参数对内置钢板组合剪力墙抗震性能的影响。计算结果表明,与普通钢筋混凝土剪力墙相比,内置钢板可以明显提高构件的承载力、延性和滞回耗能;轴压比和配钢率对组合剪力墙的抗震性能有较大影响。     

Seismic capacity of irregular unreinforced masonry walls with openings

Masonry buildings are often characterized by geometric irregularities. In many cases, such buildings meet global regularity requirements provided by seismic codes, but they are composed by irregular walls with openings. The latter are masonry walls characterized by (i) openings of different sizes, (ii) openings misaligned in the horizontal and/or vertical direction, or (iii) a variable number of openings per story. An irregular layout of openings can induce not only a nonuniform distribution of gravity loads among masonry piers but also unfavorable damage localizations resulting in a premature collapse of the wall and hence a higher seismic vulnerability. This paper is aimed at providing a simplified methodology to assess the effects of irregularities on the in‐plane seismic capacity of unreinforced masonry (URM) walls with openings. To this end, a macroelement method was developed and validated through experimental results available in the literature. The proposed methodology was based on the quantification of wall irregularities by means of geometric indices and their effects on seismic capacity of URM walls with openings through both sensitivity and regression analyses. Sensitivity analysis was based on a high number of static pushover analyses and allowed to assess variations in key seismic capacity parameters. Regression analysis let to describe each capacity parameter under varying irregularity index, providing empirical models for seismic assessment of irregular URM walls with openings. The in‐plane seismic capacity was found to be significantly affected by wall irregularities, especially in the case of openings with different heights. Copyright © 2012 John Wiley & Sons, Ltd.     

混凝土核心筒的有限元模拟及若干参数的影响分析

运用ABAQUS分析软件,建立水平荷载作用下的钢筋混凝土核心筒有限元模型,进行非线性分析,并将分析结果与大比例试件的试验结果对比,对所采用的有限元模型加以验证。在此基础上,进行改变钢筋混凝土核心筒轴压比、高宽比和筒壁厚度的受力过程模拟分析,研究这些参数对筒体性能的影响。结果表明：随着轴压比的增大,筒体的破坏由受拉向受压破坏转变,筒体最大水平承载力经历先增加后减小的变化,延性变差;随着高宽比的增大,筒体破坏形态由剪切向弯曲破坏转变,延性增加,整体弯曲作用更加明显,最大底部剪力减小;随着壁厚的增大,试件破坏由截面压屈失稳向墙肢底部受弯破坏转变,墙肢破坏区域沿高度方向发展,耗能能力更强,承载力明显增大,变形能力显著增加。     

An experimental study of a damage‐controllable plastic‐hinge‐supported wall structure

The reinforced concrete (RC) shear wall serves as one of the most important components sustaining lateral seismic forces. Although they allow advanced seismic performance to be achieved, RC shear walls are rather difficult to repair once the physical plastic hinge at the bottom part has been formed. To overcome this, a damage‐controllable plastic hinge with a large energy dissipation capacity is developed herein, in which the sectional forces are decoupled and sustained separately by different components. The components sustaining the axial and the shear forces all remain elastic even under a rarely occurred earthquake, while the bending components yield and dissipate seismic energy during a design‐level earthquake. This design makes the behavior of the system more predictable and thus more easily customizable to different performance demands. Moreover, the energy dissipation components can be conveniently replaced to fully restore the occupancy function of a building. To examine the seismic behavior of the newly developed component, 3 one third‐scale specimens were tested quasi‐statically, including 1 RC wall complying with the current design codes of China and 2 installed with the damage‐controllable plastic hinges. Each wall was designed to have the same strength. The experimental results demonstrated that the plastic‐hinge‐supported walls had a better energy dissipation capacity and damage controllability than the RC specimen. Both achieved drift ratios greater than 3% under a steadily increasing lateral force.     

高强钢筋混凝土短肢剪力墙抗震性能试验研究

通过对采用高强钢筋的6片T形混凝土短肢剪力墙和采用高强钢筋高强混凝土的6片L形短肢剪力墙进行低周往复加载试验,研究了T形和L形的破坏形态与性能差异,分析了高厚比、轴压比、配箍间距等参数对构件破坏形态、滞回耗能、骨架曲线、延性及耗能等抗震性能的影响,对比分析了构件与普通短肢剪力墙的抗震性能差异。试验结果表明:采用腹板端部箍筋加密的方式可减轻构件端部的损伤和降低正负向加载时承载力和延性的不对称性;T形构件中高厚比为5的试件表现为弯曲破坏,其他构件表现为弯剪破坏;试验中高厚比小的构件相对于高厚比大的试件延性耗能更好,轴压比增大,构件承载力提高但延性降低;与普通短肢剪力墙相比,T形短肢剪力墙承载力和变形能力提高,耗能增加,L形短肢剪力墙承载力提高较大,极限位移增大,构件后期变形能力略有降低,但可以满足抗震性能要求。     

Out‐of‐plane seismic response of vertically spanning URM walls connected to flexible diaphragms

A simplified numerical model was used to investigate the out‐of‐plane seismic response of vertically spanning unreinforced masonry (URM) wall strips. The URM wall strips were assumed to span between two flexible diaphragms and to develop a horizontal crack above the wall mid‐height. Three degrees of freedom were used to accommodate the wall displacement at the crack height and at the diaphragm connections, and the wall dynamic stability was studied. The equations of dynamic motion were obtained using principles of rocking mechanics of rigid bodies, and the formulae were modified to include semi‐rigid wall behaviour. Parametric studies were conducted that included calculation of the wall response for different values of diaphragm stiffness, wall properties, applied overburden, wall geometry and earthquake ground motions. The results of the study suggest that stiffening the horizontal diaphragms of typical low‐rise URM buildings will amplify the out‐of‐plane acceleration demand imposed on the wall and especially on the wall–diaphragm connections. It was found that upper‐storey walls connected to two flexible diaphragms had reduced stability for applied earthquake accelerograms having dominant frequency content that was comparable with the frequency of the diaphragms. It was also found that the applied overburden reduced wall stability by reducing the allowable wall rotations. The results of this study suggest that the existing American Society of Civil Engineers recommendations for assessment of vertically spanning walls overestimate the stability of top‐storey walls in multi‐storey buildings in high‐seismic regions or for walls connected to larger period (less stiff) diaphragms. Copyright © 2015 John Wiley & Sons, Ltd.     

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。     

Seismic behavior and modeling of steel reinforced concrete (SRC) walls

The steel reinforced concrete (SRC) wall consists of structural steel embedded at the boundary elements of a reinforced concrete (RC) wall. The use of SRC walls has gained popularity in the construction of high‐rise buildings because of their superior performance over conventional RC walls. This paper presents a series of quasi‐static tests used to examine the behavior of SRC walls subjected to high axial force and lateral cyclic loading. The SRC wall specimens showed increased flexural strength and deformation capacity relative to their RC wall counterpart. The flexural strength of SRC walls was found to increase with increasing area ratio of embedded structural steel, while the section type of embedded steel did not affect the wall's strength. The SRC walls under high axial force ratio had an ultimate lateral drift ratio of approximately 1.4%. In addition, a multi‐layer shell element model was developed for the SRC walls and was implemented in the OpenSees program. The numerical model was validated through comparison with the test data. The model was able to predict the lateral stiffness, strength and deformation capacities of SRC walls with a reasonable level of accuracy. Finally, a number of issues for the design of SRC walls are discussed, along with a collection and analysis of the test data, including (1) evaluation of flexural strength, (2) calculation of effective flexural stiffness, and (3) inelastic deformation capacity of SRC walls. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental research on behavior of 460 MPa high strength steel I-section columns under cyclic loading

To investigate the seismic behavior of I-section columns made of 460 MPa high strength steel(HSS), six specimens were tested under constant axial load and cyclic horizontal load. The specimens were designed with different width-to-thickness ratios and loaded under different axial load ratios. For each specimen, the failure mode was observed and hysteretic curve was measured. Comparison of different specimens on hysteretic characteristic, energy dissipation capacity and deformation capacity were further investigated. Test results showed that the degradation of bearing capacity was due to local buckling of flange and web. Under the same axial load ratio, as width-to-thickness ratio increased, the deformation area of local buckling became smaller. And also, displacement level at both peak load and failure load became smaller. In addition, the full extent of hysteretic curve, energy dissipation capacity, ultimate story drift angle decreased, and capacity degradation occurred more rapidly with the increase of width-to-thickness ratio or axial load ratio. Based on the capacity of story drift angle, limiting values which shall not be exceeded are suggested respectively for flange and web plate of 460 MPa HSS I-section columns when used in SMFs and in IMFs in the case of axial load ratio no more than 0.2. Such values should be smaller when the axial load ratio increases.     

高强混凝土剪力墙非线性有限元分析

为适应高强材料在土木工程结构中的应用发展需要,本文研究高强混凝土剪力墙在不同参数影响下的受力状态、应力分布以及承载力的变化规律,为高强混凝土剪力墙设计提出合理建议.利用有限元分析软件对高强混凝土剪力墙进行模拟分析,并将模拟结果与试验结果进行对比.在确定数值分析结果的正确性后,进行不同轴压比、剪跨比及不同配筋条件下该类构件数值模拟分析,以研究各参数对高强混凝土剪力墙延性的影响.明确各参数对高强混凝土剪力墙受力性能的影响效果,得出高强混凝土剪力墙承载力随各参数变化的规律.     

免拆超高性能混凝土模板钢筋混凝土柱抗震性能研究

为研究预制超高性能混凝土(UHPC)模板钢筋混凝土(RC)柱的抗震性能,并验证预制UHPC模板在往复荷载作用下是否发生剥离,考虑轴压比、剪跨比、箍筋间距和保护层厚度,设计制作6根免拆模板柱(PTC)和1根RC对比柱试件,对其进行拟静力试验,研究其破坏形态、滞回性能、变形和耗能能力以及强度和刚度退化规律等。结果表明,与加载方向垂直的预制UHPC模板大约在PTC试件峰值荷载的70%时发生剥离,与加载方向平行的预制UHPC模板在试件最终破坏时剥离;在剪跨比、轴压比和箍筋数量均分别相同的条件下,由UHPC模板加10 mm混凝土作为保护层的试件,其抗震性能相对较好,但其承载力和前期刚度略有减小。     

Steel slit shear walls with double‐tapered links capable of condition assessment

The concept of using a hysteretic damper as a condition assessment device that functions immediately after a damaging earthquake is realized by making use of the residual out‐of‐plane deformation of links that are arranged in slit shear walls. According to the proposed inspection procedure, the maximum drift ratio experienced by the slit wall is estimated based on the number of torsionally deformed links whose dimensions are determined so that the links would exhibit notable torsional deformation at the target deformations. The adoption of a double‐tapered shape for the links enables us to significantly increase the amount of out‐of‐plane deformation. The relationship between the dimensions and the torsional deformation of the links is established using numerical simulations. The effectiveness of the proposed condition assessment scenario is verified by using a series of cyclic loading tests for individual links and groups of links. As a hysteretic damper, the strength and stiffness of the links predicted by design equations matched well with test results. Copyright © 2014 John Wiley & Sons, Ltd.     

Bidirectional behavior of unreinforced masonry walls

Most of the studies related to the modeling of masonry structures have by far investigated either the in‐plane (IP) or the out‐of‐plane (OP) behavior of walls. However, seismic loads mostly impose simultaneous IP and OP demands on load‐bearing or shear masonry walls. Thus, there is a need to reconsider design equations of unreinforced masonry walls by taking into account bidirectional effects. The intent of this study is to investigate the bidirectional behavior of an unreinforced masonry wall with a typical aspect ratio under different displacement‐controlled loading directions making use of finite element analysis. For this purpose, the numerical procedure is first validated against the results of the tests on walls with different failure modes conducted by the authors. Afterward, the response of the wall systems is evaluated with increasing top displacement having different orientations. A set of 19 monotonic and three cyclic loading analyses are performed, and the results are discussed in terms of the variation of failure modes and load–displacement diagrams. Moreover, the results of wall capacity in each loading condition are compared with those of the ASCE41‐06 formulations. The results indicate that the direction of the resultant force, vectorial summation of IP and OP forces, of the wall is initially proportional to the ratio of stiffness in the IP and the OP directions. However, with the increase of damage, the resultant force direction inclines towards the wall's longitudinal direction regardless of the direction of the imposed displacement. Finally, recommendations are made for applicability of ASCE41‐06 formulations under different bidirectional loading conditions. Copyright © 2014 John Wiley & Sons, Ltd.