梁铰型屈服RC框架结构地震弹塑性位移增大系数研究

本文通过弹性和弹塑性时程分析,研究了水平地震作用下梁铰型屈服RC框架模型结构的楼层屈服剪力系数、基本自振周期、楼层数3个因素对弹塑性位移增大系数的影响,通过非线性回归分析给出了弹塑性层间位移增大系数经验公式;通过分析滞回耗能沿楼层高度的分布,初步确定了梁铰型屈服RC框架结构的薄弱楼层位置;基于结构损伤分析,讨论了抗震规范中RC框架结构弹塑性层间位移角限值的水准。     

Nonsymmetrical loading protocols for shear links in eccentrically braced frames

The AISC Seismic Provisions for Structural Steel Buildings (AISC 341-16) provide a testing protocol for qualification of link-to-column connections in eccentrically braced frames (EBFs). This symmetrical testing protocol was developed by conducting nonlinear time history analysis on representative EBFs designed according to the International Building Code. Although the testing protocol is intended for qualification of link-to-column connections, many research programs have employed this recommended protocol for testing of shear links. Recent numerical investigations on constructed EBFs and archetype models showed that links can be subjected to one-sided loadings with significantly higher link rotation angles than the codified limits. A numerical study has been undertaken to develop nonsymmetrical loading protocols for shear links in EBFs. Pursuant to this goal, 20 EBF archetypes were designed according to the ASCE7-16 standard. The main parameters investigated were the link length to bay width ratio (e/L), number of stories, type of EBF, and the ground motion level. The archetypes were subjected to maximum considered earthquake and collapse level earthquake as recommended by FEMA P695. The results showed that the history of link rotation is single sided and depends strongly on e/L and the level of ground motion. Nonsymmetrical loading protocols that depend on the aforementioned variables were developed and are presented herein.     

Deflection amplification factor for estimating seismic lateral deformations of RC frames

Different values have been assigned to the ratio of the defl ection amplifi cation factor(Cd) to the response modifi cation factor(R) for a specifi ed force-resisting system in the seismic design provisions while the same application is defi ned for it. An analytical study of the seismic responses of several reinforced concrete frames subjected to a suite of earthquake records performed in this research indicate that the stories’ overstrength and stiffness distribution along the structural height can affect local defl ections more than global ones. Therefore, the Cd/R ratio is calculated based on the ratio of both maximum inelastic to maximum elastic displacements and interstory drifts. Due to damage concentration in some specifi c stories, the defl ection amplifi cation factor calculated based on inelastic interstory drifts was larger than that of the inelastic displacements. Consequently, a minimum value of 1.0 is recommended for the Cd/R ratio in order to estimate maximum inelastic drifts. The ratio of inelastic to elastic displacement was generally found to increase slightly along the structural height for the studied RC models. In addition, it was detected that the story damage indices of the studied RC frames decrease when the inverted value of inelastic interstory drift ratios are increased through a(negative) power form.     

Evaluation of displacement coefficient method for seismically retrofitted buildings with various ductility capacities

This research study is aimed at evaluating the accuracy of the displacement coefficient method (DCM) of FEMA 440 and associated nonlinear static procedure (NLSP) for actual buildings with soft story mechanism and various ductility capacities. The DCM and associated NLSP are evaluated using two existing seismically vulnerable buildings with soft story mechanism. The buildings are first retrofitted using a ductile steel‐brace‐link system to represent those with good ductility capacity and then retrofitted with RC squat infill shear panels (SISPs) to represent those with relatively poor ductility capacity. The evaluation of the DCM of FEMA 440 and associated NLSP is then performed by comparing the roof displacements (target displacements), maximum interstory drifts, and maximum plastic hinge rotations of the original and retrofitted buildings obtained from NLSP (at the target displacement level of DCM) with those obtained from nonlinear response history (NRH) analyses for three different seismic performance levels. It is observed that the DCM, and hence, the NLSP fail to accurately predict the NRH analyses results mainly due to uncertainties in the coefficient C₁ of the DCM in the short period range, the inability of the DCM to capture the failure of structural members beyond a certain lateral displacement or plastic rotation limit and associated soft story mechanism. Copyright © 2013 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.     

A numerical study on response factors for steel wall–frame systems

A numerical investigation was undertaken to evaluate the response of dual structural systems that consisting of steel plate shear walls and moment‐resisting frames. The primary objective of the study was to investigate the influence of elastic base shear distribution between the wall and the frame on the global system response. A total of 10 walls and 30 wall–frame systems, ranging from 3 to 15 stories, were selected for numerical assessment. These systems represent cases in which the elastic base shear resisted by the frame has a share of 10, 25, or 50% of the total base shear resisted by the dual system. The numerical study consisted of 1600 time history analyses employing three‐dimensional finite elements. All 40 structures were separately analyzed for elastic and inelastic response by subjecting them to the selected suite of earthquake records. Interstory drifts, top story drift, base shears resisted by the wall, and the frame were collected during each analysis. Based on the analysis results, important response quantities, such as the strength reduction, the overstrength, and the displacement amplification factors, are evaluated herein. Results are presented in terms of displacement measures, such as the interstory drift ratio and the top story drift ratio. Analysis results revealed that the increase in the strength reduction factor with the amount of load share is insignificant. Furthermore, there is an inverse relationship between the ductility reduction and the overtsrength. Copyright © 2010 John Wiley & Sons, Ltd.     

利用等位移原则估计高层结构的非弹性地震反应(二)

通过高层结构弹性和非弹性地震时程反应分析,研究了两者的位移反应关系。结果表明：结构在不同地震作用下非弹性总位移角反应的平均值与弹性反应十分接近,基本符合等位移原则,可以用后者分析结果直接估计前者;结构最大层间位移角反应的平均值在弱和中等非线性阶段亦与弹性反应十分接近,在强非线性阶段则大于弹性反应,经数据拟合,初步提供了一个在此阶段由弹性最大层间位移角反应估计非弹性反应的近似公式。     

Evaluation of the response modification coefficient and collapse potential of special concentrically braced frames

Special concentrically braced frames (SCBFs) are commonly used for seismic design of buildings. Their large elastic stiffness and strength efficiently sustains the seismic demands during smaller, more frequent earthquakes. During large, infrequent earthquakes, SCBFs exhibit highly nonlinear behavior due to brace buckling and yielding and the inelastic behavior induced by secondary deformation of the framing system. These response modes reduce the system demands relative to an elastic system without supplemental damping using a response modification coefficient, commonly termed the R factor. More recently, procedures put forth in FEMAP695 have been made to quantify the R factor through a formalized procedure that accounts for collapse potential. The primary objective of the research in this paper was to evaluate the approach for SCBFs. An improved model for SCBFs that permits simulation of brace fracture was used to conduct response history analyses. A series of three‐story, nine‐story and 20‐story SCBFs were designed and evaluated. Initially, the FEMAP695 method was conducted to estimate collapse and the corresponding R factor. An alternate procedure for scaling the multiple acceleration records to the seismic design hazard was also evaluated. The results show significant variation between the two methods. Of the three variations of buildings studied, the largest vulnerability was identified for the three‐story building. To achieve a consistent margin of safety against collapse, a significantly lower R factor is required for the low‐rise SCBFs (three‐story), whereas the mid‐rise and high‐rise SCBFs (nine‐story and 20‐story) may continue to use the current value of 6, as provided in ASCE‐07. Copyright © 2013 John Wiley & Sons, Ltd.     

Torsional balance of plan‐asymmetric structures with frictional dampers: analytical results

This investigation deals with the torsional balance of the earthquake response and design of elastic asymmetric structures with frictional dampers. Plan asymmetry leads to an uneven lateral deformation demand among structural members and to unbalanced designs with larger capacities in some resisting planes. Frictional dampers are capable of controlling lateral‐torsional coupling by placing the so‐called empirical center of balance (ECB) of the structure at equal distance from all edges of the building. This rule is developed for single‐story systems with linear and inelastic behavior. However, recently obtained theoretical and experimental results demonstrate that this rule carries over to multistory structures. Results show that the peak displacement demand at the building edges and that of resisting planes equidistant from the geometric center may be similar if the damper is optimally placed. It is also shown that torsional amplification of the edge displacements of arbitrary asymmetric structures relative to the displacement of the symmetric counterparts are approximately bound by a factor of 2. Furthermore, frictional dampers are equally effective in controlling lateral‐torsional coupling of torsionally flexible as well as stiff structures. Copyright © 2005 John Wiley & Sons, Ltd.     

Effect of soil depth on inelastic seismic response of structures

Effect of depth of soil stratum on estimated inelastic displacement of three typical structures, viz. a four storey building, a continuous bridge, and a tower, is studied and adequacy of the site amplification models of the current design codes and available empirical relationships is examined. The structures are assumed to be located on well-defined sites with varying bedrock depths, and effect of depth on elastic response spectrum, site amplification factor, displacement modification factor and inelastic displacement is studied, numerically, for two values of PGA. It is observed that soil depth has a significant effect on elastic as well as inelastic response of the structures; however, the effect of soil amplification on inelastic response is not as pronounced as in case of elastic response. Therefore, use of empirical site amplification models based on elastic response may be too conservative, for estimating inelastic response.     

Limitations on linear elastic procedures in performance assessment of regular frames

Linear elastic analysis procedures are employed exclusively in the traditional seismic design of new structures and widely employed in the seismic assessment of existing structures. It is also a convenient tool for the initial checking of deformations in displacement‐based design. The limitations that should be imposed on linear elastic procedures have been evaluated in this study by comparing the deformation‐based response quantities obtained from response spectrum analysis with those from the nonlinear time history analysis. Both procedures were applied to different design variants of 5, 8, and 12 story moment frames, subjected to 20 strong motion components exhibiting a variety of intensities. Member plastic rotations and interstory drift ratios were employed as the basic response parameter in performance assessment. It has been found that average column demand to capacity ratio (DCR) (the ratio of flexural demand from linear elastic analysis to flexural capacity) and average beam DCR at the critical story are the most effective parameters in determining the validity range of linear elastic procedures in regular moment frames. Limiting values for these response parameters are proposed. Furthermore, amplification factors for member rotation demands predicted by the linear procedures are suggested for moment frames when these limiting values are exceeded. These factors ensure that the amplified linear elastic rotations are not smaller than 84 percentile (mean – 1sigma) of the rotations obtained from nonlinear time history analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Determination of column size for displacement‐based design of reinforced concrete frame buildings

This article reports a method to determine the storey‐wise column size for displacement‐based design of reinforced concrete frame buildings with a wide range of storey drift and building plan. The method uses a computer program based algorithm. The basic relation used in the algorithm is formulated by considering the various possible deformation components involved in the overall frame deformation. As a necessity to represent the deformation component due to plastic rotation of beam members, a relation between the beam plastic rotation and the target‐drift is adopted. To control the dynamic amplification of interstorey drift, a target‐drift dependant design‐drift reduction factor is used. The dynamic amplification of column moment is accounted with the help of an approximate conversion of fundamental period of the building from the effective period of the equivalent SDOF system. To avoid the formation of plastic hinge in column members, a design‐drift dependant column–beam moment capacity ratio is used. The method successfully determines the storey‐wise column size for buildings of four plans of different varieties, heights up to 12 storeys and target‐drift up to 3%. Copyright © 2013 John Wiley & Sons, Ltd.     

On the inelastic seismic response of asymmetric buildings under bi‐axial excitation

The elastic and inelastic seismic response of plan‐asymmetric regular multi‐storey steel‐frame buildings has been investigated under bi‐directional horizontal ground motions. Symmetric variants of these buildings were designed according to Eurocodes 3 and 8. Asymmetric buildings were created by assuming a mass eccentricity in each of the two principal directions. The torsional response in the elastic and inelastic range is qualitatively similar with the exception of the stiff edge in the strong direction of torsionally stiff buildings and the stiff edge in the weak direction of torsionally flexible buildings. The response is influenced by the intensity of ground motion, i.e. by the magnitude of plastic deformation. In the limiting case of very strong ground motion, the behaviour of initially torsionally stiff and initially torsionally flexible buildings may become qualitatively similar. A decrease in stiffness due to plastic deformations in one direction may substantially influence the behaviour in the orthogonal direction. The response strongly depends on the detailed characteristics of the ground motion. On average, torsional effects are reduced with increasing plastic deformations, unless the plastic deformations are small. Taking into account also the dispersion of results which is generally larger in the inelastic range than in the elastic one, it can be concluded that (a) the amplification of displacements determined by the elastic analysis can be used as a rough estimate also in the inelastic range and (b) any favourable torsional effect on the stiff side of torsionally stiff buildings, which may arise from elastic analysis, may disappear in the inelastic range. The conclusions are limited to fairly regular buildings and subject to further investigations. Copyright © 2005 John Wiley & Sons, Ltd.     

Elastic and inelastic drift performance optimization for reinforced concrete buildings under earthquake loads

This paper presents an effective optimization technique for the elastic and inelastic drift performance design of reinforced concrete buildings under response spectrum loading and pushover loading. Attempts have been made to develop an automatic optimal elastic and inelastic drift design of concrete framework structures. The entire optimization procedure can be divided into elastic design optimization and inelastic design optimization. Using the principle of virtual work, the elastic drift response generated by the response spectrum loading and the inelastic drift response produced by the non‐linear pushover loading can be explicitly expressed in terms of element sizing design variables. The optimization methodology for the solution of the explicit design problem of buildings is fundamentally based on the Optimality Criteria approach. One ten‐story, two‐bay building frame example is presented to illustrate the effectiveness and practicality of the proposed optimal design method. While rapid convergence in a few design cycles is found in the elastic optimization process, relatively slow but steady and smooth convergence of the optimal performance‐based design is found in the inelastic optimization process. Copyright © 2004 John Wiley & Sons, Ltd.     

Replaceable links with direct brace attachments for eccentrically braced frames

This paper reports findings of an experimental study conducted on replaceable links for steel eccentrically braced frames (EBFs). A replaceable link detail which is based on splicing the directly connected braces and the beam outside the link is proposed. This detail eliminates the need to use hydraulic jacks and flame cutting operations for replacement purposes. Performance of this proposed replaceable link was studied by conducting eight nearly full‐scale EBF tests under quasi‐static cyclic loading. The link length ratio, stiffening of the link, loading protocol, connection type, bolt pretension, gap size of splice connections, and demand‐to‐capacity ratios of members were considered as the prime variables. The specimens primarily showed two types of failure modes: link web fracture and fracture of the flange at the link‐to‐brace connection. No failures were observed at the splice connections indicating that the proposed replaceable link detail provides an excellent response. The inelastic rotation capacity provided by the replaceable links satisfied the requirements of the AISC Seismic Provisions for Structural Steel Buildings (AISC341–10). The overstrength factor of the links exceeded 2.0, which is larger than the value assumed for EBF links by design provisions. The high level of overstrength resulted in brace buckling in one of the specimens demonstrating the importance of overstrength factor used for EBF links. Copyright © 2017 John Wiley & Sons, Ltd.     

On the inelastic torsional response of single‐storey structures under bi‐axial excitation

An attempt has been made to explore the general trends in the seismic response of plan‐asymmetric structures without any restrictions imposed by a particular code. Systems with structural elements in both orthogonal directions under bi‐directional excitation were studied. Idealized single‐storey models with bi‐axial eccentricity were employed. The systems were torsionally stiff and, in the majority of cases, mass‐eccentric. The main findings are: in general, inelastic torsional response is qualitatively similar to elastic torsional response. Quantitatively, the torsional effect on the flexible side, expressed as an increase of displacements due to torsion, decreases slightly with increasing plastic deformation, unless the plastic deformations are small. The response on the stiff side generally strongly depends on the effect of several modes of vibration and on the influence of the ground motion in the transverse direction. These influences depend on the structural and ground motion characteristics in both directions. Reduction of displacements due to torsion, typical for elastic torsionally stiff structures, usually decreases with increasing plastic deformations. As an additional effect of large plastic deformations, a flattening of the displacement envelopes in the horizontal plane usually occurs, indicating that torsional effects in the inelastic range are generally smaller than in the elastic range. The dispersion of the results of inelastic torsional response analysis is generally larger than that of elastic analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Predominant period and equivalent viscous damping ratio identification for a full‐scale building shake table test

The predominant period and corresponding equivalent viscous damping ratio, also known in various loading codes as effective period and effective damping coefficient, are two important parameters employed in the seismic design of base‐isolated and conventional building structures. Accurate determination of these two parameters can reduce the uncertainty in the computation of lateral displacement demands and interstory drifts for a given seismic design spectrum. This paper estimates these two parameters from data sets recorded from a full‐scale five‐story reinforced concrete building subjected to seismic base excitations of various intensities in base‐isolated and fixed‐base configurations on the outdoor shake table at the University of California, San Diego. The scope of this paper includes all test motions in which the yielding of the reinforcement has not occurred and the response can still be considered ‘elastic’. The data sets are used with three system identification methods to determine the predominant period of response for each of the test configurations. One of the methods also determines the equivalent viscous damping ratio corresponding to the predominant period. It was found that the predominant period of the fixed‐base building lengthened from 0.52 to 1.30 s. This corresponded to a significant reduction in effective system stiffness to about 16% of the original stiffness. The paper then establishes a correlation between predominant period and peak ground velocity. Finally, the predominant periods and equivalent viscous damping ratios recommended by the ASCE 7‐10 loading standard are compared with those determined from the test building. Copyright © 2017 John Wiley & Sons, Ltd.     

Estimation of inelastic seismic deformations in asymmetric multistorey RC buildings

Four real buildings with three to six stories, strong irregularities in plan and little engineered earthquake resistance are subjected to inelastic response‐history analyses under 56 bidirectional EC8‐spectra‐compatible motions. The average chord rotation demand at each member end over the 56 response‐history analyses is compared to the chord rotation from elastic static analysis with inverted triangular lateral forces or modal response spectrum analysis. The storey‐average inelastic‐to‐elastic‐chord‐rotation‐ratio was found fairly constant in all stories, except when static elastic analysis is applied to buildings with large higher mode effects. Except for such buildings, static elastic analysis gives more uniform ratios of inelastic chord rotations to elastic ones within and among stories than modal response spectrum analysis, but generally lower than 1.0. With increasing EPA the building‐average inelastic‐to‐elastic‐chord‐rotation‐ratio decreases but scatter in the results increases. Static elastic analysis tends to overestimate the inelastic torsional effects at the flexible or central part of the torsionally flexible buildings and underestimate them at their stiff side. Modal response spectrum analysis tends to overestimate the inelastic torsional effects at the stiff or central part of the torsionally stiff buildings and underestimate them at the flexible side. Overall, for multistorey RC buildings that typically have fundamental periods in the velocity‐sensitive part of the spectrum, elastic modal response spectrum analysis with 5% damping gives on average unbiased and fairly accurate estimates of member inelastic chord rotations. If higher modes are not significant, elastic static analysis in general overestimates inelastic chord rotations of such buildings, even when torsional effects are present. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamic collapse analysis for a reinforced concrete frame sustaining shear and axial failures

Shaking table test results from a one‐story, two‐bay reinforced concrete frame sustaining shear and axial failures are compared with nonlinear dynamic analyses using models developed for the collapse assessment of older reinforced concrete buildings. The models provided reasonable estimates of the overall frame response and lateral strength degradation; however, the measured drifts were underestimated by the models. Selected model parameters were varied to investigate the sensitivity of the calculated response to changes in the drift at shear failure, rate of shear strength degradation, and drift at axial failure. For the selected ground motion, the drift at shear failure and rate of shear strength degradation did not have a significant impact on the calculated peak drift. By incorporating shear and axial‐load failure models, the analytical model is shown to be capable of predicting the axial‐load failure for a hypothetical frame with three nonductile columns. Improvements are needed in drift demand estimates from nonlinear dynamic analysis if such analyses are to be used in displacement‐based performance assessments. Copyright © 2008 John Wiley & Sons, Ltd.     

Inelastic displacement ratios for evaluation of structures built on soft soil sites

This paper summarizes the results of a comprehensive statistical study aimed at evaluating peak lateral inelastic displacement demands of structures with known lateral strength and stiffness built on soft soil site conditions. For that purpose, empirical information on inelastic displacement ratios which are defined as the ratio of peak lateral inelastic displacement demands to peak elastic displacement demands are investigated. Inelastic displacement ratios were computed from the response of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to 118 earthquake ground motions recorded on bay‐mud sites of the San Francisco Bay Area and on soft soil sites located in the former lake‐bed zone of Mexico City. Mean inelastic displacement ratios and their corresponding scatter are presented for both ground motion ensembles. The influence of period of vibration normalized by the predominant period of the ground motion, the level of lateral strength, earthquake magnitude, and distance to the source are evaluated and discussed. In addition, the effects of post‐yield stiffness and of stiffness and strength degradation on inelastic displacement ratios are also investigated. It is concluded that magnitude and distance to the source have negligible effects on constant‐strength inelastic displacement ratios. Results also indicate that weak and stiffness‐degrading structures in the short spectral region could experience inelastic displacement demands larger than those corresponding to non‐degrading structures. Finally, a simplified equation obtained using regression analyses aimed at estimating mean inelastic displacement ratios is proposed for assisting structural engineers in performance‐based assessment of structures built on soft soil sites. Copyright © 2006 John Wiley & Sons, Ltd.