剪切型结构的抗震强度折减系数研究

为了研究剪切型结构抗震强度需求的变化规律,本文基于单自由度体系的非线性时程分析,研究了不同场地条件下延性折减系数与位移延性系数和结构自振周期的关系;采用修正等效单自由度体系位移延性折减系数的方法,研究了剪切型多自由度体系的延性折减系数;以基于中国建筑抗震规范设计的代表不同抗震能力要求的RC框架结构为分析对象,通过静力弹塑性分析,研究了RC框架结构的体系超强能力。分析结果表明场地类别、位移延性水准和结构振动周期对单自由度体系的延性折减系数有显著的影响;多自由度体系的抗震延性折减系数明显比其相应的等效单自由度体系的抗震延性折减系数小;RC框架结构的超强系数一般随结构楼层数的增加而减小,随抗震设防烈度的增大而减小,内框架的超强系数比边框架的超强系数大。     

Response reduction factor of irregular RC buildings in Kathmandu valley

Most current seismic design includes the nonlinear response of a structure through a response reduction factor(R). This allows the designer to use a linear elastic force-based approach while accounting for nonlinear behavior and deformation limits. In fact, the response reduction factor is used in modern seismic codes to scale down the elastic response of a structure. This study focuses on estimating the actual ‘R' value for engineered design/construction of reinforced concrete(RC) buildings in Kathmandu valley. The ductility and overstrength of representative RC buildings in Kathmandu are investigated. Nonlinear pushover analysis was performed on structural models in order to evaluate the seismic performance of buildings. Twelve representative engineered irregular buildings with a variety of characteristics located in the Kathmandu valley were selected and studied. Furthermore, the effects of overstrength on the ductility factor, beam column capacity ratio on the building ductility, and load path on the response reduction factor, are examined. Finally, the results are further analyzed and compared with different structural parameters of the buildings.     

Behavior of ductile steel X-braced RC frames in seismic zones

A satisfactory ductile performance of moment-resisting reinforced concrete concentric braced frame structures (RC-MRCBFs) is not warranted by only following the provisions proposed in Mexico’s Federal District Code (MFDC-04). The nonlinear behavior of low to medium rise ductile RC-MRCBFs using steel X-bracing susceptible to buckling is evaluated in this study. The height of the studied structures ranges from 4 to 20 stories and they were located for design in the lake-bed zone of Mexico City. The design of RC-MRCBFs was carried out considering variable contribution of the two main lines of defense of the dual system (RC columns and steel braces). In order to observe the principal elements responsible for dissipating the earthquake input energy, yielding mappings for different load-steps were obtained using both nonlinear static and dynamic analyses. Some design parameters currently proposed in MFDC-04 as global ductility capacities, overstrength reduction factors and story drifts corresponding to different limit states were assessed as a function of both the considered shear strength and slenderness ratios for the studied RC-MRCBFs using pushover analyses. Additionally, envelopes of response maxima of dynamic parameters were obtained from the story and global hysteresis curves. Finally, a brief discussion regarding residual drifts, residual drift ratios, mappings of residual deformations in steel braces and residual rotations in RC beams and columns is presented. From the analysis of the obtained results, it is concluded that when a suitable design criterion is considered, good structural behavior of RC-MRCBFs with steel-X bracing can be obtained. It is also observed that the shear strength balance has an impact in the height-wise distribution of residual drifts, and an important “shake-down” effect is obtained for all cases. There is a need to improve design parameters currently proposed in MFDC to promote an adequate seismic performance of RC-MRCBFs.

     

Nonlinear seismic analysis of unsymmetric-plan structures retrofitted by hysteretic damped braces

A displacement-based design procedure using hysteretic damped braces (HYDBs) is proposed for the seismic retrofitting of unsymmetric-plan structures. An expression of the viscous damping equivalent to the hysteretic energy dissipated by the damped braced frame is proposed under bidirectional seismic loads, where corrective factors are assumed as a function of design parameters of the HYDBs. To this end, the nonlinear dynamic analysis of an equivalent two degree of freedom system is firstly carried out on seven pairs of real ground motions whose displacement response spectra match, on average, the design spectrum proposed by the Italian seismic code for a high-risk seismic zone and a medium subsoil class. Then, the extended N2 method considered by the European seismic code, which combines the nonlinear static analysis along the in-plan principal directions of the structure with elastic modal analysis, is adopted to evaluate the higher mode torsional effects. The town hall of Spilinga (Italy), a reinforced concrete (r.c.) framed building with an L-shaped plan, is supposed to be retrofitted with HYDBs. Six structural solutions are compared considering two alternative in-plan distributions of the HYDBs, to eliminate (elastic) torsional effects, and three design values of the frame ductility combined with a constant design value of the damper ductility. To check the effectiveness and reliability of the DBD procedure, the nonlinear static analysis of the test structures is carried out, by evaluating the vulnerability index of r.c. frame members and the ductility demand of HYDBs for different in-plan directions of the seismic loads.     

Seismic performance of R/C frames with overstrength discontinuities in elevation

The paper presents the results of a research study concerning the seismic response and design of r/c frames with overstrength discontinuities in elevation. The discontinuities are obtained assigning overstrengths either to the beams or to the columns of a “regular frame” (assumed as reference). Two “regular frames” are designed: one according to the Eurocode 8 (EC8) medium ductility class (DCM) rules and the other one according to the EC8 high ductility class (DCH) rules. For all frames the criteria of vertical strength irregularity of many international seismic codes are applied. Non linear static and dynamic analyses are performed; mechanical non linearity is concentrated at the element ends. These analyses are carried out according to EC8 provisions: for non linear static analysis the N2 method is applied; in the case of non linear time-history analyses, seven real earthquakes, selected in order to fit on average the elastic design spectrum, are used as input. The seismic response of frames characterised by the assigned overstrength is not very different with respect to the “regular frame” one; furthermore all the frames satisfy the Ultimate Limit State, verified by the application of non linear static and dynamic analyses. This demonstrates that the sensitivity of frames, designed according to EC8 medium and high ductility classes, to overstrength vertical variations is low. Consequently, international code provisions on vertical strength regularity should be reviewed.     

Estimation of seismic drift and ductility demands in planar regular X‐braced steel frames

This paper summarizes the results of an extensive study on the inelastic seismic response of X‐braced steel buildings. More than 100 regular multi‐storey tension‐compression X‐braced steel frames are subjected to an ensemble of 30 ordinary (i.e. without near fault effects) ground motions. The records are scaled to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, brace slenderness ratio and column stiffness strongly influence the amplitude and heightwise distribution of inelastic deformation. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer a direct estimation of drift and ductility demands. The uncertainty of this estimation due to the record‐to‐record variability is discussed in detail. More specifically, given the strength (or behaviour) reduction factor, the proposed formulae provide reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum cyclic ductility of the diagonals along the height of the structure. The strength reduction factor refers to the point of the first buckling of the diagonals in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This design‐oriented feature enables both the rapid seismic assessment of existing structures and the direct deformation‐controlled seismic design of new ones. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic retrofitting with buckling restrained braces: Application to an existing non-ductile RC framed building

This paper assesses the seismic performance of typical reinforced concrete (RC) existing framed structures designed for gravity loads only. The sample two-storey structural system exhibits high vulnerability, i.e. low lateral resistance and limited translation ductility; hence an effective strategy scheme for seismic retrofitting was deemed necessary. Such a scheme comprises buckling restrained braces (BRBs) placed along the perimeter frames of the multi-storey building. The adopted design approach assumes that the global response of the inelastic framed structure is the sum of the elastic frame (primary system) and the system comprising perimeter diagonal braces (secondary system); the latter braces absorb and dissipate a large amount of hysteretic energy under earthquake ground motions. Comprehensive nonlinear static (pushover) and dynamic (response history) analyses were carried out for both the as-built and retrofitted structures to investigate the efficiency of the adopted intervention strategy. A set of seven code-compliant natural earthquake records was selected and employed to perform inelastic response history analyses at serviceability (operational and damageability limit states, OLS and DLS) and ultimate limit states (life safety and collapse prevention limit states, LSLS and CPLS). Both global and local lateral displacements are notably reduced after the seismic retrofit of the existing system. In the as-built structure, the damage is primarily concentrated at the second floor (storey mechanism); the computed interstorey drifts are 2.43% at CPLS and 1.92% at LSLS for modal distribution of lateral forces. Conversely, for the retrofitted system, the estimated values of interstorey drifts (d/h) are halved; the maximum d/h are 0.84% at CPLS (along the Y-direction) and 0.65% at LSLS (yet along the Y-direction). The values of the global overstrength Ω vary between 2.14 and 2.54 for the retrofitted structure; similarly, the translation ductility μ_Δ-values range between 2.07 and 2.36. The response factor (R- or q-factor) is on average equal to 5.0. It is also found that, for the braced frame, under moderate-to-high magnitude earthquakes, the average period elongation is about 30%, while for the existing building the elongation is negligible (lower than 5%). The inelastic response of the existing structure is extremely limited. Conversely, BRBs are effective to enhance the ductility and energy dissipation of the sample as-built structural system. Extensive nonlinear dynamic analyses showed that more than 60% of input seismic energy is dissipated by the BRBs at ultimate limit states. The estimated maximum axial ductility of the braces is about 10; the latter value of translation ductility is compliant with BRBs available on the market. At DLS, the latter devices exhibit an elastic behaviour. It can thus be concluded that, under moderate and high magnitude earthquakes, the damage is concentrated in the added dampers and the response of the existing RC framed structure (bare frame) is chiefly elastic.     

Simplified seismic sidesway collapse analysis of frame buildings

This paper presents the development and assessment of a simplified procedure for estimating the seismic sidesway collapse margin ratio of building structures. The proposed procedure is based on the development of a robust database of seismic peak displacement responses of nonlinear single‐degree‐of‐freedom systems for various seismic intensities and uses nonlinear static (pushover) analysis without the need for nonlinear time history dynamic analysis. The proposed simplified procedure is assessed by comparing its collapse capacity predictions on 72 different building structures with those obtained by nonlinear incremental dynamic analyses. The proposed simplified procedure offers a simple, yet efficient, computational/analytical tool that is capable of predicting collapse capacities with acceptable accuracy for a wide variety of frame building structures. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic safety of low ductility structures used in Spain

The most important aspects of the design, seismic damage evaluation and safety assessment of structures with low ductility like waffle slabs buildings or flat beams framed buildings are examined in this work. These reinforced concrete structural typologies are the most used in Spain for new buildings but many seismic codes do not recommend them in seismic areas. Their expected seismic performance and safety are evaluated herein by means of incremental non linear structural analysis (pushover analysis) and incremental dynamic analysis which provides capacity curves allowing evaluating their seismic behavior. The seismic hazard is described by means of the reduced 5% damped elastic response spectrum of the Spanish seismic design code. The most important results of the study are the fragility curves calculated for the mentioned building types, which allow obtaining the probability of different damage states of the structures as well as damage probability matrices. The results, which show high vulnerability of the studied low ductility building classes, are compared with those corresponding to ductile framed structures.     

Effectiveness of nonlinear static procedures for slender masonry towers

This paper investigates the accuracy of pushover-based methods in predicting the seismic response of slender masonry towers, through comparison with the results from a large number of nonlinear time-history dynamic analyses. In particular, conventional pushover analyses, in both their force- and displacement-based variants, are considered, and seismic assessment through the well-established N2 method is also addressed. The study is conducted by applying a simple non-linear elastic model recently developed and implemented in the computational code MADY to represent slender masonry structures. The model enables both pushover analyses and non-linear dynamic analyses to be performed with a minimum of effort. A multi-record incremental dynamic analysis carried out for a quite large number of structural cases, each of which is subjected to a comprehensive set of dynamic nonlinear analyses, is used to evaluate the accuracy of pushover methods in predicting the global structural response, as represented by the usual capacity curve together with a damage curve, both of which are compared with dynamic envelopes. Local responses, in terms of lateral displacements and the distribution of damage along the tower height are also compared. The results reveal that the key issue in the accuracy of pushover methods is the nature of the lateral load applied, that is, whether it is a force or a displacement. Different ranges of expected deformation are suggested for adopting each type of lateral load to better represent the actual behaviour of masonry towers and their damage under seismic events through pushover methods.     

Seismic analysis of diagrid structural frames with shear-link fuse devices

This paper presents a new concept for enhancing the seismic ductility and damping capacity of diagrid structural frames by using shear-link fuse devices and its seismic performance is assessed through nonlinear static and dynamic analysis.The architectural elegancy of the diagrid structure attributed to its triangular leaning member configuration and high structural redundancy make this system a desirable choice for tall building design.However,forming a stable energy dissipation mechanism in diagrid framing remains to be investigated to expand its use in regions with high seismicity.To address this issue,a diagrid framing design is proposed here which provides a competitive design option in highly seismic regions through its increased ductility and improved energy dissipation capacity provided by replaceable shear links interconnecting the diagonal members at their ends.The structural characteristics and seismic behavior(capacity,stiffness,energy dissipation,ductility) of the diagrid structural frame are demonstrated with a 21-story building diagrid frame subjected to nonlinear static and dynamic analysis.The findings from the nonlinear time history analysis verify that satisfactory seismic performance can be achieved by the proposed diagrid frame subjected to design basis earthquakes in California.In particular,one appealing feature of the proposed diagrid building is its reduced residual displacement after strong earthquakes.     

Generalized force vectors for multi‐mode pushover analysis

A generalized pushover analysis (GPA) procedure is developed for estimating the inelastic seismic response of structures under earthquake ground excitations. The procedure comprises applying different generalized force vectors separately to the structure in an incremental form with increasing amplitude until a prescribed seismic demand is attained for each generalized force vector. A generalized force vector is expressed as a combination of modal forces, and simulates the instantaneous force distribution acting on the system when a given response parameter reaches its maximum value during dynamic response to a seismic excitation. While any response parameter can be selected arbitrarily, generalized force vectors in the presented study are derived for maximum interstory drift parameters. The maximum value of any other response parameter is then obtained from the envelope of GPAs results. Each nonlinear static analysis under a generalized force vector activates the entire multi‐degree of freedom effects simultaneously. Accordingly, inelastic actions develop in members with the contribution of all ‘instantaneous modes’ in the nonlinear response range. Target seismic demands for interstory drifts at the selected stories are calculated from the associated drift expressions. The implementation of the proposed GPA is simpler compared with nonlinear response history analysis, whereas it is less demanding in computational effort when compared with several multi‐mode adaptive nonlinear static procedures. Moreover, it does not suffer from the statistical combination of inelastic modal responses obtained separately. The results obtained from building frames have demonstrated that GPA is successful in estimating maximum member deformations and member forces with reference to the response history analysis. When the response is linear elastic, GPA and response spectrum analysis produce identical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Ductility demands on buckling-restrained braced frames under earthquake loading

Accurate estimates of ductility demands on buckling-restrained braced frames (BRBFs) are crucial to performance-based design of BRBFs. An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS Center, Lehigh University to prepare for an upcoming experimental program. The analysis program DRAIN-2DX was used to model a one-bay, four-story prototype BRBF including material and geometric nonlinearities. The bucklingrestrained brace (BRB) model incorporates both isotropic and kinematic hardening. Nonlinear static pushover and timehistory analyses were performed on the prototype BRBF. Performance objectives for the BRBs were defined and uscd to evaluate thc time-history analysis results. Particular emphasis was placed on global ductility demands and ductility demands oa the BRBs. These demands were compared with anticipated ductility capacities. The analysis results, along with results from similar previous studics, are used to evaluate the BRBF design provisions that have been recommended for codification in the United States. Thc results show that BRB maximum ductility demands can be as high as 20 to 25. These demands significantly exceed those anticipated by the BRBF recommended provisions. Results from the static pushover and timehistory analyses are used to demonstrate why the ductility demands exceed those anticipated by the recommended provisions.The BRB qualification testing protocol contained in the BRBF recommended provisions is shown to be inadequate because it requires only a maximum ductility demand of at most 7.5. Modifications to the testing protocol are recommended.     

RC框架结构超强系数与地震经济损失风险分析

基于现行的中国抗震设计规范,设计了6个不同参数的钢筋混凝土框架结构模型,利用静力弹塑性(Pushover)分析方法求得各个框架结构的超强系数;同时,利用基于性能的抗震设计(PBSD)的方法,通过增量动力分析(IDA)、易损性分析和地震损失风险分析等,定量的求出各个框架结构的经济损失风险,并比较了不同框架结构超强系数和经...     

Experimental tests on full‐scale RC unretrofitted frame and retrofitted with buckling‐restrained braces

The results of experimental tests carried out on reinforced concrete (RC) full‐scale 2‐storey 2‐bays framed buildings are presented. The unretrofitted frame was designed for gravity loads only and without seismic details; such frame was assumed as a benchmark system in this study. A similar RC frame was retrofitted with buckling‐restrained braces (BRBs). The earthquake structural performance of both prototypes was investigated experimentally using displacement‐controlled pushover static and cyclic lateral loads. Modal response properties of the prototypes were also determined before and after the occurrence of structural damage. The results of the dynamic response analyses were utilized to assess the existing design rules for the estimation of the elastic and inelastic period of vibrations. Similarly, the values of equivalent damping were compared with code‐base relationships. It was found that the existing formulations need major revisions when they are used to predict the structural response of as‐built RC framed buildings. The equivalent damping ratio ξ_eq was augmented by more than 50% when the BRBs was employed as bracing system. For the retrofitted frame, the overstrength Ω and the ductility µ are 1.6 and 4.1, respectively; the estimated R‐factor is 6.5. The use of BRBs is thus a viable means to enhance efficiently the lateral stiffness and strength, the energy absorption and dissipation capacity of the existing RC substandard frame buildings. The foundation systems and the existing members of the superstructure are generally not overstressed as the seismic demand imposed on them can be controlled by the axial stiffness and the yielding force of the BRBs. Copyright © 2011 John Wiley & Sons, Ltd.     

Corrective eccentricities for assessment by the nonlinear static method of 3D structures subjected to bidirectional ground motions

Nonlinear static methods are reliable in the evaluation of the seismic response of planar structural schemes, but they are not very effective in the assessment of three-dimensional building structures. The authors of this paper have recently proposed a nonlinear static approach for asymmetric structures, which is an improvement on that stipulated by seismic codes. This method is based on the observation that the distribution of the maximum dynamic displacements of the deck can be enveloped by two pushover analyses performed by applying the lateral force with two eccentricities with respect to the center of mass of the deck. These eccentricities, named “corrective eccentricities”, are defined so that the two corresponding pushover analyses provide displacements that are equal to those evaluated by nonlinear dynamic analysis at the two sides of the deck. In this paper, the corrective eccentricities are determined for a wide set of single-story systems. The equations for their analytical evaluation are determined and their reliability is demonstrated. Finally, the analysis of a multi-story structure is conducted to show how the method can be applied to real buildings. Copyright © 2012 John Wiley & Sons, Ltd.     

高强钢组合偏心支撑框架抗震性能研究

高强钢组合K型偏心支撑框架耗能梁段和支撑采用Q345钢,其余构件采用Q460钢,不仅能有效减小构件截面、节约钢材、降低造价,而且有助于推广高强钢的应用。为了比较高强钢组合K型偏心支撑框架与Q345钢K型偏心支撑框架的抗震性能,在试验研究的基础上,设计两组共8个不同层数的高强钢组合K型偏心支撑框架与Q345钢K型偏心支撑框架,并分别对其进行非线性静力推覆分析和动力时程分析,对比分析两种结构形式的承载力、刚度、延性以及地震作用下层间变形能力和耗能梁段。结果表明:在满足抗震性能要求的前提下,相同设计条件下高强钢组合K型偏心支撑框架变形略差于Q345钢K型偏心支撑框架,但是其构件截面较小,可以节省钢材,降低工程造价,具有较高的经济效益。     

Steel rings as seismic fuses for enhancing ductility of cross braced frames

A new remedy is proposed in this study to increase the ductility of cross-braced frames to a level comparable with ductile moment frames. The suggested system consists of one or two concentric steel rings installed in the cross-braced bay vertically. The steel rings are designed such that they fail in bending sooner than failure of the braces in compression.Then the rings act as seismic fuses with multiple bending plastic hinges. Using nonlinear static analysis, it is shown that the proposed sys...     

Effects of torsion on the behavior of peripheral steel‐braced frame systems

In this study, the torsional response of buildings with peripheral steel‐braced frame lateral systems is evaluated. A three‐dimensional model of a three story braced frame with various levels of eccentricity is created and the effects of torsion on the seismic response is assessed for four hazard levels. The response history analysis results indicate that, unlike frame structures, the torsional amplifications in the inelastic systems exceed those of corresponding elastic systems and tend to increase with an increase in the level of inelasticity. The ability of two simplified procedures, elastic response spectrum analysis and pushover analysis, to capture the torsional amplifications in steel‐braced frames is evaluated. Copyright © 2010 John Wiley & Sons, Ltd.     

应用弹塑性反应谱对IDA方法的改进研究

针对传统IDA方法中结构的加速度反应远高于SPO分析结果的现象,采用弹塑性反应谱作为IDA的烈度度量,同时给出随地震烈度改变而不断变化的屈服强度系数,提出了改进的IDA方法,更有效地考虑了结构的非线性地震反应特征。实际工程分析表明,改进的IDA方法能够体现结构的非线性受力反应,同时兼顾结构的动力反应特征,与SPO曲线和由规范计算得到的结构承载力有更好的可比较性。