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 buckling- restrained brace(BRB)model incorporates both isotropic and kinematic hardening.Nonlinear static pushover and time- history analyses were performed on the prototype BRBF.Performance objectives for the BRBs were defined and used to evaluate the time-history analysis results.Particular emphasis was placed on global ductility demands and ductility demands on the BRBs.These demands were compared with anticipated ductility capacities.The analysis results,along with results from similar previous studies,are used to evaluate the BRBF design provisions that have been recommended for codification in the United States.The 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 time- history 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.

Experimental and numerical study of buckling-restrained braces configured with out-of-plane eccentricity under cyclic loading

This study focuses on variations in the hysteretic behavior of buckling-restrained braces(BRBs)configured with or without out-of-plane eccentricity under cyclic loading.Quasi-static experiments and numerical simulations were carried out on concentrically and eccentrically loaded BRB specimens to investigate the mechanical properties,energy dissipation performance,stress distribution,and high-order deformation pattern.The experimental and numerical results showed that compared to the concentrically loaded BRBs,the stiffness,yield force,cumulated plastic ductility(CPD)coefficient,equivalent viscous damping coefficient and energy dissipation decreased,and the yield displacement and compression strength adjustment factor increased for the eccentrically loaded BRBs.With the existence of the out-of-plane eccentricity,the initial yield position changes from the yield segment to the junction between the yield segment and transition segment under a tensile load,while the initial high-order buckling pattern changes from a first-order C-shape to a secondorder S-shape under a compressive load.

Assessment of buckling-restrained braced frame reliability using an experimental limit-state model and stochastic dynamic analysis

Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame （BRBF） reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that： （1） quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; （2） quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and （3） evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves （i.e., conditional probabilities of brace failure given ground shaking intensity parameters） were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.

Peak displacement patterns for the performance-based seismic design of steel eccentrically braced frames

Performance-based seismic design(PBSD) aims to assess structures at different damage states. Since damage can be directly associated to displacements, seismic design with consideration of displacement seems to be logical. In this study, simple formulae to estimate the peak floor displacement patterns of eccentrically braced frames(EBFs) at different performance levels subjected to earthquake ground motions are proposed. These formulae are applicable in a PBSD and especially in direct displacement-based design(DDBD). Parametric study is conducted on a group of 30 EBFs under a set of 15 far field and near field accelerograms which they scaled to different amplitudes to adapt various performance levels. The results of thousands of nonlinear dynamic analyses of EBFs have been post-processed by nonlinear regression analysis in order to recognize the major parameters that influence the peak displacement pattern of these frames. Results show that suggested displacement patterns have relatively good agreement with those acquired by an exact nonlinear dynamic analysis.

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 system can be designed to behave like cross-braced frames with regard to stiffness and strength,and like special moment frames with regard to ductility.Seismic design factors for the proposed system are recommended based on nonlinear pushover and cyclic analysis studies.

Parametric Study on Cable-Stayed and Knee-Braced Steel Portal Frames

To improve wind resistance capacity of cable-braced steel portal frames,a double-braced portal frame was proposed by adding two pre-stressed knee braces to a cable-braced portal frame. To study the reasonable range of application and method of cable parameter determination for this novel structure,the influences of load condition, span, base constraint, and cable parameters on structural performance were investigated by using the finite element code SAP2000. The results show that pre-stressed knee braces can effectively resist both uplifted and lateral wind loads,so this cablestayed and knee-braced steel portal frame is suitable for large wind.When the vertical load is comparable with the wind load,this novel type of portal frames is suitable for a medium span( 21-48 m). The cables in the cable brace can be determined by structural vertical stiffness,and the cables in the knee brace can be designed as the same as those in the cable-stayed part for the reason that their cross sectional area has only a weak effect on the structure. If no cable fails,the pretension variation of the cable does not affect the stiffness of the portal frame. The cable in the cable brace,working together with the cables in the knee braces,can ease uneven distribution of internal force,and their pretensions can be determined according to actual engineering projects.

Optimization of design parameters for controlled rocking steel braced dual-frames

A controlled rocking concentrically steel braced frame(CR-CSBF)is introduced as an alternative to conventional methods to prevent major structural damage during large earthquakes.It is equipped with elastic post-tensioned(PT)cables and replaceable devices or fuses to provide overturning resistance and dissipate energy,respectively.Although CR-CSBFs are not officially legalized in globally valid codes for new buildings,it is expected to be presented in them in the near future.The main goal of this study is to determine the optimal design parameters consist of the yield strength and modulus of elasticity of the fuse,the initial force of the PT cable,and the gravity load on the rocking column,considering different heights of the frame,spanning ratios and ground motion types for dual-configuration CR-CSBF.Nonlinear time-history analyses are performed in OpenSees.This study aims to define the optimal input variables as effective design parameters of CR-CSBFs by comparing four seismic responses consisting of story drift,roof displacement,roof acceleration and base shear,and also using the Euclidean metric optimization method.Despite the previous research,this study is innovative and first of its kind.The results demonstrate that the optimal design parameters are variable for various conditions.

Nonlinear Seismic Response of Steel Concentrically Braced Frames Using Endurance Time Analysis Method

In present paper application of Endurance Time Analysis （ETA） method in nonlinear seismic assessment of steel concentrically braced frames is studied. In this method structure is subjected to a set of predesigned increasing acceleration functions and various responses of the structure are recorded during synthetic seismic excitation. The averages of maximum values for various responses in Nonlinear Time-History Analyses （NTHA） extracted from real ground motions are expected to be close to those obtained from ETA up to equivalent target time. For this purpose a set of 9, 11, 13 and 15 stories steel frames were designed and plastic hinge method was selected as source of nonlinearity in all cases. Responses were compared based on interstory drift ratio and story shear in two methods and results show satisfactory consistency between two methods. Finally, it was concluded that the ETA method can be used as alternative method in nonlinear seismic analysis of concentrically braced steel frames.

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 lakebed 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 diff erent 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 diff erent 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” eff ect 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.

Shaking table test and numerical analysis of a 1:12 scale model of a special concentrically braced steel frame with pinned connections

This paper describes shaking table tests of a 1：12 scale model of a special concentrically braced steel frame with pinned connections, which was fabricated according to a one-bay braced frame selected from a typical main factory building of a large thermal power plant. In order to investigate the seismic performance of this type of structure, several ground motion accelerations with different levels for seismic intensity Ⅷ, based on the Chinese Code for Seismic Design of Buildings, were selected to excite the model. The results show that the design methods of the members and the connections are adequate and that the structural system will perform well in regions of high seismicity. In addition to the tests, numerical simulations were also conducted and the results showed good agreement with the test results. Thus, the numerical model is shown to be accurate and the beam element can be used to model this structural system.

Experimental study on the seismic response of braced reinforced concrete frame with irregular columns

A 15-storey K-braced reinforced concrete model frame with irregular columns, i.e., T-shaped, L-shaped, as well as ＋-shaped columns, was constructed and tested on the six-degree-of-freedom shaking table at the State Key Laboratory for Disaster Reduction in Civil Engineering in Tongji, China. Two types of earthquake records, El-Centro wave （south-north direction） and Shanghai artificial wave （SHAW） with various peak accelerations and principal-secondary sequences, were input and experimentally studied. Based on the shaking table tests and theoretical analysis, several observations can be made. The failure sequence of the model structure is brace→beam→column→joints, so that the design philosophy for several lines of defense has been achieved. Earthquake waves with different spectrums not only influence the magnitude and distribution of the earthquake force and the storey shear force, but also obviously affect the magnitude of the displacement response. The aftershock seismic response of previously damaged reinforced concrete braced frames with irregular columns possesses the equivalent elastic performance characteristic. Generally speaking, from the aspects of failure features and drift ratio, this type of reinforced concrete structure provides adequate earthquake resistance and can be promoted for use in China.

Development and subassemblage cyclic testing of hybrid buckling-restrained steel braces

Buckling-restrained braced frames(BRBFs) are vulnerable to relatively higher post-earthquake residual drifts under high intensity ground shakings. This is primarily due to the low axial elastic and post-elastic stiffness of bucklingrestrained braces(BRBs) satisfying the design force demand requirements. In the present study, a hybrid buckling restrained bracing system consisting of a short yielding core length BRB component and a conventional buckling-type brace component connected in series has been developed with an aim to increase the axial stiffness of braces. This study is focused on the experimental investigation of six hybrid bucking restrained braces(HBRBs) to investigate their overall behavior, loadresisting capacity, strength-adjustment factors and energy dissipation potential. The main parameters varied are the crosssectional area, the yielding length of core elements as well as the detailing of buckling-restraining system of short yielding core length BRBs. Test results showed that the HBRBs with yielding core length in the range of 30% of work-point to workpoint lengths withstood an axial strain of 6% without any instability and can deliver stable and balanced hysteretic response and excellent energy dissipation under reversed cyclic loading conditions.

Application of buckling-restrained braces in the seismic control of suspension bridges

Buckling-restrained braces(BRBs)are widely used to improve the seismic performance of buildings.This paper aims to introduce BRBs to suspension bridges and assess the seismic performance of bridges with BRBs.Taking the Dadu River Bridge as a case study,an FEA model of the bridge is established,and different seismic measures(BRBs between the deck and the tower,BRBs at the middle of the span to replace the inclined suspenders to connect the deck and the main cables,fluid viscous dampers(FVDs)between the deck and the tower,the combination of BRBs to replace the inclined suspenders as well as FVDs between the deck and the tower)are applied to the suspension bridge.The influence of the parameters of BRBs on the seismic response of the suspension bridge is studied,and the performance of the bridge with BRBs is compared with that of the bridge with FVDs.The results indicate that the use of BRBs in place of the inclined suspenders is beneficial to reduce the displacement of the deck and limit the shear force and bending moment of the tower.The seismic performance of the suspension bridge with BRBs and FVDs is better than that of the bridge with BRBs or FVDs.Therefore,the application of BRBs is a feasible method to improve the seismic performance of the suspension bridge.

Stability Performance of Buckling-Restrained Brace with Brace Joints

The stability and ductility of four buckling-restrained braces (BRBs) with brace joints were studied. The load-carrying element of BRB was fabricated with steel (Chinese Q235), and a layer of colloidal silica sheet (0.5 mm in thickness) or four layers of plastic film (0.2 mm in thickness) were used as unbonding materials to provide space to prevent the buckling of inner core in higher modes and facilitate its lateral expansion in case of compression. Based on the equation of BRBs with brace joints of different restrained stiffnesses, the buckling load is calculated considering the initial geometric imperfections and residual stress, and the theoretical values agree well with the experiment results. It is concluded that the buckling load and ductility of BRBs are influenced greatly by the restrained stiffness of brace joints. If the restrained stiffness is deficient, the unstrained segment of BRBs with less stiffness will buckle firstly. As a result, the ultimate load of BRBs decreases, and the maximum compression load is reduced to about 65% of the maximum tension load; the stiffness also degenerates, and there is a long decreasing stage on the back-bone curve in compression phase; the ductility decreases, i.e., the ultimate tension ductility and ultimate compression ductility are approximately 15 and 1.3 respectively, and the cumulative plastic ductility is only approximately 200. If the restrained stiffness of joint is large enough, the stability will be improved as follows: the yielding strength and ultimate strength of BRBs are nearly the same, and there is an obvious strain intensification in both tension and compression phases; the ductility of brace also increases obviously, i.e., the ultimate tension ductility and ultimate compression ductility are both approximately 14, and the cumulative plastic ductility reaches 782.

Seismic response of high-rise steel framed buildings with Chevron-braced designed according to Venezuelan codes

The object of this study is to determine the seismic response of regular high-rise steel buildings with chevron-braced frames. Mechanics models of three buildings of 14, 18 and 20 stories are studied, all of them with similar geometric characteristics in plant and elevation. These models are realized using prescriptions and parameters from venezuelan design codes. The seismic action is carry on through varius synthetic design spectrum compatible accelerograms defined by the seismic codes in this study, with three levels of intensity corresponding to three specific Limit States. Dynamic analysis is used to compute parameters of ductility, over strength and maximum displacements. From these results it can be concluded that chevron-braced frames presented a good overall performance and non V-braced frames show greater damage due to dynamic actions, validating non linear dynamic analysis as a very powerful tool to seismic-resistance design and chevron-braced frames as a very useful choice in improving the response of tall steel structures. since this lateral bracing system is absent from Venezuelan seismic codes.

Seismic performance and resilience of composite damping self-centering braced frame structures

A magnetorheological self-centering brace(MR–SCB)has been proposed to improve the energy dissipation capability of the brace.In this paper,a 15-story MR–SCB braced frame is numerically analyzed to examine its seismic performance and resilience.The MR–SCB provides higher lateral stiffness than the buckling restrained brace and greater energy dissipation capability than the existing self-centering brace.The brace also exhibits a reliable recentering capacity.Under rare earthquakes,the maximum average residual deformation ratio of the structure is less than the 0.5%limit.Under mega earthquakes,the maximum average interstory drift ratio of the structure does not exceed the 2.0%elastoplastic limit,and its maximum average floor acceleration ratio is 1.57.The effects of mainshock and aftershock on the structural behavior are also investigated.The interstory drift and residual deformation of the structure increase with the increase of the intensity of the aftershock.Under aftershocks with the same intensity as the mainshocks,the maximum increment of the residual deformation ratio of the structure is 81.8%,and the average interstory drift ratios of the 12^(th),7^(th),and 3^(rd)stories of the structure are increased by 13.4%,9.2%and 7.5%,respectively.The strong aftershock may significantly cause increased damage to the structure,and increase its collapse risk and residual deformation.

Effectiveness of two conventional methods for seismic retrofit of steel and RC moment resisting frames based on damage control criteria

This study investigates the efficiency of two types of rehabilitation methods based on economic justification that can lead to logical decision making between the retrofitting schemes. Among various rehabilitation methods, concentric chevron bracing（CCB） and cylindrical friction damper（CFD） were selected. The performance assessment procedure of the frames is divided into two distinct phases. First, the limit state probabilities of the structures before and after rehabilitation are investigated. In the second phase, the seismic risk of structures in terms of life safety and financial losses（decision variables） using the recently published FEMA P58 methodology is evaluated. The results show that the proposed retrofitting methods improve the serviceability and life safety performance levels of steel and RC structures at different rates when subjected to earthquake loads. Moreover, these procedures reveal that financial losses are greatly decreased, and were more tangible by the application of CFD rather than using CCB. Although using both retrofitting methods reduced damage state probabilities, incorporation of a site-specific seismic hazard curve to evaluate mean annual occurrence frequency at the collapse prevention limit state caused unexpected results to be obtained. Contrary to CFD, the collapse probability of the structures retrofitted with CCB increased when compared with the primary structures.

Seismic retrofitting of reinforced concrete frame structures using GFRP-tube-confined-concrete composite braces

This paper presents a new type of structural bracing intended for seismic retrofitting use in framed structures. This special composite brace, termed glass-fiber-reinforced-polymer （GFRP）-tube-confined-concrete composite brace, is comprised of concrete confined by a GFRP tube and an inner steel core for energy dissipation. Together with a contribution from the GFRP-tube confined concrete, the composite brace shows a substantially increased stiffness to control story drift, which is often a preferred feature in seismic retrofitting. An analysis model is established and implemented in a general finite element analysis program - OpenSees, for simulating the load-displacement behavior of the composite brace. Using this model, a parametric study of the hysteretic behavior （energy dissipation, stiffness, ductility and strength） of the composite brace was conducted under static cyclic loading and it was found that the area ratio of steel core to concrete has the greatest influence among all the parameters considered. To demonstrate the application of the composite brace in seismic retrofitting, a three-story nonductile reinforced concrete （RC） frame structure was retrofitted with the composite braces. Pushover analysis and nonlinear time-history analyses of the retrofitted RC frame structure was performed by employing a suite of 20 strong ground motion earthquake records. The analysis results show that the composite braces can effectively reduce the peak seismic responses of the RC frame structure without significantly increasing the base shear demand.

Seismic Design Loads of Truss Arch Frames with Ceilings subjected to Vertical and Horizontal Earthquake Motions

Spatial structures such as a gymnasium and an exhibition hall often use ceilings because of enhancing sound effects and reducing heating bills. Although the ceiling members fell down on a large scale due to the seismic motion according to the past great earthquake disaster reports, structural engineers particularly do not carry out the seismic design. The study gives structural engineers the equivalent static loads for the design of the earthquake-proof design of the ceiling system. In particular, it is significant to investigate the dynamic behavior and the applied seismic loads for the complicated vibration of the long span arch building structures with RC columns.

钢支撑-钢筋混凝土掉层框架结构抗震性能试验研究

为改善坡地钢筋混凝土(RC)掉层框架结构抗侧刚度分布的不均匀性,设计了一栋在上接地层设置钢支撑的RC掉层框架结构,按1/4比例提取其顺坡向中榀框架下部5层子结构为试验对象,开展钢支撑-RC掉层框架拟静力试验,观测试件的破坏过程,并对比RC掉层框架试验所得试件的破坏形态,分析试件滞回性能、延性和刚度退化等抗震性能指标。结果表明:试件的最终破坏是以第4层柱底混凝土压溃,梁端混凝土剥落、底部钢筋断裂,顶层柱顶混凝土剥落为标志。与RC掉层框架试验结果相比,钢支撑-RC掉层框架试件上接地柱的破坏明显减轻,柱端破坏分布也更为均匀,避免了掉层框架结构“半层破坏模式”的出现,改善了结构的耗能和抗地震倒塌能力。但试件上接地层相邻上一层的变形和破坏程度较大,应对该楼层的柱端进行适当的抗震加强;设置钢支撑后,试件的滞回曲线较为饱满,并具有良好的延性(正、负向加载的位移延性系数分别可达5.13、5.69),正负向加载的刚度退化曲线也趋于对称。