A design procedure for suspended zipper‐braced frames in the framework of Eurocode 8

In the recent past, suspended zipper‐braced frames were proposed to avoid one‐storey collapse mechanisms and dynamic instability under severe ground motions. In this paper, the design procedure suggested by Yang et al. is first slightly modified to conform to the design approach and capacity design rules stipulated in Eurocode 8 for concentrically braced frames. The procedure is applied to a set of suspended zipper‐braced frames with different number of storeys and founded on either soft or rock soil. The structural response of these frames is analysed to highlight qualities and deficiencies and to assess the critics reported by other researchers with regard to the design procedure by Yang et al. Then, improvements are proposed to this procedure to enhance the energy dissipation of the chevron braces and the response of the structural system as well. The effectiveness of the design proposals is evaluated by incremental dynamic analysis on structures with different geometric properties, gravity loads and soil of foundation. Copyright © 2017 John Wiley & Sons, Ltd.     

Development of a ten-element hybrid simulation platform and an adjustable yielding brace for performance evaluation of multi-story braced frames subjected to earthquakes

This paper presents a ten-element hybrid (experimental-numerical) simulation platform, referred to as UT10, which was developed for running hybrid simulations of braced frames with up to ten large-capacity physical brace specimens. This paper presents the details of the development of different components of UT10 and an adjustable yielding brace (AYB) specimen, which was designed to perform hybrid simulations with UT10. As the first application of UT10, a five-story buckling-restrained braced frame and a special concentrically braced frame (BRBF and SCBF) were designed and tested with AYB specimens and buckling specimens representing the braces. Cyclic tests of the AYB, one- and three-element hybrid simulations of the BRBF, and four-element hybrid simulations of the SCBF inside the UT10 confirmed the functionality of UT10 for running hybrid simulations on multiple specimens. The tests also indicated that AYB was capable of producing a stable hysteretic response with characteristics similar to BRBs. Comparison of the results of the hybrid simulations of the BRBF and SCBF with their fully numerical models showed that the modeling inaccuracies of the yielding braces could potentially affect the global response of the multi-story braced frames further emphasizing the need for experimental calibration or hybrid simulation for achieving more accurate response predictions. UT10 provides a simple and reconfigurable platform that can be used to achieve a realistic understanding of the seismic response of multi-story frames with yielding braces, distinguish their modeling limitations, and improve different modeling techniques available for their seismic response prediction.     

Hybrid testing and modeling of a suspended zipper steel frame

An analytical and experimental study has been conducted to evaluate the seismic performance of a three‐story suspended zipper steel frame. The frame was concentrically braced and had zipper struts to transfer the unbalanced forces induced on the beams due to the buckling of the lower‐story braces. The experimental study was conducted with the hybrid test technique, in which only the bottom‐story braces of the three‐story frame were physically tested, while the behavior of the rest of the frame was modeled using a general structural analysis software. The paper discusses issues pertinent to the calibration of the computer model for the analytical substructure as well as for the entire frame, including the selection of an appropriate damping matrix, and the modeling of the buckling behavior of the braces and bracing connections. The analytical model of the entire frame was validated with the hybrid tests and was able to accurately capture the material and geometric nonlinearities that developed when the braces yielded and buckled. This study has demonstrated the usefulness of hybrid testing in improving analytical models and modeling assumptions and providing information that cannot be obtained from an analytical study alone. The results have shown that the suspended zipper frame can distribute the brace nonlinearity over the first two stories as intended in the design and will not have catastrophic failure under the design‐level earthquakes considered in this study, despite the significant inelastic deformations. Copyright © 2009 John Wiley & Sons, Ltd.     

Steel frames with bracing mechanism and hysteretic dampers

A new earthquake resistant structural system for multi‐storey frame structures, based on a dual function of its bracing components, is developed. This consists of a hysteretic damper device and a cross‐bracing mechanism with a kinetic closed circuit, working only in tension, so that cable members can be used for this purpose. Solutions are presented regarding the connections' design of three types of structural frame system, that are concerned throughout the study: braced moment free frame, braced moment resisting frame with moment free supports, and with moment resisting supports. The dynamic behaviour of the system is investigated on the basis of an SDOF model, and based on the response spectra method an approximate design approach of the controlled structures is shown. From the time history analysis of the structural systems for the El Centro earthquake the areas of appropriate stiffness relations of the frames to the hysteretic dampers and the cable braces are deduced, so that the energy dissipation of the system may be controlled by the damper‐cable bracing mechanism. Based on the results of these studies, a predesign approach is developed for the implementation of the control system in frame structures. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

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

<正>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 intensityⅧ,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.     

消能支撑框架结构的非线性分析

本文介绍了六榀钢筋混凝土支撑框架模型（两榀为普通支撑框架，另四榀为消能支撑框架）在低周反复荷载作用下的工作性能和试验结果；编制了非线性程序，对试验模型进行了计算分析，计算结果和试验实测值符合较好；另外还计算了两榀足尺消能支撑框架结构，研究不同的消能器滑移荷载对结构抗震能力的影响，结果表明消能支撑框架结构具有良好、稳定的抗震性能。     

A cantilever beam analogy for quantifying higher mode effects in multistorey buildings

This paper examines higher mode effects in systems where the ductile mechanism for seismic design is the base moment‐rotation response. The modal properties of flexural and shear beams with uniform mass and elasticity and with a variable amount of base rotational restraint are derived. As the base fixity is released, the first mode becomes the rigid body rotation of the beam about the base, but the higher modes change much less, particularly for the shear beam model. Most response quantities that are of interest in the seismic design of typical mid‐rise buildings are controlled by the first two lateral modes, except at locations along the height where the second mode contributes little. However, the third and higher lateral modes are more significant for high‐rise buildings. Based on the theory of uniform cantilever shear beams, expressions are developed to avoid the need for a modal analysis to estimate the overturning moment, storey shear, and floor acceleration envelopes. Considering the measured response from the shake table testing of a large‐scale eight‐storey controlled rocking steel braced frame, the proposed expressions are shown to be of similar or better accuracy to a modified modal superposition technique, which combines the higher mode response from an elastic modal analysis with the response associated with achieving the maximum base overturning moment according to an inverted triangular load distribution. Because the proposed method uses only parameters that are available at the initial design stage, avoiding the analysis of a structural model, it is likely to be especially useful for preliminary design. Copyright © 2015 John Wiley & Sons, Ltd.     

Shake table test and numerical study of self‐centering steel frame with SMA braces

Given their excellent self‐centering and energy‐dissipating capabilities, superelastic shape memory alloys (SMAs) become an emerging structural material in the field of earthquake engineering. This paper presents experimental and numerical studies on a scaled self‐centering steel frame with novel SMA braces (SMAB), which utilize superelastic Ni–Ti wires. The braces were fabricated and cyclically characterized before their installation in a two‐story one‐bay steel frame. The equivalent viscous damping ratio and ‘post‐yield’ stiffness ratio of the tested braces are around 5% and 0.15, respectively. In particular, the frame was seismically designed with nearly all pin connections, including the pinned column bases. To assess the seismic performance of the SMA braced frame (SMABF), a series of shake table tests were conducted, in which the SMABF was subjected to ground motions with incremental seismic intensity levels. No repair or replacement of structural members was performed during the entire series of tests. Experimental results showed that the SMAB could withstand several strong earthquakes with very limited capacity degradation. Thanks to the self‐centering capacity and pin‐connection design, the steel frame was subjected to limited damage and zero residual deformation even if the peak interstory drift ratio exceeded 2%. Good agreement was found between the experimental results and numerical simulations. The current study validates the prospect of using SMAB as a standalone seismic‐resisting component in critical building structures when high seismic performance or earthquake resilience is desirable under moderate and strong earthquakes. Copyright © 2016 John Wiley & Sons, Ltd.     

Hybrid simulation testing of a self‐centering rocking steel braced frame system

The self‐centering rocking steel frame is a seismic force resisting system in which a gap is allowed to form between a concentrically braced steel frame and the foundation. Downward vertical force applied to the rocking frame by post‐tensioning acts to close the uplifting gap and thus produces a restoring force. A key feature of the system is replaceable energy‐dissipating devices that act as structural fuses by producing high initial system stiffness and then yielding to dissipate energy from the input loading and protect the remaining portions of the structure from damage. In this research, a series of large‐scale hybrid simulation tests were performed to investigate the seismic performance of the self‐centering rocking steel frame and in particular, the ability of the controlled rocking system to self‐center the entire building. The hybrid simulation experiments were conducted in conjunction with computational modules, one that simulated the destabilizing P‐Δ effect and another module that simulated the hysteretic behavior of the rest of the building including simple composite steel/concrete shear beam‐to‐column connections and partition walls. These tests complement a series of quasi‐static cyclic and dynamic shake table tests that have been conducted on this system in prior work. The hybrid simulation tests validated the expected seismic performance as the system was subjected to ground motions in excess of the maximum considered earthquake, produced virtually no residual drift after every ground motion, did not produce inelasticity in the steel frame or post‐tensioning, and concentrated the inelasticity in fuse elements that were easily replaced. Copyright © 2014 John Wiley & Sons, Ltd.     

高层高强钢组合偏心支撑框架抗震性能简化分析

高强钢组合偏心支撑钢框架是一种新型的抗震结构体系,为分析其抗震性能,利用ABAQUS有限元软件建立了简化分析模型。在验证该简化模型合理有效的基础上,建立了某十层算例的整体模型,施加竖向荷载的同时施加水平倒三角形循环荷载作用,进而分析了该算例的滞回性能。研究表明:本文提出的简化分析模型不仅可以较准确的模拟该结构体系的延性和抗侧刚度,还可以有效预测结构的变形分布和非线性性能。     

Dynamic and equivalent static procedures for capacity design of controlled rocking steel braced frames

Controlled rocking steel braced frames (CRSBFs) have been proposed as a low‐damage seismic force resisting system with reliable self‐centring capabilities. Vertical post‐tensioning tendons are designed to self‐centre the system after rocking, and energy dissipation may be provided to limit the peak displacements. The post‐tensioning and energy dissipation can be designed using simple methods that rely primarily on the first‐mode response. However, the frame member forces are highly influenced by the higher‐mode response, resulting in more complex methods to design the frame members. This paper examines previous proposals and also proposes two new capacity design methods for CRSBFs. The first is a dynamic procedure that requires a truncated response spectrum analysis on a model of the frame with modified boundary conditions to consider the rocking behaviour. The second is an equivalent static method that does not require any modifications to the elastic frame model, instead using theory‐based lateral force distributions to consider the higher modes of the rocking structure. Neither method requires empirical calibration. The dynamic procedure is used to design two sets of CRSBFs with three, six, nine, twelve and eighteen stories, one set using a response modification factor of R = 8 and the other using up to R = 20. Based on the results of 800 nonlinear time history analyses, both methods are generally more accurate than the previous capacity design methods and at least as simple to implement. Finally, the displacement results suggest that taller CRSBFs designed using could still limit interstorey drifts to approximately 2.5% at the maximum considered earthquake level in the cases considered. Copyright © 2016 John Wiley & Sons, Ltd.     

Modified seismic design of concentrically braced frames considering flexural demand on columns

Special concentrically braced frames (SCBFs) are considered as one of the most economical and effective lateral force‐resisting systems in structures located in the regions of high seismicity. Steel braces in a braced frame undergo large axial deformations in tension and compression to dissipate the seismic energy. However, past studies have shown that SCBFs exhibit the soft‐story hinge mechanisms and unpredictable failure patterns under earthquake loading conditions. These inelastic responses along with the use of continuous structural sections as columns over consecutive floors induce flexural demand that is not considered in the current design practice. In this study, the evaluation of seismic performance of nine SCBFs designed as per the current practice has been carried out for three different story heights (i.e., three‐story, six‐story, and nine‐story) and three types of brace configurations (namely, chevron, split X, and single X). Three additional design techniques are also explored based on (i) the inclusion of column moments in the design; (ii) the theory of formation of plastic hinges; and (iii) the design of braces considering the forces computed at their post‐buckled stages. Nonlinear dynamic analyses of these study frames have been evaluated numerically using a computer software Perform‐3D for a suite of 40 ground motions representing the design basis earthquake and maximum considered earthquake hazard levels. Analyses results showed that the SCBFs designed as per the modified procedures achieved the desired performance objectives without the formation of soft‐story mechanism. Copyright © 2017 John Wiley & Sons, Ltd.     

Hybrid formulation of operator splitting (OS) and Newmark‐β methods for collaborative structural analysis (CSA)

A collaborative structural analysis (CSA) system is developed, which is capable of performing highly sophisticated structural analyses utilizing beneficial features of existing individual structural analysis programs. In the system, the global equations of motion for the overall structural system are formulated in the host program. Some substructures, whose behaviors are relatively simple, are directly solved in the host program, whereas those having complex behavior are analyzed by the station programs. A time‐consuming static condensation procedure is needed for the substructures analyzed by the station programs if adopting an implicit integration scheme. The operator splitting (OS) method, which does not require tangential stiffness, can be used to improve the system efficiency. To this end, a hybrid formulation of the Newmark‐β and OS methods is proposed, and a CSA scheme based on the hybrid formulation is developed. In the CSA system adopting the hybrid formulation, the degrees of freedom whose tangential stiffness are unavailable are formulated by the OS method, whereas the rest are still formulated by the commonly used Newmark‐β method. Using the system, analyses of a three‐story‐braced steel moment‐resisting frame are conducted. In the analyses, the column bases are analyzed using the commercial finite element method software ABAQUS, and the remaining structural elements are analyzed using a frame analysis program called NETLYS. Results suggest that the hybrid formulation is very effective for the CSA system. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic performance of chevron-configured special concentrically braced frames with yielding beams

Current seismic design requirements for special concentrically braced frames (SCBFs) in chevron configurations require that the beams supporting the braces be designed to resist the demands resulting from the simultaneous yielding of the tension brace and degraded, post-buckling strength of the compression brace. Recent research, including large-scale experiments and detailed finite-element analyses, has demonstrated that limited beam yielding is not detrimental to chevron braced frame behavior and actually increases the story drift at which the braces fracture. These findings have resulted in new expressions for computing beam demands in chevron SCBFs that reduce the demand in the tension brace to be equal to the expected compressive capacity at buckling of the compression brace. In turn, the resultant force on the beam is reduced as is the required size of the beam. Further study was undertaken to investigate the seismic performance of buildings with SCBFs, including chevron SCBFs with and without yielding beams and X-braced frames. Prototype three- and nine-story braced frames were designed using all three framing systems, that is, chevron, chevron with yielding beams, and X SCBFs, resulting in six building frames. The nonlinear dynamic response was studied for ground motions simulating two different seismic hazard levels. The results were used to characterize the seismic performance in terms of the probability of salient damage states including brace fracture, beam vertical deformation, and collapse. The results demonstrate that the seismic performance of chevron SCBFs with limited beam yielding performs as well as or better than the conventionally designed chevron and X SCBFs.     

Seismic performance and new design procedure for chevron‐braced frames

The paper is concerned with the seismic design of steel‐braced frames in which the braces are configured in a chevron pattern. According to EuroCode 8 (EC8), the behaviour factor q, which allows for the trade‐off between the strength and ductility, is set at 2.5 for chevron‐braced frames, while 6.5 is assigned for most ductile steel moment‐resisting frames. Strength deterioration in post‐buckling regime varies with the brace's slenderness, but EC8 adopts a unique q value irrespective of the brace slenderness. The study focuses on reevaluation of the q value adequate for the seismic design of chevron‐braced frames. The present EC8 method for the calculation of brace strength supplies significantly different elastic stiffnesses and actual strengths for different values of brace slenderness. A new method to estimate the strength of a chevron brace pair is proposed, in which the yield strength (for the brace in tension) and the post‐buckling strength (for the brace in compression) are considered. The new method ensures an identical elastic stiffness and a similar strength regardless of the brace slenderness. The advantage of the proposed method over the conventional EC8 method is demonstrated for the capacity of the proposed method to control the maximum inter‐storey drift. The q values adequate for the chevron‐braced frames are examined in reference to the maximum inter‐storey drifts sustained by most ductile moment‐resisting frames. When the proposed method is employed for strength calculation, the q value of 3.5 is found to be reasonable. It is notable that the proposed method does not require larger cross‐sections for the braces compared to the cross‐sections required for the present EC8 method. Copyright © 2005 John Wiley & Sons, Ltd.     

Rigid‐plastic models for the seismic design and assessment of steel framed structures

This paper demonstrates the applicability of response history analysis based on rigid‐plastic models for the seismic assessment and design of steel buildings. The rigid‐plastic force–deformation relationship as applied in steel moment‐resisting frames (MRF) is re‐examined and new rigid‐plastic models are developed for concentrically‐braced frames and dual structural systems consisting of MRF coupled with braced systems. This paper demonstrates that such rigid‐plastic models are able to predict global seismic demands with reasonable accuracy. It is also shown that, the direct relationship that exists between peak displacement and the plastic capacity of rigid‐plastic oscillators can be used to define the level of seismic demand for a given performance target. Copyright© 2009 John Wiley & Sons, Ltd.     

Steel buckling‐restrained braced frames with single and dual corner gusset connections: seismic tests and analyses

The design of a three‐story buckling‐restrained braced frame (BRBF) with a single‐diagonal sandwiched BRB and corner gusset was evaluated in cyclic tests of a one‐story, one‐bay BRBF subassembly and dynamic analyses of the frame subjected to earthquakes. The test focused on evaluating (1) the seismic performance of a sandwiched BRB installed in a frame, (2) the effects of free‐edge stiffeners and dual gusset configurations on the corner gusset behavior, (3) the frame and brace action forces in the corner gusset, and (4) the failure mode of the BRBF under the maximum considerable earthquake level. The subassembly frame performed well up to a drift of 2.5% with a maximum axial strain of 1.7% in the BRB. Without free‐edge stiffeners, the single corner gusset plate buckled at a significantly lower strength than that predicted by the specificationof American Institute of Steel Construction (2005). The buckling could be eliminated by using dual corner gusset plates similar in size to the single gusset plate. At low drifts, the frame action force on the corner gusset was of the same magnitude as the brace force. At high drifts, however, the frame action force significantly increased and caused weld fractures at column‐to‐gusset edges. Nonlinear time history analyses were performed on the three‐story BRBF to obtain seismic demands under both design and maximum considerable levels of earthquake loading. The analytical results confirmed that the BRB and corner gusset plate achieved peak drift under cyclic loading test. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic retrofit of low‐rise steel buildings in Canada using rocking steel braced frames

This article examines the use of rocking steel braced frames for the retrofit of existing seismically deficient steel building structures. Rocking is also used to achieve superior seismic performance to reduce repair costs and disruption time after earthquakes. The study focuses on low‐rise buildings for which re‐centring is solely provided by gravity loads rather than added post‐tensioning elements. Friction energy dissipative (ED) devices are used to control drifts. The system is applied to 2‐storey and 3‐storey structures located in 2 seismically active regions of Canada. Firm ground and soft soil conditions are considered. The seismic performance of the retrofit scheme is evaluated using nonlinear dynamic analysis and ASCE 41‐13. For all structures, rocking permits to achieve immediate occupancy performance under 2% in 50 years seismic hazard if the braces and their connections at the building's top storeys are strengthened to resist amplified forces due to higher mode response. Base shears are also increased due to higher modes. Impact at column bases upon rocking induces magnified column forces and vertical response in the gravity system. Friction ED is found more effective for drift control than systems with ring springs or bars yielding in tension. Drifts are sufficiently small to achieve position retention performance for most nonstructural components. Horizontal accelerations are generally lower than predicted from ASCE 41 for regular nonrocking structures. Vertical accelerations in the gravity framing directly connected to the rocking frame are however higher than those predicted for ordinary structures. Vertical ground motions have limited effect on frame response.     

Seismic design and test of gusset connections for buckling‐restrained braced frames

The corner gusset plates in a steel braced frame can be subjected to forces not only from the brace but also from the effects of the frame actions. In this study, several finite element models are constructed to analyze the gusset‐to‐beam and gusset‐to‐column interface forces. It is found that the frame actions affect the gusset interface force distributions significantly. A simplified strut model to represent the gusset plate is adopted to evaluate the frame action forces. In addition, the generalized uniform force method is adopted as it provides more freedom for designers to configure the gusset plate shapes than using the uniform force method. In this paper, a performance‐based design method is proposed. The gusset interface force demands take into account the combined effect of the brace maximum axial force capacity and the peak beam shear possibly developed in the frame. The specimen design and key results of a series of full‐scale three‐story buckling‐restrained braced frame (BRBF) hybrid tests are discussed. The gusset interface cracks observed at inter‐story drift greater than 0.03 radians can be well predicted by using the proposed design method. The BRBF tests and analyses confirm that the proposed design method is reasonable. The effectiveness of varying the width of gusset edge stiffeners in reducing the gusset tip stress concentrations is also investigated. This paper concludes with recommendations for the seismic design of BRBF corner gusset plates. Copyright © 2013 John Wiley & Sons, Ltd.