SUMMARYModern self-centering controlled rocking special concentrically braced frame (SC-CR SCBF) is capable of reducing structural damage compared with conventional buildings following an earthquake. This investigation quantifies three seismic performance factors, including over-strength factor (Ω 0 ), period-based ductility (μ T ) and response modification coefficient (R), for low-and mid-rise SC-CR SCBFs. Nonlinear static analysis is conducted to derive Ω 0 and μ T factors for 12 SC-CR archetypes. Validity of trial R coefficient is also evaluated using a collapse-based assessment procedure by comparing adjusted collapse margin ratios with the established acceptance criteria. Results indicate that the Ω 0 and μ T factors are in the range of 1.39 to 2.29 and 12.25 to 29.0, respectively, and R of 8 is proposed for design of SC-CR archetypes. A reliability study is also performed to examine the effects of modeling and ground motion parameters on the safety margin of designed SC-CR archetypes with the proposed R value. Results indicate that the design of mid-rise space archetypes in high-seismicity regions with the R coefficient of 8 is more reliable than that of the low-rise perimeter ones in low-seismicity regions.

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A modern self-centring braced frame equipped with post-tensioned cables and replaceable fuses is capable of rocking on its foundation during an earthquake. The aim of this paper is to evaluate the seismic performance of a controlled-rocking braced frame and compare its efficiency with a similar fixed-based braced frame. A non-linear time history analysis is conducted for a set of archetypes, varying in height, seismic design category, and seismic frame type. A sensitivity analysis is performed to examine the effects of modelling and ground motion parameters. Results indicate that the rocking system is capable of enhancing the performance of a conventional braced frame by features such as the controlled rocking mode, self-centring and concentrated damage to replaceable fuses.

Direct displacement-based design (DDBD) procedure utilizes an equivalent singledegree-of-freedom model to predict seismic demands while neglecting the higher mode effects. Controlled rocking steel cores (CRSCs) vibrate in the first mode of vibration; however, higher modes greatly influence the member forces. Previous studies, in which DDBD has been utilized, have not quantified the contribution of higher mode demands to CRSC's assemblies. This paper aims to extend the DDBD (EDDBD) procedure for low-damage buildings, equipped with CRSCs. Modal responses are combined with modified SRSS at the design displacement. Design is formulated for the strength and stiffness of the CRSC components. The application of the proposed design approach is illustrated by 3-, 9-, and 15-story archetypes. Results verified by nonlinear dynamic analyses demonstrate the high precision of EDDBD in the design of low-to mid-rise CRSCs. The proposed procedure is applicable to commercial software. K E Y W O R D S controlled rocking core, direct displacement-based design, higher mode effects 1 | INTRODUCTION Current building codes implement both force-based design (FBD) and displacement-based design (DBD) methods for the seismic design of conventional buildings. Although FBD procedures are commonly used in most of the national seismic codes, DBD methods have provided a real correlation between displacement and damage extent. The DBD procedure can be categorized into "predesigned" and "design-led to analysis" (DLA) approaches. [1] In the predesigned method, the already-designed system is being checked to satisfy the drift requirement, [2,3] whereas in DLA methods such as DDBD and equal displacement-based procedures, the structure models by a single-degree-of-freedom (SDOF) system. The DDBD is an applicable design method, in which a multi-degree-of-freedom (MDOF) structure is substituted with an SDOF model, secant stiffness, and equivalent viscous damping associated with the design displacement. In the theoretical basis, the DDBD starts with desired target displacement, and it ends with the design demands. The pioneer efforts in proposing DDBD methods are related to Priestley et al., [4-8] as well as Calvi and Kingsley, [9] Kowalsky et al., [10] and Fardis and Panagiotakos. [11,12] This method is utilized for the design of a wide range of structural systems. For example, Priestley et al. [13,14] proposed a simplified DDBD method for precast concrete jointed structures and reinforced concrete frames. The efficient application of standard DBD for semirigid steel frames was investigated by Pirmoz and Liu. [15] Shahi e al. [16] examined the seismic performance of steel stud bracing walls and found that demands determined from standard DDBD method using inelastic spectra were in better agreement with NLTHA results than the equivalent damping approach. Comprehensive and well-validated studies have also been conducted in the recent past to use the DDBD procedure for masonry wall structures, [17,18] frame-wall structures, [19-21] and timber structures. [...

Mass isolation of structures is an efficient vibration-control technique for reducing earthquake effects on buildings. This paper introduces a vertical seismic isolated rocking-core system (VSI-RCS) in which a controlled rocking-core is separated from the frame by viscous fuses. The controlled rocking-core provides the self-centring capability while the viscous dampers limit the lateral displacement and dissipate the majority of the seismic energy. An analytical solution is proposed for estimation of the optimal damping constant of the dampers along with the corresponding fundamental frequencies and damping ratio of the VSI-RCS. A parametric study was carried out to quantify non-classical dynamic characteristics and spectral analysis was performed to examine the seismic performance of the VSI-RCS compared with rocking-core systems. The proposed formulas were found to be applicable for rapid eigen-analysis and, compared with non-isolated rocking-core systems, proper seismic efficiency of the VSI-RCS was observed.

Modern rocking and stepping cores have been known as the efficient self-centering earthquake-resisting systems (SC-ERSs). The current article proposes an approximate equivalent linear (EL) model for rapid estimation of the SC-ERS displacement. An equivalent damping ratio and effective stiffness are formulated for flag-shaped hysteresis of a fully SC-ERS. The approximate EL model is first established using secant stiffness and Jacobsen's damping model. Nonlinear response history analyses are carried out to compare exact and approximated peak displacements. Findings reveal that EL analysis of the SC-ERS based on Jacobsen's damping leads to underestimation of the maximum inelastic displacement. Accordingly, a new optimal damping formula is proposed using a genetic algorithm and nonlinear regression analyses. The improved EL model is validated by practical examples, and the results show acceptable accuracy in design-level displacement estimation. KEYWORDS equivalent linear model, flag-shaped hysteresis, optimization analysis, secant stiffness, selfcentering systems, viscous damping model 1 | INTRODUCTIONOn the basis of the traditional ductility-based design concept, structural members allow for sustaining of uniform damage. Nevertheless, buildings experience severe damage following a large earthquake, which lead to socioeconomic losses due to business downtime and repair costs. In recent years, self-centering earthquake-resisting systems (SC-ERSs) have been developed to provide a sustainable system through directing seismic damage to replaceable devices. Figure 1a shows examples of rocking and stepping self-centering systems including single or coupled stepping braced frames, [1][2][3][4][5][6][7][8] pin-supported rocking frame or wall, [9][10][11] rocking precast concrete wall, [12][13][14][15] and self-centering timber frames. [16,17] These lateral resisting systems are generally composed of bounded or unbounded posttensioning (PT), replaceable energy dissipation (ED) devices, rigid strut beam, bumper, and special diaphragm connections. Regardless of the SC-ERS components, a flag-shaped hysteresis is representative of their total seismic responses. Figure 1b depicts a sample of push-pull curves of the system characterized by uplift ( F up − Δ up ) and yield ( F y − Δ y ) parameters along with postyield stiffness (α) and ED index (β). Prior to unloading the system ( F d − Δ d ), the response is generally composed of three main branches. In the first branch that terminates when the system is uplifted, the SC-ERS has a large initial elastic stiffness and behaves as conventional buildings. Nevertheless, in the second branch, the system stiffness is reduced and sways on its foundation, which leads to the system yielding point. The yielding point is the beginning of the third branch with the hardening stiffness of α. Note that geometric nonlinearity is controlled using PT and ED devices. Accordingly, the PT cable provides adjustable restoring forces, and the ED device produces required ED capacity during the unloading ph...