Direct Displacement-based Design Research Articles

Hysteresis damping ratio for moment steel frame evaluation using DDBD

AbstractThe main purpose of this paper is to propose a model for estimating the hysteresis damping ratio of moment steel frames and compare them with the results obtained using direct displacement-based design. In this study, different models of steel bending frames were examined by using several type of analysis to obtain this ratio. Thirty-steel frame models with 3, 6, 9, 12, and 15 floors and 3 and 6 bay with 6 m span length were analyzed and evaluated. The results showed that the equivalent damping ratio at the level of safety based on Jacobsen and Jennings, and the values of the equivalent damping relationships according to FEMA-440 vary from the empirical formula proposed in displacement-based design-2012. Therefore, in the ductility domain the exponential relationship form was more consistent with the results used. A new formula was proposed to calculate the hysteresis damping ratio, and it is more accurate than the empirical formula proposed in displacement-based design-2012.

Displacement-based design procedure for the seismic retrofit of existing buildings with self-centering dissipative braces

Existing framed buildings, especially those designed according to outdated seismic codes, often offer inadequate seismic protection levels due to material degradation, low amount of reinforcement and poor construction details. Among the possible retrofit strategies, elasto-plastic dissipative braces (EPDBs) can be installed to provide supplemental stiffness and energy dissipation in the main resisting frame. Since they are based on the plastic deformation of sacrificial steel components, EPDBs are inherently affected by scarce recentering capability, i.e., presence of residual deformation at the end of the mainshock that could impair their effectiveness for aftershock events. As demonstrated in recent seismic sequences, there might be not enough time to restore (e.g., though hydraulic actuators and a reaction frame) the undeformed configuration of the structure before a subsequent shock. This issue can be overcome through self-centering dissipative braces (SCDBs), i.e., braces equipped with dampers characterized by a “flag-shaped” hysteretic behavior, which inherently facilitates the immediate re-centering of the frame. Despite this evident benefit, there is still lack of practical design procedures for the seismic retrofit of buildings through SCDBs. To fill this gap, a direct displacement-based design procedure for SCDBs tailored to building frames is here conceived and illustrated. The proposed method aims at achieving simultaneously two performance requirements: (i) a target maximum roof displacement under the ultimate-limit-state seismic event; (ii) the absence of significant residual inter-storey drifts at the end of the shaking. The implementation of the procedure is described by two applications to a steel and to a reinforced concrete case-study building. Nonlinear time-history analyses are carried out to prove the effectiveness of the proposed method, along with a comparison of the seismic performance offered by SCDBs versus traditional EPDBs implemented in the same case-study buildings.

Calibration of Equivalent Viscous Damping Expressions for Displacement-Based Design and Application to RC Frames

Equivalent viscous damping plays a central role in displacement-based design procedures. In this paper, approaches for estimating the equivalent viscous damping of RC frame buildings are proposed. At first, the analytical formulation of Blandon and Priestley was analysed, and then a calibration of the coefficients of this formulation was performed. Compared with the work of Blandon and Priestley, a larger set of synthetic accelerograms, related to different types of soil and different intensities, and a wider range of the effective periods were considered. In particular, two different sets of parameters are proposed: the first is usable in the case of spectra obtained numerically (approach 1), and the second is usable in the case of code-based spectra and damping modification factor (approach 2). To test the performed calibration and to compare the considered formulations (i.e., the proposed and literature equations), the direct displacement-based design procedure has been applied to three case studies of reinforced concrete frame structures, and then pushover and nonlinear time-history analyses have been performed. The results show that the use of the calibrated parameters (for both the considered approaches) has determined more conservative results, in terms of design base shear and maximum drift from NLTH. Moreover, the average displacement profiles and the inter-storey drifts obtained from time-history analyses for the frames designed with the calibrated parameters match better the design profile.

Substructure-based design method for vertically irregular steel buckling-restrained braced frame structures

Buckling-restrained braces (BRBs) can mitigate the uneven inter-story drifts of vertically irregular steel frame structures during earthquakes, preventing unfavorable seismic forces and failure patterns. However, the structural lateral displacement profile of vertically irregular steel buckling-restrained braced frame structures (VSBFSs) can hardly be predicted; hence, parameter tuning and iterative designing are commonly required in conventional direct displacement-based design (DDBD) methods, which strongly rely on the experience of designers and consumes a considerable amount of time. This study proposes a substructure-based design (SBD) method developed explicitly for VSBFSs. In this method, the substructures of every story of a VSBFS are separated from the entire structure and individually analyzed in the subsequent procedures. The boundary conditions of the substructures are initially simplified as hinges, and an explicit equation of BRB stiffness and inter-story drift for the substructures is established. An iterative calculation procedure is consequently applied to correct the equation by considering the influence of the constraints of adjacent stories. In this manner, the inter-story drifts of all the stories of the entire structure uniformly converge to the predetermined targets, in which the demand of BRBs for each story is also determined. Compared with conventional DDBD methods, the proposed method does not assume the structural lateral displacement profile and is not based on experience, yielding relatively economical and safe design outcomes in a timely manner. The proposed SBD method was first validated by comparing it with existing elastic and elastoplastic design methods through a 15-story VSBFS example. Then, the applicability of the SBD method was further explored through four 6-story VSBFSs with different plan layout reductions and two VSBFSs with heights of 20 stories and 30 stories. Finally, the SBD method was applied to redesign the BRBs of a vertically irregular thermal power plant model (an example of a VSBFS) in a shaking table test.

Application of Endurance Time Method in Seismic Assessment of RC Frames Designed by Direct Displacement-Based Procedure

This paper addresses the Direct Displacement-Based Design (DDBD) approach of multi-story RC frame structures consistent with changes ‎to design criteria between Turkish earthquake codes of TSC-2007 and TBEC-2018. The corresponding response modification factor (R) of structures designed based on the DDBD approach is also estimated in this research. The design base shear forces of both codes are compared considering different R factors and also with that of the DDBD approach. The results showed that the DDBD approach, as per TBEC-2018, provides RC frame structures with higher R values compared to the similar approach in accordance with TSC-2007. The Endurance Time (ET) method is a time history-based procedure for seismic assessment of ‎structures ‎under intensifying dynamic excitations aided to judge their performance at various intensity levels. Since, up to now, the ET method has not been considered to evaluate the performance of the structures designed by the DDBD approach, this paper addresses this issue. The ET ‎performance curves of RC frames show that structures designed by the DDBD approach in ‎accordance with TBEC-2018 exhibit higher Interstory Drift Ratios (IDRs) values than TSC-2007 at various hazard levels.

Seismic performance quantification and direct displacement-based design of CLT-glulam hybrid structures

By incorporating cross-laminated timber (CLT) shear walls for glulam frames, CLT-glulam hybrid structures provide a prospective solution for multi-story timber construction. This paper aims to develop a direct displacement-based design (DDBD) approach for CLT-glulam hybrid structures, with the maximum inter-story drift ratio (MaxISDR) and the maximum inter-story CLT shear wall damage index (MaxISWDI) as engineering demand parameters (EDPs). To address the knowledge gaps in developing the DDBD approach, a series of incremental dynamic analyses (IDAs) was conducted on 12 prototype CLT-glulam hybrid structures. The IDA results served as a database for quantifying performance levels and base shear distributions of CLT-glulam hybrid structures. The results showed that the MaxISWDI limits governed by connection damage were respectively 0.18, 0.48, and 0.72 for immediate occupancy (IO), life safety (LS), and collapse prevention (CP) performance levels. The connection-damage-associated MaxISDR limits were 1.5 %, 3.9 %, and 5.4 % for IO, LS, and CP performance levels, with the MaxISDR limit governed by global stability being 2.7 % for CP performance level. Analytical models were then developed to establish the displacement profile for CLT-glulam hybrid structures, differentiating between platform-type and balloon-type CLT shear wall subsystems. With the acquired knowledge and results, the DDBD approach was extended for the seismic design of CLT-glulam hybrid structures, with a case study provided to demonstrate the design procedure.

Seismic vulnerability assessment of post-tensioned timber building fitted with dissipative bracing systems

A post-tensioned (PT) timber building coupled with dissipative bracing systems is a sustainable seismic-resistant structural system. This system combines desirable qualities of self-centering, energy dissipation, and lightweight timber, which attracts lesser seismic force and contributes to a better resilient system. Despite significant advancement in the provision of these sustainable seismic-resistant timber-based structural archetypes, more study is required to derive a fuller knowledge of the behaviour of these innovative structural systems under a range of ground motion intensities and limited state capacities. Direct displacement-based design, a performance-based design approach, is used for the design of this system, and performance assessment is carried out using nonlinear dynamic analysis. This study investigates the performance of the braced PT frame under different limit state considerations using ground motion records consistent with the NBC 2020 seismic hazard.

Direct displacement-based design of dissipative bracings for seismic retrofit of reinforced concrete buildings

A non-iterative direct displacement-based method is proposed for the design of dissipative bracings for seismic retrofit of gravity-load-designed (GLD) reinforced concrete (RC) frames. The design methodology aims at limiting the interstorey drifts of the GLD frame to prevent damage in the existing columns, by appropriately designing both stiffness and damping of the bracings. The method is based on a simplified yet accurate representation of the braced frame, through a so-called stick model, whose elements stiffness and damping are obtained by equivalent linearization of each braced storey. This allows performing a simplified modal analysis and obtaining an optimal design of the bracing system at each storey, both in terms of stiffness and damping. The design method efficiency has been validated by assessing the obtained performance of three GLD RC frames retrofitted with bracing systems and by comparing the outcomes with two other design methods available in the literature.

Nonlinear analysis model and seismic resilience assessment of LEM-filled CFS residence

Lightweight EPS materials (LEM)-filled cold-formed steel (CFS) shear wall structure is a new type of green, low-carbon and prefabricated rural residence, which has drawn in expanding consideration due to the promotion of the rural revitalization strategy. However, most of the existing research on this type of residence has focused on its behaviours of components, with little attention was paid to its overall response to resist earthquake disasters. During the past two decades, significant advancements have been made in effectively mitigating building collapses and reducing casualties resulting from earthquakes. Thus, the concept of seismic resilience is proposed, and the seismic performance requirements of structural design have been elevated from “safety” to “resilience”. To analyze the seismic resilience of LEM-filled CFS residence, this paper proposed a strut and tie- equivalent spring model to establish the simplified analysis model of a single composite wall, and the precision of the model was confirmed by test results, in which the nonlinear characteristic and the supporting effect of fillers was considered. Subsequently, three LEM-filled CFS residences are designed using the direct displacement-based design method. Then the three-D models are established for nonlinear analysis, and the inter-drift ratio (IDR) and residual inter-drift ratio (RIDR) are adopted to estimate the seismic response of the three archetypes. The seismic resilience of the three archetypes are assessed based on FEMA P58. This paper would provide a guidance for the nonlinear analysis and seismic resilience assessment of this type of residences, and promote the application and popularization of this kind of residence.

Inelastic response spectra for an integrated displacement and energy-based seismic design (DEBD) of structures

The severe socio-economic impact of recent earthquakes has further highlighted the crucial need for a paradigm shift in performance-based design criteria and objectives towards a low-damage design philosophy, in order to reduce losses in terms of human lives, repair/reconstruction costs, and recovery time (deaths, dollars and downtime). Currently, displacement-based parameters are typically adopted to design/assess the seismic performance of the structures, by limiting the maximum displacement or the maximum interstorey drift ratio (IDR) reached by the structure under different earthquake intensities. However and arguably, displacement-based quantities are characterized by inherent weaknesses, since, for instance, they are not cumulated parameters, thus not able to capture directly the effects of multiple cycles, deterioration and damage cumulation. Therefore, in the last decades, energy-based approaches were investigated and developed in order to establish alternative engineering demand parameters for the assessment of post-event damage through a dynamic energy balance. Towards the main goal of developing an integrated Displacement and Energy-Based Design/assessment procedure (DEBD) for actual use in practice, this research work proposes an innovative approach based on the use of inelastic spectra correlating the energy components with the corresponding maximum displacement response parameters of the structure. In practical terms, the proposal is to further integrate and develop the well-known Direct Displacement-Based Design, by directly adopting the hysteretic energy as an additional design parameter. The energy inelastic spectra are developed through an extensive parametric analysis of Single-Degree-of-Freedom (SDoF) systems, with different nonlinear hysteretic models. In such an approach, the maximum seismic energy demand imparted to a structure can be directly predicted and controlled, whilst distinguishing the various components of the energy balance, including the hysteretic one. The effects of near-field and far-field earthquakes are also investigated. Results show that in the first case the seismic demand is concentrated in the peak of a few large cycles that absorb the demand energy induced by the high component in peak ground velocity in the second case the higher equivalent number of plastic cycles tends to become critical for structures with inadequate structural details and prone to suffer by cumulative cycles and overall plastic fatigue mechanisms.

Seismic performance of self-centering braced rocking frame with novel self-centering friction dampers characterized by low-secondary stiffness

Research has demonstrated that self-centering energy dissipation dampers (SCEDs) are effective devices for reducing the residual deformation of structures after a strong earthquake. However, the equivalent damping ratio of SCEDs is relatively lower than that of conventional dampers such as viscous dampers, BRBs, or friction dampers. According to displacement spectrums, the lower damping ratio could result in a lower natural period and higher equivalent stiffness of structures for a given displacement target, and thus the structures could attract more earthquake action to the structures. To alleviate the problem, a novel self-centering damper composed of elastic post-buckling plates and adjustable friction devices (PBSCFD) was proposed and used as the self-centering braces for a self-centering braced rocking frame (SBRF) structure for example. First, the theoretical force-displacement relationship of the PBSCFD was derived based on its configuration and work principle, and then a scaled PBSCFD was manufactured and tested to investigate its mechanical properties and verify the theoretical constitutive model. Subsequently, the SBRF structure with PBSCFDs was designed by the direct displacement-based seismic design method (DDBD), and its seismic performance was examined by elastic–plastic time-history analysis. Finally, the effects of the secondary stiffness ratio of the self-centering braces on seismic mitigation of the SBRF structure were investigated. The results show that PBSCFDs is characterized by classic self-centering behavior with low secondary stiffness, which can be designed to obtain significant control effects on the base/interstorey shear and interstorey drift ratio of the SBRF structure under rare and extremely rare earthquake compared to the conventional SCEDs with significant secondary stiffness.

Direct displacement‑based seismic design for a retrofitted RC frame by hinged wall with BRBs at base

A hinged wall (HW) with buckling-restrained braces (BRBs) at the base (HWBB) has been proposed to enhance the seismic performance of a reinforced concrete frame (RCF). In this study, a new direct displacement-based design procedure based on the bottom shear method (DDBDP-BSM) is proposed for low- and multi-rise RCFs with an HWBB (RCF-HWBB). First, the theoretical relationship between the basic period target and displacement target of the RCF-HWBB was deduced based on the DDBDP-BSM and performance targets. Then, a method to determine the HW configuration and BRB sectional area was proposed. Finally, the optimal selection of earthquake intensity at BRB yielding and the applicability of the DDBDP-BSM on a high-rise RCF-HWBB were investigated through a comparison between the design results and the time history analysis results.

Hybrid self-centering dual rocking core system for seismic resilience by controlling both structural and nonstructural damage

This study proposes a novel hybrid self-centering dual rocking core (HSDRC) system with structural and nonstructural damage control functions for the building structure’s seismic resilience. The rigid rocking cores (RCs), viscous dampers (VDs), and shear friction spring dampers (SFDs) are introduced in HSDRC systems. The rocking cores with pinned bases are adopted for promoting uniform inter-story drifts over the building height. The SFDs are introduced to dissipate hysteretic energy and bring self-centering capacity by eliminating residual deformation. The VD’s velocity-proportional damping can help HSDRC systems control the nonstructural damage and building content’s damage sensitive to absolute floor accelerations. The expected behavior of HSDRC systems is first described. A direct displacement-based design (DDBD) method is following proposed to achieve the desired nonlinear behavior of HSDRC. Following the developed DDBD procedure, six HSDRC systems are designed. For highlighting the advantages of HSDRC systems compared to the existing self-centering energy-absorbing rocking core (SEDRC) system, two SEDRC systems are also designed. Nonlinear dynamics were included for investigating the performance of the designed systems subjected to seismic events. The numerical results demonstrate that the designed HSDRC systems show the expected nonlinear behavior and achieve the design target, confirming the developed DDBD method’s effectiveness. Compared to SEDRC systems, the newly proposed HSDRC systems show smaller absolute floor acceleration responses while obtaining the comparative capacity in controlling both peak and residual inters-tory drifts, indicating the proposed HSDRC systems can be a promising seismic resilient structural system for both structural and nonstructural damage control.

SEISMIC VULNERABILITY ASSESSMENT OF BASE-ISOLATED RC FRAME BUILDING USING DDBD METHOD

The direct displacement-based design (DDBD) method is widely used worldwide because it allows structures to be designed based on their expected performance criteria. The DDBD approach is utilized so that base-isolated building structures can meet the seismic performance parameters established by the displacement threshold. In the present study, an 8-story, 10-story and 12-storey base-isolated RC frame building is designed using the latest Indian seismic standards, with lead rubber bearing (LRB) as the base-isolation system. Force-based and DDBD methodology is implemented and compared for the selected base-isolated RC frame buildings. The nonlinear time-history analysis is conducted to evaluate the nonlinear lateral response of the RC frame buildings. The results indicated that the traditional force-based method shows almost 12% less top-storey displacement than the DDBD approach. The DDBD approach provides enhanced reliability, simplicity, and convenience in seismic design for base-isolated building frames with LRBs, making the observations more dependable and easier to employ.

Hybrid force-displacement-based design methods for self-centering wall structures

Self-centering wall structures (SCWs) are well-developed resilient structures and are being gradually implemented in practical engineering. The direct displacement-based design (DDBD) method is commonly adopted for the seismic design of SCWs due to its predictable displacement pattern. Due to the complexity of DDBD, practical engineers still commonly use the present force-based design (FBD) methods. However, the existing FBD method is inapplicable when the deformation of SCWs is large. To make the design procedure more acceptable to engineers and promote SCWs in real practice, three design methods were proposed: a force-based design method by empirical formula, a force-based method by iteration, and a hybrid force-displacement-based design method (HBD). The applicability of FBD by existing empirical formulas of structural periods in several codes for SCWs was discussed. In FBD by iteration, the initial prestress is iterated to determine secant stiffness and the structural period so that SCWs can be designed following its constitutive relationships. HBD is carried out by comparing the resistance of the structure under the target displacement with the earthquake demand according to the deformation mode of the SCWs. Compared with the existing DDBD methods, the proposed design methods can simplify the design process in engineering applications while keeping the design outcomes consistent with DDBD and proved to be reasonable with nonlinear time history analysis. In addition, the FBD method by empirical formula and the HBD method can be implemented in the four-level seismic fortifications currently proposed in China. The proposed methods solve the issues of the existing FBD and could be a reference for engineers to design SCWs in engineering practice.

Impact of ground motion directionality (RotDnn) on the coupled and uncoupled inelastic response of RC circular cantilever columns

Directionality in the representation of earthquake demand for structural seismic design has surfaced as a subject of debate in recent years. Design spectra, as defined in building and bridge codes, account for directionality by considering the peak response in all possible orientations of the motion using the RotDnn measure, where “nn” is the percentile of the peak response. Current seismic hazard maps are based on ground motion models that use the RotD50 spectra (median peak response). However, since 2009, building codes have adopted RotD100 spectra (maximum peak response), raising concern among researchers and engineers. The first objective of this study is to evaluate the impact of design spectra definition, RotD50 or RotD100, on the bidirectional inelastic response of azimuth-independent RC systems. Upcoming updates to seismic hazard maps highlight the need of understanding the implication of this choice in bridge design. While previous research focused on the relationship between RotD50 and RotD100, this work assesses the impact of each definition on the inelastic seismic response of RC circular columns designed following the Direct Displacement-Based Design approach and verified through nonlinear time history analyses (NTHA) using ground motions from shallow crustal active and subduction zone regions. The ratios of NTHA to design displacement confirm that RotD100 spectra should be used to design azimuth-independent RC systems and provide the first known verification of DDBD for bidirectional loading (second objective). These ratios are a function of ductility level, tectonic regime, effective period, and coupling (which is the third objective). Overall results show that RC circular cantilever columns designed to RotD100 spectra show less deviation from the expected design displacement than columns designed to RotD50 spectra. This study presents the first step in resolving the ongoing debate over spectra definition and provides recommendations for displacement demand estimations for response spectra-based design approaches.

A novel self-centering friction damper with elastic post-buckling plates to retrofit bridge bents

The self-centering energy dissipation dampers (SCEDs) have been demonstrated in mitigating the residual deformation of structures under strong ground motions. However, existing researches show that the damping force demand of SCEDs is higher than conventional dampers such as viscous dampers, BRBs or friction dampers for same design displacement of self-centering retrofitted structures, which could lead to higher base shear and acceleration responses of structures. In order to alleviate the problem, a novel self-centering damper composed of elastic post-buckling plates and adjustable friction devices (PBSCFD) was proposed. Compared with conventional SCEDs, the proposed PBSCFD has low secondary stiffness and adjustable energy dissipation capacity, which is beneficial to control the additional internal force of members adjacent to the damper in self-centering retrofitted structures. Based on the configuration and working principle of the PBSCFD, the theoretical force-displacement relationship of the damper was derived. Subsequently, a scaled PBSCFD was manufactured and tested under quasi-static loading to investigate its mechanical properties and to verify the theoretical constitutive model. In order to demonstrate the seismic performance of PBSCFDs, the double-column bridge bent retrofitted with PBSCFDs was designed by direct displacement-based seismic design method (DDBD), and its seismic performance was examined by elastic-plastic time-history analysis. Finally, effects of secondary stiffness ratio of self-centering dampers on seismic mitigation of self-centering retrofitted bridge bent were investigated. The results show that PBSCFDs have certain advantages in controlling the base shear and acceleration of the retrofitted bridge bent compared to conventional SCEDs with significant secondary stiffness.

An equivalent damping ratio that accounts for ground-motion spectral shape for displacement-based design of flag-shaped hysteresis systems

Direct displacement–based design (DDBD) methodologies simplify the estimation of the seismic deformation demands of a nonlinear system by replacing it with an equivalent linear system that is characterized by an effective stiffness and equivalent damping ratio (EDR). The calculated EDR for flag-shaped hysteresis relationships vary greatly among existing DDBD methodologies, and these methodologies display a strong bias according to the shape of the ground-motion response spectrum. In the work reported here, the limitations of existing methods are demonstrated for three sets of ground-motions: a set of far-field ground-motions, a set of near-field ground-motions, and a set of physics-based simulated ground-motions that account for the effects of a deep sedimentary basin. The effect of spectral shape can be quantified by a new measure of spectral shape that is based on the spectral displacement ordinates between the system’s initial and equivalent periods. To address the limitations of existing methodologies, a new equation for calculating EDR was developed based on numerous nonlinear history analyses for all three sets of ground-motions and for a wide range of systems with flag-shaped hysteresis. In comparison with existing equations, the proposed equation for calculating EDR improves the accuracy of the DDBD methodology by lowering the bias and dispersion of the ratio between the displacement calculated by nonlinear analysis and the displacement calculated with the equivalent linear system. The usage of the new EDR equation in DDBD requires iteration, but neither numerical modeling nor analysis is needed. Specific steps of the application are demonstrated for a system with a flag-shaped hysteresis.

Empirical formulation for the estimate of the equivalent viscous damping of infilled RC frames

The direct displacement-based design (DDBD) is based on the equivalence between the nonlinear hysteretic response of a structure and a simple linear oscillator with equivalent viscous damping (EVD). Typically the EVD is calibrated for different types of structures as a function of the ductility. However, those simple relationships exhibit a huge dispersion and uncertainty since the specific properties of the structural system are not considered. This work proposes an original approach for estimating the EVD of infilled reinforced concrete (RC) frames. We focus on a ductility demand corresponding to an ultimate limit state and we investigate the effect of the properties of infilled RC frames on the EVD. A data-driven hysteresis model proposed by the authors in a previous research is implemented in OpenSees to represent the nonlinear response of infill panels. The optimal EVD at the ultimate limit state is computed using an extensive series of time-history analyses (THAs) on a dataset of 14 infilled RC frames. Afterwards, an empirical correlation law for the estimate of the optimal EVD is calibrated as a function of the geometrical and mechanical properties of infilled RC frames. This formula is meant to be a practical tool for a preliminary design of infilled RC frames. A comparison with the EVD estimated by quasi-static tests and the EVD of bare frames is made. The methods and results presented in this work may be the basis for more robust predictions of the EVD of infilled RC structures.

Direct displacement-based design of SEDRC systems considering higher mode effects

Self-centering energy-absorbing dual rocking core (SEDRC) system was recently proposed for obtaining damage-free performance under design earthquakes or low damage under extreme earthquakes in steel building structures. Although the SEDRC system can mainly deform based on the fundamental mode shape, the higher modes may significantly impact the structural element forces. This research intends to investigate the effects of higher mode on the seismic performance and structural member force demands of the SEDRC system under earthquakes and propose a performance-based design (PBD) method considering the higher mode effects. The formulation for calculating the design base shear pondering the influence of higher mode is deduced. The detailed design steps and equations for calculating the force demands of structural members are presented. Three archetypes, including nine-, fifteen-, and twenty-story SEDRC systems, respectively, are designed according to the PBD method. Moreover, the other six corresponding archetypes are designed according to the previous design process without consideration of higher mode effects as comparative buildings. Nonlinear dynamic analyses were performed to evaluate the seismic responses of the designed structures. The analysis results validate the high precision of the proposed methodology in designing multi-story to high-rise SEDRC systems.