Residual Inter-story Drift Ratios Research Articles

Comparative seismic performance evaluation of friction, self-centering and hybrid self-centering dampers

This study explores comparative seismic performance of a shape memory alloy (SMA)-only device, a friction damper, and a hybrid self-centering device. The self-centering device considered in this study, named as superelastic friction dampers (SFDs), is a hybrid damper operating on a mechanism where SMA cables and frictional components are arranged in parallel. A detailed description of the device and an experimental characterization of mechanical behavior are presented first. Then, an 8-story archetype steel frame building is designed and modeled with each seismic protection device (SMA-only, hybrid self-centering, and friction only). To enable comparative performance assessment, each device is designed to have similar initial stiffness and the same maximum force at design displacement. Nonlinear time history analyses are conducted using a total of 44 ground motion records. The results are evaluated to compare performance of each frame design at design-basis and maximum considered earthquake hazard levels. Next, a risk-based seismic hazard demand analysis framework that involves comprehensive incremental dynamic analyses is employed for further assessing the performance of each system. The experimental results validate the parallel working mechanism of SMA cables and frictional components in the SFD, with 90% of the damper deformations recovered. Comparative analysis of seismic responses demonstrates the excellent performance of the SFDs in reducing interstory drift ratio, residual interstory drift ratio, and absolute acceleration responses. Furthermore, fragility analysis and risk-based seismic hazard assessment further reveal that the SFDs provide a well-balanced combination of energy dissipation capability and self-centering ability, thereby enhancing the seismic resilience of structures.

Optimal seismic design for self-centering concrete wall structures equipped with U-shaped flexural plate dissipaters

In self-centering wall (SCW) structural system, additional energy dissipation devices are crucial members that are expected to provide both partial lateral force resistance and energy dissipation capacity aiming at mitigating structural response. This research aims to develop a seismic design framework based on particle swarm optimization algorithm for SCW structures equipped with U-Shaped Flexural Plates (UFPs), which can be used to seek out the optimal configuration of UFPs of each floor to reduce seismic response, while maintaining a constant total lateral force resistance provided by all UFPs. For validation, a 10-story SCW structure is chosen as the design case. Specifically, two configurations are considered: a 10-story SCW structure equipped with identical UFPs following conventional design (SCF10-Original) and one equipped with UFPs from optimized configuration (SCF10-Optimized). Their drift and acceleration response are calculated and compared under different seismic intensities through nonlinear time history analysis (NATH). The results demonstrate that the optimized configuration of UFPs can significantly mitigate the drift response in SCW structure. For instance, the maximum inter-story drift ratios of SCF10-Optimized are 0.2 % smaller than those of SCF10-Original under maximum considered earthquake, while the maximum residual inter-story drift ratios of SCF10-Optimized are only half those of SCF10-Original under Extremely Rare Earthquake. Furthermore, the optimized UFPs can effectively reduce the maximum floor acceleration response under various seismic intensities. Therefore, the optimized configuration of UFPs is more effective in reducing both structural and non-structural damage for SCW structural systems compared to conventional configuration. It is also found that greater energy dissipation levels in SCW structure equipped with UFPs may not always result in smaller seismic response, while the configuration of UFPs may play a major influencing factor due to different inter-story lateral force resistance and inter-story energy dissipation demands of SCW structure.

A Novel Dual Self-Centering Friction Damper for Seismic Responses Control of Steel Frame

Due to their weight, the seismic response control of buildings needs a large-scale damper. To reduce the consumption of shape memory alloys (SMAs), this study proposed a dual self-centering pattern accomplished by the coil springs and SMA, which could drive the energy dissipation device to recenter. Combined with the friction energy dissipation device (FD), the dual self-centering friction damper (D-SCFD) was designed, and the motivation and parameters were described. The mechanical properties of D-SCFD, including the simplified D-SCFD mechanical model, theoretical index calculations of recentering, and energy dissipation performance, were then investigated. The seismic response mitigation of the steel frame adopting the D-SCFDs under consecutive strong earthquakes was finally analyzed. The results showed that a decrease in the consumption of SMA by the dual self-centering pattern was feasible, especially in the case of low demand for the recentering performance. Reducing the D-SCFD’s recentering performance hardly affected the steel frame’s residual inter-story drift ratios when the residual deformation rate was less than 50%, which can help strengthen the controls on the steel frame’s peak seismic responses. It is recommended to utilize the D-SCFD with not too high a recentering performance to mitigate the seismic response of the structure.

Cyclic loading tests and numerical simulations of an assembled X-shaped flexural steel damper

This paper proposes an assembled X-shaped flexural steel damper. Welding is waived for the novel damper. As the kernel element of the damper, the X-shaped flexural steel plates have the advantages of ease of installation and replacement if necessary. In the analytical part, the effective height of the flexural steel plate was suggested, and then, the yield displacement, yield load and initial stiffness of the damper were derived. The proof-of-concept cyclic loading test was conducted using one reduced-scale specimen within a four-bar linkage experimental setup. The hysteretic performance indexes, including strength, stiffness and energy dissipation, were quantified. The high-fidelity finite element (FE) models were established by ABAQUS. The parametric study was further conducted based on the verified FE model. The considered parameters were the height and thickness of the steel plates. The testing results indicate that the proposed damper has plump hysteretic curve with good energy dissipation capacity and excellent ductility, although slight slip behavior can be found due to the gap caused by the assembling process. The results obtained from analytical method and numerical model are in good agreement with the experimental data. The results of parametric analysis show that the numerical results well agree with analytical predictions, indicating the numerical model can reflect the mechanical behavior of AXSFD. A benchmark frame building was selected to demonstrate the seismic control efficacy of the damper. The nonlinear time history analysis results indicate that the damper reduced both peak and residual interstory drift ratios for the protected structure.

Seismic behaviour of post-earthquake composite frame structures with different damage levels

Since earthquakes pose a huge threat to buildings, the post-earthquake safety assessment is quite important, especially in earthquake-prone areas. This paper investigates the seismic performance of post-earthquake composite frame structures with different damage levels. Two-stage nonlinear time history analysis is carried out for a ten-story steel–concrete composite frame and the peak ground acceleration (PGA) of the seismic waves is used as the main parameter characterizing the seismic intensity and damage level. In the first stage, the seismic waves with the PGAs of 0.20 g, 0.30 g and 0.40 g are applied to the frame to result in three different damage levels. The peak inter-story drift ratios, residual inter-story drift ratios and plastic hinge ratios of the structure in the first-stage earthquakes are analysed, which presents a uniform distribution pattern for the three damage levels. The composite frame is evaluated as structurally safe at all three damage levels based on the limits of residual inter-story drift ratios given in current standards. In the second stage, the seismic waves with the PGA of 0.40 g are used to explore the residual capacity of the structure subjected to strong earthquakes. The dynamic responses of the intact structure and the structure with different damage levels are compared. The results indicate that despite the recognised structural safety, pre-existing seismic damage can enlarge the lateral deformation, reduce the internal forces and resistance capacity and increase the plastic hinges when the composite frame is exposed to the second-stage earthquakes. Generally, the damage caused by earthquakes with the PGA of 0.40 g will have an obvious influence on the seismic behaviour of the post-earthquake structure, in which situation further safety assessment and structural repairs are necessary.

Machine learning-based prediction of residual drift and seismic risk assessment of steel moment-resisting frames considering soil-structure interaction

Nowadays, due to improvements in seismic codes and computational devices, retrofitting buildings is an important topic, in which, permanent deformation of buildings, known as Residual Interstory Drift Ratio (RIDR), plays a crucial role. To provide an accurate yet reliable prediction model, 32 improved Machine Learning (ML) algorithms were considered using the Python software to investigate the best method for estimating Maximum Interstory Drift Ratio (IDRmax) and RIDR of 384 Steel Moment-Resisting Frames (SMRFs). In addition, the curve plot ability of methods was investigated to provide an estimation of Median of IDA curve (IDAMed) and Seismic Failure Probability curve (SFPCurve) considering Soil-Structure Interaction (SSI) effects. It is noteworthy that ML algorithms were improved with a pipeline-based hyper-parameters Fine-Tuning (FT) method followed by forward and backward feature selection methodologies to avoid overfitting and data leakage issues. The improved methods were evaluated to find the best prediction model regarding seismic demands. The results show that proposed methods have higher prediction accuracy and curve fitting ability (i.e. more than 95%) that can be used to estimate IDAMed and SFPCurve of a structure to accelerate the seismic risk assessment. A prediction tool is introduced to use the methods of this study for estimating abovementioned seismic demands.

Gravity framing and composite action effects on residual drifts of steel SMFs

In this study, the effects of gravity framing and composite action on the residual drift performance of steel special moment frames (SMFs) are investigated. Four steel structures including 4-, 8-, 12-, and 20-story SMFs are selected, and nonlinear models are created by considering the effects of gravity framing and composite action and neglecting these effects. Nonlinear dynamic analyses are performed on the structures subjected to the design basis earthquake (DBE) level ground motions. Under the DBE hazard level, accounting for the effects of gravity framing and composite action can reduce the maximum of median residual interstory drift ratios between 32% and 74%, when compared with that obtained by neglecting these effects. Incremental dynamic analyses are performed on the structures assuming the maximum residual interstory drift ratio (MRD) as the engineering demand parameter and four MRD limit states of 0.2%, 0.5%, 1.0%, and 2.0% to assess the residual drift performance of the structures in a probabilistic framework. The results show that considering the effects of gravity framing and composite action leads to significant decreases in the mean annual frequencies of exceeding different MRD limit states (i.e., λMRD values). These effects have the lowest impact on the λMRD values when the MRD is 0.2%. However, they have the highest impact on the λMRD values when the MRD is 1.0%.

Effects of aftershocks on the performance of steel building frames

Damages done by the earthquake excitation have attracted a significant amount of attention on aftershock effects on building structures. Seismic design of buildings is done without paying much attention to the repeated sequence of mainshock-aftershock events. It has been found that a structure may sustain the mainshock but is damaged during the aftershock. In this paper, the performance of steel building frames is evaluated with respect to the aftershocks followed by the mainshock. For this purpose, 4-, 8- and 12-story steel building frames are considered and are subject to synthesized earthquake, response spectrum compatible mainshock-aftershock sequences. For making the sequences, Bath’s law is applied. A nonlinear time history analysis is performed for a variety of synthesized sequences of the mainshock and aftershocks. The variation is implemented by selecting any single mainshock out of an ensemble of 8 mainshocks. In the sequence, a maximum of seven aftershocks followed by a mainshock is used. Time history record used for the analysis is developed by joining the synthesised earthquakes in series keeping a gap of of the 40 s between two events. The performance parameters used in the study are maximum inter-story drift ratio during an event (MIDR), residual inter-story drift ratio after the event (RIDR), maximum residual top story displacement and spread of hinges. The performances of the three building frames are compared in the study. It is seen that the 12-story frame is damaged to collapse level after 3 aftershocks, while the 4- and 8-story building frames survive seven aftershocks.

Seismic performance of RC frames with self-centering precast post-tensioned connections considering the effect of infill walls

This paper presents the seismic performance evaluation of self-centering precast post-tensioned concrete (SCPPTC) frames with infill walls. The SCPPTC connection system consists of all-steel bamboo-shaped energy dissipaters (SBED) and prestressed tendons, which provide energy dissipation capacity and self-centering capability, respectively. Using modeling parameters calibrated with experimental tests, nonlinear numerical models of SBED, SCPPTC connection, infill walls, and 2D SCPPTC frames were developed in OpenSees, to compare the performance of the structures with different types of infill wall layouts. Nonlinear static pushover and incremental dynamic analysis (IDA) were performed to study the effect of infill walls on the overall response of SCPPTC frames, in terms of stiffness, strength, maximum interstory drift ratio,θmax, the maximum residual interstory drift ratio, θr,max, and the normalized post-tensioned force. Using the IDA results, the study also developed fragility curves and estimated the collapse margin ratios. The results demonstrated that the shear strength of the SCPPTC frame was improved from 4.19% to 12.2%, and the initial secant stiffness of the SCPPTC frame was augmented from 22.9% to 88.3% with increasing filling rate. The totally infilled SCPPTC frame (SCPPTC-ToI) exhibits a 19.86% lower θmax than that of pilotis-infilled SCPPTC frame (SCPPTC-PiI) under rare earthquakes, and the maximum prestress of SCPPTC-ToI was also 7.14% lower than that of SCPPTC-PiI. With the increase in filling rate, θr,max increased by a maximum of 120.45%. The pronounced soft layer led to the highest failure and collapse probabilities of SCPPTC-PiI among all SCPPTC frames at the same performance level.

Two-Parameter–Based Damage Measure for Probabilistic Seismic Analysis of Concrete Structures

Traditional seismic fragility analysis defines the structural damage measure (DM) as a single parameter based on either strength, displacement, damage, or energy to evaluate the postearthquake performance of the structure, thus it is difficult to fully catch the behavior characteristics of the structures, e.g., both the maximum deformation capacity and the repairability of the structure. In this paper, we developed a multiparameter-based DM (mDM) index (here actually two parameters) for the probabilistic seismic analysis of reinforced concrete (RC) structures to capture a more comprehensive view of structural performance. Two parameters (i.e., the maximum interstory drift ratio θmax and the maximum residual interstory drift ratio θr,max) are combined to represent the overall structural performance, and different combination rules are investigated. To verify the superiority of the proposed mDM, the fragility analysis of three different structures is conducted, i.e., ordinary RC structure, aging RC structure, and new self-centering structure. The fragility curves derived from single DM and mDM are compared, and it is found that fragility curves with mDM can reflect both the maximum displacement and residual displacement features of the structure, thus mDM gives a more comprehensive and synthesis assessment of the postearthquake performance of the structure, which is beneficial for informed decision-making.

Peak and residual deformation-based seismic design for multi-story hybrid concentrically braced frames

Recently, using two and more types of braces in a concentrically braced frame (CBF) has been demonstrated to be effective for developing seismic resilient structures. The hybrid CBF with the combination of buckling-restrained braces (BRBs) and self-centering braces (SCBs) is promising to realize the desirable seismic performance. However, the seismic design method for the hybrid CBFs can rarely be found. To this end, the general behavior of the hybrid CBF is first introduced. Through nonlinear time history analysis (NLTHA) on single-degree-of-freedom (SDOF) systems, the seismic responses of the hybrid CBFs are investigated comprehensively. Based on the SDOF analytical results, a performance-based seismic design (PBSD) method is introduced to size the hybrid CBFs. The essential advantage of the PBSD method is that the peak and residual inter-story drift ratios can be jointly selected as the performance targets. A benchmark six-story CBF was selected as the example building to demonstrate the method. The system-level NLTHA under a suite of ground motion earthquakes was conducted to examine the accuracy of the method. The results indicated that the hybrid CBF designed by the PBSD method could well meet the prescribed performance targets, i.e., both the peak and residual inter-story drift ratios are well controlled within performance limits. Moreover, the optimal design hysteretic parameters are suggested to eliminate the residual inter-story drift ratios and minimize the peak floor accelerations.

Self-Centering Rotational Joints for Seismic Resilient Steel Moment Resisting Frame

A novel self-centering rotational joint (SCRJ) was proposed to replace the plastic hinge at the beam end to achieve a seismic resilient frame without diminishing the structural usability. The quasi-static cyclic tests of the SCRJs with different sets of friction components and disc springs were conducted, with the results showing that the precompressive force, stiffness of the compressive force, and slope angle of the right helicoid surfaces can significantly affect the hysteresis behavior. The hysteresis curve of the SCRJ demonstrates a flag shape with four characteristic states: activation state, ultimate state, reversal activation state, and deactivation state. The displacement-based design approach was adopted for the resilient steel moment resisting frame structure with the SCRJs based on which a six-story resilient frame structure was designed with the SCRJs at the beam ends. The nonlinear dynamic analysis shows that the interstory drift ratio and residual interstory drift ratio of the resilient frame structure can meet the design objectives, in which the SCRJs reach the plastic state (caused by geometric nonlinearity) more easily than conventional plastic hinges (caused by material plasticity), resulting in larger deformations, and can effectively dissipate seismic energy and protect the main frame from yielding under the rarely occurring earthquake (ROE) level.

Effectiveness of the Seesaw System as a Means of Seismic Upgrading in Older, Non-Ductile Reinforced Concrete Buildings

This work investigates and discusses the effectiveness of the seesaw system when installed in an older, non-ductile reinforced concrete (RC) building for seismic upgrading purposes. In particular, two different configurations of the seesaw system are assumed in a two-storey 3D RC framed building which was designed according to older seismic provisions and, thus, is susceptible to flexural and shear failures. To check if there is any merit in employing the seesaw system in this RC building, non-linear time-history (NLTH) analyses are conducting using 11 seismic motions. Peak values for inter-story drift ratios (IDR), residual inter-story drift ratios (RIDR) and floor accelerations (FA) are computed, and the sequence and cause (i.e., due to surpass of flexural or shear strength) of plastic hinge formations are monitored. Leaving aside any issues related to fabrication and cost, interpretation of the results obtained by the aforementioned seismic response indices for the RC building under study leads to the conclusion that the seesaw system can be a retrofitting scheme for the seismic upgrading of older, non-ductile RC framed buildings.

Seismic performance evaluation of steel buckling-restrained braced frames including SMA materials

The permanent deformation of the building after seismic excitations can be determined by the Maximum Residual Interstory Drift Ratio (MR-IDR), which may be used for measuring the damage states. Low-post yield stiffness of the steel buckling-restrained braced frame (BRBF) makes this system vulnerable to large MR-IDR after a severe earthquake event. To overcome this issue, this paper investigates the seismic limit state performances of low- to mid-rise BRBFs with two- to eight-story levels (i.e. 2-Story, 4-Story, 6-Story, and 8-Story) adopting different lateral force-resisting systems using Viscous Dampers (VDs) and Shape Memory Alloys (SMAs). For this purpose, BRBFs improved with different implementation of SMAs and VDs, and Incremental Dynamic Analyses (IDAs) were performed based on Maximum Interstory Drift Ratio (M-IDR) and MR-IDR demands. Results showed that VDs and SMAs can decrease the values of maximum moment and rotation of hinges of structural members. Implementing both SMAs and VDs can significantly improve the seismic performance level and collapse failure probability of BRBFs more effectively than using one of the VDs or SMAs; then, it can be recommended to control the MR-IDR of BRBFs. To use the results, graphical user interface has been developed to estimate the improvements in the M-IDR and MR-IDR demands.

Study on numerical seismic performance evaluation of 3D building frame with smart self-centering BRBs system

Structures are generally designed to withstand the applied loads safely. However, in order to secure the stability of structures from earthquakes, which are unpredictable natural disasters, seismic damage reduction technology is required, and various technologies are being developed so far. Recently, to resist seismic loads, new materials are used to reinforce structural members, or technologies to control vibration by applying seismic devices are being developed. In particular, Shape Memory Alloy (SMA), also known as a smart alloy, has a unique re-centering capacity that exhibits a flag-shaped hysteresis curve, so when applied in a structural system, it can provide safer structural performance with higher serviceability. In this study, to prove the structural stability of the SMA buckling restrained brace (BRB) system to which the seismic isolation is applied, a study was conducted to evaluate the seismic performance according to the structural material, type, and device. Response of SMA BRB and base isolation system has been calibrated by following quasi-static and dynamic loading test and substantially matches empirical results. A prototype steel frame has been designed by following standard code which has a single-story basement assumed to be surround by well graded sandy soil. In addition, two different column system has been considered namely as, Hollow Steel Section (HSS) and Concrete Filled Steel Tubes (CFST). For the nonlinear dynamic analysis, two sets of 11 bidirectional artificial earthquakes were considered, and the interstory drift ratio (IDR) and residual interstory drift ratio (RIDR) were considered as main performance evaluation parameters. In moderate ground motion, the performance of the SMA BRB was found to be higher compared to the steel BRB and base isolation system due to its superior self-centering capacity. However, in strong ground motions, periodic damage degrades the performance of the SMA BRB, which was found to be nearly identical to the steel BRB, but still superior to the base isolation system. This performance evaluation study will help to understand design aspects of seismic protection systems for similar types of building frames.

Cyclic loading tests of a resilient hinged self-centering RC wall

To reduce the residual drift of the reinforced concrete shear wall (RCSW), this paper proposes a resilient hinged self-centering shear wall (RHSCSW) in which two tension–compression-symmetrical disc spring devices (TCSDSDs) and a restraint plate form a resilient bottom that prevents plastic deformation on the wallboard. Cyclic loading tests are conducted on a TCSDSD specimen, an RCSW specimen, and two RHSCSW specimens to investigate their hysteretic responses. The experimental results indicate that the TCSDSD exhibits a symmetrical flag-shaped hysteretic behavior, and its macro-mechanical properties can be described by eight stiffness variables and four force variables. Benefiting from the self-centering characteristic of the TCSDSD, the maximum residual inter-story drift ratio of the RHSCSW is only 0.37% with a maximum inter-story drift ratio of 4%, while that of the RCSW reaches 0.94% with an inter-story drift ratio of only 2%. Moreover, the total energy dissipation of the RHSCSW is found to be 25.4% higher than that of the RCSW. The equivalent viscous damping ratio of the RHSCSW is almost constant because the axial displacements of the TCSDSDs are almost linear with the lateral drift of the RHSCSW.

Experimental investigation of a new self-centering shear wall with resilient hinge devices

In order to reduce the residual displacement of building structures caused by the damage on the reinforced concrete shear wall, this study develops a novel self-centering shear wall with resilient hinge devices. One device and three wall specimens are designed, and their hysteretic performance is investigated under low cyclic loading tests. The resilient hinge device which uses disc springs as the spring system is essentially a self-centering axial loaded device with an asymmetric flag-shaped hysteretic response. The experimental results demonstrate that the novel wall exhibits symmetrical flag-shaped hysteretic behavior and has a high self-centering performance. Its residual inter-story drift ratio is only 0.58% at a loading inter-story drift ratio reaching 3%. Compared with the conventional wall, the proposed self-centering shear wall has less wallboard damage, 10% degradation in peak bearing capacity, at least 50% improvement in deformation capacity, 26% degradation in equivalent viscous damping ratio, and 70% increase in total energy dissipation.

Mainshock-aftershock effect on the seismic performance of multi-story CBFs equipped with SMA-friction damping braces

This paper aims to understand the effect of mainshock-aftershock earthquake sequences on the seismic performance of multi-story concentrically braced frames (CBFs) equipped with shape memory alloy (SMA) friction damping braces (SMAFDBs), based on a comparison with those equipped with buckling-restrained braces (BRBs). The SMAFDB is a serial connection of SMA damper and friction damper. The friction damper starts to slip and serves as the “fuse” element to protect the SMA damper under destructive earthquake events. Ten ground motion records corresponding to the maximum considered earthquake (MCE) hazard level are defined as the mainshock input, and the aftershock input is generated by appropriately scaling the mainshock input to four seismic hazard levels. To achieve a fair comparison, the considered CBFs are first designed to exhibit identical mean height-wise peak interstory drift ratios under the design-basis earthquake (DBE) ground motions. Then, these two frames are subjected to four suites of mainshock-aftershock earthquake sequences and their seismic responses are compared against each other. It indicates that both the peak and residual interstory drift ratios of the SMAFDB frame (SMAFDBF) are smaller than that of the BRB frame (BRBF) on average during the aftershock earthquakes, which is found primarily attributed to the fact that the former suffers from smaller post-mainshock residual deformation. The higher seismic capacity of the SMAFDBF over the BRBF is also confirmed by conducting fragility analysis. Finally, the recentering capacity under aftershock earthquakes are analyzed for both frames, based on the maximum residual interstory drift ratios.

Seismic performance analysis of multi-story steel frames equipped with FeSMA BRBs

Buckling-restrained braces (BRBs) have been widely used in seismic prone areas around the world. However, one major problem associated with the steel BRB frames is the excessive residual deformation under strong earthquakes, mainly due to the low post-yield stiffness ratio of the steel BRBs. Recently, the community has fabricated the iron-based shape memory alloy (FeSMA) BRBs, which exhibited full hysteresis with high post-yield stiffness ratios, but the seismic behavior of the FeSMA BRB frames still remains unknown. As such, this paper conducts seismic performance analysis of multi-story steel frames equipped with the FeSMA BRBs, through a comparison with those equipped with conventional steel BRBs. Incremental dynamic analysis (IDA) is further conducted to establish the probability seismic demand models. Based on the IDA data, bivariate fragility analysis is conducted to quantify the probability of exceedance, conditioned on various limitations of the maximum and residual interstory drift ratios. According to current analysis, it indicates that both the maximum interstory drift ratios and the maximum floor accelerations are comparable between these two types of BRB frames. The major advantage of the FeSMA BRBs over the steel BRBs is that the former can better control residual interstory drift ratios.

Seismic retrofitting of SMRFs using varied yielding cross-section damper: A companion paper

This paper is a companion paper to our recent research titled “Seismic Performance of a New S-shaped Mild Steel Damper with Varied Yielding Cross-sections”. In this study, the newly developed varied yielding cross-section damper is employed for seismic retrofitting of steel moment-resisting frames (SMRFs) and a retrofitting design method without performing nonlinear time-history analysis is proposed. The damper has the feature of preventing energy dissipation plate from plasticity concentration-induced failure and of being conveniently replaced post-earthquake. Its hysteretic behavior has been verified through a series of cyclic loading tests. Three prototypes respectively with 3, 9 and 20 stories are adopted as typical low-, mid- and high-rise SMRFs to be damper-retrofitted. And the dampers are designed using the proposed retrofitting procedure in which performance objective of different seismic hazard level and story drift concentration are incorporated. Subsequently, experimentally validated numerical modelling approach for the damper is provided, and detailed numerical models for the bare frames (BFs) and damper-retrofitted frames (DFs) are established. In order to analyze the effectiveness of the developed dampers and the retrofitting design method, seismic performance of the BFs and DFs is assessed by conducting pushover and nonlinear dynamic analyses. The results indicate that the retrofitting strategy can significantly enhance the bearing capacity against strong earthquakes and mitigate the structural damages by reducing inter-story drift ratio and residual inter-story drift ratio; the proposed retrofitting design procedure has ability to achieve the expected seismic performance level and mitigate the story drift concentration.