Flag-shaped Hysteresis Research Articles

Design recommendations for self-centering buckling restrained braces

Self-centering buckling-restrained braces (SC-BRBs) have typical flag-shaped hysteresis. Differing from conventional buckling-restrained braces (BRBs) which can result in significant residual drifts, the SC-BRB incorporates additional prestressing elements, so that it can recenter after earthquakes, which is critical for seismic resilience. Current seismic design procedures can be used to calculate the key properties of conventional braces (e.g. BRB), but they cannot be used to determine the additional hysteretic properties of SC-BRB braces. To achieve a comprehensive understanding of the performances of SC-BRB systems and develop their design recommendations, this paper conducted a parametric study of two typical SC-BRB systems, using a 12-story steel braced frame office building. Then, the overall behavior of the SC-BRB system was compared with those of a BRB system and two self-centering energy dissipative brace systems. The selection of SC-BRB properties appeared to be a tradeoff between demands on component properties and seismic performances. The criteria for proportioning the system were suggested. Numerical results showed that, although the SC-BRB systems had smaller residual drifts than the BRB system, they generated more significant high-mode effect than the other comparable systems.

Investigation on a self-centering beam-column joint with tapered steel plate dampers

To improve the seismic resilience of steel moment-resisting frames, a new type of self-centering (SC) beam-column joint equipped with inclined tapered steel plate dampers is introduced in the current study. Firstly, the mechanical property of the SC beam-column joint is theoretically analyzed. Then, four SC joint assembly specimens, with study parameters of dimension and number of the tapered steel plates, are experimentally investigated under incremental cyclic loading tests. The proposed joint exhibits stable flag-shaped hysteresis curves and negligible residual deformation after unloading, which indicates that the joint can dissipate seismic energy well and at the same time have SC capability under earthquakes, thus reducing the cost of post-earthquake restoration. A comprehensive numerical simulation method is proposed to reproduce the hysteretic responses of the new SC beam-column joint. Subsequently, a series of parametric analyses are conducted to investigate the contributing factors affecting the seismic behaviors of the joint in terms of hysteresis, moment bearing capacity, energy dissipation, and SC capability.

Design, manufacturing, and performance evaluation of a novel smart roller bearing equipped with shape memory alloy wires

In this study, a new type of seismic isolation device, called shape memory alloy (SMA) wire-based roller bearing (SMA-RB) is developed and introduced. The SMA-RB has been designed, manufactured, and experimentally tested. This bearing consists of cylindrical roller bearings and SMA wires with straight or cross configurations, as supplementary damping elements. In such a smart bearing, the superelastic (SE) SMA wires are passed through the hooks/pulleys attached to the supporting plates of the bearings in different configurations. The rollers provide lateral flexibility, and SMA wires supply energy dissipation and self-centering (SC) properties. In the manufacturing stage, a new mechanism for coupling wires (i.e. SMA wire joiner/coupler) is proposed. The results show that SMA wires, made of nickle titanium (NiTi), provide a SC damping mechanism with almost zero residual deformation which can effectively control the device from over-displacement. While using pulleys and newly designed wire joiners in the SMA-RB, the bearing can experience a stable cyclic behavior. Since the rollers generate a negligible amount of frictional force, the SE NiTi wires with a flag-shaped hysteresis mainly contribute to the overall shear hysteretic response of the SMA-RB. A triangular-shaped constitutive model can be used to accurately describe the hysteretic behavior of SMA-RB with different wire configurations.

Cyclic behavior of SMA slip friction damper

This paper proposes a new type of self-centering (SC) damper which exploits the shape memory alloy (SMA) bolts and variable friction mechanism, termed the SMA slip friction damper (SMASFD). The theoretical equations governing the force–displacement relationship, the equivalent stiffness and the equivalent viscous damping are first derived. Then, the application potential of such damper is briefly discussed. In the experimental study, the results of the experimental validations of the SMA bolts and the friction mechanism are presented, followed by the results of proof-of-concept test on the fabricated SMASFDs. According to the testing results, the damper exhibited a symmetric tension–compression flag-shaped hysteresis characterized by excellent SC capacity and good damping capability. The prestrain treatment was applied to the SMA bolts in one test, which was found effectively increased the initial stiffness of the damper. To provide a further understanding on the damper and examine the stress and strain demands of the components, high-fidelity finite element models were established for numerical simulations. Both the analytical method and numerical simulation were validated by the experimental data.

Shake-table testing of 2-story steel framed building with self-centering modular panels and slit steel plate walls

Recent numerical study and cyclic testing results have suggested that the self-centering modular panels (SCMP) offer a promising prefabricated structural panel technology for enhanced seismic performance of beam-through steel frames (BTSFs). Several types of seismic fuse devices, including tension-only braces and slit steel plate shear walls (SWs) for energy dissipation, have been studied for their viability in adoption by SCMP. To further investigate the dynamic response and resilience behavior of this seismic-force-resisting system, shaking table tests have been conducted on a 2-story SCMP-BTSF building model with SWs as seismic fuse device. Two far-field ground motion records with various intensity levels were used in the shake table tests. The presented experimental testing study is the first shaking table test of SCMP-BTSF, which is a newly proposed pre-fabricated structure system with self-centering features. Nonlinear finite element (FE) model was also established to perform time history analysis of the test structure and assist with specimen design. The shake test results show that the structure response under frequent ground motions meets the inter-story drift limit given in Chinese code - GB 50011–2010 (Code for Seismic Design of Buildings, abbreviated as CSDB hereafter). When the hazard level was greater than that of frequent ground motions, the system exhibited flag-shaped hysteresis curves of the story shear as expected. It is observed that the SWs dissipated seismic energy through yielding and buckling of steel slats between slits, while other structural members and PTFs remained elastic. No cracks were seen in the concrete floor slabs after all shake table tests. After replacing SWs, the test structure showed nearly identical dynamic properties and seismic responses to the original test structure.

Hysteresis behavior of bottom-story self-centering shear wall with steel brace-assembled bottom

A self-centering shear wall (SC-SW) with a steel brace-assembled bottom is proposed to avoid the residual drift of reinforced concrete shear walls (RCSWs) due to damage in corners and achieve an adequate earthquake-resilience. The residual displacement of traditional RCSW is caused by the bending and shear deformations of the plastic hinge and the deformation of the upper plate, as is confirmed by a cyclic loading test on a typical RCSW specimen. A steel brace-assembled bottom consisting of a steel V-shaped connecting beam, a bearing, and two self-centering braces is designed to control the residual deformation of the RCSW plastic hinge zone. The simplified equations governing the skeleton curve of the SC-SW are derived. An RCSW and SC-SW with the same initial stiffness and ultimate bearing capacity are simulated and compared via the experimentally validated finite element model. The results indicate that the SC-SW exhibits a flag-shaped hysteresis response with an excellent self-centering capability. The maximum residual story drift ratio is less than 0.125%. The skeleton curve equations agree well with the measured data of the analytical specimen. The overall performance of the SC-SW is primarily affected by the braces. The energy dissipation capability of the SC-SW remains insufficient due to the lesser development of plastic deformation.

Performance assessment of disc spring-based self-centering braces for seismic hazard mitigation

A novel type of self-centering bracing system employing a disc spring-based damper is presented in this study. The proposed damper employs a special detailing which enables fast assembly and reliable mechanical performance, and has high flexibilities in load resistance, deformability and energy dissipation capacity, catering to various design objectives. The working principle of the damper is first introduced, followed by a comprehensive experimental study on six full-scale damper specimens subjected to different loading protocols. The specimens exhibit very stable flag-shaped hysteretic behavior and are fully reusable with almost no damage after experiencing the considered test sequence. Reliable energy dissipation is provided by the dampers with little sensitivity to the repeated cyclic loading, where a typical equivalent viscous damping of 20% is achieved at large deformations. The work is then extended to a system level analysis, considering varying brace parameters, to evaluate the effectiveness of the self-centering bracing system in seismic control. A buckling-restrained braced frame is also included in the analysis for comparison. Among other findings, the study indicates that the fullness of the flag-shaped hysteresis is a critical factor affecting the key structural performances. In particular, decreasing the energy dissipation factor is effective in eliminating the residual deformation, but at the cost of amplified peak deformation and floor acceleration responses. A “partial self-centering” system, which allows certain static residual deformation of the brace, is found to simultaneously suppress the peak deformation, residual deformation, and peak floor acceleration.

Study on seismic performance of prefabricated self-centering steel frame

Unexpected plastic damage and residual drift can be usually observed in traditional rigid-connection steel frames (RCSFs) after severe earthquakes. To enhance seismic performance of the RCSFs, this paper proposes a novel prefabricated self-centering steel frame (PSCSF) that incorporates pre-pressed composite combination disc spring (CCDS) installed in the column bases to provide satisfactory re-centering capability and eliminate residual deformation along with buckling restrained braces (BRBs) set at the bottom flange of steel beam to dissipate seismic input energy and reduce structural damage. Firstly, configuration details and design methodology of the PSCSF are introduced. A quasi-static loading test was conducted on the PSCSF specimen to investigate cyclic hysteretic response of the proposed innovative frame. Secondly, finite element analyses were performed with the aid of software ABAQUS to reveal seismic mechanism of PSCSF. Finally, the restoring force model of PSCSF was established based on mechanical analyses and theoretical calculation results were compared with experimental results to validate the correctness of the proposed model. The research results indicate that the PSCSF specimen exhibits full double flag-shaped hysteresis curves subjected to cyclic loading, demonstrating that the PSCSF possesses favorable self-centering capability and desirable energy dissipation capacity as well as stable mechanical behavior for the predefined target displacement. The beam and column maintain elastic and plastic damage is confined to the BRBs during entire loading process. The simulation results agree well with the test results, demonstrating that the established finite element model can capture cyclic response of the PSCSF under cyclic loading. The theoretical results calculated by restoring force model are in good accordance with the test results, confirming that the established restoring force model can reasonably predict the hysteretic behavior of the PSCSF under low cycle reversed loading.

Pulse-like near-fault ground motion effects on controlled rocking steel cores

Controlled rocking steel cores (CRSCs) with reliable self-centering capability have been known as a low-damage seismic force-resisting system. The flag-shaped hysteresis response of CRSCs can be provided using unbonded post-tensioning tendons and replaceable energy dissipation devices. This paper examines the seismic performance of CRSCs subjected to a suite of pulse-like near-field and far-field ground motions. Non-linear dynamic response analysis is performed for 3-, 6-, 9-, and 12-story archetypes with single and coupled configurations. Results are quantified for different seismic responses, and the influences of earthquake type and structural configuration are compared from various aspects. The findings indicate remarkable changes in the performance of CRSCs due to modeling and ground motion properties. The outcomes reveal that rocking-core archetypes are efficient for mitigating residual damage and restricting peak displacements under both far- and near-field motions.

Development of superelastic SMA angles as seismic-resistant self-centering devices

Given their inherent unique superelasticity, the use of shape memory alloys (SMAs) to build seismic-resistant self-centering devices has presented attractive prospects in the field of earthquake resilience. This work investigates the mechanical behavior of superelastic SMA angles subjected cyclic loading. The deformation mechanism in superelastic SMA angles is elaborated first. Subsequently, experimental investigations of SMA angles are conducted using different loading protocols. Various mechanical properties, such as strength, self-centering and energy dissipation capabilities, are evaluated under varying loading amplitudes. Testing results show SMA angles can exhibit satisfactory flag-shaped hysteresis loops under multiple loading cycles. Different measures, such as the training process or the inclusion of reversed compressive cycles, can stabilize the hysteresis loops effectively and minimize the strength degradation and residual deformation in the repeated cycles. The cyclic behavior of the SMA angles is also simulated by using the finite element method to complement the observation and understanding obtained from the experiments. The proposed SMA angles are expected to offer an effective self-centering function to engineering structures toward earthquake resilience.

Nonlinear seismic performance of beam-through steel frames with self-centering modular panel and replaceable hysteretic dampers

In this numerical simulation study, the nonlinear seismic performance of a new type of seismic resisting modular panel termed SCMP-RHDs (self-centering modular panels with replaceable hysteretic dampers) is investigated and presented. A one-story SCMP-RHD modular panel can be prefabricated in shop and inserted into building frame bays on site. The focus of this study is to look into the nonlinear seismic behavior and effectiveness of SCMP-RHDs systems with different designs in seismic response control when applied to multi-story buildings with steel beam-through steel frames (BTSFs). Both analytical formulation and numerical simulation study results show that SCMP-RHDs panels can be designed to exhibit a flag-shaped hysteresis loop and their energy dissipation capacity can be adjusted through separate design of RHD devices. Two prototype buildings with 3-story and a 6-story steel frames respectively, were designed in this study for a site located in Los Angeles, California. Numerical simulation models are validated by comparing finite element (FE) models with corresponding analytical models. Nonlinear time history analysis of the two prototype buildings subjected to an ensemble of 20 earthquake ground motion records reveals that the prototype buildings can re-center after strong earthquakes and plasticity induced damage can be confined to RHDs in the structures through careful design.

Experimental study on damage-controllable rocking walls with resilient corners

Polyurethane elastomer was employed in the concrete rocking element in an innovative way to limit the corner damage during rocking. A damage-controllable rocking wall consisting of rocking elements, resilient corners, connecting beams, unbonded post-tensioned tendons and replaceable dampers was developed. Cyclic tests on damage-controllable rocking walls were conducted by changing the conditions of dampers, corner elastomers and tendons to investigate their seismic performance. Two sets of reusable reinforced concrete rocking elements were repeatedly used seven times. The horizontal displacement of the specimen was mainly caused by rigid body rotation. The deformations of the rocking elements were quite limited, and no flexural cracks were observed in any tests. All the specimens performed well with a good capacity for low damage. Energy dissipation was generated by the attached dampers, and the equivalent viscous damping coefficient of the proposed wall was proportional to the yield strength of dampers. The damaged damper can be replaced conveniently after each test, whereas the corner elastomers remained elastic. Specimens without damping exhibited a bilinear elastic response and were completely self-centring after testing. Specimens with a suitable initial post-tensioned force and damping exhibited flag-shaped hysteresis with minor residual drifts.

Residual drift mitigation for bridges retrofitted with buckling restrained braces or self centering energy dissipation devices

A three-column reinforced concrete bridge bent that did not have reinforcement details necessary to provide adequate load capacity and displacement ductility was evaluated under seismic excitations. Two retrofit methods for improving its seismic performance were examined: (i) Buckling Restrained Braces (BRBs), and (ii) Self Centering Energy Dissipation devices (SCEDs). The numerical model of the bridge bent was validated with previous in-situ quasi-static experiments of a full-scale bent. The BRB inelastic behavior was modeled using isotropic and kinematic strain hardening properties. Flag-shaped hysteresis with slip deformation and bearing were used to model the SCED. The numerical models of the BRB and SCED were validated with full-scale experiments of the brace members. Nonlinear time-history analysis was carried out using far-field and pulse-type ground motion sets to evaluate the seismic performance of the as-built and retrofitted bridge bents in the transverse direction. The performance limit states were defined using HAZUS criteria. Incremental dynamic analysis (IDA) was implemented to evaluate the performance of the two retrofit methods up to the collapse limit state. The results show that a retrofit with either BRBs or SCEDs improves the seismic performance of the bridge bent by decreasing drift ratio demands, and reducing the maximum steel and concrete column strains. The BRB and SCED braces reduce damage to the concrete columns by dissipating a significant portion of the input seismic energy. SCED retrofit reduces the bridge bent residual drift ratio under strong earthquakes to acceptable levels; this improves post-earthquake serviceability, increases bridge resilience and keeps repair costs low. Bridge bent peak and residual drift ratio demands were found to be higher under far-field ground motions compared to pulse-type ground motions.

Numerical simulation and behavior insights of steel columns with SMA bolts towards earthquake resilience

Shape memory alloys (SMAs) are high-performance metallic materials that can experience large strain and still recover their initial shape through either temperature-induced effect (shape memory) or stress-induced effect (superelasticity). The superelasticity of SMAs is very attractive to the earthquake resilient design because of the inherent material feature with excellent self-centering (SC) and energy dissipation capabilities. This paper presents a comprehensive numerical simulation of the steel columns with SMA bolts. A finite element model was validated by tests of two SC steel columns in terms of global hysteresis loops and local strain states. Subsequently, special attention to the effects of prestrain in the SMA bolts, bidirectional loading, and multi-earthquake loading was paid to offer insights into the cyclic responses of the SC steel column. Results showed that the steel columns equipped with SMA bolts could exhibit satisfactory and stable flag-shaped hysteresis loops with excellent SC and energy dissipation capabilities under different loading conditions. In addition, SC column exhibited nearly equivalent seismic performance under multi-earthquake loading. Therefore, the SC steel columns can achieve earthquake resilient design that requires no (or minimal) repair even after strong earthquakes and remains highly functional for immediate aftershocks or future earthquakes.

An Empirical Formulation for the Damping Ratio of Shape Memory Alloy for Base-Isolated Structures

Shape Memory Alloys (SMAs) are now widely used as a damping element into the isolation systems. The pre-stressed SMAs exhibit hysteretic damping through a nonlinear flag-shaped hysteresis loop. Many nonlinear models of the SMA are available to depict such behavior. The nonlinear models require a lot of effort and computational time for the analysis of base-isolated structures. Therefore, the codes recommend that a nonlinear model can be replaced by an equivalent linear model in the analysis. Linearization is a method to convert the nonlinearity of a system into a system with analogues linear parameters. This paper proposes an empirical equation for a damping ratio to get a linear damping coefficient of the SMAs which can be used in the seismic analysis of base-isolated structures. The evaluation of any damping ratio using the traditional system identification method does not give precise solutions due to variation in hysteretic parameters and the unpredictable nature of an earthquake. The empirical equation is proposed using a set of optimal statistical data obtained from the seismic analysis of a base isolated structure. Moreover, analysis of the base isolated structure using the newly modified equivalent elastic-viscous SMA model gives comparable and conservative results with a nonlinear SMA model as compared to the existing elastic-viscous SMA model. Since the hysteresis parameters are used to derive the empirical equation for the damping ratio, this equation is also applicable for any type of structure.

Superelastic shape memory alloy flag-shaped hysteresis model with sliding response from residual deformation: Experimental and numerical study

Superelastic shape memory alloy exhibits flag-shaped hysteresis with self-centering capability. Nevertheless, shape memory alloy undergoes some residual deformation after large plastic strain, especially under repeated cyclic loading. In order to accurately simulate this behavior during nonlinear dynamic time-history analysis, a shape memory alloy flag-shaped hysteresis model with sliding response has been developed. This article shows the gradual development process of this new hysteresis model and provides analysis and verification results to support this claim. A MATLAB-based superelastic uniaxial shape memory alloy material hysteresis model has been developed and was incorporated into a finite element program specifically designed for the piston-based self-centering bracing. This piston-based self-centering bracing system uses superelastic shape memory alloy bars for its energy dissipation and self-centering capability. A proof-of-concept brace specimen was fabricated and tested where numerical and experimental results showed excellent matching. The finite element program was utilized to capture the varying nonlinear quasi-static response of the piston-based self-centering brace. Finally, the piston-based self-centering brace responses from this analysis were used to develop a novel shape memory alloy flag-shaped hysteresis model with sliding response, which was implemented in finite element analysis and design software, S-FRAME. Nonlinear dynamic time-history analysis proves the effectiveness of such bracing in steel frames in reducing interstory drift.

Seismic performance and damage analysis of RC frame–core tube building with self-centering braces

This paper examines the seismic responses of a reinforced concrete (RC) frame–core tube building with pre-pressed spring self-centering energy dissipation braces (PS-SCEDBs). The PS-SCEDB is a passive energy dissipation device with disc springs and friction pads. Parameters of PS-SCEDBs installed on the structure are designed according to the principle of equivalent stiffness, based on the parameters of a buckling-restrained brace (BRB) equipped on the original RC frame–core tube structure. The constitutive models of self-centering flag-shaped and bilinear elastoplastic hysteresis for PS-SCEDBs and BRBs, respectively, are developed and experimentally verified. The seismic performance of RC frame–core tube structures with PS-SCEDBs and BRBs, respectively, are studied and compared using non-linear time history analysis. Results show that the PS-SCEDB can substantially reduce residual drift ratios of a concentrically braced building while still capable of effectively controlling the peak inter-story drift ratio and damage of components adjacent to braces under rare earthquakes. The structure with PS-SCEDBs can effectively dissipate seismic energy without increasing damage to beams, columns, and shear walls.

High-performance self-centering steel columns with shape memory alloy bolts: Design procedure and experimental evaluation

Steel moment-resisting frames are popular structural systems used extensively around the world. However, conventional column base connections are vulnerable to large residual deformation after strong earthquakes. By contrast, shape memory alloys (SMAs), which are high-performance metallic materials, can experience large strains and still recover their initial shape through either heating (shape memory effect) or unloading (superelastic effect). The superelastic behavior of SMAs is appealing to the earthquake engineering community because of the material’s excellent self-centering (SC) and energy dissipation capabilities. In this paper, a novel type of steel columns equipped with NiTi SMA bolts was introduced and its potential for achieving earthquake resilience were investigated. Structural details of the column base and mechanical properties of the SMA bolts were described first. Subsequently, an analytical model of the SC column for different limit states and the corresponding design procedure were presented. The seismic behaviors of two steel column specimens were experimentally tested to investigate the effects of the initial prestrain in the SMA bolts and the axial compressive force in the column under cyclic loading. Results showed that the steel columns equipped with SMA bolts exhibited satisfactory and stable flag-shaped hysteresis loops with excellent SC and moderate energy dissipation capabilities. More importantly, SMA bolts with prestrain could still be tightened after removal of lateral force. Therefore, the proposed SC column could achieve seismic resilience design that requires no (or minimal) repair even after strong earthquakes and remains highly functional for aftershocks or future earthquakes. In addition, the analytical model was verified through a comparison with test results obtained at key limit states.

Superelastic SMA U-shaped dampers with self-centering functions

As high-performance metallic materials, shape memory alloys (SMAs) have been investigated increasingly by the earthquake engineering community in recent years, because of their remarkable self-centering (SC) and energy-dissipating capabilities. This paper systematically presents an experimental study on a novel superelastic SMA U-shaped damper (SMA-UD) with SC function under cyclic loading. The mechanical properties, including strength, SC ability, and energy-dissipating capability with varying loading amplitudes and strain rates are evaluated. Test results show that excellent and stable flag-shaped hysteresis loops are exhibited in multiple loading cycles. Strain rate has a negligible effect on the cyclic behavior of the SMA-UD within the dynamic frequency range of typical interest in earthquake engineering. Furthermore, a numerical investigation is performed to understand the mechanical behavior of the SMA-UD. The numerical model is calibrated against the experimental results with reasonable accuracy. Then, the stress–strain states with different phase transformations are also discussed.

Nonlinear displacement ratio for seismic design of self-centering buckling-restrained braced steel frame considering trilinear hysteresis behavior

Self-centering buckling-restrained braced steel frames (SCBRBFs) have drawn increasing attention due to the resilience of this kind of structural system in post-earthquake repair. Constant-strength reduction factor (constant-R) inelastic displacement ratio (CR) can be used for direct inelastic displacement evaluation or design of SCBRBFs. In previous studies, bilinear hysteresis assumption was generally adopted for the self-centering structures, although actual trilinear flag-shaped hysteresis was commonly observed for most of the previously proposed metallic energy-dissipation self-centering systems, such as SCBRBFs. In this study, trilinear hysteresis of the SCBRBF, presented as a combination of the bilinear elastoplastic restoring force of the energy dissipation (ED) system and the bilinear elastic restoring force of the self-centering (SC) system, is considered in the determination of the CR ratio spectra of such system. Comparison between the bilinear SC systems and the trilinear SCBRBFs is discussed to highlight the effect of the trilinear hysteresis on the nonlinear displacement of SCBRBFs. Key parameters affecting the CR ratio are determined, in which the initial stiffness ratio of the ED system to the SC system, αc, is the additional parameter proposed to reflect the trilinear property of SCBRBF. Optimal ranges of these parameters and their effects on the CR spectra are also discussed by nonlinear response history analysis. Nonlinear regression analysis is then performed to obtain the function of CR with respect to the aforementioned parameters for quick and direct displacement evaluation. Nonlinear time history analysis (NTHA) demonstrates that the CR ratios of SCBRBF, determined by the previously derived CR functions from bilinear hysteresis, are often overestimated, while those predicted by the proposed CR functions from trilinear hysteresis show better agreement with the numerical results in extremely-low and medium-to-long period region. Numerical nonlinear displacement ratios of a one-story six-bay and a six-story six-bay SCBRBFs are computed by NTHA to validate the effectiveness of the proposed CR functions.